diff options
Diffstat (limited to 'test')
| -rw-r--r-- | test/crypt/Makefile | 146 | ||||
| -rw-r--r-- | test/math/Makefile | 182 | ||||
| -rw-r--r-- | test/math/econst.c | 192 | ||||
| -rw-r--r-- | test/math/eexp.c | 154 | ||||
| -rw-r--r-- | test/math/ehead.h | 84 | ||||
| -rw-r--r-- | test/math/elog.c | 184 | ||||
| -rw-r--r-- | test/math/eparanoi.c | 7100 | ||||
| -rw-r--r-- | test/math/epow.c | 430 | ||||
| -rw-r--r-- | test/math/etanh.c | 104 | ||||
| -rw-r--r-- | test/math/etodec.c | 362 | ||||
| -rw-r--r-- | test/math/ieee.c | 8238 | ||||
| -rw-r--r-- | test/math/ieetst.c | 1700 | ||||
| -rw-r--r-- | test/math/ieetst.doc | 264 | ||||
| -rw-r--r-- | test/math/mconf.h | 216 | ||||
| -rw-r--r-- | test/math/mtherr.c | 192 |
15 files changed, 9774 insertions, 9774 deletions
diff --git a/test/crypt/Makefile b/test/crypt/Makefile index fe743aa45..a965466f3 100644 --- a/test/crypt/Makefile +++ b/test/crypt/Makefile @@ -1,73 +1,73 @@ -# Makefile for uClibc
-#
-# Copyright (C) 2002 Erik Andersen <andersen@uclibc.org>
-#
-# This program is free software; you can redistribute it and/or modify it under
-# the terms of the GNU Library General Public License as published by the Free
-# Software Foundation; either version 2 of the License, or (at your option) any
-# later version.
-#
-# This program is distributed in the hope that it will be useful, but WITHOUT
-# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
-# FOR A PARTICULAR PURPOSE. See the GNU Library General Public License for more
-# details.
-#
-# You should have received a copy of the GNU Library General Public License
-# along with this program; if not, write to the Free Software Foundation, Inc.,
-# 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
-
-
-
-TESTDIR=../
-include $(TESTDIR)/Rules.mak
-
-TARGETS=diff md5c-test
-EXTRA_LIBS=-lcrypt
-
-all: $(TARGETS)
-
-crypt: crypt.c Makefile $(TESTDIR)/Config $(TESTDIR)/Rules.mak $(CC)
- -@ echo "-------"
- -@ echo " "
- -@ echo "Compiling vs uClibc: "
- -@ echo " "
- $(CC) $(CFLAGS) -c $< -o $@.o
- $(CC) $(LDFLAGS) $@.o -o $@ $(EXTRA_LIBS)
- $(STRIPTOOL) -x -R .note -R .comment $@
- -./$@ < crypt.input > $@.out 2>&1
- -@ echo " "
-
-crypt_glibc: crypt.c Makefile $(TESTDIR)/Config $(TESTDIR)/Rules.mak $(CC)
- -@ echo "-------"
- -@ echo " "
- -@ echo "Compiling vs uClibc: "
- -@ echo " "
- $(HOST_CC) $(GLIBC_CFLAGS) -c $< -o $@.o
- $(HOST_CC) $(GLIBC_LDFLAGS) $@.o -o $@ $(EXTRA_LIBS)
- $(STRIPTOOL) -x -R .note -R .comment $@
- -./$@ < crypt.input > $@.out 2>&1
- -@ echo " "
-
-diff: crypt_glibc crypt
- -@ echo "-------"
- -@ echo " "
- -@ echo "Diffing output: "
- -@ echo " "
- -diff -u crypt_glibc.out crypt.out
- -@ echo " "
-
-md5c-test: md5c-test.c Makefile $(TESTDIR)/Config $(TESTDIR)/Rules.mak $(CC)
- -@ echo "-------"
- -@ echo " "
- -@ echo "Compiling vs uClibc: "
- -@ echo " "
- $(CC) $(CFLAGS) -c $< -o $@.o
- $(CC) $(LDFLAGS) $@.o -o $@ $(EXTRA_LIBS)
- $(STRIPTOOL) -x -R .note -R .comment $@
- -./$@
- -@ echo " "
-
-clean:
- rm -f *.[oa] *~ core crypt_glibc crypt crypt_glibc.out crypt.out md5c-test
-
-
+# Makefile for uClibc +# +# Copyright (C) 2002 Erik Andersen <andersen@uclibc.org> +# +# This program is free software; you can redistribute it and/or modify it under +# the terms of the GNU Library General Public License as published by the Free +# Software Foundation; either version 2 of the License, or (at your option) any +# later version. +# +# This program is distributed in the hope that it will be useful, but WITHOUT +# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +# FOR A PARTICULAR PURPOSE. See the GNU Library General Public License for more +# details. +# +# You should have received a copy of the GNU Library General Public License +# along with this program; if not, write to the Free Software Foundation, Inc., +# 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + + + +TESTDIR=../ +include $(TESTDIR)/Rules.mak + +TARGETS=crypt md5c-test +EXTRA_LIBS=-lcrypt + +all: $(TARGETS) + +crypt: crypt.c Makefile $(TESTDIR)/Config $(TESTDIR)/Rules.mak $(CC) + -@ echo "-------" + -@ echo " " + -@ echo "Compiling vs uClibc: " + -@ echo " " + $(CC) $(CFLAGS) -c $< -o $@.o + $(CC) $(LDFLAGS) $@.o -o $@ $(EXTRA_LIBS) + $(STRIPTOOL) -x -R .note -R .comment $@ + -./$@ < crypt.input #> $@.out 2>&1 + -@ echo " " + +crypt_glibc: crypt.c Makefile $(TESTDIR)/Config $(TESTDIR)/Rules.mak $(CC) + -@ echo "-------" + -@ echo " " + -@ echo "Compiling vs uClibc: " + -@ echo " " + $(HOST_CC) $(GLIBC_CFLAGS) -c $< -o $@.o + $(HOST_CC) $(GLIBC_LDFLAGS) $@.o -o $@ $(EXTRA_LIBS) + $(STRIPTOOL) -x -R .note -R .comment $@ + -./$@ < crypt.input > $@.out 2>&1 + -@ echo " " + +diff: crypt_glibc crypt + -@ echo "-------" + -@ echo " " + -@ echo "Diffing output: " + -@ echo " " + -diff -u crypt_glibc.out crypt.out + -@ echo " " + +md5c-test: md5c-test.c Makefile $(TESTDIR)/Config $(TESTDIR)/Rules.mak $(CC) + -@ echo "-------" + -@ echo " " + -@ echo "Compiling vs uClibc: " + -@ echo " " + $(CC) $(CFLAGS) -c $< -o $@.o + $(CC) $(LDFLAGS) $@.o -o $@ $(EXTRA_LIBS) + $(STRIPTOOL) -x -R .note -R .comment $@ + -./$@ + -@ echo " " + +clean: + rm -f *.[oa] *~ core crypt_glibc crypt crypt_glibc.out crypt.out md5c-test + + diff --git a/test/math/Makefile b/test/math/Makefile index be7f261de..4d0bc5ee6 100644 --- a/test/math/Makefile +++ b/test/math/Makefile @@ -1,91 +1,91 @@ -# Makefile for uClibc
-#
-# Copyright (C) 2000,2001 Erik Andersen <andersen@uclibc.org>
-#
-# This program is free software; you can redistribute it and/or modify it under
-# the terms of the GNU Library General Public License as published by the Free
-# Software Foundation; either version 2 of the License, or (at your option) any
-# later version.
-#
-# This program is distributed in the hope that it will be useful, but WITHOUT
-# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
-# FOR A PARTICULAR PURPOSE. See the GNU Library General Public License for more
-# details.
-#
-# You should have received a copy of the GNU Library General Public License
-# along with this program; if not, write to the Free Software Foundation, Inc.,
-# 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
-
-
-
-# Unix makefile for ieetst, eparanoi.
-# Set LARGEMEM 1 in qcalc.h for 32-bit memory addresses.
-# Define computer type and/or endianness in mconf.h.
-#
-# Configure eparanoi.c for desired arithmetic test;
-# also define appropriate version of setprec.o, or use a stub that
-# does no FPU setup. To test native arithmetic, eparanoi uses
-# the system libraries only; compile simply by `cc eparanoi.c -lm'.
-#
-
-TESTDIR=../
-include $(TESTDIR)/Rules.mak
-
-
-#CC = gcc
-#CFLAGS= -O
-INCS= mconf.h ehead.h
-OBJS = ieee.o econst.o eexp.o elog.o epow.o etanh.o etodec.o mtherr.o #setprec.o
-TARGETS=ieetst eparanoi
-
-all: $(TARGETS)
-
-ieetst: ieetst.o $(OBJS) drand.o $(INCS)
- $(CC) -o ieetst ieetst.o $(OBJS) drand.o -lc -lm
-
-eparanoi: eparanoi.o $(OBJS) $(INCS)
- $(CC) -o eparanoi eparanoi.o $(OBJS) -lc -lm
-
-#setprec.o: setprec.387
-# as -o setprec.o setprec.387
-
-#setprec.o: setprec.688
-# as -o setprec.o setprec.688
-
-ieee.o: ieee.c $(INCS)
- $(CC) $(CFLAGS) -c ieee.c
-
-econst.o: econst.c $(INCS)
- $(CC) $(CFLAGS) -c econst.c
-
-elog.o: elog.c $(INCS)
- $(CC) $(CFLAGS) -c elog.c
-
-eexp.o: eexp.c $(INCS)
- $(CC) $(CFLAGS) -c eexp.c
-
-etanh.o: etanh.c $(INCS)
- $(CC) $(CFLAGS) -c etanh.c
-
-epow.o: epow.c $(INCS)
- $(CC) $(CFLAGS) -c epow.c
-
-mtherr.o: mtherr.c $(INCS)
- $(CC) $(CFLAGS) -c mtherr.c
-
-ieetst.o: ieetst.c $(INCS)
- $(CC) $(CFLAGS) -c ieetst.c
-
-drand.o: drand.c $(INCS)
- $(CC) $(CFLAGS) -c drand.c
-
-etodec.o: etodec.c $(INCS)
- $(CC) $(CFLAGS) -c etodec.c
-
-eparanoi.o: eparanoi.c $(INCS)
- $(CC) $(CFLAGS) -c eparanoi.c
-
-clean:
- rm -f *.[oa] *~ core $(TARGETS)
-
-
+# Makefile for uClibc +# +# Copyright (C) 2000,2001 Erik Andersen <andersen@uclibc.org> +# +# This program is free software; you can redistribute it and/or modify it under +# the terms of the GNU Library General Public License as published by the Free +# Software Foundation; either version 2 of the License, or (at your option) any +# later version. +# +# This program is distributed in the hope that it will be useful, but WITHOUT +# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +# FOR A PARTICULAR PURPOSE. See the GNU Library General Public License for more +# details. +# +# You should have received a copy of the GNU Library General Public License +# along with this program; if not, write to the Free Software Foundation, Inc., +# 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + + + +# Unix makefile for ieetst, eparanoi. +# Set LARGEMEM 1 in qcalc.h for 32-bit memory addresses. +# Define computer type and/or endianness in mconf.h. +# +# Configure eparanoi.c for desired arithmetic test; +# also define appropriate version of setprec.o, or use a stub that +# does no FPU setup. To test native arithmetic, eparanoi uses +# the system libraries only; compile simply by `cc eparanoi.c -lm'. +# + +TESTDIR=../ +include $(TESTDIR)/Rules.mak + + +#CC = gcc +#CFLAGS= -O +INCS= mconf.h ehead.h +OBJS = ieee.o econst.o eexp.o elog.o epow.o etanh.o etodec.o mtherr.o #setprec.o +TARGETS=ieetst eparanoi + +all: $(TARGETS) + +ieetst: ieetst.o $(OBJS) drand.o $(INCS) + $(CC) -o ieetst ieetst.o $(OBJS) drand.o -lc -lm + +eparanoi: eparanoi.o $(OBJS) $(INCS) + $(CC) -o eparanoi eparanoi.o $(OBJS) -lc -lm + +#setprec.o: setprec.387 +# as -o setprec.o setprec.387 + +#setprec.o: setprec.688 +# as -o setprec.o setprec.688 + +ieee.o: ieee.c $(INCS) + $(CC) $(CFLAGS) -c ieee.c + +econst.o: econst.c $(INCS) + $(CC) $(CFLAGS) -c econst.c + +elog.o: elog.c $(INCS) + $(CC) $(CFLAGS) -c elog.c + +eexp.o: eexp.c $(INCS) + $(CC) $(CFLAGS) -c eexp.c + +etanh.o: etanh.c $(INCS) + $(CC) $(CFLAGS) -c etanh.c + +epow.o: epow.c $(INCS) + $(CC) $(CFLAGS) -c epow.c + +mtherr.o: mtherr.c $(INCS) + $(CC) $(CFLAGS) -c mtherr.c + +ieetst.o: ieetst.c $(INCS) + $(CC) $(CFLAGS) -c ieetst.c + +drand.o: drand.c $(INCS) + $(CC) $(CFLAGS) -c drand.c + +etodec.o: etodec.c $(INCS) + $(CC) $(CFLAGS) -c etodec.c + +eparanoi.o: eparanoi.c $(INCS) + $(CC) $(CFLAGS) -c eparanoi.c + +clean: + rm -f *.[oa] *~ core $(TARGETS) + + diff --git a/test/math/econst.c b/test/math/econst.c index 21523e568..cfddbe3e2 100644 --- a/test/math/econst.c +++ b/test/math/econst.c @@ -1,96 +1,96 @@ -/* econst.c */
-/* e type constants used by high precision check routines */
-
-#include "ehead.h"
-
-
-#if NE == 10
-/* 0.0 */
-unsigned short ezero[NE] =
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,};
-
-/* 5.0E-1 */
-unsigned short ehalf[NE] =
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3ffe,};
-
-/* 1.0E0 */
-unsigned short eone[NE] =
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3fff,};
-
-/* 2.0E0 */
-unsigned short etwo[NE] =
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x4000,};
-
-/* 3.2E1 */
-unsigned short e32[NE] =
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x4004,};
-
-/* 6.93147180559945309417232121458176568075500134360255E-1 */
-unsigned short elog2[NE] =
- {0x40f3, 0xf6af, 0x03f2, 0xb398,
- 0xc9e3, 0x79ab, 0150717, 0013767, 0130562, 0x3ffe,};
-
-/* 1.41421356237309504880168872420969807856967187537695E0 */
-unsigned short esqrt2[NE] =
- {0x1d6f, 0xbe9f, 0x754a, 0x89b3,
- 0x597d, 0x6484, 0174736, 0171463, 0132404, 0x3fff,};
-
-/* 3.14159265358979323846264338327950288419716939937511E0 */
-unsigned short epi[NE] =
- {0x2902, 0x1cd1, 0x80dc, 0x628b,
- 0xc4c6, 0xc234, 0020550, 0155242, 0144417, 0040000,};
-
-/* 5.7721566490153286060651209008240243104215933593992E-1 */
-unsigned short eeul[NE] = {
-0xd1be,0xc7a4,0076660,0063743,0111704,0x3ffe,};
-
-#else
-
-/* 0.0 */
-unsigned short ezero[NE] = {
-0, 0000000,0000000,0000000,0000000,0000000,};
-/* 5.0E-1 */
-unsigned short ehalf[NE] = {
-0, 0000000,0000000,0000000,0100000,0x3ffe,};
-/* 1.0E0 */
-unsigned short eone[NE] = {
-0, 0000000,0000000,0000000,0100000,0x3fff,};
-/* 2.0E0 */
-unsigned short etwo[NE] = {
-0, 0000000,0000000,0000000,0100000,0040000,};
-/* 3.2E1 */
-unsigned short e32[NE] = {
-0, 0000000,0000000,0000000,0100000,0040004,};
-/* 6.93147180559945309417232121458176568075500134360255E-1 */
-unsigned short elog2[NE] = {
-0xc9e4,0x79ab,0150717,0013767,0130562,0x3ffe,};
-/* 1.41421356237309504880168872420969807856967187537695E0 */
-unsigned short esqrt2[NE] = {
-0x597e,0x6484,0174736,0171463,0132404,0x3fff,};
-/* 2/sqrt(PI) =
- * 1.12837916709551257389615890312154517168810125865800E0 */
-unsigned short eoneopi[NE] = {
-0x71d5,0x688d,0012333,0135202,0110156,0x3fff,};
-/* 3.14159265358979323846264338327950288419716939937511E0 */
-unsigned short epi[NE] = {
-0xc4c6,0xc234,0020550,0155242,0144417,0040000,};
-/* 5.7721566490153286060651209008240243104215933593992E-1 */
-unsigned short eeul[NE] = {
-0xd1be,0xc7a4,0076660,0063743,0111704,0x3ffe,};
-#endif
-extern unsigned short ezero[];
-extern unsigned short ehalf[];
-extern unsigned short eone[];
-extern unsigned short etwo[];
-extern unsigned short e32[];
-extern unsigned short elog2[];
-extern unsigned short esqrt2[];
-extern unsigned short eoneopi[];
-extern unsigned short epi[];
-extern unsigned short eeul[];
-
+/* econst.c */ +/* e type constants used by high precision check routines */ + +#include "ehead.h" + + +#if NE == 10 +/* 0.0 */ +unsigned short ezero[NE] = + {0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,}; + +/* 5.0E-1 */ +unsigned short ehalf[NE] = + {0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3ffe,}; + +/* 1.0E0 */ +unsigned short eone[NE] = + {0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3fff,}; + +/* 2.0E0 */ +unsigned short etwo[NE] = + {0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x4000,}; + +/* 3.2E1 */ +unsigned short e32[NE] = + {0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x4004,}; + +/* 6.93147180559945309417232121458176568075500134360255E-1 */ +unsigned short elog2[NE] = + {0x40f3, 0xf6af, 0x03f2, 0xb398, + 0xc9e3, 0x79ab, 0150717, 0013767, 0130562, 0x3ffe,}; + +/* 1.41421356237309504880168872420969807856967187537695E0 */ +unsigned short esqrt2[NE] = + {0x1d6f, 0xbe9f, 0x754a, 0x89b3, + 0x597d, 0x6484, 0174736, 0171463, 0132404, 0x3fff,}; + +/* 3.14159265358979323846264338327950288419716939937511E0 */ +unsigned short epi[NE] = + {0x2902, 0x1cd1, 0x80dc, 0x628b, + 0xc4c6, 0xc234, 0020550, 0155242, 0144417, 0040000,}; + +/* 5.7721566490153286060651209008240243104215933593992E-1 */ +unsigned short eeul[NE] = { +0xd1be,0xc7a4,0076660,0063743,0111704,0x3ffe,}; + +#else + +/* 0.0 */ +unsigned short ezero[NE] = { +0, 0000000,0000000,0000000,0000000,0000000,}; +/* 5.0E-1 */ +unsigned short ehalf[NE] = { +0, 0000000,0000000,0000000,0100000,0x3ffe,}; +/* 1.0E0 */ +unsigned short eone[NE] = { +0, 0000000,0000000,0000000,0100000,0x3fff,}; +/* 2.0E0 */ +unsigned short etwo[NE] = { +0, 0000000,0000000,0000000,0100000,0040000,}; +/* 3.2E1 */ +unsigned short e32[NE] = { +0, 0000000,0000000,0000000,0100000,0040004,}; +/* 6.93147180559945309417232121458176568075500134360255E-1 */ +unsigned short elog2[NE] = { +0xc9e4,0x79ab,0150717,0013767,0130562,0x3ffe,}; +/* 1.41421356237309504880168872420969807856967187537695E0 */ +unsigned short esqrt2[NE] = { +0x597e,0x6484,0174736,0171463,0132404,0x3fff,}; +/* 2/sqrt(PI) = + * 1.12837916709551257389615890312154517168810125865800E0 */ +unsigned short eoneopi[NE] = { +0x71d5,0x688d,0012333,0135202,0110156,0x3fff,}; +/* 3.14159265358979323846264338327950288419716939937511E0 */ +unsigned short epi[NE] = { +0xc4c6,0xc234,0020550,0155242,0144417,0040000,}; +/* 5.7721566490153286060651209008240243104215933593992E-1 */ +unsigned short eeul[NE] = { +0xd1be,0xc7a4,0076660,0063743,0111704,0x3ffe,}; +#endif +extern unsigned short ezero[]; +extern unsigned short ehalf[]; +extern unsigned short eone[]; +extern unsigned short etwo[]; +extern unsigned short e32[]; +extern unsigned short elog2[]; +extern unsigned short esqrt2[]; +extern unsigned short eoneopi[]; +extern unsigned short epi[]; +extern unsigned short eeul[]; + diff --git a/test/math/eexp.c b/test/math/eexp.c index dd2a64e1c..14ea9899d 100644 --- a/test/math/eexp.c +++ b/test/math/eexp.c @@ -1,77 +1,77 @@ -/* xexp.c */
-/* exponential function check routine */
-/* by Stephen L. Moshier. */
-
-
-#include "ehead.h"
-
-/*
-extern int powinited;
-extern short maxposint[], maxnegint[];
-*/
-
-void eexp( x, y )
-unsigned short *x, *y;
-{
-unsigned short num[NE], den[NE], x2[NE];
-long i;
-unsigned short sign, expchk;
-
-/* range reduction theory: x = i + f, 0<=f<1;
- * e**x = e**i * e**f
- * e**i = 2**(i/log 2).
- * Let i/log2 = i1 + f1, 0<=f1<1.
- * Then e**i = 2**i1 * 2**f1, so
- * e**x = 2**i1 * e**(log 2 * f1) * e**f.
- */
-/*
-if( powinited == 0 )
- initpow();
-*/
-if( ecmp(x, ezero) == 0 )
- {
- emov( eone, y );
- return;
- }
-emov(x, x2);
-expchk = x2[NE-1];
-sign = expchk & 0x8000;
-x2[NE-1] &= 0x7fff;
-
-/* Test for excessively large argument */
-expchk &= 0x7fff;
-if( expchk > (EXONE + 15) )
- {
- eclear( y );
- if( sign == 0 )
- einfin( y );
- return;
- }
-
-eifrac( x2, &i, num ); /* x = i + f */
-
-if( i != 0 )
- {
- ltoe( &i, den ); /* floating point i */
- ediv( elog2, den, den ); /* i/log 2 */
- eifrac( den, &i, den ); /* i/log 2 = i1 + f1 */
- emul( elog2, den, den ); /* log 2 * f1 */
- eadd( den, num, x2 ); /* log 2 * f1 + f */
- }
-
-/*x2[NE-1] -= 1;*/
-eldexp( x2, -1L, x2 ); /* divide by 2 */
-etanh( x2, x2 ); /* tanh( x/2 ) */
-eadd( x2, eone, num ); /* 1 + tanh */
-eneg( x2 );
-eadd( x2, eone, den ); /* 1 - tanh */
-ediv( den, num, y ); /* (1 + tanh)/(1 - tanh) */
-
-/*y[NE-1] += i;*/
-if( sign )
- {
- ediv( y, eone, y );
- i = -i;
- }
-eldexp( y, i, y ); /* multiply by 2**i */
-}
+/* xexp.c */ +/* exponential function check routine */ +/* by Stephen L. Moshier. */ + + +#include "ehead.h" + +/* +extern int powinited; +extern short maxposint[], maxnegint[]; +*/ + +void eexp( x, y ) +unsigned short *x, *y; +{ +unsigned short num[NE], den[NE], x2[NE]; +long i; +unsigned short sign, expchk; + +/* range reduction theory: x = i + f, 0<=f<1; + * e**x = e**i * e**f + * e**i = 2**(i/log 2). + * Let i/log2 = i1 + f1, 0<=f1<1. + * Then e**i = 2**i1 * 2**f1, so + * e**x = 2**i1 * e**(log 2 * f1) * e**f. + */ +/* +if( powinited == 0 ) + initpow(); +*/ +if( ecmp(x, ezero) == 0 ) + { + emov( eone, y ); + return; + } +emov(x, x2); +expchk = x2[NE-1]; +sign = expchk & 0x8000; +x2[NE-1] &= 0x7fff; + +/* Test for excessively large argument */ +expchk &= 0x7fff; +if( expchk > (EXONE + 15) ) + { + eclear( y ); + if( sign == 0 ) + einfin( y ); + return; + } + +eifrac( x2, &i, num ); /* x = i + f */ + +if( i != 0 ) + { + ltoe( &i, den ); /* floating point i */ + ediv( elog2, den, den ); /* i/log 2 */ + eifrac( den, &i, den ); /* i/log 2 = i1 + f1 */ + emul( elog2, den, den ); /* log 2 * f1 */ + eadd( den, num, x2 ); /* log 2 * f1 + f */ + } + +/*x2[NE-1] -= 1;*/ +eldexp( x2, -1L, x2 ); /* divide by 2 */ +etanh( x2, x2 ); /* tanh( x/2 ) */ +eadd( x2, eone, num ); /* 1 + tanh */ +eneg( x2 ); +eadd( x2, eone, den ); /* 1 - tanh */ +ediv( den, num, y ); /* (1 + tanh)/(1 - tanh) */ + +/*y[NE-1] += i;*/ +if( sign ) + { + ediv( y, eone, y ); + i = -i; + } +eldexp( y, i, y ); /* multiply by 2**i */ +} diff --git a/test/math/ehead.h b/test/math/ehead.h index 746b60df7..24c95ce05 100644 --- a/test/math/ehead.h +++ b/test/math/ehead.h @@ -1,42 +1,42 @@ -
-/* Include file for extended precision arithmetic programs.
- */
-
-/* Number of 16 bit words in external x type format */
-#define NE 6
-
-/* Number of 16 bit words in internal format */
-#define NI (NE+3)
-
-/* Array offset to exponent */
-#define E 1
-
-/* Array offset to high guard word */
-#define M 2
-
-/* Number of bits of precision */
-#define NBITS ((NI-4)*16)
-
-/* Maximum number of decimal digits in ASCII conversion
- * = NBITS*log10(2)
- */
-#define NDEC (NBITS*8/27)
-
-/* The exponent of 1.0 */
-#define EXONE (0x3fff)
-
-void eadd(), esub(), emul(), ediv();
-int ecmp(), enormlz(), eshift();
-void eshup1(), eshup8(), eshup6(), eshdn1(), eshdn8(), eshdn6();
-void eabs(), eneg(), emov(), eclear(), einfin(), efloor();
-void eldexp(), efrexp(), eifrac(), ltoe();
-void esqrt(), elog(), eexp(), etanh(), epow();
-void asctoe(), asctoe24(), asctoe53(), asctoe64();
-void etoasc(), e24toasc(), e53toasc(), e64toasc();
-void etoe64(), etoe53(), etoe24(), e64toe(), e53toe(), e24toe();
-void mtherr();
-extern unsigned short ezero[], ehalf[], eone[], etwo[];
-extern unsigned short elog2[], esqrt2[];
-
-
-/* by Stephen L. Moshier. */
+ +/* Include file for extended precision arithmetic programs. + */ + +/* Number of 16 bit words in external x type format */ +#define NE 6 + +/* Number of 16 bit words in internal format */ +#define NI (NE+3) + +/* Array offset to exponent */ +#define E 1 + +/* Array offset to high guard word */ +#define M 2 + +/* Number of bits of precision */ +#define NBITS ((NI-4)*16) + +/* Maximum number of decimal digits in ASCII conversion + * = NBITS*log10(2) + */ +#define NDEC (NBITS*8/27) + +/* The exponent of 1.0 */ +#define EXONE (0x3fff) + +void eadd(), esub(), emul(), ediv(); +int ecmp(), enormlz(), eshift(); +void eshup1(), eshup8(), eshup6(), eshdn1(), eshdn8(), eshdn6(); +void eabs(), eneg(), emov(), eclear(), einfin(), efloor(); +void eldexp(), efrexp(), eifrac(), ltoe(); +void esqrt(), elog(), eexp(), etanh(), epow(); +void asctoe(), asctoe24(), asctoe53(), asctoe64(); +void etoasc(), e24toasc(), e53toasc(), e64toasc(); +void etoe64(), etoe53(), etoe24(), e64toe(), e53toe(), e24toe(); +void mtherr(); +extern unsigned short ezero[], ehalf[], eone[], etwo[]; +extern unsigned short elog2[], esqrt2[]; + + +/* by Stephen L. Moshier. */ diff --git a/test/math/elog.c b/test/math/elog.c index 8afc1e5b4..bc517b197 100644 --- a/test/math/elog.c +++ b/test/math/elog.c @@ -1,92 +1,92 @@ -/* xlog.c */
-/* natural logarithm */
-/* by Stephen L. Moshier. */
-
-#include "mconf.h"
-#include "ehead.h"
-
-
-
-void elog( x, y )
-unsigned short *x, *y;
-{
-unsigned short xx[NE], z[NE], a[NE], b[NE], t[NE], qj[NE];
-long ex;
-int fex;
-
-
-if( x[NE-1] & (unsigned short )0x8000 )
- {
- eclear(y);
- mtherr( "elog", DOMAIN );
- return;
- }
-if( ecmp( x, ezero ) == 0 )
- {
- einfin( y );
- eneg(y);
- mtherr( "elog", SING );
- return;
- }
-if( ecmp( x, eone ) == 0 )
- {
- eclear( y );
- return;
- }
-
-/* range reduction: log x = log( 2**ex * m ) = ex * log2 + log m */
-efrexp( x, &fex, xx );
-/*
-emov(x, xx );
-ex = xx[NX-1] & 0x7fff;
-ex -= 0x3ffe;
-xx[NX-1] = 0x3ffe;
-*/
-
-/* Adjust range to 1/sqrt(2), sqrt(2) */
-esqrt2[NE-1] -= 1;
-if( ecmp( xx, esqrt2 ) < 0 )
- {
- fex -= 1;
- emul( xx, etwo, xx );
- }
-esqrt2[NE-1] += 1;
-
-esub( eone, xx, a );
-if( a[NE-1] == 0 )
- {
- eclear( y );
- goto logdon;
- }
-eadd( eone, xx, b );
-ediv( b, a, y ); /* store (x-1)/(x+1) in y */
-
-emul( y, y, z );
-
-emov( eone, a );
-emov( eone, b );
-emov( eone, qj );
-do
- {
- eadd( etwo, qj, qj ); /* 2 * i + 1 */
- emul( z, a, a );
- ediv( qj, a, t );
- eadd( t, b, b );
- }
-while( ((b[NE-1] & 0x7fff) - (t[NE-1] & 0x7fff)) < NBITS );
-
-
-emul( b, y, y );
-emul( y, etwo, y );
-
-logdon:
-
-/* now add log of 2**ex */
-if( fex != 0 )
- {
- ex = fex;
- ltoe( &ex, b );
- emul( elog2, b, b );
- eadd( b, y, y );
- }
-}
+/* xlog.c */ +/* natural logarithm */ +/* by Stephen L. Moshier. */ + +#include "mconf.h" +#include "ehead.h" + + + +void elog( x, y ) +unsigned short *x, *y; +{ +unsigned short xx[NE], z[NE], a[NE], b[NE], t[NE], qj[NE]; +long ex; +int fex; + + +if( x[NE-1] & (unsigned short )0x8000 ) + { + eclear(y); + mtherr( "elog", DOMAIN ); + return; + } +if( ecmp( x, ezero ) == 0 ) + { + einfin( y ); + eneg(y); + mtherr( "elog", SING ); + return; + } +if( ecmp( x, eone ) == 0 ) + { + eclear( y ); + return; + } + +/* range reduction: log x = log( 2**ex * m ) = ex * log2 + log m */ +efrexp( x, &fex, xx ); +/* +emov(x, xx ); +ex = xx[NX-1] & 0x7fff; +ex -= 0x3ffe; +xx[NX-1] = 0x3ffe; +*/ + +/* Adjust range to 1/sqrt(2), sqrt(2) */ +esqrt2[NE-1] -= 1; +if( ecmp( xx, esqrt2 ) < 0 ) + { + fex -= 1; + emul( xx, etwo, xx ); + } +esqrt2[NE-1] += 1; + +esub( eone, xx, a ); +if( a[NE-1] == 0 ) + { + eclear( y ); + goto logdon; + } +eadd( eone, xx, b ); +ediv( b, a, y ); /* store (x-1)/(x+1) in y */ + +emul( y, y, z ); + +emov( eone, a ); +emov( eone, b ); +emov( eone, qj ); +do + { + eadd( etwo, qj, qj ); /* 2 * i + 1 */ + emul( z, a, a ); + ediv( qj, a, t ); + eadd( t, b, b ); + } +while( ((b[NE-1] & 0x7fff) - (t[NE-1] & 0x7fff)) < NBITS ); + + +emul( b, y, y ); +emul( y, etwo, y ); + +logdon: + +/* now add log of 2**ex */ +if( fex != 0 ) + { + ex = fex; + ltoe( &ex, b ); + emul( elog2, b, b ); + eadd( b, y, y ); + } +} diff --git a/test/math/eparanoi.c b/test/math/eparanoi.c index 0e479f9f5..84cab73f8 100644 --- a/test/math/eparanoi.c +++ b/test/math/eparanoi.c @@ -1,3550 +1,3550 @@ -/* paranoia.c arithmetic tester
- *
- * This is an implementation of the PARANOIA program. It substitutes
- * subroutine calls for ALL floating point arithmetic operations.
- * This permits you to substitute your own experimental versions of
- * arithmetic routines. It also defeats compiler optimizations,
- * so for native arithmetic you can be pretty sure you are testing
- * the arithmetic and not the compiler.
- *
- * This version of PARANOIA omits the display of division by zero.
- * It also omits the test for extra precise subexpressions, since
- * they cannot occur in this context. Otherwise it includes all the
- * tests of the 27 Jan 86 distribution, plus a few additional tests.
- * Commentary has been reduced to a minimum in order to make the program
- * smaller.
- *
- * The original PARANOIA program, written by W. Kahan, C version
- * by Thos Sumner and David Gay, can be downloaded free from the
- * Internet NETLIB. An MSDOS disk can be obtained for $15 from:
- * Richard Karpinski
- * 6521 Raymond Street
- * Oakland, CA 94609
- *
- * Steve Moshier, 28 Oct 88
- * last rev: 23 May 92
- */
-
-#define DEBUG 0
-
-/* To use the native arithmetic of the computer, define NATIVE
- * to be 1. To use your own supplied arithmetic routines, NATIVE is 0.
- */
-#define NATIVE 0
-
-/* gcc real.c interface */
-#define L128DOUBLE 0
-
-#include <stdio.h>
-
-
-
-
-/* Data structure of floating point number. If NATIVE was
- * selected above, you can define LDOUBLE 1 to test 80-bit long double
- * precision or define it 0 to test 64-bit double precision.
-*/
-#define LDOUBLE 0
-#if NATIVE
-
-#define NE 1
-#if LDOUBLE
-#define FSIZE long double
-#define FLOAT(x) FSIZE x[NE]
-static FSIZE eone[NE] = {1.0L}; /* The constant 1.0 */
-#define ZSQRT sqrtl
-#define ZLOG logl
-#define ZFLOOR floorl
-#define ZPOW powl
-long double sqrtl(), logl(), floorl(), powl();
-#define FSETUP einit
-#else /* not LDOUBLE */
-#define FSIZE double
-#define FLOAT(x) FSIZE x[NE]
-static FSIZE eone[NE] = {1.0}; /* The constant 1.0 */
-#define ZSQRT sqrt
-#define ZLOG log
-#define ZFLOOR floor
-#define ZPOW pow
-double sqrt(), log(), floor(), pow();
-/* Coprocessor initialization,
- * defeat underflow trap or what have you.
- * This is required mainly on i386 and 68K processors.
- */
-#define FSETUP dprec
-#endif /* double, not LDOUBLE */
-
-#else /* not NATIVE */
-
-/* Setup for extended double type.
- * Put NE = 10 for real.c operating with TFmode support (16-byte reals)
- * Put NE = 6 for real.c operating with XFmode support (10- or 12-byte reals)
- * The value of NE must agree with that in ehead.h, if ieee.c is used.
- */
-#define NE 6
-#define FSIZE unsigned short
-#define FLOAT(x) unsigned short x[NE]
-extern unsigned short eone[];
-#define FSETUP einit
-
-/* default for FSETUP */
-/*
-einit()
-{}
-*/
-
-error(s)
-char *s;
-{
-printf( "error: %s\n", s );
-}
-
-#endif /* not NATIVE */
-
-
-
-#if L128DOUBLE
-/* real.c interface */
-
-#undef FSETUP
-#define FSETUP efsetup
-
-FLOAT(enone);
-
-#define ONE enone
-
-/* Use emov to convert from widest type to widest type, ... */
-/*
-#define ENTOE emov
-#define ETOEN emov
-*/
-
-/* ... else choose e24toe, e53toe, etc. */
-#define ENTOE e64toe
-#define ETOEN etoe64
-#define NNBITS 64
-
-#define NIBITS ((NE-1)*16)
-extern int rndprc;
-
-efsetup()
-{
-rndprc = NNBITS;
-ETOEN(eone, enone);
-}
-
-add(a,b,c)
-FLOAT(a);
-FLOAT(b);
-FLOAT(c);
-{
-unsigned short aa[10], bb[10], cc[10];
-
-ENTOE(a,aa);
-ENTOE(b,bb);
-eadd(aa,bb,cc);
-ETOEN(cc,c);
-}
-
-sub(a,b,c)
-FLOAT(a);
-FLOAT(b);
-FLOAT(c);
-{
-unsigned short aa[10], bb[10], cc[10];
-
-ENTOE(a,aa);
-ENTOE(b,bb);
-esub(aa,bb,cc);
-ETOEN(cc,c);
-}
-
-mul(a,b,c)
-FLOAT(a);
-FLOAT(b);
-FLOAT(c);
-{
-unsigned short aa[10], bb[10], cc[10];
-
-ENTOE(a,aa);
-ENTOE(b,bb);
-emul(aa,bb,cc);
-ETOEN(cc,c);
-}
-
-div(a,b,c)
-FLOAT(a);
-FLOAT(b);
-FLOAT(c);
-{
-unsigned short aa[10], bb[10], cc[10];
-
-ENTOE(a,aa);
-ENTOE(b,bb);
-ediv(aa,bb,cc);
-ETOEN(cc,c);
-}
-
-int cmp(a,b)
-FLOAT(a);
-FLOAT(b);
-{
-unsigned short aa[10], bb[10];
-int c;
-int ecmp();
-
-ENTOE(a,aa);
-ENTOE(b,bb);
-c = ecmp(aa,bb);
-return(c);
-}
-
-mov(a,b)
-FLOAT(a);
-FLOAT(b);
-{
-int i;
-
-for( i=0; i<NE; i++ )
- b[i] = a[i];
-}
-
-
-neg(a)
-FLOAT(a);
-{
-unsigned short aa[10];
-
-ENTOE(a,aa);
-eneg(aa);
-ETOEN(aa,a);
-}
-
-clear(a)
-FLOAT(a);
-{
-int i;
-
-for( i=0; i<NE; i++ )
- a[i] = 0;
-}
-
-FABS(a)
-FLOAT(a);
-{
-unsigned short aa[10];
-
-ENTOE(a,aa);
-eabs(aa);
-ETOEN(aa,a);
-}
-
-FLOOR(a,b)
-FLOAT(a);
-FLOAT(b);
-{
-unsigned short aa[10], bb[10];
-
-ENTOE(a,aa);
-efloor(aa,bb);
-ETOEN(bb,b);
-}
-
-LOG(a,b)
-FLOAT(a);
-FLOAT(b);
-{
-unsigned short aa[10], bb[10];
-int rndsav;
-
-ENTOE(a,aa);
-rndsav = rndprc;
-rndprc = NIBITS;
-elog(aa,bb);
-rndprc = rndsav;
-ETOEN(bb,b);
-}
-
-POW(a,b,c)
-FLOAT(a);
-FLOAT(b);
-FLOAT(c);
-{
-unsigned short aa[10], bb[10], cc[10];
-int rndsav;
-
-ENTOE(a,aa);
-ENTOE(b,bb);
-rndsav = rndprc;
-rndprc = NIBITS;
-epow(aa,bb,cc);
-rndprc = rndsav;
-ETOEN(cc,c);
-}
-
-SQRT(a,b)
-FLOAT(a);
-FLOAT(b);
-{
-unsigned short aa[10], bb[10];
-
-ENTOE(a,aa);
-esqrt(aa,bb);
-ETOEN(bb,b);
-}
-
-FTOL(x,ip,f)
-FLOAT(x);
-long *ip;
-FLOAT(f);
-{
-unsigned short xx[10], ff[10];
-
-ENTOE(x,xx);
-eifrac(xx,ip,ff);
-ETOEN(ff,f);
-}
-
-LTOF(ip,x)
-long *ip;
-FLOAT(x);
-{
-unsigned short xx[10];
-ltoe(ip,xx);
-ETOEN(xx,x);
-}
-
-TOASC(a,b,c)
-FLOAT(a);
-int b;
-char *c;
-{
-unsigned short xx[10];
-
-ENTOE(a,xx);
-etoasc(xx,b,c);
-}
-
-#else /* not L128DOUBLE */
-
-#define ONE eone
-
-/* Note all arguments of operation subroutines are pointers. */
-/* c = b + a */
-#define add(a,b,c) eadd(a,b,c)
-/* c = b - a */
-#define sub(a,b,c) esub(a,b,c)
-/* c = b * a */
-#define mul(a,b,c) emul(a,b,c)
-/* c = b / a */
-#define div(a,b,c) ediv(a,b,c)
-/* 1 if a>b, 0 if a==b, -1 if a<b */
-#define cmp(a,b) ecmp(a,b)
-/* b = a */
-#define mov(a,b) emov(a,b)
-/* a = -a */
-#define neg(a) eneg(a)
-/* a = 0 */
-#define clear(a) eclear(a)
-
-#define FABS(x) eabs(x)
-#define FLOOR(x,y) efloor(x,y)
-#define LOG(x,y) elog(x,y)
-#define POW(x,y,z) epow(x,y,z)
-#define SQRT(x,y) esqrt(x,y)
-
-/* x = &FLOAT input, i = &long integer part, f = &FLOAT fractional part */
-#define FTOL(x,i,f) eifrac(x,i,f)
-
-/* i = &long integer input, x = &FLOAT output */
-#define LTOF(i,x) ltoe(i,x)
-
-/* Convert FLOAT a to decimal ASCII string with b digits */
-#define TOASC(a,b,c) etoasc(a,b,c)
-#endif /* not L128DOUBLE */
-
-
-
-/* The following subroutines are implementations of the above
- * named functions, using the native or default arithmetic.
- */
-#if NATIVE
-eadd(a,b,c)
-FSIZE *a, *b, *c;
-{
-*c = *b + *a;
-}
-
-esub(a,b,c)
-FSIZE *a, *b, *c;
-{
-*c = *b - *a;
-}
-
-emul(a,b,c)
-FSIZE *a, *b, *c;
-{
-*c = (*b) * (*a);
-}
-
-ediv(a,b,c)
-FSIZE *a, *b, *c;
-{
-*c = (*b) / (*a);
-}
-
-
-/* Important note: comparison can be done by subracting
- * or by a compare instruction that may or may not be
- * equivalent to subtracting.
- */
-ecmp(a,b)
-FSIZE *a, *b;
-{
-if( (*a) > (*b) )
- return( 1 );
-if( (*a) < (*b) )
- return( -1 );
-if( (*a) != (*b) )
- goto cmpf;
-if( (*a) == (*b) )
- return( 0 );
-cmpf:
-printf( "Compare fails\n" );
-return(0);
-}
-
-
-emov( a, b )
-FSIZE *a, *b;
-{
-*b = *a;
-}
-
-eneg( a )
-FSIZE *a;
-{
-*a = -(*a);
-}
-
-eclear(a)
-FSIZE *a;
-{
-*a = 0.0;
-}
-
-eabs(x)
-FSIZE *x;
-{
-if( (*x) < 0.0 )
- *x = -(*x);
-}
-
-efloor(x,y)
-FSIZE *x, *y;
-{
-
-*y = (FSIZE )ZFLOOR( *x );
-}
-
-elog(x,y)
-FSIZE *x, *y;
-{
-
-*y = (FSIZE )ZLOG( *x );
-}
-
-epow(x,y,z)
-FSIZE *x, *y, *z;
-{
-
-*z = (FSIZE )ZPOW( *x, *y );
-}
-
-esqrt(x,y)
-FSIZE *x, *y;
-{
-
-*y = (FSIZE )ZSQRT( *x );
-}
-
-
-eifrac(x,i,f)
-FSIZE *x;
-long *i;
-FSIZE *f;
-{
-FSIZE y;
-
-y = (FSIZE )ZFLOOR( *x );
-if( y < 0.0 )
- {
- *f = y - *x;
- *i = -y;
- }
-else
- {
- *f = *x - y;
- *i = y;
- }
-}
-
-
-ltoe(i,x)
-long *i;
-FSIZE *x;
-{
-*x = *i;
-}
-
-
-etoasc(a,str,n)
-FSIZE *a;
-char *str;
-int n;
-{
-double x;
-
-x = (double )(*a);
-sprintf( str, " %.17e ", x );
-}
-
-/* default for FSETUP */
-einit()
-{}
-
-#endif /* NATIVE */
-
-
-
-
-FLOAT(Radix);
-FLOAT(BInvrse);
-FLOAT(RadixD2);
-FLOAT(BMinusU2);
-/*Small floating point constants.*/
-FLOAT(Zero);
-FLOAT(Half);
-FLOAT(One);
-FLOAT(Two);
-FLOAT(Three);
-FLOAT(Four);
-FLOAT(Five);
-FLOAT(Six);
-FLOAT(Eight);
-FLOAT(Nine);
-FLOAT(Ten);
-FLOAT(TwentySeven);
-FLOAT(ThirtyTwo);
-FLOAT(TwoForty);
-FLOAT(MinusOne );
-FLOAT(OneAndHalf);
-
-/*Integer constants*/
-int NoTrials = 20; /*Number of tests for commutativity. */
-#define False 0
-#define True 1
-
-/* Definitions for declared types
- Guard == (Yes, No);
- Rounding == (Chopped, Rounded, Other);
- Message == packed array [1..40] of char;
- Class == (Flaw, Defect, Serious, Failure);
- */
-#define Yes 1
-#define No 0
-#define Chopped 2
-#define Rounded 1
-#define Other 0
-#define Flaw 3
-#define Defect 2
-#define Serious 1
-#define Failure 0
-
-typedef int Guard, Rounding, Class;
-typedef char Message;
-
-/* Declarations of Variables */
-FLOAT(AInvrse);
-FLOAT(A1);
-FLOAT(C);
-FLOAT(CInvrse);
-FLOAT(D);
-FLOAT(FourD);
-FLOAT(E0);
-FLOAT(E1);
-FLOAT(Exp2);
-FLOAT(E3);
-FLOAT(MinSqEr);
-FLOAT(SqEr);
-FLOAT(MaxSqEr);
-FLOAT(E9);
-FLOAT(Third);
-FLOAT(F6);
-FLOAT(F9);
-FLOAT(H);
-FLOAT(HInvrse);
-FLOAT(StickyBit);
-FLOAT(J);
-FLOAT(MyZero);
-FLOAT(Precision);
-FLOAT(Q);
-FLOAT(Q9);
-FLOAT(R);
-FLOAT(Random9);
-FLOAT(T);
-FLOAT(Underflow);
-FLOAT(S);
-FLOAT(OneUlp);
-FLOAT(UfThold);
-FLOAT(U1);
-FLOAT(U2);
-FLOAT(V);
-FLOAT(V0);
-FLOAT(V9);
-FLOAT(W);
-FLOAT(X);
-FLOAT(X1);
-FLOAT(X2);
-FLOAT(X8);
-FLOAT(Random1);
-FLOAT(Y);
-FLOAT(YY1);
-FLOAT(Y2);
-FLOAT(Random2);
-FLOAT(Z);
-FLOAT(PseudoZero);
-FLOAT(Z1);
-FLOAT(Z2);
-FLOAT(Z9);
-static FLOAT(t);
-FLOAT(t2);
-FLOAT(Sqarg);
-int ErrCnt[4];
-int fpecount;
-int Milestone;
-int PageNo;
-int I, M, N, N1, stkflg;
-Guard GMult, GDiv, GAddSub;
-Rounding RMult, RDiv, RAddSub, RSqrt;
-int Break, Done, NotMonot, Monot, Anomaly, IEEE;
-int SqRWrng, UfNGrad;
-int k, k2;
-int Indx;
-char ch[8];
-
-long lngint, lng2; /* intermediate for conversion between int and FLOAT */
-
-/* Computed constants. */
-/*U1 gap below 1.0, i.e, 1.0-U1 is next number below 1.0 */
-/*U2 gap above 1.0, i.e, 1.0+U2 is next number above 1.0 */
-
-
-show( x )
-short x[];
-{
-int i;
-char s[80];
-
-/* Number of 16-bit groups to display */
-#if NATIVE
-#if LDOUBLE
-#define NPRT (sizeof( long double )/2)
-#else
-#define NPRT (sizeof( double )/2)
-#endif
-#else
-#define NPRT NE
-#endif
-
-TOASC( x, s, 70 );
-printf( "%s\n", s );
-for( i=0; i<NPRT; i++ )
- printf( "%04x ", x[i] & 0xffff );
-printf( "\n" );
-}
-
-/* define NOSIGNAL */
-#ifndef NOSIGNAL
-#include <signal.h>
-#endif
-#include <setjmp.h>
-jmp_buf ovfl_buf;
-/*typedef int (*Sig_type)();*/
-typedef void (*Sig_type)();
-Sig_type sigsave;
-
-/* Floating point exception receiver */
-void sigfpe()
-{
-fpecount++;
-printf( "\n* * * FLOATING-POINT ERROR * * *\n" );
-/* reinitialize the floating point unit */
-FSETUP();
-fflush(stdout);
-if( sigsave )
- {
-#ifndef NOSIGNAL
- signal( SIGFPE, sigsave );
-#endif
- sigsave = 0;
- longjmp( ovfl_buf, 1 );
- }
-abort();
-}
-
-
-main()
-{
-
-/* Do coprocessor or other initializations */
-FSETUP();
-
-printf(
- "This version of paranoia omits test for extra precise subexpressions\n" );
-printf( "and includes a few additional tests.\n" );
-
-clear(Zero);
-printf( "0 = " );
-show( Zero );
-mov( ONE, One);
-printf( "1 = " );
-show( One );
-add( One, One, Two );
-printf( "1+1 = " );
-show( Two );
-add( Two, One, Three );
-add( Three, One, Four );
-add( Four, One, Five );
-add( Five, One, Six );
-add( Four, Four, Eight );
-mul( Three, Three, Nine );
-add( Nine, One, Ten );
-mul( Nine, Three, TwentySeven );
-mul( Four, Eight, ThirtyTwo );
-mul( Four, Five, t );
-mul( t, Three, t );
-mul( t, Four, TwoForty );
-mov( One, MinusOne );
-neg( MinusOne );
-div( Two, One, Half );
-add( One, Half, OneAndHalf );
-ErrCnt[Failure] = 0;
-ErrCnt[Serious] = 0;
-ErrCnt[Defect] = 0;
-ErrCnt[Flaw] = 0;
-PageNo = 1;
-#ifndef NOSIGNAL
-signal( SIGFPE, sigfpe );
-#endif
-printf("Program is now RUNNING tests on small integers:\n");
-
-add( Zero, Zero, t );
-if( cmp( t, Zero ) != 0)
- {
- printf( "0+0 != 0\n" );
- ErrCnt[Failure] += 1;
- }
-sub( One, One, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "1-1 != 0\n" );
- ErrCnt[Failure] += 1;
- }
-if( cmp( One, Zero ) <= 0 )
- {
- printf( "1 <= 0\n" );
- ErrCnt[Failure] += 1;
- }
-add( One, One, t );
-if( cmp( t, Two ) != 0 )
- {
- printf( "1+1 != 2\n" );
- ErrCnt[Failure] += 1;
- }
-mov( Zero, Z );
-neg( Z );
-FLOOR( Z, t );
-if( cmp(t,Zero) != 0 )
- {
- ErrCnt[Serious] += 1;
- printf( "FLOOR(-0) should equal 0, is = " );
- show( t );
- }
-if( cmp(Z, Zero) != 0)
- {
- ErrCnt[Failure] += 1;
- printf("Comparison alleges that -0.0 is Non-zero!\n");
- }
-else
- {
- div( TwoForty, One, U1 ); /* U1 = 0.001 */
- mov( One, Radix );
- TstPtUf();
- }
-add( Two, One, t );
-if( cmp( t, Three ) != 0 )
- {
- printf( "2+1 != 3\n" );
- ErrCnt[Failure] += 1;
- }
-add( Three, One, t );
-if( cmp( t, Four ) != 0 )
- {
- printf( "3+1 != 4\n" );
- ErrCnt[Failure] += 1;
- }
-mov( Two, t );
-neg( t );
-mul( Two, t, t );
-add( Four, t, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "4+2*(-2) != 0\n" );
- ErrCnt[Failure] += 1;
- }
-sub( Three, Four, t );
-sub( One, t, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "4-3-1 != 0\n" );
- ErrCnt[Failure] += 1;
- }
- sub( One, Zero, t );
-if( cmp( t, MinusOne ) != 0 )
- {
- printf( "-1 != 0-1\n" );
- ErrCnt[Failure] += 1;
- }
-add( One, MinusOne, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "1+(-1) != 0\n" );
- ErrCnt[Failure] += 1;
- }
-mov( One, t );
-FABS( t );
-add( MinusOne, t, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "-1+abs(1) != 0\n" );
- ErrCnt[Failure] += 1;
- }
-mul( MinusOne, MinusOne, t );
-add( MinusOne, t, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "-1+(-1)*(-1) != 0\n" );
- ErrCnt[Failure] += 1;
- }
-add( Half, MinusOne, t );
-add( Half, t, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "1/2 + (-1) + 1/2 != 0\n" );
- ErrCnt[Failure] += 1;
- }
-Milestone = 10;
-mul( Three, Three, t );
-if( cmp( t, Nine ) != 0 )
- {
- printf( "3*3 != 9\n" );
- ErrCnt[Failure] += 1;
- }
-mul( Nine, Three, t );
-if( cmp( t, TwentySeven ) != 0 )
- {
- printf( "3*9 != 27\n" );
- ErrCnt[Failure] += 1;
- }
-add( Four, Four, t );
-if( cmp( t, Eight ) != 0 )
- {
- printf( "4+4 != 8\n" );
- ErrCnt[Failure] += 1;
- }
-mul( Eight, Four, t );
-if( cmp( t, ThirtyTwo ) != 0 )
- {
- printf( "8*4 != 32\n" );
- ErrCnt[Failure] += 1;
- }
-sub( TwentySeven, ThirtyTwo, t );
-sub( Four, t, t );
-sub( One, t, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "32-27-4-1 != 0\n" );
- ErrCnt[Failure] += 1;
- }
-add( Four, One, t );
-if( cmp( t, Five ) != 0 )
- {
- printf( "4+1 != 5\n" );
- ErrCnt[Failure] += 1;
- }
-mul( Four, Five, t );
-mul( Three, t, t );
-mul( Four, t, t );
-if( cmp( t, TwoForty ) != 0 )
- {
- printf( "4*5*3*4 != 240\n" );
- ErrCnt[Failure] += 1;
- }
-div( Three, TwoForty, t );
-mul( Four, Four, t2 );
-mul( Five, t2, t2 );
-sub( t2, t2, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "240/3 - 4*4*5 != 0\n" );
- ErrCnt[Failure] += 1;
- }
-div( Four, TwoForty, t );
-mul( Five, Three, t2 );
-mul( Four, t2, t2 );
-sub( t2, t, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "240/4 - 5*3*4 != 0\n" );
- ErrCnt[Failure] += 1;
- }
-div( Five, TwoForty, t );
-mul( Four, Three, t2 );
-mul( Four, t2, t2 );
-sub( t2, t, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "240/5 - 4*3*4 != 0\n" );
- ErrCnt[Failure] += 1;
- }
-if(ErrCnt[Failure] == 0)
- {
-printf("-1, 0, 1/2, 1, 2, 3, 4, 5, 9, 27, 32 & 240 are O.K.\n\n");
- }
-printf("Searching for Radix and Precision.\n");
-mov( One, W );
-do
- {
- add( W, W, W );
- add( W, One, Y );
- sub( W, Y, Z );
- sub( One, Z, Y );
- mov( Y, t );
- FABS(t);
- add( MinusOne, t, t );
- k = cmp( t, Zero );
- }
-while( k < 0 );
-/*.. now W is just big enough that |((W+1)-W)-1| >= 1 ...*/
-mov( Zero, Precision );
-mov( One, Y );
-do
- {
- add( W, Y, Radix );
- add( Y, Y, Y );
- sub( W, Radix, Radix );
- k = cmp( Radix, Zero );
- }
-while( k == 0);
-
-if( cmp(Radix, Two) < 0 )
- mov( One, Radix );
-printf("Radix = " );
-show( Radix );
-if( cmp(Radix, One) != 0)
- {
- mov( One, W );
- do
- {
- add( One, Precision, Precision );
- mul( W, Radix, W );
- add( W, One, Y );
- sub( W, Y, t );
- k = cmp( t, One );
- }
- while( k == 0 );
- }
-/* now W == Radix^Precision is barely too big to satisfy (W+1)-W == 1 */
-div( W, One, U1 );
-mul( Radix, U1, U2 );
-printf( "Closest relative separation found is U 1 = " );
-show( U1 );
-printf( "Recalculating radix and precision." );
-
-/*save old values*/
-mov( Radix, E0 );
-mov( U1, E1 );
-mov( U2, E9 );
-mov( Precision, E3 );
-
-div( Three, Four, X );
-sub( One, X, Third );
-sub( Third, Half, F6 );
-add( F6, F6, X );
-sub( Third, X, X );
-FABS( X );
-if( cmp(X, U2) < 0 )
- mov( U2, X );
-
-/*... now X = (unknown no.) ulps of 1+...*/
-do
- {
- mov( X, U2 );
-/* Y = Half * U2 + ThirtyTwo * U2 * U2; */
- mul( ThirtyTwo, U2, t );
- mul( t, U2, t );
- mul( Half, U2, Y );
- add( t, Y, Y );
- add( One, Y, Y );
- sub( One, Y, X );
- k = cmp( U2, X );
- k2 = cmp( X, Zero );
- }
-while ( ! ((k <= 0) || (k2 <= 0)));
-
-/*... now U2 == 1 ulp of 1 + ... */
-div( Three, Two, X );
-sub( Half, X, F6 );
-add( F6, F6, Third );
-sub( Half, Third, X );
-add( F6, X, X );
-FABS( X );
-if( cmp(X, U1) < 0 )
- mov( U1, X );
-
-/*... now X == (unknown no.) ulps of 1 -... */
-do
- {
- mov( X, U1 );
- /* Y = Half * U1 + ThirtyTwo * U1 * U1;*/
- mul( ThirtyTwo, U1, t );
- mul( U1, t, t );
- mul( Half, U1, Y );
- add( t, Y, Y );
- sub( Y, Half, Y );
- add( Half, Y, X );
- sub( X, Half, Y );
- add( Half, Y, X );
- k = cmp( U1, X );
- k2 = cmp( X, Zero );
- } while ( ! ((k <= 0) || (k2 <= 0)));
-/*... now U1 == 1 ulp of 1 - ... */
-if( cmp( U1, E1 ) == 0 )
- printf("confirms closest relative separation U1 .\n");
-else
- {
- printf("gets better closest relative separation U1 = " );
- show( U1 );
- }
-div( U1, One, W );
-sub( U1, Half, F9 );
-add( F9, Half, F9 );
-div( U1, U2, t );
-div( TwoForty, One, t2 );
-add( t2, t, t );
-FLOOR( t, Radix );
-if( cmp(Radix, E0) == 0 )
- printf("Radix confirmed.\n");
-else
- {
- printf("MYSTERY: recalculated Radix = " );
- show( Radix );
- mov( E0, Radix );
- }
-add( Eight, Eight, t );
-if( cmp( Radix, t ) > 0 )
- {
- printf( "Radix is too big: roundoff problems\n" );
- ErrCnt[Defect] += 1;
- }
-k = 1;
-if( cmp( Radix, Two ) == 0 )
- k = 0;
-if( cmp( Radix, Ten ) == 0 )
- k = 0;
-if( cmp( Radix, One ) == 0 )
- k = 0;
-if( k != 0 )
- {
- printf( "Radix is not as good as 2 or 10\n" );
- ErrCnt[Flaw] += 1;
- }
-/*=============================================*/
-Milestone = 20;
-/*=============================================*/
-sub( Half, F9, t );
-if( cmp( t, Half ) >= 0 )
- {
- printf( "(1-U1)-1/2 < 1/2 is FALSE, prog. fails?\n" );
- ErrCnt[Failure] += 1;
- }
-mov( F9, X );
-I = 1;
-sub( Half, X, Y );
-sub( Half, Y, Z );
-if( (cmp( X, One ) == 0) && (cmp( Z, Zero) != 0) )
- {
- printf( "Comparison is fuzzy ,X=1 but X-1/2-1/2 != 0\n" );
- ErrCnt[Failure] += 1;
- }
-add( One, U2, X );
-I = 0;
-/*=============================================*/
-Milestone = 25;
-/*=============================================*/
-/*... BMinusU2 = nextafter(Radix, 0) */
-
-sub( One, Radix, BMinusU2 );
-sub( U2, BMinusU2, t );
-add( One, t, BMinusU2 );
-/* Purify Integers */
-if( cmp(Radix,One) != 0 )
- {
-/*X = - TwoForty * LOG(U1) / LOG(Radix);*/
- LOG( U1, X );
- LOG( Radix, t );
- div( t, X, X );
- mul( TwoForty, X, X );
- neg( X );
-
- add( Half, X, Y );
- FLOOR( Y, Y );
- sub( Y, X, t );
- FABS( t );
- mul( Four, t, t );
- if( cmp( t, One ) < 0 )
- mov( Y, X );
- div( TwoForty, X, Precision );
- add( Half, Precision, Y );
- FLOOR( Y, Y );
- sub( Y, Precision, t );
- FABS( t );
- mul( TwoForty, t, t );
- if( cmp( t, Half ) < 0 )
- mov( Y, Precision );
- }
-FLOOR( Precision, t );
-if( (cmp( Precision, t ) != 0) || (cmp( Radix, One ) == 0) )
- {
- printf("Precision cannot be characterized by an Integer number\n");
- printf("of significant digits but, by itself, this is a minor flaw.\n");
