mirror of
https://github.com/autc04/Retro68.git
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3744 lines
69 KiB
C
3744 lines
69 KiB
C
/* Extended precision arithmetic functions for long double I/O.
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* This program has been placed in the public domain.
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*/
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#include <_ansi.h>
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#include <reent.h>
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#include <string.h>
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#include <stdlib.h>
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#include "mprec.h"
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/* These are the externally visible entries. */
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/* linux name: long double _IO_strtold (char *, char **); */
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long double _strtold (char *, char **);
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char * _ldtoa_r (struct _reent *, long double, int, int, int *, int *, char **);
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int _ldcheck (long double *);
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#if 0
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void _IO_ldtostr(long double *, char *, int, int, char);
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#endif
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/* Number of 16 bit words in external x type format */
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#define NE 10
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/* Number of 16 bit words in internal format */
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#define NI (NE+3)
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/* Array offset to exponent */
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#define E 1
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/* Array offset to high guard word */
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#define M 2
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/* Number of bits of precision */
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#define NBITS ((NI-4)*16)
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/* Maximum number of decimal digits in ASCII conversion
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* = NBITS*log10(2)
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*/
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#define NDEC (NBITS*8/27)
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/* The exponent of 1.0 */
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#define EXONE (0x3fff)
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/* Maximum exponent digits - base 10 */
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#define MAX_EXP_DIGITS 5
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/* Control structure for long double conversion including rounding precision values.
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* rndprc can be set to 80 (if NE=6), 64, 56, 53, or 24 bits.
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*/
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typedef struct
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{
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int rlast;
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int rndprc;
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int rw;
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int re;
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int outexpon;
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unsigned short rmsk;
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unsigned short rmbit;
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unsigned short rebit;
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unsigned short rbit[NI];
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unsigned short equot[NI];
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} LDPARMS;
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static void esub(short unsigned int *a, short unsigned int *b, short unsigned int *c, LDPARMS *ldp);
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static void emul(short unsigned int *a, short unsigned int *b, short unsigned int *c, LDPARMS *ldp);
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static void ediv(short unsigned int *a, short unsigned int *b, short unsigned int *c, LDPARMS *ldp);
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static int ecmp(short unsigned int *a, short unsigned int *b);
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static int enormlz(short unsigned int *x);
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static int eshift(short unsigned int *x, int sc);
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static void eshup1(register short unsigned int *x);
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static void eshup8(register short unsigned int *x);
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static void eshup6(register short unsigned int *x);
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static void eshdn1(register short unsigned int *x);
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static void eshdn8(register short unsigned int *x);
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static void eshdn6(register short unsigned int *x);
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static void eneg(short unsigned int *x);
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static void emov(register short unsigned int *a, register short unsigned int *b);
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static void eclear(register short unsigned int *x);
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static void einfin(register short unsigned int *x, register LDPARMS *ldp);
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static void efloor(short unsigned int *x, short unsigned int *y, LDPARMS *ldp);
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static void etoasc(short unsigned int *x, char *string, int ndigs, int outformat, LDPARMS *ldp);
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union uconv
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{
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unsigned short pe;
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long double d;
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};
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#if LDBL_MANT_DIG == 24
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static void e24toe(short unsigned int *pe, short unsigned int *y, LDPARMS *ldp);
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#elif LDBL_MANT_DIG == 53
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static void e53toe(short unsigned int *pe, short unsigned int *y, LDPARMS *ldp);
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#elif LDBL_MANT_DIG == 64
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static void e64toe(short unsigned int *pe, short unsigned int *y, LDPARMS *ldp);
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#else
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static void e113toe(short unsigned int *pe, short unsigned int *y, LDPARMS *ldp);
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#endif
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/* econst.c */
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/* e type constants used by high precision check routines */
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#if NE == 10
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/* 0.0 */
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static unsigned short ezero[NE] =
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{0x0000, 0x0000, 0x0000, 0x0000,
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0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,};
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/* 1.0E0 */
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static unsigned short eone[NE] =
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{0x0000, 0x0000, 0x0000, 0x0000,
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0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3fff,};
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#else
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/* 0.0 */
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static unsigned short ezero[NE] = {
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0, 0000000,0000000,0000000,0000000,0000000,};
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/* 1.0E0 */
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static unsigned short eone[NE] = {
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0, 0000000,0000000,0000000,0100000,0x3fff,};
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#endif
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/* Debugging routine for displaying errors */
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#ifdef DEBUG
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/* Notice: the order of appearance of the following
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* messages is bound to the error codes defined
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* in mconf.h.
