/* Extended precision arithmetic functions for long double I/O. * This program has been placed in the public domain. */ /* These are the externally visible entries. */ long double _IO_strtold (char *, char **); char * _IO_ldtoa(long double, int, int, int *, int *, char **); /* Number of 16 bit words in external x type format */ #define NE 10 /* Number of 16 bit words in internal format */ #define NI (NE+3) /* Array offset to exponent */ #define E 1 /* Array offset to high guard word */ #define M 2 /* Number of bits of precision */ #define NBITS ((NI-4)*16) /* Maximum number of decimal digits in ASCII conversion * = NBITS*log10(2) */ #define NDEC (NBITS*8/27) /* The exponent of 1.0 */ #define EXONE (0x3fff) static void esub(short unsigned int *a, short unsigned int *b, short unsigned int *c); static void emul(short unsigned int *a, short unsigned int *b, short unsigned int *c); static void ediv(short unsigned int *a, short unsigned int *b, short unsigned int *c); static int ecmp(short unsigned int *a, short unsigned int *b); static int enormlz(short unsigned int *x); static int eshift(short unsigned int *x, int sc); static void eshup1(register short unsigned int *x); static void eshup8(register short unsigned int *x); static void eshup6(register short unsigned int *x); static void eshdn1(register short unsigned int *x); static void eshdn8(register short unsigned int *x); static void eshdn6(register short unsigned int *x); static void eneg(short unsigned int *x); static void emov(register short unsigned int *a, register short unsigned int *b); static void eclear(register short unsigned int *x); static void einfin(register short unsigned int *x); static void efloor(short unsigned int *x, short unsigned int *y); static void etoasc(short unsigned int *x, char *string, int ndigs); static void e64toe(short unsigned int *pe, short unsigned int *y); static int mtherr(char *name, int code); #define UNUSED 0 #if UNUSED static void eabs(short unsigned int *x); static void eldexp(short unsigned int *x, long int pwr2, short unsigned int *y); static void efrexp(short unsigned int *x, long int *exp, short unsigned int *s); static void eifrac(short unsigned int *x, long int *i, short unsigned int *frac); static void ltoe(long int *lp, short unsigned int *y); static void esqrt(short int *x, short int *y); /* void elog(), eexp(), etanh(), epow(); */ static void asctoe(char *s, short unsigned int *y); static void asctoe24(char *s, short unsigned int *y); static void asctoe53(char *s, short unsigned int *y); static void e24toasc(short unsigned int *x, char *string, int ndigs); static void e53toasc(short unsigned int *x, char *string, int ndigs); static void e64toasc(short unsigned int *x, char *string, int ndigs); static void eremain(short unsigned int *a, short unsigned int *b, short unsigned int *c); static void einit(void); static void eadd(short unsigned int *a, short unsigned int *b, short unsigned int *c); static void asctoe64(char *s, short unsigned int *y); static void etoe64(short unsigned int *x, short unsigned int *e); static void etoe53(short unsigned int *x, short unsigned int *e); static void etoe24(short unsigned int *x, short unsigned int *e); static void e53toe(short unsigned int *pe, short unsigned int *y); static void e24toe(short unsigned int *pe, short unsigned int *y); #endif /* econst.c */ /* e type constants used by high precision check routines */ #if NE == 10 /* 0.0 */ static unsigned short ezero[NE] = {0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,}; /* 1.0E0 */ static unsigned short eone[NE] = {0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3fff,}; #if UNUSED /* 5.0E-1 */ static unsigned short ehalf[NE] = {0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3ffe,}; /* 2.0E0 */ static unsigned short etwo[NE] = {0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x4000,}; /* 3.2E1 */ static unsigned short e32[NE] = {0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x4004,}; /* 6.93147180559945309417232121458176568075500134360255E-1 */ static unsigned short elog2[NE] = {0x40f3, 0xf6af, 0x03f2, 0xb398, 0xc9e3, 0x79ab, 0150717, 0013767, 0130562, 0x3ffe,}; /* 1.41421356237309504880168872420969807856967187537695E0 */ static unsigned short esqrt2[NE] = {0x1d6f, 0xbe9f, 0x754a, 0x89b3, 0x597d, 0x6484, 0174736, 0171463, 0132404, 0x3fff,}; /* 