- }
-if( cmp(Radix, One) == 0 )
- printf("logarithmic encoding has precision characterized solely by U1.\n");
-else
- {
- printf("The number of significant digits of the Radix is " );
- show( Precision );
- }
-mul( U2, Nine, t );
-mul( Nine, t, t );
-mul( TwoForty, t, t );
-if( cmp( t, One ) >= 0 )
- {
- printf( "Precision worse than 5 decimal figures\n" );
- ErrCnt[Serious] += 1;
- }
-/*=============================================*/
-Milestone = 30;
-/*=============================================*/
-/* Test for extra-precise subepressions has been deleted. */
-Milestone = 35;
-/*=============================================*/
-if( cmp(Radix,Two) >= 0 )
- {
- mul( Radix, Radix, t );
- div( t, W, X );
- add( X, One, Y );
- sub( X, Y, Z );
- add( Z, U2, T );
- sub( Z, T, X );
- if( cmp( X, U2 ) != 0 )
- {
- printf( "Subtraction is not normalized X=Y,X+Z != Y+Z!\n" );
- ErrCnt[Failure] += 1;
- }
- if( cmp(X,U2) == 0 )
- printf("Subtraction appears to be normalized, as it should be.");
- }
-
-printf("\nChecking for guard digit in *, /, and -.\n");
-mul( F9, One, Y );
-mul( One, F9, Z );
-sub( Half, F9, X );
-sub( Half, Y, Y );
-sub( X, Y, Y );
-sub( Half, Z, Z );
-sub( X, Z, Z );
-add( One, U2, X );
-mul( X, Radix, T );
-mul( Radix, X, R );
-sub( Radix, T, X );
-mul( Radix, U2, t );
-sub( t, X, X );
-sub( Radix, R, T );
-mul( Radix, U2, t );
-sub( t, T, T );
-sub( One, Radix, t );
-mul( t, X, X );
-sub( One, Radix, t );
-mul( t, T, T );
-
-k = cmp(X,Zero);
-k |= cmp(Y,Zero);
-k |= cmp(Z,Zero);
-k |= cmp(T,Zero);
-if( k == 0 )
- GMult = Yes;
-else
- {
- GMult = No;
- ErrCnt[Serious] += 1;
- printf( "* lacks a Guard Digit, so 1*X != X\n" );
- }
-mul( Radix, U2, Z );
-add( One, Z, X );
-add( X, Z, Y );
-mul( X, X, t );
-sub( t, Y, Y );
-FABS( Y );
-sub( U2, Y, Y );
-sub( U2, One, X );
-sub( U2, X, Z );
-mul( X, X, t );
-sub( t, Z, Z );
-FABS( Z );
-sub( U1, Z, Z );
-if( (cmp(Y,Zero) > 0) || (cmp(Z,Zero) > 0) )
- {
- ErrCnt[Failure] += 1;
- printf( "* gets too many final digits wrong.\n" );
- }
-sub( U2, One, Y );
-add( One, U2, X );
-div( Y, One, Z );
-sub( X, Z, Y );
-div( Three, One, X );
-div( Nine, Three, Z );
-sub( Z, X, X );
-div( TwentySeven, Nine, T );
-sub( T, Z, Z );
-k = cmp( X, Zero );
-k |= cmp( Y, Zero );
-k |= cmp( Z, Zero );
-if( k )
- {
- ErrCnt[Defect] += 1;
-printf( "Division lacks a Guard Digit, so error can exceed 1 ulp\n" );
-printf( "or 1/3 and 3/9 and 9/27 may disagree\n" );
- }
-div( One, F9, Y );
-sub( Half, F9, X );
-sub( Half, Y, Y );
-sub( X, Y, Y );
-add( One, U2, X );
-div( One, X, T );
-sub( X, T, X );
-k = cmp( X, Zero );
-k |= cmp( Y, Zero );
-k |= cmp( Z, Zero );
-if( k == 0 )
- GDiv = Yes;
-else
- {
- GDiv = No;
- ErrCnt[Serious] += 1;
- printf( "Division lacks a Guard Digit, so X/1 != X\n" );
- }
-add( One, U2, X );
-div( X, One, X );
-sub( Half, X, Y );
-sub( Half, Y, Y );
-if( cmp(Y,Zero) >= 0 )
- {
- ErrCnt[Serious] += 1;
- printf( "Computed value of 1/1.000..1 >= 1\n" );
- }
-sub( U2, One, X );
-mul( Radix, U2, Y );
-add( One, Y, Y );
-mul( X, Radix, Z );
-mul( Y, Radix, T );
-div( Radix, Z, R );
-div( Radix, T, StickyBit );
-sub( X, R, X );
-sub( Y, StickyBit, Y );
-k = cmp( X, Zero );
-k |= cmp( Y, Zero );
-if( k )
- {
- ErrCnt[Failure] += 1;
- printf( "* and/or / gets too many last digits wrong\n" );
- }
-sub( U1, One, Y );
-sub( F9, One, X );
-sub( Y, One, Y );
-sub( U2, Radix, T );
-sub( BMinusU2, Radix, Z );
-sub( T, Radix, T );
-k = cmp( X, U1 );
-k |= cmp( Y, U1 );
-k |= cmp( Z, U2 );
-k |= cmp( T, U2 );
-if( k == 0 )
- GAddSub = Yes;
-else
- {
- GAddSub = No;
- ErrCnt[Serious] += 1;
- printf( "- lacks Guard Digit, so cancellation is obscured\n" );
- }
-sub( One, F9, t );
-if( (cmp(F9,One) != 0) && (cmp(t,Zero) >= 0) )
- {
- ErrCnt[Serious] += 1;
- printf("comparison alleges (1-U1) < 1 although\n");
- printf(" subtration yields (1-U1) - 1 = 0 , thereby vitiating\n");
- printf(" such precautions against division by zero as\n");
- printf(" ... if (X == 1.0) {.....} else {.../(X-1.0)...}\n");
- }
-if (GMult == Yes && GDiv == Yes && GAddSub == Yes)
- printf(" *, /, and - appear to have guard digits, as they should.\n");
-/*=============================================*/
-Milestone = 40;
-/*=============================================*/
-printf("Checking rounding on multiply, divide and add/subtract.\n");
-RMult = Other;
-RDiv = Other;
-RAddSub = Other;
-div( Two, Radix, RadixD2 );
-mov( Two, A1 );
-Done = False;
-do
- {
- mov( Radix, AInvrse );
- do
- {
- mov( AInvrse, X );
- div( A1, AInvrse, AInvrse );
- FLOOR( AInvrse, t );
- k = cmp( t, AInvrse );
- }
- while( ! (k != 0 ) );
- k = cmp( X, One );
- k2 = cmp( A1, Three );
- Done = (k == 0) || (k2 > 0);
- if(! Done)
- add( Nine, One, A1 );
- }
-while( ! (Done));
-if( cmp(X, One) == 0 )
- mov( Radix, A1 );
-div( A1, One, AInvrse );
-mov( A1, X );
-mov( AInvrse, Y );
-Done = False;
-do
- {
- mul( X, Y, Z );
- sub( Half, Z, Z );
- if( cmp( Z, Half ) != 0 )
- {
- ErrCnt[Failure] += 1;
- printf( "X * (1/X) differs from 1\n" );
- }
- k = cmp( X, Radix );
- Done = (k == 0);
- mov( Radix, X );
- div( X, One, Y );
- }
-while( ! (Done));
-
-add( One, U2, Y2 );
-sub( U2, One, YY1 );
-sub( U2, OneAndHalf, X );
-add( OneAndHalf, U2, Y );
-sub( U2, X, Z );
-mul( Z, Y2, Z );
-mul( Y, YY1, T );
-sub( X, Z, Z );
-sub( X, T, T );
-mul( X, Y2, X );
-add( Y, U2, Y );
-mul( Y, YY1, Y );
-sub( OneAndHalf, X, X );
-sub( OneAndHalf, Y, Y );
-k = cmp( X, Zero );
-k |= cmp( Y, Zero );
-k |= cmp( Z, Zero );
-if( cmp( T, Zero ) > 0 )
- k = 1;
-if( k == 0 )
- {
- add( OneAndHalf, U2, X );
- mul( X, Y2, X );
- sub( U2, OneAndHalf, Y );
- sub( U2, Y, Y );
- add( OneAndHalf, U2, Z );
- add( U2, Z, Z );
- sub( U2, OneAndHalf, T );
- mul( T, YY1, T );
- add( Z, U2, t );
- sub( t, X, X );
- mul( Y, YY1, StickyBit );
- mul( Z, Y2, S );
- sub( Y, T, T );
- sub( Y, U2, Y );
- add( StickyBit, Y, Y );
-/* Z = S - (Z + U2 + U2); */
- add( Z, U2, t );
- add( t, U2, t );
- sub( t, S, Z );
- add( Y2, U2, t );
- mul( t, YY1, StickyBit );
- mul( Y2, YY1, YY1 );
- sub( Y2, StickyBit, StickyBit );
- sub( Half, YY1, YY1 );
- k = cmp( X, Zero );
- k |= cmp( Y, Zero );
- k |= cmp( Z, Zero );
- k |= cmp( T, Zero );
- k |= cmp( StickyBit, Zero );
- k |= cmp( YY1, Half );
- if( k == 0 )
- {
- RMult = Rounded;
- printf("Multiplication appears to round correctly.\n");
- }
- else
- {
- add( X, U2, t );
- k = cmp( t, Zero );
- if( cmp( Y, Zero ) >= 0 )
- k |= 1;
- add( Z, U2, t );
- k |= cmp( t, Zero );
- if( cmp( T, Zero ) >= 0 )
- k |= 1;
- add( StickyBit, U2, t );
- k |= cmp( t, Zero );
- if( cmp(YY1, Half) >= 0 )
- k |= 1;
- if( k == 0 )
- {
- printf("Multiplication appears to chop.\n");
- }
- else
- {
- printf("* is neither chopped nor correctly rounded.\n");
- }
- if( (RMult == Rounded) && (GMult == No) )
- printf("Multiplication has inconsistent result");
- }
- }
-else
- printf("* is neither chopped nor correctly rounded.\n");
-
-/*=============================================*/
-Milestone = 45;
-/*=============================================*/
-add( One, U2, Y2 );
-sub( U2, One, YY1 );
-add( OneAndHalf, U2, Z );
-add( Z, U2, Z );
-div( Y2, Z, X );
-sub( U2, OneAndHalf, T );
-sub( U2, T, T );
-sub( U2, T, Y );
-div( YY1, Y, Y );
-add( Z, U2, Z );
-div( Y2, Z, Z );
-sub( OneAndHalf, X, X );
-sub( T, Y, Y );
-div( YY1, T, T );
-add( OneAndHalf, U2, t );
-sub( t, Z, Z );
-sub( OneAndHalf, U2, t );
-add( t, T, T );
-k = 0;
-if( cmp( X, Zero ) > 0 )
- k = 1;
-if( cmp( Y, Zero ) > 0 )
- k = 1;
-if( cmp( Z, Zero ) > 0 )
- k = 1;
-if( cmp( T, Zero ) > 0 )
- k = 1;
-if( k == 0 )
- {
- div( Y2, OneAndHalf, X );
- sub( U2, OneAndHalf, Y );
- add( U2, OneAndHalf, Z );
- sub( Y, X, X );
- div( YY1, OneAndHalf, T );
- div( YY1, Y, Y );
- add( Z, U2, t );
- sub( t, T, T );
- sub( Z, Y, Y );
- div( Y2, Z, Z );
- add( Y2, U2, YY1 );
- div( Y2, YY1, YY1 );
- sub( OneAndHalf, Z, Z );
- sub( Y2, YY1, Y2 );
- sub( U1, F9, YY1 );
- div( F9, YY1, YY1 );
- k = cmp( X, Zero );
- k |= cmp( Y, Zero );
- k |= cmp( Z, Zero );
- k |= cmp( T, Zero );
- k |= cmp( Y2, Zero );
- sub( Half, YY1, t );
- sub( Half, F9, t2 );
- k |= cmp( t, t2 );
- if( k == 0 )
- {
- RDiv = Rounded;
- printf("Division appears to round correctly.\n");
- if(GDiv == No)
- printf("Division test inconsistent\n");
- }
- else
- {
- k = 0;
- if( cmp( X, Zero ) >= 0 )
- k = 1;
- if( cmp( Y, Zero ) >= 0 )
- k = 1;
- if( cmp( Z, Zero ) >= 0 )
- k = 1;
- if( cmp( T, Zero ) >= 0 )
- k = 1;
- if( cmp( Y, Zero ) >= 0 )
- k = 1;
- sub( Half, YY1, t );
- sub( Half, F9, t2 );
- if( cmp( t, t2 ) >= 0 )
- k = 1;
- if( k == 0 )
- {
- RDiv = Chopped;
- printf("Division appears to chop.\n");
- }
- }
- }
-if(RDiv == Other)
- printf("/ is neither chopped nor correctly rounded.\n");
-div( Radix, One, BInvrse );
-mul( BInvrse, Radix, t );
-sub( Half, t, t );
-if( cmp( t, Half ) != 0 )
- {
- ErrCnt[Failure] += 1;
- printf( "Radix * ( 1 / Radix ) differs from 1\n" );
- }
-
-Milestone = 50;
-/*=============================================*/
-add( F9, U1, t );
-sub( Half, t, t );
-k = cmp( t, Half );
-add( BMinusU2, U2, t );
-sub( One, t, t );
-sub( One, Radix, t2 );
-k |= cmp( t, t2 );
-if( k != 0 )
- {
- ErrCnt[Failure] += 1;
- printf( "Incomplete carry-propagation in Addition\n" );
- }
-mul( U1, U1, X );
-sub( X, One, X );
-sub( U2, One, Y );
-mul( U2, Y, Y );
-add( One, Y, Y );
-sub( Half, F9, Z );
-sub( Half, X, X );
-sub( Z, X, X );
-sub( One, Y, Y );
-if( (cmp(X,Zero) == 0) && (cmp(Y,Zero) == 0) )
- {
- RAddSub = Chopped;
- printf("Add/Subtract appears to be chopped.\n");
- }
-if(GAddSub == Yes)
- {
- add( Half, U2, X );
- mul( X, U2, X );
- sub( U2, Half, Y );
- mul( Y, U2, Y );
- add( One, X, X );
- add( One, Y, Y );
- add( One, U2, t );
- sub( X, t, X );
- sub( Y, One, Y );
- k = cmp(X,Zero);
- if( k )
- printf( "1+U2-[u2(1/2+U2)+1] != 0\n" );
- k2 = cmp(Y,Zero);
- if( k2 )
- printf( "1-[U2(1/2-U2)+1] != 0\n" );
- k |= k2;
- if( k == 0 )
- {
- add( Half, U2, X );
- mul( X, U1, X );
- sub( U2, Half, Y );
- mul( Y, U1, Y );
- sub( X, One, X );
- sub( Y, One, Y );
- sub( X, F9, X );
- sub( Y, One, Y );
- k = cmp(X,Zero);
- if( k )
- printf( "F9-[1-U1(1/2+U2)] != 0\n" );
- k2 = cmp(Y,Zero);
- if( k2 )
- printf( "1-[1-U1(1/2-U2)] != 0\n" );
- k |= k2;
- if( k == 0 )
- {
- RAddSub = Rounded;
- printf("Addition/Subtraction appears to round correctly.\n");
- if(GAddSub == No)
- printf( "Add/Subtract test inconsistent\n");
- }
- else
- {
- printf("Addition/Subtraction neither rounds nor chops.\n");
- }
- }
- else
- printf("Addition/Subtraction neither rounds nor chops.\n");
- }
-else
- printf("Addition/Subtraction neither rounds nor chops.\n");
-
-mov( One, S );
-add( One, Half, X );
-mul( Half, X, X );
-add( One, X, X );
-add( One, U2, Y );
-mul( Y, Half, Y );
-sub( Y, X, Z );
-sub( X, Y, T );
-add( Z, T, StickyBit );
-if( cmp(StickyBit, Zero) != 0 )
- {
- mov( Zero, S );
- ErrCnt[Flaw] += 1;
- printf( "(X - Y) + (Y - X) is non zero!\n" );
- }
-mov( Zero, StickyBit );
-FLOOR( RadixD2, t );
-k2 = cmp( t, RadixD2 );
-k = 1;
-if( (GMult == Yes) && (GDiv == Yes) && (GAddSub == Yes)
- && (RMult == Rounded) && (RDiv == Rounded)
- && (RAddSub == Rounded) && (k2 == 0) )
- {
- printf("Checking for sticky bit.\n");
- k = 0;
- add( Half, U1, X );
- mul( X, U2, X );
- mul( Half, U2, Y );
- add( One, Y, Z );
- add( One, X, T );
- sub( One, Z, t );
- sub( One, T, t2 );
- if( cmp(t,Zero) > 0 )
- {
- k = 1;
- printf( "[1+(1/2)U2]-1 > 0\n" );
- }
- if( cmp(t2,U2) < 0 )
- {
- k = 1;
- printf( "[1+U2(1/2+U1)]-1 < U2\n" );
- }
- add( T, Y, Z );
- sub( X, Z, Y );
- sub( T, Z, t );
- sub( T, Y, t2 );
- if( cmp(t,U2) < 0 )
- {
- k = 1;
- printf( "[[1+U2(1/2+U1)]+(1/2)U2]-[1+U2(1/2+U1)] < U2\n" );
- }
- if( cmp(t2,Zero) != 0 )
- {
- k = 1;
- printf( "(1/2)U2-[1+U2(1/2+U1)] != 0\n" );
- }
- add( Half, U1, X );
- mul( X, U1, X );
- mul( Half, U1, Y );
- sub( Y, One, Z );
- sub( X, One, T );
- sub( One, Z, t );
- sub( F9, T, t2 );
- if( cmp(t,Zero) != 0 )
- {
- k = 1;
- printf( "(1-(1/2)U1)-1 != 0\n" );
- }
- if( cmp(t2,Zero) != 0 )
- {
- k = 1;
- printf( "[1-U1(1/2+U1)]-F9 != 0\n" );
- }
- sub( U1, Half, Z );
- mul( Z, U1, Z );
- sub( Z, F9, T );
- sub( Y, F9, Q );
- sub( F9, T, t );
- if( cmp( t, Zero ) != 0 )
- {
- k = 1;
- printf( "[F9-U1(1/2-U1)]-F9 != 0\n" );
- }
- sub( U1, F9, t );
- sub( Q, t, t );
- if( cmp( t, Zero ) != 0 )
- {
- k = 1;
- printf( "(F9-U1)-(F9-(1/2)U1) != 0\n" );
- }
- add( One, U2, Z );
- mul( Z, OneAndHalf, Z );
- add( OneAndHalf, U2, T );
- sub( Z, T, T );
- add( U2, T, T );
- div( Radix, Half, X );
- add( One, X, X );
- mul( Radix, U2, Y );
- add( One, Y, Y );
- mul( X, Y, Z );
- if( cmp( T, Zero ) != 0 )
- {
- k = 1;
- printf( "(3/2+U2)-3/2(1+U2)+U2 != 0\n" );
- }
- mul( Radix, U2, t );
- add( X, t, t );
- sub( Z, t, t );
- if( cmp( t, Zero ) != 0 )
- {
- k = 1;
- printf( "(1+1/2Radix)+Radix*U2-[1+1/(2Radix)][1+Radix*U2] != 0\n" );
- }
- if( cmp(Radix, Two) != 0 )
- {
- add( Two, U2, X );
- div( Two, X, Y );
- sub( One, Y, t );
- if( cmp( t, Zero) != 0 )
- k = 1;
- }
- }
-if( k == 0 )
- {
- printf("Sticky bit apparently used correctly.\n");
- mov( One, StickyBit );
- }
-else
- {
- printf("Sticky bit used incorrectly or not at all.\n");
- }
-
-if( GMult == No || GDiv == No || GAddSub == No ||
- RMult == Other || RDiv == Other || RAddSub == Other)
- {
- ErrCnt[Flaw] += 1;
- printf("lack(s) of guard digits or failure(s) to correctly round or chop\n");
-printf( "(noted above) count as one flaw in the final tally below\n" );
- }
-/*=============================================*/
-Milestone = 60;
-/*=============================================*/
-printf("\n");
-printf("Does Multiplication commute? ");
-printf("Testing on %d random pairs.\n", NoTrials);
-SQRT( Three, Random9 );
-mov( Third, Random1 );
-I = 1;
-do
- {
- Random();
- mov( Random1, X );
- Random();
- mov( Random1, Y );
- mul( Y, X, Z9 );
- mul( X, Y, Z );
- sub( Z9, Z, Z9 );
- I = I + 1;
- }
-while ( ! ((I > NoTrials) || (cmp(Z9,Zero) != 0)));
-if(I == NoTrials)
- {
- div( Three, Half, t );
- add( One, t, Random1 );
- add( U2, U1, t );
- add( t, One, Random2 );
- mul( Random1, Random2, Z );
- mul( Random2, Random1, Y );
-/* Z9 = (One + Half / Three) * ((U2 + U1) + One) - (One + Half /
- * Three) * ((U2 + U1) + One);
- */
- div( Three, Half, t2 );
- add( One, t2, t2 );
- add( U2, U1, t );
- add( t, One, t );
- mul( t2, t, Z9 );
- mul( t2, t, t );
- sub( t, Z9, Z9 );
- }
-if(! ((I == NoTrials) || (cmp(Z9,Zero) == 0)))
- {
- ErrCnt[Defect] += 1;
- printf( "X * Y == Y * X trial fails.\n");
- }
-else
- {
- printf(" No failures found in %d integer pairs.\n", NoTrials);
- }
-/*=============================================*/
-Milestone = 70;
-/*=============================================*/
-sqtest();
-Milestone = 90;
-pow1test();
-
-Milestone = 110;
-
-printf("Seeking Underflow thresholds UfThold and E0.\n");
-mov( U1, D );
-FLOOR( Precision, t );
-if( cmp(Precision, t) != 0 )
- {
- mov( BInvrse, D );
- mov( Precision, X );
- do
- {
- mul( D, BInvrse, D );
- sub( One, X, X );
- }
- while( cmp(X, Zero) > 0 );
- }
-mov( One, Y );
-mov( D, Z );
-/* ... D is power of 1/Radix < 1. */
-sigsave = sigfpe;
-if( setjmp(ovfl_buf) )
- goto under0;
-do
- {
- mov( Y, C );
- mov( Z, Y );
- mul( Y, Y, Z );
- add( Z, Z, t );
- }
-while( (cmp(Y,Z) > 0) && (cmp(t,Z) > 0) );
-
-under0:
-sigsave = 0;
-
-mov( C, Y );
-mul( Y, D, Z );
-sigsave = sigfpe;
-if( setjmp(ovfl_buf) )
- goto under1;
-do
- {
- mov( Y, C );
- mov( Z, Y );
- mul( Y, D, Z );
- add( Z, Z, t );
- }
-while( (cmp(Y,Z) > 0) && (cmp(t,Z) > 0) );
-
-under1:
-sigsave = 0;
-
-if( cmp(Radix,Two) < 0 )
- mov( Two, HInvrse );
-else
- mov( Radix, HInvrse );
-div( HInvrse, One, H );
-/* ... 1/HInvrse == H == Min(1/Radix, 1/2) */
-div( C, One, CInvrse );
-mov( C, E0 );
-mul( E0, H, Z );
-/* ...1/Radix^(BIG Integer) << 1 << CInvrse == 1/C */
-sigsave = sigfpe;
-if( setjmp(ovfl_buf) )
- goto under2;
-do
- {
- mov( E0, Y );
- mov( Z, E0 );
- mul( E0, H, Z );
- add( Z, Z, t );
- }
-while( (cmp(E0,Z) > 0) && (cmp(t,Z) > 0) );
-
-under2:
-sigsave = 0;
-
-mov( E0, UfThold );
-mov( Zero, E1 );
-mov( Zero, Q );
-mov( U2, E9 );
-add( One, E9, S );
-mul( C, S, D );
-if( cmp(D,C) <= 0 )
- {
- mul( Radix, U2, E9 );
- add( One, E9, S );
- mul( C, S, D );
- if( cmp(D, C) <= 0 )
- {
- ErrCnt[Failure] += 1;
- printf( "multiplication gets too many last digits wrong.\n" );
- mov( E0, Underflow );
- mov( Zero, YY1 );
- mov( Z, PseudoZero );
- }
- }
-else
- {
- mov( D, Underflow );
- mul( Underflow, H, PseudoZero );
- mov( Zero, UfThold );
- do
- {
- mov( Underflow, YY1 );
- mov( PseudoZero, Underflow );
- add( E1, E1, t );
- if( cmp(t, E1) <= 0)
- {
- mul( Underflow, HInvrse, Y2 );
- sub( Y2, YY1, E1 );
- FABS( E1 );
- mov( YY1, Q );
- if( (cmp( UfThold, Zero ) == 0)
- && (cmp(YY1, Y2) != 0) )
- mov( YY1, UfThold );
- }
- mul( PseudoZero, H, PseudoZero );
- add( PseudoZero, PseudoZero, t );
- }
- while( (cmp(Underflow, PseudoZero) > 0)
- && (cmp(t, PseudoZero) > 0) );
- }
-/* Comment line 4530 .. 4560 */
-if( cmp(PseudoZero, Zero) != 0 )
- {
- printf("\n");
- mov(PseudoZero, Z );
-/* ... Test PseudoZero for "phoney- zero" violates */
-/* ... PseudoZero < Underflow or PseudoZero < PseudoZero + PseudoZero
- ... */
- if( cmp(PseudoZero, Zero) <= 0 )
- {
- ErrCnt[Failure] += 1;
- printf("Positive expressions can underflow to an\n");
- printf("allegedly negative value\n");
- printf("PseudoZero that prints out as: " );
- show( PseudoZero );
- mov( PseudoZero, X );
- neg( X );
- if( cmp(X, Zero) <= 0 )
- {
- printf("But -PseudoZero, which should be\n");
- printf("positive, isn't; it prints out as " );
- show( X );
- }
- }
- else
- {
- ErrCnt[Flaw] += 1;
- printf( "Underflow can stick at an allegedly positive\n");
- printf("value PseudoZero that prints out as " );
- show( PseudoZero );
- }
-/* TstPtUf();*/
- }
-
-/*=============================================*/
-Milestone = 120;
-/*=============================================*/
-mul( CInvrse, Y, t );
-mul( CInvrse, YY1, t2 );
-if( cmp(t,t2) > 0 )
- {
- mul( H, S, S );
- mov( Underflow, E0 );
- }
-if(! ((cmp(E1,Zero) == 0) || (cmp(E1,E0) == 0)) )
- {
- ErrCnt[Defect] += 1;
- if( cmp(E1,E0) < 0 )
- {
- printf("Products underflow at a higher");
- printf(" threshold than differences.\n");
- if( cmp(PseudoZero,Zero) == 0 )
- mov( E1, E0 );
- }
- else
- {
- printf("Difference underflows at a higher");
- printf(" threshold than products.\n");
- }
- }
-printf("Smallest strictly positive number found is E0 = " );
-show( E0 );
-mov( E0, Z );
-TstPtUf();
-mov( E0, Underflow );
-if(N == 1)
- mov( Y, Underflow );
-I = 4;
-if( cmp(E1,Zero) == 0 )
- I = 3;
-if( cmp( UfThold,Zero) == 0 )
- I = I - 2;
-UfNGrad = True;
-switch(I)
- {
- case 1:
- mov( Underflow, UfThold );
- mul( CInvrse, Q, t );
- mul( CInvrse, Y, t2 );
- mul( t2, S, t2 );
- if( cmp( t, t2 ) != 0 )
- {
- mov( Y, UfThold );
- ErrCnt[Failure] += 1;
- printf( "Either accuracy deteriorates as numbers\n");
- printf("approach a threshold = " );
- show( UfThold );
- printf(" coming down from " );
- show( C );
- printf(" or else multiplication gets too many last digits wrong.\n");
- }
- break;
-
- case 2:
- ErrCnt[Failure] += 1;
- printf( "Underflow confuses Comparison which alleges that\n");
- printf("Q == Y while denying that |Q - Y| == 0; these values\n");
- printf("print out as Q = " );
- show( Q );
- printf( ", Y = " );
- show( Y );
- sub( Y2, Q, t );
- FABS(t);
- printf ("|Q - Y| = " );
- show( t );
- mov( Q, UfThold );
- break;
-
- case 3:
- mov( X, X );
- break;
-
- case 4:
- div( E9, E1, t );
- sub( t, UfThold, t );
- FABS(t);
- if( (cmp(Q,UfThold) == 0) && (cmp(E1,E0) == 0)
- && (cmp(t,E1) <= 0) )
- {
- UfNGrad = False;
- printf("Underflow is gradual; it incurs Absolute Error =\n");
- printf("(roundoff in UfThold) < E0.\n");
- mul( E0, CInvrse, Y );
- add( OneAndHalf, U2, t );
- mul( Y, t, Y );
- add( One, U2, X );
- mul( CInvrse, X, X );
- div( X, Y, t );
- IEEE = (cmp(t,E0) == 0);
- if( IEEE == 0 )
- {
- printf( "((CInvrse E0) (1.5+U2)) / (CInvrse (1+U2)) != E0\n" );
- printf( "CInvrse = " );
- show( CInvrse );
- printf( "E0 = " );
- show( E0 );
- printf( "U2 = " );
- show( U2 );
- printf( "X = " );
- show(X);
- printf( "Y = " );
- show(Y);
- printf( "Y/X = " );
- show(t);
- }
- }
- }
-if(UfNGrad)
- {
- printf("\n");
- div( UfThold, Underflow, R );
- SQRT( R, R );
- if( cmp(R,H) <= 0)
- {
- mul( R, UfThold, Z );
-/* X = Z * (One + R * H * (One + H));*/
- add( One, H, X );
- mul( H, X, X );
- mul( R, X, X );
- add( One, X, X );
- mul( Z, X, X );
- }
- else
- {
- mov( UfThold, Z );
-/*X = Z * (One + H * H * (One + H));*/
- add( One, H, X );
- mul( H, X, X );
- mul( H, X, X );
- add( One, X, X );
- mul( Z, X, X );
- }
- sub( Z, X, t );
-/* if(! ((cmp(X,Z) == 0) || (cmp(t,Zero) != 0)) )*/
- if( (cmp(X,Z) != 0) && (cmp(t,Zero) == 0) )
- {
-/* ErrCnt[Flaw] += 1;*/
- ErrCnt[Serious] += 1;
- printf("X = " );
- show( X );
- printf( "\tis not equal to Z = " );
- show( Z );
-/* sub( Z, X, Z9 );*/
- printf("yet X - Z yields " );
- show( t );
- printf("which compares equal to " );
- show( Zero );
- printf(" Should this NOT signal Underflow, ");
- printf("this is a SERIOUS DEFECT\nthat causes ");
- printf("confusion when innocent statements like\n");;
- printf(" if (X == Z) ... else");
- printf(" ... (f(X) - f(Z)) / (X - Z) ...\n");
- printf("encounter Division by Zero although actually\n");
- printf("X / Z = 1 + " );
- div( Z, X, t );
- sub( Half, t, t );
- sub( Half, t, t );
- show(t);
- }
- }
-printf("The Underflow threshold is " );
-show( UfThold );
-printf( "below which calculation may suffer larger Relative error than" );
-printf( " merely roundoff.\n");
-mul( U1, U1, Y2 );
-mul( Y2, Y2, Y );
-mul( Y, U1, Y2 );
-if( cmp( Y2,UfThold) <= 0 )
- {
- if( cmp(Y,E0) > 0 )
- {
- ErrCnt[Defect] += 1;
- I = 5;
- }
- else
- {
- ErrCnt[Serious] += 1;
- I = 4;
- }
- printf("Range is too narrow; U1^%d Underflows.\n", I);
- }
-Milestone = 130;
-
-/*Y = - FLOOR(Half - TwoForty * LOG(UfThold) / LOG(HInvrse)) / TwoForty;*/
-LOG( UfThold, Y );
-LOG( HInvrse, t );
-div( t, Y, Y );
-mul( TwoForty, Y, Y );
-sub( Y, Half, Y );
-FLOOR( Y, Y );
-div( TwoForty, Y, Y );
-neg(Y);
-sub( One, Y, Y2 ); /* ***** changed from Y2 = Y + Y */
-printf("Since underflow occurs below the threshold\n");
-printf("UfThold = " );
-show( HInvrse );
-printf( "\tto the power " );
-show( Y );
-printf( "only underflow should afflict the expression " );
-show( HInvrse );
-printf( "\tto the power " );
-show( Y2 );
-POW( HInvrse, Y2, V9 );
-printf("Actually calculating yields: " );
-show( V9 );
-add( Radix, Radix, t );
-add( t, E9, t );
-mul( t, UfThold, t );
-if( (cmp(V9,Zero) < 0) || (cmp(V9,t) > 0) )
- {
- ErrCnt[Serious] += 1;
- printf( "this is not between 0 and underflow\n");
- printf(" threshold = " );
- show( UfThold );
- }
-else
- {
- add( One, E9, t );
- mul( UfThold, t, t );
- if( cmp(V9,t) <= 0 )
- printf("This computed value is O.K.\n");
- else
- {
- ErrCnt[Defect] += 1;
- printf( "this is not between 0 and underflow\n");
- printf(" threshold = " );
- show( UfThold );
- }
- }
-
-Milestone = 140;
-
-pow2test();
-
-/*=============================================*/
-Milestone = 160;
-/*=============================================*/
-Pause();
-printf("Searching for Overflow threshold:\n");
-printf("This may generate an error.\n");
-sigsave = sigfpe;
-I = 0;
-mov( CInvrse, Y ); /* a large power of 2 */
-neg(Y);
-mul( HInvrse, Y, V9 ); /* HInvrse = 2 */
-if (setjmp(ovfl_buf))
- goto overflow;
-do
- {
- mov( Y, V );
- mov( V9, Y );
- mul( HInvrse, Y, V9 );
- }
-while( cmp(V9,Y) < 0 ); /* V9 = 2 * Y */
-I = 1;
-
-overflow:
-
-show( HInvrse );
-printf( "\ttimes " );
-show( Y );
-printf( "\tequals " );
-show( V9 );
-
-mov( V9, Z );
-printf("Can `Z = -Y' overflow?\n");
-printf("Trying it on Y = " );
-show(Y);
-mov( Y, V9 );
-neg( V9 );
-mov( V9, V0 );
-sub( Y, V, t );
-add( V, V0, t2 );
-if( cmp(t,t2) == 0 )
- printf("Seems O.K.\n");
-else
- {
- printf("finds a Flaw, -(-Y) differs from Y.\n");
- printf( "V-Y=t:" );
- show(V);
- show(Y);
- show(t);
- printf( "V+V0=t2:" );
- show(V);
- show(V0);
- show(t2);
- ErrCnt[Flaw] += 1;
- }
-if( (cmp(Z, Y) != 0) && (I != 0) )
- {
- ErrCnt[Serious] += 1;
- printf("overflow past " );
- show( Y );
- printf( "\tshrinks to " );
- show( Z );
- printf( "= Y * " );
- show( HInvrse );
- }
-/*Y = V * (HInvrse * U2 - HInvrse);*/
-mul( HInvrse, U2, Y );
-sub( HInvrse, Y, Y );
-mul( V, Y, Y );
-/*Z = Y + ((One - HInvrse) * U2) * V;*/
-sub( HInvrse, One, Z );
-mul( Z, U2, Z );
-mul( Z, V, Z );
-add( Y, Z, Z );
-if( cmp(Z,V0) < 0 )
- mov( Z, Y );
-if( cmp(Y,V0) < 0)
- mov( Y, V );
-sub( V, V0, t );
-if( cmp(t,V0) < 0 )
- mov( V0, V );
-printf("Overflow threshold is V = " );
-show( V );
-if(I)
- {
- printf("Overflow saturates at V0 = " );
- show( V0 );
- }
-else
-printf("There is no saturation value because the system traps on overflow.\n");
-
-mul( V, One, V9 );
-printf("No Overflow should be signaled for V * 1 = " );
-show( V9 );
-div( One, V, V9 );
- printf(" nor for V / 1 = " );
- show( V9 );
- printf("Any overflow signal separating this * from the one\n");
- printf("above is a DEFECT.\n");
-/*=============================================*/
-Milestone = 170;
-/*=============================================*/
-mov( V, t );
-neg( t );
-k = 0;
-if( cmp(t,V) >= 0 )
- k = 1;
-mov( V0, t );
-neg( t );
-if( cmp(t,V0) >= 0 )
- k = 1;
-mov( UfThold, t );
-neg(t);
-if( cmp(t,V) >= 0 )
- k = 1;
-if( cmp(UfThold,V) >= 0 )
- k = 1;
-if( k != 0 )
- {
- ErrCnt[Failure] += 1;
- printf( "Comparisons involving +-");
- show( V );
- show( V0 );
- show( UfThold );
- printf("are confused by Overflow." );
- }
-/*=============================================*/
-Milestone = 175;
-/*=============================================*/
-printf("\n");
-for(Indx = 1; Indx <= 3; ++Indx) {
- switch(Indx)
- {
- case 1: mov(UfThold, Z); break;
- case 2: mov( E0, Z); break;
- case 3: mov(PseudoZero, Z); break;
- }
-if( cmp(Z, Zero) != 0 )
- {
- SQRT( Z, V9 );
- mul( V9, V9, Y );
- mul( Radix, E9, t );
- sub( t, One, t );
- div( t, Y, t );
- add( One, Radix, t2 );
- add( t2, E9, t2 );
- mul( t2, Z, t2 );
- if( (cmp(t,Z) < 0) || (cmp(Y,t2) > 0) )
- {
- if( cmp(V9,U1) > 0 )
- ErrCnt[Serious] += 1;
- else
- ErrCnt[Defect] += 1;
- printf("Comparison alleges that what prints as Z = " );
- show( Z );
- printf(" is too far from sqrt(Z) ^ 2 = " );
- show( Y );
- }
- }
-}
-
-Milestone = 180;
-
-for(Indx = 1; Indx <= 2; ++Indx)
- {
- if(Indx == 1)
- mov( V, Z );
- else
- mov( V0, Z );
- SQRT( Z, V9 );
- mul( Radix, E9, X );
- sub( X, One, X );
- mul( X, V9, X );
- mul( V9, X, V9 );
- mul( Two, Radix, t );
- mul( t, E9, t );
- sub( t, One, t );
- mul( t, Z, t );
- if( (cmp(V9,t) < 0) || (cmp(V9,Z) > 0) )
- {
- mov( V9, Y );
- if( cmp(X,W) < 0 )
- ErrCnt[Serious] += 1;
- else
- ErrCnt[Defect] += 1;
- printf("Comparison alleges that Z = " );
- show( Z );
- printf(" is too far from sqrt(Z) ^ 2 :" );
- show( Y );
- }
- }
-
-Milestone = 190;
-
-Pause();
-mul( UfThold, V, X );
-mul( Radix, Radix, Y );
-mul( X, Y, t );
-if( (cmp(t,One) < 0) || (cmp(X,Y) > 0) )
- {
- mul( X, Y, t );
- div( U1, Y, t2 );
- if( (cmp(t,U1) < 0) || (cmp(X,t2) > 0) )
- {
- ErrCnt[Defect] += 1;
- printf( "Badly " );
- }
- else
- {
- ErrCnt[Flaw] += 1;
- }
- printf(" unbalanced range; UfThold * V = " );
- show( X );
- printf( "\tis too far from 1.\n");
- }
-Milestone = 200;
-
-for(Indx = 1; Indx <= 5; ++Indx)
- {
- mov( F9, X );
- switch(Indx)
- {
- case 2: add( One, U2, X ); break;
- case 3: mov( V, X ); break;
- case 4: mov(UfThold,X); break;
- case 5: mov(Radix,X);
- }
- mov( X, Y );
-
- sigsave = sigfpe;
- if (setjmp(ovfl_buf))
- {
- printf(" X / X traps when X = " );
- show( X );
- }
- else
- {
-/*V9 = (Y / X - Half) - Half;*/
- div( X, Y, t );
- sub( Half, t, t );
- sub( Half, t, V9 );
- if( cmp(V9,Zero) == 0 )
- continue;
- mov( U1, t );
- neg(t);
- if( (cmp(V9,t) == 0) && (Indx < 5) )
- {
- ErrCnt[Flaw] += 1;
- }
- else
- {
- ErrCnt[Serious] += 1;
- }
- printf(" X / X differs from 1 when X = " );
- show( X );
- printf(" instead, X / X - 1/2 - 1/2 = " );
- show( V9 );
- }
- }
-
- Pause();
- printf("\n");
- {
- static char *msg[] = {
- "FAILUREs encountered =",
- "SERIOUS DEFECTs discovered =",
- "DEFECTs discovered =",
- "FLAWs discovered =" };
- int i;
- for(i = 0; i < 4; i++) if (ErrCnt[i])
- printf("The number of %-29s %d.\n",
- msg[i], ErrCnt[i]);
- }
- printf("\n");
- if ((ErrCnt[Failure] + ErrCnt[Serious] + ErrCnt[Defect]
- + ErrCnt[Flaw]) > 0) {
- if ((ErrCnt[Failure] + ErrCnt[Serious] + ErrCnt[
- Defect] == 0) && (ErrCnt[Flaw] > 0)) {
- printf("The arithmetic diagnosed seems ");
- printf("satisfactory though flawed.\n");
- }
- if ((ErrCnt[Failure] + ErrCnt[Serious] == 0)
- && ( ErrCnt[Defect] > 0)) {
- printf("The arithmetic diagnosed may be acceptable\n");
- printf("despite inconvenient Defects.\n");
- }
- if ((ErrCnt[Failure] + ErrCnt[Serious]) > 0) {
- printf("The arithmetic diagnosed has ");
- printf("unacceptable serious defects.\n");
- }
- if (ErrCnt[Failure] > 0) {
- printf("Fatal FAILURE may have spoiled this");
- printf(" program's subsequent diagnoses.\n");
- }
- }
- else {
- printf("No failures, defects nor flaws have been discovered.\n");
- if (! ((RMult == Rounded) && (RDiv == Rounded)
- && (RAddSub == Rounded) && (RSqrt == Rounded)))
- printf("The arithmetic diagnosed seems satisfactory.\n");
- else {
- k = 0;
- if( cmp( Radix, Two ) == 0 )
- k = 1;
- if( cmp( Radix, Ten ) == 0 )
- k = 1;
- if( (cmp(StickyBit,One) >= 0) && (k == 1) )
- {
- printf("Rounding appears to conform to ");
- printf("the proposed IEEE standard P");
- k = 0;
- k |= cmp( Radix, Two );
- mul( Four, Three, t );
- mul( t, Two, t );
- sub( t, Precision, t );
- sub( TwentySeven, Precision, t2 );
- sub( TwentySeven, t2, t2 );
- add( t2, One, t2 );
- mul( t2, t, t );
- if( (cmp(Radix,Two) == 0)
- && (cmp(t,Zero) == 0) )
- printf("754");
- else
- printf("854");
- if(IEEE)
- printf(".\n");
- else
- {
- printf(",\nexcept for possibly Double Rounding");
- printf(" during Gradual Underflow.\n");
- }
- }
- printf("The arithmetic diagnosed appears to be excellent!\n");
- }
- }
- if (fpecount)
- printf("\nA total of %d floating point exceptions were registered.\n",
- fpecount);
- printf("END OF TEST.\n");
- }
-
-
-/* Random */
-/* Random computes
- X = (Random1 + Random9)^5
- Random1 = X - FLOOR(X) + 0.000005 * X;
- and returns the new value of Random1
-*/
-
-
-static int randflg = 0;
-FLOAT(C5em6);
-
-Random()
-{
-
-if( randflg == 0 )
- {
- mov( Six, t );
- neg(t);
- POW( Ten, t, t );
- mul( Five, t, C5em6 );
- randflg = 1;
- }
-add( Random1, Random9, t );
-mul( t, t, t2 );
-mul( t2, t2, t2 );
-mul( t, t2, t );
-FLOOR(t, t2 );
-sub( t2, t, t2 );
-mul( t, C5em6, t );
-add( t, t2, Random1 );
-/*return(Random1);*/
-}
-
-/* SqXMinX */
-
-SqXMinX( ErrKind )
-int ErrKind;
-{
-mul( X, BInvrse, t2 );
-sub( t2, X, t );
-/*SqEr = ((SQRT(X * X) - XB) - XA) / OneUlp;*/
-mul( X, X, Sqarg );
-SQRT( Sqarg, SqEr );
-sub( t2, SqEr, SqEr );
-sub( t, SqEr, SqEr );
-div( OneUlp, SqEr, SqEr );
-if( cmp(SqEr,Zero) != 0)
- {
- Showsq( 0 );
- add( J, One, J );
- ErrCnt[ErrKind] += 1;
- printf("sqrt of " );
- mul( X, X, t );
- show( t );
- printf( "minus " );
- show( X );
- printf( "equals " );
- mul( OneUlp, SqEr, t );
- show( t );
- printf("\tinstead of correct value 0 .\n");
- }
-}
-
-/* NewD */
-
-NewD()
-{
-mul( Z1, Q, X );
-/*X = FLOOR(Half - X / Radix) * Radix + X;*/
-div( Radix, X, t );
-sub( t, Half, t );
-FLOOR( t, t );
-mul( t, Radix, t );
-add( t, X, X );
-/*Q = (Q - X * Z) / Radix + X * X * (D / Radix);*/
-mul( X, Z, t );
-sub( t, Q, t );
-div( Radix, t, t );
-div( Radix, D, t2 );
-mul( X, t2, t2 );
-mul( X, t2, t2 );
-add( t, t2, Q );
-/*Z = Z - Two * X * D;*/
-mul( Two, X, t );
-mul( t, D, t );
-sub( t, Z, Z );
-
-if( cmp(Z,Zero) <= 0)
- {
- neg(Z);
- neg(Z1);
- }
-mul( Radix, D, D );
-}
-
-/* SR3750 */
-
-SR3750()
-{
-sub( Radix, X, t );
-sub( Radix, Z2, t2 );
-k = 0;
-if( cmp(t,t2) < 0 )
- k = 1;
-sub( Z2, X, t );
-sub( Z2, W, t2 );
-if( cmp(t,t2) > 0 )
- k = 1;
-/*if (! ((X - Radix < Z2 - Radix) || (X - Z2 > W - Z2))) {*/
-if( k == 0 )
- {
- I = I + 1;
- mul( X, D, X2 );
- mov( X2, Sqarg );
- SQRT( X2, X2 );
-/*Y2 = (X2 - Z2) - (Y - Z2);*/
- sub( Z2, X2, Y2 );
- sub( Z2, Y, t );
- sub( t, Y2, Y2 );
- sub( Half, Y, X2 );
- div( X2, X8, X2 );
- mul( Half, X2, t );
- mul( t, X2, t );
- sub( t, X2, X2 );
-/*SqEr = (Y2 + Half) + (Half - X2);*/
- add( Y2, Half, SqEr );
- sub( X2, Half, t );
- add( t, SqEr, SqEr );
- Showsq( -1 );
- sub( X2, Y2, SqEr );
- Showsq( 1 );
- }
-}
-
-/* IsYeqX */
-
-IsYeqX()
-{
-if( cmp(Y,X) != 0 )
- {
- if (N <= 0)
- {
- if( (cmp(Z,Zero) == 0) && (cmp(Q,Zero) <= 0) )
- printf("WARNING: computing\n");
- else
- {
- ErrCnt[Defect] += 1;
- printf( "computing\n");
- }
- show( Z );
- printf( "\tto the power " );
- show( Q );
- printf("\tyielded " );
- show( Y );
- printf("\twhich compared unequal to correct " );
- show( X );
- sub( X, Y, t );
- printf("\t\tthey differ by " );
- show( t );
- }
- N = N + 1; /* ... count discrepancies. */
- }
-}
-
-/* SR3980 */
-
-SR3980()
-{
-long li;
-
-do
- {
-/*Q = (FLOAT) I;*/
- li = I;
- LTOF( &li, Q );
- POW( Z, Q, Y );
- IsYeqX();
- if(++I > M)
- break;
- mul( Z, X, X );
- }
-while( cmp(X,W) < 0 );
-}
-
-/* PrintIfNPositive */
-
-PrintIfNPositive()
-{
-if(N > 0)
- printf("Similar discrepancies have occurred %d times.\n", N);
-}
-
-
-/* TstPtUf */
-
-TstPtUf()
-{
-N = 0;
-if( cmp(Z,Zero) != 0)
- {
- printf( "Z = " );
- show(Z);
- printf("Since comparison denies Z = 0, evaluating ");
- printf("(Z + Z) / Z should be safe.\n");
- sigsave = sigfpe;
- if (setjmp(ovfl_buf))
- goto very_serious;
- add( Z, Z, Q9 );
- div( Z, Q9, Q9 );
- printf("What the machine gets for (Z + Z) / Z is " );
- show( Q9 );
- sub( Two, Q9, t );
- FABS(t);
- mul( Radix, U2, t2 );
- if( cmp(t,t2) < 0 )
- {
- printf("This is O.K., provided Over/Underflow");
- printf(" has NOT just been signaled.\n");
- }
- else
- {
- if( (cmp(Q9,One) < 0) || (cmp(Q9,Two) > 0) )
- {
-very_serious:
- N = 1;
- ErrCnt [Serious] = ErrCnt [Serious] + 1;
- printf("This is a VERY SERIOUS DEFECT!\n");
- }
- else
- {
- N = 1;
- ErrCnt[Defect] += 1;
- printf("This is a DEFECT!\n");
- }
- }
- mul( Z, One, V9 );
- mov( V9, Random1 );
- mul( One, Z, V9 );
- mov( V9, Random2 );
- div( One, Z, V9 );
- if( (cmp(Z,Random1) == 0) && (cmp(Z,Random2) == 0)
- && (cmp(Z,V9) == 0) )
- {
- if (N > 0)
- Pause();
- }
- else
- {
- N = 1;
- ErrCnt[Defect] += 1;
- printf( "What prints as Z = ");
- show( Z );
- printf( "\tcompares different from " );
- if( cmp(Z,Random1) != 0)
- {
- printf("Z * 1 = " );
- show( Random1 );
- }
- if( (cmp(Z,Random2) != 0)
- || (cmp(Random2,Random1) != 0) )
- {
- printf("1 * Z == " );
- show( Random2 );
- }
- if( cmp(Z,V9) != 0 )
- {
- printf("Z / 1 = " );
- show( V9 );
- }
- if( cmp(Random2,Random1) != 0 )
- {
- ErrCnt[Defect] += 1;
- printf( "Multiplication does not commute!\n");
- printf("\tComparison alleges that 1 * Z = " );
- show(Random2);
- printf("\tdiffers from Z * 1 = " );
- show(Random1);
- }
- Pause();
- }
- }
-}
-
-Pause()
-{
-}
-
-Sign( x, y )
-FSIZE *x, *y;
-{
-
-if( cmp( x, Zero ) < 0 )
- {
- mov( One, y );
- neg( y );
- }
-else
- {
- mov( One, y );
- }
-}
-
-sqtest()
-{
-printf("\nRunning test of square root(x).\n");
-
-RSqrt = Other;
-k = 0;
-SQRT( Zero, t );
-k |= cmp( Zero, t );
-mov( Zero, t );
-neg(t);
-SQRT( t, t2 );
-k |= cmp( t, t2 );
-SQRT( One, t );
-k |= cmp( One, t );
-if( k != 0 )
- {
- ErrCnt[Failure] += 1;
- printf( "Square root of 0.0, -0.0 or 1.0 wrong\n");
- }
-mov( Zero, MinSqEr );
-mov( Zero, MaxSqEr );
-mov( Zero, J );
-mov( Radix, X );
-mov( U2, OneUlp );
-SqXMinX( Serious );
-mov( BInvrse, X );
-mul( BInvrse, U1, OneUlp );
-SqXMinX( Serious );
-mov( U1, X );
-mul( U1, U1, OneUlp );
-SqXMinX( Serious );
-if( cmp(J,Zero) != 0)
- Pause();
-printf("Testing if sqrt(X * X) == X for %d Integers X.\n", NoTrials);
-mov( Zero, J );
-mov( Two, X );
-mov( Radix, Y );
-if( cmp(Radix,One) != 0 )
- {
- lngint = NoTrials;
- LTOF( &lngint, t );
- FTOL( t, &lng2, X );
- if( lngint != lng2 )
- {
- printf( "Integer conversion error\n" );
- exit(1);
- }
- do
- {
- mov( Y, X );
- mul( Radix, Y, Y );
- sub( X, Y, t2 );
- }
- while( ! (cmp(t2,t) >= 0) );
- }
-mul( X, U2, OneUlp );
-I = 1;
-while(I < 10)
- {
- add( X, One, X );
- SqXMinX( Defect );
- if( cmp(J,Zero) > 0 )
- break;
- I = I + 1;
- }
-printf("Test for sqrt monotonicity.\n");
-I = - 1;
-mov( BMinusU2, X );
-mov( Radix, Y );
-mul( Radix, U2, Z );
-add( Radix, Z, Z );
-NotMonot = False;
-Monot = False;
-while( ! (NotMonot || Monot))
- {
- I = I + 1;
- SQRT(X, X);
- SQRT(Y,Q);
- SQRT(Z,Z);
- if( (cmp(X,Q) > 0) || (cmp(Q,Z) > 0) )
- NotMonot = True;
- else
- {
- add( Q, Half, Q );
- FLOOR( Q, Q );
- mul( Q, Q, t );
- if( (I > 0) || (cmp(Radix,t) == 0) )
- Monot = True;
- else if (I > 0)
- {
- if(I > 1)
- Monot = True;
- else
- {
- mul( Y, BInvrse, Y );
- sub( U1, Y, X );
- add( Y, U1, Z );
- }
- }
- else
- {
- mov( Q, Y );
- sub( U2, Y, X );
- add( Y, U2, Z );
- }
- }
- }
-if( Monot )
- printf("sqrt has passed a test for Monotonicity.\n");
-else
- {
- ErrCnt[Defect] += 1;
- printf("sqrt(X) is non-monotonic for X near " );
- show(Y);
- }
-/*=============================================*/
-Milestone = 80;
-/*=============================================*/
-add( MinSqEr, Half, MinSqEr );
-sub( Half, MaxSqEr, MaxSqEr);
-/*Y = (SQRT(One + U2) - One) / U2;*/
-add( One, U2, Sqarg );
-SQRT( Sqarg, Y );
-sub( One, Y, Y );
-div( U2, Y, Y );
-/*SqEr = (Y - One) + U2 / Eight;*/
-sub( One, Y, t );
-div( Eight, U2, SqEr );
-add( t, SqEr, SqEr );
-Showsq( 1 );
-div( Eight, U2, SqEr );
-add( Y, SqEr, SqEr );
-Showsq( -1 );
-/*Y = ((SQRT(F9) - U2) - (One - U2)) / U1;*/
-mov( F9, Sqarg );
-SQRT( Sqarg, Y );
-sub( U2, Y, Y );
-sub( U2, One, t );
-sub( t, Y, Y );
-div( U1, Y, Y );
-div( Eight, U1, SqEr );
-add( Y, SqEr, SqEr );
-Showsq( 1 );
-/*SqEr = (Y + One) + U1 / Eight;*/
-div( Eight, U1, t );
-add( Y, One, SqEr );
-add( SqEr, t, SqEr );
-Showsq( -1 );
-mov( U2, OneUlp );
-mov( OneUlp, X );
-for( Indx = 1; Indx <= 3; ++Indx)
- {
-/*Y = SQRT((X + U1 + X) + F9);*/
- add( X, U1, Y );
- add( Y, X, Y );
- add( Y, F9, Y );
- mov( Y, Sqarg );
- SQRT( Sqarg, Y );
-/*Y = ((Y - U2) - ((One - U2) + X)) / OneUlp;*/
- sub( U2, One, t );
- add( t, X, t );
- sub( U2, Y, Y );
- sub( t, Y, Y );
- div( OneUlp, Y, Y );
-/*Z = ((U1 - X) + F9) * Half * X * X / OneUlp;*/
- sub( X, U1, t );
- add( t, F9, t );
- mul( t, Half, t );
- mul( t, X, t );
- mul( t, X, t );
- div( OneUlp, t, Z );
- add( Y, Half, SqEr );
- add( SqEr, Z, SqEr );
- Showsq( -1 );
- sub( Half, Y, SqEr );
- add( SqEr, Z, SqEr );
- Showsq( 1 );
- if(((Indx == 1) || (Indx == 3)))
- {
-/*X = OneUlp * Sign (X) * FLOOR(Eight / (Nine * SQRT(OneUlp)));*/
- mov( OneUlp, Sqarg );
- SQRT( Sqarg, t );
- mul( Nine, t, t );
- div( t, Eight, t );
- FLOOR( t, t );
- Sign( X, t2 );
- mul( t2, t, t );
- mul( OneUlp, t, X );
- }
- else
- {
- mov( U1, OneUlp );
- mov( OneUlp, X );
- neg( X );
- }
- }
-/*=============================================*/
-Milestone = 85;
-/*=============================================*/
-SqRWrng = False;
-Anomaly = False;
-if( cmp(Radix,One) != 0 )
- {
- printf("Testing whether sqrt is rounded or chopped.\n");
-/*D = FLOOR(Half + POW(Radix, One + Precision - FLOOR(Precision)));*/
- FLOOR( Precision, t2 );
- add( One, Precision, t );
- sub( t2, t, t );
- POW( Radix, t, D );
- add( Half, D, D );
- FLOOR( D, D );
-/* ... == Radix^(1 + fract) if (Precision == Integer + fract. */
- div( Radix, D, X );
- div( A1, D, Y );
- FLOOR( X, t );
- FLOOR( Y, t2 );
- if( (cmp(X,t) != 0) || (cmp(Y,t2) != 0) )
- {
- Anomaly = True;
- printf( "Anomaly 1\n" );
- }
- else
- {
- mov( Zero, X );
- mov( X, Z2 );
- mov( One, Y );
- mov( Y, Y2 );
- sub( One, Radix, Z1 );
- mul( Four, D, FourD );
- do
- {
- if( cmp(Y2,Z2) >0 )
- {
- mov( Radix, Q );
- mov( Y, YY1 );
- do
- {
-/*X1 = FABS(Q + FLOOR(Half - Q / YY1) * YY1);*/
- div( YY1, Q, t );
- sub( t, Half, t );
- FLOOR( t, t );
- mul( t, YY1, t );
- add( Q, t, X1 );
- FABS( X1 );
- mov( YY1, Q );
- mov( X1, YY1 );
- }
- while( ! (cmp(X1,Zero) <= 0) );
- if( cmp(Q,One) <= 0 )
- {
- mov( Y2, Z2 );
- mov( Y, Z );
- }
- }
- add( Y, Two, Y );
- add( X, Eight, X );
- add( Y2, X, Y2 );
- if( cmp(Y2,FourD) >= 0 )
- sub( FourD, Y2, Y2 );
- }
- while( ! (cmp(Y,D) >= 0) );
- sub( Z2, FourD, X8 );
- mul( Z, Z, Q );
- add( X8, Q, Q );
- div( FourD, Q, Q );
- div( Eight, X8, X8 );
- FLOOR( Q, t );
- if( cmp(Q,t) != 0 )
- {
- Anomaly = True;
- printf( "Anomaly 2\n" );
- }
- else
- {
- Break = False;
- do
- {
- mul( Z1, Z, X );
-/*X = X - FLOOR(X / Radix) * Radix;*/
- div( Radix, X, t );
- FLOOR( t, t );
- mul( t, Radix, t );
- sub( t, X, X );
- if( cmp(X,One) == 0 )
- Break = True;
- else
- sub( One, Z1, Z1 );
- }
- while( ! (Break || (cmp(Z1,Zero) <= 0)) );
- if( (cmp(Z1,Zero) <= 0) && (! Break))
- {
- printf( "Anomaly 3\n" );
- Anomaly = True;
- }
- else
- {
- if( cmp(Z1,RadixD2) > 0)
- sub( Radix, Z1, Z1 );
- do
- {
- NewD();
- mul( U2, D, t );
- }
- while( ! (cmp(t,F9) >= 0) );
- mul( D, Radix, t );
- sub( D, t, t );
- sub( D, W, t2 );
- if (cmp(t,t2) != 0 )
- {
- printf( "Anomaly 4\n" );
- Anomaly = True;
- }
- else
- {
- mov( D, Z2 );
- I = 0;
- add( One, Z, t );
- mul( t, Half, t );
- add( D, t, Y );
- add( D, Z, X );
- add( X, Q, X );
- SR3750();
- sub( Z, One, t );
- mul( t, Half, t );
- add( D, t, Y );
- add( Y, D, Y );
- sub( Z, D, X );
- add( X, D, X );
- add( X, Q, t );
- add( t, X, X );
- SR3750();
- NewD();
- sub( Z2, D, t );
- sub( Z2, W, t2 );
- if(cmp(t,t2) != 0 )
- {
- printf( "Anomaly 5\n" );
- Anomaly = True;
- }
- else
- {
-/*Y = (D - Z2) + (Z2 + (One - Z) * Half);*/
- sub( Z, One, t );
- mul( t, Half, t );
- add( Z2, t, t );
- sub( Z2, D, Y );
- add( Y, t, Y );
-/*X = (D - Z2) + (Z2 - Z + Q);*/
- sub( Z, Z2, t );
- add( t, Q, t );
- sub( Z2, D, X );
- add( X, t, X );
- SR3750();
- add( One, Z, Y );
- mul( Y, Half, Y );
- mov( Q, X );
- SR3750();
- if(I == 0)
- {
- printf( "Anomaly 6\n" );
- Anomaly = True;
- }
- }
- }
- }
- }
- }
- if ((I == 0) || Anomaly)
- {
- ErrCnt[Failure] += 1;
- printf( "Anomalous arithmetic with Integer < \n");
- printf("Radix^Precision = " );
- show( W );
- printf(" fails test whether sqrt rounds or chops.\n");
- SqRWrng = True;
- }
- }
-if(! Anomaly)
- {
- if(! ((cmp(MinSqEr,Zero) < 0) || (cmp(MaxSqEr,Zero) > 0))) {
- RSqrt = Rounded;
- printf("Square root appears to be correctly rounded.\n");
- }
- else
- {
- k = 0;
- add( MaxSqEr, U2, t );
- sub( Half, U2, t2 );
- if( cmp(t,t2) > 0 )
- k = 1;
- if( cmp( MinSqEr, Half ) > 0 )
- k = 1;
- add( MinSqEr, Radix, t );
- if( cmp( t, Half ) < 0 )
- k = 1;
- if( k == 1 )
- SqRWrng = True;
- else
- {
- RSqrt = Chopped;
- printf("Square root appears to be chopped.\n");
- }
- }
- }
-if( SqRWrng )
- {
- printf("Square root is neither chopped nor correctly rounded.\n");
- printf("Observed errors run from " );
- sub( Half, MinSqEr, t );
- show( t );
- printf("\tto " );
- add( Half, MaxSqEr, t );
- show( t );
- printf( "ulps.\n" );
- sub( MinSqEr, MaxSqEr, t );
- mul( Radix, Radix, t2 );
- if( cmp( t, t2 ) >= 0 )
- {
- ErrCnt[Serious] += 1;
- printf( "sqrt gets too many last digits wrong\n");
- }
- }
-}
-
-Showsq( arg )
-int arg;
-{
-
-k = 0;
-if( arg <= 0 )
- {
- if( cmp(SqEr,MinSqEr) < 0 )
- {
- k = 1;
- mov( SqEr, MinSqEr );
- }
- }
-if( arg >= 0 )
- {
- if( cmp(SqEr,MaxSqEr) > 0 )
- {
- k = 2;
- mov( SqEr, MaxSqEr );
- }
- }
-#if DEBUG
-if( k != 0 )
- {
- printf( "Square root of " );
- show( arg );
- printf( "\tis in error by " );
- show( SqEr );
- }
-#endif
-}
-
-
-pow1test()
-{
-
-/*=============================================*/
-Milestone = 90;
-/*=============================================*/
-Pause();
-printf("Testing powers Z^i for small Integers Z and i.\n");
-N = 0;
-/* ... test powers of zero. */
-I = 0;
-mov( Zero, Z );
-neg(Z);
-M = 3;
-Break = False;
-do
- {
- mov( One, X );
- SR3980();
- if(I <= 10)
- {
- I = 1023;
- SR3980();
- }
- if( cmp(Z,MinusOne) == 0 )
- Break = True;
- else
- {
- mov( MinusOne, Z );
- PrintIfNPositive();
- N = 0;
-/* .. if(-1)^N is invalid, replace MinusOne by One. */
- I = - 4;
- }
- }
-while( ! Break );
-PrintIfNPositive();
-N1 = N;
-N = 0;
-mov( A1, Z );
-/*M = FLOOR(Two * LOG(W) / LOG(A1));*/
-LOG( W, t );
-mul( Two, t, t );
-FLOOR( t, t );
-LOG( A1, t2 );
-div( t2, t, t );
-FTOL( t, &lngint, t2 );
-M = lngint;
-Break = False;
-do
- {
- mov( Z, X );
- I = 1;
- SR3980();
- if( cmp(Z,AInvrse) == 0 )
- Break = True;
- else
- mov( AInvrse, Z );
- }
-while( ! (Break) );
-/*=============================================*/
-Milestone = 100;
-/*=============================================*/
-/* Powers of Radix have been tested, */
-/* next try a few primes */
-
-M = NoTrials;
-
-mov( Three, Z );
-do
- {
- mov( Z, X );
- I = 1;
- SR3980();
- do
- {
- add( Z, Two, Z );
- div( Three, Z, t );
- FLOOR( t, t );
- mul( Three, t, t );
- }
- while( cmp(t,Z) == 0 );
- mul( Eight, Three, t );
- }
-while( cmp(Z,t) < 0 );
-
-if(N > 0)