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*/
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static char *ermsg[7] = {
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"unknown", /* error code 0 */
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"domain", /* error code 1 */
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"singularity", /* et seq. */
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"overflow",
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"underflow",
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"total loss of precision",
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"partial loss of precision"
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};
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#define mtherr(name, code) printf( "\n%s %s error\n", name, ermsg[code] );
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#else
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#define mtherr(name, code)
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#endif
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/* ieee.c
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*
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* Extended precision IEEE binary floating point arithmetic routines
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*
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* Numbers are stored in C language as arrays of 16-bit unsigned
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* short integers. The arguments of the routines are pointers to
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* the arrays.
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*
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*
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* External e type data structure, simulates Intel 8087 chip
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* temporary real format but possibly with a larger significand:
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*
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* NE-1 significand words (least significant word first,
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* most significant bit is normally set)
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* exponent (value = EXONE for 1.0,
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* top bit is the sign)
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*
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*
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* Internal data structure of a number (a "word" is 16 bits):
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*
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* ei[0] sign word (0 for positive, 0xffff for negative)
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* ei[1] biased exponent (value = EXONE for the number 1.0)
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* ei[2] high guard word (always zero after normalization)
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* ei[3]
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* to ei[NI-2] significand (NI-4 significand words,
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* most significant word first,
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* most significant bit is set)
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* ei[NI-1] low guard word (0x8000 bit is rounding place)
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*
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*
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*
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* Routines for external format numbers
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*
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* asctoe( string, e ) ASCII string to extended double e type
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* asctoe64( string, &d ) ASCII string to long double
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* asctoe53( string, &d ) ASCII string to double
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* asctoe24( string, &f ) ASCII string to single
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* asctoeg( string, e, prec, ldp ) ASCII string to specified precision
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* e24toe( &f, e, ldp ) IEEE single precision to e type
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* e53toe( &d, e, ldp ) IEEE double precision to e type
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* e64toe( &d, e, ldp ) IEEE long double precision to e type
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* e113toe( &d, e, ldp ) IEEE long double precision to e type
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* eabs(e) absolute value
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* eadd( a, b, c ) c = b + a
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* eclear(e) e = 0
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* ecmp (a, b) Returns 1 if a > b, 0 if a == b,
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* -1 if a < b, -2 if either a or b is a NaN.
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* ediv( a, b, c, ldp ) c = b / a
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* efloor( a, b, ldp ) truncate to integer, toward -infinity
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* efrexp( a, exp, s ) extract exponent and significand
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* eifrac( e, &l, frac ) e to long integer and e type fraction
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* euifrac( e, &l, frac ) e to unsigned long integer and e type fraction
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* einfin( e, ldp ) set e to infinity, leaving its sign alone
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* eldexp( a, n, b ) multiply by 2**n
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* emov( a, b ) b = a
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* emul( a, b, c, ldp ) c = b * a
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* eneg(e) e = -e
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* eround( a, b ) b = nearest integer value to a
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* esub( a, b, c, ldp ) c = b - a
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* e24toasc( &f, str, n ) single to ASCII string, n digits after decimal
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* e53toasc( &d, str, n ) double to ASCII string, n digits after decimal
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* e64toasc( &d, str, n ) long double to ASCII string
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* etoasc(e,str,n,fmt,ldp)e to ASCII string, n digits after decimal
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* etoe24( e, &f ) convert e type to IEEE single precision
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* etoe53( e, &d ) convert e type to IEEE double precision
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* etoe64( e, &d ) convert e type to IEEE long double precision
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* ltoe( &l, e ) long (32 bit) integer to e type
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* ultoe( &l, e ) unsigned long (32 bit) integer to e type
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* eisneg( e ) 1 if sign bit of e != 0, else 0
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* eisinf( e ) 1 if e has maximum exponent (non-IEEE)
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* or is infinite (IEEE)
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* eisnan( e ) 1 if e is a NaN
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* esqrt( a, b ) b = square root of a
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*
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*
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* Routines for internal format numbers
