Add in some math lib tests

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+

+                  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