- {
- printf("Errors like this may invalidate financial calculations\n");
- printf("\tinvolving interest rates.\n");
- }
-PrintIfNPositive();
-N += N1;
-if(N == 0)
- printf("... no discrepancies found.\n");
-if(N > 0)
- Pause();
-else printf("\n");
-}
-
-
-
-pow2test()
-{
-printf("\n");
-/* ...calculate Exp2 == exp(2) == 7.38905 60989 30650 22723 04275-... */
-mov( Zero, X );
-mov( Two, t2 ); /*I = 2;*/
-
-mul( Two, Three, Y );
-mov( Zero, Q );
-N = 0;
-do
- {
- mov( X, Z );
- add( t2, One, t2 ); /*I = I + 1;*/
- add( t2, t2, t );
- div( t, Y, Y ); /*Y = Y / (I + I);*/
- add( Y, Q, R );
- add( Z, R, X );
- sub( X, Z, Q );
- add( Q, R, Q );
- }
-while( cmp(X,Z) > 0 );
-
-/*Z = (OneAndHalf + One / Eight) + X / (OneAndHalf * ThirtyTwo);*/
-div( Eight, One, t );
-add( OneAndHalf, t, Z );
-mul( OneAndHalf, ThirtyTwo, t );
-div( t, X, t );
-add( Z, t, Z );
-mul( Z, Z, X );
-mul( X, X, Exp2 );
-mov( F9, X );
-sub( U1, X, Y );
-printf("Testing X^((X + 1) / (X - 1)) vs. exp(2) = " );
-show( Exp2 );
-printf( "\tas X -> 1.\n" );
-for(I = 1;;)
- {
- sub( BInvrse, X, Z );
-/*Z = (X + One) / (Z - (One - BInvrse));*/
- add( X, One, t2 );
- sub( BInvrse, One, t );
- sub( t, Z, t );
- div( t, t2, Z );
- POW( X, Z, Sqarg );
- sub( Exp2, Sqarg, Q );
- mov( Q, t );
- FABS( t );
- mul( TwoForty, U2, t2 );
- if( cmp( t, t2 ) > 0 )
- {
- N = 1;
- sub( BInvrse, X, V9 );
- sub( BInvrse, One, t );
- sub( t, V9, V9 );
- ErrCnt[Defect] += 1;
- printf( "Calculated " );
- show( Sqarg );
- printf(" for \t(1 + " );
- show( V9 );
- printf( "\tto the power " );
- show( Z );
- printf("\tdiffers from correct value by " );
- show( Q );
- printf("\tThis much error may spoil financial\n");
- printf("\tcalculations involving tiny interest rates.\n");
- break;
- }
- else
- {
- sub( X, Y, Z );
- mul( Z, Two, Z );
- add( Z, Y, Z );
- mov( Y, X );
- mov( Z, Y );
- sub( F9, X, Z );
- mul( Z, Z, Z );
- add( Z, One, Z );
- if( (cmp(Z,One) > 0) && (I < NoTrials) )
- I++;
- else
- {
- if( cmp(X,One) > 0 )
- {
- if(N == 0)
- printf("Accuracy seems adequate.\n");
- break;
- }
- else
- {
- add( One, U2, X );
- add( U2, U2, Y );
- add( X, Y, Y );
- I = 1;
- }
- }
- }
- }
-/*=============================================*/
-Milestone = 150;
-/*=============================================*/
-printf("Testing powers Z^Q at four nearly extreme values.\n");
-N = 0;
-mov( A1, Z );
-/*Q = FLOOR(Half - LOG(C) / LOG(A1));*/
-LOG( C, t );
-LOG( A1, t2 );
-div( t2, t, t );
-sub( t, Half, t );
-FLOOR( t, Q );
-Break = False;
-do
- {
- mov( CInvrse, X );
- POW( Z, Q, Y );
- IsYeqX();
- neg(Q);
- mov( C, X );
- POW( Z, Q, Y );
- IsYeqX();
- if( cmp(Z,One) < 0 )
- Break = True;
- else
- mov( AInvrse, Z );
- }
-while( ! (Break));
-PrintIfNPositive();
-if(N == 0)
- printf(" ... no discrepancies found.\n");
-printf("\n");
-}
+/* paranoia.c arithmetic tester + * + * This is an implementation of the PARANOIA program. It substitutes + * subroutine calls for ALL floating point arithmetic operations. + * This permits you to substitute your own experimental versions of + * arithmetic routines. It also defeats compiler optimizations, + * so for native arithmetic you can be pretty sure you are testing + * the arithmetic and not the compiler. + * + * This version of PARANOIA omits the display of division by zero. + * It also omits the test for extra precise subexpressions, since + * they cannot occur in this context. Otherwise it includes all the + * tests of the 27 Jan 86 distribution, plus a few additional tests. + * Commentary has been reduced to a minimum in order to make the program + * smaller. + * + * The original PARANOIA program, written by W. Kahan, C version + * by Thos Sumner and David Gay, can be downloaded free from the + * Internet NETLIB. An MSDOS disk can be obtained for $15 from: + * Richard Karpinski + * 6521 Raymond Street + * Oakland, CA 94609 + * + * Steve Moshier, 28 Oct 88 + * last rev: 23 May 92 + */ + +#define DEBUG 0 + +/* To use the native arithmetic of the computer, define NATIVE + * to be 1. To use your own supplied arithmetic routines, NATIVE is 0. + */ +#define NATIVE 0 + +/* gcc real.c interface */ +#define L128DOUBLE 0 + +#include <stdio.h> + + + + +/* Data structure of floating point number. If NATIVE was + * selected above, you can define LDOUBLE 1 to test 80-bit long double + * precision or define it 0 to test 64-bit double precision. +*/ +#define LDOUBLE 0 +#if NATIVE + +#define NE 1 +#if LDOUBLE +#define FSIZE long double +#define FLOAT(x) FSIZE x[NE] +static FSIZE eone[NE] = {1.0L}; /* The constant 1.0 */ +#define ZSQRT sqrtl +#define ZLOG logl +#define ZFLOOR floorl +#define ZPOW powl +long double sqrtl(), logl(), floorl(), powl(); +#define FSETUP einit +#else /* not LDOUBLE */ +#define FSIZE double +#define FLOAT(x) FSIZE x[NE] +static FSIZE eone[NE] = {1.0}; /* The constant 1.0 */ +#define ZSQRT sqrt +#define ZLOG log +#define ZFLOOR floor +#define ZPOW pow +double sqrt(), log(), floor(), pow(); +/* Coprocessor initialization, + * defeat underflow trap or what have you. + * This is required mainly on i386 and 68K processors. + */ +#define FSETUP dprec +#endif /* double, not LDOUBLE */ + +#else /* not NATIVE */ + +/* Setup for extended double type. + * Put NE = 10 for real.c operating with TFmode support (16-byte reals) + * Put NE = 6 for real.c operating with XFmode support (10- or 12-byte reals) + * The value of NE must agree with that in ehead.h, if ieee.c is used. + */ +#define NE 6 +#define FSIZE unsigned short +#define FLOAT(x) unsigned short x[NE] +extern unsigned short eone[]; +#define FSETUP einit + +/* default for FSETUP */ +/* +einit() +{} +*/ + +error(s) +char *s; +{ +printf( "error: %s\n", s ); +} + +#endif /* not NATIVE */ + + + +#if L128DOUBLE +/* real.c interface */ + +#undef FSETUP +#define FSETUP efsetup + +FLOAT(enone); + +#define ONE enone + +/* Use emov to convert from widest type to widest type, ... */ +/* +#define ENTOE emov +#define ETOEN emov +*/ + +/* ... else choose e24toe, e53toe, etc. */ +#define ENTOE e64toe +#define ETOEN etoe64 +#define NNBITS 64 + +#define NIBITS ((NE-1)*16) +extern int rndprc; + +efsetup() +{ +rndprc = NNBITS; +ETOEN(eone, enone); +} + +add(a,b,c) +FLOAT(a); +FLOAT(b); +FLOAT(c); +{ +unsigned short aa[10], bb[10], cc[10]; + +ENTOE(a,aa); +ENTOE(b,bb); +eadd(aa,bb,cc); +ETOEN(cc,c); +} + +sub(a,b,c) +FLOAT(a); +FLOAT(b); +FLOAT(c); +{ +unsigned short aa[10], bb[10], cc[10]; + +ENTOE(a,aa); +ENTOE(b,bb); +esub(aa,bb,cc); +ETOEN(cc,c); +} + +mul(a,b,c) +FLOAT(a); +FLOAT(b); +FLOAT(c); +{ +unsigned short aa[10], bb[10], cc[10]; + +ENTOE(a,aa); +ENTOE(b,bb); +emul(aa,bb,cc); +ETOEN(cc,c); +} + +div(a,b,c) +FLOAT(a); +FLOAT(b); +FLOAT(c); +{ +unsigned short aa[10], bb[10], cc[10]; + +ENTOE(a,aa); +ENTOE(b,bb); +ediv(aa,bb,cc); +ETOEN(cc,c); +} + +int cmp(a,b) +FLOAT(a); +FLOAT(b); +{ +unsigned short aa[10], bb[10]; +int c; +int ecmp(); + +ENTOE(a,aa); +ENTOE(b,bb); +c = ecmp(aa,bb); +return(c); +} + +mov(a,b) +FLOAT(a); +FLOAT(b); +{ +int i; + +for( i=0; i<NE; i++ ) + b[i] = a[i]; +} + + +neg(a) +FLOAT(a); +{ +unsigned short aa[10]; + +ENTOE(a,aa); +eneg(aa); +ETOEN(aa,a); +} + +clear(a) +FLOAT(a); +{ +int i; + +for( i=0; i<NE; i++ ) + a[i] = 0; +} + +FABS(a) +FLOAT(a); +{ +unsigned short aa[10]; + +ENTOE(a,aa); +eabs(aa); +ETOEN(aa,a); +} + +FLOOR(a,b) +FLOAT(a); +FLOAT(b); +{ +unsigned short aa[10], bb[10]; + +ENTOE(a,aa); +efloor(aa,bb); +ETOEN(bb,b); +} + +LOG(a,b) +FLOAT(a); +FLOAT(b); +{ +unsigned short aa[10], bb[10]; +int rndsav; + +ENTOE(a,aa); +rndsav = rndprc; +rndprc = NIBITS; +elog(aa,bb); +rndprc = rndsav; +ETOEN(bb,b); +} + +POW(a,b,c) +FLOAT(a); +FLOAT(b); +FLOAT(c); +{ +unsigned short aa[10], bb[10], cc[10]; +int rndsav; + +ENTOE(a,aa); +ENTOE(b,bb); +rndsav = rndprc; +rndprc = NIBITS; +epow(aa,bb,cc); +rndprc = rndsav; +ETOEN(cc,c); +} + +SQRT(a,b) +FLOAT(a); +FLOAT(b); +{ +unsigned short aa[10], bb[10]; + +ENTOE(a,aa); +esqrt(aa,bb); +ETOEN(bb,b); +} + +FTOL(x,ip,f) +FLOAT(x); +long *ip; +FLOAT(f); +{ +unsigned short xx[10], ff[10]; + +ENTOE(x,xx); +eifrac(xx,ip,ff); +ETOEN(ff,f); +} + +LTOF(ip,x) +long *ip; +FLOAT(x); +{ +unsigned short xx[10]; +ltoe(ip,xx); +ETOEN(xx,x); +} + +TOASC(a,b,c) +FLOAT(a); +int b; +char *c; +{ +unsigned short xx[10]; + +ENTOE(a,xx); +etoasc(xx,b,c); +} + +#else /* not L128DOUBLE */ + +#define ONE eone + +/* Note all arguments of operation subroutines are pointers. */ +/* c = b + a */ +#define add(a,b,c) eadd(a,b,c) +/* c = b - a */ +#define sub(a,b,c) esub(a,b,c) +/* c = b * a */ +#define mul(a,b,c) emul(a,b,c) +/* c = b / a */ +#define div(a,b,c) ediv(a,b,c) +/* 1 if a>b, 0 if a==b, -1 if a<b */ +#define cmp(a,b) ecmp(a,b) +/* b = a */ +#define mov(a,b) emov(a,b) +/* a = -a */ +#define neg(a) eneg(a) +/* a = 0 */ +#define clear(a) eclear(a) + +#define FABS(x) eabs(x) +#define FLOOR(x,y) efloor(x,y) +#define LOG(x,y) elog(x,y) +#define POW(x,y,z) epow(x,y,z) +#define SQRT(x,y) esqrt(x,y) + +/* x = &FLOAT input, i = &long integer part, f = &FLOAT fractional part */ +#define FTOL(x,i,f) eifrac(x,i,f) + +/* i = &long integer input, x = &FLOAT output */ +#define LTOF(i,x) ltoe(i,x) + +/* Convert FLOAT a to decimal ASCII string with b digits */ +#define TOASC(a,b,c) etoasc(a,b,c) +#endif /* not L128DOUBLE */ + + + +/* The following subroutines are implementations of the above + * named functions, using the native or default arithmetic. + */ +#if NATIVE +eadd(a,b,c) +FSIZE *a, *b, *c; +{ +*c = *b + *a; +} + +esub(a,b,c) +FSIZE *a, *b, *c; +{ +*c = *b - *a; +} + +emul(a,b,c) +FSIZE *a, *b, *c; +{ +*c = (*b) * (*a); +} + +ediv(a,b,c) +FSIZE *a, *b, *c; +{ +*c = (*b) / (*a); +} + + +/* Important note: comparison can be done by subracting + * or by a compare instruction that may or may not be + * equivalent to subtracting. + */ +ecmp(a,b) +FSIZE *a, *b; +{ +if( (*a) > (*b) ) + return( 1 ); +if( (*a) < (*b) ) + return( -1 ); +if( (*a) != (*b) ) + goto cmpf; +if( (*a) == (*b) ) + return( 0 ); +cmpf: +printf( "Compare fails\n" ); +return(0); +} + + +emov( a, b ) +FSIZE *a, *b; +{ +*b = *a; +} + +eneg( a ) +FSIZE *a; +{ +*a = -(*a); +} + +eclear(a) +FSIZE *a; +{ +*a = 0.0; +} + +eabs(x) +FSIZE *x; +{ +if( (*x) < 0.0 ) + *x = -(*x); +} + +efloor(x,y) +FSIZE *x, *y; +{ + +*y = (FSIZE )ZFLOOR( *x ); +} + +elog(x,y) +FSIZE *x, *y; +{ + +*y = (FSIZE )ZLOG( *x ); +} + +epow(x,y,z) +FSIZE *x, *y, *z; +{ + +*z = (FSIZE )ZPOW( *x, *y ); +} + +esqrt(x,y) +FSIZE *x, *y; +{ + +*y = (FSIZE )ZSQRT( *x ); +} + + +eifrac(x,i,f) +FSIZE *x; +long *i; +FSIZE *f; +{ +FSIZE y; + +y = (FSIZE )ZFLOOR( *x ); +if( y < 0.0 ) + { + *f = y - *x; + *i = -y; + } +else + { + *f = *x - y; + *i = y; + } +} + + +ltoe(i,x) +long *i; +FSIZE *x; +{ +*x = *i; +} + + +etoasc(a,str,n) +FSIZE *a; +char *str; +int n; +{ +double x; + +x = (double )(*a); +sprintf( str, " %.17e ", x ); +} + +/* default for FSETUP */ +einit() +{} + +#endif /* NATIVE */ + + + + +FLOAT(Radix); +FLOAT(BInvrse); +FLOAT(RadixD2); +FLOAT(BMinusU2); +/*Small floating point constants.*/ +FLOAT(Zero); +FLOAT(Half); +FLOAT(One); +FLOAT(Two); +FLOAT(Three); +FLOAT(Four); +FLOAT(Five); +FLOAT(Six); +FLOAT(Eight); +FLOAT(Nine); +FLOAT(Ten); +FLOAT(TwentySeven); +FLOAT(ThirtyTwo); +FLOAT(TwoForty); +FLOAT(MinusOne ); +FLOAT(OneAndHalf); + +/*Integer constants*/ +int NoTrials = 20; /*Number of tests for commutativity. */ +#define False 0 +#define True 1 + +/* Definitions for declared types + Guard == (Yes, No); + Rounding == (Chopped, Rounded, Other); + Message == packed array [1..40] of char; + Class == (Flaw, Defect, Serious, Failure); + */ +#define Yes 1 +#define No 0 +#define Chopped 2 +#define Rounded 1 +#define Other 0 +#define Flaw 3 +#define Defect 2 +#define Serious 1 +#define Failure 0 + +typedef int Guard, Rounding, Class; +typedef char Message; + +/* Declarations of Variables */ +FLOAT(AInvrse); +FLOAT(A1); +FLOAT(C); +FLOAT(CInvrse); +FLOAT(D); +FLOAT(FourD); +FLOAT(E0); +FLOAT(E1); +FLOAT(Exp2); +FLOAT(E3); +FLOAT(MinSqEr); +FLOAT(SqEr); +FLOAT(MaxSqEr); +FLOAT(E9); +FLOAT(Third); +FLOAT(F6); +FLOAT(F9); +FLOAT(H); +FLOAT(HInvrse); +FLOAT(StickyBit); +FLOAT(J); +FLOAT(MyZero); +FLOAT(Precision); +FLOAT(Q); +FLOAT(Q9); +FLOAT(R); +FLOAT(Random9); +FLOAT(T); +FLOAT(Underflow); +FLOAT(S); +FLOAT(OneUlp); +FLOAT(UfThold); +FLOAT(U1); +FLOAT(U2); +FLOAT(V); +FLOAT(V0); +FLOAT(V9); +FLOAT(W); +FLOAT(X); +FLOAT(X1); +FLOAT(X2); +FLOAT(X8); +FLOAT(Random1); +FLOAT(Y); +FLOAT(YY1); +FLOAT(Y2); +FLOAT(Random2); +FLOAT(Z); +FLOAT(PseudoZero); +FLOAT(Z1); +FLOAT(Z2); +FLOAT(Z9); +static FLOAT(t); +FLOAT(t2); +FLOAT(Sqarg); +int ErrCnt[4]; +int fpecount; +int Milestone; +int PageNo; +int I, M, N, N1, stkflg; +Guard GMult, GDiv, GAddSub; +Rounding RMult, RDiv, RAddSub, RSqrt; +int Break, Done, NotMonot, Monot, Anomaly, IEEE; +int SqRWrng, UfNGrad; +int k, k2; +int Indx; +char ch[8]; + +long lngint, lng2; /* intermediate for conversion between int and FLOAT */ + +/* Computed constants. */ +/*U1 gap below 1.0, i.e, 1.0-U1 is next number below 1.0 */ +/*U2 gap above 1.0, i.e, 1.0+U2 is next number above 1.0 */ + + +show( x ) +short x[]; +{ +int i; +char s[80]; + +/* Number of 16-bit groups to display */ +#if NATIVE +#if LDOUBLE +#define NPRT (sizeof( long double )/2) +#else +#define NPRT (sizeof( double )/2) +#endif +#else +#define NPRT NE +#endif + +TOASC( x, s, 70 ); +printf( "%s\n", s ); +for( i=0; i<NPRT; i++ ) + printf( "%04x ", x[i] & 0xffff ); +printf( "\n" ); +} + +/* define NOSIGNAL */ +#ifndef NOSIGNAL +#include <signal.h> +#endif +#include <setjmp.h> +jmp_buf ovfl_buf; +/*typedef int (*Sig_type)();*/ +typedef void (*Sig_type)(); +Sig_type sigsave; + +/* Floating point exception receiver */ +void sigfpe() +{ +fpecount++; +printf( "\n* * * FLOATING-POINT ERROR * * *\n" ); +/* reinitialize the floating point unit */ +FSETUP(); +fflush(stdout); +if( sigsave ) + { +#ifndef NOSIGNAL + signal( SIGFPE, sigsave ); +#endif + sigsave = 0; + longjmp( ovfl_buf, 1 ); + } +abort(); +} + + +main() +{ + +/* Do coprocessor or other initializations */ +FSETUP(); + +printf( + "This version of paranoia omits test for extra precise subexpressions\n" ); +printf( "and includes a few additional tests.\n" ); + +clear(Zero); +printf( "0 = " ); +show( Zero ); +mov( ONE, One); +printf( "1 = " ); +show( One ); +add( One, One, Two ); +printf( "1+1 = " ); +show( Two ); +add( Two, One, Three ); +add( Three, One, Four ); +add( Four, One, Five ); +add( Five, One, Six ); +add( Four, Four, Eight ); +mul( Three, Three, Nine ); +add( Nine, One, Ten ); +mul( Nine, Three, TwentySeven ); +mul( Four, Eight, ThirtyTwo ); +mul( Four, Five, t ); +mul( t, Three, t ); +mul( t, Four, TwoForty ); +mov( One, MinusOne ); +neg( MinusOne ); +div( Two, One, Half ); +add( One, Half, OneAndHalf ); +ErrCnt[Failure] = 0; +ErrCnt[Serious] = 0; +ErrCnt[Defect] = 0; +ErrCnt[Flaw] = 0; +PageNo = 1; +#ifndef NOSIGNAL +signal( SIGFPE, sigfpe ); +#endif +printf("Program is now RUNNING tests on small integers:\n"); + +add( Zero, Zero, t ); +if( cmp( t, Zero ) != 0) + { + printf( "0+0 != 0\n" ); + ErrCnt[Failure] += 1; + } +sub( One, One, t ); +if( cmp( t, Zero ) != 0 ) + { + printf( "1-1 != 0\n" ); + ErrCnt[Failure] += 1; + } +if( cmp( One, Zero ) <= 0 ) + { + printf( "1 <= 0\n" ); + ErrCnt[Failure] += 1; + } +add( One, One, t ); +if( cmp( t, Two ) != 0 ) + { + printf( "1+1 != 2\n" ); + ErrCnt[Failure] += 1; + } +mov( Zero, Z ); +neg( Z ); +FLOOR( Z, t ); +if( cmp(t,Zero) != 0 ) + { + ErrCnt[Serious] += 1; + printf( "FLOOR(-0) should equal 0, is = " ); + show( t ); + } +if( cmp(Z, Zero) != 0) + { + ErrCnt[Failure] += 1; + printf("Comparison alleges that -0.0 is Non-zero!\n"); + } +else + { + div( TwoForty, One, U1 ); /* U1 = 0.001 */ + mov( One, Radix ); + TstPtUf(); + } +add( Two, One, t ); +if( cmp( t, Three ) != 0 ) + { + printf( "2+1 != 3\n" ); + ErrCnt[Failure] += 1; + } +add( Three, One, t ); +if( cmp( t, Four ) != 0 ) + { + printf( "3+1 != 4\n" ); + ErrCnt[Failure] += 1; + } +mov( Two, t ); +neg( t ); +mul( Two, t, t ); +add( Four, t, t ); +if( cmp( t, Zero ) != 0 ) + { + printf( "4+2*(-2) != 0\n" ); + ErrCnt[Failure] += 1; + } +sub( Three, Four, t ); +sub( One, t, t ); +if( cmp( t, Zero ) != 0 ) + { + printf( "4-3-1 != 0\n" ); + ErrCnt[Failure] += 1; + } + sub( One, Zero, t ); +if( cmp( t, MinusOne ) != 0 ) + { + printf( "-1 != 0-1\n" ); + ErrCnt[Failure] += 1; + } +add( One, MinusOne, t ); +if( cmp( t, Zero ) != 0 ) + { + printf( "1+(-1) != 0\n" ); + ErrCnt[Failure] += 1; + } +mov( One, t ); +FABS( t ); +add( MinusOne, t, t ); +if( cmp( t, Zero ) != 0 ) + { + printf( "-1+abs(1) != 0\n" ); + ErrCnt[Failure] += 1; + } +mul( MinusOne, MinusOne, t ); +add( MinusOne, t, t ); +if( cmp( t, Zero ) != 0 ) + { + printf( "-1+(-1)*(-1) != 0\n" ); + ErrCnt[Failure] += 1; + } +add( Half, MinusOne, t ); +add( Half, t, t ); +if( cmp( t, Zero ) != 0 ) + { + printf( "1/2 + (-1) + 1/2 != 0\n" ); + ErrCnt[Failure] += 1; + } +Milestone = 10; +mul( Three, Three, t ); +if( cmp( t, Nine ) != 0 ) + { + printf( "3*3 != 9\n" ); + ErrCnt[Failure] += 1; + } +mul( Nine, Three, t ); +if( cmp( t, TwentySeven ) != 0 ) + { + printf( "3*9 != 27\n" ); + ErrCnt[Failure] += 1; + } +add( Four, Four, t ); +if( cmp( t, Eight ) != 0 ) + { + printf( "4+4 != 8\n" ); + ErrCnt[Failure] += 1; + } +mul( Eight, Four, t ); +if( cmp( t, ThirtyTwo ) != 0 ) + { + printf( "8*4 != 32\n" ); + ErrCnt[Failure] += 1; + } +sub( TwentySeven, ThirtyTwo, t ); +sub( Four, t, t ); +sub( One, t, t ); +if( cmp( t, Zero ) != 0 ) + { + printf( "32-27-4-1 != 0\n" ); + ErrCnt[Failure] += 1; + } +add( Four, One, t ); +if( cmp( t, Five ) != 0 ) + { + printf( "4+1 != 5\n" ); + ErrCnt[Failure] += 1; + } +mul( Four, Five, t ); +mul( Three, t, t ); +mul( Four, t, t ); +if( cmp( t, TwoForty ) != 0 ) + { + printf( "4*5*3*4 != 240\n" ); + ErrCnt[Failure] += 1; + } +div( Three, TwoForty, t ); +mul( Four, Four, t2 ); +mul( Five, t2, t2 ); +sub( t2, t2, t ); +if( cmp( t, Zero ) != 0 ) + { + printf( "240/3 - 4*4*5 != 0\n" ); + ErrCnt[Failure] += 1; + } +div( Four, TwoForty, t ); +mul( Five, Three, t2 ); +mul( Four, t2, t2 ); +sub( t2, t, t ); +if( cmp( t, Zero ) != 0 ) + { + printf( "240/4 - 5*3*4 != 0\n" ); + ErrCnt[Failure] += 1; + } +div( Five, TwoForty, t ); +mul( Four, Three, t2 ); +mul( Four, t2, t2 ); +sub( t2, t, t ); +if( cmp( t, Zero ) != 0 ) + { + printf( "240/5 - 4*3*4 != 0\n" ); + ErrCnt[Failure] += 1; + } +if(ErrCnt[Failure] == 0) + { +printf("-1, 0, 1/2, 1, 2, 3, 4, 5, 9, 27, 32 & 240 are O.K.\n\n"); + } +printf("Searching for Radix and Precision.\n"); +mov( One, W ); +do + { + add( W, W, W ); + add( W, One, Y ); + sub( W, Y, Z ); + sub( One, Z, Y ); + mov( Y, t ); + FABS(t); + add( MinusOne, t, t ); + k = cmp( t, Zero ); + } +while( k < 0 ); +/*.. now W is just big enough that |((W+1)-W)-1| >= 1 ...*/ +mov( Zero, Precision ); +mov( One, Y ); +do + { + add( W, Y, Radix ); + add( Y, Y, Y ); + sub( W, Radix, Radix ); + k = cmp( Radix, Zero ); + } +while( k == 0); + +if( cmp(Radix, Two) < 0 ) + mov( One, Radix ); +printf("Radix = " ); +show( Radix ); +if( cmp(Radix, One) != 0) + { + mov( One, W ); + do + { + add( One, Precision, Precision ); + mul( W, Radix, W ); + add( W, One, Y ); + sub( W, Y, t ); + k = cmp( t, One ); + } + while( k == 0 ); + } +/* now W == Radix^Precision is barely too big to satisfy (W+1)-W == 1 */ +div( W, One, U1 ); +mul( Radix, U1, U2 ); +printf( "Closest relative separation found is U 1 = " ); +show( U1 ); +printf( "Recalculating radix and precision." ); + +/*save old values*/ +mov( Radix, E0 ); +mov( U1, E1 ); +mov( U2, E9 ); +mov( Precision, E3 ); + +div( Three, Four, X ); +sub( One, X, Third ); +sub( Third, Half, F6 ); +add( F6, F6, X ); +sub( Third, X, X ); +FABS( X ); +if( cmp(X, U2) < 0 ) + mov( U2, X ); + +/*... now X = (unknown no.) ulps of 1+...*/ +do + { + mov( X, U2 ); +/* Y = Half * U2 + ThirtyTwo * U2 * U2; */ + mul( ThirtyTwo, U2, t ); + mul( t, U2, t ); + mul( Half, U2, Y ); + add( t, Y, Y ); + add( One, Y, Y ); + sub( One, Y, X ); + k = cmp( U2, X ); + k2 = cmp( X, Zero ); + } +while ( ! ((k <= 0) || (k2 <= 0))); + +/*... now U2 == 1 ulp of 1 + ... */ +div( Three, Two, X ); +sub( Half, X, F6 ); +add( F6, F6, Third ); +sub( Half, Third, X ); +add( F6, X, X ); +FABS( X ); +if( cmp(X, U1) < 0 ) + mov( U1, X ); + +/*... now X == (unknown no.) ulps of 1 -... */ +do + { + mov( X, U1 ); + /* Y = Half * U1 + ThirtyTwo * U1 * U1;*/ + mul( ThirtyTwo, U1, t ); + mul( U1, t, t ); + mul( Half, U1, Y ); + add( t, Y, Y ); + sub( Y, Half, Y ); + add( Half, Y, X ); + sub( X, Half, Y ); + add( Half, Y, X ); + k = cmp( U1, X ); + k2 = cmp( X, Zero ); + } while ( ! ((k <= 0) || (k2 <= 0))); +/*... now U1 == 1 ulp of 1 - ... */ +if( cmp( U1, E1 ) == 0 ) + printf("confirms closest relative separation U1 .\n"); +else + { + printf("gets better closest relative separation U1 = " ); + show( U1 ); + } +div( U1, One, W ); +sub( U1, Half, F9 ); +add( F9, Half, F9 ); +div( U1, U2, t ); +div( TwoForty, One, t2 ); +add( t2, t, t ); +FLOOR( t, Radix ); +if( cmp(Radix, E0) == 0 ) + printf("Radix confirmed.\n"); +else + { + printf("MYSTERY: recalculated Radix = " ); + show( Radix ); + mov( E0, Radix ); + } +add( Eight, Eight, t ); +if( cmp( Radix, t ) > 0 ) + { + printf( "Radix is too big: roundoff problems\n" ); + ErrCnt[Defect] += 1; + } +k = 1; +if( cmp( Radix, Two ) == 0 ) + k = 0; +if( cmp( Radix, Ten ) == 0 ) + k = 0; +if( cmp( Radix, One ) == 0 ) + k = 0; +if( k != 0 ) + { + printf( "Radix is not as good as 2 or 10\n" ); + ErrCnt[Flaw] += 1; + } +/*=============================================*/ +Milestone = 20; +/*=============================================*/ +sub( Half, F9, t ); +if( cmp( t, Half ) >= 0 ) + { + printf( "(1-U1)-1/2 < 1/2 is FALSE, prog. fails?\n" ); + ErrCnt[Failure] += 1; + } +mov( F9, X ); +I = 1; +sub( Half, X, Y ); +sub( Half, Y, Z ); +if( (cmp( X, One ) == 0) && (cmp( Z, Zero) != 0) ) + { + printf( "Comparison is fuzzy ,X=1 but X-1/2-1/2 != 0\n" ); + ErrCnt[Failure] += 1; + } +add( One, U2, X ); +I = 0; +/*=============================================*/ +Milestone = 25; +/*=============================================*/ +/*... BMinusU2 = nextafter(Radix, 0) */ + +sub( One, Radix, BMinusU2 ); +sub( U2, BMinusU2, t ); +add( One, t, BMinusU2 ); +/* Purify Integers */ +if( cmp(Radix,One) != 0 ) + { +/*X = - TwoForty * LOG(U1) / LOG(Radix);*/ + LOG( U1, X ); + LOG( Radix, t ); + div( t, X, X ); + mul( TwoForty, X, X ); + neg( X ); + + add( Half, X, Y ); + FLOOR( Y, Y ); + sub( Y, X, t ); + FABS( t ); + mul( Four, t, t ); + if( cmp( t, One ) < 0 ) + mov( Y, X ); + div( TwoForty, X, Precision ); + add( Half, Precision, Y ); + FLOOR( Y, Y ); + sub( Y, Precision, t ); + FABS( t ); + mul( TwoForty, t, t ); + if( cmp( t, Half ) < 0 ) + mov( Y, Precision ); + } +FLOOR( Precision, t ); +if( (cmp( Precision, t ) != 0) || (cmp( Radix, One ) == 0) ) + { + printf("Precision cannot be characterized by an Integer number\n"); + printf("of significant digits but, by itself, this is a minor flaw.\n"); + } +if( cmp(Radix, One) == 0 ) + printf("logarithmic encoding has precision characterized solely by U1.\n"); +else + { + printf("The number of significant digits of the Radix is " ); + show( Precision ); + } +mul( U2, Nine, t ); +mul( Nine, t, t ); +mul( TwoForty, t, t ); +if( cmp( t, One ) >= 0 ) + { + printf( "Precision worse than 5 decimal figures\n" ); + ErrCnt[Serious] += 1; + } +/*=============================================*/ +Milestone = 30; +/*=============================================*/ +/* Test for extra-precise subepressions has been deleted. */ +Milestone = 35; +/*=============================================*/ +if( cmp(Radix,Two) >= 0 ) + { + mul( Radix, Radix, t ); + div( t, W, X ); + add( X, One, Y ); + sub( X, Y, Z ); + add( Z, U2, T ); + sub( Z, T, X ); + if( cmp( X, U2 ) != 0 ) + { + printf( "Subtraction is not normalized X=Y,X+Z != Y+Z!\n" ); + ErrCnt[Failure] += 1; + } + if( cmp(X,U2) == 0 ) + printf("Subtraction appears to be normalized, as it should be."); + } + +printf("\nChecking for guard digit in *, /, and -.\n"); +mul( F9, One, Y ); +mul( One, F9, Z ); +sub( Half, F9, X ); +sub( Half, Y, Y ); +sub( X, Y, Y ); +sub( Half, Z, Z ); +sub( X, Z, Z ); +add( One, U2, X ); +mul( X, Radix, T ); +mul( Radix, X, R ); +sub( Radix, T, X ); +mul( Radix, U2, t ); +sub( t, X, X ); +sub( Radix, R, T ); +mul( Radix, U2, t ); +sub( t, T, T ); +sub( One, Radix, t ); +mul( t, X, X ); +sub( One, Radix, t ); +mul( t, T, T ); + +k = cmp(X,Zero); +k |= cmp(Y,Zero); +k |= cmp(Z,Zero); +k |= cmp(T,Zero); +if( k == 0 ) + GMult = Yes; +else + { + GMult = No; + ErrCnt[Serious] += 1; + printf( "* lacks a Guard Digit, so 1*X != X\n" ); + } +mul( Radix, U2, Z ); +add( One, Z, X ); +add( X, Z, Y ); +mul( X, X, t ); +sub( t, Y, Y ); +FABS( Y ); +sub( U2, Y, Y ); +sub( U2, One, X ); +sub( U2, X, Z ); +mul( X, X, t ); +sub( t, Z, Z ); +FABS( Z ); +sub( U1, Z, Z ); +if( (cmp(Y,Zero) > 0) || (cmp(Z,Zero) > 0) ) + { + ErrCnt[Failure] += 1; + printf( "* gets too many final digits wrong.\n" ); + } +sub( U2, One, Y ); +add( One, U2, X ); +div( Y, One, Z ); +sub( X, Z, Y ); +div( Three, One, X ); +div( Nine, Three, Z ); +sub( Z, X, X ); +div( TwentySeven, Nine, T ); +sub( T, Z, Z ); +k = cmp( X, Zero ); +k |= cmp( Y, Zero ); +k |= cmp( Z, Zero ); +if( k ) + { + ErrCnt[Defect] += 1; +printf( "Division lacks a Guard Digit, so error can exceed 1 ulp\n" ); +printf( "or 1/3 and 3/9 and 9/27 may disagree\n" ); + } +div( One, F9, Y ); +sub( Half, F9, X ); +sub( Half, Y, Y ); +sub( X, Y, Y ); +add( One, U2, X ); +div( One, X, T ); +sub( X, T, X ); +k = cmp( X, Zero ); +k |= cmp( Y, Zero ); +k |= cmp( Z, Zero ); +if( k == 0 ) + GDiv = Yes; +else + { + GDiv = No; + ErrCnt[Serious] += 1; + printf( "Division lacks a Guard Digit, so X/1 != X\n" ); + } +add( One, U2, X ); +div( X, One, X ); +sub( Half, X, Y ); +sub( Half, Y, Y ); +if( cmp(Y,Zero) >= 0 ) + { + ErrCnt[Serious] += 1; + printf( "Computed value of 1/1.000..1 >= 1\n" ); + } +sub( U2, One, X ); +mul( Radix, U2, Y ); +add( One, Y, Y ); +mul( X, Radix, Z ); +mul( Y, Radix, T ); +div( Radix, Z, R ); +div( Radix, T, StickyBit ); +sub( X, R, X ); +sub( Y, StickyBit, Y ); +k = cmp( X, Zero ); +k |= cmp( Y, Zero ); +if( k ) + { + ErrCnt[Failure] += 1; + printf( "* and/or / gets too many last digits wrong\n" ); + } +sub( U1, One, Y ); +sub( F9, One, X ); +sub( Y, One, Y ); +sub( U2, Radix, T ); +sub( BMinusU2, Radix, Z ); +sub( T, Radix, T ); +k = cmp( X, U1 ); +k |= cmp( Y, U1 ); +k |= cmp( Z, U2 ); +k |= cmp( T, U2 ); +if( k == 0 ) + GAddSub = Yes; +else + { + GAddSub = No; + ErrCnt[Serious] += 1; + printf( "- lacks Guard Digit, so cancellation is obscured\n" ); + } +sub( One, F9, t ); +if( (cmp(F9,One) != 0) && (cmp(t,Zero) >= 0) ) + { + ErrCnt[Serious] += 1; + printf("comparison alleges (1-U1) < 1 although\n"); + printf(" subtration yields (1-U1) - 1 = 0 , thereby vitiating\n"); + printf(" such precautions against division by zero as\n"); + printf(" ... if (X == 1.0) {.....} else {.../(X-1.0)...}\n"); + } +if (GMult == Yes && GDiv == Yes && GAddSub == Yes) + printf(" *, /, and - appear to have guard digits, as they should.\n"); +/*=============================================*/ +Milestone = 40; +/*=============================================*/ +printf("Checking rounding on multiply, divide and add/subtract.\n"); +RMult = Other; +RDiv = Other; +RAddSub = Other; +div( Two, Radix, RadixD2 ); +mov( Two, A1 ); +Done = False; +do + { + mov( Radix, AInvrse ); + do + { + mov( AInvrse, X ); + div( A1, AInvrse, AInvrse ); + FLOOR( AInvrse, t ); + k = cmp( t, AInvrse ); + } + while( ! (k != 0 ) ); + k = cmp( X, One ); + k2 = cmp( A1, Three ); + Done = (k == 0) || (k2 > 0); + if(! Done) + add( Nine, One, A1 ); + } +while( ! (Done)); +if( cmp(X, One) == 0 ) + mov( Radix, A1 ); +div( A1, One, AInvrse ); +mov( A1, X ); +mov( AInvrse, Y ); +Done = False; +do + { + mul( X, Y, Z ); + sub( Half, Z, Z ); + if( cmp( Z, Half ) != 0 ) + { + ErrCnt[Failure] += 1; + printf( "X * (1/X) differs from 1\n" ); + } + k = cmp( X, Radix ); + Done = (k == 0); + mov( Radix, X ); + div( X, One, Y ); + } +while( ! (Done)); + +add( One, U2, Y2 ); +sub( U2, One, YY1 ); +sub( U2, OneAndHalf, X ); +add( OneAndHalf, U2, Y ); +sub( U2, X, Z ); +mul( Z, Y2, Z ); +mul( Y, YY1, T ); +sub( X, Z, Z ); +sub( X, T, T ); +mul( X, Y2, X ); +add( Y, U2, Y ); +mul( Y, YY1, Y ); +sub( OneAndHalf, X, X ); +sub( OneAndHalf, Y, Y ); +k = cmp( X, Zero ); +k |= cmp( Y, Zero ); +k |= cmp( Z, Zero ); +if( cmp( T, Zero ) > 0 ) + k = 1; +if( k == 0 ) + { + add( OneAndHalf, U2, X ); + mul( X, Y2, X ); + sub( U2, OneAndHalf, Y ); + sub( U2, Y, Y ); + add( OneAndHalf, U2, Z ); + add( U2, Z, Z ); + sub( U2, OneAndHalf, T ); + mul( T, YY1, T ); + add( Z, U2, t ); + sub( t, X, X ); + mul( Y, YY1, StickyBit ); + mul( Z, Y2, S ); + sub( Y, T, T ); + sub( Y, U2, Y ); + add( StickyBit, Y, Y ); +/* Z = S - (Z + U2 + U2); */ + add( Z, U2, t ); + add( t, U2, t ); + sub( t, S, Z ); + add( Y2, U2, t ); + mul( t, YY1, StickyBit ); + mul( Y2, YY1, YY1 ); + sub( Y2, StickyBit, StickyBit ); + sub( Half, YY1, YY1 ); + k = cmp( X, Zero ); + k |= cmp( Y, Zero ); + k |= cmp( Z, Zero ); + k |= cmp( T, Zero ); + k |= cmp( StickyBit, Zero ); + k |= cmp( YY1, Half ); + if( k == 0 ) + { + RMult = Rounded; + printf("Multiplication appears to round correctly.\n"); + } + else + { + add( X, U2, t ); + k = cmp( t, Zero ); + if( cmp( Y, Zero ) >= 0 ) + k |= 1; + add( Z, U2, t ); + k |= cmp( t, Zero ); + if( cmp( T, Zero ) >= 0 ) + k |= 1; + add( StickyBit, U2, t ); + k |= cmp( t, Zero ); + if( cmp(YY1, Half) >= 0 ) + k |= 1; + if( k == 0 ) + { + printf("Multiplication appears to chop.\n"); + } + else + { + printf("* is neither chopped nor correctly rounded.\n"); + } + if( (RMult == Rounded) && (GMult == No) ) + printf("Multiplication has inconsistent result"); + } + } +else + printf("* is neither chopped nor correctly rounded.\n"); + +/*=============================================*/ +Milestone = 45; +/*=============================================*/ +add( One, U2, Y2 ); +sub( U2, One, YY1 ); +add( OneAndHalf, U2, Z ); +add( Z, U2, Z ); +div( Y2, Z, X ); +sub( U2, OneAndHalf, T ); +sub( U2, T, T ); +sub( U2, T, Y ); +div( YY1, Y, Y ); +add( Z, U2, Z ); +div( Y2, Z, Z ); +sub( OneAndHalf, X, X ); +sub( T, Y, Y ); +div( YY1, T, T ); +add( OneAndHalf, U2, t ); +sub( t, Z, Z ); +sub( OneAndHalf, U2, t ); +add( t, T, T ); +k = 0; +if( cmp( X, Zero ) > 0 ) + k = 1; +if( cmp( Y, Zero ) > 0 ) + k = 1; +if( cmp( Z, Zero ) > 0 ) + k = 1; +if( cmp( T, Zero ) > 0 ) + k = 1; +if( k == 0 ) + { + div( Y2, OneAndHalf, X ); + sub( U2, OneAndHalf, Y ); + add( U2, OneAndHalf, Z ); + sub( Y, X, X ); + div( YY1, OneAndHalf, T ); + div( YY1, Y, Y ); + add( Z, U2, t ); + sub( t, T, T ); + sub( Z, Y, Y ); + div( Y2, Z, Z ); + add( Y2, U2, YY1 ); + div( Y2, YY1, YY1 ); + sub( OneAndHalf, Z, Z ); + sub( Y2, YY1, Y2 ); + sub( U1, F9, YY1 ); + div( F9, YY1, YY1 ); + k = cmp( X, Zero ); + k |= cmp( Y, Zero ); + k |= cmp( Z, Zero ); + k |= cmp( T, Zero ); + k |= cmp( Y2, Zero ); + sub( Half, YY1, t ); + sub( Half, F9, t2 ); + k |= cmp( t, t2 ); + if( k == 0 ) + { + RDiv = Rounded; + printf("Division appears to round correctly.\n"); + if(GDiv == No) + printf("Division test inconsistent\n"); + } + else + { + k = 0; + if( cmp( X, Zero ) >= 0 ) + k = 1; + if( cmp( Y, Zero ) >= 0 ) + k = 1; + if( cmp( Z, Zero ) >= 0 ) + k = 1; + if( cmp( T, Zero ) >= 0 ) + k = 1; + if( cmp( Y, Zero ) >= 0 ) + k = 1; + sub( Half, YY1, t ); + sub( Half, F9, t2 ); + if( cmp( t, t2 ) >= 0 ) + k = 1; + if( k == 0 ) + { + RDiv = Chopped; + printf("Division appears to chop.\n"); + } + } + } +if(RDiv == Other) + printf("/ is neither chopped nor correctly rounded.\n"); +div( Radix, One, BInvrse ); +mul( BInvrse, Radix, t ); +sub( Half, t, t ); +if( cmp( t, Half ) != 0 ) + { + ErrCnt[Failure] += 1; + printf( "Radix * ( 1 / Radix ) differs from 1\n" ); + } + +Milestone = 50; +/*=============================================*/ +add( F9, U1, t ); +sub( Half, t, t ); +k = cmp( t, Half ); +add( BMinusU2, U2, t ); +sub( One, t, t ); +sub( One, Radix, t2 ); +k |= cmp( t, t2 ); +if( k != 0 ) + { + ErrCnt[Failure] += 1; + printf( "Incomplete carry-propagation in Addition\n" ); + } +mul( U1, U1, X ); +sub( X, One, X ); +sub( U2, One, Y ); +mul( U2, Y, Y ); +add( One, Y, Y ); +sub( Half, F9, Z ); +sub( Half, X, X ); +sub( Z, X, X ); +sub( One, Y, Y ); +if( (cmp(X,Zero) == 0) && (cmp(Y,Zero) == 0) ) + { + RAddSub = Chopped; + printf("Add/Subtract appears to be chopped.\n"); + } +if(GAddSub == Yes) + { + add( Half, U2, X ); + mul( X, U2, X ); + sub( U2, Half, Y ); + mul( Y, U2, Y ); + add( One, X, X ); + add( One, Y, Y ); + add( One, U2, t ); + sub( X, t, X ); + sub( Y, One, Y ); + k = cmp(X,Zero); + if( k ) + printf( "1+U2-[u2(1/2+U2)+1] != 0\n" ); + k2 = cmp(Y,Zero); + if( k2 ) + printf( "1-[U2(1/2-U2)+1] != 0\n" ); + k |= k2; + if( k == 0 ) + { + add( Half, U2, X ); + mul( X, U1, X ); + sub( U2, Half, Y ); + mul( Y, U1, Y ); + sub( X, One, X ); + sub( Y, One, Y ); + sub( X, F9, X ); + sub( Y, One, Y ); + k = cmp(X,Zero); + if( k ) + printf( "F9-[1-U1(1/2+U2)] != 0\n" ); + k2 = cmp(Y,Zero); + if( k2 ) + printf( "1-[1-U1(1/2-U2)] != 0\n" ); + k |= k2; + if( k == 0 ) + { + RAddSub = Rounded; + printf("Addition/Subtraction appears to round correctly.\n"); + if(GAddSub == No) + printf( "Add/Subtract test inconsistent\n"); + } + else + { + printf("Addition/Subtraction neither rounds nor chops.\n"); + } + } + else + printf("Addition/Subtraction neither rounds nor chops.\n"); + } +else + printf("Addition/Subtraction neither rounds nor chops.\n"); + +mov( One, S ); +add( One, Half, X ); +mul( Half, X, X ); +add( One, X, X ); +add( One, U2, Y ); +mul( Y, Half, Y ); +sub( Y, X, Z ); +sub( X, Y, T ); +add( Z, T, StickyBit ); +if( cmp(StickyBit, Zero) != 0 ) + { + mov( Zero, S ); + ErrCnt[Flaw] += 1; + printf( "(X - Y) + (Y - X) is non zero!\n" ); + } +mov( Zero, StickyBit ); +FLOOR( RadixD2, t ); +k2 = cmp( t, RadixD2 ); +k = 1; +if( (GMult == Yes) && (GDiv == Yes) && (GAddSub == Yes) + && (RMult == Rounded) && (RDiv == Rounded) + && (RAddSub == Rounded) && (k2 == 0) ) + { + printf("Checking for sticky bit.\n"); + k = 0; + add( Half, U1, X ); + mul( X, U2, X ); + mul( Half, U2, Y ); + add( One, Y, Z ); + add( One, X, T ); + sub( One, Z, t ); + sub( One, T, t2 ); + if( cmp(t,Zero) > 0 ) + { + k = 1; + printf( "[1+(1/2)U2]-1 > 0\n" ); + } + if( cmp(t2,U2) < 0 ) + { + k = 1; + printf( "[1+U2(1/2+U1)]-1 < U2\n" ); + } + add( T, Y, Z ); + sub( X, Z, Y ); + sub( T, Z, t ); + sub( T, Y, t2 ); + if( cmp(t,U2) < 0 ) + { + k = 1; + printf( "[[1+U2(1/2+U1)]+(1/2)U2]-[1+U2(1/2+U1)] < U2\n" ); + } + if( cmp(t2,Zero) != 0 ) + { + k = 1; + printf( "(1/2)U2-[1+U2(1/2+U1)] != 0\n" ); + } + add( Half, U1, X ); + mul( X, U1, X ); + mul( Half, U1, Y ); + sub( Y, One, Z ); + sub( X, One, T ); + sub( One, Z, t ); + sub( F9, T, t2 ); + if( cmp(t,Zero) != 0 ) + { + k = 1; + printf( "(1-(1/2)U1)-1 != 0\n" ); + } + if( cmp(t2,Zero) != 0 ) + { + k = 1; + printf( "[1-U1(1/2+U1)]-F9 != 0\n" ); + } + sub( U1, Half, Z ); + mul( Z, U1, Z ); + sub( Z, F9, T ); + sub( Y, F9, Q ); + sub( F9, T, t ); + if( cmp( t, Zero ) != 0 ) + { + k = 1; + printf( "[F9-U1(1/2-U1)]-F9 != 0\n" ); + } + sub( U1, F9, t ); + sub( Q, t, t ); + if( cmp( t, Zero ) != 0 ) + { + k = 1; + printf( "(F9-U1)-(F9-(1/2)U1) != 0\n" ); + } + add( One, U2, Z ); + mul( Z, OneAndHalf, Z ); + add( OneAndHalf, U2, T ); + sub( Z, T, T ); + add( U2, T, T ); + div( Radix, Half, X ); + add( One, X, X ); + mul( Radix, U2, Y ); + add( One, Y, Y ); + mul( X, Y, Z ); + if( cmp( T, Zero ) != 0 ) + { + k = 1; + printf( "(3/2+U2)-3/2(1+U2)+U2 != 0\n" ); + } + mul( Radix, U2, t ); + add( X, t, t ); + sub( Z, t, t ); + if( cmp( t, Zero ) != 0 ) + { + k = 1; + printf( "(1+1/2Radix)+Radix*U2-[1+1/(2Radix)][1+Radix*U2] != 0\n" ); + } + if( cmp(Radix, Two) != 0 ) + { + add( Two, U2, X ); + div( Two, X, Y ); + sub( One, Y, t ); + if( cmp( t, Zero) != 0 ) + k = 1; + } + } +if( k == 0 ) + { + printf("Sticky bit apparently used correctly.\n"); + mov( One, StickyBit ); + } +else + { + printf("Sticky bit used incorrectly or not at all.\n"); + } + +if( GMult == No || GDiv == No || GAddSub == No || + RMult == Other || RDiv == Other || RAddSub == Other) + { + ErrCnt[Flaw] += 1; + printf("lack(s) of guard digits or failure(s) to correctly round or chop\n"); +printf( "(noted above) count as one flaw in the final tally below\n" ); + } +/*=============================================*/ +Milestone = 60; +/*=============================================*/ +printf("\n"); +printf("Does Multiplication commute? "); +printf("Testing on %d random pairs.\n", NoTrials); +SQRT( Three, Random9 ); +mov( Third, Random1 ); +I = 1; +do + { + Random(); + mov( Random1, X ); + Random(); + mov( Random1, Y ); + mul( Y, X, Z9 ); + mul( X, Y, Z ); + sub( Z9, Z, Z9 ); + I = I + 1; + } +while ( ! ((I > NoTrials) || (cmp(Z9,Zero) != 0))); +if(I == NoTrials) + { + div( Three, Half, t ); + add( One, t, Random1 ); + add( U2, U1, t ); + add( t, One, Random2 ); + mul( Random1, Random2, Z ); + mul( Random2, Random1, Y ); +/* Z9 = (One + Half / Three) * ((U2 + U1) + One) - (One + Half / + * Three) * ((U2 + U1) + One); + */ + div( Three, Half, t2 ); + add( One, t2, t2 ); + add( U2, U1, t ); + add( t, One, t ); + mul( t2, t, Z9 ); + mul( t2, t, t ); + sub( t, Z9, Z9 ); + } +if(! ((I == NoTrials) || (cmp(Z9,Zero) == 0))) + { + ErrCnt[Defect] += 1; + printf( "X * Y == Y * X trial fails.\n"); + } +else + { + printf(" No failures found in %d integer pairs.\n", NoTrials); + } +/*=============================================*/ +Milestone = 70; +/*=============================================*/ +sqtest(); +Milestone = 90; +pow1test(); + +Milestone = 110; + +printf("Seeking Underflow thresholds UfThold and E0.\n"); +mov( U1, D ); +FLOOR( Precision, t ); +if( cmp(Precision, t) != 0 ) + { + mov( BInvrse, D ); + mov( Precision, X ); + do + { + mul( D, BInvrse, D ); + sub( One, X, X ); + } + while( cmp(X, Zero) > 0 ); + } +mov( One, Y ); +mov( D, Z ); +/* ... D is power of 1/Radix < 1. */ +sigsave = sigfpe; +if( setjmp(ovfl_buf) ) + goto under0; +do + { + mov( Y, C ); + mov( Z, Y ); + mul( Y, Y, Z ); + add( Z, Z, t ); + } +while( (cmp(Y,Z) > 0) && (cmp(t,Z) > 0) ); + +under0: +sigsave = 0; + +mov( C, Y ); +mul( Y, D, Z ); +sigsave = sigfpe; +if( setjmp(ovfl_buf) ) + goto under1; +do + { + mov( Y, C ); + mov( Z, Y ); + mul( Y, D, Z ); + add( Z, Z, t ); + } +while( (cmp(Y,Z) > 0) && (cmp(t,Z) > 0) ); + +under1: +sigsave = 0; + +if( cmp(Radix,Two) < 0 ) + mov( Two, HInvrse ); +else + mov( Radix, HInvrse ); +div( HInvrse, One, H ); +/* ... 1/HInvrse == H == Min(1/Radix, 1/2) */ +div( C, One, CInvrse ); +mov( C, E0 ); +mul( E0, H, Z ); +/* ...1/Radix^(BIG Integer) << 1 << CInvrse == 1/C */ +sigsave = sigfpe; +if( setjmp(ovfl_buf) ) + goto under2; +do + { + mov( E0, Y ); + mov( Z, E0 ); + mul( E0, H, Z ); + add( Z, Z, t ); + } +while( (cmp(E0,Z) > 0) && (cmp(t,Z) > 0) ); + +under2: +sigsave = 0; + +mov( E0, UfThold ); +mov( Zero, E1 ); +mov( Zero, Q ); +mov( U2, E9 ); +add( One, E9, S ); +mul( C, S, D ); +if( cmp(D,C) <= 0 ) + { + mul( Radix, U2, E9 ); + add( One, E9, S ); + mul( C, S, D ); + if( cmp(D, C) <= 0 ) + { + ErrCnt[Failure] += 1; + printf( "multiplication gets too many last digits wrong.\n" ); + mov( E0, Underflow ); + mov( Zero, YY1 ); + mov( Z, PseudoZero ); + } + } +else + { + mov( D, Underflow ); + mul( Underflow, H, PseudoZero ); + mov( Zero, UfThold ); + do + { + mov( Underflow, YY1 ); + mov( PseudoZero, Underflow ); + add( E1, E1, t ); + if( cmp(t, E1) <= 0) + { + mul( Underflow, HInvrse, Y2 ); + sub( Y2, YY1, E1 ); + FABS( E1 ); + mov( YY1, Q ); + if( (cmp( UfThold, Zero ) == 0) + && (cmp(YY1, Y2) != 0) ) + mov( YY1, UfThold ); + } + mul( PseudoZero, H, PseudoZero ); + add( PseudoZero, PseudoZero, t ); + } + while( (cmp(Underflow, PseudoZero) > 0) + && (cmp(t, PseudoZero) > 0) ); + } +/* Comment line 4530 .. 4560 */ +if( cmp(PseudoZero, Zero) != 0 ) + { + printf("\n"); + mov(PseudoZero, Z ); +/* ... Test PseudoZero for "phoney- zero" violates */ +/* ... PseudoZero < Underflow or PseudoZero < PseudoZero + PseudoZero + ... */ + if( cmp(PseudoZero, Zero) <= 0 ) + { + ErrCnt[Failure] += 1; + printf("Positive expressions can underflow to an\n"); + printf("allegedly negative value\n"); + printf("PseudoZero that prints out as: " ); + show( PseudoZero ); + mov( PseudoZero, X ); + neg( X ); + if( cmp(X, Zero) <= 0 ) + { + printf("But -PseudoZero, which should be\n"); + printf("positive, isn't; it prints out as " ); + show( X ); + } + } + else + { + ErrCnt[Flaw] += 1; + printf( "Underflow can stick at an allegedly positive\n"); + printf("value PseudoZero that prints out as " ); + show( PseudoZero ); + } +/* TstPtUf();*/ + } + +/*=============================================*/ +Milestone = 120; +/*=============================================*/ +mul( CInvrse, Y, t ); +mul( CInvrse, YY1, t2 ); +if( cmp(t,t2) > 0 ) + { + mul( H, S, S ); + mov( Underflow, E0 ); + } +if(! ((cmp(E1,Zero) == 0) || (cmp(E1,E0) == 0)) ) + { + ErrCnt[Defect] += 1; + if( cmp(E1,E0) < 0 ) + { + printf("Products underflow at a higher"); + printf(" threshold than differences.\n"); + if( cmp(PseudoZero,Zero) == 0 ) + mov( E1, E0 ); + } + else + { + printf("Difference underflows at a higher"); + printf(" threshold than products.\n"); + } + } +printf("Smallest strictly positive number found is E0 = " ); +show( E0 ); +mov( E0, Z ); +TstPtUf(); +mov( E0, Underflow ); +if(N == 1) + mov( Y, Underflow ); +I = 4; +if( cmp(E1,Zero) == 0 ) + I = 3; +if( cmp( UfThold,Zero) == 0 ) + I = I - 2; +UfNGrad = True; +switch(I) + { + case 1: + mov( Underflow, UfThold ); + mul( CInvrse, Q, t ); + mul( CInvrse, Y, t2 ); + mul( t2, S, t2 ); + if( cmp( t, t2 ) != 0 ) + { + mov( Y, UfThold ); + ErrCnt[Failure] += 1; + printf( "Either accuracy deteriorates as numbers\n"); + printf("approach a threshold = " ); + show( UfThold ); + printf(" coming down from " ); + show( C ); + printf(" or else multiplication gets too many last digits wrong.\n"); + } + break; + + case 2: + ErrCnt[Failure] += 1; + printf( "Underflow confuses Comparison which alleges that\n"); + printf("Q == Y while denying that |Q - Y| == 0; these values\n"); + printf("print out as Q = " ); + show( Q ); + printf( ", Y = " ); + show( Y ); + sub( Y2, Q, t ); + FABS(t); + printf ("|Q - Y| = " ); + show( t ); + mov( Q, UfThold ); + break; + + case 3: + mov( X, X ); + break; + + case 4: + div( E9, E1, t ); + sub( t, UfThold, t ); + FABS(t); + if( (cmp(Q,UfThold) == 0) && (cmp(E1,E0) == 0) + && (cmp(t,E1) <= 0) ) + { + UfNGrad = False; + printf("Underflow is gradual; it incurs Absolute Error =\n"); + printf("(roundoff in UfThold) < E0.\n"); + mul( E0, CInvrse, Y ); + add( OneAndHalf, U2, t ); + mul( Y, t, Y ); + add( One, U2, X ); + mul( CInvrse, X, X ); + div( X, Y, t ); + IEEE = (cmp(t,E0) == 0); + if( IEEE == 0 ) + { + printf( "((CInvrse E0) (1.5+U2)) / (CInvrse (1+U2)) != E0\n" ); + printf( "CInvrse = " ); + show( CInvrse ); + printf( "E0 = " ); + show( E0 ); + printf( "U2 = " ); + show( U2 ); + printf( "X = " ); + show(X); + printf( "Y = " ); + show(Y); + printf( "Y/X = " ); + show(t); + } + } + } +if(UfNGrad) + { + printf("\n"); + div( UfThold, Underflow, R ); + SQRT( R, R ); + if( cmp(R,H) <= 0) + { + mul( R, UfThold, Z ); +/* X = Z * (One + R * H * (One + H));*/ + add( One, H, X ); + mul( H, X, X ); + mul( R, X, X ); + add( One, X, X ); + mul( Z, X, X ); + } + else + { + mov( UfThold, Z ); +/*X = Z * (One + H * H * (One + H));*/ + add( One, H, X ); + mul( H, X, X ); + mul( H, X, X ); + add( One, X, X ); + mul( Z, X, X ); + } + sub( Z, X, t ); +/* if(! ((cmp(X,Z) == 0) || (cmp(t,Zero) != 0)) )*/ + if( (cmp(X,Z) != 0) && (cmp(t,Zero) == 0) ) + { +/* ErrCnt[Flaw] += 1;*/ + ErrCnt[Serious] += 1; + printf("X = " ); + show( X ); + printf( "\tis not equal to Z = " ); + show( Z ); +/* sub( Z, X, Z9 );*/ + printf("yet X - Z yields " ); + show( t ); + printf("which compares equal to " ); + show( Zero ); + printf(" Should this NOT signal Underflow, "); + printf("this is a SERIOUS DEFECT\nthat causes "); + printf("confusion when innocent statements like\n");; + printf(" if (X == Z) ... else"); + printf(" ... (f(X) - f(Z)) / (X - Z) ...\n"); + printf("encounter Division by Zero although actually\n"); + printf("X / Z = 1 + " ); + div( Z, X, t ); + sub( Half, t, t ); + sub( Half, t, t ); + show(t); + } + } +printf("The Underflow threshold is " ); +show( UfThold ); +printf( "below which calculation may suffer larger Relative error than" ); +printf( " merely roundoff.\n"); +mul( U1, U1, Y2 ); +mul( Y2, Y2, Y ); +mul( Y, U1, Y2 ); +if( cmp( Y2,UfThold) <= 0 ) + { + if( cmp(Y,E0) > 0 ) + { + ErrCnt[Defect] += 1; + I = 5; + } + else + { + ErrCnt[Serious] += 1; + I = 4; + } + printf("Range is too narrow; U1^%d Underflows.