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Diffstat (limited to 'test/math/ieee.c')
| -rw-r--r-- | test/math/ieee.c | 4119 |
1 files changed, 0 insertions, 4119 deletions
diff --git a/test/math/ieee.c b/test/math/ieee.c deleted file mode 100644 index 17efea01c..000000000 --- a/test/math/ieee.c +++ /dev/null @@ -1,4119 +0,0 @@ -/* 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 ); -} |