/* Extended precision arithmetic functions for long double I/O. * This program has been placed in the public domain. */ #include <_ansi.h> #include #include #include #include "mprec.h" /* These are the externally visible entries. */ /* linux name: long double _IO_strtold (char *, char **); */ long double _strtold (char *, char **); char *_ldtoa_r (struct _reent *, long double, int, int, int *, int *, char **); int _ldcheck (long double *); #if 0 void _IO_ldtostr (long double *, char *, int, int, char); #endif /* 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) /* Maximum exponent digits - base 10 */ #define MAX_EXP_DIGITS 5 /* Control structure for long double conversion including rounding precision values. * rndprc can be set to 80 (if NE=6), 64, 56, 53, or 24 bits. */ typedef struct { int rlast; int rndprc; int rw; int re; int outexpon; unsigned short rmsk; unsigned short rmbit; unsigned short rebit; unsigned short rbit[NI]; unsigned short equot[NI]; } LDPARMS; static void esub (const short unsigned int *a, const short unsigned int *b, short unsigned int *c, LDPARMS * ldp); static void emul (const short unsigned int *a, const short unsigned int *b, short unsigned int *c, LDPARMS * ldp); static void ediv (const short unsigned int *a, const short unsigned int *b, short unsigned int *c, LDPARMS * ldp); static int ecmp (const short unsigned int *a, const 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 const 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, register LDPARMS * ldp); static void efloor (short unsigned int *x, short unsigned int *y, LDPARMS * ldp); static void etoasc (short unsigned int *x, char *string, int ndigs, int outformat, LDPARMS * ldp); union uconv { unsigned short pe; long double d; }; #if LDBL_MANT_DIG == 24 static void e24toe (short unsigned int *pe, short unsigned int *y, LDPARMS * ldp); #elif LDBL_MANT_DIG == 53 static void e53toe (short unsigned int *pe, short unsigned int *y, LDPARMS * ldp); #elif LDBL_MANT_DIG == 64 static void e64toe (short unsigned int *pe, short unsigned int *y, LDPARMS * ldp); #else static void e113toe (short unsigned int *pe, short unsigned int *y, LDPARMS * ldp); #endif /* econst.c */ /* e type constants used by high precision check routines */ #if NE == 10 /* 0.0 */ static const unsigned short ezero[NE] = { 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, }; /* 1.0E0 */ static const unsigned short eone[NE] = { 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3fff, }; #else /* 0.0 */ static const unsigned short ezero[NE] = { 0, 0000000, 0000000, 0000000, 0000000, 0000000, }; /* 1.0E0 */ static const unsigned short eone[NE] = { 0, 0000000, 0000000, 0000000, 0100000, 0x3fff, }; #endif /* Debugging routine for displaying errors */ #ifdef DEBUG /* Notice: the order of appearance of the following * messages is bound to the error codes defined * in mconf.h. */ static const char *const ermsg[7] = { "unknown", /* error code 0 */ "domain", /* error code 1 */ "singularity", /* et seq. */ "overflow", "underflow", "total loss of precision", "partial loss of precision" }; #define mtherr(name, code) printf( "\n%s %s error\n", name, ermsg[code] ); #else #define mtherr(name, code) #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, ldp ) ASCII string to specified precision * e24toe( &f, e, ldp ) IEEE single precision to e type * e53toe( &d, e, ldp ) IEEE double precision to e type * e64toe( &d, e, ldp ) IEEE long double precision to e type * e113toe( &d, e, ldp ) 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, ldp ) c = b / a * efloor( a, b, ldp ) 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, ldp ) 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, ldp ) c = b * a * eneg(e) e = -e * eround( a, b ) b = nearest integer value to a * esub( a, b, c, ldp ) 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,fmt,ldp)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, ldp ) divide significands, bi = bi / ai * emdnorm(ai,l,s,exp,ldp) normalize and round off * emovi( a, ai ) convert external a to internal ai * emovo( ai, a, ldp ) convert internal ai to external a * emovz( ai, bi ) bi = ai, low guard word of bi = 0 * emulm( ai, bi, ldp ) 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 USE_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 * 22 Nov 00 Revised to fit into newlib by Jeff Johnston * * Author: S. L. Moshier. * * Copyright (c) 1984,2000 S.L. Moshier * * Permission to use, copy, modify, and distribute this software for any * purpose without fee is hereby granted, provided that this entire notice * is included in all copies of any software which is or includes a copy * or modification of this software and in all copies of the supporting * documentation for such software. * * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED * WARRANTY. IN PARTICULAR, THE AUTHOR MAKES NO REPRESENTATION * OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY OF THIS * SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. * */ #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 */ #ifndef DEC #ifdef __IEEE_LITTLE_ENDIAN #define IBMPC 1 #else /* !__IEEE_LITTLE_ENDIAN */ #define MIEEE 1 #endif /* !__IEEE_LITTLE_ENDIAN */ #endif /* !DEC */ /* Define 1 for ANSI C atan2() function * See atan.c and clog.c. */ #define ANSIC 1 /*define VOLATILE volatile*/ #define VOLATILE #define NANS #define USE_INFINITY /* NaN's require infinity support. */ #ifdef NANS #ifndef INFINITY #define USE_INFINITY #endif #endif /* This handles 64-bit long ints. */ #define LONGBITS (8 * sizeof(long)) 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, LDPARMS * ldp); #if 0 /* Broken, unusable implementation of strtold */ static int asctoeg (char *ss, short unsigned int *y, int oprec, LDPARMS * ldp); #endif static void enan (short unsigned int *nan, int size); #if LDBL_MANT_DIG == 24 static void toe24 (short unsigned int *x, short unsigned int *y); #elif LDBL_MANT_DIG == 53 static void toe53 (short unsigned int *x, short unsigned int *y); #elif LDBL_MANT_DIG == 64 static void toe64 (short unsigned int *a, short unsigned int *b); #else static void toe113 (short unsigned int *a, short unsigned int *b); #endif static void eiremain (short unsigned int *den, short unsigned int *num, LDPARMS * ldp); static int ecmpm (register short unsigned int *a, register short unsigned int *b); static int edivm (short unsigned int *den, short unsigned int *num, LDPARMS * ldp); static int emulm (short unsigned int *a, short unsigned int *b, LDPARMS * ldp); static int eisneg (const short unsigned int *x); static int eisinf (const short unsigned int *x); static void emovi (const short unsigned int *a, short unsigned int *b); static void emovo (short unsigned int *a, short unsigned int *b, LDPARMS * ldp); static void emovz (register short unsigned int *a, register short unsigned int *b); static void ecleaz (register short unsigned int *xi); static void eadd1 (const short unsigned int *a, const short unsigned int *b, short unsigned int *c, int subflg, LDPARMS * ldp); static int eisnan (const short unsigned int *x); static int eiisnan (short unsigned int *x); #ifdef DEC static void etodec (), todec (), dectoe (); #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 < NE; i++) *x++ = 0; } /* Move external format number from a to b. * * emov( a, b ); */ static void emov (register const short unsigned int *a, register short unsigned int *b) { register int i; for (i = 0; i < NE; i++) *b++ = *a++; } /* ; Negate external format number ; ; unsigned short x[NE]; ; eneg( x ); */ static void eneg (short unsigned int *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. */ static int eisneg (const short unsigned int *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. */ static int eisinf (const short unsigned int *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. */ static int eisnan (const short unsigned int *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. */ static void einfin (register short unsigned int *x, register LDPARMS * ldp) { register int