\n", I); + } +Milestone = 130; + +/*Y = - FLOOR(Half - TwoForty * LOG(UfThold) / LOG(HInvrse)) / TwoForty;*/ +LOG( UfThold, Y ); +LOG( HInvrse, t ); +div( t, Y, Y ); +mul( TwoForty, Y, Y ); +sub( Y, Half, Y ); +FLOOR( Y, Y ); +div( TwoForty, Y, Y ); +neg(Y); +sub( One, Y, Y2 ); /* ***** changed from Y2 = Y + Y */ +printf("Since underflow occurs below the threshold\n"); +printf("UfThold = " ); +show( HInvrse ); +printf( "\tto the power " ); +show( Y ); +printf( "only underflow should afflict the expression " ); +show( HInvrse ); +printf( "\tto the power " ); +show( Y2 ); +POW( HInvrse, Y2, V9 ); +printf("Actually calculating yields: " ); +show( V9 ); +add( Radix, Radix, t ); +add( t, E9, t ); +mul( t, UfThold, t ); +if( (cmp(V9,Zero) < 0) || (cmp(V9,t) > 0) ) + { + ErrCnt[Serious] += 1; + printf( "this is not between 0 and underflow\n"); + printf(" threshold = " ); + show( UfThold ); + } +else + { + add( One, E9, t ); + mul( UfThold, t, t ); + if( cmp(V9,t) <= 0 ) + printf("This computed value is O.K.\n"); + else + { + ErrCnt[Defect] += 1; + printf( "this is not between 0 and underflow\n"); + printf(" threshold = " ); + show( UfThold ); + } + } + +Milestone = 140; + +pow2test(); + +/*=============================================*/ +Milestone = 160; +/*=============================================*/ +Pause(); +printf("Searching for Overflow threshold:\n"); +printf("This may generate an error.\n"); +sigsave = sigfpe; +I = 0; +mov( CInvrse, Y ); /* a large power of 2 */ +neg(Y); +mul( HInvrse, Y, V9 ); /* HInvrse = 2 */ +if (setjmp(ovfl_buf)) + goto overflow; +do + { + mov( Y, V ); + mov( V9, Y ); + mul( HInvrse, Y, V9 ); + } +while( cmp(V9,Y) < 0 ); /* V9 = 2 * Y */ +I = 1; + +overflow: + +show( HInvrse ); +printf( "\ttimes " ); +show( Y ); +printf( "\tequals " ); +show( V9 ); + +mov( V9, Z ); +printf("Can `Z = -Y' overflow?\n"); +printf("Trying it on Y = " ); +show(Y); +mov( Y, V9 ); +neg( V9 ); +mov( V9, V0 ); +sub( Y, V, t ); +add( V, V0, t2 ); +if( cmp(t,t2) == 0 ) + printf("Seems O.K.\n"); +else + { + printf("finds a Flaw, -(-Y) differs from Y.\n"); + printf( "V-Y=t:" ); + show(V); + show(Y); + show(t); + printf( "V+V0=t2:" ); + show(V); + show(V0); + show(t2); + ErrCnt[Flaw] += 1; + } +if( (cmp(Z, Y) != 0) && (I != 0) ) + { + ErrCnt[Serious] += 1; + printf("overflow past " ); + show( Y ); + printf( "\tshrinks to " ); + show( Z ); + printf( "= Y * " ); + show( HInvrse ); + } +/*Y = V * (HInvrse * U2 - HInvrse);*/ +mul( HInvrse, U2, Y ); +sub( HInvrse, Y, Y ); +mul( V, Y, Y ); +/*Z = Y + ((One - HInvrse) * U2) * V;*/ +sub( HInvrse, One, Z ); +mul( Z, U2, Z ); +mul( Z, V, Z ); +add( Y, Z, Z ); +if( cmp(Z,V0) < 0 ) + mov( Z, Y ); +if( cmp(Y,V0) < 0) + mov( Y, V ); +sub( V, V0, t ); +if( cmp(t,V0) < 0 ) + mov( V0, V ); +printf("Overflow threshold is V = " ); +show( V ); +if(I) + { + printf("Overflow saturates at V0 = " ); + show( V0 ); + } +else +printf("There is no saturation value because the system traps on overflow.\n"); + +mul( V, One, V9 ); +printf("No Overflow should be signaled for V * 1 = " ); +show( V9 ); +div( One, V, V9 ); + printf(" nor for V / 1 = " ); + show( V9 ); + printf("Any overflow signal separating this * from the one\n"); + printf("above is a DEFECT.\n"); +/*=============================================*/ +Milestone = 170; +/*=============================================*/ +mov( V, t ); +neg( t ); +k = 0; +if( cmp(t,V) >= 0 ) + k = 1; +mov( V0, t ); +neg( t ); +if( cmp(t,V0) >= 0 ) + k = 1; +mov( UfThold, t ); +neg(t); +if( cmp(t,V) >= 0 ) + k = 1; +if( cmp(UfThold,V) >= 0 ) + k = 1; +if( k != 0 ) + { + ErrCnt[Failure] += 1; + printf( "Comparisons involving +-"); + show( V ); + show( V0 ); + show( UfThold ); + printf("are confused by Overflow." ); + } +/*=============================================*/ +Milestone = 175; +/*=============================================*/ +printf("\n"); +for(Indx = 1; Indx <= 3; ++Indx) { + switch(Indx) + { + case 1: mov(UfThold, Z); break; + case 2: mov( E0, Z); break; + case 3: mov(PseudoZero, Z); break; + } +if( cmp(Z, Zero) != 0 ) + { + SQRT( Z, V9 ); + mul( V9, V9, Y ); + mul( Radix, E9, t ); + sub( t, One, t ); + div( t, Y, t ); + add( One, Radix, t2 ); + add( t2, E9, t2 ); + mul( t2, Z, t2 ); + if( (cmp(t,Z) < 0) || (cmp(Y,t2) > 0) ) + { + if( cmp(V9,U1) > 0 ) + ErrCnt[Serious] += 1; + else + ErrCnt[Defect] += 1; + printf("Comparison alleges that what prints as Z = " ); + show( Z ); + printf(" is too far from sqrt(Z) ^ 2 = " ); + show( Y ); + } + } +} + +Milestone = 180; + +for(Indx = 1; Indx <= 2; ++Indx) + { + if(Indx == 1) + mov( V, Z ); + else + mov( V0, Z ); + SQRT( Z, V9 ); + mul( Radix, E9, X ); + sub( X, One, X ); + mul( X, V9, X ); + mul( V9, X, V9 ); + mul( Two, Radix, t ); + mul( t, E9, t ); + sub( t, One, t ); + mul( t, Z, t ); + if( (cmp(V9,t) < 0) || (cmp(V9,Z) > 0) ) + { + mov( V9, Y ); + if( cmp(X,W) < 0 ) + ErrCnt[Serious] += 1; + else + ErrCnt[Defect] += 1; + printf("Comparison alleges that Z = " ); + show( Z ); + printf(" is too far from sqrt(Z) ^ 2 :" ); + show( Y ); + } + } + +Milestone = 190; + +Pause(); +mul( UfThold, V, X ); +mul( Radix, Radix, Y ); +mul( X, Y, t ); +if( (cmp(t,One) < 0) || (cmp(X,Y) > 0) ) + { + mul( X, Y, t ); + div( U1, Y, t2 ); + if( (cmp(t,U1) < 0) || (cmp(X,t2) > 0) ) + { + ErrCnt[Defect] += 1; + printf( "Badly " ); + } + else + { + ErrCnt[Flaw] += 1; + } + printf(" unbalanced range; UfThold * V = " ); + show( X ); + printf( "\tis too far from 1.\n"); + } +Milestone = 200; + +for(Indx = 1; Indx <= 5; ++Indx) + { + mov( F9, X ); + switch(Indx) + { + case 2: add( One, U2, X ); break; + case 3: mov( V, X ); break; + case 4: mov(UfThold,X); break; + case 5: mov(Radix,X); + } + mov( X, Y ); + + sigsave = sigfpe; + if (setjmp(ovfl_buf)) + { + printf(" X / X traps when X = " ); + show( X ); + } + else + { +/*V9 = (Y / X - Half) - Half;*/ + div( X, Y, t ); + sub( Half, t, t ); + sub( Half, t, V9 ); + if( cmp(V9,Zero) == 0 ) + continue; + mov( U1, t ); + neg(t); + if( (cmp(V9,t) == 0) && (Indx < 5) ) + { + ErrCnt[Flaw] += 1; + } + else + { + ErrCnt[Serious] += 1; + } + printf(" X / X differs from 1 when X = " ); + show( X ); + printf(" instead, X / X - 1/2 - 1/2 = " ); + show( V9 ); + } + } + + Pause(); + printf("\n"); + { + static char *msg[] = { + "FAILUREs encountered =", + "SERIOUS DEFECTs discovered =", + "DEFECTs discovered =", + "FLAWs discovered =" }; + int i; + for(i = 0; i < 4; i++) if (ErrCnt[i]) + printf("The number of %-29s %d.\n", + msg[i], ErrCnt[i]); + } + printf("\n"); + if ((ErrCnt[Failure] + ErrCnt[Serious] + ErrCnt[Defect] + + ErrCnt[Flaw]) > 0) { + if ((ErrCnt[Failure] + ErrCnt[Serious] + ErrCnt[ + Defect] == 0) && (ErrCnt[Flaw] > 0)) { + printf("The arithmetic diagnosed seems "); + printf("satisfactory though flawed.\n"); + } + if ((ErrCnt[Failure] + ErrCnt[Serious] == 0) + && ( ErrCnt[Defect] > 0)) { + printf("The arithmetic diagnosed may be acceptable\n"); + printf("despite inconvenient Defects.\n"); + } + if ((ErrCnt[Failure] + ErrCnt[Serious]) > 0) { + printf("The arithmetic diagnosed has "); + printf("unacceptable serious defects.\n"); + } + if (ErrCnt[Failure] > 0) { + printf("Fatal FAILURE may have spoiled this"); + printf(" program's subsequent diagnoses.\n"); + } + } + else { + printf("No failures, defects nor flaws have been discovered.\n"); + if (! ((RMult == Rounded) && (RDiv == Rounded) + && (RAddSub == Rounded) && (RSqrt == Rounded))) + printf("The arithmetic diagnosed seems satisfactory.\n"); + else { + k = 0; + if( cmp( Radix, Two ) == 0 ) + k = 1; + if( cmp( Radix, Ten ) == 0 ) + k = 1; + if( (cmp(StickyBit,One) >= 0) && (k == 1) ) + { + printf("Rounding appears to conform to "); + printf("the proposed IEEE standard P"); + k = 0; + k |= cmp( Radix, Two ); + mul( Four, Three, t ); + mul( t, Two, t ); + sub( t, Precision, t ); + sub( TwentySeven, Precision, t2 ); + sub( TwentySeven, t2, t2 ); + add( t2, One, t2 ); + mul( t2, t, t ); + if( (cmp(Radix,Two) == 0) + && (cmp(t,Zero) == 0) ) + printf("754"); + else + printf("854"); + if(IEEE) + printf(".\n"); + else + { + printf(",\nexcept for possibly Double Rounding"); + printf(" during Gradual Underflow.\n"); + } + } + printf("The arithmetic diagnosed appears to be excellent!\n"); + } + } + if (fpecount) + printf("\nA total of %d floating point exceptions were registered.\n", + fpecount); + printf("END OF TEST.\n"); + } + + +/* Random */ +/* Random computes + X = (Random1 + Random9)^5 + Random1 = X - FLOOR(X) + 0.000005 * X; + and returns the new value of Random1 +*/ + + +static int randflg = 0; +FLOAT(C5em6); + +Random() +{ + +if( randflg == 0 ) + { + mov( Six, t ); + neg(t); + POW( Ten, t, t ); + mul( Five, t, C5em6 ); + randflg = 1; + } +add( Random1, Random9, t ); +mul( t, t, t2 ); +mul( t2, t2, t2 ); +mul( t, t2, t ); +FLOOR(t, t2 ); +sub( t2, t, t2 ); +mul( t, C5em6, t ); +add( t, t2, Random1 ); +/*return(Random1);*/ +} + +/* SqXMinX */ + +SqXMinX( ErrKind ) +int ErrKind; +{ +mul( X, BInvrse, t2 ); +sub( t2, X, t ); +/*SqEr = ((SQRT(X * X) - XB) - XA) / OneUlp;*/ +mul( X, X, Sqarg ); +SQRT( Sqarg, SqEr ); +sub( t2, SqEr, SqEr ); +sub( t, SqEr, SqEr ); +div( OneUlp, SqEr, SqEr ); +if( cmp(SqEr,Zero) != 0) + { + Showsq( 0 ); + add( J, One, J ); + ErrCnt[ErrKind] += 1; + printf("sqrt of " ); + mul( X, X, t ); + show( t ); + printf( "minus " ); + show( X ); + printf( "equals " ); + mul( OneUlp, SqEr, t ); + show( t ); + printf("\tinstead of correct value 0 .\n"); + } +} + +/* NewD */ + +NewD() +{ +mul( Z1, Q, X ); +/*X = FLOOR(Half - X / Radix) * Radix + X;*/ +div( Radix, X, t ); +sub( t, Half, t ); +FLOOR( t, t ); +mul( t, Radix, t ); +add( t, X, X ); +/*Q = (Q - X * Z) / Radix + X * X * (D / Radix);*/ +mul( X, Z, t ); +sub( t, Q, t ); +div( Radix, t, t ); +div( Radix, D, t2 ); +mul( X, t2, t2 ); +mul( X, t2, t2 ); +add( t, t2, Q ); +/*Z = Z - Two * X * D;*/ +mul( Two, X, t ); +mul( t, D, t ); +sub( t, Z, Z ); + +if( cmp(Z,Zero) <= 0) + { + neg(Z); + neg(Z1); + } +mul( Radix, D, D ); +} + +/* SR3750 */ + +SR3750() +{ +sub( Radix, X, t ); +sub( Radix, Z2, t2 ); +k = 0; +if( cmp(t,t2) < 0 ) + k = 1; +sub( Z2, X, t ); +sub( Z2, W, t2 ); +if( cmp(t,t2) > 0 ) + k = 1; +/*if (! ((X - Radix < Z2 - Radix) || (X - Z2 > W - Z2))) {*/ +if( k == 0 ) + { + I = I + 1; + mul( X, D, X2 ); + mov( X2, Sqarg ); + SQRT( X2, X2 ); +/*Y2 = (X2 - Z2) - (Y - Z2);*/ + sub( Z2, X2, Y2 ); + sub( Z2, Y, t ); + sub( t, Y2, Y2 ); + sub( Half, Y, X2 ); + div( X2, X8, X2 ); + mul( Half, X2, t ); + mul( t, X2, t ); + sub( t, X2, X2 ); +/*SqEr = (Y2 + Half) + (Half - X2);*/ + add( Y2, Half, SqEr ); + sub( X2, Half, t ); + add( t, SqEr, SqEr ); + Showsq( -1 ); + sub( X2, Y2, SqEr ); + Showsq( 1 ); + } +} + +/* IsYeqX */ + +IsYeqX() +{ +if( cmp(Y,X) != 0 ) + { + if (N <= 0) + { + if( (cmp(Z,Zero) == 0) && (cmp(Q,Zero) <= 0) ) + printf("WARNING: computing\n"); + else + { + ErrCnt[Defect] += 1; + printf( "computing\n"); + } + show( Z ); + printf( "\tto the power " ); + show( Q ); + printf("\tyielded " ); + show( Y ); + printf("\twhich compared unequal to correct " ); + show( X ); + sub( X, Y, t ); + printf("\t\tthey differ by " ); + show( t ); + } + N = N + 1; /* ... count discrepancies. */ + } +} + +/* SR3980 */ + +SR3980() +{ +long li; + +do + { +/*Q = (FLOAT) I;*/ + li = I; + LTOF( &li, Q ); + POW( Z, Q, Y ); + IsYeqX(); + if(++I > M) + break; + mul( Z, X, X ); + } +while( cmp(X,W) < 0 ); +} + +/* PrintIfNPositive */ + +PrintIfNPositive() +{ +if(N > 0) + printf("Similar discrepancies have occurred %d times.\n", N); +} + + +/* TstPtUf */ + +TstPtUf() +{ +N = 0; +if( cmp(Z,Zero) != 0) + { + printf( "Z = " ); + show(Z); + printf("Since comparison denies Z = 0, evaluating "); + printf("(Z + Z) / Z should be safe.\n"); + sigsave = sigfpe; + if (setjmp(ovfl_buf)) + goto very_serious; + add( Z, Z, Q9 ); + div( Z, Q9, Q9 ); + printf("What the machine gets for (Z + Z) / Z is " ); + show( Q9 ); + sub( Two, Q9, t ); + FABS(t); + mul( Radix, U2, t2 ); + if( cmp(t,t2) < 0 ) + { + printf("This is O.K., provided Over/Underflow"); + printf(" has NOT just been signaled.\n"); + } + else + { + if( (cmp(Q9,One) < 0) || (cmp(Q9,Two) > 0) ) + { +very_serious: + N = 1; + ErrCnt [Serious] = ErrCnt [Serious] + 1; + printf("This is a VERY SERIOUS DEFECT!\n"); + } + else + { + N = 1; + ErrCnt[Defect] += 1; + printf("This is a DEFECT!\n"); + } + } + mul( Z, One, V9 ); + mov( V9, Random1 ); + mul( One, Z, V9 ); + mov( V9, Random2 ); + div( One, Z, V9 ); + if( (cmp(Z,Random1) == 0) && (cmp(Z,Random2) == 0) + && (cmp(Z,V9) == 0) ) + { + if (N > 0) + Pause(); + } + else + { + N = 1; + ErrCnt[Defect] += 1; + printf( "What prints as Z = "); + show( Z ); + printf( "\tcompares different from " ); + if( cmp(Z,Random1) != 0) + { + printf("Z * 1 = " ); + show( Random1 ); + } + if( (cmp(Z,Random2) != 0) + || (cmp(Random2,Random1) != 0) ) + { + printf("1 * Z == " ); + show( Random2 ); + } + if( cmp(Z,V9) != 0 ) + { + printf("Z / 1 = " ); + show( V9 ); + } + if( cmp(Random2,Random1) != 0 ) + { + ErrCnt[Defect] += 1; + printf( "Multiplication does not commute!\n"); + printf("\tComparison alleges that 1 * Z = " ); + show(Random2); + printf("\tdiffers from Z * 1 = " ); + show(Random1); + } + Pause(); + } + } +} + +Pause() +{ +} + +Sign( x, y ) +FSIZE *x, *y; +{ + +if( cmp( x, Zero ) < 0 ) + { + mov( One, y ); + neg( y ); + } +else + { + mov( One, y ); + } +} + +sqtest() +{ +printf("\nRunning test of square root(x).\n"); + +RSqrt = Other; +k = 0; +SQRT( Zero, t ); +k |= cmp( Zero, t ); +mov( Zero, t ); +neg(t); +SQRT( t, t2 ); +k |= cmp( t, t2 ); +SQRT( One, t ); +k |= cmp( One, t ); +if( k != 0 ) + { + ErrCnt[Failure] += 1; + printf( "Square root of 0.0, -0.0 or 1.0 wrong\n"); + } +mov( Zero, MinSqEr ); +mov( Zero, MaxSqEr ); +mov( Zero, J ); +mov( Radix, X ); +mov( U2, OneUlp ); +SqXMinX( Serious ); +mov( BInvrse, X ); +mul( BInvrse, U1, OneUlp ); +SqXMinX( Serious ); +mov( U1, X ); +mul( U1, U1, OneUlp ); +SqXMinX( Serious ); +if( cmp(J,Zero) != 0) + Pause(); +printf("Testing if sqrt(X * X) == X for %d Integers X.\n", NoTrials); +mov( Zero, J ); +mov( Two, X ); +mov( Radix, Y ); +if( cmp(Radix,One) != 0 ) + { + lngint = NoTrials; + LTOF( &lngint, t ); + FTOL( t, &lng2, X ); + if( lngint != lng2 ) + { + printf( "Integer conversion error\n" ); + exit(1); + } + do + { + mov( Y, X ); + mul( Radix, Y, Y ); + sub( X, Y, t2 ); + } + while( ! (cmp(t2,t) >= 0) ); + } +mul( X, U2, OneUlp ); +I = 1; +while(I < 10) + { + add( X, One, X ); + SqXMinX( Defect ); + if( cmp(J,Zero) > 0 ) + break; + I = I + 1; + } +printf("Test for sqrt monotonicity.\n"); +I = - 1; +mov( BMinusU2, X ); +mov( Radix, Y ); +mul( Radix, U2, Z ); +add( Radix, Z, Z ); +NotMonot = False; +Monot = False; +while( ! (NotMonot || Monot)) + { + I = I + 1; + SQRT(X, X); + SQRT(Y,Q); + SQRT(Z,Z); + if( (cmp(X,Q) > 0) || (cmp(Q,Z) > 0) ) + NotMonot = True; + else + { + add( Q, Half, Q ); + FLOOR( Q, Q ); + mul( Q, Q, t ); + if( (I > 0) || (cmp(Radix,t) == 0) ) + Monot = True; + else if (I > 0) + { + if(I > 1) + Monot = True; + else + { + mul( Y, BInvrse, Y ); + sub( U1, Y, X ); + add( Y, U1, Z ); + } + } + else + { + mov( Q, Y ); + sub( U2, Y, X ); + add( Y, U2, Z ); + } + } + } +if( Monot ) + printf("sqrt has passed a test for Monotonicity.\n"); +else + { + ErrCnt[Defect] += 1; + printf("sqrt(X) is non-monotonic for X near " ); + show(Y); + } +/*=============================================*/ +Milestone = 80; +/*=============================================*/ +add( MinSqEr, Half, MinSqEr ); +sub( Half, MaxSqEr, MaxSqEr); +/*Y = (SQRT(One + U2) - One) / U2;*/ +add( One, U2, Sqarg ); +SQRT( Sqarg, Y ); +sub( One, Y, Y ); +div( U2, Y, Y ); +/*SqEr = (Y - One) + U2 / Eight;*/ +sub( One, Y, t ); +div( Eight, U2, SqEr ); +add( t, SqEr, SqEr ); +Showsq( 1 ); +div( Eight, U2, SqEr ); +add( Y, SqEr, SqEr ); +Showsq( -1 ); +/*Y = ((SQRT(F9) - U2) - (One - U2)) / U1;*/ +mov( F9, Sqarg ); +SQRT( Sqarg, Y ); +sub( U2, Y, Y ); +sub( U2, One, t ); +sub( t, Y, Y ); +div( U1, Y, Y ); +div( Eight, U1, SqEr ); +add( Y, SqEr, SqEr ); +Showsq( 1 ); +/*SqEr = (Y + One) + U1 / Eight;*/ +div( Eight, U1, t ); +add( Y, One, SqEr ); +add( SqEr, t, SqEr ); +Showsq( -1 ); +mov( U2, OneUlp ); +mov( OneUlp, X ); +for( Indx = 1; Indx <= 3; ++Indx) + { +/*Y = SQRT((X + U1 + X) + F9);*/ + add( X, U1, Y ); + add( Y, X, Y ); + add( Y, F9, Y ); + mov( Y, Sqarg ); + SQRT( Sqarg, Y ); +/*Y = ((Y - U2) - ((One - U2) + X)) / OneUlp;*/ + sub( U2, One, t ); + add( t, X, t ); + sub( U2, Y, Y ); + sub( t, Y, Y ); + div( OneUlp, Y, Y ); +/*Z = ((U1 - X) + F9) * Half * X * X / OneUlp;*/ + sub( X, U1, t ); + add( t, F9, t ); + mul( t, Half, t ); + mul( t, X, t ); + mul( t, X, t ); + div( OneUlp, t, Z ); + add( Y, Half, SqEr ); + add( SqEr, Z, SqEr ); + Showsq( -1 ); + sub( Half, Y, SqEr ); + add( SqEr, Z, SqEr ); + Showsq( 1 ); + if(((Indx == 1) || (Indx == 3))) + { +/*X = OneUlp * Sign (X) * FLOOR(Eight / (Nine * SQRT(OneUlp)));*/ + mov( OneUlp, Sqarg ); + SQRT( Sqarg, t ); + mul( Nine, t, t ); + div( t, Eight, t ); + FLOOR( t, t ); + Sign( X, t2 ); + mul( t2, t, t ); + mul( OneUlp, t, X ); + } + else + { + mov( U1, OneUlp ); + mov( OneUlp, X ); + neg( X ); + } + } +/*=============================================*/ +Milestone = 85; +/*=============================================*/ +SqRWrng = False; +Anomaly = False; +if( cmp(Radix,One) != 0 ) + { + printf("Testing whether sqrt is rounded or chopped.\n"); +/*D = FLOOR(Half + POW(Radix, One + Precision - FLOOR(Precision)));*/ + FLOOR( Precision, t2 ); + add( One, Precision, t ); + sub( t2, t, t ); + POW( Radix, t, D ); + add( Half, D, D ); + FLOOR( D, D ); +/* ... == Radix^(1 + fract) if (Precision == Integer + fract. */ + div( Radix, D, X ); + div( A1, D, Y ); + FLOOR( X, t ); + FLOOR( Y, t2 ); + if( (cmp(X,t) != 0) || (cmp(Y,t2) != 0) ) + { + Anomaly = True; + printf( "Anomaly 1\n" ); + } + else + { + mov( Zero, X ); + mov( X, Z2 ); + mov( One, Y ); + mov( Y, Y2 ); + sub( One, Radix, Z1 ); + mul( Four, D, FourD ); + do + { + if( cmp(Y2,Z2) >0 ) + { + mov( Radix, Q ); + mov( Y, YY1 ); + do + { +/*X1 = FABS(Q + FLOOR(Half - Q / YY1) * YY1);*/ + div( YY1, Q, t ); + sub( t, Half, t ); + FLOOR( t, t ); + mul( t, YY1, t ); + add( Q, t, X1 ); + FABS( X1 ); + mov( YY1, Q ); + mov( X1, YY1 ); + } + while( ! (cmp(X1,Zero) <= 0) ); + if( cmp(Q,One) <= 0 ) + { + mov( Y2, Z2 ); + mov( Y, Z ); + } + } + add( Y, Two, Y ); + add( X, Eight, X ); + add( Y2, X, Y2 ); + if( cmp(Y2,FourD) >= 0 ) + sub( FourD, Y2, Y2 ); + } + while( ! (cmp(Y,D) >= 0) ); + sub( Z2, FourD, X8 ); + mul( Z, Z, Q ); + add( X8, Q, Q ); + div( FourD, Q, Q ); + div( Eight, X8, X8 ); + FLOOR( Q, t ); + if( cmp(Q,t) != 0 ) + { + Anomaly = True; + printf( "Anomaly 2\n" ); + } + else + { + Break = False; + do + { + mul( Z1, Z, X ); +/*X = X - FLOOR(X / Radix) * Radix;*/ + div( Radix, X, t ); + FLOOR( t, t ); + mul( t, Radix, t ); + sub( t, X, X ); + if( cmp(X,One) == 0 ) + Break = True; + else + sub( One, Z1, Z1 ); + } + while( ! (Break || (cmp(Z1,Zero) <= 0)) ); + if( (cmp(Z1,Zero) <= 0) && (! Break)) + { + printf( "Anomaly 3\n" ); + Anomaly = True; + } + else + { + if( cmp(Z1,RadixD2) > 0) + sub( Radix, Z1, Z1 ); + do + { + NewD(); + mul( U2, D, t ); + } + while( ! (cmp(t,F9) >= 0) ); + mul( D, Radix, t ); + sub( D, t, t ); + sub( D, W, t2 ); + if (cmp(t,t2) != 0 ) + { + printf( "Anomaly 4\n" ); + Anomaly = True; + } + else + { + mov( D, Z2 ); + I = 0; + add( One, Z, t ); + mul( t, Half, t ); + add( D, t, Y ); + add( D, Z, X ); + add( X, Q, X ); + SR3750(); + sub( Z, One, t ); + mul( t, Half, t ); + add( D, t, Y ); + add( Y, D, Y ); + sub( Z, D, X ); + add( X, D, X ); + add( X, Q, t ); + add( t, X, X ); + SR3750(); + NewD(); + sub( Z2, D, t ); + sub( Z2, W, t2 ); + if(cmp(t,t2) != 0 ) + { + printf( "Anomaly 5\n" ); + Anomaly = True; + } + else + { +/*Y = (D - Z2) + (Z2 + (One - Z) * Half);*/ + sub( Z, One, t ); + mul( t, Half, t ); + add( Z2, t, t ); + sub( Z2, D, Y ); + add( Y, t, Y ); +/*X = (D - Z2) + (Z2 - Z + Q);*/ + sub( Z, Z2, t ); + add( t, Q, t ); + sub( Z2, D, X ); + add( X, t, X ); + SR3750(); + add( One, Z, Y ); + mul( Y, Half, Y ); + mov( Q, X ); + SR3750(); + if(I == 0) + { + printf( "Anomaly 6\n" ); + Anomaly = True; + } + } + } + } + } + } + if ((I == 0) || Anomaly) + { + ErrCnt[Failure] += 1; + printf( "Anomalous arithmetic with Integer < \n"); + printf("Radix^Precision = " ); + show( W ); + printf(" fails test whether sqrt rounds or chops.\n"); + SqRWrng = True; + } + } +if(! Anomaly) + { + if(! ((cmp(MinSqEr,Zero) < 0) || (cmp(MaxSqEr,Zero) > 0))) { + RSqrt = Rounded; + printf("Square root appears to be correctly rounded.\n"); + } + else + { + k = 0; + add( MaxSqEr, U2, t ); + sub( Half, U2, t2 ); + if( cmp(t,t2) > 0 ) + k = 1; + if( cmp( MinSqEr, Half ) > 0 ) + k = 1; + add( MinSqEr, Radix, t ); + if( cmp( t, Half ) < 0 ) + k = 1; + if( k == 1 ) + SqRWrng = True; + else + { + RSqrt = Chopped; + printf("Square root appears to be chopped.\n"); + } + } + } +if( SqRWrng ) + { + printf("Square root is neither chopped nor correctly rounded.\n"); + printf("Observed errors run from " ); + sub( Half, MinSqEr, t ); + show( t ); + printf("\tto " ); + add( Half, MaxSqEr, t ); + show( t ); + printf( "ulps.\n" ); + sub( MinSqEr, MaxSqEr, t ); + mul( Radix, Radix, t2 ); + if( cmp( t, t2 ) >= 0 ) + { + ErrCnt[Serious] += 1; + printf( "sqrt gets too many last digits wrong\n"); + } + } +} + +Showsq( arg ) +int arg; +{ + +k = 0; +if( arg <= 0 ) + { + if( cmp(SqEr,MinSqEr) < 0 ) + { + k = 1; + mov( SqEr, MinSqEr ); + } + } +if( arg >= 0 ) + { + if( cmp(SqEr,MaxSqEr) > 0 ) + { + k = 2; + mov( SqEr, MaxSqEr ); + } + } +#if DEBUG +if( k != 0 ) + { + printf( "Square root of " ); + show( arg ); + printf( "\tis in error by " ); + show( SqEr ); + } +#endif +} + + +pow1test() +{ + +/*=============================================*/ +Milestone = 90; +/*=============================================*/ +Pause(); +printf("Testing powers Z^i for small Integers Z and i.\n"); +N = 0; +/* ... test powers of zero. */ +I = 0; +mov( Zero, Z ); +neg(Z); +M = 3; +Break = False; +do + { + mov( One, X ); + SR3980(); + if(I <= 10) + { + I = 1023; + SR3980(); + } + if( cmp(Z,MinusOne) == 0 ) + Break = True; + else + { + mov( MinusOne, Z ); + PrintIfNPositive(); + N = 0; +/* .. if(-1)^N is invalid, replace MinusOne by One. */ + I = - 4; + } + } +while( ! Break ); +PrintIfNPositive(); +N1 = N; +N = 0; +mov( A1, Z ); +/*M = FLOOR(Two * LOG(W) / LOG(A1));*/ +LOG( W, t ); +mul( Two, t, t ); +FLOOR( t, t ); +LOG( A1, t2 ); +div( t2, t, t ); +FTOL( t, &lngint, t2 ); +M = lngint; +Break = False; +do + { + mov( Z, X ); + I = 1; + SR3980(); + if( cmp(Z,AInvrse) == 0 ) + Break = True; + else + mov( AInvrse, Z ); + } +while( ! (Break) ); +/*=============================================*/ +Milestone = 100; +/*=============================================*/ +/* Powers of Radix have been tested, */ +/* next try a few primes */ + +M = NoTrials; + +mov( Three, Z ); +do + { + mov( Z, X ); + I = 1; + SR3980(); + do + { + add( Z, Two, Z ); + div( Three, Z, t ); + FLOOR( t, t ); + mul( Three, t, t ); + } + while( cmp(t,Z) == 0 ); + mul( Eight, Three, t ); + } +while( cmp(Z,t) < 0 ); + +if(N > 0) + { + printf("Errors like this may invalidate financial calculations\n"); + printf("\tinvolving interest rates.\n"); + } +PrintIfNPositive(); +N += N1; +if(N == 0) + printf("... no discrepancies found.\n"); +if(N > 0) + Pause(); +else printf("\n"); +} + + + +pow2test() +{ +printf("\n"); +/* ...calculate Exp2 == exp(2) == 7.38905 60989 30650 22723 04275-... */ +mov( Zero, X ); +mov( Two, t2 ); /*I = 2;*/ + +mul( Two, Three, Y ); +mov( Zero, Q ); +N = 0; +do + { + mov( X, Z ); + add( t2, One, t2 ); /*I = I + 1;*/ + add( t2, t2, t ); + div( t, Y, Y ); /*Y = Y / (I + I);*/ + add( Y, Q, R ); + add( Z, R, X ); + sub( X, Z, Q ); + add( Q, R, Q ); + } +while( cmp(X,Z) > 0 ); + +/*Z = (OneAndHalf + One / Eight) + X / (OneAndHalf * ThirtyTwo);*/ +div( Eight, One, t ); +add( OneAndHalf, t, Z ); +mul( OneAndHalf, ThirtyTwo, t ); +div( t, X, t ); +add( Z, t, Z ); +mul( Z, Z, X ); +mul( X, X, Exp2 ); +mov( F9, X ); +sub( U1, X, Y ); +printf("Testing X^((X + 1) / (X - 1)) vs. exp(2) = " ); +show( Exp2 ); +printf( "\tas X -> 1.\n" ); +for(I = 1;;) + { + sub( BInvrse, X, Z ); +/*Z = (X + One) / (Z - (One - BInvrse));*/ + add( X, One, t2 ); + sub( BInvrse, One, t ); + sub( t, Z, t ); + div( t, t2, Z ); + POW( X, Z, Sqarg ); + sub( Exp2, Sqarg, Q ); + mov( Q, t ); + FABS( t ); + mul( TwoForty, U2, t2 ); + if( cmp( t, t2 ) > 0 ) + { + N = 1; + sub( BInvrse, X, V9 ); + sub( BInvrse, One, t ); + sub( t, V9, V9 ); + ErrCnt[Defect] += 1; + printf( "Calculated " ); + show( Sqarg ); + printf(" for \t(1 + " ); + show( V9 ); + printf( "\tto the power " ); + show( Z ); + printf("\tdiffers from correct value by " ); + show( Q ); + printf("\tThis much error may spoil financial\n"); + printf("\tcalculations involving tiny interest rates.\n"); + break; + } + else + { + sub( X, Y, Z ); + mul( Z, Two, Z ); + add( Z, Y, Z ); + mov( Y, X ); + mov( Z, Y ); + sub( F9, X, Z ); + mul( Z, Z, Z ); + add( Z, One, Z ); + if( (cmp(Z,One) > 0) && (I < NoTrials) ) + I++; + else + { + if( cmp(X,One) > 0 ) + { + if(N == 0) + printf("Accuracy seems adequate.\n"); + break; + } + else + { + add( One, U2, X ); + add( U2, U2, Y ); + add( X, Y, Y ); + I = 1; + } + } + } + } +/*=============================================*/ +Milestone = 150; +/*=============================================*/ +printf("Testing powers Z^Q at four nearly extreme values.\n"); +N = 0; +mov( A1, Z ); +/*Q = FLOOR(Half - LOG(C) / LOG(A1));*/ +LOG( C, t ); +LOG( A1, t2 ); +div( t2, t, t ); +sub( t, Half, t ); +FLOOR( t, Q ); +Break = False; +do + { + mov( CInvrse, X ); + POW( Z, Q, Y ); + IsYeqX(); + neg(Q); + mov( C, X ); + POW( Z, Q, Y ); + IsYeqX(); + if( cmp(Z,One) < 0 ) + Break = True; + else + mov( AInvrse, Z ); + } +while( ! (Break)); +PrintIfNPositive(); +if(N == 0) + printf(" ... no discrepancies found.\n"); +printf("\n"); +} diff --git a/test/math/epow.c b/test/math/epow.c index cc4994fe7..d756eaee0 100644 --- a/test/math/epow.c +++ b/test/math/epow.c @@ -1,215 +1,215 @@ -/* epow.c */
-/* power function: z = x**y */
-/* by Stephen L. Moshier. */
-
-
-#include "ehead.h"
-#define MAXPOS ((long) (((unsigned long) ~(0L)) >> 1))
-#define MAXNEG (-MAXPOS)
-/* #define MAXNEG (-MAXPOS - 1L) */
-
-extern int rndprc;
-void epowi();
-static void epowr();
-
-
-/* Run-time determination of largest integers */
-
-int powinited = 0;
-unsigned short maxposint[NE], maxnegint[NE];
-
-void initpow()
-{
-long li;
-
-li = MAXPOS;
-ltoe( &li, maxposint );
-li = MAXNEG;
-ltoe( &li, maxnegint );
-powinited = 1;
-}
-
-
-
-
-void epow( x, y, z )
-unsigned short *x, *y, *z;
-{
-unsigned short w[NE];
-int rndsav;
-long li;
-
-if( powinited == 0 )
- initpow();
-
-/* Check for integer power. */
-
-efloor( y, w );
-if( (ecmp(y,w) == 0)
- && (ecmp(maxposint,w) >= 0)
- && (ecmp(w,maxnegint) >= 0) )
- {
- eifrac( y, &li, w );
- epowi( x, y, z );
- return;
- }
-epowr( x, y, z );
-}
-
-
-
-
-/* y is integer valued. */
-
-void epowi( x, y, z )
-unsigned short x[], y[], z[];
-{
-unsigned short w[NE];
-long li, lx;
-unsigned long lu;
-int rndsav;
-unsigned short signx;
-/* unsigned short signy; */
-
-if( powinited == 0 )
- initpow();
-
-rndsav = rndprc;
-
-if( (ecmp(y,maxposint) > 0) || (ecmp(maxnegint,y) > 0) )
- {
- epowr( x, y, z );
- return;
- }
-
-eifrac( y, &li, w );
-if( li < 0 )
- lx = -li;
-else
- lx = li;
-
-/*
-if( (x[NE-1] & (unsigned short )0x7fff) == 0 )
-*/
-
-if( ecmp( x, ezero) == 0 )
- {
- if( li == 0 )
- {
- emov( eone, z );
- return;
- }
- else if( li < 0 )
- {
- einfin( z );
- return;
- }
- else
- {
- eclear( z );
- return;
- }
- }
-
-if( li == 0L )
- {
- emov( eone, z );
- return;
- }
-
-emov( x, w );
-signx = w[NE-1] & (unsigned short )0x8000;
-w[NE-1] &= (unsigned short )0x7fff;
-
-/* Overflow detection */
-/*
-lx = li * (w[NE-1] - 0x3fff);
-if( lx > 16385L )
- {
- einfin( z );
- mtherr( "epowi", OVERFLOW );
- goto done;
- }
-if( lx < -16450L )
- {
- eclear( z );
- return;
- }
-*/
-rndprc = NBITS;
-
-if( li < 0 )
- {
- lu = (unsigned int )( -li );
-/* signy = 0xffff;*/
- ediv( w, eone, w );
- }
-else
- {
- lu = (unsigned int )li;
-/* signy = 0;*/
- }
-
-/* First bit of the power */
-if( lu & 1 )
- {
- emov( w, z );
- }
-else
- {
- emov( eone, z );
- signx = 0;
- }
-
-
-lu >>= 1;
-while( lu != 0L )
- {
- emul( w, w, w ); /* arg to the 2-to-the-kth power */
- if( lu & 1L ) /* if that bit is set, then include in product */
- emul( w, z, z );
- lu >>= 1;
- }
-
-
-done:
-
-if( signx )
- eneg( z ); /* odd power of negative number */
-
-/*
-if( signy )
- {
- if( ecmp( z, ezero ) != 0 )
- {
- ediv( z, eone, z );
- }
- else
- {
- einfin( z );
- printf( "epowi OVERFLOW\n" );
- }
- }
-*/
-rndprc = rndsav;
-emul( eone, z, z );
-}
-
-
-
-/* z = exp( y * log(x) ) */
-
-static void epowr( x, y, z )
-unsigned short *x, *y, *z;
-{
-unsigned short w[NE];
-int rndsav;
-
-rndsav = rndprc;
-rndprc = NBITS;
-elog( x, w );
-emul( y, w, w );
-eexp( w, z );
-rndprc = rndsav;
-emul( eone, z, z );
-}
+/* epow.c */ +/* power function: z = x**y */ +/* by Stephen L. Moshier. */ + + +#include "ehead.h" +#define MAXPOS ((long) (((unsigned long) ~(0L)) >> 1)) +#define MAXNEG (-MAXPOS) +/* #define MAXNEG (-MAXPOS - 1L) */ + +extern int rndprc; +void epowi(); +static void epowr(); + + +/* Run-time determination of largest integers */ + +int powinited = 0; +unsigned short maxposint[NE], maxnegint[NE]; + +void initpow() +{ +long li; + +li = MAXPOS; +ltoe( &li, maxposint ); +li = MAXNEG; +ltoe( &li, maxnegint ); +powinited = 1; +} + + + + +void epow( x, y, z ) +unsigned short *x, *y, *z; +{ +unsigned short w[NE]; +int rndsav; +long li; + +if( powinited == 0 ) + initpow(); + +/* Check for integer power. */ + +efloor( y, w ); +if( (ecmp(y,w) == 0) + && (ecmp(maxposint,w) >= 0) + && (ecmp(w,maxnegint) >= 0) ) + { + eifrac( y, &li, w ); + epowi( x, y, z ); + return; + } +epowr( x, y, z ); +} + + + + +/* y is integer valued. */ + +void epowi( x, y, z ) +unsigned short x[], y[], z[]; +{ +unsigned short w[NE]; +long li, lx; +unsigned long lu; +int rndsav; +unsigned short signx; +/* unsigned short signy; */ + +if( powinited == 0 ) + initpow(); + +rndsav = rndprc; + +if( (ecmp(y,maxposint) > 0) || (ecmp(maxnegint,y) > 0) ) + { + epowr( x, y, z ); + return; + } + +eifrac( y, &li, w ); +if( li < 0 ) + lx = -li; +else + lx = li; + +/* +if( (x[NE-1] & (unsigned short )0x7fff) == 0 ) +*/ + +if( ecmp( x, ezero) == 0 ) + { + if( li == 0 ) + { + emov( eone, z ); + return; + } + else if( li < 0 ) + { + einfin( z ); + return; + } + else + { + eclear( z ); + return; + } + } + +if( li == 0L ) + { + emov( eone, z ); + return; + } + +emov( x, w ); +signx = w[NE-1] & (unsigned short )0x8000; +w[NE-1] &= (unsigned short )0x7fff; + +/* Overflow detection */ +/* +lx = li * (w[NE-1] - 0x3fff); +if( lx > 16385L ) + { + einfin( z ); + mtherr( "epowi", OVERFLOW ); + goto done; + } +if( lx < -16450L ) + { + eclear( z ); + return; + } +*/ +rndprc = NBITS; + +if( li < 0 ) + { + lu = (unsigned int )( -li ); +/* signy = 0xffff;*/ + ediv( w, eone, w ); + } +else + { + lu = (unsigned int )li; +/* signy = 0;*/ + } + +/* First bit of the power */ +if( lu & 1 ) + { + emov( w, z ); + } +else + { + emov( eone, z ); + signx = 0; + } + + +lu >>= 1; +while( lu != 0L ) + { + emul( w, w, w ); /* arg to the 2-to-the-kth power */ + if( lu & 1L ) /* if that bit is set, then include in product */ + emul( w, z, z ); + lu >>= 1; + } + + +done: + +if( signx ) + eneg( z ); /* odd power of negative number */ + +/* +if( signy ) + { + if( ecmp( z, ezero ) != 0 ) + { + ediv( z, eone, z ); + } + else + { + einfin( z ); + printf( "epowi OVERFLOW\n" ); + } + } +*/ +rndprc = rndsav; +emul( eone, z, z ); +} + + + +/* z = exp( y * log(x) ) */ + +static void epowr( x, y, z ) +unsigned short *x, *y, *z; +{ +unsigned short w[NE]; +int rndsav; + +rndsav = rndprc; +rndprc = NBITS; +elog( x, w ); +emul( y, w, w ); +eexp( w, z ); +rndprc = rndsav; +emul( eone, z, z ); +} diff --git a/test/math/etanh.c b/test/math/etanh.c index c74b4700a..8014c6d93 100644 --- a/test/math/etanh.c +++ b/test/math/etanh.c @@ -1,52 +1,52 @@ -/* xtanh.c */
-/* hyperbolic tangent check routine */
-/* this subroutine is used by the exponential function routine */
-/* by Stephen L. Moshier. */
-
-
-
-#include "ehead.h"
-
-
-void etanh( x, y )
-unsigned short *x, *y;
-{
-unsigned short e[NE], r[NE], j[NE], xx[NE], m2[NE];
-short i, n;
-long lj;
-
-emov( x, r );
-r[NE-1] &= (unsigned short )0x7fff;
-if( ecmp(r, eone) >= 0 )
- {
-/* tanh(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x))
- * Note eexp() calls xtanh, but with an argument less than (1 + log 2)/2.
- */
- eexp( r, e );
- ediv( e, eone, r );
- esub( r, e, xx );
- eadd( r, e, j );
- ediv( j, xx, y );
- return;
- }
-
-emov( etwo, m2 );
-eneg( m2 );
-
-n = NBITS/8; /* Number of terms to do in the continued fraction */
-lj = 2 * n + 1;
-ltoe( &lj, j );
-
-emov( j, e );
-emul( x, x, xx );
-
-/* continued fraction */
-for( i=0; i<n; i++)
- {
- ediv( e, xx, r );
- eadd( m2, j, j );
- eadd( r, j, e );
- }
-
-ediv( e, x, y );
-}
+/* xtanh.c */ +/* hyperbolic tangent check routine */ +/* this subroutine is used by the exponential function routine */ +/* by Stephen L. Moshier. */ + + + +#include "ehead.h" + + +void etanh( x, y ) +unsigned short *x, *y; +{ +unsigned short e[NE], r[NE], j[NE], xx[NE], m2[NE]; +short i, n; +long lj; + +emov( x, r ); +r[NE-1] &= (unsigned short )0x7fff; +if( ecmp(r, eone) >= 0 ) + { +/* tanh(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x)) + * Note eexp() calls xtanh, but with an argument less than (1 + log 2)/2. + */ + eexp( r, e ); + ediv( e, eone, r ); + esub( r, e, xx ); + eadd( r, e, j ); + ediv( j, xx, y ); + return; + } + +emov( etwo, m2 ); +eneg( m2 ); + +n = NBITS/8; /* Number of terms to do in the continued fraction */ +lj = 2 * n + 1; +ltoe( &lj, j ); + +emov( j, e ); +emul( x, x, xx ); + +/* continued fraction */ +for( i=0; i<n; i++) + { + ediv( e, xx, r ); + eadd( m2, j, j ); + eadd( r, j, e ); + } + +ediv( e, x, y ); +} diff --git a/test/math/etodec.c b/test/math/etodec.c index 29fee34cd..22545d6fb 100644 --- a/test/math/etodec.c +++ b/test/math/etodec.c @@ -1,181 +1,181 @@ -#include "ehead.h"
-void emovi(), emovo(), ecleaz(), eshdn8(), emdnorm();
-void todec();
-/*
-; convert DEC double precision to e type
-; double d;
-; short e[NE];
-; dectoe( &d, e );
-*/
-void dectoe( d, e )
-unsigned short *d;
-unsigned short *e;
-{
-unsigned short y[NI];
-register unsigned short r, *p;
-
-ecleaz(y); /* start with a zero */
-p = y; /* point to our number */
-r = *d; /* get DEC exponent word */
-if( *d & (unsigned int )0x8000 )
- *p = 0xffff; /* fill in our sign */
-++p; /* bump pointer to our exponent word */
-r &= 0x7fff; /* strip the sign bit */
-if( r == 0 ) /* answer = 0 if high order DEC word = 0 */
- goto done;
-
-
-r >>= 7; /* shift exponent word down 7 bits */
-r += EXONE - 0201; /* subtract DEC exponent offset */
- /* add our e type exponent offset */
-*p++ = r; /* to form our exponent */
-
-r = *d++; /* now do the high order mantissa */
-r &= 0177; /* strip off the DEC exponent and sign bits */
-r |= 0200; /* the DEC understood high order mantissa bit */
-*p++ = r; /* put result in our high guard word */
-
-*p++ = *d++; /* fill in the rest of our mantissa */
-*p++ = *d++;
-*p = *d;
-
-eshdn8(y); /* shift our mantissa down 8 bits */
-done:
-emovo( y, e );
-}
-
-
-
-/*
-; convert e type to DEC double precision
-; double d;
-; short e[NE];
-; etodec( e, &d );
-*/
-#if 0
-static unsigned short decbit[NI] = {0,0,0,0,0,0,0200,0};
-void etodec( x, d )
-unsigned short *x, *d;
-{
-unsigned short xi[NI];
-register unsigned short r;
-int i, j;
-
-emovi( x, xi );
-*d = 0;
-if( xi[0] != 0 )
- *d = 0100000;
-r = xi[E];
-if( r < (EXONE - 128) )
- goto zout;
-i = xi[M+4];
-if( (i & 0200) != 0 )
- {
- if( (i & 0377) == 0200 )
- {
- if( (i & 0400) != 0 )
- {
- /* check all less significant bits */
- for( j=M+5; j<NI; j++ )
- {
- if( xi[j] != 0 )
- goto yesrnd;
- }
- }
- goto nornd;
- }
-yesrnd:
- eaddm( decbit, xi );
- r -= enormlz(xi);
- }
-
-nornd:
-
-r -= EXONE;
-r += 0201;
-if( r < 0 )
- {
-zout:
- *d++ = 0;
- *d++ = 0;
- *d++ = 0;
- *d++ = 0;
- return;
- }
-if( r >= 0377 )
- {
- *d++ = 077777;
- *d++ = -1;
- *d++ = -1;
- *d++ = -1;
- return;
- }
-r &= 0377;
-r <<= 7;
-eshup8( xi );
-xi[M] &= 0177;
-r |= xi[M];
-*d++ |= r;
-*d++ = xi[M+1];
-*d++ = xi[M+2];
-*d++ = xi[M+3];
-}
-#else
-
-extern int rndprc;
-
-void etodec( x, d )
-unsigned short *x, *d;
-{
-unsigned short xi[NI];
-long exp;
-int rndsav;
-
-emovi( x, xi );
-exp = (long )xi[E] - (EXONE - 0201); /* adjust exponent for offsets */
-/* round off to nearest or even */
-rndsav = rndprc;
-rndprc = 56;
-emdnorm( xi, 0, 0, exp, 64 );
-rndprc = rndsav;
-todec( xi, d );
-}
-
-void todec( x, y )
-unsigned short *x, *y;
-{
-unsigned short i;
-unsigned short *p;
-
-p = x;
-*y = 0;
-if( *p++ )
- *y = 0100000;
-i = *p++;
-if( i == 0 )
- {
- *y++ = 0;
- *y++ = 0;
- *y++ = 0;
- *y++ = 0;
- return;
- }
-if( i > 0377 )
- {
- *y++ |= 077777;
- *y++ = 0xffff;
- *y++ = 0xffff;
- *y++ = 0xffff;
- return;
- }
-i &= 0377;
-i <<= 7;
-eshup8( x );
-x[M] &= 0177;
-i |= x[M];
-*y++ |= i;
-*y++ = x[M+1];
-*y++ = x[M+2];
-*y++ = x[M+3];
-}
-#endif
+#include "ehead.h" +void emovi(), emovo(), ecleaz(), eshdn8(), emdnorm(); +void todec(); +/* +; convert DEC double precision to e type +; double d; +; short e[NE]; +; dectoe( &d, e ); +*/ +void dectoe( d, e ) +unsigned short *d; +unsigned short *e; +{ +unsigned short y[NI]; +register unsigned short r, *p; + +ecleaz(y); /* start with a zero */ +p = y; /* point to our number */ +r = *d; /* get DEC exponent word */ +if( *d & (unsigned int )0x8000 ) + *p = 0xffff; /* fill in our sign */ +++p; /* bump pointer to our exponent word */ +r &= 0x7fff; /* strip the sign bit */ +if( r == 0 ) /* answer = 0 if high order DEC word = 0 */ + goto done; + + +r >>= 7; /* shift exponent word down 7 bits */ +r += EXONE - 0201; /* subtract DEC exponent offset */ + /* add our e type exponent offset */ +*p++ = r; /* to form our exponent */ + +r = *d++; /* now do the high order mantissa */ +r &= 0177; /* strip off the DEC exponent and sign bits */ +r |= 0200; /* the DEC understood high order mantissa bit */ +*p++ = r; /* put result in our high guard word */ + +*p++ = *d++; /* fill in the rest of our mantissa */ +*p++ = *d++; +*p = *d; + +eshdn8(y); /* shift our mantissa down 8 bits */ +done: +emovo( y, e ); +} + + + +/* +; convert e type to DEC double precision +; double d; +; short e[NE]; +; etodec( e, &d ); +*/ +#if 0 +static unsigned short decbit[NI] = {0,0,0,0,0,0,0200,0}; +void etodec( x, d ) +unsigned short *x, *d; +{ +unsigned short xi[NI]; +register unsigned short r; +int i, j; + +emovi( x, xi ); +*d = 0; +if( xi[0] != 0 ) + *d = 0100000; +r = xi[E]; +if( r < (EXONE - 128) ) + goto zout; +i = xi[M+4]; +if( (i & 0200) != 0 ) + { + if( (i & 0377) == 0200 ) + { + if( (i & 0400) != 0 ) + { + /* check all less significant bits */ + for( j=M+5; j<NI; j++ ) + { + if( xi[j] != 0 ) + goto yesrnd; + } + } + goto nornd; + } +yesrnd: + eaddm( decbit, xi ); + r -= enormlz(xi); + } + +nornd: + +r -= EXONE; +r += 0201; +if( r < 0 ) + { +zout: + *d++ = 0; + *d++ = 0; + *d++ = 0; + *d++ = 0; + return; + } +if( r >= 0377 ) + { + *d++ = 077777; + *d++ = -1; + *d++ = -1; + *d++ = -1; + return; + } +r &= 0377; +r <<= 7; +eshup8( xi ); +xi[M] &= 0177; +r |= xi[M]; +*d++ |= r; +*d++ = xi[M+1]; +*d++ = xi[M+2]; +*d++ = xi[M+3]; +} +#else + +extern int rndprc; + +void etodec( x, d ) +unsigned short *x, *d; +{ +unsigned short xi[NI]; +long exp; +int rndsav; + +emovi( x, xi ); +exp = (long )xi[E] - (EXONE - 0201); /* adjust exponent for offsets */ +/* round off to nearest or even */ +rndsav = rndprc; +rndprc = 56; +emdnorm( xi, 0, 0, exp, 64 ); +rndprc = rndsav; +todec( xi, d ); +} + +void todec( x, y ) +unsigned short *x, *y; +{ +unsigned short i; +unsigned short *p; + +p = x; +*y = 0; +if( *p++ ) + *y = 0100000; +i = *p++; +if( i == 0 ) + { + *y++ = 0; + *y++ = 0; + *y++ = 0; + *y++ = 0; + return; + } +if( i > 0377 ) + { + *y++ |= 077777; + *y++ = 0xffff; + *y++ = 0xffff; + *y++ = 0xffff; + return; + } +i &= 0377; +i <<= 7; +eshup8( x ); +x[M] &= 0177; +i |= x[M]; +*y++ |= i; +*y++ = x[M+1]; +*y++ = x[M+2]; +*y++ = x[M+3]; +} +#endif diff --git a/test/math/ieee.c b/test/math/ieee.c index 914d62cbb..17efea01c 100644 --- a/test/math/ieee.c +++ b/test/math/ieee.c @@ -1,4119 +1,4119 @@ -/* ieee.c
- *
- * Extended precision IEEE binary floating point arithmetic routines
- *
- * Numbers are stored in C language as arrays of 16-bit unsigned
- * short integers. The arguments of the routines are pointers to
- * the arrays.
- *
- *
- * External e type data structure, simulates Intel 8087 chip
- * temporary real format but possibly with a larger significand:
- *
- * NE-1 significand words (least significant word first,
- * most significant bit is normally set)
- * exponent (value = EXONE for 1.0,
- * top bit is the sign)
- *
- *
- * Internal data structure of a number (a "word" is 16 bits):
- *
- * ei[0] sign word (0 for positive, 0xffff for negative)
- * ei[1] biased exponent (value = EXONE for the number 1.0)
- * ei[2] high guard word (always zero after normalization)
- * ei[3]
- * to ei[NI-2] significand (NI-4 significand words,
- * most significant word first,
- * most significant bit is set)
- * ei[NI-1] low guard word (0x8000 bit is rounding place)
- *
- *
- *
- * Routines for external format numbers
- *
- * asctoe( string, e ) ASCII string to extended double e type
- * asctoe64( string, &d ) ASCII string to long double
- * asctoe53( string, &d ) ASCII string to double
- * asctoe24( string, &f ) ASCII string to single
- * asctoeg( string, e, prec ) ASCII string to specified precision
- * e24toe( &f, e ) IEEE single precision to e type
- * e53toe( &d, e ) IEEE double precision to e type
- * e64toe( &d, e ) IEEE long double precision to e type
- * eabs(e) absolute value
- * eadd( a, b, c ) c = b + a
- * eclear(e) e = 0
- * ecmp (a, b) Returns 1 if a > b, 0 if a == b,
- * -1 if a < b, -2 if either a or b is a NaN.
- * ediv( a, b, c ) c = b / a
- * efloor( a, b ) truncate to integer, toward -infinity
- * efrexp( a, exp, s ) extract exponent and significand
- * eifrac( e, &l, frac ) e to long integer and e type fraction
- * euifrac( e, &l, frac ) e to unsigned long integer and e type fraction
- * einfin( e ) set e to infinity, leaving its sign alone
- * eldexp( a, n, b ) multiply by 2**n
- * emov( a, b ) b = a
- * emul( a, b, c ) c = b * a
- * eneg(e) e = -e
- * eround( a, b ) b = nearest integer value to a
- * esub( a, b, c ) c = b - a
- * e24toasc( &f, str, n ) single to ASCII string, n digits after decimal
- * e53toasc( &d, str, n ) double to ASCII string, n digits after decimal
- * e64toasc( &d, str, n ) long double to ASCII string
- * etoasc( e, str, n ) e to ASCII string, n digits after decimal
- * etoe24( e, &f ) convert e type to IEEE single precision
- * etoe53( e, &d ) convert e type to IEEE double precision
- * etoe64( e, &d ) convert e type to IEEE long double precision
- * ltoe( &l, e ) long (32 bit) integer to e type
- * ultoe( &l, e ) unsigned long (32 bit) integer to e type
- * eisneg( e ) 1 if sign bit of e != 0, else 0
- * eisinf( e ) 1 if e has maximum exponent (non-IEEE)
- * or is infinite (IEEE)
- * eisnan( e ) 1 if e is a NaN
- * esqrt( a, b ) b = square root of a
- *
- *
- * Routines for internal format numbers
- *
- * eaddm( ai, bi ) add significands, bi = bi + ai
- * ecleaz(ei) ei = 0
- * ecleazs(ei) set ei = 0 but leave its sign alone
- * ecmpm( ai, bi ) compare significands, return 1, 0, or -1
- * edivm( ai, bi ) divide significands, bi = bi / ai
- * emdnorm(ai,l,s,exp) normalize and round off
- * emovi( a, ai ) convert external a to internal ai
- * emovo( ai, a ) convert internal ai to external a
- * emovz( ai, bi ) bi = ai, low guard word of bi = 0
- * emulm( ai, bi ) multiply significands, bi = bi * ai
- * enormlz(ei) left-justify the significand
- * eshdn1( ai ) shift significand and guards down 1 bit
- * eshdn8( ai ) shift down 8 bits
- * eshdn6( ai ) shift down 16 bits
- * eshift( ai, n ) shift ai n bits up (or down if n < 0)
- * eshup1( ai ) shift significand and guards up 1 bit
- * eshup8( ai ) shift up 8 bits
- * eshup6( ai ) shift up 16 bits
- * esubm( ai, bi ) subtract significands, bi = bi - ai
- *
- *
- * The result is always normalized and rounded to NI-4 word precision
- * after each arithmetic operation.
- *
- * Exception flags are NOT fully supported.
- *
- * Define INFINITY in mconf.h for support of infinity; otherwise a
- * saturation arithmetic is implemented.
- *
- * Define NANS for support of Not-a-Number items; otherwise the
- * arithmetic will never produce a NaN output, and might be confused
- * by a NaN input.
- * If NaN's are supported, the output of ecmp(a,b) is -2 if
- * either a or b is a NaN. This means asking if(ecmp(a,b) < 0)
- * may not be legitimate. Use if(ecmp(a,b) == -1) for less-than
- * if in doubt.
- * Signaling NaN's are NOT supported; they are treated the same
- * as quiet NaN's.
- *
- * Denormals are always supported here where appropriate (e.g., not
- * for conversion to DEC numbers).