3.14159265358979323846264338327950288419716939937511E0 */ static unsigned short epi[NE] = {0x2902, 0x1cd1, 0x80dc, 0x628b, 0xc4c6, 0xc234, 0020550, 0155242, 0144417, 0040000,}; /* 5.7721566490153286060651209008240243104215933593992E-1 */ static unsigned short eeul[NE] = { 0xd1be,0xc7a4,0076660,0063743,0111704,0x3ffe,}; #endif /* UNUSED */ #else /* 0.0 */ static unsigned short ezero[NE] = { 0, 0000000,0000000,0000000,0000000,0000000,}; /* 1.0E0 */ static unsigned short eone[NE] = { 0, 0000000,0000000,0000000,0100000,0x3fff,}; #if UNUSED /* 5.0E-1 */ static unsigned short ehalf[NE] = { 0, 0000000,0000000,0000000,0100000,0x3ffe,}; /* 2.0E0 */ static unsigned short etwo[NE] = { 0, 0000000,0000000,0000000,0100000,0040000,}; /* 3.2E1 */ static unsigned short e32[NE] = { 0, 0000000,0000000,0000000,0100000,0040004,}; /* 6.93147180559945309417232121458176568075500134360255E-1 */ static unsigned short elog2[NE] = { 0xc9e4,0x79ab,0150717,0013767,0130562,0x3ffe,}; /* 1.41421356237309504880168872420969807856967187537695E0 */ static unsigned short esqrt2[NE] = { 0x597e,0x6484,0174736,0171463,0132404,0x3fff,}; /* 2/sqrt(PI) = * 1.12837916709551257389615890312154517168810125865800E0 */ static unsigned short eoneopi[NE] = { 0x71d5,0x688d,0012333,0135202,0110156,0x3fff,}; /* 3.14159265358979323846264338327950288419716939937511E0 */ static unsigned short epi[NE] = { 0xc4c6,0xc234,0020550,0155242,0144417,0040000,}; /* 5.7721566490153286060651209008240243104215933593992E-1 */ static unsigned short eeul[NE] = { 0xd1be,0xc7a4,0076660,0063743,0111704,0x3ffe,}; #endif /* UNUSED */ #endif /* 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 * 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 /* #include "\usr\include\stdio.h" */ /*#include "ehead.h"*/ /*#include "mconf.h"*/ /* mconf.h * * Common include file for math routines * * * * SYNOPSIS: * * #include "mconf.h" * * * * DESCRIPTION: * * This file contains definitions for error codes that are * passed to the common error handling routine mtherr() * (which see). * * The file also includes a conditional assembly definition * for the type of computer arithmetic (IEEE, DEC, Motorola * IEEE, or UNKnown). * * For Digital Equipment PDP-11 and VAX computers, certain * IBM systems, and others that use numbers with a 56-bit * significand, the symbol DEC should be defined. In this * mode, most floating point constants are given as arrays * of octal integers to eliminate decimal to binary conversion * errors that might be introduced by the compiler. * * For computers, such as IBM PC, that follow the IEEE * Standard for Binary Floating Point Arithmetic (ANSI/IEEE * Std 754-1985), the symbol IBMPC should be defined. These * numbers have 53-bit significands. In this mode, constants * are provided as arrays of hexadecimal 16 bit integers. * * To accommodate other types of computer arithmetic, all * constants are also provided in a normal decimal radix * which one can hope are correctly converted to a suitable * format by the available C language compiler. To invoke * this mode, the symbol UNK is defined. * * An important difference among these modes is a predefined * set of machine arithmetic constants for each. The numbers * MACHEP (the machine roundoff error), MAXNUM (largest number * represented), and several other parameters are preset by * the configuration symbol. Check the file const.c to * ensure that these values are correct for your computer. * * For ANSI C compatibility, define ANSIC equal to 1. Currently * this affects only the atan2() function and others that use it. */ /* Constant definitions for math error conditions */ #define DOMAIN 1 /* argument domain error */ #define SING 2 /* argument singularity */ #define OVERFLOW 3 /* overflow range error */ #define UNDERFLOW 4 /* underflow range error */ #define TLOSS 5 /* total loss of precision */ #define PLOSS 6 /* partial loss of precision */ #define EDOM 33 #define ERANGE 34 typedef struct { double r; double i; }cmplx; /* Type of computer arithmetic */ /* PDP-11, Pro350, VAX: */ /*define DEC 1*/ /* Intel IEEE, low order words come first: */ #define IBMPC 1 /* Motorola IEEE, high order words come first * (Sun workstation): */ /* #define MIEEE 1 */ /* UNKnown arithmetic, invokes coefficients given in * normal decimal format. Beware of range boundary * problems (MACHEP, MAXLOG, etc. in const.c) and * roundoff problems in pow.c: */ /*define UNK 1*/ /* Define 1 for ANSI C atan2() function * See atan.c and clog.c. */ #define ANSIC 1 /*define VOLATILE volatile*/ #define VOLATILE /* For 12-byte long doubles on an i386, pad a 16-bit short 0 * to the end of real constants initialized by integer arrays. * * #define XPD 0, * * Otherwise, the type is 10 bytes long and XPD should be * defined blank. * * #define XPD */ #define XPD 0, /* #define XPD */ #define NANS #define INFINITY /* 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. */ static int rndprc = NBITS; /* extern int rndprc; */ static void eaddm(short unsigned int *x, short unsigned int *y); static void esubm(short unsigned int *x, short unsigned int *y); static void emdnorm(short unsigned int *s, int lost, int subflg, long int exp, int rcntrl); static void asctoeg(char *ss, short unsigned int *y, int oprec); static void enan(short unsigned int *nan, int size); static void toe24(short unsigned int *x, short unsigned int *y); static void toe53(short unsigned int *x, short unsigned int *y); static void toe64(short unsigned int *a, short unsigned int *b); static void toe113(short unsigned int *a, short unsigned int *b); static void eiremain(short unsigned int *den, short unsigned int *num); static int ecmpm(register short unsigned int *a, register short unsigned int *b); static int edivm(short unsigned int *den, short unsigned int *num); static int emulm(short unsigned int *a, short unsigned int *b); static int eisneg(short unsigned int *x); static int eisinf(short unsigned int *x); static void emovi(short unsigned int *a, short unsigned int *b); static void emovo(short unsigned int *a, short unsigned int *b); static void emovz(register short unsigned int *a, register short unsigned int *b); static void ecleaz(register short unsigned int *xi); static void eadd1(short unsigned int *a, short unsigned int *b, short unsigned int *c); static int eisnan(short unsigned int *x); static int eiisnan(short unsigned int *x); #ifdef DEC static void etodec(), todec(), dectoe(); #endif #if UNUSED static void einit(void) { } #endif /* ; Clear out entire external format number. ; ; unsigned short x[]; ; eclear( x ); */ static void eclear(register short unsigned int *x) { register int i; for( i=0; i b ; 0 if a == b ; -1 if a < b */ static int ecmpm(register short unsigned int *a, register short unsigned int *b) { int i; a += M; /* skip up to significand area */ b += M; for( i=M; i *(--b) ) return(1); else return(-1); } /* ; Shift significand down by 1 bit */ static void eshdn1(register short unsigned int *x) { register unsigned short bits; int i; x += M; /* point to significand area */ bits = 0; for( i=M; i>= 1; if( bits & 2 ) *x |= 0x8000; bits <<= 1; ++x; } } /* ; Shift significand up by 1 bit */ static void eshup1(register short unsigned int *x) { register unsigned short bits; int i; x += NI-1; bits = 0; for( i=M; i>= 8; *x |= oldbyt; oldbyt = newbyt; ++x; } } /* ; Shift significand up by 8 bits */ static void eshup8(register short unsigned int *x) { int i; register unsigned short newbyt, oldbyt; x += NI-1; oldbyt = 0; for( i=M; i> 8; *x <<= 8; *x |= oldbyt; oldbyt = newbyt; --x; } } /* ; Shift significand up by 16 bits */ static void eshup6(register short unsigned int *x) { int i; register unsigned short *p; p = x + M; x += M + 1; for( i=M; i> 16) + (m >> 16) + *pp; *pp = (unsigned short )carry; *(pp-1) = carry >> 16; } } for( i=M; i 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 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. */ if( (exp <= 0) && (rndprc != 64) && (rndprc != NBITS) ) { 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( (exp <= 0) && (rndprc != 64) && (rndprc != NBITS) ) { 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 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 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 */ static void ediv(short unsigned int *a, short unsigned int *b, short unsigned int *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>= 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 */ } #endif /* UNUSED */ static void e64toe(short unsigned int *pe, short unsigned int *y) { unsigned short yy[NI]; unsigned short *p, *q, *e; int i; e = pe; p = yy; for( i=0; i>= 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 ); } #endif /* UNUSED */ #if UNUSED