From 1077fa4d772832f77a677ce7fb7c2d513b959e3f Mon Sep 17 00:00:00 2001
From: Eric Andersen <andersen@codepoet.org>
Date: Thu, 10 May 2001 00:40:28 +0000
Subject: uClibc now has a math library.  muahahahaha!  -Erik

---
 libm/ldouble/ieee.c | 4182 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 4182 insertions(+)
 create mode 100644 libm/ldouble/ieee.c

(limited to 'libm/ldouble/ieee.c')

diff --git a/libm/ldouble/ieee.c b/libm/ldouble/ieee.c
new file mode 100644
index 000000000..584329b0c
--- /dev/null
+++ b/libm/ldouble/ieee.c
@@ -0,0 +1,4182 @@
+/*							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 <math.h>
+#include "ehead.h"
+
+/* Change UNK into something else. */
+#ifdef UNK
+#undef UNK
+#if BIGENDIAN
+#define MIEEE 1
+#else
+#define IBMPC 1
+#endif
+#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;
+
+#ifdef ANSIPROT
+extern void eaddm ( unsigned short *, unsigned short * );
+extern void esubm ( unsigned short *, unsigned short * );
+extern void emdnorm ( unsigned short *, int, int, long, int );
+extern void asctoeg ( char *, unsigned short *, int );
+extern void enan ( unsigned short *, int );
+extern void asctoe24 ( char *, unsigned short * );
+extern void asctoe53 ( char *, unsigned short * );
+extern void asctoe64 ( char *, unsigned short * );
+extern void asctoe113 ( char *, unsigned short * );
+extern void eremain ( unsigned short *, unsigned short *, unsigned short * );
+extern void einit ( void );
+extern void eiremain ( unsigned short *, unsigned short * );
+extern int ecmp ( unsigned short *, unsigned short * );
+extern int edivm ( unsigned short *, unsigned short * );
+extern int emulm ( unsigned short *, unsigned short * );
+extern int eisneg ( unsigned short * );
+extern int eisinf ( unsigned short * );
+extern void emovi ( unsigned short *, unsigned short * );
+extern void emovo ( unsigned short *, unsigned short * );
+extern void emovz ( unsigned short *, unsigned short * );
+extern void ecleaz ( unsigned short * );
+extern void eadd1 ( unsigned short *, unsigned short *, unsigned short * );
+extern int eisnan ( unsigned short * );
+extern int eiisnan ( unsigned short * );
+static void toe24( unsigned short *, unsigned short * );
+static void toe53( unsigned short *, unsigned short * );
+static void toe64( unsigned short *, unsigned short * );
+static void toe113( unsigned short *, unsigned short * );
+void einfin ( unsigned short * );
+void eshdn1 ( unsigned short * );
+void eshup1 ( unsigned short * );
+void eshup6 ( unsigned short * );
+void eshdn6 ( unsigned short * );
+void eshup8 ( unsigned short * );
+void eshdn8 ( unsigned short * );
+void m16m ( unsigned short, unsigned short *, unsigned short * );
+int ecmpm ( unsigned short *, unsigned short * );
+int enormlz ( unsigned short * );
+void ecleazs ( unsigned short * );
+int eshift ( unsigned short *, int );
+void emov ( unsigned short *, unsigned short * );
+void eneg ( unsigned short * );
+void eclear ( unsigned short * );
+void efloor ( unsigned short *, unsigned short * );
+void eadd ( unsigned short *, unsigned short *, unsigned short * );
+void esub ( unsigned short *, unsigned short *, unsigned short * );
+void ediv ( unsigned short *, unsigned short *, unsigned short * );
+void emul ( unsigned short *, unsigned short *, unsigned short * );
+void e24toe ( unsigned short *, unsigned short * );
+void e53toe ( unsigned short *, unsigned short * );
+void e64toe ( unsigned short *, unsigned short * );
+void e113toe ( unsigned short *, unsigned short * );
+void etoasc ( unsigned short *, char *, int );
+static int eiisinf ( unsigned short * );
+#else
+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(), ecmpm(), enormlz(), eshift();
+void einfin(), eshdn1(), eshup1(), eshup6(), eshdn6();
+void eshup8(), eshdn8(), m16m();
+void eadd(), esub(), ediv(), emul();
+void ecleazs(), emov(), eneg(), eclear(), efloor();
+void e24toe(), e53toe(), e64toe(), e113toe(), etoasc();
+static int eiisinf();
+#endif
+
+
+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 significane.
+ */
+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 * ((unsigned long)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.
+ */
+#ifdef 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:
+#ifdef 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, sign;
+long lt, lta, ltb;
+
+/* IEEE says if result is not a NaN, the sign is "-" if and only if
+   operands have opposite signs -- but flush -0 to 0 later if not IEEE.  */
+sign = eisneg(a) ^ eisneg(b);
+
+#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) )
+	{
+	einfin(c);
+	goto divsign;
+	}
+if( eisinf(a) )
+	{
+	eclear(c);
+	goto divsign;
+	}
+#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);
+	goto divsign;
+	}
+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;
+			}
+		}
+	einfin(c);
+	mtherr( "ediv", SING );
+	goto divsign;
+	}
+dnzro2:
+
+i = edivm( ai, bi );
+/* calculate exponent */
+lt = ltb - lta + EXONE;
+emdnorm( bi, i, 0, lt, 64 );
+emovo( bi, c );
+
+divsign:
+
+if( sign )
+	*(c+(NE-1)) |= 0x8000;
+else
+	*(c+(NE-1)) &= ~0x8000;
+}
+
+
+
+/*
+;	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, sign;
+long lt, lta, ltb;
+
+/* IEEE says if result is not a NaN, the sign is "-" if and only if
+   operands have opposite signs -- but flush -0 to 0 later if not IEEE.  */
+sign = eisneg(a) ^ eisneg(b);
+
+#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) )
+	{
+	einfin(c);
+	goto mulsign;
+	}
+#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);
+	goto mulsign;
+	}
+mnzer1:
+
+if( bi[E] == 0 )
+	{
+	for( i=1; i<NI-1; i++ )
+		{
+		if( bi[i] != 0 )
+			{
+			ltb -= enormlz( bi );
+			goto mnzer2;
+			}
+		}
+	eclear(c);
+	goto mulsign;
+	}
+mnzer2:
+
+/* Multiply significands */
+j = emulm( ai, bi );
+/* calculate exponent */
+lt = lta + ltb - (EXONE - 1);
+emdnorm( bi, j, 0, lt, 64 );
+emovo( bi, c );
+/*  IEEE says sign is "-" if and only if operands have opposite signs.  */
+mulsign:
+if( sign )
+	*(c+(NE-1)) |= 0x8000;
+else
+	*(c+(NE-1)) &= ~0x8000;
+}
+
+
+
+
+/*
+; 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 i;
+
+e = pe;
+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 )
+unsigned 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 );
+}
-- 
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