- */
-
-/*
- * Revision history:
- *
- * 5 Jan 84 PDP-11 assembly language version
- * 2 Mar 86 fixed bug in asctoq()
- * 6 Dec 86 C language version
- * 30 Aug 88 100 digit version, improved rounding
- * 15 May 92 80-bit long double support
- *
- * Author: S. L. Moshier.
- */
-
-#include <stdio.h>
-/* #include "\usr\include\stdio.h" */
-#include "ehead.h"
-#include "mconf.h"
-
-/* Change UNK into something else. */
-#ifdef UNK
-#undef UNK
-#define IBMPC 1
-#endif
-
-/* NaN's require infinity support. */
-#ifdef NANS
-#ifndef INFINITY
-#define INFINITY
-#endif
-#endif
-
-/* This handles 64-bit long ints. */
-#define LONGBITS (8 * sizeof(long))
-
-/* Control register for rounding precision.
- * This can be set to 80 (if NE=6), 64, 56, 53, or 24 bits.
- */
-int rndprc = NBITS;
-extern int rndprc;
-
-void eaddm(), esubm(), emdnorm(), asctoeg(), enan();
-static void toe24(), toe53(), toe64(), toe113();
-void eremain(), einit(), eiremain();
-int ecmpm(), edivm(), emulm(), eisneg(), eisinf();
-void emovi(), emovo(), emovz(), ecleaz(), eadd1();
-void etodec(), todec(), dectoe();
-int eisnan(), eiisnan();
-
-
-
-void einit()
-{
-}
-
-/*
-; Clear out entire external format number.
-;
-; unsigned short x[];
-; eclear( x );
-*/
-
-void eclear( x )
-register unsigned short *x;
-{
-register int i;
-
-for( i=0; i<NE; i++ )
- *x++ = 0;
-}
-
-
-
-/* Move external format number from a to b.
- *
- * emov( a, b );
- */
-
-void emov( a, b )
-register unsigned short *a, *b;
-{
-register int i;
-
-for( i=0; i<NE; i++ )
- *b++ = *a++;
-}
-
-
-/*
-; Absolute value of external format number
-;
-; short x[NE];
-; eabs( x );
-*/
-
-void eabs(x)
-unsigned short x[]; /* x is the memory address of a short */
-{
-
-x[NE-1] &= 0x7fff; /* sign is top bit of last word of external format */
-}
-
-
-
-
-/*
-; Negate external format number
-;
-; unsigned short x[NE];
-; eneg( x );
-*/
-
-void eneg(x)
-unsigned short x[];
-{
-
-#ifdef NANS
-if( eisnan(x) )
- return;
-#endif
-x[NE-1] ^= 0x8000; /* Toggle the sign bit */
-}
-
-
-
-/* Return 1 if external format number is negative,
- * else return zero.
- */
-int eisneg(x)
-unsigned short x[];
-{
-
-#ifdef NANS
-if( eisnan(x) )
- return( 0 );
-#endif
-if( x[NE-1] & 0x8000 )
- return( 1 );
-else
- return( 0 );
-}
-
-
-/* Return 1 if external format number has maximum possible exponent,
- * else return zero.
- */
-int eisinf(x)
-unsigned short x[];
-{
-
-if( (x[NE-1] & 0x7fff) == 0x7fff )
- {
-#ifdef NANS
- if( eisnan(x) )
- return( 0 );
-#endif
- return( 1 );
- }
-else
- return( 0 );
-}
-
-/* Check if e-type number is not a number.
- */
-int eisnan(x)
-unsigned short x[];
-{
-
-#ifdef NANS
-int i;
-/* NaN has maximum exponent */
-if( (x[NE-1] & 0x7fff) != 0x7fff )
- return (0);
-/* ... and non-zero significand field. */
-for( i=0; i<NE-1; i++ )
- {
- if( *x++ != 0 )
- return (1);
- }
-#endif
-return (0);
-}
-
-/*
-; Fill entire number, including exponent and significand, with
-; largest possible number. These programs implement a saturation
-; value that is an ordinary, legal number. A special value
-; "infinity" may also be implemented; this would require tests
-; for that value and implementation of special rules for arithmetic
-; operations involving inifinity.
-*/
-
-void einfin(x)
-register unsigned short *x;
-{
-register int i;
-
-#ifdef INFINITY
-for( i=0; i<NE-1; i++ )
- *x++ = 0;
-*x |= 32767;
-#else
-for( i=0; i<NE-1; i++ )
- *x++ = 0xffff;
-*x |= 32766;
-if( rndprc < NBITS )
- {
- if (rndprc == 113)
- {
- *(x - 9) = 0;
- *(x - 8) = 0;
- }
- if( rndprc == 64 )
- {
- *(x-5) = 0;
- }
- if( rndprc == 53 )
- {
- *(x-4) = 0xf800;
- }
- else
- {
- *(x-4) = 0;
- *(x-3) = 0;
- *(x-2) = 0xff00;
- }
- }
-#endif
-}
-
-
-
-/* Move in external format number,
- * converting it to internal format.
- */
-void emovi( a, b )
-unsigned short *a, *b;
-{
-register unsigned short *p, *q;
-int i;
-
-q = b;
-p = a + (NE-1); /* point to last word of external number */
-/* get the sign bit */
-if( *p & 0x8000 )
- *q++ = 0xffff;
-else
- *q++ = 0;
-/* get the exponent */
-*q = *p--;
-*q++ &= 0x7fff; /* delete the sign bit */
-#ifdef INFINITY
-if( (*(q-1) & 0x7fff) == 0x7fff )
- {
-#ifdef NANS
- if( eisnan(a) )
- {
- *q++ = 0;
- for( i=3; i<NI; i++ )
- *q++ = *p--;
- return;
- }
-#endif
- for( i=2; i<NI; i++ )
- *q++ = 0;
- return;
- }
-#endif
-/* clear high guard word */
-*q++ = 0;
-/* move in the significand */
-for( i=0; i<NE-1; i++ )
- *q++ = *p--;
-/* clear low guard word */
-*q = 0;
-}
-
-
-/* Move internal format number out,
- * converting it to external format.
- */
-void emovo( a, b )
-unsigned short *a, *b;
-{
-register unsigned short *p, *q;
-unsigned short i;
-
-p = a;
-q = b + (NE-1); /* point to output exponent */
-/* combine sign and exponent */
-i = *p++;
-if( i )
- *q-- = *p++ | 0x8000;
-else
- *q-- = *p++;
-#ifdef INFINITY
-if( *(p-1) == 0x7fff )
- {
-#ifdef NANS
- if( eiisnan(a) )
- {
- enan( b, NBITS );
- return;
- }
-#endif
- einfin(b);
- return;
- }
-#endif
-/* skip over guard word */
-++p;
-/* move the significand */
-for( i=0; i<NE-1; i++ )
- *q-- = *p++;
-}
-
-
-
-
-/* Clear out internal format number.
- */
-
-void ecleaz( xi )
-register unsigned short *xi;
-{
-register int i;
-
-for( i=0; i<NI; i++ )
- *xi++ = 0;
-}
-
-/* same, but don't touch the sign. */
-
-void ecleazs( xi )
-register unsigned short *xi;
-{
-register int i;
-
-++xi;
-for(i=0; i<NI-1; i++)
- *xi++ = 0;
-}
-
-
-
-
-/* Move internal format number from a to b.
- */
-void emovz( a, b )
-register unsigned short *a, *b;
-{
-register int i;
-
-for( i=0; i<NI-1; i++ )
- *b++ = *a++;
-/* clear low guard word */
-*b = 0;
-}
-
-/* Return nonzero if internal format number is a NaN.
- */
-
-int eiisnan (x)
-unsigned short x[];
-{
-int i;
-
-if( (x[E] & 0x7fff) == 0x7fff )
- {
- for( i=M+1; i<NI; i++ )
- {
- if( x[i] != 0 )
- return(1);
- }
- }
-return(0);
-}
-
-#ifdef INFINITY
-/* Return nonzero if internal format number is infinite. */
-
-static int
-eiisinf (x)
- unsigned short x[];
-{
-
-#ifdef NANS
- if (eiisnan (x))
- return (0);
-#endif
- if ((x[E] & 0x7fff) == 0x7fff)
- return (1);
- return (0);
-}
-#endif
-
-/*
-; Compare significands of numbers in internal format.
-; Guard words are included in the comparison.
-;
-; unsigned short a[NI], b[NI];
-; cmpm( a, b );
-;
-; for the significands:
-; returns +1 if a > b
-; 0 if a == b
-; -1 if a < b
-*/
-int ecmpm( a, b )
-register unsigned short *a, *b;
-{
-int i;
-
-a += M; /* skip up to significand area */
-b += M;
-for( i=M; i<NI; i++ )
- {
- if( *a++ != *b++ )
- goto difrnt;
- }
-return(0);
-
-difrnt:
-if( *(--a) > *(--b) )
- return(1);
-else
- return(-1);
-}
-
-
-/*
-; Shift significand down by 1 bit
-*/
-
-void eshdn1(x)
-register unsigned short *x;
-{
-register unsigned short bits;
-int i;
-
-x += M; /* point to significand area */
-
-bits = 0;
-for( i=M; i<NI; i++ )
- {
- if( *x & 1 )
- bits |= 1;
- *x >>= 1;
- if( bits & 2 )
- *x |= 0x8000;
- bits <<= 1;
- ++x;
- }
-}
-
-
-
-/*
-; Shift significand up by 1 bit
-*/
-
-void eshup1(x)
-register unsigned short *x;
-{
-register unsigned short bits;
-int i;
-
-x += NI-1;
-bits = 0;
-
-for( i=M; i<NI; i++ )
- {
- if( *x & 0x8000 )
- bits |= 1;
- *x <<= 1;
- if( bits & 2 )
- *x |= 1;
- bits <<= 1;
- --x;
- }
-}
-
-
-
-/*
-; Shift significand down by 8 bits
-*/
-
-void eshdn8(x)
-register unsigned short *x;
-{
-register unsigned short newbyt, oldbyt;
-int i;
-
-x += M;
-oldbyt = 0;
-for( i=M; i<NI; i++ )
- {
- newbyt = *x << 8;
- *x >>= 8;
- *x |= oldbyt;
- oldbyt = newbyt;
- ++x;
- }
-}
-
-/*
-; Shift significand up by 8 bits
-*/
-
-void eshup8(x)
-register unsigned short *x;
-{
-int i;
-register unsigned short newbyt, oldbyt;
-
-x += NI-1;
-oldbyt = 0;
-
-for( i=M; i<NI; i++ )
- {
- newbyt = *x >> 8;
- *x <<= 8;
- *x |= oldbyt;
- oldbyt = newbyt;
- --x;
- }
-}
-
-/*
-; Shift significand up by 16 bits
-*/
-
-void eshup6(x)
-register unsigned short *x;
-{
-int i;
-register unsigned short *p;
-
-p = x + M;
-x += M + 1;
-
-for( i=M; i<NI-1; i++ )
- *p++ = *x++;
-
-*p = 0;
-}
-
-/*
-; Shift significand down by 16 bits
-*/
-
-void eshdn6(x)
-register unsigned short *x;
-{
-int i;
-register unsigned short *p;
-
-x += NI-1;
-p = x + 1;
-
-for( i=M; i<NI-1; i++ )
- *(--p) = *(--x);
-
-*(--p) = 0;
-}
-
-/*
-; Add significands
-; x + y replaces y
-*/
-
-void eaddm( x, y )
-unsigned short *x, *y;
-{
-register unsigned long a;
-int i;
-unsigned int carry;
-
-x += NI-1;
-y += NI-1;
-carry = 0;
-for( i=M; i<NI; i++ )
- {
- a = (unsigned long )(*x) + (unsigned long )(*y) + carry;
- if( a & 0x10000 )
- carry = 1;
- else
- carry = 0;
- *y = (unsigned short )a;
- --x;
- --y;
- }
-}
-
-/*
-; Subtract significands
-; y - x replaces y
-*/
-
-void esubm( x, y )
-unsigned short *x, *y;
-{
-unsigned long a;
-int i;
-unsigned int carry;
-
-x += NI-1;
-y += NI-1;
-carry = 0;
-for( i=M; i<NI; i++ )
- {
- a = (unsigned long )(*y) - (unsigned long )(*x) - carry;
- if( a & 0x10000 )
- carry = 1;
- else
- carry = 0;
- *y = (unsigned short )a;
- --x;
- --y;
- }
-}
-
-
-/* Divide significands */
-
-static unsigned short equot[NI] = {0}; /* was static */
-
-#if 0
-int edivm( den, num )
-unsigned short den[], num[];
-{
-int i;
-register unsigned short *p, *q;
-unsigned short j;
-
-p = &equot[0];
-*p++ = num[0];
-*p++ = num[1];
-
-for( i=M; i<NI; i++ )
- {
- *p++ = 0;
- }
-
-/* Use faster compare and subtraction if denominator
- * has only 15 bits of significance.
- */
-p = &den[M+2];
-if( *p++ == 0 )
- {
- for( i=M+3; i<NI; i++ )
- {
- if( *p++ != 0 )
- goto fulldiv;
- }
- if( (den[M+1] & 1) != 0 )
- goto fulldiv;
- eshdn1(num);
- eshdn1(den);
-
- p = &den[M+1];
- q = &num[M+1];
-
- for( i=0; i<NBITS+2; i++ )
- {
- if( *p <= *q )
- {
- *q -= *p;
- j = 1;
- }
- else
- {
- j = 0;
- }
- eshup1(equot);
- equot[NI-2] |= j;
- eshup1(num);
- }
- goto divdon;
- }
-
-/* The number of quotient bits to calculate is
- * NBITS + 1 scaling guard bit + 1 roundoff bit.
- */
-fulldiv:
-
-p = &equot[NI-2];
-for( i=0; i<NBITS+2; i++ )
- {
- if( ecmpm(den,num) <= 0 )
- {
- esubm(den, num);
- j = 1; /* quotient bit = 1 */
- }
- else
- j = 0;
- eshup1(equot);
- *p |= j;
- eshup1(num);
- }
-
-divdon:
-
-eshdn1( equot );
-eshdn1( equot );
-
-/* test for nonzero remainder after roundoff bit */
-p = &num[M];
-j = 0;
-for( i=M; i<NI; i++ )
- {
- j |= *p++;
- }
-if( j )
- j = 1;
-
-
-for( i=0; i<NI; i++ )
- num[i] = equot[i];
-return( (int )j );
-}
-
-/* Multiply significands */
-int emulm( a, b )
-unsigned short a[], b[];
-{
-unsigned short *p, *q;
-int i, j, k;
-
-equot[0] = b[0];
-equot[1] = b[1];
-for( i=M; i<NI; i++ )
- equot[i] = 0;
-
-p = &a[NI-2];
-k = NBITS;
-while( *p == 0 ) /* significand is not supposed to be all zero */
- {
- eshdn6(a);
- k -= 16;
- }
-if( (*p & 0xff) == 0 )
- {
- eshdn8(a);
- k -= 8;
- }
-
-q = &equot[NI-1];
-j = 0;
-for( i=0; i<k; i++ )
- {
- if( *p & 1 )
- eaddm(b, equot);
-/* remember if there were any nonzero bits shifted out */
- if( *q & 1 )
- j |= 1;
- eshdn1(a);
- eshdn1(equot);
- }
-
-for( i=0; i<NI; i++ )
- b[i] = equot[i];
-
-/* return flag for lost nonzero bits */
-return(j);
-}
-
-#else
-
-/* Multiply significand of e-type number b
-by 16-bit quantity a, e-type result to c. */
-
-void m16m( a, b, c )
-unsigned short a;
-unsigned short b[], c[];
-{
-register unsigned short *pp;
-register unsigned long carry;
-unsigned short *ps;
-unsigned short p[NI];
-unsigned long aa, m;
-int i;
-
-aa = a;
-pp = &p[NI-2];
-*pp++ = 0;
-*pp = 0;
-ps = &b[NI-1];
-
-for( i=M+1; i<NI; i++ )
- {
- if( *ps == 0 )
- {
- --ps;
- --pp;
- *(pp-1) = 0;
- }
- else
- {
- m = (unsigned long) aa * *ps--;
- carry = (m & 0xffff) + *pp;
- *pp-- = (unsigned short )carry;
- carry = (carry >> 16) + (m >> 16) + *pp;
- *pp = (unsigned short )carry;
- *(pp-1) = carry >> 16;
- }
- }
-for( i=M; i<NI; i++ )
- c[i] = p[i];
-}
-
-
-/* Divide significands. Neither the numerator nor the denominator
-is permitted to have its high guard word nonzero. */
-
-
-int edivm( den, num )
-unsigned short den[], num[];
-{
-int i;
-register unsigned short *p;
-unsigned long tnum;
-unsigned short j, tdenm, tquot;
-unsigned short tprod[NI+1];
-
-p = &equot[0];
-*p++ = num[0];
-*p++ = num[1];
-
-for( i=M; i<NI; i++ )
- {
- *p++ = 0;
- }
-eshdn1( num );
-tdenm = den[M+1];
-for( i=M; i<NI; i++ )
- {
- /* Find trial quotient digit (the radix is 65536). */
- tnum = (((unsigned long) num[M]) << 16) + num[M+1];
-
- /* Do not execute the divide instruction if it will overflow. */
- if( (tdenm * 0xffffL) < tnum )
- tquot = 0xffff;
- else
- tquot = tnum / tdenm;
-
- /* Prove that the divide worked. */
-/*
- tcheck = (unsigned long )tquot * tdenm;
- if( tnum - tcheck > tdenm )
- tquot = 0xffff;
-*/
- /* Multiply denominator by trial quotient digit. */
- m16m( tquot, den, tprod );
- /* The quotient digit may have been overestimated. */
- if( ecmpm( tprod, num ) > 0 )
- {
- tquot -= 1;
- esubm( den, tprod );
- if( ecmpm( tprod, num ) > 0 )
- {
- tquot -= 1;
- esubm( den, tprod );
- }
- }
-/*
- if( ecmpm( tprod, num ) > 0 )
- {
- eshow( "tprod", tprod );
- eshow( "num ", num );
- printf( "tnum = %08lx, tden = %04x, tquot = %04x\n",
- tnum, den[M+1], tquot );
- }
-*/
- esubm( tprod, num );
-/*
- if( ecmpm( num, den ) >= 0 )
- {
- eshow( "num ", num );
- eshow( "den ", den );
- printf( "tnum = %08lx, tden = %04x, tquot = %04x\n",
- tnum, den[M+1], tquot );
- }
-*/
- equot[i] = tquot;
- eshup6(num);
- }
-/* test for nonzero remainder after roundoff bit */
-p = &num[M];
-j = 0;
-for( i=M; i<NI; i++ )
- {
- j |= *p++;
- }
-if( j )
- j = 1;
-
-for( i=0; i<NI; i++ )
- num[i] = equot[i];
-
-return( (int )j );
-}
-
-
-
-/* Multiply significands */
-int emulm( a, b )
-unsigned short a[], b[];
-{
-unsigned short *p, *q;
-unsigned short pprod[NI];
-unsigned short j;
-int i;
-
-equot[0] = b[0];
-equot[1] = b[1];
-for( i=M; i<NI; i++ )
- equot[i] = 0;
-
-j = 0;
-p = &a[NI-1];
-q = &equot[NI-1];
-for( i=M+1; i<NI; i++ )
- {
- if( *p == 0 )
- {
- --p;
- }
- else
- {
- m16m( *p--, b, pprod );
- eaddm(pprod, equot);
- }
- j |= *q;
- eshdn6(equot);
- }
-
-for( i=0; i<NI; i++ )
- b[i] = equot[i];
-
-/* return flag for lost nonzero bits */
-return( (int)j );
-}
-
-
-/*
-eshow(str, x)
-char *str;
-unsigned short *x;
-{
-int i;
-
-printf( "%s ", str );
-for( i=0; i<NI; i++ )
- printf( "%04x ", *x++ );
-printf( "\n" );
-}
-*/
-#endif
-
-
-
-/*
- * Normalize and round off.
- *
- * The internal format number to be rounded is "s".
- * Input "lost" indicates whether the number is exact.
- * This is the so-called sticky bit.
- *
- * Input "subflg" indicates whether the number was obtained
- * by a subtraction operation. In that case if lost is nonzero
- * then the number is slightly smaller than indicated.
- *
- * Input "exp" is the biased exponent, which may be negative.
- * the exponent field of "s" is ignored but is replaced by
- * "exp" as adjusted by normalization and rounding.
- *
- * Input "rcntrl" is the rounding control.
- */
-
-static int rlast = -1;
-static int rw = 0;
-static unsigned short rmsk = 0;
-static unsigned short rmbit = 0;
-static unsigned short rebit = 0;
-static int re = 0;
-static unsigned short rbit[NI] = {0,0,0,0,0,0,0,0};
-
-void emdnorm( s, lost, subflg, exp, rcntrl )
-unsigned short s[];
-int lost;
-int subflg;
-long exp;
-int rcntrl;
-{
-int i, j;
-unsigned short r;
-
-/* Normalize */
-j = enormlz( s );
-
-/* a blank significand could mean either zero or infinity. */
-#ifndef INFINITY
-if( j > NBITS )
- {
- ecleazs( s );
- return;
- }
-#endif
-exp -= j;
-#ifndef INFINITY
-if( exp >= 32767L )
- goto overf;
-#else
-if( (j > NBITS) && (exp < 32767L) )
- {
- ecleazs( s );
- return;
- }
-#endif
-if( exp < 0L )
- {
- if( exp > (long )(-NBITS-1) )
- {
- j = (int )exp;
- i = eshift( s, j );
- if( i )
- lost = 1;
- }
- else
- {
- ecleazs( s );
- return;
- }
- }
-/* Round off, unless told not to by rcntrl. */
-if( rcntrl == 0 )
- goto mdfin;
-/* Set up rounding parameters if the control register changed. */
-if( rndprc != rlast )
- {
- ecleaz( rbit );
- switch( rndprc )
- {
- default:
- case NBITS:
- rw = NI-1; /* low guard word */
- rmsk = 0xffff;
- rmbit = 0x8000;
- rebit = 1;
- re = rw - 1;
- break;
- case 113:
- rw = 10;
- rmsk = 0x7fff;
- rmbit = 0x4000;
- rebit = 0x8000;
- re = rw;
- break;
- case 64:
- rw = 7;
- rmsk = 0xffff;
- rmbit = 0x8000;
- rebit = 1;
- re = rw-1;
- break;
-/* For DEC arithmetic */
- case 56:
- rw = 6;
- rmsk = 0xff;
- rmbit = 0x80;
- rebit = 0x100;
- re = rw;
- break;
- case 53:
- rw = 6;
- rmsk = 0x7ff;
- rmbit = 0x0400;
- rebit = 0x800;
- re = rw;
- break;
- case 24:
- rw = 4;
- rmsk = 0xff;
- rmbit = 0x80;
- rebit = 0x100;
- re = rw;
- break;
- }
- rbit[re] = rebit;
- rlast = rndprc;
- }
-
-/* Shift down 1 temporarily if the data structure has an implied
- * most significant bit and the number is denormal.
- * For rndprc = 64 or NBITS, there is no implied bit.
- * But Intel long double denormals lose one bit of significance even so.
- */
-#if IBMPC
-if( (exp <= 0) && (rndprc != NBITS) )
-#else
-if( (exp <= 0) && (rndprc != 64) && (rndprc != NBITS) )
-#endif
- {
- lost |= s[NI-1] & 1;
- eshdn1(s);
- }
-/* Clear out all bits below the rounding bit,
- * remembering in r if any were nonzero.
- */
-r = s[rw] & rmsk;
-if( rndprc < NBITS )
- {
- i = rw + 1;
- while( i < NI )
- {
- if( s[i] )
- r |= 1;
- s[i] = 0;
- ++i;
- }
- }
-s[rw] &= ~rmsk;
-if( (r & rmbit) != 0 )
- {
- if( r == rmbit )
- {
- if( lost == 0 )
- { /* round to even */
- if( (s[re] & rebit) == 0 )
- goto mddone;
- }
- else
- {
- if( subflg != 0 )
- goto mddone;
- }
- }
- eaddm( rbit, s );
- }
-mddone:
-#if IBMPC
-if( (exp <= 0) && (rndprc != NBITS) )
-#else
-if( (exp <= 0) && (rndprc != 64) && (rndprc != NBITS) )
-#endif
- {
- eshup1(s);
- }
-if( s[2] != 0 )
- { /* overflow on roundoff */
- eshdn1(s);
- exp += 1;
- }
-mdfin:
-s[NI-1] = 0;
-if( exp >= 32767L )
- {
-#ifndef INFINITY
-overf:
-#endif
-#ifdef INFINITY
- s[1] = 32767;
- for( i=2; i<NI-1; i++ )
- s[i] = 0;
-#else
- s[1] = 32766;
- s[2] = 0;
- for( i=M+1; i<NI-1; i++ )
- s[i] = 0xffff;
- s[NI-1] = 0;
- if( (rndprc < 64) || (rndprc == 113) )
- {
- s[rw] &= ~rmsk;
- if( rndprc == 24 )
- {
- s[5] = 0;
- s[6] = 0;
- }
- }
-#endif
- return;
- }
-if( exp < 0 )
- s[1] = 0;
-else
- s[1] = (unsigned short )exp;
-}
-
-
-
-/*
-; Subtract external format numbers.
-;
-; unsigned short a[NE], b[NE], c[NE];
-; esub( a, b, c ); c = b - a
-*/
-
-static int subflg = 0;
-
-void esub( a, b, c )
-unsigned short *a, *b, *c;
-{
-
-#ifdef NANS
-if( eisnan(a) )
- {
- emov (a, c);
- return;
- }
-if( eisnan(b) )
- {
- emov(b,c);
- return;
- }
-/* Infinity minus infinity is a NaN.
- * Test for subtracting infinities of the same sign.
- */
-if( eisinf(a) && eisinf(b) && ((eisneg (a) ^ eisneg (b)) == 0))
- {
- mtherr( "esub", DOMAIN );
- enan( c, NBITS );
- return;
- }
-#endif
-subflg = 1;
-eadd1( a, b, c );
-}
-
-
-/*
-; Add.
-;
-; unsigned short a[NE], b[NE], c[NE];
-; eadd( a, b, c ); c = b + a
-*/
-void eadd( a, b, c )
-unsigned short *a, *b, *c;
-{
-
-#ifdef NANS
-/* NaN plus anything is a NaN. */
-if( eisnan(a) )
- {
- emov(a,c);
- return;
- }
-if( eisnan(b) )
- {
- emov(b,c);
- return;
- }
-/* Infinity minus infinity is a NaN.
- * Test for adding infinities of opposite signs.
- */
-if( eisinf(a) && eisinf(b)
- && ((eisneg(a) ^ eisneg(b)) != 0) )
- {
- mtherr( "eadd", DOMAIN );
- enan( c, NBITS );
- return;
- }
-#endif
-subflg = 0;
-eadd1( a, b, c );
-}
-
-void eadd1( a, b, c )
-unsigned short *a, *b, *c;
-{
-unsigned short ai[NI], bi[NI], ci[NI];
-int i, lost, j, k;
-long lt, lta, ltb;
-
-#ifdef INFINITY
-if( eisinf(a) )
- {
- emov(a,c);
- if( subflg )
- eneg(c);
- return;
- }
-if( eisinf(b) )
- {
- emov(b,c);
- return;
- }
-#endif
-emovi( a, ai );
-emovi( b, bi );
-if( subflg )
- ai[0] = ~ai[0];
-
-/* compare exponents */
-lta = ai[E];
-ltb = bi[E];
-lt = lta - ltb;
-if( lt > 0L )
- { /* put the larger number in bi */
- emovz( bi, ci );
- emovz( ai, bi );
- emovz( ci, ai );
- ltb = bi[E];
- lt = -lt;
- }
-lost = 0;
-if( lt != 0L )
- {
- if( lt < (long )(-NBITS-1) )
- goto done; /* answer same as larger addend */
- k = (int )lt;
- lost = eshift( ai, k ); /* shift the smaller number down */
- }
-else
- {
-/* exponents were the same, so must compare significands */
- i = ecmpm( ai, bi );
- if( i == 0 )
- { /* the numbers are identical in magnitude */
- /* if different signs, result is zero */
- if( ai[0] != bi[0] )
- {
- eclear(c);
- return;
- }
- /* if same sign, result is double */
- /* double denomalized tiny number */
- if( (bi[E] == 0) && ((bi[3] & 0x8000) == 0) )
- {
- eshup1( bi );
- goto done;
- }
- /* add 1 to exponent unless both are zero! */
- for( j=1; j<NI-1; j++ )
- {
- if( bi[j] != 0 )
- {
-/* This could overflow, but let emovo take care of that. */
- ltb += 1;
- break;
- }
- }
- bi[E] = (unsigned short )ltb;
- goto done;
- }
- if( i > 0 )
- { /* put the larger number in bi */
- emovz( bi, ci );
- emovz( ai, bi );
- emovz( ci, ai );
- }
- }
-if( ai[0] == bi[0] )
- {
- eaddm( ai, bi );
- subflg = 0;
- }
-else
- {
- esubm( ai, bi );
- subflg = 1;
- }
-emdnorm( bi, lost, subflg, ltb, 64 );
-
-done:
-emovo( bi, c );
-}
-
-
-
-/*
-; Divide.
-;
-; unsigned short a[NE], b[NE], c[NE];
-; ediv( a, b, c ); c = b / a
-*/
-void ediv( a, b, c )
-unsigned short *a, *b, *c;
-{
-unsigned short ai[NI], bi[NI];
-int i;
-long lt, lta, ltb;
-
-#ifdef NANS
-/* Return any NaN input. */
-if( eisnan(a) )
- {
- emov(a,c);
- return;
- }
-if( eisnan(b) )
- {
- emov(b,c);
- return;
- }
-/* Zero over zero, or infinity over infinity, is a NaN. */
-if( ((ecmp(a,ezero) == 0) && (ecmp(b,ezero) == 0))
- || (eisinf (a) && eisinf (b)) )
- {
- mtherr( "ediv", DOMAIN );
- enan( c, NBITS );
- return;
- }
-#endif
-/* Infinity over anything else is infinity. */
-#ifdef INFINITY
-if( eisinf(b) )
- {
- if( eisneg(a) ^ eisneg(b) )
- *(c+(NE-1)) = 0x8000;
- else
- *(c+(NE-1)) = 0;
- einfin(c);
- return;
- }
-if( eisinf(a) )
- {
- eclear(c);
- return;
- }
-#endif
-emovi( a, ai );
-emovi( b, bi );
-lta = ai[E];
-ltb = bi[E];
-if( bi[E] == 0 )
- { /* See if numerator is zero. */
- for( i=1; i<NI-1; i++ )
- {
- if( bi[i] != 0 )
- {
- ltb -= enormlz( bi );
- goto dnzro1;
- }
- }
- eclear(c);
- return;
- }
-dnzro1:
-
-if( ai[E] == 0 )
- { /* possible divide by zero */
- for( i=1; i<NI-1; i++ )
- {
- if( ai[i] != 0 )
- {
- lta -= enormlz( ai );
- goto dnzro2;
- }
- }
- if( ai[0] == bi[0] )
- *(c+(NE-1)) = 0;
- else
- *(c+(NE-1)) = 0x8000;
- einfin(c);
- mtherr( "ediv", SING );
- return;
- }
-dnzro2:
-
-i = edivm( ai, bi );
-/* calculate exponent */
-lt = ltb - lta + EXONE;
-emdnorm( bi, i, 0, lt, 64 );
-/* set the sign */
-if( ai[0] == bi[0] )
- bi[0] = 0;
-else
- bi[0] = 0Xffff;
-emovo( bi, c );
-}
-
-
-
-/*
-; Multiply.
-;
-; unsigned short a[NE], b[NE], c[NE];
-; emul( a, b, c ); c = b * a
-*/
-void emul( a, b, c )
-unsigned short *a, *b, *c;
-{
-unsigned short ai[NI], bi[NI];
-int i, j;
-long lt, lta, ltb;
-
-#ifdef NANS
-/* NaN times anything is the same NaN. */
-if( eisnan(a) )
- {
- emov(a,c);
- return;
- }
-if( eisnan(b) )
- {
- emov(b,c);
- return;
- }
-/* Zero times infinity is a NaN. */
-if( (eisinf(a) && (ecmp(b,ezero) == 0))
- || (eisinf(b) && (ecmp(a,ezero) == 0)) )
- {
- mtherr( "emul", DOMAIN );
- enan( c, NBITS );
- return;
- }
-#endif
-/* Infinity times anything else is infinity. */
-#ifdef INFINITY
-if( eisinf(a) || eisinf(b) )
- {
- if( eisneg(a) ^ eisneg(b) )
- *(c+(NE-1)) = 0x8000;
- else
- *(c+(NE-1)) = 0;
- einfin(c);
- return;
- }
-#endif
-emovi( a, ai );
-emovi( b, bi );
-lta = ai[E];
-ltb = bi[E];
-if( ai[E] == 0 )
- {
- for( i=1; i<NI-1; i++ )
- {
- if( ai[i] != 0 )
- {
- lta -= enormlz( ai );
- goto mnzer1;
- }
- }
- eclear(c);
- return;
- }
-mnzer1:
-
-if( bi[E] == 0 )
- {
- for( i=1; i<NI-1; i++ )
- {
- if( bi[i] != 0 )
- {
- ltb -= enormlz( bi );
- goto mnzer2;
- }
- }
- eclear(c);
- return;
- }
-mnzer2:
-
-/* Multiply significands */
-j = emulm( ai, bi );
-/* calculate exponent */
-lt = lta + ltb - (EXONE - 1);
-emdnorm( bi, j, 0, lt, 64 );
-/* calculate sign of product */
-if( ai[0] == bi[0] )
- bi[0] = 0;
-else
- bi[0] = 0xffff;
-emovo( bi, c );
-}
-
-
-
-
-/*
-; Convert IEEE double precision to e type
-; double d;
-; unsigned short x[N+2];
-; e53toe( &d, x );
-*/
-void e53toe( pe, y )
-unsigned short *pe, *y;
-{
-#ifdef DEC
-
-dectoe( pe, y ); /* see etodec.c */
-
-#else
-
-register unsigned short r;
-register unsigned short *p, *e;
-unsigned short yy[NI];
-int denorm, k;
-
-e = pe;
-denorm = 0; /* flag if denormalized number */
-ecleaz(yy);
-#ifdef IBMPC
-e += 3;
-#endif
-r = *e;
-yy[0] = 0;
-if( r & 0x8000 )
- yy[0] = 0xffff;
-yy[M] = (r & 0x0f) | 0x10;
-r &= ~0x800f; /* strip sign and 4 significand bits */
-#ifdef INFINITY
-if( r == 0x7ff0 )
- {
-#ifdef NANS
-#ifdef IBMPC
- if( ((pe[3] & 0xf) != 0) || (pe[2] != 0)
- || (pe[1] != 0) || (pe[0] != 0) )
- {
- enan( y, NBITS );
- return;
- }
-#else
- if( ((pe[0] & 0xf) != 0) || (pe[1] != 0)
- || (pe[2] != 0) || (pe[3] != 0) )
- {
- enan( y, NBITS );
- return;
- }
-#endif
-#endif /* NANS */
- eclear( y );
- einfin( y );
- if( yy[0] )
- eneg(y);
- return;
- }
-#endif
-r >>= 4;
-/* If zero exponent, then the significand is denormalized.
- * So, take back the understood high significand bit. */
-if( r == 0 )
- {
- denorm = 1;
- yy[M] &= ~0x10;
- }
-r += EXONE - 01777;
-yy[E] = r;
-p = &yy[M+1];
-#ifdef IBMPC
-*p++ = *(--e);
-*p++ = *(--e);
-*p++ = *(--e);
-#endif
-#ifdef MIEEE
-++e;
-*p++ = *e++;
-*p++ = *e++;
-*p++ = *e++;
-#endif
-(void )eshift( yy, -5 );
-if( denorm )
- { /* if zero exponent, then normalize the significand */
- if( (k = enormlz(yy)) > NBITS )
- ecleazs(yy);
- else
- yy[E] -= (unsigned short )(k-1);
- }
-emovo( yy, y );
-#endif /* not DEC */
-}
-
-void e64toe( pe, y )
-unsigned short *pe, *y;
-{
-unsigned short yy[NI];
-unsigned short *p, *q, *e;
-int i;
-
-e = pe;
-p = yy;
-for( i=0; i<NE-5; i++ )
- *p++ = 0;
-#ifdef IBMPC
-for( i=0; i<5; i++ )
- *p++ = *e++;
-#endif
-#ifdef DEC
-for( i=0; i<5; i++ )
- *p++ = *e++;
-#endif
-#ifdef MIEEE
-p = &yy[0] + (NE-1);
-*p-- = *e++;
-++e;
-for( i=0; i<4; i++ )
- *p-- = *e++;
-#endif
-
-#ifdef IBMPC
-/* For Intel long double, shift denormal significand up 1
- -- but only if the top significand bit is zero. */
-if((yy[NE-1] & 0x7fff) == 0 && (yy[NE-2] & 0x8000) == 0)
- {
- unsigned short temp[NI+1];
- emovi(yy, temp);
- eshup1(temp);
- emovo(temp,y);
- return;
- }
-#endif
-#ifdef INFINITY
-/* Point to the exponent field. */
-p = &yy[NE-1];
-if( *p == 0x7fff )
- {
-#ifdef NANS
-#ifdef IBMPC
- for( i=0; i<4; i++ )
- {
- if((i != 3 && pe[i] != 0)
- /* Check for Intel long double infinity pattern. */
- || (i == 3 && pe[i] != 0x8000))
- {
- enan( y, NBITS );
- return;
- }
- }
-#else
- for( i=1; i<=4; i++ )
- {
- if( pe[i] != 0 )
- {
- enan( y, NBITS );
- return;
- }
- }
-#endif
-#endif /* NANS */
- eclear( y );
- einfin( y );
- if( *p & 0x8000 )
- eneg(y);
- return;
- }
-#endif
-p = yy;
-q = y;
-for( i=0; i<NE; i++ )
- *q++ = *p++;
-}
-
-void e113toe(pe,y)
-unsigned short *pe, *y;
-{
-register unsigned short r;
-unsigned short *e, *p;
-unsigned short yy[NI];
-int denorm, i;
-
-e = pe;
-denorm = 0;
-ecleaz(yy);
-#ifdef IBMPC
-e += 7;
-#endif
-r = *e;
-yy[0] = 0;
-if( r & 0x8000 )
- yy[0] = 0xffff;
-r &= 0x7fff;
-#ifdef INFINITY
-if( r == 0x7fff )
- {
-#ifdef NANS
-#ifdef IBMPC
- for( i=0; i<7; i++ )
- {
- if( pe[i] != 0 )
- {
- enan( y, NBITS );
- return;
- }
- }
-#else
- for( i=1; i<8; i++ )
- {
- if( pe[i] != 0 )
- {
- enan( y, NBITS );
- return;
- }
- }
-#endif
-#endif /* NANS */
- eclear( y );
- einfin( y );
- if( *e & 0x8000 )
- eneg(y);
- return;
- }
-#endif /* INFINITY */
-yy[E] = r;
-p = &yy[M + 1];
-#ifdef IBMPC
-for( i=0; i<7; i++ )
- *p++ = *(--e);
-#endif
-#ifdef MIEEE
-++e;
-for( i=0; i<7; i++ )
- *p++ = *e++;
-#endif
-/* If denormal, remove the implied bit; else shift down 1. */
-if( r == 0 )
- {
- yy[M] = 0;
- }
-else
- {
- yy[M] = 1;
- eshift( yy, -1 );
- }
-emovo(yy,y);
-}
-
-
-/*
-; Convert IEEE single precision to e type
-; float d;
-; unsigned short x[N+2];
-; dtox( &d, x );
-*/
-void e24toe( pe, y )
-unsigned short *pe, *y;
-{
-register unsigned short r;
-register unsigned short *p, *e;
-unsigned short yy[NI];
-int denorm, k;
-
-e = pe;
-denorm = 0; /* flag if denormalized number */
-ecleaz(yy);
-#ifdef IBMPC
-e += 1;
-#endif
-#ifdef DEC
-e += 1;
-#endif
-r = *e;
-yy[0] = 0;
-if( r & 0x8000 )
- yy[0] = 0xffff;
-yy[M] = (r & 0x7f) | 0200;
-r &= ~0x807f; /* strip sign and 7 significand bits */
-#ifdef INFINITY
-if( r == 0x7f80 )
- {
-#ifdef NANS
-#ifdef MIEEE
- if( ((pe[0] & 0x7f) != 0) || (pe[1] != 0) )
- {
- enan( y, NBITS );
- return;
- }
-#else
- if( ((pe[1] & 0x7f) != 0) || (pe[0] != 0) )
- {
- enan( y, NBITS );
- return;
- }
-#endif
-#endif /* NANS */
- eclear( y );
- einfin( y );
- if( yy[0] )
- eneg(y);
- return;
- }
-#endif
-r >>= 7;
-/* If zero exponent, then the significand is denormalized.
- * So, take back the understood high significand bit. */
-if( r == 0 )
- {
- denorm = 1;
- yy[M] &= ~0200;
- }
-r += EXONE - 0177;
-yy[E] = r;
-p = &yy[M+1];
-#ifdef IBMPC
-*p++ = *(--e);
-#endif
-#ifdef DEC
-*p++ = *(--e);
-#endif
-#ifdef MIEEE
-++e;
-*p++ = *e++;
-#endif
-(void )eshift( yy, -8 );
-if( denorm )
- { /* if zero exponent, then normalize the significand */
- if( (k = enormlz(yy)) > NBITS )
- ecleazs(yy);
- else
- yy[E] -= (unsigned short )(k-1);
- }
-emovo( yy, y );
-}
-
-void etoe113(x,e)
-unsigned short *x, *e;
-{
-unsigned short xi[NI];
-long exp;
-int rndsav;
-
-#ifdef NANS
-if( eisnan(x) )
- {
- enan( e, 113 );
- return;
- }
-#endif
-emovi( x, xi );
-exp = (long )xi[E];
-#ifdef INFINITY
-if( eisinf(x) )
- goto nonorm;
-#endif
-/* round off to nearest or even */
-rndsav = rndprc;
-rndprc = 113;
-emdnorm( xi, 0, 0, exp, 64 );
-rndprc = rndsav;
-nonorm:
-toe113 (xi, e);
-}
-
-/* move out internal format to ieee long double */
-static void toe113(a,b)
-unsigned short *a, *b;
-{
-register unsigned short *p, *q;
-unsigned short i;
-
-#ifdef NANS
-if( eiisnan(a) )
- {
- enan( b, 113 );
- return;
- }
-#endif
-p = a;
-#ifdef MIEEE
-q = b;
-#else
-q = b + 7; /* point to output exponent */
-#endif
-
-/* If not denormal, delete the implied bit. */
-if( a[E] != 0 )
- {
- eshup1 (a);
- }
-/* combine sign and exponent */
-i = *p++;
-#ifdef MIEEE
-if( i )
- *q++ = *p++ | 0x8000;
-else
- *q++ = *p++;
-#else
-if( i )
- *q-- = *p++ | 0x8000;
-else
- *q-- = *p++;
-#endif
-/* skip over guard word */
-++p;
-/* move the significand */
-#ifdef MIEEE
-for (i = 0; i < 7; i++)
- *q++ = *p++;
-#else
-for (i = 0; i < 7; i++)
- *q-- = *p++;
-#endif
-}
-
-
-void etoe64( x, e )
-unsigned short *x, *e;
-{
-unsigned short xi[NI];
-long exp;
-int rndsav;
-
-#ifdef NANS
-if( eisnan(x) )
- {
- enan( e, 64 );
- return;
- }
-#endif
-emovi( x, xi );
-exp = (long )xi[E]; /* adjust exponent for offset */
-#ifdef INFINITY
-if( eisinf(x) )
- goto nonorm;
-#endif
-/* round off to nearest or even */
-rndsav = rndprc;
-rndprc = 64;
-emdnorm( xi, 0, 0, exp, 64 );
-rndprc = rndsav;
-nonorm:
-toe64( xi, e );
-}
-
-/* move out internal format to ieee long double */
-static void toe64( a, b )
-unsigned short *a, *b;
-{
-register unsigned short *p, *q;
-unsigned short i;
-
-#ifdef NANS
-if( eiisnan(a) )
- {
- enan( b, 64 );
- return;
- }
-#endif
-#ifdef IBMPC
-/* Shift Intel denormal significand down 1. */
-if( a[E] == 0 )
- eshdn1(a);
-#endif
-p = a;
-#ifdef MIEEE
-q = b;
-#else
-q = b + 4; /* point to output exponent */
-#if 1
-/* NOTE: if data type is 96 bits wide, clear the last word here. */
-*(q+1)= 0;
-#endif
-#endif
-
-/* combine sign and exponent */
-i = *p++;
-#ifdef MIEEE
-if( i )
- *q++ = *p++ | 0x8000;
-else
- *q++ = *p++;
-*q++ = 0;
-#else
-if( i )
- *q-- = *p++ | 0x8000;
-else
- *q-- = *p++;
-#endif
-/* skip over guard word */
-++p;
-/* move the significand */
-#ifdef MIEEE
-for( i=0; i<4; i++ )
- *q++ = *p++;
-#else
-#ifdef INFINITY
-if (eiisinf (a))
- {
- /* Intel long double infinity. */
- *q-- = 0x8000;
- *q-- = 0;
- *q-- = 0;
- *q = 0;
- return;
- }
-#endif
-for( i=0; i<4; i++ )
- *q-- = *p++;
-#endif
-}
-
-
-/*
-; e type to IEEE double precision
-; double d;
-; unsigned short x[NE];
-; etoe53( x, &d );
-*/
-
-#ifdef DEC
-
-void etoe53( x, e )
-unsigned short *x, *e;
-{
-etodec( x, e ); /* see etodec.c */
-}
-
-static void toe53( x, y )
-unsigned short *x, *y;
-{
-todec( x, y );
-}
-
-#else
-
-void etoe53( x, e )
-unsigned short *x, *e;
-{
-unsigned short xi[NI];
-long exp;
-int rndsav;
-
-#ifdef NANS
-if( eisnan(x) )
- {
- enan( e, 53 );
- return;
- }
-#endif
-emovi( x, xi );
-exp = (long )xi[E] - (EXONE - 0x3ff); /* adjust exponent for offsets */
-#ifdef INFINITY
-if( eisinf(x) )
- goto nonorm;
-#endif
-/* round off to nearest or even */
-rndsav = rndprc;
-rndprc = 53;
-emdnorm( xi, 0, 0, exp, 64 );
-rndprc = rndsav;
-nonorm:
-toe53( xi, e );
-}
-
-
-static void toe53( x, y )
-unsigned short *x, *y;
-{
-unsigned short i;
-unsigned short *p;
-
-
-#ifdef NANS
-if( eiisnan(x) )
- {
- enan( y, 53 );
- return;
- }
-#endif
-p = &x[0];
-#ifdef IBMPC
-y += 3;
-#endif
-*y = 0; /* output high order */
-if( *p++ )
- *y = 0x8000; /* output sign bit */
-
-i = *p++;
-if( i >= (unsigned int )2047 )
- { /* Saturate at largest number less than infinity. */
-#ifdef INFINITY
- *y |= 0x7ff0;
-#ifdef IBMPC
- *(--y) = 0;
- *(--y) = 0;
- *(--y) = 0;
-#endif
-#ifdef MIEEE
- ++y;
- *y++ = 0;
- *y++ = 0;
- *y++ = 0;
-#endif
-#else
- *y |= (unsigned short )0x7fef;
-#ifdef IBMPC
- *(--y) = 0xffff;
- *(--y) = 0xffff;
- *(--y) = 0xffff;
-#endif
-#ifdef MIEEE
- ++y;
- *y++ = 0xffff;
- *y++ = 0xffff;
- *y++ = 0xffff;
-#endif
-#endif
- return;
- }
-if( i == 0 )
- {
- (void )eshift( x, 4 );
- }
-else
- {
- i <<= 4;
- (void )eshift( x, 5 );
- }
-i |= *p++ & (unsigned short )0x0f; /* *p = xi[M] */
-*y |= (unsigned short )i; /* high order output already has sign bit set */
-#ifdef IBMPC
-*(--y) = *p++;
-*(--y) = *p++;
-*(--y) = *p;
-#endif
-#ifdef MIEEE
-++y;
-*y++ = *p++;
-*y++ = *p++;
-*y++ = *p++;
-#endif
-}
-
-#endif /* not DEC */
-
-
-
-/*
-; e type to IEEE single precision
-; float d;
-; unsigned short x[N+2];
-; xtod( x, &d );
-*/
-void etoe24( x, e )
-unsigned short *x, *e;
-{
-long exp;
-unsigned short xi[NI];
-int rndsav;
-
-#ifdef NANS
-if( eisnan(x) )
- {
- enan( e, 24 );
- return;
- }
-#endif
-emovi( x, xi );
-exp = (long )xi[E] - (EXONE - 0177); /* adjust exponent for offsets */
-#ifdef INFINITY
-if( eisinf(x) )
- goto nonorm;
-#endif
-/* round off to nearest or even */
-rndsav = rndprc;
-rndprc = 24;
-emdnorm( xi, 0, 0, exp, 64 );
-rndprc = rndsav;
-nonorm:
-toe24( xi, e );
-}
-
-static void toe24( x, y )
-unsigned short *x, *y;
-{
-unsigned short i;
-unsigned short *p;
-
-#ifdef NANS
-if( eiisnan(x) )
- {
- enan( y, 24 );
- return;
- }
-#endif
-p = &x[0];
-#ifdef IBMPC
-y += 1;
-#endif
-#ifdef DEC
-y += 1;
-#endif
-*y = 0; /* output high order */
-if( *p++ )
- *y = 0x8000; /* output sign bit */
-
-i = *p++;
-if( i >= 255 )
- { /* Saturate at largest number less than infinity. */
-#ifdef INFINITY
- *y |= (unsigned short )0x7f80;
-#ifdef IBMPC
- *(--y) = 0;
-#endif
-#ifdef DEC
- *(--y) = 0;
-#endif
-#ifdef MIEEE
- ++y;
- *y = 0;
-#endif
-#else
- *y |= (unsigned short )0x7f7f;
-#ifdef IBMPC
- *(--y) = 0xffff;
-#endif
-#ifdef DEC
- *(--y) = 0xffff;
-#endif
-#ifdef MIEEE
- ++y;
- *y = 0xffff;
-#endif
-#endif
- return;
- }
-if( i == 0 )
- {
- (void )eshift( x, 7 );
- }
-else
- {
- i <<= 7;
- (void )eshift( x, 8 );
- }
-i |= *p++ & (unsigned short )0x7f; /* *p = xi[M] */
-*y |= i; /* high order output already has sign bit set */
-#ifdef IBMPC
-*(--y) = *p;
-#endif
-#ifdef DEC
-*(--y) = *p;
-#endif
-#ifdef MIEEE
-++y;
-*y = *p;
-#endif
-}
-
-
-/* Compare two e type numbers.
- *
- * unsigned short a[NE], b[NE];
- * ecmp( a, b );
- *
- * returns +1 if a > b
- * 0 if a == b
- * -1 if a < b
- * -2 if either a or b is a NaN.
- */
-int ecmp( a, b )
-unsigned short *a, *b;
-{
-unsigned short ai[NI], bi[NI];
-register unsigned short *p, *q;
-register int i;
-int msign;
-
-#ifdef NANS
-if (eisnan (a) || eisnan (b))
- return( -2 );
-#endif
-emovi( a, ai );
-p = ai;
-emovi( b, bi );
-q = bi;
-
-if( *p != *q )
- { /* the signs are different */
-/* -0 equals + 0 */
- for( i=1; i<NI-1; i++ )
- {
- if( ai[i] != 0 )
- goto nzro;
- if( bi[i] != 0 )
- goto nzro;
- }
- return(0);
-nzro:
- if( *p == 0 )
- return( 1 );
- else
- return( -1 );
- }
-/* both are the same sign */
-if( *p == 0 )
- msign = 1;
-else
- msign = -1;
-i = NI-1;
-do
- {
- if( *p++ != *q++ )
- {
- goto diff;
- }
- }
-while( --i > 0 );
-
-return(0); /* equality */
-
-
-
-diff:
-
-if( *(--p) > *(--q) )
- return( msign ); /* p is bigger */
-else
- return( -msign ); /* p is littler */
-}
-
-
-
-
-/* Find nearest integer to x = floor( x + 0.5 )
- *
- * unsigned short x[NE], y[NE]
- * eround( x, y );
- */
-void eround( x, y )
-unsigned short *x, *y;
-{
-
-eadd( ehalf, x, y );
-efloor( y, y );
-}
-
-
-
-
-/*
-; convert long (32-bit) integer to e type
-;
-; long l;
-; unsigned short x[NE];
-; ltoe( &l, x );
-; note &l is the memory address of l
-*/
-void ltoe( lp, y )
-long *lp; /* lp is the memory address of a long integer */
-unsigned short *y; /* y is the address of a short */
-{
-unsigned short yi[NI];
-unsigned long ll;
-int k;
-
-ecleaz( yi );
-if( *lp < 0 )
- {
- ll = (unsigned long )( -(*lp) ); /* make it positive */
- yi[0] = 0xffff; /* put correct sign in the e type number */
- }
-else
- {
- ll = (unsigned long )( *lp );
- }
-/* move the long integer to yi significand area */
-if( sizeof(long) == 8 )
- {
- yi[M] = (unsigned short) (ll >> (LONGBITS - 16));
- yi[M + 1] = (unsigned short) (ll >> (LONGBITS - 32));
- yi[M + 2] = (unsigned short) (ll >> 16);
- yi[M + 3] = (unsigned short) ll;
- yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */
- }
-else
- {
- yi[M] = (unsigned short )(ll >> 16);
- yi[M+1] = (unsigned short )ll;
- yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */
- }
-if( (k = enormlz( yi )) > NBITS ) /* normalize the significand */
- ecleaz( yi ); /* it was zero */
-else
- yi[E] -= (unsigned short )k; /* subtract shift count from exponent */
-emovo( yi, y ); /* output the answer */
-}
-
-/*
-; convert unsigned long (32-bit) integer to e type
-;
-; unsigned long l;
-; unsigned short x[NE];
-; ltox( &l, x );
-; note &l is the memory address of l
-*/
-void ultoe( lp, y )
-unsigned long *lp; /* lp is the memory address of a long integer */
-unsigned short *y; /* y is the address of a short */
-{
-unsigned short yi[NI];
-unsigned long ll;
-int k;
-
-ecleaz( yi );
-ll = *lp;
-
-/* move the long integer to ayi significand area */
-if( sizeof(long) == 8 )
- {
- yi[M] = (unsigned short) (ll >> (LONGBITS - 16));
- yi[M + 1] = (unsigned short) (ll >> (LONGBITS - 32));
- yi[M + 2] = (unsigned short) (ll >> 16);
- yi[M + 3] = (unsigned short) ll;
- yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */
- }
-else
- {
- yi[M] = (unsigned short )(ll >> 16);
- yi[M+1] = (unsigned short )ll;
- yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */
- }
-if( (k = enormlz( yi )) > NBITS ) /* normalize the significand */
- ecleaz( yi ); /* it was zero */
-else
- yi[E] -= (unsigned short )k; /* subtract shift count from exponent */
-emovo( yi, y ); /* output the answer */
-}
-
-
-/*
-; Find long integer and fractional parts
-
-; long i;
-; unsigned short x[NE], frac[NE];
-; xifrac( x, &i, frac );
-
- The integer output has the sign of the input. The fraction is
- the positive fractional part of abs(x).
-*/
-void eifrac( x, i, frac )
-unsigned short *x;
-long *i;
-unsigned short *frac;
-{
-unsigned short xi[NI];
-int j, k;
-unsigned long ll;
-
-emovi( x, xi );
-k = (int )xi[E] - (EXONE - 1);
-if( k <= 0 )
- {
-/* if exponent <= 0, integer = 0 and real output is fraction */
- *i = 0L;
- emovo( xi, frac );
- return;
- }
-if( k > (8 * sizeof(long) - 1) )
- {
-/*
-; long integer overflow: output large integer
-; and correct fraction
-*/
- j = 8 * sizeof(long) - 1;
- if( xi[0] )
- *i = (long) ((unsigned long) 1) << j;
- else
- *i = (long) (((unsigned long) (~(0L))) >> 1);
- (void )eshift( xi, k );
- }
-if( k > 16 )
- {
-/*
- Shift more than 16 bits: shift up k-16 mod 16
- then shift by 16's.
-*/
- j = k - ((k >> 4) << 4);
- eshift (xi, j);
- ll = xi[M];
- k -= j;
- do
- {
- eshup6 (xi);
- ll = (ll << 16) | xi[M];
- }
- while ((k -= 16) > 0);
- *i = ll;
- if (xi[0])
- *i = -(*i);
- }
-else
- {
-/* shift not more than 16 bits */
- eshift( xi, k );
- *i = (long )xi[M] & 0xffff;
- if( xi[0] )
- *i = -(*i);
- }
-xi[0] = 0;
-xi[E] = EXONE - 1;
-xi[M] = 0;
-if( (k = enormlz( xi )) > NBITS )
- ecleaz( xi );
-else
- xi[E] -= (unsigned short )k;
-
-emovo( xi, frac );
-}
-
-
-/*
-; Find unsigned long integer and fractional parts
-
-; unsigned long i;
-; unsigned short x[NE], frac[NE];
-; xifrac( x, &i, frac );
-
- A negative e type input yields integer output = 0
- but correct fraction.
-*/
-void euifrac( x, i, frac )
-unsigned short *x;
-unsigned long *i;
-unsigned short *frac;
-{
-unsigned short xi[NI];
-int j, k;
-unsigned long ll;
-
-emovi( x, xi );
-k = (int )xi[E] - (EXONE - 1);
-if( k <= 0 )
- {
-/* if exponent <= 0, integer = 0 and argument is fraction */
- *i = 0L;
- emovo( xi, frac );
- return;
- }
-if( k > (8 * sizeof(long)) )
- {
-/*
-; long integer overflow: output large integer
-; and correct fraction
-*/
- *i = ~(0L);
- (void )eshift( xi, k );
- }
-else if( k > 16 )
- {
-/*
- Shift more than 16 bits: shift up k-16 mod 16
- then shift up by 16's.
-*/
- j = k - ((k >> 4) << 4);
- eshift (xi, j);
- ll = xi[M];
- k -= j;
- do
- {
- eshup6 (xi);
- ll = (ll << 16) | xi[M];
- }
- while ((k -= 16) > 0);
- *i = ll;
- }
-else
- {
-/* shift not more than 16 bits */
- eshift( xi, k );
- *i = (long )xi[M] & 0xffff;
- }
-
-if( xi[0] ) /* A negative value yields unsigned integer 0. */
- *i = 0L;
-
-xi[0] = 0;
-xi[E] = EXONE - 1;
-xi[M] = 0;
-if( (k = enormlz( xi )) > NBITS )
- ecleaz( xi );
-else
- xi[E] -= (unsigned short )k;
-
-emovo( xi, frac );
-}
-
-
-
-/*
-; Shift significand
-;
-; Shifts significand area up or down by the number of bits
-; given by the variable sc.
-*/
-int eshift( x, sc )
-unsigned short *x;
-int sc;
-{
-unsigned short lost;
-unsigned short *p;
-
-if( sc == 0 )
- return( 0 );
-
-lost = 0;
-p = x + NI-1;
-
-if( sc < 0 )
- {
- sc = -sc;
- while( sc >= 16 )
- {
- lost |= *p; /* remember lost bits */
- eshdn6(x);
- sc -= 16;
- }
-
- while( sc >= 8 )
- {
- lost |= *p & 0xff;
- eshdn8(x);
- sc -= 8;
- }
-
- while( sc > 0 )
- {
- lost |= *p & 1;
- eshdn1(x);
- sc -= 1;
- }
- }
-else
- {
- while( sc >= 16 )
- {
- eshup6(x);
- sc -= 16;
- }
-
- while( sc >= 8 )
- {
- eshup8(x);
- sc -= 8;
- }
-
- while( sc > 0 )
- {
- eshup1(x);
- sc -= 1;
- }
- }
-if( lost )
- lost = 1;
-return( (int )lost );
-}
-
-
-
-/*
-; normalize
-;
-; Shift normalizes the significand area pointed to by argument
-; shift count (up = positive) is returned.
-*/
-int enormlz(x)
-unsigned short x[];
-{
-register unsigned short *p;
-int sc;
-
-sc = 0;
-p = &x[M];
-if( *p != 0 )
- goto normdn;
-++p;
-if( *p & 0x8000 )
- return( 0 ); /* already normalized */
-while( *p == 0 )
- {
- eshup6(x);
- sc += 16;
-/* With guard word, there are NBITS+16 bits available.
- * return true if all are zero.
- */
- if( sc > NBITS )
- return( sc );
- }
-/* see if high byte is zero */
-while( (*p & 0xff00) == 0 )
- {
- eshup8(x);
- sc += 8;
- }
-/* now shift 1 bit at a time */
-while( (*p & 0x8000) == 0)
- {
- eshup1(x);
- sc += 1;
- if( sc > (NBITS+16) )
- {
- mtherr( "enormlz", UNDERFLOW );
- return( sc );
- }
- }
-return( sc );
-
-/* Normalize by shifting down out of the high guard word
- of the significand */
-normdn:
-
-if( *p & 0xff00 )
- {
- eshdn8(x);
- sc -= 8;
- }
-while( *p != 0 )
- {
- eshdn1(x);
- sc -= 1;
-
- if( sc < -NBITS )
- {
- mtherr( "enormlz", OVERFLOW );
- return( sc );
- }
- }
-return( sc );
-}
-
-
-
-
-/* Convert e type number to decimal format ASCII string.
- * The constants are for 64 bit precision.