static void etoe113(short unsigned int *x, short unsigned int *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); } #endif /* UNUSED */ /* move out internal format to ieee long double */ static void toe113(short unsigned int *a, short unsigned int *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 } #if UNUSED static void etoe64(short unsigned int *x, short unsigned int *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 ); } #endif /* move out internal format to ieee long double */ static void toe64(short unsigned int *a, short unsigned int *b) { register unsigned short *p, *q; unsigned short i; #ifdef NANS if( eiisnan(a) ) { enan( b, 64 ); return; } #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 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 static 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 #if UNUSED static void etoe53(short unsigned int *x, short unsigned int *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 ); } #endif /* UNUSED */ static void toe53(short unsigned int *x, short unsigned int *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 ); */ #if UNUSED static void etoe24(short unsigned int *x, short unsigned int *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 ); } #endif /* UNUSED */ static void toe24(short unsigned int *x, short unsigned int *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. */ static int ecmp(short unsigned int *a, short unsigned int *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 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 ); */ #if UNUSED static void eround(short unsigned int *x, short unsigned int *y) { eadd( ehalf, x, y ); efloor( y, y ); } #endif /* UNUSED */ /* ; 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 */ #if UNUSED static void ltoe(long int *lp, short unsigned int *y) { 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 */ } #endif /* UNUSED */ /* ; 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 */ #if UNUSED static void ultoe(long unsigned int *lp, short unsigned int *y) /* lp is the memory address of a long integer */ /* 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 */ } #endif /* UNUSED */ /* ; 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). */ #if UNUSED static void eifrac(short unsigned int *x, long int *i, short unsigned int *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 ); } #endif /* UNUSED */ /* ; 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. */ #if UNUSED static void euifrac(short unsigned int *x, long unsigned int *i, short unsigned int *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 ); } #endif /* UNUSED */ /* ; Shift significand ; ; Shifts significand area up or down by the number of bits ; given by the variable sc. */ static int eshift(short unsigned int *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. */ static int enormlz(short unsigned int *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 #if UNUSED static void e24toasc(short unsigned int *x, char *string, int ndigs) { unsigned short w[NI]; e24toe( x, w ); etoasc( w, string, ndigs ); } #endif #if UNUSED static void e53toasc(short unsigned int *x, char *string, int ndigs) { unsigned short w[NI]; e53toe( x, w ); etoasc( w, string, ndigs ); } #endif #if UNUSED static void e64toasc(short unsigned int *x, char *string, int ndigs) { unsigned short w[NI]; e64toe( x, w ); etoasc( w, string, ndigs ); } #endif #if UNUSED static void e113toasc (short unsigned int *x, char *string, int ndigs) { unsigned short w[NI]; e113toe (x, w); etoasc (w, string, ndigs); } #endif /* UNUSED */ /* ASCII string output for unix */ /* This routine will not return more than NDEC+1 digits. */ static char outstr[128]; static int outexpon; static int outformat = -1; char * _IO_ldtoa(long double d, int mode, int ndigits, int *decpt, int *sign, char **rve) { unsigned short e[NI]; char *s, *p; int k; e64toe( (unsigned short *)&d, e ); if( eisneg(e) ) *sign = 1; else *sign = 0; /* Mode 3 is "f" format. */ if( mode != 3 ) ndigits -= 1; /* Mode 0 is for %.999 format, which is supposed to give a minimum length string that will convert back to the same binary value. For now, just ask for 20 digits which is enough but sometimes too many. */ if( mode == 0 ) ndigits = 20; /* This sanity limit must agree with the corresponding one in etoasc, to keep straight the