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*
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* eaddm( ai, bi ) add significands, bi = bi + ai
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* ecleaz(ei) ei = 0
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* ecleazs(ei) set ei = 0 but leave its sign alone
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* ecmpm( ai, bi ) compare significands, return 1, 0, or -1
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* edivm( ai, bi, ldp ) divide significands, bi = bi / ai
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* emdnorm(ai,l,s,exp,ldp) normalize and round off
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* emovi( a, ai ) convert external a to internal ai
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* emovo( ai, a, ldp ) convert internal ai to external a
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* emovz( ai, bi ) bi = ai, low guard word of bi = 0
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* emulm( ai, bi, ldp ) multiply significands, bi = bi * ai
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* enormlz(ei) left-justify the significand
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* eshdn1( ai ) shift significand and guards down 1 bit
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* eshdn8( ai ) shift down 8 bits
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* eshdn6( ai ) shift down 16 bits
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* eshift( ai, n ) shift ai n bits up (or down if n < 0)
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* eshup1( ai ) shift significand and guards up 1 bit
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* eshup8( ai ) shift up 8 bits
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* eshup6( ai ) shift up 16 bits
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* esubm( ai, bi ) subtract significands, bi = bi - ai
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*
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*
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* The result is always normalized and rounded to NI-4 word precision
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* after each arithmetic operation.
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*
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* Exception flags are NOT fully supported.
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*
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* Define USE_INFINITY in mconf.h for support of infinity; otherwise a
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* saturation arithmetic is implemented.
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*
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* Define NANS for support of Not-a-Number items; otherwise the
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* arithmetic will never produce a NaN output, and might be confused
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* by a NaN input.
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* If NaN's are supported, the output of ecmp(a,b) is -2 if
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* either a or b is a NaN. This means asking if(ecmp(a,b) < 0)
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* may not be legitimate. Use if(ecmp(a,b) == -1) for less-than
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* if in doubt.
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* Signaling NaN's are NOT supported; they are treated the same
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* as quiet NaN's.
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*
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* Denormals are always supported here where appropriate (e.g., not
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* for conversion to DEC numbers).
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*/
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/*
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* Revision history:
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*
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* 5 Jan 84 PDP-11 assembly language version
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* 6 Dec 86 C language version
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* 30 Aug 88 100 digit version, improved rounding
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* 15 May 92 80-bit long double support
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* 22 Nov 00 Revised to fit into newlib by Jeff Johnston <jjohnstn@redhat.com>
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*
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* Author: S. L. Moshier.
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*
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* Copyright (c) 1984,2000 S.L. Moshier
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*
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* Permission to use, copy, modify, and distribute this software for any
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* purpose without fee is hereby granted, provided that this entire notice
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* is included in all copies of any software which is or includes a copy
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* or modification of this software and in all copies of the supporting
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* documentation for such software.
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*
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* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
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* WARRANTY. IN PARTICULAR, THE AUTHOR MAKES NO REPRESENTATION
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* OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY OF THIS
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* SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
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*
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*/
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#include <stdio.h>
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/* #include "\usr\include\stdio.h" */
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/*#include "ehead.h"*/
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/*#include "mconf.h"*/
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/* mconf.h
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*
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* Common include file for math routines
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*
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*
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*
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* SYNOPSIS:
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*
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* #include "mconf.h"
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*
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*
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*
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* DESCRIPTION:
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*
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* This file contains definitions for error codes that are
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* passed to the common error handling routine mtherr()
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* (which see).
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*
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* The file also includes a conditional assembly definition
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* for the type of computer arithmetic (IEEE, DEC, Motorola
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* IEEE, or UNKnown).