i; #ifdef USE_INFINITY for (i = 0; i < NE - 1; i++) *x++ = 0; *x |= 32767; ldp = ldp; #else for (i = 0; i < NE - 1; i++) *x++ = 0xffff; *x |= 32766; if (ldp->rndprc < NBITS) { if (ldp->rndprc == 113) { *(x - 9) = 0; *(x - 8) = 0; } if (ldp->rndprc == 64) { *(x - 5) = 0; } if (ldp->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. */ static void emovi (const short unsigned int *a, short unsigned int *b) { register const unsigned short *p; register unsigned short *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 USE_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. */ static void emovo (short unsigned int *a, short unsigned int *b, LDPARMS * ldp) { 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 USE_INFINITY if (*(p - 1) == 0x7fff) { #ifdef NANS if (eiisnan (a)) { enan (b, NBITS); return; } #endif einfin (b, ldp); return; } #endif /* skip over guard word */ ++p; /* move the significand */ for (i = 0; i < NE - 1; i++) *q-- = *p++; } /* Clear out internal format number. */ static void ecleaz (register short unsigned int *xi) { register int i; for (i = 0; i < NI; i++) *xi++ = 0; } /* same, but don't touch the sign. */ static void ecleazs (register short unsigned int *xi) { register int i; ++xi; for (i = 0; i < NI - 1; i++) *xi++ = 0; } /* Move internal format number from a to b. */ static void emovz (register short unsigned int *a, register short unsigned int *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. */ static int eiisnan (short unsigned int *x) { int i; if ((x[E] & 0x7fff) == 0x7fff) { for (i = M + 1; i < NI; i++) { if (x[i] != 0) return (1); } } return (0); } #if LDBL_MANT_DIG == 64 /* Return nonzero if internal format number is infinite. */ static int eiisinf (unsigned short x[]) { #ifdef NANS if (eiisnan (x)) return (0); #endif if ((x[E] & 0x7fff) == 0x7fff) return (1); return (0); } #endif /* LDBL_MANT_DIG == 64 */ /* ; 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 */ 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 < NI; i++) { if (*a++ != *b++) goto difrnt; } return (0); difrnt: if (*(--a) > *(--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 < NI; i++) { if (*x & 1) bits |= 1; *x >>= 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 < NI; i++) { if (*x & 0x8000) bits |= 1; *x <<= 1; if (bits & 2) *x |= 1; bits <<= 1; --x; } } /* ; Shift significand down by 8 bits */ static void eshdn8 (register short unsigned int *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 */ static void eshup8 (register short unsigned int *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 */ static void eshup6 (register short unsigned int *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 */ static void eshdn6 (register short unsigned int *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 */ static void eaddm (short unsigned int *x, short unsigned int *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 */ static void esubm (short unsigned int *x, short unsigned int *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 */ /* Multiply significand of e-type number b by 16-bit quantity a, e-type result to c. */ static void m16m (short unsigned int a, short unsigned int *b, short unsigned int *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. */ static int edivm (short unsigned int *den, short unsigned int *num, LDPARMS * ldp) { int i; register unsigned short *p; unsigned long tnum; unsigned short j, tdenm, tquot; unsigned short tprod[NI + 1]; unsigned short *equot = ldp->equot; 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 * 0xffffUL) < 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 */ static int emulm (short unsigned int *a, short unsigned int *b, LDPARMS * ldp) { unsigned short *p, *q; unsigned short pprod[NI]; unsigned short j; int i; unsigned short *equot = ldp->equot; 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); } /* static void eshow(str, x) char *str; unsigned short *x; { int i; printf( "%s ", str ); for( i=0; i NBITS) { ecleazs (s); return; } #endif exp -= j; #ifndef USE_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 (ldp->rndprc != ldp->rlast) { ecleaz (ldp->rbit); switch (ldp->rndprc) { default: case NBITS: ldp->rw = NI - 1; /* low guard word */ ldp->rmsk = 0xffff; ldp->rmbit = 0x8000; ldp->rebit = 1; ldp->re = ldp->rw - 1; break; case 113: ldp->rw = 10; ldp->rmsk = 0x7fff; ldp->rmbit = 0x4000; ldp->rebit = 0x8000; ldp->re = ldp->rw; break; case 64: ldp->rw = 7; ldp->rmsk = 0xffff; ldp->rmbit = 0x8000; ldp->rebit = 1; ldp->re = ldp->rw - 1; break; /* For DEC arithmetic */ case 56: ldp->rw = 6; ldp->rmsk = 0xff; ldp->rmbit = 0x80; ldp->rebit = 0x100; ldp->re = ldp->rw; break; case 53: ldp->rw = 6; ldp->rmsk = 0x7ff; ldp->rmbit = 0x0400; ldp->rebit = 0x800; ldp->re = ldp->rw; break; case 24: ldp->rw = 4; ldp->rmsk = 0xff; ldp->rmbit = 0x80; ldp->rebit = 0x100; ldp->re = ldp->rw; break; } ldp->rbit[ldp->re] = ldp->rebit; ldp->rlast = ldp->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) && (ldp->rndprc != NBITS)) #else if ((exp <= 0) && (ldp->rndprc != 64) && (ldp->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[ldp->rw] & ldp->rmsk; if (ldp->rndprc < NBITS) { i = ldp->rw + 1; while (i < NI) { if (s[i]) r |= 1; s[i] = 0; ++i; } } s[ldp->rw] &= ~ldp->rmsk; if ((r & ldp->rmbit) != 0) { if (r == ldp->rmbit) { if (lost == 0) { /* round to even */ if ((s[ldp->re] & ldp->rebit) == 0) goto mddone; } else { if (subflg != 0) goto mddone; } } eaddm (ldp->rbit, s); } mddone: #if IBMPC if ((exp <= 0) && (ldp->rndprc != NBITS)) #else if ((exp <= 0) && (ldp->rndprc != 64) && (ldp->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 USE_INFINITY overf: #endif #ifdef USE_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 ((ldp->rndprc < 64) || (ldp->rndprc == 113)) { s[ldp->rw] &= ~ldp->rmsk; if (ldp->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]; ; LDPARMS *ldp; ; esub( a, b, c, ldp ); c = b - a */ static void esub (const short unsigned int *a, const short unsigned int *b, short unsigned int *c, LDPARMS * ldp) { #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 eadd1 (a, b, c, 1, ldp); } static void eadd1 (const short unsigned int *a, const short unsigned int *b, short unsigned int *c, int subflg, LDPARMS * ldp) { unsigned short ai[NI], bi[NI], ci[NI]; int i, lost, j, k; long lt, lta, ltb; #ifdef USE_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, ldp); done: emovo (bi, c, ldp); } /* ; Divide. ; ; unsigned short a[NE], b[NE], c[NE]; ; LDPARMS *ldp; ; ediv( a, b, c, ldp ); c = b / a */ static void ediv (const short unsigned int *a, const short unsigned int *b, short unsigned int *c, LDPARMS * ldp) { 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 USE_INFINITY if (eisinf (b)) { if (eisneg (a) ^ eisneg (b)) *(c + (NE - 1)) = 0x8000; else *(c + (NE - 1)) = 0; einfin (c, ldp); 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, ldp); mtherr ("ediv", SING); return; } dnzro2: i = edivm (ai, bi, ldp); /* calculate exponent */ lt = ltb - lta + EXONE; emdnorm (bi, i, 0, lt, 64, ldp); /* set the sign */ if (ai[0] == bi[0]) bi[0] = 0; else bi[0] = 0Xffff; emovo (bi, c, ldp); } /* ; Multiply. ; ; unsigned short a[NE], b[NE], c[NE]; ; LDPARMS *ldp ; emul( a, b, c, ldp ); c = b * a */ static void emul (const short unsigned int *a, const short unsigned int *b, short unsigned int *c, LDPARMS * ldp) { 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 USE_INFINITY if (eisinf (a) || eisinf (b)) { if (eisneg (a) ^ eisneg (b)) *(c + (NE - 1)) = 0x8000; else *(c + (NE - 1)) = 0; einfin (c, ldp); 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, ldp); /* calculate exponent */ lt = lta + ltb - (EXONE - 1); emdnorm (bi, j, 0, lt, 64, ldp); /* calculate sign of product */ if (ai[0] == bi[0]) bi[0] = 0; else bi[0] = 0xffff; emovo (bi, c, ldp); } #if LDBL_MANT_DIG > 64 static void e113toe (short unsigned int *pe, short unsigned int *y, LDPARMS * ldp) { 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 USE_INFINITY if (r == 0x7fff) { #ifdef NANS #ifdef IBMPC for (i = 0; i < 7; i++) { if (pe[i] != 0) { enan (y, NBITS); return; } } #else /* !IBMPC */ for (i = 1; i < 8; i++) { if (pe[i] != 0) { enan (y, NBITS); return; } } #endif /* !IBMPC */ #endif /* NANS */ eclear (y); einfin (y, ldp); 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); #else /* IBMPC */ ++e; for (i = 0; i < 7; i++) *p++ = *e++; #endif /* IBMPC */ /* 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, ldp); } /* move out internal format to ieee long double */ static void __attribute__ ((__unused__)) 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 } #endif /* LDBL_MANT_DIG > 64 */ #if LDBL_MANT_DIG == 64 static void e64toe (short unsigned int *pe, short unsigned int *y, LDPARMS * ldp) { 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; /* MIEEE skips over 2nd short */ 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, ldp); return; } #endif #ifdef USE_INFINITY /* Point to the exponent field. */ p = &yy[NE - 1]; if ((*p & 0x7fff) == 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; } } #endif #ifdef MIEEE for (i = 2; i <= 5; i++) { if (pe[i] != 0) { enan (y, NBITS); return; } } #endif #endif /* NANS */ eclear (y); einfin (y, ldp); if (*p & 0x8000) eneg (y); return; } #endif /* USE_INFINITY */ p = yy; q = y; for (i = 0; i < NE; i++) *q++ = *p++; } /* move out internal format to ieee long double */ static void __attribute__ ((__unused__)) 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 #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 */ /* NOTE: Intel data type is 96 bits wide, clear the last word here. */ *(q + 1) = 0; #endif /* combine sign and exponent */ i = *p++; #ifdef MIEEE if (i) *q++ = *p++ | 0x8000; else *q++ = *p++; *q++ = 0; /* leave 2nd short blank */ #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 USE_INFINITY #ifdef IBMPC if (eiisinf (a)) { /* Intel long double infinity. */ *q-- = 0x8000; *q-- = 0; *q-- = 0; *q = 0; return; } #endif /* IBMPC */ #endif /* USE_INFINITY */ for (i = 0; i < 4; i++) *q-- = *p++; #endif } #endif /* LDBL_MANT_DIG == 64 */ #if LDBL_MANT_DIG == 53 /* ; Convert IEEE double precision to e type ; double d; ; unsigned short x[N+2]; ; e53toe( &d, x ); */ static void e53toe (short unsigned int *pe, short unsigned int *y, LDPARMS * ldp) { #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 #ifdef DEC 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 USE_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 /* !IBMPC */ if (((pe[0] & 0xf) != 0) || (pe[1] != 0) || (pe[2] != 0) || (pe[3] != 0)) { enan (y, NBITS); return; } #endif /* !IBMPC */ #endif /* NANS */ eclear (y); einfin (y, ldp); 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); #else /* !IBMPC */ ++e; *p++ = *e++; *p++ = *e++; *p++ = *e++; #endif /* !IBMPC */ (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, ldp); #endif /* !DEC */ } /* ; 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 __attribute__ ((__unused__)) toe53 (x, y) unsigned short *x, *y; { todec (x, y); } #else static void __attribute__ ((__unused__)) 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 #ifdef DEC 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 USE_INFINITY *y |= 0x7ff0; #ifdef IBMPC *(--y) = 0; *(--y) = 0; *(--y) = 0; #else /* !IBMPC */ ++y; *y++ = 0; *y++ = 0; *y++ = 0; #endif /* IBMPC */ #else /* !USE_INFINITY */ *y |= (unsigned short) 0x7fef; #ifdef IBMPC *(--y) = 0xffff; *(--y) = 0xffff; *(--y) = 0xffff; #else /* !IBMPC */ ++y; *y++ = 0xffff; *y++ = 0xffff; *y++ = 0xffff; #endif #endif /* !USE_INFINITY */ 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; #else /* !IBMPC */ ++y; *y++ = *p++; *y++ = *p++; *y++ = *p++; #endif /* !IBMPC */ } #endif /* not DEC */ #endif /* LDBL_MANT_DIG == 53 */ #if LDBL_MANT_DIG == 24 /* ; Convert IEEE single precision to e type ; float d; ; unsigned short x[N+2]; ; dtox( &d, x ); */ void e24toe (short unsigned int *pe, short unsigned int *y, LDPARMS * ldp) { 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 USE_INFINITY if (r == 0x7f80) { #ifdef NANS #ifdef MIEEE if (((pe[0] & 