- */
-
-#define NTEN 12
-#define MAXP 4096
-
-#if NE == 10
-static unsigned short etens[NTEN + 1][NE] =
-{
- {0x6576, 0x4a92, 0x804a, 0x153f,
- 0xc94c, 0x979a, 0x8a20, 0x5202, 0xc460, 0x7525,}, /* 10**4096 */
- {0x6a32, 0xce52, 0x329a, 0x28ce,
- 0xa74d, 0x5de4, 0xc53d, 0x3b5d, 0x9e8b, 0x5a92,}, /* 10**2048 */
- {0x526c, 0x50ce, 0xf18b, 0x3d28,
- 0x650d, 0x0c17, 0x8175, 0x7586, 0xc976, 0x4d48,},
- {0x9c66, 0x58f8, 0xbc50, 0x5c54,
- 0xcc65, 0x91c6, 0xa60e, 0xa0ae, 0xe319, 0x46a3,},
- {0x851e, 0xeab7, 0x98fe, 0x901b,
- 0xddbb, 0xde8d, 0x9df9, 0xebfb, 0xaa7e, 0x4351,},
- {0x0235, 0x0137, 0x36b1, 0x336c,
- 0xc66f, 0x8cdf, 0x80e9, 0x47c9, 0x93ba, 0x41a8,},
- {0x50f8, 0x25fb, 0xc76b, 0x6b71,
- 0x3cbf, 0xa6d5, 0xffcf, 0x1f49, 0xc278, 0x40d3,},
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0xf020, 0xb59d, 0x2b70, 0xada8, 0x9dc5, 0x4069,},
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0400, 0xc9bf, 0x8e1b, 0x4034,},
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x2000, 0xbebc, 0x4019,},
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0x9c40, 0x400c,},
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0xc800, 0x4005,},
- {0x0000, 0x0000, 0x0000, 0x0000,
- 0x0000, 0x0000, 0x0000, 0x0000, 0xa000, 0x4002,}, /* 10**1 */
-};
-
-static unsigned short emtens[NTEN + 1][NE] =
-{
- {0x2030, 0xcffc, 0xa1c3, 0x8123,
- 0x2de3, 0x9fde, 0xd2ce, 0x04c8, 0xa6dd, 0x0ad8,}, /* 10**-4096 */
- {0x8264, 0xd2cb, 0xf2ea, 0x12d4,
- 0x4925, 0x2de4, 0x3436, 0x534f, 0xceae, 0x256b,}, /* 10**-2048 */
- {0xf53f, 0xf698, 0x6bd3, 0x0158,
- 0x87a6, 0xc0bd, 0xda57, 0x82a5, 0xa2a6, 0x32b5,},
- {0xe731, 0x04d4, 0xe3f2, 0xd332,
- 0x7132, 0xd21c, 0xdb23, 0xee32, 0x9049, 0x395a,},
- {0xa23e, 0x5308, 0xfefb, 0x1155,
- 0xfa91, 0x1939, 0x637a, 0x4325, 0xc031, 0x3cac,},
- {0xe26d, 0xdbde, 0xd05d, 0xb3f6,
- 0xac7c, 0xe4a0, 0x64bc, 0x467c, 0xddd0, 0x3e55,},
- {0x2a20, 0x6224, 0x47b3, 0x98d7,
- 0x3f23, 0xe9a5, 0xa539, 0xea27, 0xa87f, 0x3f2a,},
- {0x0b5b, 0x4af2, 0xa581, 0x18ed,
- 0x67de, 0x94ba, 0x4539, 0x1ead, 0xcfb1, 0x3f94,},
- {0xbf71, 0xa9b3, 0x7989, 0xbe68,
- 0x4c2e, 0xe15b, 0xc44d, 0x94be, 0xe695, 0x3fc9,},
- {0x3d4d, 0x7c3d, 0x36ba, 0x0d2b,
- 0xfdc2, 0xcefc, 0x8461, 0x7711, 0xabcc, 0x3fe4,},
- {0xc155, 0xa4a8, 0x404e, 0x6113,
- 0xd3c3, 0x652b, 0xe219, 0x1758, 0xd1b7, 0x3ff1,},
- {0xd70a, 0x70a3, 0x0a3d, 0xa3d7,
- 0x3d70, 0xd70a, 0x70a3, 0x0a3d, 0xa3d7, 0x3ff8,},
- {0xcccd, 0xcccc, 0xcccc, 0xcccc,
- 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0x3ffb,}, /* 10**-1 */
-};
-#else
-static unsigned short etens[NTEN+1][NE] = {
-{0xc94c,0x979a,0x8a20,0x5202,0xc460,0x7525,},/* 10**4096 */
-{0xa74d,0x5de4,0xc53d,0x3b5d,0x9e8b,0x5a92,},/* 10**2048 */
-{0x650d,0x0c17,0x8175,0x7586,0xc976,0x4d48,},
-{0xcc65,0x91c6,0xa60e,0xa0ae,0xe319,0x46a3,},
-{0xddbc,0xde8d,0x9df9,0xebfb,0xaa7e,0x4351,},
-{0xc66f,0x8cdf,0x80e9,0x47c9,0x93ba,0x41a8,},
-{0x3cbf,0xa6d5,0xffcf,0x1f49,0xc278,0x40d3,},
-{0xf020,0xb59d,0x2b70,0xada8,0x9dc5,0x4069,},
-{0x0000,0x0000,0x0400,0xc9bf,0x8e1b,0x4034,},
-{0x0000,0x0000,0x0000,0x2000,0xbebc,0x4019,},
-{0x0000,0x0000,0x0000,0x0000,0x9c40,0x400c,},
-{0x0000,0x0000,0x0000,0x0000,0xc800,0x4005,},
-{0x0000,0x0000,0x0000,0x0000,0xa000,0x4002,}, /* 10**1 */
-};
-
-static unsigned short emtens[NTEN+1][NE] = {
-{0x2de4,0x9fde,0xd2ce,0x04c8,0xa6dd,0x0ad8,}, /* 10**-4096 */
-{0x4925,0x2de4,0x3436,0x534f,0xceae,0x256b,}, /* 10**-2048 */
-{0x87a6,0xc0bd,0xda57,0x82a5,0xa2a6,0x32b5,},
-{0x7133,0xd21c,0xdb23,0xee32,0x9049,0x395a,},
-{0xfa91,0x1939,0x637a,0x4325,0xc031,0x3cac,},
-{0xac7d,0xe4a0,0x64bc,0x467c,0xddd0,0x3e55,},
-{0x3f24,0xe9a5,0xa539,0xea27,0xa87f,0x3f2a,},
-{0x67de,0x94ba,0x4539,0x1ead,0xcfb1,0x3f94,},
-{0x4c2f,0xe15b,0xc44d,0x94be,0xe695,0x3fc9,},
-{0xfdc2,0xcefc,0x8461,0x7711,0xabcc,0x3fe4,},
-{0xd3c3,0x652b,0xe219,0x1758,0xd1b7,0x3ff1,},
-{0x3d71,0xd70a,0x70a3,0x0a3d,0xa3d7,0x3ff8,},
-{0xcccd,0xcccc,0xcccc,0xcccc,0xcccc,0x3ffb,}, /* 10**-1 */
-};
-#endif
-
-void e24toasc( x, string, ndigs )
-unsigned short x[];
-char *string;
-int ndigs;
-{
-unsigned short w[NI];
-
-e24toe( x, w );
-etoasc( w, string, ndigs );
-}
-
-
-void e53toasc( x, string, ndigs )
-unsigned short x[];
-char *string;
-int ndigs;
-{
-unsigned short w[NI];
-
-e53toe( x, w );
-etoasc( w, string, ndigs );
-}
-
-
-void e64toasc( x, string, ndigs )
-unsigned short x[];
-char *string;
-int ndigs;
-{
-unsigned short w[NI];
-
-e64toe( x, w );
-etoasc( w, string, ndigs );
-}
-
-void e113toasc (x, string, ndigs)
-unsigned short x[];
-char *string;
-int ndigs;
-{
-unsigned short w[NI];
-
-e113toe (x, w);
-etoasc (w, string, ndigs);
-}
-
-
-void etoasc( x, string, ndigs )
-unsigned short x[];
-char *string;
-int ndigs;
-{
-long digit;
-unsigned short y[NI], t[NI], u[NI], w[NI];
-unsigned short *p, *r, *ten;
-unsigned short sign;
-int i, j, k, expon, rndsav;
-char *s, *ss;
-unsigned short m;
-
-rndsav = rndprc;
-#ifdef NANS
-if( eisnan(x) )
- {
- sprintf( string, " NaN " );
- goto bxit;
- }
-#endif
-rndprc = NBITS; /* set to full precision */
-emov( x, y ); /* retain external format */
-if( y[NE-1] & 0x8000 )
- {
- sign = 0xffff;
- y[NE-1] &= 0x7fff;
- }
-else
- {
- sign = 0;
- }
-expon = 0;
-ten = &etens[NTEN][0];
-emov( eone, t );
-/* Test for zero exponent */
-if( y[NE-1] == 0 )
- {
- for( k=0; k<NE-1; k++ )
- {
- if( y[k] != 0 )
- goto tnzro; /* denormalized number */
- }
- goto isone; /* legal all zeros */
- }
-tnzro:
-
-/* Test for infinity.
- */
-if( y[NE-1] == 0x7fff )
- {
- if( sign )
- sprintf( string, " -Infinity " );
- else
- sprintf( string, " Infinity " );
- goto bxit;
- }
-
-/* Test for exponent nonzero but significand denormalized.
- * This is an error condition.
- */
-if( (y[NE-1] != 0) && ((y[NE-2] & 0x8000) == 0) )
- {
- mtherr( "etoasc", DOMAIN );
- sprintf( string, "NaN" );
- goto bxit;
- }
-
-/* Compare to 1.0 */
-i = ecmp( eone, y );
-if( i == 0 )
- goto isone;
-
-if( i < 0 )
- { /* Number is greater than 1 */
-/* Convert significand to an integer and strip trailing decimal zeros. */
- emov( y, u );
- u[NE-1] = EXONE + NBITS - 1;
-
- p = &etens[NTEN-4][0];
- m = 16;
-do
- {
- ediv( p, u, t );
- efloor( t, w );
- for( j=0; j<NE-1; j++ )
- {
- if( t[j] != w[j] )
- goto noint;
- }
- emov( t, u );
- expon += (int )m;
-noint:
- p += NE;
- m >>= 1;
- }
-while( m != 0 );
-
-/* Rescale from integer significand */
- u[NE-1] += y[NE-1] - (unsigned int )(EXONE + NBITS - 1);
- emov( u, y );
-/* Find power of 10 */
- emov( eone, t );
- m = MAXP;
- p = &etens[0][0];
- while( ecmp( ten, u ) <= 0 )
- {
- if( ecmp( p, u ) <= 0 )
- {
- ediv( p, u, u );
- emul( p, t, t );
- expon += (int )m;
- }
- m >>= 1;
- if( m == 0 )
- break;
- p += NE;
- }
- }
-else
- { /* Number is less than 1.0 */
-/* Pad significand with trailing decimal zeros. */
- if( y[NE-1] == 0 )
- {
- while( (y[NE-2] & 0x8000) == 0 )
- {
- emul( ten, y, y );
- expon -= 1;
- }
- }
- else
- {
- emovi( y, w );
- for( i=0; i<NDEC+1; i++ )
- {
- if( (w[NI-1] & 0x7) != 0 )
- break;
-/* multiply by 10 */
- emovz( w, u );
- eshdn1( u );
- eshdn1( u );
- eaddm( w, u );
- u[1] += 3;
- while( u[2] != 0 )
- {
- eshdn1(u);
- u[1] += 1;
- }
- if( u[NI-1] != 0 )
- break;
- if( eone[NE-1] <= u[1] )
- break;
- emovz( u, w );
- expon -= 1;
- }
- emovo( w, y );
- }
- k = -MAXP;
- p = &emtens[0][0];
- r = &etens[0][0];
- emov( y, w );
- emov( eone, t );
- while( ecmp( eone, w ) > 0 )
- {
- if( ecmp( p, w ) >= 0 )
- {
- emul( r, w, w );
- emul( r, t, t );
- expon += k;
- }
- k /= 2;
- if( k == 0 )
- break;
- p += NE;
- r += NE;
- }
- ediv( t, eone, t );
- }
-isone:
-/* Find the first (leading) digit. */
-emovi( t, w );
-emovz( w, t );
-emovi( y, w );
-emovz( w, y );
-eiremain( t, y );
-digit = equot[NI-1];
-while( (digit == 0) && (ecmp(y,ezero) != 0) )
- {
- eshup1( y );
- emovz( y, u );
- eshup1( u );
- eshup1( u );
- eaddm( u, y );
- eiremain( t, y );
- digit = equot[NI-1];
- expon -= 1;
- }
-s = string;
-if( sign )
- *s++ = '-';
-else
- *s++ = ' ';
-/* Examine number of digits requested by caller. */
-if( ndigs < 0 )
- ndigs = 0;
-if( ndigs > NDEC )
- ndigs = NDEC;
-if( digit == 10 )
- {
- *s++ = '1';
- *s++ = '.';
- if( ndigs > 0 )
- {
- *s++ = '0';
- ndigs -= 1;
- }
- expon += 1;
- }
-else
- {
- *s++ = (char )digit + '0';
- *s++ = '.';
- }
-/* Generate digits after the decimal point. */
-for( k=0; k<=ndigs; k++ )
- {
-/* multiply current number by 10, without normalizing */
- eshup1( y );
- emovz( y, u );
- eshup1( u );
- eshup1( u );
- eaddm( u, y );
- eiremain( t, y );
- *s++ = (char )equot[NI-1] + '0';
- }
-digit = equot[NI-1];
---s;
-ss = s;
-/* round off the ASCII string */
-if( digit > 4 )
- {
-/* Test for critical rounding case in ASCII output. */
- if( digit == 5 )
- {
- emovo( y, t );
- if( ecmp(t,ezero) != 0 )
- goto roun; /* round to nearest */
- if( (*(s-1) & 1) == 0 )
- goto doexp; /* round to even */
- }
-/* Round up and propagate carry-outs */
-roun:
- --s;
- k = *s & 0x7f;
-/* Carry out to most significant digit? */
- if( k == '.' )
- {
- --s;
- k = *s;
- k += 1;
- *s = (char )k;
-/* Most significant digit carries to 10? */
- if( k > '9' )
- {
- expon += 1;
- *s = '1';
- }
- goto doexp;
- }
-/* Round up and carry out from less significant digits */
- k += 1;
- *s = (char )k;
- if( k > '9' )
- {
- *s = '0';
- goto roun;
- }
- }
-doexp:
-/*
-if( expon >= 0 )
- sprintf( ss, "e+%d", expon );
-else
- sprintf( ss, "e%d", expon );
-*/
- sprintf( ss, "E%d", expon );
-bxit:
-rndprc = rndsav;
-}
-
-
-
-
-/*
-; ASCTOQ
-; ASCTOQ.MAC LATEST REV: 11 JAN 84
-; SLM, 3 JAN 78
-;
-; Convert ASCII string to quadruple precision floating point
-;
-; Numeric input is free field decimal number
-; with max of 15 digits with or without
-; decimal point entered as ASCII from teletype.
-; Entering E after the number followed by a second
-; number causes the second number to be interpreted
-; as a power of 10 to be multiplied by the first number
-; (i.e., "scientific" notation).
-;
-; Usage:
-; asctoq( string, q );
-*/
-
-/* ASCII to single */
-void asctoe24( s, y )
-char *s;
-unsigned short *y;
-{
-asctoeg( s, y, 24 );
-}
-
-
-/* ASCII to double */
-void asctoe53( s, y )
-char *s;
-unsigned short *y;
-{
-#ifdef DEC
-asctoeg( s, y, 56 );
-#else
-asctoeg( s, y, 53 );
-#endif
-}
-
-
-/* ASCII to long double */
-void asctoe64( s, y )
-char *s;
-unsigned short *y;
-{
-asctoeg( s, y, 64 );
-}
-
-/* ASCII to 128-bit long double */
-void asctoe113 (s, y)
-char *s;
-unsigned short *y;
-{
-asctoeg( s, y, 113 );
-}
-
-/* ASCII to super double */
-void asctoe( s, y )
-char *s;
-unsigned short *y;
-{
-asctoeg( s, y, NBITS );
-}
-
-/* Space to make a copy of the input string: */
-static char lstr[82] = {0};
-
-void asctoeg( ss, y, oprec )
-char *ss;
-unsigned short *y;
-int oprec;
-{
-unsigned short yy[NI], xt[NI], tt[NI];
-int esign, decflg, sgnflg, nexp, exp, prec, lost;
-int k, trail, c, rndsav;
-long lexp;
-unsigned short nsign, *p;
-char *sp, *s;
-
-/* Copy the input string. */
-s = ss;
-while( *s == ' ' ) /* skip leading spaces */
- ++s;
-sp = lstr;
-for( k=0; k<79; k++ )
- {
- if( (*sp++ = *s++) == '\0' )
- break;
- }
-*sp = '\0';
-s = lstr;
-
-rndsav = rndprc;
-rndprc = NBITS; /* Set to full precision */
-lost = 0;
-nsign = 0;
-decflg = 0;
-sgnflg = 0;
-nexp = 0;
-exp = 0;
-prec = 0;
-ecleaz( yy );
-trail = 0;
-
-nxtcom:
-k = *s - '0';
-if( (k >= 0) && (k <= 9) )
- {
-/* Ignore leading zeros */
- if( (prec == 0) && (decflg == 0) && (k == 0) )
- goto donchr;
-/* Identify and strip trailing zeros after the decimal point. */
- if( (trail == 0) && (decflg != 0) )
- {
- sp = s;
- while( (*sp >= '0') && (*sp <= '9') )
- ++sp;
-/* Check for syntax error */
- c = *sp & 0x7f;
- if( (c != 'e') && (c != 'E') && (c != '\0')
- && (c != '\n') && (c != '\r') && (c != ' ')
- && (c != ',') )
- goto error;
- --sp;
- while( *sp == '0' )
- *sp-- = 'z';
- trail = 1;
- if( *s == 'z' )
- goto donchr;
- }
-/* If enough digits were given to more than fill up the yy register,
- * continuing until overflow into the high guard word yy[2]
- * guarantees that there will be a roundoff bit at the top
- * of the low guard word after normalization.
- */
- if( yy[2] == 0 )
- {
- if( decflg )
- nexp += 1; /* count digits after decimal point */
- eshup1( yy ); /* multiply current number by 10 */
- emovz( yy, xt );
- eshup1( xt );
- eshup1( xt );
- eaddm( xt, yy );
- ecleaz( xt );
- xt[NI-2] = (unsigned short )k;
- eaddm( xt, yy );
- }
- else
- {
- /* Mark any lost non-zero digit. */
- lost |= k;
- /* Count lost digits before the decimal point. */
- if (decflg == 0)
- nexp -= 1;
- }
- prec += 1;
- goto donchr;
- }
-
-switch( *s )
- {
- case 'z':
- break;
- case 'E':
- case 'e':
- goto expnt;
- case '.': /* decimal point */
- if( decflg )
- goto error;
- ++decflg;
- break;
- case '-':
- nsign = 0xffff;
- if( sgnflg )
- goto error;
- ++sgnflg;
- break;
- case '+':
- if( sgnflg )
- goto error;
- ++sgnflg;
- break;
- case ',':
- case ' ':
- case '\0':
- case '\n':
- case '\r':
- goto daldone;
- case 'i':
- case 'I':
- goto infinite;
- default:
- error:
-#ifdef NANS
- enan( yy, NI*16 );
-#else
- mtherr( "asctoe", DOMAIN );
- ecleaz(yy);
-#endif
- goto aexit;
- }
-donchr:
-++s;
-goto nxtcom;
-
-/* Exponent interpretation */
-expnt:
-
-esign = 1;
-exp = 0;
-++s;
-/* check for + or - */
-if( *s == '-' )
- {
- esign = -1;
- ++s;
- }
-if( *s == '+' )
- ++s;
-while( (*s >= '0') && (*s <= '9') )
- {
- exp *= 10;
- exp += *s++ - '0';
- if (exp > 4977)
- {
- if (esign < 0)
- goto zero;
- else
- goto infinite;
- }
- }
-if( esign < 0 )
- exp = -exp;
-if( exp > 4932 )
- {
-infinite:
- ecleaz(yy);
- yy[E] = 0x7fff; /* infinity */
- goto aexit;
- }
-if( exp < -4977 )
- {
-zero:
- ecleaz(yy);
- goto aexit;
- }
-
-daldone:
-nexp = exp - nexp;
-/* Pad trailing zeros to minimize power of 10, per IEEE spec. */
-while( (nexp > 0) && (yy[2] == 0) )
- {
- emovz( yy, xt );
- eshup1( xt );
- eshup1( xt );
- eaddm( yy, xt );
- eshup1( xt );
- if( xt[2] != 0 )
- break;
- nexp -= 1;
- emovz( xt, yy );
- }
-if( (k = enormlz(yy)) > NBITS )
- {
- ecleaz(yy);
- goto aexit;
- }
-lexp = (EXONE - 1 + NBITS) - k;
-emdnorm( yy, lost, 0, lexp, 64 );
-/* convert to external format */
-
-
-/* Multiply by 10**nexp. If precision is 64 bits,
- * the maximum relative error incurred in forming 10**n
- * for 0 <= n <= 324 is 8.2e-20, at 10**180.
- * For 0 <= n <= 999, the peak relative error is 1.4e-19 at 10**947.
- * For 0 >= n >= -999, it is -1.55e-19 at 10**-435.
- */
-lexp = yy[E];
-if( nexp == 0 )
- {
- k = 0;
- goto expdon;
- }
-esign = 1;
-if( nexp < 0 )
- {
- nexp = -nexp;
- esign = -1;
- if( nexp > 4096 )
- { /* Punt. Can't handle this without 2 divides. */
- emovi( etens[0], tt );
- lexp -= tt[E];
- k = edivm( tt, yy );
- lexp += EXONE;
- nexp -= 4096;
- }
- }
-p = &etens[NTEN][0];
-emov( eone, xt );
-exp = 1;
-do
- {
- if( exp & nexp )
- emul( p, xt, xt );
- p -= NE;
- exp = exp + exp;
- }
-while( exp <= MAXP );
-
-emovi( xt, tt );
-if( esign < 0 )
- {
- lexp -= tt[E];
- k = edivm( tt, yy );
- lexp += EXONE;
- }
-else
- {
- lexp += tt[E];
- k = emulm( tt, yy );
- lexp -= EXONE - 1;
- }
-
-expdon:
-
-/* Round and convert directly to the destination type */
-if( oprec == 53 )
- lexp -= EXONE - 0x3ff;
-else if( oprec == 24 )
- lexp -= EXONE - 0177;
-#ifdef DEC
-else if( oprec == 56 )
- lexp -= EXONE - 0201;
-#endif
-rndprc = oprec;
-emdnorm( yy, k, 0, lexp, 64 );
-
-aexit:
-
-rndprc = rndsav;
-yy[0] = nsign;
-switch( oprec )
- {
-#ifdef DEC
- case 56:
- todec( yy, y ); /* see etodec.c */
- break;
-#endif
- case 53:
- toe53( yy, y );
- break;
- case 24:
- toe24( yy, y );
- break;
- case 64:
- toe64( yy, y );
- break;
- case 113:
- toe113( yy, y );
- break;
- case NBITS:
- emovo( yy, y );
- break;
- }
-}
-
-
-
-/* y = largest integer not greater than x
- * (truncated toward minus infinity)
- *
- * unsigned short x[NE], y[NE]
- *
- * efloor( x, y );
- */
-static unsigned short bmask[] = {
-0xffff,
-0xfffe,
-0xfffc,
-0xfff8,
-0xfff0,
-0xffe0,
-0xffc0,
-0xff80,
-0xff00,
-0xfe00,
-0xfc00,
-0xf800,
-0xf000,
-0xe000,
-0xc000,
-0x8000,
-0x0000,
-};
-
-void efloor( x, y )
-unsigned short x[], y[];
-{
-register unsigned short *p;
-int e, expon, i;
-unsigned short f[NE];
-
-emov( x, f ); /* leave in external format */
-expon = (int )f[NE-1];
-e = (expon & 0x7fff) - (EXONE - 1);
-if( e <= 0 )
- {
- eclear(y);
- goto isitneg;
- }
-/* number of bits to clear out */
-e = NBITS - e;
-emov( f, y );
-if( e <= 0 )
- return;
-
-p = &y[0];
-while( e >= 16 )
- {
- *p++ = 0;
- e -= 16;
- }
-/* clear the remaining bits */
-*p &= bmask[e];
-/* truncate negatives toward minus infinity */
-isitneg:
-
-if( (unsigned short )expon & (unsigned short )0x8000 )
- {
- for( i=0; i<NE-1; i++ )
- {
- if( f[i] != y[i] )
- {
- esub( eone, y, y );
- break;
- }
- }
- }
-}
-
-
-/* unsigned short x[], s[];
- * long *exp;
- *
- * efrexp( x, exp, s );
- *
- * Returns s and exp such that s * 2**exp = x and .5 <= s < 1.
- * For example, 1.1 = 0.55 * 2**1
- * Handles denormalized numbers properly using long integer exp.
- */
-void efrexp( x, exp, s )
-unsigned short x[];
-long *exp;
-unsigned short s[];
-{
-unsigned short xi[NI];
-long li;
-
-emovi( x, xi );
-li = (long )((short )xi[1]);
-
-if( li == 0 )
- {
- li -= enormlz( xi );
- }
-xi[1] = 0x3ffe;
-emovo( xi, s );
-*exp = li - 0x3ffe;
-}
-
-
-
-/* unsigned short x[], y[];
- * long pwr2;
- *
- * eldexp( x, pwr2, y );
- *
- * Returns y = x * 2**pwr2.
- */
-void eldexp( x, pwr2, y )
-unsigned short x[];
-long pwr2;
-unsigned short y[];
-{
-unsigned short xi[NI];
-long li;
-int i;
-
-emovi( x, xi );
-li = xi[1];
-li += pwr2;
-i = 0;
-emdnorm( xi, i, i, li, 64 );
-emovo( xi, y );
-}
-
-
-/* c = remainder after dividing b by a
- * Least significant integer quotient bits left in equot[].
- */
-void eremain( a, b, c )
-unsigned short a[], b[], c[];
-{
-unsigned short den[NI], num[NI];
-
-#ifdef NANS
-if( eisinf(b) || (ecmp(a,ezero) == 0) || eisnan(a) || eisnan(b))
- {
- enan( c, NBITS );
- return;
- }
-#endif
-if( ecmp(a,ezero) == 0 )
- {
- mtherr( "eremain", SING );
- eclear( c );
- return;
- }
-emovi( a, den );
-emovi( b, num );
-eiremain( den, num );
-/* Sign of remainder = sign of quotient */
-if( a[0] == b[0] )
- num[0] = 0;
-else
- num[0] = 0xffff;
-emovo( num, c );
-}
-
-
-void eiremain( den, num )
-unsigned short den[], num[];
-{
-long ld, ln;
-unsigned short j;
-
-ld = den[E];
-ld -= enormlz( den );
-ln = num[E];
-ln -= enormlz( num );
-ecleaz( equot );
-while( ln >= ld )
- {
- if( ecmpm(den,num) <= 0 )
- {
- esubm(den, num);
- j = 1;
- }
- else
- {
- j = 0;
- }
- eshup1(equot);
- equot[NI-1] |= j;
- eshup1(num);
- ln -= 1;
- }
-emdnorm( num, 0, 0, ln, 0 );
-}
-
-/* NaN bit patterns
- */
-#ifdef MIEEE
-unsigned short nan113[8] = {
- 0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff};
-unsigned short nan64[6] = {0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff};
-unsigned short nan53[4] = {0x7fff, 0xffff, 0xffff, 0xffff};
-unsigned short nan24[2] = {0x7fff, 0xffff};
-#endif
-
-#ifdef IBMPC
-unsigned short nan113[8] = {0, 0, 0, 0, 0, 0, 0xc000, 0xffff};
-unsigned short nan64[6] = {0, 0, 0, 0xc000, 0xffff, 0};
-unsigned short nan53[4] = {0, 0, 0, 0xfff8};
-unsigned short nan24[2] = {0, 0xffc0};
-#endif
-
-
-void enan (nan, size)
-unsigned short *nan;
-int size;
-{
-int i, n;
-unsigned short *p;
-
-switch( size )
- {
-#ifndef DEC
- case 113:
- n = 8;
- p = nan113;
- break;
-
- case 64:
- n = 6;
- p = nan64;
- break;
-
- case 53:
- n = 4;
- p = nan53;
- break;
-
- case 24:
- n = 2;
- p = nan24;
- break;
-
- case NBITS:
- for( i=0; i<NE-2; i++ )
- *nan++ = 0;
- *nan++ = 0xc000;
- *nan++ = 0x7fff;
- return;
-
- case NI*16:
- *nan++ = 0;
- *nan++ = 0x7fff;
- *nan++ = 0;
- *nan++ = 0xc000;
- for( i=4; i<NI; i++ )
- *nan++ = 0;
- return;
-#endif
- default:
- mtherr( "enan", DOMAIN );
- return;
- }
-for (i=0; i < n; i++)
- *nan++ = *p++;
-}
-
-
-
-/* Longhand square root. */
-
-static int esqinited = 0;
-static unsigned short sqrndbit[NI];
-
-void esqrt( x, y )
-short *x, *y;
-{
-unsigned short temp[NI], num[NI], sq[NI], xx[NI];
-int i, j, k, n, nlups;
-long m, exp;
-
-if( esqinited == 0 )
- {
- ecleaz( sqrndbit );
- sqrndbit[NI-2] = 1;
- esqinited = 1;
- }
-/* Check for arg <= 0 */
-i = ecmp( x, ezero );
-if( i <= 0 )
- {
-#ifdef NANS
- if (i == -2)
- {
- enan (y, NBITS);
- return;
- }
-#endif
- eclear(y);
- if( i < 0 )
- mtherr( "esqrt", DOMAIN );
- return;
- }
-
-#ifdef INFINITY
-if( eisinf(x) )
- {
- eclear(y);
- einfin(y);
- return;
- }
-#endif
-/* Bring in the arg and renormalize if it is denormal. */
-emovi( x, xx );
-m = (long )xx[1]; /* local long word exponent */
-if( m == 0 )
- m -= enormlz( xx );
-
-/* Divide exponent by 2 */
-m -= 0x3ffe;
-exp = (unsigned short )( (m / 2) + 0x3ffe );
-
-/* Adjust if exponent odd */
-if( (m & 1) != 0 )
- {
- if( m > 0 )
- exp += 1;
- eshdn1( xx );
- }
-
-ecleaz( sq );
-ecleaz( num );
-n = 8; /* get 8 bits of result per inner loop */
-nlups = rndprc;
-j = 0;
-
-while( nlups > 0 )
- {
-/* bring in next word of arg */
- if( j < NE )
- num[NI-1] = xx[j+3];
-/* Do additional bit on last outer loop, for roundoff. */
- if( nlups <= 8 )
- n = nlups + 1;
- for( i=0; i<n; i++ )
- {
-/* Next 2 bits of arg */
- eshup1( num );
- eshup1( num );
-/* Shift up answer */
- eshup1( sq );
-/* Make trial divisor */
- for( k=0; k<NI; k++ )
- temp[k] = sq[k];
- eshup1( temp );
- eaddm( sqrndbit, temp );
-/* Subtract and insert answer bit if it goes in */
- if( ecmpm( temp, num ) <= 0 )
- {
- esubm( temp, num );
- sq[NI-2] |= 1;
- }
- }
- nlups -= n;
- j += 1;
- }
-
-/* Adjust for extra, roundoff loop done. */
-exp += (NBITS - 1) - rndprc;
-
-/* Sticky bit = 1 if the remainder is nonzero. */
-k = 0;
-for( i=3; i<NI; i++ )
- k |= (int )num[i];
-
-/* Renormalize and round off. */
-emdnorm( sq, k, 0, exp, 64 );
-emovo( sq, y );
-}
+/* ieee.c + * + * Extended precision IEEE binary floating point arithmetic routines + * + * Numbers are stored in C language as arrays of 16-bit unsigned + * short integers. The arguments of the routines are pointers to + * the arrays. + * + * + * External e type data structure, simulates Intel 8087 chip + * temporary real format but possibly with a larger significand: + * + * NE-1 significand words (least significant word first, + * most significant bit is normally set) + * exponent (value = EXONE for 1.0, + * top bit is the sign) + * + * + * Internal data structure of a number (a "word" is 16 bits): + * + * ei[0] sign word (0 for positive, 0xffff for negative) + * ei[1] biased exponent (value = EXONE for the number 1.0) + * ei[2] high guard word (always zero after normalization) + * ei[3] + * to ei[NI-2] significand (NI-4 significand words, + * most significant word first, + * most significant bit is set) + * ei[NI-1] low guard word (0x8000 bit is rounding place) + * + * + * + * Routines for external format numbers + * + * asctoe( string, e ) ASCII string to extended double e type + * asctoe64( string, &d ) ASCII string to long double + * asctoe53( string, &d ) ASCII string to double + * asctoe24( string, &f ) ASCII string to single + * asctoeg( string, e, prec ) ASCII string to specified precision + * e24toe( &f, e ) IEEE single precision to e type + * e53toe( &d, e ) IEEE double precision to e type + * e64toe( &d, e ) IEEE long double precision to e type + * eabs(e) absolute value + * eadd( a, b, c ) c = b + a + * eclear(e) e = 0 + * ecmp (a, b) Returns 1 if a > b, 0 if a == b, + * -1 if a < b, -2 if either a or b is a NaN. + * ediv( a, b, c ) c = b / a + * efloor( a, b ) truncate to integer, toward -infinity + * efrexp( a, exp, s ) extract exponent and significand + * eifrac( e, &l, frac ) e to long integer and e type fraction + * euifrac( e, &l, frac ) e to unsigned long integer and e type fraction + * einfin( e ) set e to infinity, leaving its sign alone + * eldexp( a, n, b ) multiply by 2**n + * emov( a, b ) b = a + * emul( a, b, c ) c = b * a + * eneg(e) e = -e + * eround( a, b ) b = nearest integer value to a + * esub( a, b, c ) c = b - a + * e24toasc( &f, str, n ) single to ASCII string, n digits after decimal + * e53toasc( &d, str, n ) double to ASCII string, n digits after decimal + * e64toasc( &d, str, n ) long double to ASCII string + * etoasc( e, str, n ) e to ASCII string, n digits after decimal + * etoe24( e, &f ) convert e type to IEEE single precision + * etoe53( e, &d ) convert e type to IEEE double precision + * etoe64( e, &d ) convert e type to IEEE long double precision + * ltoe( &l, e ) long (32 bit) integer to e type + * ultoe( &l, e ) unsigned long (32 bit) integer to e type + * eisneg( e ) 1 if sign bit of e != 0, else 0 + * eisinf( e ) 1 if e has maximum exponent (non-IEEE) + * or is infinite (IEEE) + * eisnan( e ) 1 if e is a NaN + * esqrt( a, b ) b = square root of a + * + * + * Routines for internal format numbers + * + * eaddm( ai, bi ) add significands, bi = bi + ai + * ecleaz(ei) ei = 0 + * ecleazs(ei) set ei = 0 but leave its sign alone + * ecmpm( ai, bi ) compare significands, return 1, 0, or -1 + * edivm( ai, bi ) divide significands, bi = bi / ai + * emdnorm(ai,l,s,exp) normalize and round off + * emovi( a, ai ) convert external a to internal ai + * emovo( ai, a ) convert internal ai to external a + * emovz( ai, bi ) bi = ai, low guard word of bi = 0 + * emulm( ai, bi ) multiply significands, bi = bi * ai + * enormlz(ei) left-justify the significand + * eshdn1( ai ) shift significand and guards down 1 bit + * eshdn8( ai ) shift down 8 bits + * eshdn6( ai ) shift down 16 bits + * eshift( ai, n ) shift ai n bits up (or down if n < 0) + * eshup1( ai ) shift significand and guards up 1 bit + * eshup8( ai ) shift up 8 bits + * eshup6( ai ) shift up 16 bits + * esubm( ai, bi ) subtract significands, bi = bi - ai + * + * + * The result is always normalized and rounded to NI-4 word precision + * after each arithmetic operation. + * + * Exception flags are NOT fully supported. + * + * Define INFINITY in mconf.h for support of infinity; otherwise a + * saturation arithmetic is implemented. + * + * Define NANS for support of Not-a-Number items; otherwise the + * arithmetic will never produce a NaN output, and might be confused + * by a NaN input. + * If NaN's are supported, the output of ecmp(a,b) is -2 if + * either a or b is a NaN. This means asking if(ecmp(a,b) < 0) + * may not be legitimate. Use if(ecmp(a,b) == -1) for less-than + * if in doubt. + * Signaling NaN's are NOT supported; they are treated the same + * as quiet NaN's. + * + * Denormals are always supported here where appropriate (e.g., not + * for conversion to DEC numbers). + */ + +/* + * Revision history: + * + * 5 Jan 84 PDP-11 assembly language version + * 2 Mar 86 fixed bug in asctoq() + * 6 Dec 86 C language version + * 30 Aug 88 100 digit version, improved rounding + * 15 May 92 80-bit long double support + * + * Author: S. L. Moshier. + */ + +#include <stdio.h> +/* #include "\usr\include\stdio.h" */ +#include "ehead.h" +#include "mconf.h" + +/* Change UNK into something else. */ +#ifdef UNK +#undef UNK +#define IBMPC 1 +#endif + +/* NaN's require infinity support. */ +#ifdef NANS +#ifndef INFINITY +#define INFINITY +#endif +#endif + +/* This handles 64-bit long ints. */ +#define LONGBITS (8 * sizeof(long)) + +/* Control register for rounding precision. + * This can be set to 80 (if NE=6), 64, 56, 53, or 24 bits. + */ +int rndprc = NBITS; +extern int rndprc; + +void eaddm(), esubm(), emdnorm(), asctoeg(), enan(); +static void toe24(), toe53(), toe64(), toe113(); +void eremain(), einit(), eiremain(); +int ecmpm(), edivm(), emulm(), eisneg(), eisinf(); +void emovi(), emovo(), emovz(), ecleaz(), eadd1(); +void etodec(), todec(), dectoe(); +int eisnan(), eiisnan(); + + + +void einit() +{ +} + +/* +; Clear out entire external format number. +; +; unsigned short x[]; +; eclear( x ); +*/ + +void eclear( x ) +register unsigned short *x; +{ +register int i; + +for( i=0; i<NE; i++ ) + *x++ = 0; +} + + + +/* Move external format number from a to b. + * + * emov( a, b ); + */ + +void emov( a, b ) +register unsigned short *a, *b; +{ +register int i; + +for( i=0; i<NE; i++ ) + *b++ = *a++; +} + + +/* +; Absolute value of external format number +; +; short x[NE]; +; eabs( x ); +*/ + +void eabs(x) +unsigned short x[]; /* x is the memory address of a short */ +{ + +x[NE-1] &= 0x7fff; /* sign is top bit of last word of external format */ +} + + + + +/* +; Negate external format number +; +; unsigned short x[NE]; +; eneg( x ); +*/ + +void eneg(x) +unsigned short x[]; +{ + +#ifdef NANS +if( eisnan(x) ) + return; +#endif +x[NE-1] ^= 0x8000; /* Toggle the sign bit */ +} + + + +/* Return 1 if external format number is negative, + * else return zero. + */ +int eisneg(x) +unsigned short x[]; +{ + +#ifdef NANS +if( eisnan(x) ) + return( 0 ); +#endif +if( x[NE-1] & 0x8000 ) + return( 1 ); +else + return( 0 ); +} + + +/* Return 1 if external format number has maximum possible exponent, + * else return zero. + */ +int eisinf(x) +unsigned short x[]; +{ + +if( (x[NE-1] & 0x7fff) == 0x7fff ) + { +#ifdef NANS + if( eisnan(x) ) + return( 0 ); +#endif + return( 1 ); + } +else + return( 0 ); +} + +/* Check if e-type number is not a number. + */ +int eisnan(x) +unsigned short x[]; +{ + +#ifdef NANS +int i; +/* NaN has maximum exponent */ +if( (x[NE-1] & 0x7fff) != 0x7fff ) + return (0); +/* ... and non-zero significand field. */ +for( i=0; i<NE-1; i++ ) + { + if( *x++ != 0 ) + return (1); + } +#endif +return (0); +} + +/* +; Fill entire number, including exponent and significand, with +; largest possible number. These programs implement a saturation +; value that is an ordinary, legal number. A special value +; "infinity" may also be implemented; this would require tests +; for that value and implementation of special rules for arithmetic +; operations involving inifinity. +*/ + +void einfin(x) +register unsigned short *x; +{ +register int i; + +#ifdef INFINITY +for( i=0; i<NE-1; i++ ) + *x++ = 0; +*x |= 32767; +#else +for( i=0; i<NE-1; i++ ) + *x++ = 0xffff; +*x |= 32766; +if( rndprc < NBITS ) + { + if (rndprc == 113) + { + *(x - 9) = 0; + *(x - 8) = 0; + } + if( rndprc == 64 ) + { + *(x-5) = 0; + } + if( rndprc == 53 ) + { + *(x-4) = 0xf800; + } + else + { + *(x-4) = 0; + *(x-3) = 0; + *(x-2) = 0xff00; + } + } +#endif +} + + + +/* Move in external format number, + * converting it to internal format. + */ +void emovi( a, b ) +unsigned short *a, *b; +{ +register unsigned short *p, *q; +int i; + +q = b; +p = a + (NE-1); /* point to last word of external number */ +/* get the sign bit */ +if( *p & 0x8000 ) + *q++ = 0xffff; +else + *q++ = 0; +/* get the exponent */ +*q = *p--; +*q++ &= 0x7fff; /* delete the sign bit */ +#ifdef INFINITY +if( (*(q-1) & 0x7fff) == 0x7fff ) + { +#ifdef NANS + if( eisnan(a) ) + { + *q++ = 0; + for( i=3; i<NI; i++ ) + *q++ = *p--; + return; + } +#endif + for( i=2; i<NI; i++ ) + *q++ = 0; + return; + } +#endif +/* clear high guard word */ +*q++ = 0; +/* move in the significand */ +for( i=0; i<NE-1; i++ ) + *q++ = *p--; +/* clear low guard word */ +*q = 0; +} + + +/* Move internal format number out, + * converting it to external format. + */ +void emovo( a, b ) +unsigned short *a, *b; +{ +register unsigned short *p, *q; +unsigned short i; + +p = a; +q = b + (NE-1); /* point to output exponent */ +/* combine sign and exponent */ +i = *p++; +if( i ) + *q-- = *p++ | 0x8000; +else + *q-- = *p++; +#ifdef INFINITY +if( *(p-1) == 0x7fff ) + { +#ifdef NANS + if( eiisnan(a) ) + { + enan( b, NBITS ); + return; + } +#endif + einfin(b); + return; + } +#endif +/* skip over guard word */ +++p; +/* move the significand */ +for( i=0; i<NE-1; i++ ) + *q-- = *p++; +} + + + + +/* Clear out internal format number. + */ + +void ecleaz( xi ) +register unsigned short *xi; +{ +register int i; + +for( i=0; i<NI; i++ ) + *xi++ = 0; +} + +/* same, but don't touch the sign. */ + +void ecleazs( xi ) +register unsigned short *xi; +{ +register int i; + +++xi; +for(i=0; i<NI-1; i++) + *xi++ = 0; +} + + + + +/* Move internal format number from a to b. + */ +void emovz( a, b ) +register unsigned short *a, *b; +{ +register int i; + +for( i=0; i<NI-1; i++ ) + *b++ = *a++; +/* clear low guard word */ +*b = 0; +} + +/* Return nonzero if internal format number is a NaN. + */ + +int eiisnan (x) +unsigned short x[]; +{ +int i; + +if( (x[E] & 0x7fff) == 0x7fff ) + { + for( i=M+1; i<NI; i++ ) + { + if( x[i] != 0 ) + return(1); + } + } +return(0); +} + +#ifdef INFINITY +/* Return nonzero if internal format number is infinite. */ + +static int +eiisinf (x) + unsigned short x[]; +{ + +#ifdef NANS + if (eiisnan (x)) + return (0); +#endif + if ((x[E] & 0x7fff) == 0x7fff) + return (1); + return (0); +} +#endif + +/* +; Compare significands of numbers in internal format. +; Guard words are included in the comparison. +; +; unsigned short a[NI], b[NI]; +; cmpm( a, b ); +; +; for the significands: +; returns +1 if a > b +; 0 if a == b +; -1 if a < b +*/ +int ecmpm( a, b ) +register unsigned short *a, *b; +{ +int i; + +a += M; /* skip up to significand area */ +b += M; +for( i=M; i<NI; i++ ) + { + if( *a++ != *b++ ) + goto difrnt; + } +return(0); + +difrnt: +if( *(--a) > *(--b) ) + return(1); +else + return(-1); +} + + +/* +; Shift significand down by 1 bit +*/ + +void eshdn1(x) +register unsigned short *x; +{ +register unsigned short bits; +int i; + +x += M; /* point to significand area */ + +bits = 0; +for( i=M; i<NI; i++ ) + { + if( *x & 1 ) + bits |= 1; + *x >>= 1; + if( bits & 2 ) + *x |= 0x8000; + bits <<= 1; + ++x; + } +} + + + +/* +; Shift significand up by 1 bit +*/ + +void eshup1(x) +register unsigned short *x; +{ +register unsigned short bits; +int i; + +x += NI-1; +bits = 0; + +for( i=M; i<NI; i++ ) + { + if( *x & 0x8000 ) + bits |= 1; + *x <<= 1; + if( bits & 2 ) + *x |= 1; + bits <<= 1; + --x; + } +} + + + +/* +; Shift significand down by 8 bits +*/ + +void eshdn8(x) +register unsigned short *x; +{ +register unsigned short newbyt, oldbyt; +int i; + +x += M; +oldbyt = 0; +for( i=M; i<NI; i++ ) + { + newbyt = *x << 8; + *x >>= 8; + *x |= oldbyt; + oldbyt = newbyt; + ++x; + } +} + +/* +; Shift significand up by 8 bits +*/ + +void eshup8(x) +register unsigned short *x; +{ +int i; +register unsigned short newbyt, oldbyt; + +x += NI-1; +oldbyt = 0; + +for( i=M; i<NI; i++ ) + { + newbyt = *x >> 8; + *x <<= 8; + *x |= oldbyt; + oldbyt = newbyt; + --x; + } +} + +/* +; Shift significand up by 16 bits +*/ + +void eshup6(x) +register unsigned short *x; +{ +int i; +register unsigned short *p; + +p = x + M; +x += M + 1; + +for( i=M; i<NI-1; i++ ) + *p++ = *x++; + +*p = 0; +} + +/* +; Shift significand down by 16 bits +*/ + +void eshdn6(x) +register unsigned short *x; +{ +int i; +register unsigned short *p; + +x += NI-1; +p = x + 1; + +for( i=M; i<NI-1; i++ ) + *(--p) = *(--x); + +*(--p) = 0; +} + +/* +; Add significands +; x + y replaces y +*/ + +void eaddm( x, y ) +unsigned short *x, *y; +{ +register unsigned long a; +int i; +unsigned int carry; + +x += NI-1; +y += NI-1; +carry = 0; +for( i=M; i<NI; i++ ) + { + a = (unsigned long )(*x) + (unsigned long )(*y) + carry; + if( a & 0x10000 ) + carry = 1; + else + carry = 0; + *y = (unsigned short )a; + --x; + --y; + } +} + +/* +; Subtract significands +; y - x replaces y +*/ + +void esubm( x, y ) +unsigned short *x, *y; +{ +unsigned long a; +int i; +unsigned int carry; + +x += NI-1; +y += NI-1; +carry = 0; +for( i=M; i<NI; i++ ) + { + a = (unsigned long )(*y) - (unsigned long )(*x) - carry; + if( a & 0x10000 ) + carry = 1; + else + carry = 0; + *y = (unsigned short )a; + --x; + --y; + } +} + + +/* Divide significands */ + +static unsigned short equot[NI] = {0}; /* was static */ + +#if 0 +int edivm( den, num ) +unsigned short den[], num[]; +{ +int i; +register unsigned short *p, *q; +unsigned short j; + +p = &equot[0]; +*p++ = num[0]; +*p++ = num[1]; + +for( i=M; i<NI; i++ ) + { + *p++ = 0; + } + +/* Use faster compare and subtraction if denominator + * has only 15 bits of significance. + */ +p = &den[M+2]; +if( *p++ == 0 ) + { + for( i=M+3; i<NI; i++ ) + { + if( *p++ != 0 ) + goto fulldiv; + } + if( (den[M+1] & 1) != 0 ) + goto fulldiv; + eshdn1(num); + eshdn1(den); + + p = &den[M+1]; + q = &num[M+1]; + + for( i=0; i<NBITS+2; i++ ) + { + if( *p <= *q ) + { + *q -= *p; + j = 1; + } + else + { + j = 0; + } + eshup1(equot); + equot[NI-2] |= j; + eshup1(num); + } + goto divdon; + } + +/* The number of quotient bits to calculate is + * NBITS + 1 scaling guard bit + 1 roundoff bit. + */ +fulldiv: + +p = &equot[NI-2]; +for( i=0; i<NBITS+2; i++ ) + { + if( ecmpm(den,num) <= 0 ) + { + esubm(den, num); + j = 1; /* quotient bit = 1 */ + } + else + j = 0; + eshup1(equot); + *p |= j; + eshup1(num); + } + +divdon: + +eshdn1( equot ); +eshdn1( equot ); + +/* test for nonzero remainder after roundoff bit */ +p = &num[M]; +j = 0; +for( i=M; i<NI; i++ ) + { + j |= *p++; + } +if( j ) + j = 1; + + +for( i=0; i<NI; i++ ) + num[i] = equot[i]; +return( (int )j ); +} + +/* Multiply significands */ +int emulm( a, b ) +unsigned short a[], b[]; +{ +unsigned short *p, *q; +int i, j, k; + +equot[0] = b[0]; +equot[1] = b[1]; +for( i=M; i<NI; i++ ) + equot[i] = 0; + +p = &a[NI-2]; +k = NBITS; +while( *p == 0 ) /* significand is not supposed to be all zero */ + { + eshdn6(a); + k -= 16; + } +if( (*p & 0xff) == 0 ) + { + eshdn8(a); + k -= 8; + } + +q = &equot[NI-1]; +j = 0; +for( i=0; i<k; i++ ) + { + if( *p & 1 ) + eaddm(b, equot); +/* remember if there were any nonzero bits shifted out */ + if( *q & 1 ) + j |= 1; + eshdn1(a); + eshdn1(equot); + } + +for( i=0; i<NI; i++ ) + b[i] = equot[i]; + +/* return flag for lost nonzero bits */ +return(j); +} + +#else + +/* Multiply significand of e-type number b +by 16-bit quantity a, e-type result to c. */ + +void m16m( a, b, c ) +unsigned short a; +unsigned short b[], c[]; +{ +register unsigned short *pp; +register unsigned long carry; +unsigned short *ps; +unsigned short p[NI]; +unsigned long aa, m; +int i; + +aa = a; +pp = &p[NI-2]; +*pp++ = 0; +*pp = 0; +ps = &b[NI-1]; + +for( i=M+1; i<NI; i++ ) + { + if( *ps == 0 ) + { + --ps; + --pp; + *(pp-1) = 0; + } + else + { + m = (unsigned long) aa * *ps--; + carry = (m & 0xffff) + *pp; + *pp-- = (unsigned short )carry; + carry = (carry >> 16) + (m >> 16) + *pp; + *pp = (unsigned short )carry; + *(pp-1) = carry >> 16; + } + } +for( i=M; i<NI; i++ ) + c[i] = p[i]; +} + + +/* Divide significands. Neither the numerator nor the denominator +is permitted to have its high guard word nonzero. */ + + +int edivm( den, num ) +unsigned short den[], num[]; +{ +int i; +register unsigned short *p; +unsigned long tnum; +unsigned short j, tdenm, tquot; +unsigned short tprod[NI+1]; + +p = &equot[0]; +*p++ = num[0]; +*p++ = num[1]; + +for( i=M; i<NI; i++ ) + { + *p++ = 0; + } +eshdn1( num ); +tdenm = den[M+1]; +for( i=M; i<NI; i++ ) + { + /* Find trial quotient digit (the radix is 65536). */ + tnum = (((unsigned long) num[M]) << 16) + num[M+1]; + + /* Do not execute the divide instruction if it will overflow. */ + if( (tdenm * 0xffffL) < tnum ) + tquot = 0xffff; + else + tquot = tnum / tdenm; + + /* Prove that the divide worked. */ +/* + tcheck = (unsigned long )tquot * tdenm; + if( tnum - tcheck > tdenm ) + tquot = 0xffff; +*/ + /* Multiply denominator by trial quotient digit. */ + m16m( tquot, den, tprod ); + /* The quotient digit may have been overestimated. */ + if( ecmpm( tprod, num ) > 0 ) + { + tquot -= 1; + esubm( den, tprod ); + if( ecmpm( tprod, num ) > 0 ) + { + tquot -= 1; + esubm( den, tprod ); + } + } +/* + if( ecmpm( tprod, num ) > 0 ) + { + eshow( "tprod", tprod ); + eshow( "num ", num ); + printf( "tnum = %08lx, tden = %04x, tquot = %04x\n", + tnum, den[M+1], tquot ); + } +*/ + esubm( tprod, num ); +/* + if( ecmpm( num, den ) >= 0 ) + { + eshow( "num ", num ); + eshow( "den ", den ); + printf( "tnum = %08lx, tden = %04x, tquot = %04x\n", + tnum, den[M+1], tquot ); + } +*/ + equot[i] = tquot; + eshup6(num); + } +/* test for nonzero remainder after roundoff bit */ +p = &num[M]; +j = 0; +for( i=M; i<NI; i++ ) + { + j |= *p++; + } +if( j ) + j = 1; + +for( i=0; i<NI; i++ ) + num[i] = equot[i]; + +return( (int )j ); +} + + + +/* Multiply significands */ +int emulm( a, b ) +unsigned short a[], b[]; +{ +unsigned short *p, *q; +unsigned short pprod[NI]; +unsigned short j; +int i; + +equot[0] = b[0]; +equot[1] = b[1]; +for( i=M; i<NI; i++ ) + equot[i] = 0; + +j = 0; +p = &a[NI-1]; +q = &equot[NI-1]; +for( i=M+1; i<NI; i++ ) + { + if( *p == 0 ) + { + --p; + } + else + { + m16m( *p--, b, pprod ); + eaddm(pprod, equot); + } + j |= *q; + eshdn6(equot); + } + +for( i=0; i<NI; i++ ) + b[i] = equot[i]; + +/* return flag for lost nonzero bits */ +return( (int)j ); +} + + +/* +eshow(str, x) +char *str; +unsigned short *x; +{ +int i; + +printf( "%s ", str ); +for( i=0; i<NI; i++ ) + printf( "%04x ", *x++ ); +printf( "\n" ); +} +*/ +#endif + + + +/* + * Normalize and round off. + * + * The internal format number to be rounded is "s". + * Input "lost" indicates whether the number is exact. + * This is the so-called sticky bit. + * + * Input "subflg" indicates whether the number was obtained + * by a subtraction operation. In that case if lost is nonzero + * then the number is slightly smaller than indicated. + * + * Input "exp" is the biased exponent, which may be negative. + * the exponent field of "s" is ignored but is replaced by + * "exp" as adjusted by normalization and rounding. + * + * Input "rcntrl" is the rounding control. + */ + +static int rlast = -1; +static int rw = 0; +static unsigned short rmsk = 0; +static unsigned short rmbit = 0; +static unsigned short rebit = 0; +static int re = 0; +static unsigned short rbit[NI] = {0,0,0,0,0,0,0,0}; + +void emdnorm( s, lost, subflg, exp, rcntrl ) +unsigned short s[]; +int lost; +int subflg; +long exp; +int rcntrl; +{ +int i, j; +unsigned short r; + +/* Normalize */ +j = enormlz( s ); + +/* a blank significand could mean either zero or infinity. */ +#ifndef INFINITY +if( j > NBITS ) + { + ecleazs( s ); + return; + } +#endif +exp -= j; +#ifndef INFINITY +if( exp >= 32767L ) + goto overf; +#else +if( (j > NBITS) && (exp < 32767L) ) + { + ecleazs( s ); + return; + } +#endif +if( exp < 0L ) + { + if( exp > (long )(-NBITS-1) ) + { + j = (int )exp; + i = eshift( s, j ); + if( i ) + lost = 1; + } + else + { + ecleazs( s ); + return; + } + } +/* Round off, unless told not to by rcntrl. */ +if( rcntrl == 0 ) + goto mdfin; +/* Set up rounding parameters if the control register changed. */ +if( rndprc != rlast ) + { + ecleaz( rbit ); + switch( rndprc ) + { + default: + case NBITS: + rw = NI-1; /* low guard word */ + rmsk = 0xffff; + rmbit = 0x8000; + rebit = 1; + re = rw - 1; + break; + case 113: + rw = 10; + rmsk = 0x7fff; + rmbit = 0x4000; + rebit = 0x8000; + re = rw; + break; + case 64: + rw = 7; + rmsk = 0xffff; + rmbit = 0x8000; + rebit = 1; + re = rw-1; + break; +/* For DEC arithmetic */ + case 56: + rw = 6; + rmsk = 0xff; + rmbit = 0x80; + rebit = 0x100; + re = rw; + break; + case 53: + rw = 6; + rmsk = 0x7ff; + rmbit = 0x0400; + rebit = 0x800; + re = rw; + break; + case 24: + rw = 4; + rmsk = 0xff; + rmbit = 0x80; + rebit = 0x100; + re = rw; + break; + } + rbit[re] = rebit; + rlast = rndprc; + } + +/* Shift down 1 temporarily if the data structure has an implied + * most significant bit and the number is denormal. + * For rndprc = 64 or NBITS, there is no implied bit. + * But Intel long double denormals lose one bit of significance even so. + */ +#if IBMPC +if( (exp <= 0) && (rndprc != NBITS) ) +#else +if( (exp <= 0) && (rndprc != 64) && (rndprc != NBITS) ) +#endif + { + lost |= s[NI-1] & 1; + eshdn1(s); + } +/* Clear out all bits below the rounding bit, + * remembering in r if any were nonzero. + */ +r = s[rw] & rmsk; +if( rndprc < NBITS ) + { + i = rw + 1; + while( i < NI ) + { + if( s[i] ) + r |= 1; + s[i] = 0; + ++i; + } + } +s[rw] &= ~rmsk; +if( (r & rmbit) != 0 ) + { + if( r == rmbit ) + { + if( lost == 0 ) + { /* round to even */ + if( (s[re] & rebit) == 0 ) + goto mddone; + } + else + { + if( subflg != 0 ) + goto mddone; + } + } + eaddm( rbit, s ); + } +mddone: +#if IBMPC +if( (exp <= 0) && (rndprc != NBITS) ) +#else +if( (exp <= 0) && (rndprc != 64) && (rndprc != NBITS) ) +#endif + { + eshup1(s); + } +if( s[2] != 0 ) + { /* overflow on roundoff */ + eshdn1(s); + exp += 1; + } +mdfin: +s[NI-1] = 0; +if( exp >= 32767L ) + { +#ifndef INFINITY +overf: +#endif +#ifdef INFINITY + s[1] = 32767; + for( i=2; i<NI-1; i++ ) + s[i] = 0; +#else + s[1] = 32766; + s[2] = 0; + for( i=M+1; i<NI-1; i++ ) + s[i] = 0xffff; + s[NI-1] = 0; + if( (rndprc < 64) || (rndprc == 113) ) + { + s[rw] &= ~rmsk; + if( rndprc == 24 ) + { + s[5] = 0; + s[6] = 0; + } + } +#endif + return; + } +if( exp < 0 ) + s[1] = 0; +else + s[1] = (unsigned short )exp; +} + + + +/* +; Subtract external format numbers. +; +; unsigned short a[NE], b[NE], c[NE]; +; esub( a, b, c ); c = b - a +*/ + +static int subflg = 0; + +void esub( a, b, c ) +unsigned short *a, *b, *c; +{ + +#ifdef NANS +if( eisnan(a) ) + { + emov (a, c); + return; + } +if( eisnan(b) ) + { + emov(b,c); + return; + } +/* Infinity minus infinity is a NaN. + * Test for subtracting infinities of the same sign. + */ +if( eisinf(a) && eisinf(b) && ((eisneg (a) ^ eisneg (b)) == 0)) + { + mtherr( "esub", DOMAIN ); + enan( c, NBITS ); + return; + } +#endif +subflg = 1; +eadd1( a, b, c ); +} + + +/* +; Add. +; +; unsigned short a[NE], b[NE], c[NE]; +; eadd( a, b, c ); c = b + a +*/ +void eadd( a, b, c ) +unsigned short *a, *b, *c; +{ + +#ifdef NANS +/* NaN plus anything is a NaN. */ +if( eisnan(a) ) + { + emov(a,c); + return; + } +if( eisnan(b) ) + { + emov(b,c); + return; + } +/* Infinity minus infinity is a NaN. + * Test for adding infinities of opposite signs. + */ +if( eisinf(a) && eisinf(b) + && ((eisneg(a) ^ eisneg(b)) != 0) ) + { + mtherr( "eadd", DOMAIN ); + enan( c, NBITS ); + return; + } +#endif +subflg = 0; +eadd1( a, b, c ); +} + +void eadd1( a, b, c ) +unsigned short *a, *b, *c; +{ +unsigned short ai[NI], bi[NI], ci[NI]; +int i, lost, j, k; +long lt, lta, ltb; + +#ifdef INFINITY +if( eisinf(a) ) + { + emov(a,c); + if( subflg ) + eneg(c); + return; + } +if( eisinf(b) ) + { + emov(b,c); + return; + } +#endif +emovi( a, ai ); +emovi( b, bi ); +if( subflg ) + ai[0] = ~ai[0]; + +/* compare exponents */ +lta = ai[E]; +ltb = bi[E]; +lt = lta - ltb; +if( lt > 0L ) + { /* put the larger number in bi */ + emovz( bi, ci ); + emovz( ai, bi ); + emovz( ci, ai ); + ltb = bi[E]; + lt = -lt; + } +lost = 0; +if( lt != 0L ) + { + if( lt < (long )(-NBITS-1) ) + goto done; /* answer same as larger addend */ + k = (int )lt; + lost = eshift( ai, k ); /* shift the smaller number down */ + } +else + { +/* exponents were the same, so must compare significands */ + i = ecmpm( ai, bi ); + if( i == 0 ) + { /* the numbers are identical in magnitude */ + /* if different signs, result is zero */ + if( ai[0] != bi[0] ) + { + eclear(c); + return; + } + /* if same sign, result is double */ + /* double denomalized tiny number */ + if( (bi[E] == 0) && ((bi[3] & 0x8000) == 0) ) + { + eshup1( bi ); + goto done; + } + /* add 1 to exponent unless both are zero! */ + for( j=1; j<NI-1; j++ ) + { + if( bi[j] != 0 ) + { +/* This could overflow, but let emovo take care of that. */ + ltb += 1; + break; + } + } + bi[E] = (unsigned short )ltb; + goto done; + } + if( i > 0 ) + { /* put the larger number in bi */ + emovz( bi, ci ); + emovz( ai, bi ); + emovz( ci, ai ); + } + } +if( ai[0] == bi[0] ) + { + eaddm( ai, bi ); + subflg = 0; + } +else + { + esubm( ai, bi ); + subflg = 1; + } +emdnorm( bi, lost, subflg, ltb, 64 ); + +done: +emovo( bi, c ); +} + + + +/* +; Divide. +; +; unsigned short a[NE], b[NE], c[NE]; +; ediv( a, b, c ); c = b / a +*/ +void ediv( a, b, c ) +unsigned short *a, *b, *c; +{ +unsigned short ai[NI], bi[NI]; +int i; +long lt, lta, ltb; + +#ifdef NANS +/* Return any NaN input. */ +if( eisnan(a) ) + { + emov(a,c); + return; + } +if( eisnan(b) ) + { + emov(b,c); + return; + } +/* Zero over zero, or infinity over infinity, is a NaN. */ +if( ((ecmp(a,ezero) == 0) && (ecmp(b,ezero) == 0)) + || (eisinf (a) && eisinf (b)) ) + { + mtherr( "ediv", DOMAIN ); + enan( c, NBITS ); + return; + } +#endif +/* Infinity over anything else is infinity. */ +#ifdef INFINITY +if( eisinf(b) ) + { + if( eisneg(a) ^ eisneg(b) ) + *(c+(NE-1)) = 0x8000; + else + *(c+(NE-1)) = 0; + einfin(c); + return; + } +if( eisinf(a) ) + { + eclear(c); + return; + } +#endif +emovi( a, ai ); +emovi( b, bi ); +lta = ai[E]; +ltb = bi[E]; +if( bi[E] == 0 ) + { /* See if numerator is zero. */ + for( i=1; i<NI-1; i++ ) + { + if( bi[i] != 0 ) + { + ltb -= enormlz( bi ); + goto dnzro1; + } + } + eclear(c); + return; + } +dnzro1: + +if( ai[E] == 0 ) + { /* possible divide by zero */ + for( i=1; i<NI-1; i++ ) + { + if( ai[i] != 0 ) + { + lta -= enormlz( ai ); + goto dnzro2; + } + } + if( ai[0] == bi[0] ) + *(c+(NE-1)) = 0; + else + *(c+(NE-1)) = 0x8000; + einfin(c); + mtherr( "ediv", SING ); + return; + } +dnzro2: + +i = edivm( ai, bi ); +/* calculate exponent */ +lt = ltb - lta + EXONE; +emdnorm( bi, i, 0, lt, 64 ); +/* set the sign */ +if( ai[0] == bi[0] ) + bi[0] = 0; +else + bi[0] = 0Xffff; +emovo( bi, c ); +} + + + +/* +; Multiply. +; +; unsigned short a[NE], b[NE], c[NE]; +; emul( a, b, c ); c = b * a +*/ +void emul( a, b, c ) +unsigned short *a, *b, *c; +{ +unsigned short ai[NI], bi[NI]; +int i, j; +long lt, lta, ltb; + +#ifdef NANS +/* NaN times anything is the same NaN. */ +if( eisnan(a) ) + { + emov(a,c); + return; + } +if( eisnan(b) ) + { + emov(b,c); + return; + } +/* Zero times infinity is a NaN. */ +if( (eisinf(a) && (ecmp(b,ezero) == 0)) + || (eisinf(b) && (ecmp(a,ezero) == 0)) ) + { + mtherr( "emul", DOMAIN ); + enan( c, NBITS ); + return; + } +#endif +/* Infinity times anything else is infinity. */ +#ifdef INFINITY +if( eisinf(a) || eisinf(b) ) + { + if( eisneg(a) ^ eisneg(b) ) + *(c+(NE-1)) = 0x8000; + else + *(c+(NE-1)) = 0; + einfin(c); + return; + } +#endif +emovi( a, ai ); +emovi( b, bi ); +lta = ai[E]; +ltb = bi[E]; +if( ai[E] == 0 ) + { + for( i=1; i<NI-1; i++ ) + { + if( ai[i] != 0 ) + { + lta -= enormlz( ai ); + goto mnzer1; + } + } + eclear(c); + return; + } +mnzer1: + +if( bi[E] == 0 ) + { + for( i=1; i<NI-1; i++ ) + { + if( bi[i] != 0 ) + { + ltb -= enormlz( bi ); + goto mnzer2; + } + } + eclear(c); + return; + } +mnzer2: + +/* Multiply significands */ +j = emulm( ai, bi ); +/* calculate exponent */ +lt = lta + ltb - (EXONE - 1); +emdnorm( bi, j, 0, lt, 64 ); +/* calculate sign of product */ +if( ai[0] == bi[0] ) + bi[0] = 0; +else + bi[0] = 0xffff; +emovo( bi, c ); +} + + + + +/* +; Convert IEEE double precision to e type +; double d; +; unsigned short x[N+2]; +; e53toe( &d, x ); +*/ +void e53toe( pe, y ) +unsigned short *pe, *y; +{ +#ifdef DEC + +dectoe( pe, y ); /* see etodec.c */ + +#else + +register unsigned short r; +register unsigned short *p, *e; +unsigned short yy[NI]; +int denorm, k; + +e = pe; +denorm = 0; /* flag if denormalized number */ +ecleaz(yy); +#ifdef IBMPC +e += 3; +#endif +r = *e; +yy[0] = 0; +if( r & 0x8000 ) + yy[0] = 0xffff; +yy[M] = (r & 0x0f) | 0x10; +r &= ~0x800f; /* strip sign and 4 significand bits */ +#ifdef INFINITY +if( r == 0x7ff0 ) + { +#ifdef NANS +#ifdef IBMPC + if( ((pe[3] & 0xf) != 0) || (pe[2] != 0) + || (pe[1] != 0) || (pe[0] != 0) ) + { + enan( y, NBITS ); + return; + } +#else + if( ((pe[0] & 0xf) != 0) || (pe[1] != 0) + || (pe[2] != 0) || (pe[3] != 0) ) + { + enan( y, NBITS ); + return; + } +#endif +#endif /* NANS */ + eclear( y ); + einfin( y ); + if( yy[0] ) + eneg(y); + return; + } +#endif +r >>= 4; +/* If zero exponent, then the significand is denormalized. + * So, take back the understood high significand bit. */ +if( r == 0 ) + { + denorm = 1; + yy[M] &= ~0x10; + } +r += EXONE - 01777; +yy[E] = r; +p = &yy[M+1]; +#ifdef IBMPC +*p++ = *(--e); +*p++ = *(--e); +*p++ = *(--e); +#endif +#ifdef MIEEE +++e; +*p++ = *e++; +*p++ = *e++; +*p++ = *e++; +#endif +(void )eshift( yy, -5 ); +if( denorm ) + { /* if zero exponent, then normalize the significand */ + if( (k = enormlz(yy)) > NBITS ) + ecleazs(yy); + else + yy[E] -= (unsigned short )(k-1); + } +emovo( yy, y ); +#endif /* not DEC */ +} + +void e64toe( pe, y ) +unsigned short *pe, *y; +{ +unsigned short yy[NI]; +unsigned short *p, *q, *e; +int i; + +e = pe; +p = yy; +for( i=0; i<NE-5; i++ ) + *p++ = 0; +#ifdef IBMPC +for( i=0; i<5; i++ ) + *p++ = *e++; +#endif +#ifdef DEC +for( i=0; i<5; i++ ) + *p++ = *e++; +#endif +#ifdef MIEEE +p = &yy[0] + (NE-1); +*p-- = *e++; +++e; +for( i=0; i<4; i++ ) + *p-- = *e++; +#endif + +#ifdef IBMPC +/* For Intel long double, shift denormal significand up 1 + -- but only if the top significand bit is zero. */ +if((yy[NE-1] & 0x7fff) == 0 && (yy[NE-2] & 0x8000) == 0) + { + unsigned short temp[NI+1]; + emovi(yy, temp); + eshup1(temp); + emovo(temp,y); + return; + } +#endif +#ifdef INFINITY +/* Point to the exponent field. */ +p = &yy[NE-1]; +if( *p == 0x7fff ) + { +#ifdef NANS +#ifdef IBMPC + for( i=0; i<4; i++ ) + { + if((i != 3 && pe[i] != 0) + /* Check for Intel long double infinity pattern. */ + || (i == 3 && pe[i] != 0x8000)) + { + enan( y, NBITS ); + return; + } + } +#else + for( i=1; i<=4; i++ ) + { + if( pe[i] != 0 ) + { + enan( y, NBITS ); + return; + } + } +#endif +#endif /* NANS */ + eclear( y ); + einfin( y ); + if( *p & 0x8000 ) + eneg(y); + return; + } +#endif +p = yy; +q = y; +for( i=0; i<NE; i++ ) + *q++ = *p++; +} + +void e113toe(pe,y) +unsigned short *pe, *y; +{ +register unsigned short r; +unsigned short *e, *p; +unsigned short yy[NI]; +int denorm, i; + +e = pe; +denorm = 0; +ecleaz(yy); +#ifdef IBMPC +e += 7; +#endif +r = *e; +yy[0] = 0; +if( r & 0x8000 ) + yy[0] = 0xffff; +r &= 0x7fff; +#ifdef INFINITY +if( r == 0x7fff ) + { +#ifdef NANS +#ifdef IBMPC + for( i=0; i<7; i++ ) + { + if( pe[i] != 0 ) + { + enan( y, NBITS ); + return; + } + } +#else + for( i=1; i<8; i++ ) + { + if( pe[i] != 0 ) + { + enan( y, NBITS ); + return; + } + } +#endif +#endif /* NANS */ + eclear( y ); + einfin( y ); + if( *e & 0x8000 ) + eneg(y); + return; + } +#endif /* INFINITY */ +yy[E] = r; +p = &yy[M + 1]; +#ifdef IBMPC +for( i=0; i<7; i++ ) + *p++ = *(--e); +#endif +#ifdef MIEEE +++e; +for( i=0; i<7; i++ ) + *p++ = *e++; +#endif +/* If denormal, remove the implied bit; else shift down 1. */ +if( r == 0 ) + { + yy[M] = 0; + } +else + { + yy[M] = 1; + eshift( yy, -1 ); + } +emovo(yy,y); +} + + +/* +; Convert IEEE single precision to e type +; float d; +; unsigned short x[N+2]; +; dtox( &d, x ); +*/ +void e24toe( pe, y ) +unsigned short *pe, *y; +{ +register unsigned short r; +register unsigned short *p, *e; +unsigned short yy[NI]; +int denorm, k; + +e = pe; +denorm = 0; /* flag if denormalized number */ +ecleaz(yy); +#ifdef IBMPC +e += 1; +#endif +#ifdef DEC +e += 1; +#endif +r = *e; +yy[0] = 0; +if( r & 0x8000 ) + yy[0] = 0xffff; +yy[M] = (r & 0x7f) | 0200; +r &= ~0x807f; /* strip sign and 7 significand bits */ +#ifdef INFINITY +if( r == 0x7f80 ) + { +#ifdef NANS +#ifdef MIEEE + if( ((pe[0] & 0x7f) != 0) || (pe[1] != 0) ) + { + enan( y, NBITS ); + return; + } +#else + if( ((pe[1] & 0x7f) != 0) || (pe[0] != 0) ) + { + enan( y, NBITS ); + return; + } +#endif +#endif /* NANS */ + eclear( y ); + einfin( y ); + if( yy[0] ) + eneg(y); + return; + } +#endif +r >>= 7; +/* If zero exponent, then the significand is denormalized. + * So, take back the understood high significand bit. */ +if( r == 0 ) + { + denorm = 1; + yy[M] &= ~0200; + } +r += EXONE - 0177; +yy[E] = r; +p = &yy[M+1]; +#ifdef IBMPC +*p++ = *(--e); +#endif +#ifdef DEC +*p++ = *(--e); +#endif +#ifdef MIEEE +++e; +*p++ = *e++; +#endif +(void )eshift( yy, -8 ); +if( denorm ) + { /* if zero exponent, then normalize the significand */ + if( (k = enormlz(yy)) > NBITS ) + ecleazs(yy); + else + yy[E] -= (unsigned short )(k-1); + } +emovo( yy, y ); +} + +void etoe113(x,e) +unsigned short *x, *e; +{ +unsigned short xi[NI]; +long exp; +int rndsav; + +#ifdef NANS +if( eisnan(x) ) + { + enan( e, 113 ); + return; + } +#endif +emovi( x, xi ); +exp = (long )xi[E]; +#ifdef INFINITY +if( eisinf(x) ) + goto nonorm; +#endif +/* round off to nearest or even */ +rndsav = rndprc; +rndprc = 113; +emdnorm( xi, 0, 0, exp, 64 ); +rndprc = rndsav; +nonorm: +toe113 (xi, e); +} + +/* move out internal format to ieee long double */ +static void toe113(a,b) +unsigned short *a, *b; +{ +register unsigned short *p, *q; +unsigned short i; + +#ifdef NANS +if( eiisnan(a) ) + { + enan( b, 113 ); + return; + } +#endif +p = a; +#ifdef MIEEE +q = b; +#else +q = b + 7; /* point to output exponent */ +#endif + +/* If not denormal, delete the implied bit. */ +if( a[E] != 0 ) + { + eshup1 (a); + } +/* combine sign and exponent */ +i = *p++; +#ifdef MIEEE +if( i ) + *q++ = *p++ | 0x8000; +else + *q++ = *p++; +#else +if( i ) + *q-- = *p++ | 0x8000; +else + *q-- = *p++; +#endif +/* skip over guard word */ +++p; +/* move the significand */ +#ifdef MIEEE +for (i = 0; i < 7; i++) + *q++ = *p++; +#else +for (i = 0; i < 7; i++) + *q-- = *p++; +#endif +} + + +void etoe64( x, e ) +unsigned short *x, *e; +{ +unsigned short xi[NI]; +long exp; +int rndsav; + +#ifdef NANS +if( eisnan(x) ) + { + enan( e, 64 ); + return; + } +#endif +emovi( x, xi ); +exp = (long )xi[E]; /* adjust exponent for offset */ +#ifdef INFINITY +if( eisinf(x) ) + goto nonorm; +#endif +/* round off to nearest or even */ +rndsav = rndprc; +rndprc = 64; +emdnorm( xi, 0, 0, exp, 64 ); +rndprc = rndsav; +nonorm: +toe64( xi, e ); +} + +/* move out internal format to ieee long double */ +static void toe64( a, b ) +unsigned short *a, *b; +{ +register unsigned short *p, *q; +unsigned short i; + +#ifdef NANS +if( eiisnan(a) ) + { + enan( b, 64 ); + return; + } +#endif +#ifdef IBMPC +/* Shift Intel denormal significand down 1. */ +if( a[E] == 0 ) + eshdn1(a); +#endif +p = a; +#ifdef MIEEE +q = b; +#else +q = b + 4; /* point to output exponent */ +#if 1 +/* NOTE: if data type is 96 bits wide, clear the last word here. */ +*(q+1)= 0; +#endif +#endif + +/* combine sign and exponent */ +i = *p++; +#ifdef MIEEE +if( i ) + *q++ = *p++ | 0x8000; +else + *q++ = *p++; +*q++ = 0; +#else +if( i ) + *q-- = *p++ | 0x8000; +else + *q-- = *p++; +#endif +/* skip over guard word */ +++p; +/* move the significand */ +#ifdef MIEEE +for( i=0; i<4; i++ ) + *q++ = *p++; +#else +#ifdef INFINITY +if (eiisinf (a)) + { + /* Intel long double infinity. */ + *q-- = 0x8000; + *q-- = 0; + *q-- = 0; + *q = 0; + return; + } +#endif +for( i=0; i<4; i++ ) + *q-- = *p++; +#endif +} + + +/* +; e type to IEEE double precision +; double d; +; unsigned short x[NE]; +; etoe53( x, &d ); +*/ + +#ifdef DEC + +void etoe53( x, e ) +unsigned short *x, *e; +{ +etodec( x, e ); /* see etodec.c */ +} + +static void toe53( x, y ) +unsigned short *x, *y; +{ +todec( x, y ); +} + +#else + +void etoe53( x, e ) +unsigned short *x, *e; +{ +unsigned short xi[NI]; +long exp; +int rndsav; + +#ifdef NANS +if( eisnan(x) ) + { + enan( e, 53 ); + return; + } +#endif +emovi( x, xi ); +exp = (long )xi[E] - (EXONE - 0x3ff); /* adjust exponent for offsets */ +#ifdef INFINITY +if( eisinf(x) ) + goto nonorm; +#endif +/* round off to nearest or even */ +rndsav = rndprc; +rndprc = 53; +emdnorm( xi, 0, 0, exp, 64 ); +rndprc = rndsav; +nonorm: +toe53( xi, e ); +} + + +static void toe53( x, y ) +unsigned short *x, *y; +{ +unsigned short i; +unsigned short *p; + + +#ifdef NANS +if( eiisnan(x) ) + { + enan( y, 53 ); + return; + } +#endif +p = &x[0]; +#ifdef IBMPC +y += 3; +#endif +*y = 0; /* output high order */ +if( *p++ ) + *y = 0x8000; /* output sign bit */ + +i = *p++; +if( i >= (unsigned int )2047 ) + { /* Saturate at largest number less than infinity. */ +#ifdef INFINITY + *y |= 0x7ff0; +#ifdef IBMPC + *(--y) = 0; + *(--y) = 0; + *(--y) = 0; +#endif +#ifdef MIEEE + ++y; + *y++ = 0; + *y++ = 0; + *y++ = 0; +#endif +#else + *y |= (unsigned short )0x7fef; +#ifdef IBMPC + *(--y) = 0xffff; + *(--y) = 0xffff; + *(--y) = 0xffff; +#endif +#ifdef MIEEE + ++y; + *y++ = 0xffff; + *y++ = 0xffff; + *y++ = 0xffff; +#endif +#endif + return; + } +if( i == 0 ) + { + (void )eshift( x, 4 ); + } +else + { + i <<= 4; + (void )eshift( x, 5 ); + } +i |= *p++ & (unsigned short )0x0f; /* *p = xi[M] */ +*y |= (unsigned short )i; /* high order output already has sign bit set */ +#ifdef IBMPC +*(--y) = *p++; +*(--y) = *p++; +*(--y) = *p; +#endif +#ifdef MIEEE +++y; +*y++ = *p++; +*y++ = *p++; +*y++ = *p++; +#endif +} + +#endif /* not DEC */ + + + +/* +; e type to IEEE single precision +; float d; +; unsigned short x[N+2]; +; xtod( x, &d ); +*/ +void etoe24( x, e ) +unsigned short *x, *e; +{ +long exp; +unsigned short xi[NI]; +int rndsav; + +#ifdef NANS +if( eisnan(x) ) + { + enan( e, 24 ); + return; + } +#endif +emovi( x, xi ); +exp = (long )xi[E] - (EXONE - 0177); /* adjust exponent for offsets */ +#ifdef INFINITY +if( eisinf(x) ) + goto nonorm; +#endif +/* round off to nearest or even */ +rndsav = rndprc; +rndprc = 24; +emdnorm( xi, 0, 0, exp, 64 ); +rndprc = rndsav; +nonorm: +toe24( xi, e ); +} + +static void toe24( x, y ) +unsigned short *x, *y; +{ +unsigned short i; +unsigned short *p; + +#ifdef NANS +if( eiisnan(x) ) + { + enan( y, 24 ); + return; + } +#endif +p = &x[0]; +#ifdef IBMPC +y += 1; +#endif +#ifdef DEC +y += 1; +#endif +*y = 0; /* output high order */ +if( *p++ ) + *y = 0x8000; /* output sign bit */ + +i = *p++; +if( i >= 255 ) + { /* Saturate at largest number less than infinity. */ +#ifdef INFINITY + *y |= (unsigned short )0x7f80; +#ifdef IBMPC + *(--y) = 0; +#endif +#ifdef DEC + *(--y) = 0; +#endif +#ifdef MIEEE + ++y; + *y = 0; +#endif +#else + *y |= (unsigned short )0x7f7f; +#ifdef IBMPC + *(--y) = 0xffff; +#endif +#ifdef DEC + *(--y) = 0xffff; +#endif +#ifdef MIEEE + ++y; + *y = 0xffff; +#endif +#endif + return; + } +if( i == 0 ) + { + (void )eshift( x, 7 ); + } +else + { + i <<= 7; + (void )eshift( x, 8 ); + } +i |= *p++ & (unsigned short )0x7f; /* *p = xi[M] */ +*y |= i; /* high order output already has sign bit set */ +#ifdef IBMPC +*(--y) = *p; +#endif +#ifdef DEC +*(--y) = *p; +#endif +#ifdef MIEEE +++y; +*y = *p; +#endif +} + + +/* Compare two e type numbers. + * + * unsigned short a[NE], b[NE]; + * ecmp( a, b ); + * + * returns +1 if a > b + * 0 if a == b + * -1 if a < b + * -2 if either a or b is a NaN. + */ +int ecmp( a, b ) +unsigned short *a, *b; +{ +unsigned short ai[NI], bi[NI]; +register unsigned short *p, *q; +register int i; +int msign; + +#ifdef NANS +if (eisnan (a) || eisnan (b)) + return( -2 ); +#endif +emovi( a, ai ); +p = ai; +emovi( b, bi ); +q = bi; + +if( *p != *q ) + { /* the signs are different */ +/* -0 equals + 0 */ + for( i=1; i<NI-1; i++ ) + { + if( ai[i] != 0 ) + goto nzro; + if( bi[i] != 0 ) + goto nzro; + } + return(0); +nzro: + if( *p == 0 ) + return( 1 ); + else + return( -1 ); + } +/* both are the same sign */ +if( *p == 0 ) + msign = 1; +else + msign = -1; +i = NI-1; +do + { + if( *p++ != *q++ ) + { + goto diff; + } + } +while( --i > 0 ); + +return(0); /* equality */ + + + +diff: + +if( *(--p) > *(--q) ) + return( msign ); /* p is bigger */ +else + return( -msign ); /* p is littler */ +} + + + + +/* Find nearest integer to x = floor( x + 0.5 ) + * + * unsigned short x[NE], y[NE] + * eround( x, y ); + */ +void eround( x, y ) +unsigned short *x, *y; +{ + +eadd( ehalf, x, y ); +efloor( y, y ); +} + + + + +/* +; convert long (32-bit) integer to e type +; +; long l; +; unsigned short x[NE]; +; ltoe( &l, x ); +; note &l is the memory address of l +*/ +void ltoe( lp, y ) +long *lp; /* lp is the memory address of a long integer */ +unsigned short *y; /* y is the address of a short */ +{ +unsigned short yi[NI]; +unsigned long ll; +int k; + +ecleaz( yi ); +if( *lp < 0 ) + { + ll = (unsigned long )( -(*lp) ); /* make it positive */ + yi[0] = 0xffff; /* put correct sign in the e type number */ + } +else + { + ll = (unsigned long )( *lp ); + } +/* move the long integer to yi significand area */ +if( sizeof(long) == 8 ) + { + yi[M] = (unsigned short) (ll >> (LONGBITS - 16)); + yi[M + 1] = (unsigned short) (ll >> (LONGBITS - 32)); + yi[M + 2] = (unsigned short) (ll >> 16); + yi[M + 3] = (unsigned short) ll; + yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */ + } +else + { + yi[M] = (unsigned short )(ll >> 16); + yi[M+1] = (unsigned short )ll; + yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */ + } +if( (k = enormlz( yi )) > NBITS ) /* normalize the significand */ + ecleaz( yi ); /* it was zero */ +else + yi[E] -= (unsigned short )k; /* subtract shift count from exponent */ +emovo( yi, y ); /* output the answer */ +} + +/* +; convert unsigned long (32-bit) integer to e type +; +; unsigned long l; +; unsigned short x[NE]; +; ltox( &l, x ); +; note &l is the memory address of l +*/ +void ultoe( lp, y ) +unsigned long *lp; /* lp is the memory address of a long integer */ +unsigned short *y; /* y is the address of a short */ +{ +unsigned short yi[NI]; +unsigned long ll; +int k; + +ecleaz( yi ); +ll = *lp; + +/* move the long integer to ayi significand area */ +if( sizeof(long) == 8 ) + { + yi[M] = (unsigned short) (ll >> (LONGBITS - 16)); + yi[M + 1] = (unsigned short) (ll >> (LONGBITS - 32)); + yi[M + 2] = (unsigned short) (ll >> 16); + yi[M + 3] = (unsigned short) ll; + yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */ + } +else + { + yi[M] = (unsigned short )(ll >> 16); + yi[M+1] = (unsigned short )ll; + yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */ + } +if( (k = enormlz( yi )) > NBITS ) /* normalize the significand */ + ecleaz( yi ); /* it was zero */ +else + yi[E] -= (unsigned short )k; /* subtract shift count from exponent */ +emovo( yi, y ); /* output the answer */ +} + + +/* +; Find long integer and fractional parts + +; long i; +; unsigned short x[NE], frac[NE]; +; xifrac( x, &i, frac ); + + The integer output has the sign of the input. The fraction is + the positive fractional part of abs(x). +*/ +void eifrac( x, i, frac ) +unsigned short *x; +long *i; +unsigned short *frac; +{ +unsigned short xi[NI]; +int j, k; +unsigned long ll; + +emovi( x, xi ); +k = (int )xi[E] - (EXONE - 1); +if( k <= 0 ) + { +/* if exponent <= 0, integer = 0 and real output is fraction */ + *i = 0L; + emovo( xi, frac ); + return; + } +if( k > (8 * sizeof(long) - 1) ) + { +/* +; long integer overflow: output large integer +; and correct fraction +*/ + j = 8 * sizeof(long) - 1; + if( xi[0] ) + *i = (long) ((unsigned long) 1) << j; + else + *i = (long) (((unsigned long) (~(0L))) >> 1); + (void )eshift( xi, k ); + } +if( k > 16 ) + { +/* + Shift more than 16 bits: shift up k-16 mod 16 + then shift by 16's. +*/ + j = k - ((k >> 4) << 4); + eshift (xi, j); + ll = xi[M]; + k -= j; + do + { + eshup6 (xi); + ll = (ll << 16) | xi[M]; + } + while ((k -= 16) > 0); + *i = ll; + if (xi[0]) + *i = -(*i); + } +else + { +/* shift not more than 16 bits */ + eshift( xi, k ); + *i = (long )xi[M] & 0xffff; + if( xi[0] ) + *i = -(*i); + } +xi[0] = 0; +xi[E] = EXONE - 1; +xi[M] = 0; +if( (k = enormlz( xi )) > NBITS ) + ecleaz( xi ); +else + xi[E] -= (unsigned short )k; + +emovo( xi, frac ); +} + + +/* +; Find unsigned long integer and fractional parts + +; unsigned long i; +; unsigned short x[NE], frac[NE]; +; xifrac( x, &i, frac ); + + A negative e type input yields integer output = 0 + but correct fraction. +*/ +void euifrac( x, i, frac ) +unsigned short *x; +unsigned long *i; +unsigned short *frac; +{ +unsigned short xi[NI]; +int j, k; +unsigned long ll; + +emovi( x, xi ); +k = (int )xi[E] - (EXONE - 1); +if( k <= 0 ) + { +/* if exponent <= 0, integer = 0 and argument is fraction */ + *i = 0L; + emovo( xi, frac ); + return; + } +if( k > (8 * sizeof(long)) ) + { +/* +; long integer overflow: output large integer +; and correct fraction +*/ + *i = ~(0L); + (void )eshift( xi, k ); + } +else if( k > 16 ) + { +/* + Shift more than 16 bits: shift up k-16 mod 16 + then shift up by 16's. +*/ + j = k - ((k >> 4) << 4); + eshift (xi, j); + ll = xi[M]; + k -= j; + do + { + eshup6 (xi); + ll = (ll << 16) | xi[M]; + } + while ((k -= 16) > 0); + *i = ll; + } +else + { +/* shift not more than 16 bits */ + eshift( xi, k ); + *i = (long )xi[M] & 0xffff; + } + +if( xi[0] ) /* A negative value yields unsigned integer 0. */ + *i = 0L; + +xi[0] = 0; +xi[E] = EXONE - 1; +xi[M] = 0; +if( (k = enormlz( xi )) > NBITS ) + ecleaz( xi ); +else + xi[E] -= (unsigned short )k; + +emovo( xi, frac ); +} + + + +/* +; Shift significand +; +; Shifts significand area up or down by the number of bits +; given by the variable sc. +*/ +int eshift( x, sc ) +unsigned short *x; +int sc; +{ +unsigned short lost; +unsigned short *p; + +if( sc == 0 ) + return( 0 ); + +lost = 0; +p = x + NI-1; + +if( sc < 0 ) + { + sc = -sc; + while( sc >= 16 ) + { + lost |= *p; /* remember lost bits */ + eshdn6(x); + sc -= 16; + } + + while( sc >= 8 ) + { + lost |= *p & 0xff; + eshdn8(x); + sc -= 8; + } + + while( sc > 0 ) + { + lost |= *p & 1; + eshdn1(x); + sc -= 1; + } + } +else + { + while( sc >= 16 ) + { + eshup6(x); + sc -= 16; + } + + while( sc >= 8 ) + { + eshup8(x); + sc -= 8; + } + + while( sc > 0 ) + { + eshup1(x); + sc -= 1; + } + } +if( lost ) + lost = 1; +return( (int )lost ); +} + + + +/* +; normalize +; +; Shift normalizes the significand area pointed to by argument +; shift count (up = positive) is returned. +*/ +int enormlz(x) +unsigned short x[]; +{ +register unsigned short *p; +int sc; + +sc = 0; +p = &x[M]; +if( *p != 0 ) + goto normdn; +++p; +if( *p & 0x8000 ) + return( 0 ); /* already normalized */ +while( *p == 0 ) + { + eshup6(x); + sc += 16; +/* With guard word, there are NBITS+16 bits available. + * return true if all are zero. + */ + if( sc > NBITS ) + return( sc ); + } +/* see if high byte is zero */ +while( (*p & 0xff00) == 0 ) + { + eshup8(x); + sc += 8; + } +/* now shift 1 bit at a time */ +while( (*p & 0x8000) == 0) + { + eshup1(x); + sc += 1; + if( sc > (NBITS+16) ) + { + mtherr( "enormlz", UNDERFLOW ); + return( sc ); + } + } +return( sc ); + +/* Normalize by shifting down out of the high guard word + of the significand */ +normdn: + +if( *p & 0xff00 ) + { + eshdn8(x); + sc -= 8; + } +while( *p != 0 ) + { + eshdn1(x); + sc -= 1; + + if( sc < -NBITS ) + { + mtherr( "enormlz", OVERFLOW ); + return( sc ); + } + } +return( sc ); +} + + + + +/* Convert e type number to decimal format ASCII string. + * The constants are for 64 bit precision. + */ + +#define NTEN 12 +#define MAXP 4096 + +#if NE == 10 +static unsigned short etens[NTEN + 1][NE] = +{ + {0x6576, 0x4a92, 0x804a, 0x153f, + 0xc94c, 0x979a, 0x8a20, 0x5202, 0xc460, 0x7525,}, /* 10**4096 */ + {0x6a32, 0xce52, 0x329a, 0x28ce, + 0xa74d, 0x5de4, 0xc53d, 0x3b5d, 0x9e8b, 0x5a92,}, /* 10**2048 */ + {0x526c, 0x50ce, 0xf18b, 0x3d28, + 0x650d, 0x0c17, 0x8175, 0x7586, 0xc976, 0x4d48,}, + {0x9c66, 0x58f8, 0xbc50, 0x5c54, + 0xcc65, 0x91c6, 0xa60e, 0xa0ae, 0xe319, 0x46a3,}, + {0x851e, 0xeab7, 0x98fe, 0x901b, + 0xddbb, 0xde8d, 0x9df9, 0xebfb, 0xaa7e, 0x4351,}, + {0x0235, 0x0137, 0x36b1, 0x336c, + 0xc66f, 0x8cdf, 0x80e9, 0x47c9, 0x93ba, 0x41a8,}, + {0x50f8, 0x25fb, 0xc76b, 0x6b71, + 0x3cbf, 0xa6d5, 0xffcf, 0x1f49, 0xc278, 0x40d3,}, + {0x0000, 0x0000, 0x0000, 0x0000, + 0xf020, 0xb59d, 0x2b70, 0xada8, 0x9dc5, 0x4069,}, + {0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0400, 0xc9bf, 0x8e1b, 0x4034,}, + {0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x2000, 0xbebc, 0x4019,}, + {0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x9c40, 0x400c,}, + {0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0xc800, 0x4005,}, + {0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0xa000, 0x4002,}, /* 10**1 */ +}; + +static unsigned short emtens[NTEN + 1][NE] = +{ + {0x2030, 0xcffc, 0xa1c3, 0x8123, + 0x2de3, 0x9fde, 0xd2ce, 0x04c8, 0xa6dd, 0x0ad8,}, /* 10**-4096 */ + {0x8264, 0xd2cb, 0xf2ea, 0x12d4, + 0x4925, 0x2de4, 0x3436, 0x534f, 0xceae, 0x256b,}, /* 10**-2048 */ + {0xf53f, 0xf698, 0x6bd3, 0x0158, + 0x87a6, 0xc0bd, 0xda57, 0x82a5, 0xa2a6, 0x32b5,}, + {0xe731, 0x04d4, 0xe3f2, 0xd332, + 0x7132, 0xd21c, 0xdb23, 0xee32, 0x9049, 0x395a,}, + {0xa23e, 0x5308, 0xfefb, 0x1155, + 0xfa91, 0x1939, 0x637a, 0x4325, 0xc031, 0x3cac,}, + {0xe26d, 0xdbde, 0xd05d, 0xb3f6, + 0xac7c, 0xe4a0, 0x64bc, 0x467c, 0xddd0, 0x3e55,}, + {0x2a20, 0x6224, 0x47b3, 0x98d7, + 0x3f23, 0xe9a5, 0xa539, 0xea27, 0xa87f, 0x3f2a,}, + {0x0b5b, 0x4af2, 0xa581, 0x18ed, + 0x67de, 0x94ba, 0x4539, 0x1ead, 0xcfb1, 0x3f94,}, + {0xbf71, 0xa9b3, 0x7989, 0xbe68, + 0x4c2e, 0xe15b, 0xc44d, 0x94be, 0xe695, 0x3fc9,}, + {0x3d4d, 0x7c3d, 0x36ba, 0x0d2b, + 0xfdc2, 0xcefc, 0x8461, 0x7711, 0xabcc, 0x3fe4,}, + {0xc155, 0xa4a8, 0x404e, 0x6113, + 0xd3c3, 0x652b, 0xe219, 0x1758, 0xd1b7, 0x3ff1,}, + {0xd70a, 0x70a3, 0x0a3d, 0xa3d7, + 0x3d70, 0xd70a, 0x70a3, 0x0a3d, 0xa3d7, 0x3ff8,}, + {0xcccd, 0xcccc, 0xcccc, 0xcccc, + 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0x3ffb,}, /* 10**-1 */ +}; +#else +static unsigned short etens[NTEN+1][NE] = { +{0xc94c,0x979a,0x8a20,0x5202,0xc460,0x7525,},/* 10**4096 */ +{0xa74d,0x5de4,0xc53d,0x3b5d,0x9e8b,0x5a92,},/* 10**2048 */ +{0x650d,0x0c17,0x8175,0x7586,0xc976,0x4d48,}, +{0xcc65,0x91c6,0xa60e,0xa0ae,0xe319,0x46a3,}, +{0xddbc,0xde8d,0x9df9,0xebfb,0xaa7e,0x4351,}, +{0xc66f,0x8cdf,0x80e9,0x47c9,0x93ba,0x41a8,}, +{0x3cbf,0xa6d5,0xffcf,0x1f49,0xc278,0x40d3,}, +{0xf020,0xb59d,0x2b70,0xada8,0x9dc5,0x4069,}, +{0x0000,0x0000,0x0400,0xc9bf,0x8e1b,0x4034,}, +{0x0000,0x0000,0x0000,0x2000,0xbebc,0x4019,}, +{0x0000,0x0000,0x0000,0x0000,0x9c40,0x400c,}, +{0x0000,0x0000,0x0000,0x0000,0xc800,0x4005,}, +{0x0000,0x0000,0x0000,0x0000,0xa000,0x4002,}, /* 10**1 */ +}; + +static unsigned short emtens[NTEN+1][NE] = { +{0x2de4,0x9fde,0xd2ce,0x04c8,0xa6dd,0x0ad8,}, /* 10**-4096 */ +{0x4925,0x2de4,0x3436,0x534f,0xceae,0x256b,}, /* 10**-2048 */ +{0x87a6,0xc0bd,0xda57,0x82a5,0xa2a6,0x32b5,}, +{0x7133,0xd21c,0xdb23,0xee32,0x9049,0x395a,}, +{0xfa91,0x1939,0x637a,0x4325,0xc031,0x3cac,}, +{0xac7d,0xe4a0,0x64bc,0x467c,0xddd0,0x3e55,}, +{0x3f24,0xe9a5,0xa539,0xea27,0xa87f,0x3f2a,}, +{0x67de,0x94ba,0x4539,0x1ead,0xcfb1,0x3f94,}, +{0x4c2f,0xe15b,0xc44d,0x94be,0xe695,0x3fc9,}, +{0xfdc2,0xcefc,0x8461,0x7711,0xabcc,0x3fe4,}, +{0xd3c3,0x652b,0xe219,0x1758,0xd1b7,0x3ff1,}, +{0x3d71,0xd70a,0x70a3,0x0a3d,0xa3d7,0x3ff8,}, +{0xcccd,0xcccc,0xcccc,0xcccc,0xcccc,0x3ffb,}, /* 10**-1 */ +}; +#endif + +void e24toasc( x, string, ndigs ) +unsigned short x[]; +char *string; +int ndigs; +{ +unsigned short w[NI]; + +e24toe( x, w ); +etoasc( w, string, ndigs ); +} + + +void e53toasc( x, string, ndigs ) +unsigned short x[]; +char *string; +int ndigs; +{ +unsigned short w[NI]; + +e53toe( x, w ); +etoasc( w, string, ndigs ); +} + + +void e64toasc( x, string, ndigs ) +unsigned short x[]; +char *string; +int ndigs; +{ +unsigned short w[NI]; + +e64toe( x, w ); +etoasc( w, string, ndigs ); +} + +void e113toasc (x, string, ndigs) +unsigned short x[]; +char *string; +int ndigs; +{ +unsigned short w[NI]; + +e113toe (x, w); +etoasc (w, string, ndigs); +} + + +void etoasc( x, string, ndigs ) +unsigned short x[]; +char *string; +int ndigs; +{ +long digit; +unsigned short y[NI], t[NI], u[NI], w[NI]; +unsigned short *p, *r, *ten; +unsigned short sign; +int i, j, k, expon, rndsav; +char *s, *ss; +unsigned short m; + +rndsav = rndprc; +#ifdef NANS +if( eisnan(x) ) + { + sprintf( string, " NaN " ); + goto bxit; + } +#endif +rndprc = NBITS; /* set to full precision */ +emov( x, y ); /* retain external format */ +if( y[NE-1] & 0x8000 ) + { + sign = 0xffff; + y[NE-1] &= 0x7fff; + } +else + { + sign = 0; + } +expon = 0; +ten = &etens[NTEN][0]; +emov( eone, t ); +/* Test for zero exponent */ +if( y[NE-1] == 0 ) + { + for( k=0; k<NE-1; k++ ) + { + if( y[k] != 0 ) + goto tnzro; /* denormalized number */ + } + goto isone; /* legal all zeros */ + } +tnzro: + +/* Test for infinity. + */ +if( y[NE-1] == 0x7fff ) + { + if( sign ) + sprintf( string, " -Infinity " ); + else + sprintf( string, " Infinity " ); + goto bxit; + } + +/* Test for exponent nonzero but significand denormalized. + * This is an error condition. + */ +if( (y[NE-1] != 0) && ((y[NE-2] & 0x8000) == 0) ) + { + mtherr( "etoasc", DOMAIN ); + sprintf( string, "NaN" ); + goto bxit; + } + +/* Compare to 1.0 */ +i = ecmp( eone, y ); +if( i == 0 ) + goto isone; + +if( i < 0 ) + { /* Number is greater than 1 */ +/* Convert significand to an integer and strip trailing decimal zeros. */ + emov( y, u ); + u[NE-1] = EXONE + NBITS - 1; + + p = &etens[NTEN-4][0]; + m = 16; +do + { + ediv( p, u, t ); + efloor( t, w ); + for( j=0; j<NE-1; j++ ) + { + if( t[j] != w[j] ) + goto noint; + } + emov( t, u ); + expon += (int )m; +noint: + p += NE; + m >>= 1; + } +while( m != 0 ); + +/* Rescale from integer significand */ + u[NE-1] += y[NE-1] - (unsigned int )(EXONE + NBITS - 1); + emov( u, y ); +/* Find power of 10 */ + emov( eone, t ); + m = MAXP; + p = &etens[0][0]; + while( ecmp( ten, u ) <= 0 ) + { + if( ecmp( p, u ) <= 0 ) + { + ediv( p, u, u ); + emul( p, t, t ); + expon += (int )m; + } + m >>= 1; + if( m == 0 ) + break; + p += NE; + } + } +else + { /* Number is less than 1.0 */ +/* Pad significand with trailing decimal zeros. */ + if( y[NE-1] == 0 ) + { + while( (y[NE-2] & 0x8000) == 0 ) + { + emul( ten, y, y ); + expon -= 1; + } + } + else + { + emovi( y, w ); + for( i=0; i<NDEC+1; i++ ) + { + if( (w[NI-1] & 0x7) != 0 ) + break; +/* multiply by 10 */ + emovz( w, u ); + eshdn1( u ); + eshdn1( u ); + eaddm( w, u ); + u[1] += 3; + while( u[2] != 0 ) + { + eshdn1(u); + u[1] += 1; + } + if( u[NI-1] != 0 ) + break; + if( eone[NE-1] <= u[1] ) + break; + emovz( u, w ); + expon -= 1; + } + emovo( w, y ); + } + k = -MAXP; + p = &emtens[0][0]; + r = &etens[0][0]; + emov( y, w ); + emov( eone, t ); + while( ecmp( eone, w ) > 0 ) + { + if( ecmp( p, w ) >= 0 ) + { + emul( r, w, w ); + emul( r, t, t ); + expon += k; + } + k /= 2; + if( k == 0 ) + break; + p += NE; + r += NE; + } + ediv( t, eone, t ); + } +isone: +/* Find the first (leading) digit. */ +emovi( t, w ); +emovz( w, t ); +emovi( y, w ); +emovz( w, y ); +eiremain( t, y ); +digit = equot[NI-1]; +while( (digit == 0) && (ecmp(y,ezero) != 0) ) + { + eshup1( y ); + emovz( y, u ); + eshup1( u ); + eshup1( u ); + eaddm( u, y ); + eiremain( t, y ); + digit = equot[NI-1]; + expon -= 1; + } +s = string; +if( sign ) + *s++ = '-'; +else + *s++ = ' '; +/* Examine number of digits requested by caller. */ +if( ndigs < 0 ) + ndigs = 0; +if( ndigs > NDEC ) + ndigs = NDEC; +if( digit == 10 ) + { + *s++ = '1'; + *s++ = '.'; + if( ndigs > 0 ) + { + *s++ = '0'; + ndigs -= 1; + } + expon += 1; + } +else + { + *s++ = (char )digit + '0'; + *s++ = '.'; + } +/* Generate digits after the decimal point. */ +for( k=0; k<=ndigs; k++ ) + { +/* multiply current number by 10, without normalizing */ + eshup1( y ); + emovz( y, u ); + eshup1( u ); + eshup1( u ); + eaddm( u, y ); + eiremain( t, y ); + *s++ = (char )equot[NI-1] + '0'; + } +digit = equot[NI-1]; +--s; +ss = s; +/* round off the ASCII string */ +if( digit > 4 ) + { +/* Test for critical rounding case in ASCII output. */ + if( digit == 5 ) + { + emovo( y, t ); + if( ecmp(t,ezero) != 0 ) + goto roun; /* round to nearest */ + if( (*(s-1) & 1) == 0 ) + goto doexp; /* round to even */ + } +/* Round up and propagate carry-outs */ +roun: + --s; + k = *s & 0x7f; +/* Carry out to most significant digit? */ + if( k == '.' ) + { + --s; + k = *s; + k += 1; + *s = (char )k; +/* Most significant digit carries to 10? */ + if( k > '9' ) + { + expon += 1; + *s = '1'; + } + goto doexp; + } +/* Round up and carry out from less significant digits */ + k += 1; + *s = (char )k; + if( k > '9' ) + { + *s = '0'; + goto roun; + } + } +doexp: +/* +if( expon >= 0 ) + sprintf( ss, "e+%d", expon ); +else + sprintf( ss, "e%d", expon ); +*/ + sprintf( ss, "E%d", expon ); +bxit: +rndprc = rndsav; +} + + + + +/* +; ASCTOQ +; ASCTOQ.MAC LATEST REV: 11 JAN 84 +; SLM, 3 JAN 78 +; +; Convert ASCII string to quadruple precision floating point +; +; Numeric input is free field decimal number +; with max of 15 digits with or without +; decimal point entered as ASCII from teletype. +; Entering E after the number followed by a second +; number causes the second number to be interpreted +; as a power of 10 to be multiplied by the first number +; (i.e., "scientific" notation). +; +; Usage: +; asctoq( string, q ); +*/ + +/* ASCII to single */ +void asctoe24( s, y ) +char *s; +unsigned short *y; +{ +asctoeg( s, y, 24 ); +} + + +/* ASCII to double */ +void asctoe53( s, y ) +char *s; +unsigned short *y; +{ +#ifdef DEC +asctoeg( s, y, 56 ); +#else +asctoeg( s, y, 53 ); +#endif +} + + +/* ASCII to long double */ +void asctoe64( s, y ) +char *s; +unsigned short *y; +{ +asctoeg( s, y, 64 ); +} + +/* ASCII to 128-bit long double */ +void asctoe113 (s, y) +char *s; +unsigned short *y; +{ +asctoeg( s, y, 113 ); +} + +/* ASCII to super double */ +void asctoe( s, y ) +char *s; +unsigned short *y; +{ +asctoeg( s, y, NBITS ); +} + +/* Space to make a copy of the input string: */ +static char lstr[82] = {0}; + +void asctoeg( ss, y, oprec ) +char *ss; +unsigned short *y; +int oprec; +{ +unsigned short yy[NI], xt[NI], tt[NI]; +int esign, decflg, sgnflg, nexp, exp, prec, lost; +int k, trail, c, rndsav; +long lexp; +unsigned short nsign, *p; +char *sp, *s; + +/* Copy the input string. */ +s = ss; +while( *s == ' ' ) /* skip leading spaces */ + ++s; +sp = lstr; +for( k=0; k<79; k++ ) + { + if( (*sp++ = *s++) == '\0' ) + break; + } +*sp = '\0'; +s = lstr; + +rndsav = rndprc; +rndprc = NBITS; /* Set to full precision */ +lost = 0; +nsign = 0; +decflg = 0; +sgnflg = 0; +nexp = 0; +exp = 0; +prec = 0; +ecleaz( yy ); +trail = 0; + +nxtcom: +k = *s - '0'; +if( (k >= 0) && (k <= 9) ) + { +/* Ignore leading zeros */ + if( (prec == 0) && (decflg == 0) && (k == 0) ) + goto donchr; +/* Identify and strip trailing zeros after the decimal point. */ + if( (trail == 0) && (decflg != 0) ) + { + sp = s; + while( (*sp >= '0') && (*sp <= '9') ) + ++sp; +/* Check for syntax error */ + c = *sp & 0x7f; + if( (c != 'e') && (c != 'E') && (c != '\0') + && (c != '\n') && (c != '\r') && (c != ' ') + && (c != ',') ) + goto error; + --sp; + while( *sp == '0' ) + *sp-- = 'z'; + trail = 1; + if( *s == 'z' ) + goto donchr; + } +/* If enough digits were given to more than fill up the yy register, + * continuing until overflow into the high guard word yy[2] + * guarantees that there will be a roundoff bit at the top + * of the low guard word after normalization. + */ + if( yy[2] == 0 ) + { + if( decflg ) + nexp += 1; /* count digits after decimal point */ + eshup1( yy ); /* multiply current number by 10 */ + emovz( yy, xt ); + eshup1( xt ); + eshup1( xt ); + eaddm( xt, yy ); + ecleaz( xt ); + xt[NI-2] = (unsigned short )k; + eaddm( xt, yy ); + } + else + { + /* Mark any lost non-zero digit. */ + lost |= k; + /* Count lost digits before the decimal point. */ + if (decflg == 0) + nexp -= 1; + } + prec += 1; + goto donchr; + } + +switch( *s ) + { + case 'z': + break; + case 'E': + case 'e': + goto expnt; + case '.': /* decimal point */ + if( decflg ) + goto error; + ++decflg; + break; + case '-': + nsign = 0xffff; + if( sgnflg ) + goto error; + ++sgnflg; + break; + case '+': + if( sgnflg ) + goto error; + ++sgnflg; + break; + case ',': + case ' ': + case '\0': + case '\n': + case '\r': + goto daldone; + case 'i': + case 'I': + goto infinite; + default: + error: +#ifdef NANS + enan( yy, NI*16 ); +#else + mtherr( "asctoe", DOMAIN ); + ecleaz(yy); +#endif + goto aexit; + } +donchr: +++s; +goto nxtcom; + +/* Exponent interpretation */ +expnt: + +esign = 1; +exp = 0; +++s; +/* check for + or - */ +if( *s == '-' ) + { + esign = -1; + ++s; + } +if( *s == '+' ) + ++s; +while( (*s >= '0') && (*s <= '9') ) + { + exp *= 10; + exp += *s++ - '0'; + if (exp > 4977) + { + if (esign < 0) + goto zero; + else + goto infinite; + } + } +if( esign < 0 ) + exp = -exp; +if( exp > 4932 ) + { +infinite: + ecleaz(yy); + yy[E] = 0x7fff; /* infinity */ + goto aexit; + } +if( exp < -4977 ) + { +zero: + ecleaz(yy); + goto aexit; + } + +daldone: +nexp = exp - nexp; +/* Pad trailing zeros to minimize power of 10, per IEEE spec. */ +while( (nexp > 0) && (yy[2] == 0) ) + { + emovz( yy, xt ); + eshup1( xt ); + eshup1( xt ); + eaddm( yy, xt ); + eshup1( xt ); + if( xt[2] != 0 ) + break; + nexp -= 1; + emovz( xt, yy ); + } +if( (k = enormlz(yy)) > NBITS ) + { + ecleaz(yy); + goto aexit; + } +lexp = (EXONE - 1 + NBITS) - k; +emdnorm( yy, lost, 0, lexp, 64 ); +/* convert to external format */ + + +/* Multiply by 10**nexp. If precision is 64 bits, + * the maximum relative error incurred in forming 10**n + * for 0 <= n <= 324 is 8.2e-20, at 10**180. + * For 0 <= n <= 999, the peak relative error is 1.4e-19 at 10**947. + * For 0 >= n >= -999, it is -1.55e-19 at 10**-435. + */ +lexp = yy[E]; +if( nexp == 0 ) + { + k = 0; + goto expdon; + } +esign = 1; +if( nexp < 0 ) + { + nexp = -nexp; + esign = -1; + if( nexp > 4096 ) + { /* Punt. Can't handle this without 2 divides. */ + emovi( etens[0], tt ); + lexp -= tt[E]; + k = edivm( tt, yy ); + lexp += EXONE; + nexp -= 4096; + } + } +p = &etens[NTEN][0]; +emov( eone, xt ); +exp = 1; +do + { + if( exp & nexp ) + emul( p, xt, xt ); + p -= NE; + exp = exp + exp; + } +while( exp <= MAXP ); + +emovi( xt, tt ); +if( esign < 0 ) + { + lexp -= tt[E]; + k = edivm( tt, yy ); + lexp += EXONE; + } +else + { + lexp += tt[E]; + k = emulm( tt, yy ); + lexp -= EXONE - 1; + } + +expdon: + +/* Round and convert directly to the destination type */ +if( oprec == 53 ) + lexp -= EXONE - 0x3ff; +else if( oprec == 24 ) + lexp -= EXONE - 0177; +#ifdef DEC +else if( oprec == 56 ) + lexp -= EXONE - 0201; +#endif +rndprc = oprec; +emdnorm( yy, k, 0, lexp, 64 ); + +aexit: + +rndprc = rndsav; +yy[0] = nsign; +switch( oprec ) + { +#ifdef DEC + case 56: + todec( yy, y ); /* see etodec.c */ + break; +#endif + case 53: + toe53( yy, y ); + break; + case 24: + toe24( yy, y ); + break; + case 64: + toe64( yy, y ); + break; + case 113: + toe113( yy, y ); + break; + case NBITS: + emovo( yy, y ); + break; + } +} + + + +/* y = largest integer not greater than x + * (truncated toward minus infinity) + * + * unsigned short x[NE], y[NE] + * + * efloor( x, y ); + */ +static unsigned short bmask[] = { +0xffff, +0xfffe, +0xfffc, +0xfff8, +0xfff0, +0xffe0, +0xffc0, +0xff80, +0xff00, +0xfe00, +0xfc00, +0xf800, +0xf000, +0xe000, +0xc000, +0x8000, +0x0000, +}; + +void efloor( x, y ) +unsigned short x[], y[]; +{ +register unsigned short *p; +int e, expon, i; +unsigned short f[NE]; + +emov( x, f ); /* leave in external format */ +expon = (int )f[NE-1]; +e = (expon & 0x7fff) - (EXONE - 1); +if( e <= 0 ) + { + eclear(y); + goto isitneg; + } +/* number of bits to clear out */ +e = NBITS - e; +emov( f, y ); +if( e <= 0 ) + return; + +p = &y[0]; +while( e >= 16 ) + { + *p++ = 0; + e -= 16; + } +/* clear the remaining bits */ +*p &= bmask[e]; +/* truncate negatives toward minus infinity */ +isitneg: + +if( (unsigned short )expon & (unsigned short )0x8000 ) + { + for( i=0; i<NE-1; i++ ) + { + if( f[i] != y[i] ) + { + esub( eone, y, y ); + break; + } + } + } +} + + +/* unsigned short x[], s[]; + * long *exp; + * + * efrexp( x, exp, s ); + * + * Returns s and exp such that s * 2**exp = x and .5 <= s < 1. + * For example, 1.1 = 0.55 * 2**1 + * Handles denormalized numbers properly using long integer exp. + */ +void efrexp( x, exp, s ) +unsigned short x[]; +long *exp; +unsigned short s[]; +{ +unsigned short xi[NI]; +long li; + +emovi( x, xi ); +li = (long )((short )xi[1]); + +if( li == 0 ) + { + li -= enormlz( xi ); + } +xi[1] = 0x3ffe; +emovo( xi, s ); +*exp = li - 0x3ffe; +} + + + +/* unsigned short x[], y[]; + * long pwr2; + * + * eldexp( x, pwr2, y ); + * + * Returns y = x * 2**pwr2. + */ +void eldexp( x, pwr2, y ) +unsigned short x[]; +long pwr2; +unsigned short y[]; +{ +unsigned short xi[NI]; +long li; +int i; + +emovi( x, xi ); +li = xi[1]; +li += pwr2; +i = 0; +emdnorm( xi, i, i, li, 64 ); +emovo( xi, y ); +} + + +/* c = remainder after dividing b by a + * Least significant integer quotient bits left in equot[]. + */ +void eremain( a, b, c ) +unsigned short a[], b[], c[]; +{ +unsigned short den[NI], num[NI]; + +#ifdef NANS +if( eisinf(b) || (ecmp(a,ezero) == 0) || eisnan(a) || eisnan(b)) + { + enan( c, NBITS ); + return; + } +#endif +if( ecmp(a,ezero) == 0 ) + { + mtherr( "eremain", SING ); + eclear( c ); + return; + } +emovi( a, den ); +emovi( b, num ); +eiremain( den, num ); +/* Sign of remainder = sign of quotient */ +if( a[0] == b[0] ) + num[0] = 0; +else + num[0] = 0xffff; +emovo( num, c ); +} + + +void eiremain( den, num ) +unsigned short den[], num[]; +{ +long ld, ln; +unsigned short j; + +ld = den[E]; +ld -= enormlz( den ); +ln = num[E]; +ln -= enormlz( num ); +ecleaz( equot ); +while( ln >= ld ) + { + if( ecmpm(den,num) <= 0 ) + { + esubm(den, num); + j = 1; + } + else + { + j = 0; + } + eshup1(equot); + equot[NI-1] |= j; + eshup1(num); + ln -= 1; + } +emdnorm( num, 0, 0, ln, 0 ); +} + +/* NaN bit patterns + */ +#ifdef MIEEE +unsigned short nan113[8] = { + 0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}; +unsigned short nan64[6] = {0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}; +unsigned short nan53[4] = {0x7fff, 0xffff, 0xffff, 0xffff}; +unsigned short nan24[2] = {0x7fff, 0xffff}; +#endif + +#ifdef IBMPC +unsigned short nan113[8] = {0, 0, 0, 0, 0, 0, 0xc000, 0xffff}; +unsigned short nan64[6] = {0, 0, 0, 0xc000, 0xffff, 0}; +unsigned short nan53[4] = {0, 0, 0, 0xfff8}; +unsigned short nan24[2] = {0, 0xffc0}; +#endif + + +void enan (nan, size) +unsigned short *nan; +int size; +{ +int i, n; +unsigned short *p; + +switch( size ) + { +#ifndef DEC + case 113: + n = 8; + p = nan113; + break; + + case 64: + n = 6; + p = nan64; + break; + + case 53: + n = 4; + p = nan53; + break; + + case 24: + n = 2; + p = nan24; + break; + + case NBITS: + for( i=0; i<NE-2; i++ ) + *nan++ = 0; + *nan++ = 0xc000; + *nan++ = 0x7fff; + return; + + case NI*16: + *nan++ = 0; + *nan++ = 0x7fff; + *nan++ = 0; + *nan++ = 0xc000; + for( i=4; i<NI; i++ ) + *nan++ = 0; + return; +#endif + default: + mtherr( "enan", DOMAIN ); + return; + } +for (i=0; i < n; i++) + *nan++ = *p++; +} + + + +/* Longhand square root. */ + +static int esqinited = 0; +static unsigned short sqrndbit[NI]; + +void esqrt( x, y ) +short *x, *y; +{ +unsigned short temp[NI], num[NI], sq[NI], xx[NI]; +int i, j, k, n, nlups; +long m, exp; + +if( esqinited == 0 ) + { + ecleaz( sqrndbit ); + sqrndbit[NI-2] = 1; + esqinited = 1; + } +/* Check for arg <= 0 */ +i = ecmp( x, ezero ); +if( i <= 0 ) + { +#ifdef NANS + if (i == -2) + { + enan (y, NBITS); + return; + } +#endif + eclear(y); + if( i < 0 ) + mtherr( "esqrt", DOMAIN ); + return; + } + +#ifdef INFINITY +if( eisinf(x) ) + { + eclear(y); + einfin(y); + return; + } +#endif +/* Bring in the arg and renormalize if it is denormal. */ +emovi( x, xx ); +m = (long )xx[1]; /* local long word exponent */ +if( m == 0 ) + m -= enormlz( xx ); + +/* Divide exponent by 2 */ +m -= 0x3ffe; +exp = (unsigned short )( (m / 2) + 0x3ffe ); + +/* Adjust if exponent odd */ +if( (m & 1) != 0 ) + { + if( m > 0 ) + exp += 1; + eshdn1( xx ); + } + +ecleaz( sq ); +ecleaz( num ); +n = 8; /* get 8 bits of result per inner loop */ +nlups = rndprc; +j = 0; + +while( nlups > 0 ) + { +/* bring in next word of arg */ + if( j < NE ) + num[NI-1] = xx[j+3]; +/* Do additional bit on last outer loop, for roundoff. */ + if( nlups <= 8 ) + n = nlups + 1; + for( i=0; i<n; i++ ) + { +/* Next 2 bits of arg */ + eshup1( num ); + eshup1( num ); +/* Shift up answer */ + eshup1( sq ); +/* Make trial divisor */ + for( k=0; k<NI; k++ ) + temp[k] = sq[k]; + eshup1( temp ); + eaddm( sqrndbit, temp ); +/* Subtract and insert answer bit if it goes in */ + if( ecmpm( temp, num ) <= 0 ) + { + esubm( temp, num ); + sq[NI-2] |= 1; + } + } + nlups -= n; + j += 1; + } + +/* Adjust for extra, roundoff loop done. */ +exp += (NBITS - 1) - rndprc; + +/* Sticky bit = 1 if the remainder is nonzero. */ +k = 0; +for( i=3; i<NI; i++ ) + k |= (int )num[i]; + +/* Renormalize and round off. */ +emdnorm( sq, k, 0, exp, 64 ); +emovo( sq, y ); +} diff --git a/test/math/ieetst.c b/test/math/ieetst.c index 3c89145e3..8c2453898 100644 --- a/test/math/ieetst.c +++ b/test/math/ieetst.c @@ -1,850 +1,850 @@ -/* Floating point to ASCII input and output string test program.
- *
- * Numbers in the native machine data structure are converted
- * to e type, then to and from decimal ASCII strings. Native
- * printf() and scanf() functions are also used to produce
- * and read strings. The resulting e type binary values
- * are compared, with diagnostic printouts of any discrepancies.