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*
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* For Digital Equipment PDP-11 and VAX computers, certain
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* IBM systems, and others that use numbers with a 56-bit
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* significand, the symbol DEC should be defined. In this
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* mode, most floating point constants are given as arrays
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* of octal integers to eliminate decimal to binary conversion
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* errors that might be introduced by the compiler.
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*
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* For computers, such as IBM PC, that follow the IEEE
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* Standard for Binary Floating Point Arithmetic (ANSI/IEEE
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* Std 754-1985), the symbol IBMPC should be defined. These
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* numbers have 53-bit significands. In this mode, constants
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* are provided as arrays of hexadecimal 16 bit integers.
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*
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* To accommodate other types of computer arithmetic, all
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* constants are also provided in a normal decimal radix
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* which one can hope are correctly converted to a suitable
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* format by the available C language compiler. To invoke
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* this mode, the symbol UNK is defined.
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*
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* An important difference among these modes is a predefined
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* set of machine arithmetic constants for each. The numbers
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* MACHEP (the machine roundoff error), MAXNUM (largest number
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* represented), and several other parameters are preset by
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* the configuration symbol. Check the file const.c to
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* ensure that these values are correct for your computer.
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*
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* For ANSI C compatibility, define ANSIC equal to 1. Currently
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* this affects only the atan2() function and others that use it.
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*/
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/* Constant definitions for math error conditions
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*/
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#define DOMAIN 1 /* argument domain error */
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#define SING 2 /* argument singularity */
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#define OVERFLOW 3 /* overflow range error */
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#define UNDERFLOW 4 /* underflow range error */
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#define TLOSS 5 /* total loss of precision */
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#define PLOSS 6 /* partial loss of precision */
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#define EDOM 33
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#define ERANGE 34
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typedef struct
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{
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double r;
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double i;
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}cmplx;
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/* Type of computer arithmetic */
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#ifndef DEC
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#ifdef __IEEE_LITTLE_ENDIAN
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#define IBMPC 1
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#else /* !__IEEE_LITTLE_ENDIAN */
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#define MIEEE 1
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#endif /* !__IEEE_LITTLE_ENDIAN */
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#endif /* !DEC */
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/* Define 1 for ANSI C atan2() function
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* See atan.c and clog.c.
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*/
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#define ANSIC 1
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/*define VOLATILE volatile*/
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#define VOLATILE
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#define NANS
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#define USE_INFINITY
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/* NaN's require infinity support. */
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#ifdef NANS
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#ifndef INFINITY
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#define USE_INFINITY
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#endif
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#endif
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/* This handles 64-bit long ints. */
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#define LONGBITS (8 * sizeof(long))
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static void eaddm(short unsigned int *x, short unsigned int *y);
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static void esubm(short unsigned int *x, short unsigned int *y);
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static void emdnorm(short unsigned int *s, int lost, int subflg, long int exp, int rcntrl, LDPARMS *ldp);
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static int asctoeg(char *ss, short unsigned int *y, int oprec, LDPARMS *ldp);
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static void enan(short unsigned int *nan, int size);
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#if LDBL_MANT_DIG == 24
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static void toe24(short unsigned int *x, short unsigned int *y);
|
||
#elif LDBL_MANT_DIG == 53
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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
|
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static void toe113(short unsigned int *a, short unsigned int *b);
|
||
#endif
|
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static void eiremain(short unsigned int *den, short unsigned int *num, LDPARMS *ldp);
|
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static int ecmpm(register short unsigned int *a, register short unsigned int *b);
|
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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);
|
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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, LDPARMS *ldp);
|
||
static void emovz(register short unsigned int *a, register short unsigned int *b);
|
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static void ecleaz(register short unsigned int *xi);
|
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static void eadd1(short unsigned int *a, short unsigned int *b, short unsigned int *c, int subflg, LDPARMS *ldp);
|
||
static int eisnan(short unsigned int *x);
|
||
static int eiisnan(short unsigned int *x);
|
||
|
||
#ifdef DEC
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||
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++ )
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*x++ = 0;
|
||
}
|
||
|
||
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|
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/* Move external format number from a to b.