0x7f) != 0) || (pe[1] != 0)) { enan (y, NBITS); return; } #else /* !MIEEE */ if (((pe[1] & 0x7f) != 0) || (pe[0] != 0)) { enan (y, NBITS); return; } #endif /* !MIEEE */ #endif /* NANS */ eclear (y); einfin (y, ldp); 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, ldp); } static void __attribute__ ((__unused__)) 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 USE_INFINITY *y |= (unsigned short) 0x7f80; #ifdef IBMPC *(--y) = 0; #endif #ifdef DEC *(--y) = 0; #endif #ifdef MIEEE ++y; *y = 0; #endif #else /* !USE_INFINITY */ *y |= (unsigned short) 0x7f7f; #ifdef IBMPC *(--y) = 0xffff; #endif #ifdef DEC *(--y) = 0xffff; #endif #ifdef MIEEE ++y; *y = 0xffff; #endif #endif /* !USE_INFINITY */ 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 } #endif /* LDBL_MANT_DIG == 24 */ /* 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 (const short unsigned int *a, const 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 < 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 */ } /* ; 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 const 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 const 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 const 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 const 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 /* ASCII string outputs for unix */ #if 0 void _IO_ldtostr (x, string, ndigs, flags, fmt) long double *x; char *string; int ndigs; int flags; char fmt; { unsigned short w[NI]; char *t, *u; LDPARMS rnd; LDPARMS *ldp = &rnd; rnd.rlast = -1; rnd.rndprc = NBITS; if (sizeof (long double) == 16) e113toe ((unsigned short *) x, w, ldp); else e64toe ((unsigned short *) x, w, ldp); etoasc (w, string, ndigs, -1, ldp); if (ndigs == 0 && flags == 0) { /* Delete the decimal point unless alternate format. */ t = string; while (*t != '.') ++t; u = t + 1; while (*t != '\0') *t++ = *u++; } if (*string == ' ') { t = string; u = t + 1; while (*t != '\0') *t++ = *u++; } if (fmt == 'E') { t = string; while (*t != 'e') ++t; *t = 'E'; } } #endif /* This routine will not return more than NDEC+1 digits. */ char * _ldtoa_r (struct _reent *ptr, long double d, int mode, int ndigits, int *decpt, int *sign, char **rve) { unsigned short e[NI]; char *s, *p; int i, j, k; int orig_ndigits; LDPARMS rnd; LDPARMS *ldp = &rnd; char *outstr; char outbuf[NDEC + MAX_EXP_DIGITS + 10]; union uconv du; du.d = d; orig_ndigits = ndigits; rnd.rlast = -1; rnd.rndprc = NBITS; _REENT_CHECK_MP (ptr); /* reentrancy addition to use mprec storage pool */ if (_REENT_MP_RESULT (ptr)) { _REENT_MP_RESULT (ptr)->_k = _REENT_MP_RESULT_K (ptr); _REENT_MP_RESULT (ptr)->_maxwds = 1 << _REENT_MP_RESULT_K (ptr); Bfree (ptr, _REENT_MP_RESULT (ptr)); _REENT_MP_RESULT (ptr) = 0; } #if LDBL_MANT_DIG == 24 e24toe (&du.pe, e, ldp); #elif LDBL_MANT_DIG == 53 e53toe (&du.pe, e, ldp); #elif LDBL_MANT_DIG == 64 e64toe (&du.pe, e, ldp); #else e113toe (&du.pe, e, ldp); #endif 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; etoasc (e, outbuf, ndigits, mode, ldp); s = outbuf; if (eisinf (e) || eisnan (e)) { *decpt = 9999; goto stripspaces; } *decpt = ldp->outexpon + 1; /* Transform the string returned by etoasc into what the caller wants. */ /* Look for decimal point and delete it from the string. */ s = outbuf; 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 > outbuf) --s; *s = '\0'; stripspaces: /* Strip leading spaces and sign. */ p = outbuf; while (*p == ' ' || *p == '-') ++p; /* Find new end of string. */ s = outbuf; while ((*s++ = *p++) != '\0') ; --s; /* Strip trailing zeros. */ if (mode == 2) k = 1; else if (ndigits > ldp->outexpon) k = ndigits; else k = ldp->outexpon; while (*(s - 1) == '0' && ((s - outbuf) > 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 + ldp->outexpon) < 0)) { s = outbuf; *s = '\0'; *decpt = 0; } /* reentrancy addition to use mprec storage pool */ /* we want to have enough space to hold the formatted result */ if (mode == 3) /* f format, account for sign + dec digits + decpt + frac */ i = *decpt + orig_ndigits + 3; else /* account for sign + max precision digs + E + exp sign + exponent */ i = orig_ndigits + MAX_EXP_DIGITS + 4; j = sizeof (__ULong); for (_REENT_MP_RESULT_K (ptr) = 0; sizeof (_Bigint) - sizeof (__ULong) + j <= i; j <<= 1) _REENT_MP_RESULT_K (ptr)++; _REENT_MP_RESULT (ptr) = eBalloc (ptr, _REENT_MP_RESULT_K (ptr)); /* Copy from internal temporary buffer to permanent buffer. */ outstr = (char *) _REENT_MP_RESULT (ptr); strcpy (outstr, outbuf); if (rve) *rve = outstr + (s - outbuf); return outstr; } /* Routine used to tell if long double is NaN or Infinity or regular number. Returns: 0 = regular number 1 = Nan 2 = Infinity */ int _ldcheck (long double *d) { unsigned short e[NI]; LDPARMS rnd; LDPARMS *ldp = &rnd; union uconv du; rnd.rlast = -1; rnd.rndprc = NBITS; du.d = *d; #if LDBL_MANT_DIG == 24 e24toe (&du.pe, e, ldp); #elif LDBL_MANT_DIG == 53 e53toe (&du.pe, e, ldp); #elif LDBL_MANT_DIG == 64 e64toe (&du.pe, e, ldp); #else e113toe (&du.pe, e, ldp); #endif if ((e[NE - 1] & 0x7fff) == 0x7fff) { #ifdef NANS if (eisnan (e)) return (1); #endif return (2); } else return (0); } /* _ldcheck */ static void etoasc (short unsigned int *x, char *string, int ndigits, int outformat, LDPARMS * ldp) { long digit; unsigned short y[NI], t[NI], u[NI], w[NI]; const unsigned short *p, *r, *ten; unsigned short sign; int i, j, k, expon, rndsav, ndigs; char *s, *ss; unsigned short m; unsigned short *equot = ldp->equot; ndigs = ndigits; rndsav = ldp->rndprc; #ifdef NANS if (eisnan (x)) { sprintf (string, " NaN "); expon = 9999; goto bxit; } #endif ldp->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 "); expon = 9999; 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"); expon = 9999; 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, ldp); efloor (t, w, ldp); 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, ldp); emul (p, t, t, ldp); 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, ldp); 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, ldp); } 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, ldp); emul (r, t, t, ldp); expon += k; } k /= 2; if (k == 0) break; p += NE; r += NE; } ediv (t, eone, t, ldp); } isone: /* Find the first (leading) digit. */ emovi (t, w); emovz (w, t); emovi (y, w); emovz (w, y); eiremain (t, y, ldp); 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, ldp); 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, ldp); *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, ldp); if (ecmp (t, ezero) != 0) goto roun; /* round to nearest */ if (ndigs < 0 || (*(s - 1 - (*(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: #ifdef __GO32__ if (expon >= 0) sprintf (ss, "e+%02d", expon); else sprintf (ss, "e-%02d", -expon); #else sprintf (ss, "E%d", expon); #endif bxit: ldp->rndprc = rndsav; ldp->outexpon = expon; } #if 0 /* Broken, unusable implementation of strtold */ /* ; 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 ); */ long double _strtold (char *s, char **se) { union uconv x; LDPARMS rnd; LDPARMS *ldp = &rnd; int lenldstr; rnd.rlast = -1; rnd.rndprc = NBITS; lenldstr = asctoeg (s, &x.pe, LDBL_MANT_DIG, ldp); if (se) *se = s + lenldstr; return x.d; } #define REASONABLE_LEN 200 static int asctoeg (char *ss, short unsigned int *y, int oprec, LDPARMS * ldp) { 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; const unsigned short *p; char *sp, *s, *lstr; int lenldstr; int mflag = 0; char tmpstr[REASONABLE_LEN]; /* Copy the input string. */ c = strlen (ss) + 2; if (c <= REASONABLE_LEN) lstr = tmpstr; else { lstr = (char *) calloc (c, 1); mflag = 1; } s = ss; lenldstr = 0; while (*s == ' ') /* skip leading spaces */ { ++s; ++lenldstr; } sp = lstr; for (k = 0; k < c; k++) { if ((*sp++ = *s++) == '\0') break; } *sp = '\0'; s = lstr; rndsav = ldp->rndprc; ldp->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, ldp); /* 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, ldp); lexp += EXONE; nexp -= 4096; } } p = &etens[NTEN][0]; emov (eone, xt); exp = 1; do { if (exp & nexp) emul (p, xt, xt, ldp); p -= NE; exp = exp + exp; } while (exp <= MAXP); emovi (xt, tt); if (esign < 0) { lexp -= tt[E]; k = edivm (tt, yy, ldp); lexp += EXONE; } else { lexp += tt[E]; k = emulm (tt, yy, ldp); 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 ldp->rndprc = oprec; emdnorm (yy, k, 0, lexp, 64, ldp); aexit: ldp->rndprc = rndsav; yy[0] = nsign; switch (oprec) { #ifdef DEC case 56: todec (yy, y); /* see etodec.c */ break; #endif #if LDBL_MANT_DIG == 53 case 53: toe53 (yy, y); break; #elif LDBL_MANT_DIG == 24 case 24: toe24 (yy, y); break; #elif LDBL_MANT_DIG == 64 case 64: toe64 (yy, y); break; #elif LDBL_MANT_DIG == 113 case 113: toe113 (yy, y); break; #else case NBITS: emovo (yy, y, ldp); break; #endif } lenldstr += s - lstr; if (mflag) free (lstr); return lenldstr; } #endif /* y = largest integer not greater than x * (truncated toward minus infinity) * * unsigned short x[NE], y[NE] * LDPARMS *ldp * * efloor( x, y, ldp ); */ static const 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, LDPARMS * ldp) { 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, ldp); break; } } } } static void eiremain (short unsigned int *den, short unsigned int *num, LDPARMS * ldp) { long ld, ln; unsigned short j; unsigned short *equot = ldp->equot; 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, ldp); } /* NaN bit patterns */ #ifdef MIEEE #if !defined(__mips) static const unsigned short nan113[8] = { 0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff }; static const unsigned short nan64[6] = { 0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff }; static const unsigned short nan53[4] = { 0x7fff, 0xffff, 0xffff, 0xffff }; static const unsigned short nan24[2] = { 0x7fff, 0xffff }; #elif defined(__mips_nan2008) /* __mips */ static const unsigned short nan113[8] = { 0x7fff, 0x8000, 0, 0, 0, 0, 0, 0 }; static const unsigned short nan64[6] = { 0x7fff, 0xc000, 0, 0, 0, 0 }; static const unsigned short nan53[4] = { 0x7ff8, 0, 0, 0 }; static const unsigned short nan24[2] = { 0x7fc0, 0 }; #else /* __mips && !__mips_nan2008 */ static const unsigned short nan113[8] = { 0x7fff, 0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff }; static const unsigned short nan64[6] = { 0x7fff, 0xbfff, 0xffff, 0xffff, 0xffff, 0xffff }; static const unsigned short nan53[4] = { 0x7ff7, 0xffff, 0xffff, 0xffff }; static const unsigned short nan24[2] = { 0x7fbf, 0xffff }; #endif /* __mips && !__mips_nan2008 */ #else /* !MIEEE */ #if !defined(__mips) || defined(__mips_nan2008) static const unsigned short nan113[8] = { 0, 0, 0, 0, 0, 0, 0x8000, 0x7fff }; static const unsigned short nan64[6] = { 0, 0, 0, 0, 0xc000, 0x7fff }; static const unsigned short nan53[4] = { 0, 0, 0, 0x7ff8 }; static const unsigned short nan24[2] = { 0, 0x7fc0 }; #else /* __mips && !__mips_nan2008 */ static const unsigned short nan113[8] = { 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0x7fff, 0x7fff }; static const unsigned short nan64[6] = { 0xffff, 0xffff, 0xffff, 0xffff, 0xbfff, 0x7fff }; static const unsigned short nan53[4] = { 0xffff, 0xffff, 0xffff, 0x7ff7 }; static const unsigned short nan24[2] = { 0xffff, 0x7fbf }; #endif /* __mips && !__mips_nan2008 */ #endif /* !MIEEE */ static void enan (short unsigned int *nan, int size) { int i, n; const 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: #if !defined(__mips) || defined(__mips_nan2008) for (i = 0; i < NE - 2; i++) *nan++ = 0; *nan++ = 0xc000; #else /* __mips && !__mips_nan2008 */ for (i = 0; i < NE - 2; i++) *nan++ = 0xffff; *nan++ = 0xbfff; #endif /* __mips && !__mips_nan2008 */ *nan++ = 0x7fff; return; case NI * 16: *nan++ = 0; *nan++ = 0x7fff; *nan++ = 0; #if !defined(__mips) || defined(__mips_nan2008) *nan++ = 0xc000; for (i = 4; i < NI - 1; i++) *nan++ = 0; #else /* __mips && !__mips_nan2008 */ *nan++ = 0xbfff; for (i = 4; i < NI - 1; i++) *nan++ = 0xffff; #endif /* __mips && !__mips_nan2008 */ *nan++ = 0; return; #endif default: mtherr ("enan", DOMAIN); return; } for (i = 0; i < n; i++) *nan++ = *p++; }