1319 lines
20 KiB
C
1319 lines
20 KiB
C
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/* This file is extracted from S L Moshier's ioldoubl.c,
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* modified for use in MinGW
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*
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* 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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/*
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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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*
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* Author: S. L. Moshier.
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*
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* 6 Oct 02 Modified for MinGW by inlining utility routines,
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* removing global variables and splitting out strtold
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* from _IO_ldtoa and _IO_ldtostr.
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*
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* Danny Smith <dannysmith@users.sourceforge.net>
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*
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*/
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#include "cephes_emath.h"
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/*
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* The constants are for 64 bit precision.
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*/
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/* Move in external format number,
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* converting it to internal format.
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*/
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void __emovi(const short unsigned int * __restrict__ a,
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short unsigned int * __restrict__ b)
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{
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register const unsigned short *p;
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register unsigned short *q;
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int i;
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q = b;
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p = a + (NE-1); /* point to last word of external number */
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/* get the sign bit */
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if( *p & 0x8000 )
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*q++ = 0xffff;
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else
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*q++ = 0;
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/* get the exponent */
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*q = *p--;
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*q++ &= 0x7fff; /* delete the sign bit */
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#ifdef INFINITY
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if( (*(q-1) & 0x7fff) == 0x7fff )
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{
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#ifdef NANS
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if( __eisnan(a) )
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{
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*q++ = 0;
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for( i=3; i<NI; i++ )
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*q++ = *p--;
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return;
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}
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#endif
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for( i=2; i<NI; i++ )
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*q++ = 0;
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return;
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}
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#endif
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/* clear high guard word */
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*q++ = 0;
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/* move in the significand */
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for( i=0; i<NE-1; i++ )
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*q++ = *p--;
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/* clear low guard word */
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*q = 0;
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}
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/*
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; Add significands
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; x + y replaces y
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*/
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void __eaddm(const short unsigned int * __restrict__ x,
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short unsigned int * __restrict__ y)
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{
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register unsigned long a;
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int i;
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unsigned int carry;
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x += NI-1;
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y += NI-1;
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carry = 0;
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for( i=M; i<NI; i++ )
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{
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a = (unsigned long )(*x) + (unsigned long )(*y) + carry;
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if( a & 0x10000 )
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carry = 1;
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else
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carry = 0;
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*y = (unsigned short )a;
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--x;
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--y;
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}
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}
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/*
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; Subtract significands
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; y - x replaces y
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*/
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void __esubm(const short unsigned int * __restrict__ x,
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short unsigned int * __restrict__ y)
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{
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unsigned long a;
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int i;
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unsigned int carry;
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x += NI-1;
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y += NI-1;
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carry = 0;
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for( i=M; i<NI; i++ )
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{
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a = (unsigned long )(*y) - (unsigned long )(*x) - carry;
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if( a & 0x10000 )
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carry = 1;
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else
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carry = 0;
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*y = (unsigned short )a;
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--x;
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--y;
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}
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}
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/* Multiply significand of e-type number b
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by 16-bit quantity a, e-type result to c. */
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static void __m16m(short unsigned int a,
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short unsigned int * __restrict__ b,
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short unsigned int * __restrict__ c)
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{
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register unsigned short *pp;
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register unsigned long carry;
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unsigned short *ps;
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unsigned short p[NI];
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unsigned long aa, m;
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int i;
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aa = a;
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pp = &p[NI-2];
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*pp++ = 0;
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*pp = 0;
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ps = &b[NI-1];
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for( i=M+1; i<NI; i++ )
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{
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if( *ps == 0 )
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{
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--ps;
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--pp;
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*(pp-1) = 0;
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}
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else
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{
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m = (unsigned long) aa * *ps--;
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carry = (m & 0xffff) + *pp;
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*pp-- = (unsigned short )carry;
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carry = (carry >> 16) + (m >> 16) + *pp;
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*pp = (unsigned short )carry;
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*(pp-1) = carry >> 16;
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}
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}
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for( i=M; i<NI; i++ )
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c[i] = p[i];
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}
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/* Divide significands. Neither the numerator nor the denominator
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is permitted to have its high guard word nonzero. */
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int __edivm(short unsigned int * __restrict__ den,