|
||
*
|
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* emov( a, b );
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*/
|
||
|
||
static void emov(register 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(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(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(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(short unsigned int *a, short unsigned int *b)
|
||
{
|
||
register unsigned short *p, *q;
|
||
int i;
|
||
|
||
q = b;
|
||
p = a + (NE-1); /* point to last word of external number */
|
||
/* get the sign bit */
|
||
if( *p & 0x8000 )
|
||
*q++ = 0xffff;
|
||
else
|
||
*q++ = 0;
|
||
/* get the exponent */
|
||
*q = *p--;
|
||
*q++ &= 0x7fff; /* delete the sign bit */
|
||
#ifdef 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<NI; i++ )
|
||
printf( "%04x ", *x++ );
|
||
printf( "\n" );
|
||
}
|
||
*/
|
||
|
||
|
||
/*
|
||
* Normalize and round off.
|
||
*
|
||
* The internal format number to be rounded is "s".
|
||
* Input "lost" indicates whether the number is exact.
|
||
* This is the so-called sticky bit.
|
||
*
|
||
* Input "subflg" indicates whether the number was obtained
|
||
* by a subtraction operation. In that case if lost is nonzero
|
||
* then the number is slightly smaller than indicated.
|
||
*
|
||
* Input "exp" is the biased exponent, which may be negative.
|
||
* the exponent field of "s" is ignored but is replaced by
|
||
* "exp" as adjusted by normalization and rounding.
|
||
*
|
||
* Input "rcntrl" is the rounding control.
|
||
*/
|
||
|
||
|
||
static void emdnorm(short unsigned int *s, int lost, int subflg, long int exp, int rcntrl, LDPARMS *ldp)
|
||
{
|
||
int i, j;
|
||
unsigned short r;
|
||
|
||
/* Normalize */
|
||
j = enormlz( s );
|
||
|
||
/* a blank significand could mean either zero or infinity. */
|
||
#ifndef USE_INFINITY
|
||
if( j > 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(short unsigned int *a, 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(short unsigned int *a, 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(short unsigned int *a, 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(short unsigned int *a, 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 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 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 toe53( x, y )
|
||
unsigned short *x, *y;
|
||
{
|
||
todec( x, y );
|
||
}
|
||
|
||
#else
|
||
|
||
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
|
||
#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 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(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<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 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
|
||
|
||
|
||
|
||
/* 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) = Balloc (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];
|
||
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;
|
||
}
|
||
|
||
|
||
|
||
|
||
/*
|
||
; 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, *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;
|
||
}
|
||
|
||
|
||
|
||
/* y = largest integer not greater than x
|
||
* (truncated toward minus infinity)
|
||
*
|
||
* unsigned short x[NE], y[NE]
|
||
* LDPARMS *ldp
|
||
*
|
||
* efloor( x, y, ldp );
|
||
*/
|
||
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, 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
|
||
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};
|
||
#else /* !MIEEE */
|
||
static unsigned short nan113[8] = {0, 0, 0, 0, 0, 0, 0x8000, 0x7fff};
|
||
static unsigned short nan64[6] = {0, 0, 0, 0, 0xc000, 0x7fff};
|
||
static unsigned short nan53[4] = {0, 0, 0, 0x7ff8};
|
||
static unsigned short nan24[2] = {0, 0x7fc0};
|
||
#endif /* !MIEEE */
|
||
|
||
|
||
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<NE-2; i++ )
|
||
*nan++ = 0;
|
||
*nan++ = 0xc000;
|
||
*nan++ = 0x7fff;
|
||
return;
|
||
|
||
case NI*16:
|
||
*nan++ = 0;
|
||
*nan++ = 0x7fff;
|
||
*nan++ = 0;
|
||
*nan++ = 0xc000;
|
||
for( i=4; i<NI; i++ )
|
||
*nan++ = 0;
|
||
return;
|
||
#endif
|
||
default:
|
||
mtherr( "enan", DOMAIN );
|
||
return;
|
||
}
|
||
for (i=0; i < n; i++)
|
||
*nan++ = *p++;
|
||
}
|