returned value of outexpon. */ if( ndigits > NDEC ) ndigits = NDEC; outformat = mode; etoasc( e, outstr, ndigits ); s = outstr; if( eisinf(e) || eisnan(e) ) { *decpt = 9999; goto stripspaces; } *decpt = outexpon + 1; /* Transform the string returned by etoasc into what the caller wants. */ /* Look for decimal point and delete it from the string. */ s = outstr; while( *s != '\0' ) { if( *s == '.' ) goto yesdecpt; ++s; } goto nodecpt; yesdecpt: /* Delete the decimal point. */ while( *s != '\0' ) { *s = *(s+1); ++s; } nodecpt: /* Back up over the exponent field. */ while( *s != 'E' && s > outstr) --s; *s = '\0'; stripspaces: /* Strip leading spaces and sign. */ p = outstr; while( *p == ' ' || *p == '-') ++p; /* Find new end of string. */ s = outstr; while( (*s++ = *p++) != '\0' ) ; --s; /* Strip trailing zeros. */ if( mode == 2 ) k = 1; else if( ndigits > outexpon ) k = ndigits; else k = outexpon; while( *(s-1) == '0' && ((s - outstr) > k)) *(--s) = '\0'; /* In f format, flush small off-scale values to zero. Rounding has been taken care of by etoasc. */ if( mode == 3 && ((ndigits + outexpon) < 0)) { s = outstr; *s = '\0'; *decpt = 0; } if( rve ) *rve = s; outformat = -1; return outstr; } static void etoasc(short unsigned int *x, char *string, int ndigits) { 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, ndigs; char *s, *ss; unsigned short m; ndigs = ndigits; rndsav = rndprc; #ifdef NANS if( eisnan(x) ) { sprintf( string, " NaN " ); expon = 9999; 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>= 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 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( outformat == 3 ) ndigs += expon; /* else 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; if( ndigs < 0 ) { ss = s; goto doexp; } } 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( ndigs < 0 ) { /* This will print like "1E-6". */ *s = '1'; expon += 1; goto doexp; } else 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; outexpon = expon; } /* ; 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 */ #if UNUSED static void asctoe24(char *s, short unsigned int *y) { asctoeg( s, y, 24 ); } #endif /* ASCII to double */ #if UNUSED static void asctoe53(char *s, short unsigned int *y) { #ifdef DEC asctoeg( s, y, 56 ); #else asctoeg( s, y, 53 ); #endif } #endif /* ASCII to long double */ #if UNUSED static void asctoe64(char *s, short unsigned int *y) { asctoeg( s, y, 64 ); } #endif /* ASCII to 128-bit long double */ #if UNUSED static void asctoe113 (char *s, short unsigned int *y) { asctoeg( s, y, 113 ); } #endif /* UNUSED */ /* ASCII to super double */ #if UNUSED static void asctoe(char *s, short unsigned int *y) { asctoeg( s, y, NBITS ); } #endif /* This string input routine is for unix library. */ static int lenldstr; long double _IO_strtold (char *s, char **se) { long double x; asctoeg( s, (unsigned short *)&x, 64 ); if (se) *se = s + lenldstr; return x; } static void asctoeg(char *ss, short unsigned int *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, *lstr; /* Copy the input string. */ c = strlen (ss) + 2; lstr = (char *) alloca (c); s = ss; lenldstr = 0; while( *s == ' ' ) /* skip leading spaces */ { ++s; ++lenldstr; } sp = lstr; for( k=0; 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; } lenldstr += s - lstr; } /* 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, }; static void efloor(short unsigned int *x, short unsigned int *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= 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 static unsigned short nan113[8] = { 0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}; static unsigned short nan64[6] = {0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff}; static unsigned short nan53[4] = {0x7fff, 0xffff, 0xffff, 0xffff}; static unsigned short nan24[2] = {0x7fff, 0xffff}; #endif #ifdef IBMPC static unsigned short nan113[8] = {0, 0, 0, 0, 0, 0, 0xc000, 0xffff}; static unsigned short nan64[6] = {0, 0, 0, 0xc000, 0xffff, 0}; static unsigned short nan53[4] = {0, 0, 0, 0xfff8}; static unsigned short nan24[2] = {0, 0xffc0}; #endif static void enan (short unsigned int *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 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= 6) ) code = 0; printf( "%s error\n", ermsg[code] ); /* Return to calling * program */ return 0; }