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-rw-r--r--test/math/ieee.c8238
1 files changed, 4119 insertions, 4119 deletions
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 );
+}
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