- *
- * Steve Moshier, 16 Dec 88
- * last revision: 16 May 92
- */
-
-#include "ehead.h"
-#include "mconf.h"
-
-/* Include tests of 80-bit long double precision: */
-#define LDOUBLE 0
-/* Abort subtest after getting this many errors: */
-#define MAXERR 5
-/* Number of random arguments to try (set as large as you have
- * patience for): */
-#define NRAND 100
-/* Perform internal consistency test: */
-#define CHKINTERNAL 0
-
-static unsigned short fullp[NE], rounded[NE];
-float prec24, sprec24, ssprec24;
-double prec53, sprec53, ssprec53;
-#if LDOUBLE
-long double prec64, sprec64, ssprec64;
-#endif
-
-static unsigned short rprint[NE], rscan[NE];
-static unsigned short q1[NE], q2[NE], q5[NE];
-static unsigned short e1[NE], e2[NE], e3[NE];
-static double d1, d2;
-static int errprint = 0;
-static int errscan = 0;
-static int identerr = 0;
-static int errtot = 0;
-static int count = 0;
-static char str0[80], str1[80], str2[80], str3[80];
-static unsigned short eten[NE], maxm[NE];
-
-int m, n, k2, mprec, SPREC;
-
-char *Ten = "10.0";
-char tformat[10];
-char *format24 = "%.8e";
-#ifdef DEC
-char *format53 = "%.17e";
-#else
-char *format53 = "%.16e";
-#endif
-char *fformat24 = "%e";
-char *fformat53 = "%le";
-char *pct = "%";
-char *quo = "\042";
-#if LDOUBLE
-char *format64 = "%.20Le";
-char *fformat64 = "%Le";
-#endif
-char *format;
-char *fformat;
-char *toomany = "Too many errors; aborting this test.\n";
-
-static int mnrflag;
-static int etrflag;
-void chkit(), printerr(), mnrand(), etrand(), shownoncrit();
-void chkid(), pvec();
-
-main()
-{
-int i, iprec;
-
-printf( "Steve Moshier's printf/scanf tester, version 0.2.\n\n" );
-#ifdef DEC
- /* DEC PDP-11/VAX single precision not yet implemented */
-for( iprec = 1; iprec<2; iprec++ )
-#else
-for( iprec = 0; iprec<3; iprec++ )
-#endif
- {
- errscan = 0;
- identerr = 0;
- errprint = 0;
- eclear( rprint );
- eclear( rscan );
-
-switch( iprec )
- {
- case 0:
- SPREC = 8; /* # digits after the decimal point */
- mprec = 24; /* # bits in the significand */
- m = 9; /* max # decimal digits for correct rounding */
- n = 13; /* max power of ten for correct rounding */
- k2 = -125; /* underflow beyond 2^-k2 */
- format = format24; /* printf format string */
- fformat = fformat24; /* scanf format string */
- mnrflag = 1; /* sets interval for random numbers */
- etrflag = 1;
- printf( "Testing FLOAT precision.\n" );
- break;
-
- case 1:
-#ifdef DEC
- SPREC = 17;
- mprec = 56;
- m = 17;
- n = 27;
- k2 = -125;
- format = format53;
- fformat = fformat53;
- mnrflag = 2;
- etrflag = 1;
- printf( "Testing DEC DOUBLE precision.\n" );
- break;
-#else
- SPREC = 16;
- mprec = 53;
- m = 17;
- n = 27;
- k2 = -1021;
- format = format53;
- fformat = fformat53;
- mnrflag = 2;
- etrflag = 2;
- printf( "Testing DOUBLE precision.\n" );
- break;
-#endif
- case 2:
-#if LDOUBLE
- SPREC = 20;
- mprec = 64;
- m = 20;
- n = 34;
- k2 = -16382;
- format = format64;
- fformat = fformat64;
- mnrflag = 3;
- etrflag = 3;
- printf( "Testing LONG DOUBLE precision.\n" );
- break;
-#else
- goto nodenorm;
-#endif
- }
-
- asctoe( Ten, eten );
-/* 10^m - 1 */
- d2 = m;
- e53toe( &d2, e1 );
- epow( eten, e1, maxm );
- esub( eone, maxm, maxm );
-
-/* test 1 */
- printf( "1. Checking 10^n - 1 for n = %d to %d.\n", -m, m );
- emov( eone, q5 );
- for( count=0; count<=m; count++ )
- {
- esub( eone, q5, fullp );
- chkit( 1 );
- ediv( q5, eone, q2 );
- esub( eone, q2, fullp );
- chkit( 1 );
- emul( eten, q5, q5 );
- if( errtot >= MAXERR )
- {
- printf( "%s", toomany );
- goto end1;
- }
- }
-end1:
- printerr();
-
-
-/* test 2 */
- printf( "2. Checking powers of 10 from 10^-%d to 10^%d.\n", n, n );
- emov( eone, q5 );
- for( count=0; count<=n; count++ )
- {
- emov( q5, fullp );
- chkit( 2 );
- ediv( q5, eone, fullp );
- chkit( 2 );
- emul( eten, q5, q5 );
- if( errtot >= MAXERR )
- {
- printf( "%s", toomany );
- goto end2;
- }
- }
-end2:
- printerr();
-
-/* test 3 */
- printf( "3. Checking (10^%d-1)*10^n from n = -%d to %d.\n", m, n, n );
- emov( eone, q5 );
- for( count= -n; count<=n; count++ )
- {
- emul( maxm, q5, fullp );
- chkit( 3 );
- emov( q5, fullp );
- ediv( fullp, eone, fullp );
- emul( maxm, fullp, fullp );
- chkit( 3 );
- emul( eten, q5, q5 );
- if( errtot >= MAXERR )
- {
- printf( "%s", toomany );
- goto end3;
- }
- }
-end3:
- printerr();
-
-
-
-/* test 4 */
- printf( "4. Checking powers of 2 from 2^-24 to 2^+56.\n" );
- d1 = -24.0;
- e53toe( &d1, q1 );
- epow( etwo, q1, q5 );
-
- for( count = -24; count <= 56; count++ )
- {
- emov( q5, fullp );
- chkit( 4 );
- emul( etwo, q5, q5 );
- if( errtot >= MAXERR )
- {
- printf( "%s", toomany );
- goto end4;
- }
- }
-end4:
- printerr();
-
-
-/* test 5 */
- printf( "5. Checking 2^n - 1 for n = 0 to %d.\n", mprec );
- emov( eone, q5 );
- for( count=0; count<=mprec; count++ )
- {
- esub( eone, q5, fullp );
- chkit( 5 );
- emul( etwo, q5, q5 );
- if( errtot >= MAXERR )
- {
- printf( "%s", toomany );
- goto end5;
- }
- }
-end5:
- printerr();
-
-/* test 6 */
- printf( "6. Checking 2^n + 1 for n = 0 to %d.\n", mprec );
- emov( eone, q5 );
- for( count=0; count<=mprec; count++ )
- {
- eadd( eone, q5, fullp );
- chkit( 6 );
- emul( etwo, q5, q5 );
- if( errtot >= MAXERR )
- {
- printf( "%s", toomany );
- goto end6;
- }
- }
-end6:
- printerr();
-
-/* test 7 */
- printf(
- "7. Checking %d values M * 10^N with random integer M and N,\n",
- NRAND );
- printf(" 1 <= M <= 10^%d - 1 and -%d <= N <= +%d.\n", m, n, n );
- for( i=0; i<NRAND; i++ )
- {
- mnrand( fullp );
- chkit( 7 );
- if( errtot >= MAXERR )
- {
- printf( "%s", toomany );
- goto end7;
- }
- }
-end7:
- printerr();
-
-/* test 8 */
- printf("8. Checking critical rounding cases.\n" );
- for( i=0; i<20; i++ )
- {
- mnrand( fullp );
- eabs( fullp );
- if( ecmp( fullp, eone ) < 0 )
- ediv( fullp, eone, fullp );
- efloor( fullp, fullp );
- eadd( ehalf, fullp, fullp );
- chkit( 8 );
- if( errtot >= MAXERR )
- {
- printf( "%s", toomany );
- goto end8;
- }
- }
-end8:
- printerr();
-
-
-
-/* test 9 */
- printf("9. Testing on %d random non-denormal values.\n", NRAND );
- for( i=0; i<NRAND; i++ )
- {
- etrand( fullp );
- chkit( 9 );
- }
- printerr();
- shownoncrit();
-
-/* test 10 */
- printf(
- "Do you want to check denormal numbers in this precision ? (y/n) " );
- gets( str0 );
- if( str0[0] != 'y' )
- goto nodenorm;
-
- printf( "10. Checking denormal numbers.\n" );
-
-/* Form 2^-starting power */
- d1 = k2;
- e53toe( &d1, q1 );
- epow( etwo, q1, e1 );
-
-/* Find 2^-mprec less than starting power */
- d1 = -mprec + 4;
- e53toe( &d1, q1 );
- epow( etwo, q1, e3 );
- emul( e1, e3, e3 );
- emov( e3, e2 );
- ediv( etwo, e2, e2 );
-
- while( ecmp(e1,e2) != 0 )
- {
- eadd( e1, e2, fullp );
- switch( mprec )
- {
-#if LDOUBLE
- case 64:
- etoe64( e1, &sprec64 );
- e64toe( &sprec64, q1 );
- etoe64( fullp, &prec64 );
- e64toe( &prec64, q2 );
- break;
-#endif
-#ifdef DEC
- case 56:
-#endif
- case 53:
- etoe53( e1, &sprec53 );
- e53toe( &sprec53, q1 );
- etoe53( fullp, &prec53 );
- e53toe( &prec53, q2 );
- break;
-
- case 24:
- etoe24( e1, &sprec24 );
- e24toe( &sprec24, q1 );
- etoe24( fullp, &prec24 );
- e24toe( &prec24, q2 );
- break;
- }
- if( ecmp( q2, ezero ) == 0 )
- goto maxden;
- chkit(10);
- if( ecmp(q1,q2) == 0 )
- {
- ediv( etwo, e1, e1 );
- emov( e3, e2 );
- }
- if( errtot >= MAXERR )
- {
- printf( "%s", toomany );
- goto maxden;
- }
- ediv( etwo, e2, e2 );
- }
-maxden:
- printerr();
-nodenorm:
- printf( "\n" );
- } /* loop on precision */
-printf( "End of test.\n" );
-}
-
-#if CHKINTERNAL
-long double xprec64;
-double xprec53;
-float xprec24;
-
-/* Check binary -> printf -> scanf -> binary identity
- * of internal routines
- */
-void chkinternal( ref, tst, string )
-unsigned short ref[], tst[];
-char *string;
-{
-
-if( ecmp(ref,tst) != 0 )
- {
- printf( "internal identity compare error!\n" );
- chkid( ref, tst, string );
- }
-}
-#endif
-
-
-/* Check binary -> printf -> scanf -> binary identity
- */
-void chkid( print, scan, string )
-unsigned short print[], scan[];
-char *string;
-{
-/* Test printf-scanf identity */
-if( ecmp( print, scan ) != 0 )
- {
- pvec( print, NE );
- printf( " ->printf-> %s ->scanf->\n", string );
- pvec( scan, NE );
- printf( " is not an identity.\n" );
- ++identerr;
- }
-}
-
-
-/* Check scanf result
- */
-void chkscan( ref, tst, string )
-unsigned short ref[], tst[];
-char *string;
-{
-/* Test scanf() */
-if( ecmp( ref, tst ) != 0 )
- {
- printf( "scanf(%s) -> ", string );
- pvec( tst, NE );
- printf( "\n should be " );
- pvec( ref, NE );
- printf( ".\n" );
- ++errscan;
- ++errtot;
- }
-}
-
-
-/* Test printf() result
- */
-void chkprint( ref, tst, string )
-unsigned short ref[], tst[];
-char *string;
-{
-if( ecmp(ref, tst) != 0 )
- {
- printf( "printf( ");
- pvec( ref, NE );
- printf( ") -> %s\n", string );
- printf( " = " );
- pvec( tst, NE );
- printf( ".\n" );
- ++errprint;
- ++errtot;
- }
-}
-
-
-/* Print array of n 16-bit shorts
- */
-void pvec( x, n )
-unsigned short x[];
-int n;
-{
-int i;
-
-for( i=0; i<n; i++ )
- {
- printf( "%04x ", x[i] );
- }
-}
-
-/* Measure worst case printf rounding error
- */
-void cmpprint( ref, tst )
-unsigned short ref[], tst[];
-{
-unsigned short e[NE];
-
-if( ecmp( ref, ezero ) != 0 )
- {
- esub( ref, tst, e );
- ediv( ref, e, e );
- eabs( e );
- if( ecmp( e, rprint ) > 0 )
- emov( e, rprint );
- }
-}
-
-/* Measure worst case scanf rounding error
- */
-void cmpscan( ref, tst )
-unsigned short ref[], tst[];
-{
-unsigned short er[NE];
-
-if( ecmp( ref, ezero ) != 0 )
- {
- esub( ref, tst, er );
- ediv( ref, er, er );
- eabs( er );
- if( ecmp( er, rscan ) > 0 )
- emov( er, rscan );
- if( ecmp( er, ehalf ) > 0 )
- {
- etoasc( tst, str1, 21 );
- printf( "Bad error: scanf(%s) = %s !\n", str0, str1 );
- }
- }
-}
-
-/* Check rounded-down decimal string output of printf
- */
-void cmptrunc( ref, tst )
-unsigned short ref[], tst[];
-{
-if( ecmp( ref, tst ) != 0 )
- {
- printf( "printf(%s%s%s, %s) -> %s\n", quo, tformat, quo, str1, str2 );
- printf( "should be %s .\n", str3 );
- errprint += 1;
- }
-}
-
-
-void shownoncrit()
-{
-
-etoasc( rprint, str0, 3 );
-printf( "Maximum relative printf error found = %s .\n", str0 );
-etoasc( rscan, str0, 3 );
-printf( "Maximum relative scanf error found = %s .\n", str0 );
-}
-
-
-
-/* Produce arguments and call comparison subroutines.
- */
-void chkit( testno )
-int testno;
-{
-unsigned short t[NE], u[NE], v[NE];
-int j;
-
-switch( mprec )
- {
-#if LDOUBLE
- case 64:
- etoe64( fullp, &prec64 );
- e64toe( &prec64, rounded );
-#if CHKINTERNAL
- e64toasc( &prec64, str1, SPREC );
- asctoe64( str1, &xprec64 );
- e64toe( &xprec64, t );
- chkinternal( rounded, t, str1 );
-#endif
-/* check printf and scanf */
- sprintf( str2, format, prec64 );
- sscanf( str2, fformat, &sprec64 );
- e64toe( &sprec64, u );
- chkid( rounded, u, str2 );
- asctoe64( str2, &ssprec64 );
- e64toe( &ssprec64, v );
- chkscan( v, u, str2 );
- chkprint( rounded, v, str2 );
- if( testno < 8 )
- break;
-/* rounding error measurement */
- etoasc( fullp, str0, 24 );
- etoe64( fullp, &ssprec64 );
- e64toe( &ssprec64, u );
- sprintf( str2, format, ssprec64 );
- asctoe( str2, t );
- cmpprint( u, t );
- sscanf( str0, fformat, &sprec64 );
- e64toe( &sprec64, t );
- cmpscan( fullp, t );
- if( testno < 8 )
- break;
-/* strings rounded to less than maximum precision */
- e64toasc( &ssprec64, str1, 24 );
- for( j=SPREC-1; j>0; j-- )
- {
- e64toasc( &ssprec64, str3, j );
- asctoe( str3, v );
- sprintf( tformat, "%s.%dLe", pct, j );
- sprintf( str2, tformat, ssprec64 );
- asctoe( str2, t );
- cmptrunc( v, t );
- }
- break;
-#endif
-#ifdef DEC
- case 56:
-#endif
- case 53:
- etoe53( fullp, &prec53 );
- e53toe( &prec53, rounded );
-#if CHKINTERNAL
- e53toasc( &prec53, str1, SPREC );
- asctoe53( str1, &xprec53 );
- e53toe( &xprec53, t );
- chkinternal( rounded, t, str1 );
-#endif
- sprintf( str2, format, prec53 );
- sscanf( str2, fformat, &sprec53 );
- e53toe( &sprec53, u );
- chkid( rounded, u, str2 );
- asctoe53( str2, &ssprec53 );
- e53toe( &ssprec53, v );
- chkscan( v, u, str2 );
- chkprint( rounded, v, str2 );
- if( testno < 8 )
- break;
-/* rounding error measurement */
- etoasc( fullp, str0, 24 );
- etoe53( fullp, &ssprec53 );
- e53toe( &ssprec53, u );
- sprintf( str2, format, ssprec53 );
- asctoe( str2, t );
- cmpprint( u, t );
- sscanf( str0, fformat, &sprec53 );
- e53toe( &sprec53, t );
- cmpscan( fullp, t );
- if( testno < 8 )
- break;
- e53toasc( &ssprec53, str1, 24 );
- for( j=SPREC-1; j>0; j-- )
- {
- e53toasc( &ssprec53, str3, j );
- asctoe( str3, v );
- sprintf( tformat, "%s.%de", pct, j );
- sprintf( str2, tformat, ssprec53 );
- asctoe( str2, t );
- cmptrunc( v, t );
- }
- break;
-
- case 24:
- etoe24( fullp, &prec24 );
- e24toe( &prec24, rounded );
-#if CHKINTERNAL
- e24toasc( &prec24, str1, SPREC );
- asctoe24( str1, &xprec24 );
- e24toe( &xprec24, t );
- chkinternal( rounded, t, str1 );
-#endif
- sprintf( str2, format, prec24 );
- sscanf( str2, fformat, &sprec24 );
- e24toe( &sprec24, u );
- chkid( rounded, u, str2 );
- asctoe24( str2, &ssprec24 );
- e24toe( &ssprec24, v );
- chkscan( v, u, str2 );
- chkprint( rounded, v, str2 );
- if( testno < 8 )
- break;
-/* rounding error measurement */
- etoasc( fullp, str0, 24 );
- etoe24( fullp, &ssprec24 );
- e24toe( &ssprec24, u );
- sprintf( str2, format, ssprec24 );
- asctoe( str2, t );
- cmpprint( u, t );
- sscanf( str0, fformat, &sprec24 );
- e24toe( &sprec24, t );
- cmpscan( fullp, t );
-/*
- if( testno < 8 )
- break;
-*/
- e24toasc( &ssprec24, str1, 24 );
- for( j=SPREC-1; j>0; j-- )
- {
- e24toasc( &ssprec24, str3, j );
- asctoe( str3, v );
- sprintf( tformat, "%s.%de", pct, j );
- sprintf( str2, tformat, ssprec24 );
- asctoe( str2, t );
- cmptrunc( v, t );
- }
- break;
- }
-}
-
-
-void printerr()
-{
-if( (errscan == 0) && (identerr == 0) && (errprint == 0) )
- printf( "No errors found.\n" );
-else
- {
- printf( "%d binary -> decimal errors found.\n", errprint );
- printf( "%d decimal -> binary errors found.\n", errscan );
- }
-errscan = 0; /* reset for next test */
-identerr = 0;
-errprint = 0;
-errtot = 0;
-}
-
-
-/* Random number generator
- * in the range M * 10^N, where 1 <= M <= 10^17 - 1
- * and -27 <= N <= +27. Test values of M are logarithmically distributed
- * random integers; test values of N are uniformly distributed random integers.
- */
-
-static char *fwidth = "1.036163291797320557783096e1"; /* log(sqrt(10^9-1)) */
-static char *dwidth = "1.957197329044938830915E1"; /* log(sqrt(10^17-1)) */
-static char *ldwidth = "2.302585092994045684017491e1"; /* log(sqrt(10^20-1)) */
-
-static char *a13 = "13.0";
-static char *a27 = "27.0";
-static char *a34 = "34.0";
-static char *a10m13 = "1.0e-13";
-static unsigned short LOW[ NE ], WIDTH[NE], e27[NE], e10m13[NE];
-
-
-void mnrand( erand )
-unsigned short erand[];
-{
-unsigned short ea[NE], em[NE], en[NE], ex[NE];
-double x, a;
-
-if( mnrflag )
- {
- if( mnrflag == 3 )
- {
- asctoe( ldwidth, WIDTH );
- asctoe( a34, e27 );
- }
- if( mnrflag == 2 )
- {
- asctoe( dwidth, WIDTH );
- asctoe( a27, e27 );
- }
- if( mnrflag == 1 )
- {
- asctoe( fwidth, WIDTH );
- asctoe( a13, e27 );
- }
- asctoe( a10m13, e10m13 );
- mnrflag = 0;
- }
-drand( &x );
-e53toe( &x, ex ); /* x = WIDTH * ( x - 1.0 ) + LOW; */
-esub( eone, ex, ex );
-emul( WIDTH, ex, ex );
-eexp( ex, ex ); /* x = exp(x); */
-
-drand( &a );
-e53toe( &a, ea );
-emul( ea, ex, ea ); /* a = 1.0e-13 * x * a; */
-emul( e10m13, ea, ea );
-eabs( ea );
-eadd( ea, ex, ex ); /* add fuzz */
-emul( ex, ex, ex ); /* square it, to get range to 10^17 - 1 */
-efloor( ex, em ); /* this is M */
-
-/* Random power of 10 */
-drand( &a );
-e53toe( &a, ex );
-esub( eone, ex, ex ); /* y3 = 54.0 * ( y3 - 1.0 ) + 0.5; */
-emul( e27, ex, ex );
-eadd( ex, ex, ex );
-eadd( ehalf, ex, ex );
-efloor( ex, ex ); /* y3 = floor( y3 ) - 27.0; */
-esub( e27, ex, en ); /* this is N */
-epow( eten, en, ex );
-emul( ex, em, erand );
-}
-
-/* -ln 2^16382 */
-char *ldemin = "-1.1355137111933024058873097E4";
-char *ldewid = "2.2710274223866048117746193E4";
-/* -ln 2^1022 */
-char *demin = "-7.0839641853226410622441123E2";
-char *dewid = "1.4167928370645282124488225E3";
-/* -ln 2^125 */
-char *femin = "-8.6643397569993163677154015E1";
-char *fewid = "1.7328679513998632735430803E2";
-
-void etrand( erand )
-unsigned short erand[];
-{
-unsigned short ea[NE], ex[NE];
-double x, a;
-
-if( etrflag )
- {
- if( etrflag == 3 )
- {
- asctoe( ldemin, LOW );
- asctoe( ldewid, WIDTH );
- asctoe( a34, e27 );
- }
- if( etrflag == 2 )
- {
- asctoe( demin, LOW );
- asctoe( dewid, WIDTH );
- asctoe( a27, e27 );
- }
- if( etrflag == 1 )
- {
- asctoe( femin, LOW );
- asctoe( fewid, WIDTH );
- asctoe( a13, e27 );
- }
- asctoe( a10m13, e10m13 );
- etrflag = 0;
- }
-drand( &x );
-e53toe( &x, ex ); /* x = WIDTH * ( x - 1.0 ) + LOW; */
-esub( eone, ex, ex );
-emul( WIDTH, ex, ex );
-eadd( LOW, ex, ex );
-eexp( ex, ex ); /* x = exp(x); */
-
-/* add fuzz
- */
-drand( &a );
-e53toe( &a, ea );
-emul( ea, ex, ea ); /* a = 1.0e-13 * x * a; */
-emul( e10m13, ea, ea );
-if( ecmp( ex, ezero ) > 0 )
- eneg( ea );
-eadd( ea, ex, erand );
-}
-
+/* Floating point to ASCII input and output string test program. + * + * Numbers in the native machine data structure are converted + * to e type, then to and from decimal ASCII strings. Native + * printf() and scanf() functions are also used to produce + * and read strings. The resulting e type binary values + * are compared, with diagnostic printouts of any discrepancies. + * + * Steve Moshier, 16 Dec 88 + * last revision: 16 May 92 + */ + +#include "ehead.h" +#include "mconf.h" + +/* Include tests of 80-bit long double precision: */ +#define LDOUBLE 0 +/* Abort subtest after getting this many errors: */ +#define MAXERR 5 +/* Number of random arguments to try (set as large as you have + * patience for): */ +#define NRAND 100 +/* Perform internal consistency test: */ +#define CHKINTERNAL 0 + +static unsigned short fullp[NE], rounded[NE]; +float prec24, sprec24, ssprec24; +double prec53, sprec53, ssprec53; +#if LDOUBLE +long double prec64, sprec64, ssprec64; +#endif + +static unsigned short rprint[NE], rscan[NE]; +static unsigned short q1[NE], q2[NE], q5[NE]; +static unsigned short e1[NE], e2[NE], e3[NE]; +static double d1, d2; +static int errprint = 0; +static int errscan = 0; +static int identerr = 0; +static int errtot = 0; +static int count = 0; +static char str0[80], str1[80], str2[80], str3[80]; +static unsigned short eten[NE], maxm[NE]; + +int m, n, k2, mprec, SPREC; + +char *Ten = "10.0"; +char tformat[10]; +char *format24 = "%.8e"; +#ifdef DEC +char *format53 = "%.17e"; +#else +char *format53 = "%.16e"; +#endif +char *fformat24 = "%e"; +char *fformat53 = "%le"; +char *pct = "%"; +char *quo = "\042"; +#if LDOUBLE +char *format64 = "%.20Le"; +char *fformat64 = "%Le"; +#endif +char *format; +char *fformat; +char *toomany = "Too many errors; aborting this test.\n"; + +static int mnrflag; +static int etrflag; +void chkit(), printerr(), mnrand(), etrand(), shownoncrit(); +void chkid(), pvec(); + +main() +{ +int i, iprec; + +printf( "Steve Moshier's printf/scanf tester, version 0.2.\n\n" ); +#ifdef DEC + /* DEC PDP-11/VAX single precision not yet implemented */ +for( iprec = 1; iprec<2; iprec++ ) +#else +for( iprec = 0; iprec<3; iprec++ ) +#endif + { + errscan = 0; + identerr = 0; + errprint = 0; + eclear( rprint ); + eclear( rscan ); + +switch( iprec ) + { + case 0: + SPREC = 8; /* # digits after the decimal point */ + mprec = 24; /* # bits in the significand */ + m = 9; /* max # decimal digits for correct rounding */ + n = 13; /* max power of ten for correct rounding */ + k2 = -125; /* underflow beyond 2^-k2 */ + format = format24; /* printf format string */ + fformat = fformat24; /* scanf format string */ + mnrflag = 1; /* sets interval for random numbers */ + etrflag = 1; + printf( "Testing FLOAT precision.\n" ); + break; + + case 1: +#ifdef DEC + SPREC = 17; + mprec = 56; + m = 17; + n = 27; + k2 = -125; + format = format53; + fformat = fformat53; + mnrflag = 2; + etrflag = 1; + printf( "Testing DEC DOUBLE precision.\n" ); + break; +#else + SPREC = 16; + mprec = 53; + m = 17; + n = 27; + k2 = -1021; + format = format53; + fformat = fformat53; + mnrflag = 2; + etrflag = 2; + printf( "Testing DOUBLE precision.\n" ); + break; +#endif + case 2: +#if LDOUBLE + SPREC = 20; + mprec = 64; + m = 20; + n = 34; + k2 = -16382; + format = format64; + fformat = fformat64; + mnrflag = 3; + etrflag = 3; + printf( "Testing LONG DOUBLE precision.\n" ); + break; +#else + goto nodenorm; +#endif + } + + asctoe( Ten, eten ); +/* 10^m - 1 */ + d2 = m; + e53toe( &d2, e1 ); + epow( eten, e1, maxm ); + esub( eone, maxm, maxm ); + +/* test 1 */ + printf( "1. Checking 10^n - 1 for n = %d to %d.\n", -m, m ); + emov( eone, q5 ); + for( count=0; count<=m; count++ ) + { + esub( eone, q5, fullp ); + chkit( 1 ); + ediv( q5, eone, q2 ); + esub( eone, q2, fullp ); + chkit( 1 ); + emul( eten, q5, q5 ); + if( errtot >= MAXERR ) + { + printf( "%s", toomany ); + goto end1; + } + } +end1: + printerr(); + + +/* test 2 */ + printf( "2. Checking powers of 10 from 10^-%d to 10^%d.\n", n, n ); + emov( eone, q5 ); + for( count=0; count<=n; count++ ) + { + emov( q5, fullp ); + chkit( 2 ); + ediv( q5, eone, fullp ); + chkit( 2 ); + emul( eten, q5, q5 ); + if( errtot >= MAXERR ) + { + printf( "%s", toomany ); + goto end2; + } + } +end2: + printerr(); + +/* test 3 */ + printf( "3. Checking (10^%d-1)*10^n from n = -%d to %d.\n", m, n, n ); + emov( eone, q5 ); + for( count= -n; count<=n; count++ ) + { + emul( maxm, q5, fullp ); + chkit( 3 ); + emov( q5, fullp ); + ediv( fullp, eone, fullp ); + emul( maxm, fullp, fullp ); + chkit( 3 ); + emul( eten, q5, q5 ); + if( errtot >= MAXERR ) + { + printf( "%s", toomany ); + goto end3; + } + } +end3: + printerr(); + + + +/* test 4 */ + printf( "4. Checking powers of 2 from 2^-24 to 2^+56.\n" ); + d1 = -24.0; + e53toe( &d1, q1 ); + epow( etwo, q1, q5 ); + + for( count = -24; count <= 56; count++ ) + { + emov( q5, fullp ); + chkit( 4 ); + emul( etwo, q5, q5 ); + if( errtot >= MAXERR ) + { + printf( "%s", toomany ); + goto end4; + } + } +end4: + printerr(); + + +/* test 5 */ + printf( "5. Checking 2^n - 1 for n = 0 to %d.\n", mprec ); + emov( eone, q5 ); + for( count=0; count<=mprec; count++ ) + { + esub( eone, q5, fullp ); + chkit( 5 ); + emul( etwo, q5, q5 ); + if( errtot >= MAXERR ) + { + printf( "%s", toomany ); + goto end5; + } + } +end5: + printerr(); + +/* test 6 */ + printf( "6. Checking 2^n + 1 for n = 0 to %d.\n", mprec ); + emov( eone, q5 ); + for( count=0; count<=mprec; count++ ) + { + eadd( eone, q5, fullp ); + chkit( 6 ); + emul( etwo, q5, q5 ); + if( errtot >= MAXERR ) + { + printf( "%s", toomany ); + goto end6; + } + } +end6: + printerr(); + +/* test 7 */ + printf( + "7. Checking %d values M * 10^N with random integer M and N,\n", + NRAND ); + printf(" 1 <= M <= 10^%d - 1 and -%d <= N <= +%d.\n", m, n, n ); + for( i=0; i<NRAND; i++ ) + { + mnrand( fullp ); + chkit( 7 ); + if( errtot >= MAXERR ) + { + printf( "%s", toomany ); + goto end7; + } + } +end7: + printerr(); + +/* test 8 */ + printf("8. Checking critical rounding cases.\n" ); + for( i=0; i<20; i++ ) + { + mnrand( fullp ); + eabs( fullp ); + if( ecmp( fullp, eone ) < 0 ) + ediv( fullp, eone, fullp ); + efloor( fullp, fullp ); + eadd( ehalf, fullp, fullp ); + chkit( 8 ); + if( errtot >= MAXERR ) + { + printf( "%s", toomany ); + goto end8; + } + } +end8: + printerr(); + + + +/* test 9 */ + printf("9. Testing on %d random non-denormal values.\n", NRAND ); + for( i=0; i<NRAND; i++ ) + { + etrand( fullp ); + chkit( 9 ); + } + printerr(); + shownoncrit(); + +/* test 10 */ + printf( + "Do you want to check denormal numbers in this precision ? (y/n) " ); + gets( str0 ); + if( str0[0] != 'y' ) + goto nodenorm; + + printf( "10. Checking denormal numbers.\n" ); + +/* Form 2^-starting power */ + d1 = k2; + e53toe( &d1, q1 ); + epow( etwo, q1, e1 ); + +/* Find 2^-mprec less than starting power */ + d1 = -mprec + 4; + e53toe( &d1, q1 ); + epow( etwo, q1, e3 ); + emul( e1, e3, e3 ); + emov( e3, e2 ); + ediv( etwo, e2, e2 ); + + while( ecmp(e1,e2) != 0 ) + { + eadd( e1, e2, fullp ); + switch( mprec ) + { +#if LDOUBLE + case 64: + etoe64( e1, &sprec64 ); + e64toe( &sprec64, q1 ); + etoe64( fullp, &prec64 ); + e64toe( &prec64, q2 ); + break; +#endif +#ifdef DEC + case 56: +#endif + case 53: + etoe53( e1, &sprec53 ); + e53toe( &sprec53, q1 ); + etoe53( fullp, &prec53 ); + e53toe( &prec53, q2 ); + break; + + case 24: + etoe24( e1, &sprec24 ); + e24toe( &sprec24, q1 ); + etoe24( fullp, &prec24 ); + e24toe( &prec24, q2 ); + break; + } + if( ecmp( q2, ezero ) == 0 ) + goto maxden; + chkit(10); + if( ecmp(q1,q2) == 0 ) + { + ediv( etwo, e1, e1 ); + emov( e3, e2 ); + } + if( errtot >= MAXERR ) + { + printf( "%s", toomany ); + goto maxden; + } + ediv( etwo, e2, e2 ); + } +maxden: + printerr(); +nodenorm: + printf( "\n" ); + } /* loop on precision */ +printf( "End of test.\n" ); +} + +#if CHKINTERNAL +long double xprec64; +double xprec53; +float xprec24; + +/* Check binary -> printf -> scanf -> binary identity + * of internal routines + */ +void chkinternal( ref, tst, string ) +unsigned short ref[], tst[]; +char *string; +{ + +if( ecmp(ref,tst) != 0 ) + { + printf( "internal identity compare error!\n" ); + chkid( ref, tst, string ); + } +} +#endif + + +/* Check binary -> printf -> scanf -> binary identity + */ +void chkid( print, scan, string ) +unsigned short print[], scan[]; +char *string; +{ +/* Test printf-scanf identity */ +if( ecmp( print, scan ) != 0 ) + { + pvec( print, NE ); + printf( " ->printf-> %s ->scanf->\n", string ); + pvec( scan, NE ); + printf( " is not an identity.\n" ); + ++identerr; + } +} + + +/* Check scanf result + */ +void chkscan( ref, tst, string ) +unsigned short ref[], tst[]; +char *string; +{ +/* Test scanf() */ +if( ecmp( ref, tst ) != 0 ) + { + printf( "scanf(%s) -> ", string ); + pvec( tst, NE ); + printf( "\n should be " ); + pvec( ref, NE ); + printf( ".\n" ); + ++errscan; + ++errtot; + } +} + + +/* Test printf() result + */ +void chkprint( ref, tst, string ) +unsigned short ref[], tst[]; +char *string; +{ +if( ecmp(ref, tst) != 0 ) + { + printf( "printf( "); + pvec( ref, NE ); + printf( ") -> %s\n", string ); + printf( " = " ); + pvec( tst, NE ); + printf( ".\n" ); + ++errprint; + ++errtot; + } +} + + +/* Print array of n 16-bit shorts + */ +void pvec( x, n ) +unsigned short x[]; +int n; +{ +int i; + +for( i=0; i<n; i++ ) + { + printf( "%04x ", x[i] ); + } +} + +/* Measure worst case printf rounding error + */ +void cmpprint( ref, tst ) +unsigned short ref[], tst[]; +{ +unsigned short e[NE]; + +if( ecmp( ref, ezero ) != 0 ) + { + esub( ref, tst, e ); + ediv( ref, e, e ); + eabs( e ); + if( ecmp( e, rprint ) > 0 ) + emov( e, rprint ); + } +} + +/* Measure worst case scanf rounding error + */ +void cmpscan( ref, tst ) +unsigned short ref[], tst[]; +{ +unsigned short er[NE]; + +if( ecmp( ref, ezero ) != 0 ) + { + esub( ref, tst, er ); + ediv( ref, er, er ); + eabs( er ); + if( ecmp( er, rscan ) > 0 ) + emov( er, rscan ); + if( ecmp( er, ehalf ) > 0 ) + { + etoasc( tst, str1, 21 ); + printf( "Bad error: scanf(%s) = %s !\n", str0, str1 ); + } + } +} + +/* Check rounded-down decimal string output of printf + */ +void cmptrunc( ref, tst ) +unsigned short ref[], tst[]; +{ +if( ecmp( ref, tst ) != 0 ) + { + printf( "printf(%s%s%s, %s) -> %s\n", quo, tformat, quo, str1, str2 ); + printf( "should be %s .\n", str3 ); + errprint += 1; + } +} + + +void shownoncrit() +{ + +etoasc( rprint, str0, 3 ); +printf( "Maximum relative printf error found = %s .\n", str0 ); +etoasc( rscan, str0, 3 ); +printf( "Maximum relative scanf error found = %s .\n", str0 ); +} + + + +/* Produce arguments and call comparison subroutines. + */ +void chkit( testno ) +int testno; +{ +unsigned short t[NE], u[NE], v[NE]; +int j; + +switch( mprec ) + { +#if LDOUBLE + case 64: + etoe64( fullp, &prec64 ); + e64toe( &prec64, rounded ); +#if CHKINTERNAL + e64toasc( &prec64, str1, SPREC ); + asctoe64( str1, &xprec64 ); + e64toe( &xprec64, t ); + chkinternal( rounded, t, str1 ); +#endif +/* check printf and scanf */ + sprintf( str2, format, prec64 ); + sscanf( str2, fformat, &sprec64 ); + e64toe( &sprec64, u ); + chkid( rounded, u, str2 ); + asctoe64( str2, &ssprec64 ); + e64toe( &ssprec64, v ); + chkscan( v, u, str2 ); + chkprint( rounded, v, str2 ); + if( testno < 8 ) + break; +/* rounding error measurement */ + etoasc( fullp, str0, 24 ); + etoe64( fullp, &ssprec64 ); + e64toe( &ssprec64, u ); + sprintf( str2, format, ssprec64 ); + asctoe( str2, t ); + cmpprint( u, t ); + sscanf( str0, fformat, &sprec64 ); + e64toe( &sprec64, t ); + cmpscan( fullp, t ); + if( testno < 8 ) + break; +/* strings rounded to less than maximum precision */ + e64toasc( &ssprec64, str1, 24 ); + for( j=SPREC-1; j>0; j-- ) + { + e64toasc( &ssprec64, str3, j ); + asctoe( str3, v ); + sprintf( tformat, "%s.%dLe", pct, j ); + sprintf( str2, tformat, ssprec64 ); + asctoe( str2, t ); + cmptrunc( v, t ); + } + break; +#endif +#ifdef DEC + case 56: +#endif + case 53: + etoe53( fullp, &prec53 ); + e53toe( &prec53, rounded ); +#if CHKINTERNAL + e53toasc( &prec53, str1, SPREC ); + asctoe53( str1, &xprec53 ); + e53toe( &xprec53, t ); + chkinternal( rounded, t, str1 ); +#endif + sprintf( str2, format, prec53 ); + sscanf( str2, fformat, &sprec53 ); + e53toe( &sprec53, u ); + chkid( rounded, u, str2 ); + asctoe53( str2, &ssprec53 ); + e53toe( &ssprec53, v ); + chkscan( v, u, str2 ); + chkprint( rounded, v, str2 ); + if( testno < 8 ) + break; +/* rounding error measurement */ + etoasc( fullp, str0, 24 ); + etoe53( fullp, &ssprec53 ); + e53toe( &ssprec53, u ); + sprintf( str2, format, ssprec53 ); + asctoe( str2, t ); + cmpprint( u, t ); + sscanf( str0, fformat, &sprec53 ); + e53toe( &sprec53, t ); + cmpscan( fullp, t ); + if( testno < 8 ) + break; + e53toasc( &ssprec53, str1, 24 ); + for( j=SPREC-1; j>0; j-- ) + { + e53toasc( &ssprec53, str3, j ); + asctoe( str3, v ); + sprintf( tformat, "%s.%de", pct, j ); + sprintf( str2, tformat, ssprec53 ); + asctoe( str2, t ); + cmptrunc( v, t ); + } + break; + + case 24: + etoe24( fullp, &prec24 ); + e24toe( &prec24, rounded ); +#if CHKINTERNAL + e24toasc( &prec24, str1, SPREC ); + asctoe24( str1, &xprec24 ); + e24toe( &xprec24, t ); + chkinternal( rounded, t, str1 ); +#endif + sprintf( str2, format, prec24 ); + sscanf( str2, fformat, &sprec24 ); + e24toe( &sprec24, u ); + chkid( rounded, u, str2 ); + asctoe24( str2, &ssprec24 ); + e24toe( &ssprec24, v ); + chkscan( v, u, str2 ); + chkprint( rounded, v, str2 ); + if( testno < 8 ) + break; +/* rounding error measurement */ + etoasc( fullp, str0, 24 ); + etoe24( fullp, &ssprec24 ); + e24toe( &ssprec24, u ); + sprintf( str2, format, ssprec24 ); + asctoe( str2, t ); + cmpprint( u, t ); + sscanf( str0, fformat, &sprec24 ); + e24toe( &sprec24, t ); + cmpscan( fullp, t ); +/* + if( testno < 8 ) + break; +*/ + e24toasc( &ssprec24, str1, 24 ); + for( j=SPREC-1; j>0; j-- ) + { + e24toasc( &ssprec24, str3, j ); + asctoe( str3, v ); + sprintf( tformat, "%s.%de", pct, j ); + sprintf( str2, tformat, ssprec24 ); + asctoe( str2, t ); + cmptrunc( v, t ); + } + break; + } +} + + +void printerr() +{ +if( (errscan == 0) && (identerr == 0) && (errprint == 0) ) + printf( "No errors found.\n" ); +else + { + printf( "%d binary -> decimal errors found.\n", errprint ); + printf( "%d decimal -> binary errors found.\n", errscan ); + } +errscan = 0; /* reset for next test */ +identerr = 0; +errprint = 0; +errtot = 0; +} + + +/* Random number generator + * in the range M * 10^N, where 1 <= M <= 10^17 - 1 + * and -27 <= N <= +27. Test values of M are logarithmically distributed + * random integers; test values of N are uniformly distributed random integers. + */ + +static char *fwidth = "1.036163291797320557783096e1"; /* log(sqrt(10^9-1)) */ +static char *dwidth = "1.957197329044938830915E1"; /* log(sqrt(10^17-1)) */ +static char *ldwidth = "2.302585092994045684017491e1"; /* log(sqrt(10^20-1)) */ + +static char *a13 = "13.0"; +static char *a27 = "27.0"; +static char *a34 = "34.0"; +static char *a10m13 = "1.0e-13"; +static unsigned short LOW[ NE ], WIDTH[NE], e27[NE], e10m13[NE]; + + +void mnrand( erand ) +unsigned short erand[]; +{ +unsigned short ea[NE], em[NE], en[NE], ex[NE]; +double x, a; + +if( mnrflag ) + { + if( mnrflag == 3 ) + { + asctoe( ldwidth, WIDTH ); + asctoe( a34, e27 ); + } + if( mnrflag == 2 ) + { + asctoe( dwidth, WIDTH ); + asctoe( a27, e27 ); + } + if( mnrflag == 1 ) + { + asctoe( fwidth, WIDTH ); + asctoe( a13, e27 ); + } + asctoe( a10m13, e10m13 ); + mnrflag = 0; + } +drand( &x ); +e53toe( &x, ex ); /* x = WIDTH * ( x - 1.0 ) + LOW; */ +esub( eone, ex, ex ); +emul( WIDTH, ex, ex ); +eexp( ex, ex ); /* x = exp(x); */ + +drand( &a ); +e53toe( &a, ea ); +emul( ea, ex, ea ); /* a = 1.0e-13 * x * a; */ +emul( e10m13, ea, ea ); +eabs( ea ); +eadd( ea, ex, ex ); /* add fuzz */ +emul( ex, ex, ex ); /* square it, to get range to 10^17 - 1 */ +efloor( ex, em ); /* this is M */ + +/* Random power of 10 */ +drand( &a ); +e53toe( &a, ex ); +esub( eone, ex, ex ); /* y3 = 54.0 * ( y3 - 1.0 ) + 0.5; */ +emul( e27, ex, ex ); +eadd( ex, ex, ex ); +eadd( ehalf, ex, ex ); +efloor( ex, ex ); /* y3 = floor( y3 ) - 27.0; */ +esub( e27, ex, en ); /* this is N */ +epow( eten, en, ex ); +emul( ex, em, erand ); +} + +/* -ln 2^16382 */ +char *ldemin = "-1.1355137111933024058873097E4"; +char *ldewid = "2.2710274223866048117746193E4"; +/* -ln 2^1022 */ +char *demin = "-7.0839641853226410622441123E2"; +char *dewid = "1.4167928370645282124488225E3"; +/* -ln 2^125 */ +char *femin = "-8.6643397569993163677154015E1"; +char *fewid = "1.7328679513998632735430803E2"; + +void etrand( erand ) +unsigned short erand[]; +{ +unsigned short ea[NE], ex[NE]; +double x, a; + +if( etrflag ) + { + if( etrflag == 3 ) + { + asctoe( ldemin, LOW ); + asctoe( ldewid, WIDTH ); + asctoe( a34, e27 ); + } + if( etrflag == 2 ) + { + asctoe( demin, LOW ); + asctoe( dewid, WIDTH ); + asctoe( a27, e27 ); + } + if( etrflag == 1 ) + { + asctoe( femin, LOW ); + asctoe( fewid, WIDTH ); + asctoe( a13, e27 ); + } + asctoe( a10m13, e10m13 ); + etrflag = 0; + } +drand( &x ); +e53toe( &x, ex ); /* x = WIDTH * ( x - 1.0 ) + LOW; */ +esub( eone, ex, ex ); +emul( WIDTH, ex, ex ); +eadd( LOW, ex, ex ); +eexp( ex, ex ); /* x = exp(x); */ + +/* add fuzz + */ +drand( &a ); +e53toe( &a, ea ); +emul( ea, ex, ea ); /* a = 1.0e-13 * x * a; */ +emul( e10m13, ea, ea ); +if( ecmp( ex, ezero ) > 0 ) + eneg( ea ); +eadd( ea, ex, erand ); +} + diff --git a/test/math/ieetst.doc b/test/math/ieetst.doc index be2388bcc..bd5134beb 100644 --- a/test/math/ieetst.doc +++ b/test/math/ieetst.doc @@ -1,132 +1,132 @@ -
- ieetst, version 0.2
-
- This software tests the numerical accuracy of floating point
-binary <-> decimal string conversion, as done by your C language
-library functions printf() and scanf(), for compliance with the
-IEEE arithmetic standards ANSI/IEEE Std 754-1985 and ANSI/IEEE
-Std 854-1987. The test covers 32-bit float, 64-bit double, and
-80-bit long double precision conversions to and from decimal
-ASCII strings.
-
- The test program checks for proper implementation of the
-following specifications of the standards:
-
- (1) correctly rounded conversions of numbers of the form M *
- 10^N, where M and N are integers such that, in double precision,
- for example, |M| < 10^17, |N| <= 27.
-
- (2) binary -> decimal -> binary conversions to be an identity
- if a sufficiently large number of decimal digits is requested.
-
- (3) correctly rounded decimal outputs of less than the maximum
- number of digits
-
- (4) The maximum observed conversion error of numbers outside the
- domain covered by (1) is reported by the test program; it is
- not supposed to exceed 0.97 ulp.
-
-There are 10 separate tests. Tests 1 through 6 use values near
-2^n and 10^n. Test 7 addresses item (1) above. Test 8 checks
-the rounding of exact half-integer numbers. Test 9 is for item
-(4) above. Test 10 checks denormal numbers. Tests 8 through 10
-address item (3) using printf formats that produce outputs of 1,
-2, 3, ... digits after the decimal point. All tests check, when
-appropriate, that the binary output of scanf is the same as the
-binary input to printf, item (2).
-
-Example error messages:
-
- 0000 0000 0000 1000 8000 3f80 ->printf-> 5.87748296e-39 ->scanf->
- 0000 0000 0000 0000 8000 3f6e is not an identity.
-
- scanf(-9.9999900000000003e-01) -> 0000 4800 085f ef39 ffff bffe
- should be 0000 5000 085f ef39 ffff bffe .
-
- printf("%.14e", 6.13592315154256467968352E-3) -> 6.13592315154257e-03
- should be 6.13592315154256E-3 .
-
-Binary values are displayed as four-digit hex groups in the
-little-endian format of the internal reference arithmetic. The
-least significant 16-bit word is first, the exponent is last.
-
- The design of the test program requires knowing the binary
-data structure of the floating point format under test. For
-configuration, check the .h files carefully. All the programs
-need to be told via mconf.h if the numeric format is
-little-endian (IBMPC) or big-endian (MIEEE). If your system
-supports an 80-bit long double precision data type, define
-LDOUBLE 1 in ieetst.c; otherwise define LDOUBLE 0. A provision
-for DEC PDP-11/VAX numbers is implemented (double precision
-only). Conversions for other data structures can be added by
-analogy to the ifdefs for DEC.
-
- Most of the tests rely on comparison with the results of a
-portable reference arithmetic, contained in the file ieee.c.
-This is configured for an 80-bit significand, to have enough
-precision to satisfy the conversion requirements of IEEE 854 for
-the extended double format of IEEE 754. The reference arithmetic
-includes binary <--> ASCII conversion routines and single <-->
-double <--> extended double conversions. A strictly rounded
-square root function is given in esqrt.c. Additional functions
-are provided by elog.c, eexp.c, etanh.c, epow.c, all of which
-call on ieee.c for their arithmetic. Some of the ANSI C
-functions are supplied in ieee.c; for example, efloor(),
-efrexp(), eldexp(). The functions and the reference arithmetic
-are described further in the book _Methods and Programs for
-Mathematical Functions_ (Prentice-Hall or Simon & Schuster
-International, 1989), by S. L. Moshier.
-
- As an aid in diagnosis, a calculator program, ecalc.c, is
-supplied. It uses ieee.c for its arithmetic. Documentation for
-the calculator's user interface is in the file calc100.doc
-(calc100 is a fuller featured 100-digit version of ecalc). The
-calculator needs to be told by qcalc.h if addresses are 32 bits
-long (define LARGEMEM 1) or 16 bits long (define LARGEMEM 0).
-
- Because the source code of ieee.c is included here, a version
-of W. Kahan's PARANOIA is also provided; this has been heavily
-modified by substituting subroutine calls to ieee.c in place of
-all arithmetic operators. It is important that you use PARANOIA
-to check the arithmetic after any modifications you may make to
-ieee.c.
-
- Several systems have been tested with the initial version of
-ieetst. Sun 4 (SPARC) passes; DEC VMS C has only a small flaw;
-Microsoft flunks; ATT SysVR2 (Motorola) flunks even worse.
-
-
- Files:
-
-calc100.doc calculator documentaton
-descrip.mms part of VAX VMS makefile
-drand.c random number generator
-ecalc.c calculator
-ecalc.opt part of VAX VMS makefile
-econst.c constants for reference arithmetic
-eexp.c reference exponential function
-ehead.h declarations for reference arithmetic routines
-elog.c reference logarithm
-eparanoi.c floating point arithmetic tester
-eparanoi.opt part of VAX VMS makefile
-epow.c reference exponentiation
-esqrt.c reference square root
-etanh.c reference hyperbolic tangent
-etodec.c conversions to and from DEC double precision format
-ieee.c the reference arithmetic
-ieetst.c printf/scanf tester
-ieetst.doc this file
-ieetst.mak Microsoft make file
-ieetst.opt part of VAX VMS makefile
-makefile Unix make file
-mconf.h definitions for arithmetic format
-mtherr.c common error reporter
-qcalc.h definitions for calculator
-
-
-This software may be copied freely.
-
--- Steve Moshier
-
-v0.1 July, 1992
-v0.2 January, 1993
+ + ieetst, version 0.2 + + This software tests the numerical accuracy of floating point +binary <-> decimal string conversion, as done by your C language +library functions printf() and scanf(), for compliance with the +IEEE arithmetic standards ANSI/IEEE Std 754-1985 and ANSI/IEEE +Std 854-1987. The test covers 32-bit float, 64-bit double, and +80-bit long double precision conversions to and from decimal +ASCII strings. + + The test program checks for proper implementation of the +following specifications of the standards: + + (1) correctly rounded conversions of numbers of the form M * + 10^N, where M and N are integers such that, in double precision, + for example, |M| < 10^17, |N| <= 27. + + (2) binary -> decimal -> binary conversions to be an identity + if a sufficiently large number of decimal digits is requested. + + (3) correctly rounded decimal outputs of less than the maximum + number of digits + + (4) The maximum observed conversion error of numbers outside the + domain covered by (1) is reported by the test program; it is + not supposed to exceed 0.97 ulp. + +There are 10 separate tests. Tests 1 through 6 use values near +2^n and 10^n. Test 7 addresses item (1) above. Test 8 checks +the rounding of exact half-integer numbers. Test 9 is for item +(4) above. Test 10 checks denormal numbers. Tests 8 through 10 +address item (3) using printf formats that produce outputs of 1, +2, 3, ... digits after the decimal point. All tests check, when +appropriate, that the binary output of scanf is the same as the +binary input to printf, item (2). + +Example error messages: + + 0000 0000 0000 1000 8000 3f80 ->printf-> 5.87748296e-39 ->scanf-> + 0000 0000 0000 0000 8000 3f6e is not an identity. + + scanf(-9.9999900000000003e-01) -> 0000 4800 085f ef39 ffff bffe + should be 0000 5000 085f ef39 ffff bffe . + + printf("%.14e", 6.13592315154256467968352E-3) -> 6.13592315154257e-03 + should be 6.13592315154256E-3 . + +Binary values are displayed as four-digit hex groups in the +little-endian format of the internal reference arithmetic. The +least significant 16-bit word is first, the exponent is last. + + The design of the test program requires knowing the binary +data structure of the floating point format under test. For +configuration, check the .h files carefully. All the programs +need to be told via mconf.h if the numeric format is +little-endian (IBMPC) or big-endian (MIEEE). If your system +supports an 80-bit long double precision data type, define +LDOUBLE 1 in ieetst.c; otherwise define LDOUBLE 0. A provision +for DEC PDP-11/VAX numbers is implemented (double precision +only). Conversions for other data structures can be added by +analogy to the ifdefs for DEC. + + Most of the tests rely on comparison with the results of a +portable reference arithmetic, contained in the file ieee.c. +This is configured for an 80-bit significand, to have enough +precision to satisfy the conversion requirements of IEEE 854 for +the extended double format of IEEE 754. The reference arithmetic +includes binary <--> ASCII conversion routines and single <--> +double <--> extended double conversions. A strictly rounded +square root function is given in esqrt.c. Additional functions +are provided by elog.c, eexp.c, etanh.c, epow.c, all of which +call on ieee.c for their arithmetic. Some of the ANSI C +functions are supplied in ieee.c; for example, efloor(), +efrexp(), eldexp(). The functions and the reference arithmetic +are described further in the book _Methods and Programs for +Mathematical Functions_ (Prentice-Hall or Simon & Schuster +International, 1989), by S. L. Moshier. + + As an aid in diagnosis, a calculator program, ecalc.c, is +supplied. It uses ieee.c for its arithmetic. Documentation for +the calculator's user interface is in the file calc100.doc +(calc100 is a fuller featured 100-digit version of ecalc). The +calculator needs to be told by qcalc.h if addresses are 32 bits +long (define LARGEMEM 1) or 16 bits long (define LARGEMEM 0). + + Because the source code of ieee.c is included here, a version +of W. Kahan's PARANOIA is also provided; this has been heavily +modified by substituting subroutine calls to ieee.c in place of +all arithmetic operators. It is important that you use PARANOIA +to check the arithmetic after any modifications you may make to +ieee.c. + + Several systems have been tested with the initial version of +ieetst. Sun 4 (SPARC) passes; DEC VMS C has only a small flaw; +Microsoft flunks; ATT SysVR2 (Motorola) flunks even worse. + + + Files: + +calc100.doc calculator documentaton +descrip.mms part of VAX VMS makefile +drand.c random number generator +ecalc.c calculator +ecalc.opt part of VAX VMS makefile +econst.c constants for reference arithmetic +eexp.c reference exponential function +ehead.h declarations for reference arithmetic routines +elog.c reference logarithm +eparanoi.c floating point arithmetic tester +eparanoi.opt part of VAX VMS makefile +epow.c reference exponentiation +esqrt.c reference square root +etanh.c reference hyperbolic tangent +etodec.c conversions to and from DEC double precision format +ieee.c the reference arithmetic +ieetst.c printf/scanf tester +ieetst.doc this file +ieetst.mak Microsoft make file +ieetst.opt part of VAX VMS makefile +makefile Unix make file +mconf.h definitions for arithmetic format +mtherr.c common error reporter +qcalc.h definitions for calculator + + +This software may be copied freely. + +-- Steve Moshier + +v0.1 July, 1992 +v0.2 January, 1993 diff --git a/test/math/mconf.h b/test/math/mconf.h index cb9c3b50d..faf789b26 100644 --- a/test/math/mconf.h +++ b/test/math/mconf.h @@ -1,108 +1,108 @@ -/* mconf.h
- *
- * Common include file for math routines
- *
- *
- *
- * SYNOPSIS:
- *
- * #include "mconf.h"
- *
- *
- *
- * DESCRIPTION:
- *
- * This file contains definitions for error codes that are
- * passed to the common error handling routine mtherr()
- * (which see).
- *
- * The file also includes a conditional assembly definition
- * for the type of computer arithmetic (IEEE, DEC, Motorola
- * IEEE, or UNKnown).
- *
- * For Digital Equipment PDP-11 and VAX computers, certain
- * IBM systems, and others that use numbers with a 56-bit
- * significand, the symbol DEC should be defined. In this
- * mode, most floating point constants are given as arrays
- * of octal integers to eliminate decimal to binary conversion
- * errors that might be introduced by the compiler.
- *
- * For computers, such as IBM PC, that follow the IEEE
- * Standard for Binary Floating Point Arithmetic (ANSI/IEEE
- * Std 754-1985), the symbol IBMPC should be defined. These
- * numbers have 53-bit significands. In this mode, constants
- * are provided as arrays of hexadecimal 16 bit integers.
- *
- * To accommodate other types of computer arithmetic, all
- * constants are also provided in a normal decimal radix
- * which one can hope are correctly converted to a suitable
- * format by the available C language compiler. To invoke
- * this mode, the symbol UNK is defined.
- *
- * An important difference among these modes is a predefined
- * set of machine arithmetic constants for each. The numbers
- * MACHEP (the machine roundoff error), MAXNUM (largest number
- * represented), and several other parameters are preset by
- * the configuration symbol. Check the file const.c to
- * ensure that these values are correct for your computer.
- *
- */
-
-/*
-Cephes Math Library Release 2.0: April, 1987
-by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-/* Constant definitions for math error conditions
- */
-
-#define DOMAIN 1 /* argument domain error */
-#define SING 2 /* argument singularity */
-#define OVERFLOW 3 /* overflow range error */
-#define UNDERFLOW 4 /* underflow range error */
-#define TLOSS 5 /* total loss of precision */
-#define PLOSS 6 /* partial loss of precision */
-
-#define EDOM 33
-#define ERANGE 34
-
-/*
-typedef struct
- {
- double r;
- double i;
- }cmplx;
-*/
-
-/* Type of computer arithmetic */
-
-/* PDP-11, Pro350, VAX:
- */
-/*define DEC 1*/
-
-/* Intel IEEE, low order words come first:
- */
-#define IBMPC 1
-
-/* Motorola IEEE, high order words come first
- * (Sun workstation):
- */
-/*define MIEEE 1*/
-
-/* UNKnown arithmetic, invokes coefficients given in
- * normal decimal format. Beware of range boundary
- * problems (MACHEP, MAXLOG, etc. in const.c) and
- * roundoff problems in pow.c:
- */
- /*define UNK 1*/
-
-/* Define to ask for infinity support, else undefine. */
-#define INFINITY
-
-/* Define to ask for Not-a-Number support, else undefine. */
-#define NANS
-
-/* Define to support denormal numbers, else undefine. */
-#define DENORMAL
+/* mconf.h + * + * Common include file for math routines + * + * + * + * SYNOPSIS: + * + * #include "mconf.h" + * + * + * + * DESCRIPTION: + * + * This file contains definitions for error codes that are + * passed to the common error handling routine mtherr() + * (which see). + * + * The file also includes a conditional assembly definition + * for the type of computer arithmetic (IEEE, DEC, Motorola + * IEEE, or UNKnown). + * + * For Digital Equipment PDP-11 and VAX computers, certain + * IBM systems, and others that use numbers with a 56-bit + * significand, the symbol DEC should be defined. In this + * mode, most floating point constants are given as arrays + * of octal integers to eliminate decimal to binary conversion + * errors that might be introduced by the compiler. + * + * For computers, such as IBM PC, that follow the IEEE + * Standard for Binary Floating Point Arithmetic (ANSI/IEEE + * Std 754-1985), the symbol IBMPC should be defined. These + * numbers have 53-bit significands. In this mode, constants + * are provided as arrays of hexadecimal 16 bit integers. + * + * To accommodate other types of computer arithmetic, all + * constants are also provided in a normal decimal radix + * which one can hope are correctly converted to a suitable + * format by the available C language compiler. To invoke + * this mode, the symbol UNK is defined. + * + * An important difference among these modes is a predefined + * set of machine arithmetic constants for each. The numbers + * MACHEP (the machine roundoff error), MAXNUM (largest number + * represented), and several other parameters are preset by + * the configuration symbol. Check the file const.c to + * ensure that these values are correct for your computer. + * + */ + +/* +Cephes Math Library Release 2.0: April, 1987 +by Stephen L. Moshier +Direct inquiries to 30 Frost Street, Cambridge, MA 02140 +*/ + + +/* Constant definitions for math error conditions + */ + +#define DOMAIN 1 /* argument domain error */ +#define SING 2 /* argument singularity */ +#define OVERFLOW 3 /* overflow range error */ +#define UNDERFLOW 4 /* underflow range error */ +#define TLOSS 5 /* total loss of precision */ +#define PLOSS 6 /* partial loss of precision */ + +#define EDOM 33 +#define ERANGE 34 + +/* +typedef struct + { + double r; + double i; + }cmplx; +*/ + +/* Type of computer arithmetic */ + +/* PDP-11, Pro350, VAX: + */ +/*define DEC 1*/ + +/* Intel IEEE, low order words come first: + */ +#define IBMPC 1 + +/* Motorola IEEE, high order words come first + * (Sun workstation): + */ +/*define MIEEE 1*/ + +/* UNKnown arithmetic, invokes coefficients given in + * normal decimal format. Beware of range boundary + * problems (MACHEP, MAXLOG, etc. in const.c) and + * roundoff problems in pow.c: + */ + /*define UNK 1*/ + +/* Define to ask for infinity support, else undefine. */ +#define INFINITY + +/* Define to ask for Not-a-Number support, else undefine. */ +#define NANS + +/* Define to support denormal numbers, else undefine. */ +#define DENORMAL diff --git a/test/math/mtherr.c b/test/math/mtherr.c index de6d81b94..52e3ec2ad 100644 --- a/test/math/mtherr.c +++ b/test/math/mtherr.c @@ -1,96 +1,96 @@ -/* mtherr.c
- *
- * Library common error handling routine
- *
- *
- *
- * SYNOPSIS:
- *
- * char *fctnam;
- * int code;
- * void mtherr();
- *
- * mtherr( fctnam, code );
- *
- *
- *
- * DESCRIPTION:
- *
- * This routine may be called to report one of the following
- * error conditions (in the include file mconf.h).
- *
- * Mnemonic Value Significance
- *
- * DOMAIN 1 argument domain error
- * SING 2 function singularity
- * OVERFLOW 3 overflow range error
- * UNDERFLOW 4 underflow range error
- * TLOSS 5 total loss of precision
- * PLOSS 6 partial loss of precision
- * EDOM 33 Unix domain error code
- * ERANGE 34 Unix range error code
- *
- * The default version of the file prints the function name,
- * passed to it by the pointer fctnam, followed by the
- * error condition. The display is directed to the standard
- * output device. The routine then returns to the calling
- * program. Users may wish to modify the program to abort by
- * calling exit() under severe error conditions such as domain
- * errors.
- *
- * Since all error conditions pass control to this function,
- * the display may be easily changed, eliminated, or directed
- * to an error logging device.
- *
- * SEE ALSO:
- *
- * mconf.h
- *
- */
-
-/*
-Cephes Math Library Release 2.0: April, 1987
-by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include "mconf.h"
-
-/* Notice: the order of appearance of the following
- * messages is bound to the error codes defined
- * in mconf.h.
- */
-static char *ermsg[7] = {
-"unknown", /* error code 0 */
-"domain", /* error code 1 */
-"singularity", /* et seq. */
-"overflow",
-"underflow",
-"total loss of precision",
-"partial loss of precision"
-};
-
-
-
-void mtherr( name, code )
-char *name;
-int code;
-{
-
-/* Display string passed by calling program,
- * which is supposed to be the name of the
- * function in which the error occurred:
- */
-printf( "\n%s ", name );
-
-/* Display error message defined
- * by the code argument.
- */
-if( (code <= 0) || (code >= 6) )
- code = 0;
-printf( "%s error\n", ermsg[code] );
-
-/* Return to calling
- * program
- */
-}
+/* mtherr.c + * + * Library common error handling routine + * + * + * + * SYNOPSIS: + * + * char *fctnam; + * int code; + * void mtherr(); + * + * mtherr( fctnam, code ); + * + * + * + * DESCRIPTION: + * + * This routine may be called to report one of the following + * error conditions (in the include file mconf.h). + * + * Mnemonic Value Significance + * + * DOMAIN 1 argument domain error + * SING 2 function singularity + * OVERFLOW 3 overflow range error + * UNDERFLOW 4 underflow range error + * TLOSS 5 total loss of precision + * PLOSS 6 partial loss of precision + * EDOM 33 Unix domain error code + * ERANGE 34 Unix range error code + * + * The default version of the file prints the function name, + * passed to it by the pointer fctnam, followed by the + * error condition. The display is directed to the standard + * output device. The routine then returns to the calling + * program. Users may wish to modify the program to abort by + * calling exit() under severe error conditions such as domain + * errors. + * + * Since all error conditions pass control to this function, + * the display may be easily changed, eliminated, or directed + * to an error logging device. + * + * SEE ALSO: + * + * mconf.h + * + */ + +/* +Cephes Math Library Release 2.0: April, 1987 +by Stephen L. Moshier +Direct inquiries to 30 Frost Street, Cambridge, MA 02140 +*/ + +#include "mconf.h" + +/* Notice: the order of appearance of the following + * messages is bound to the error codes defined + * in mconf.h. + */ +static char *ermsg[7] = { +"unknown", /* error code 0 */ +"domain", /* error code 1 */ +"singularity", /* et seq. */ +"overflow", +"underflow", +"total loss of precision", +"partial loss of precision" +}; + + + +void mtherr( name, code ) +char *name; +int code; +{ + +/* Display string passed by calling program, + * which is supposed to be the name of the + * function in which the error occurred: + */ +printf( "\n%s ", name ); + +/* Display error message defined + * by the code argument. + */ +if( (code <= 0) || (code >= 6) ) + code = 0; +printf( "%s error\n", ermsg[code] ); + +/* Return to calling + * program + */ +} |