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short unsigned int * __restrict__ num)
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{
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int i;
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register unsigned short *p;
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unsigned long tnum;
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unsigned short j, tdenm, tquot;
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unsigned short tprod[NI+1];
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unsigned short equot[NI];
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p = &equot[0];
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*p++ = num[0];
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*p++ = num[1];
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for( i=M; i<NI; i++ )
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{
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*p++ = 0;
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}
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__eshdn1( num );
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tdenm = den[M+1];
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for( i=M; i<NI; i++ )
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{
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/* Find trial quotient digit (the radix is 65536). */
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tnum = (((unsigned long) num[M]) << 16) + num[M+1];
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/* Do not execute the divide instruction if it will overflow. */
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if( (tdenm * 0xffffUL) < tnum )
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tquot = 0xffff;
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else
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tquot = tnum / tdenm;
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/* Prove that the divide worked. */
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/*
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tcheck = (unsigned long )tquot * tdenm;
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if( tnum - tcheck > tdenm )
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tquot = 0xffff;
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*/
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/* Multiply denominator by trial quotient digit. */
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__m16m( tquot, den, tprod );
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/* The quotient digit may have been overestimated. */
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if( __ecmpm( tprod, num ) > 0 )
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{
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tquot -= 1;
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__esubm( den, tprod );
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if( __ecmpm( tprod, num ) > 0 )
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{
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tquot -= 1;
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__esubm( den, tprod );
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}
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}
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__esubm( tprod, num );
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equot[i] = tquot;
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__eshup6(num);
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}
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/* test for nonzero remainder after roundoff bit */
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p = &num[M];
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j = 0;
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for( i=M; i<NI; i++ )
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{
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j |= *p++;
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}
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if( j )
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j = 1;
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for( i=0; i<NI; i++ )
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num[i] = equot[i];
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return( (int )j );
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}
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/* Multiply significands */
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int __emulm(const short unsigned int * __restrict__ a,
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short unsigned int * __restrict__ b)
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{
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const unsigned short *p;
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unsigned short *q;
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unsigned short pprod[NI];
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unsigned short equot[NI];
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unsigned short j;
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int i;
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equot[0] = b[0];
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equot[1] = b[1];
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for( i=M; i<NI; i++ )
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equot[i] = 0;
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j = 0;
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p = &a[NI-1];
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q = &equot[NI-1];
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for( i=M+1; i<NI; i++ )
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{
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if( *p == 0 )
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{
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--p;
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}
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else
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{
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__m16m( *p--, b, pprod );
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__eaddm(pprod, equot);
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}
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j |= *q;
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__eshdn6(equot);
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}
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for( i=0; i<NI; i++ )
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b[i] = equot[i];
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||
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/* return flag for lost nonzero bits */
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return( (int)j );
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}
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|
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|
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/*
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* Normalize and round off.
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*
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* The internal format number to be rounded is "s".
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* Input "lost" indicates whether the number is exact.
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* This is the so-called sticky bit.
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*
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* Input "subflg" indicates whether the number was obtained
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* by a subtraction operation. In that case if lost is nonzero
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* then the number is slightly smaller than indicated.
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*
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* Input "exp" is the biased exponent, which may be negative.
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* the exponent field of "s" is ignored but is replaced by
|
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|
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* "exp" as adjusted by normalization and rounding.
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*
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* Input "rcntrl" is the rounding control.
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*
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* Input "rnprc" is precison control (64 or NBITS).
|
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|
*/
|
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|
|
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||
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void __emdnorm(short unsigned int *s, int lost, int subflg, long int exp, int rcntrl, int rndprc)
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{
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int i, j;
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unsigned short r;
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int rw = NI-1; /* low guard word */
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int re = NI-2;
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|
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const unsigned short rmsk = 0xffff;
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|
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const unsigned short rmbit = 0x8000;
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|
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#if NE == 6
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unsigned short rbit[NI] = {0,0,0,0,0,0,0,1,0};
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#else
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unsigned short rbit[NI] = {0,0,0,0,0,0,0,0,0,0,0,1,0};
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|
|
#endif
|
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|
|
|
||
|
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/* Normalize */
|
||
|
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j = __enormlz( s );
|
||
|
|
|
||
|
|
/* a blank significand could mean either zero or infinity. */
|
||
|
|
#ifndef INFINITY
|
||
|
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if( j > NBITS )
|
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|
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{
|
||
|
|
__ecleazs( s );
|
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|
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return;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
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exp -= j;
|
||
|
|
#ifndef INFINITY
|
||
|
|
if( exp >= 32767L )
|
||
|
|
goto overf;
|
||
|
|
#else
|
||
|
|
if( (j > NBITS) && (exp < 32767L) )
|
||
|
|
{
|
||
|
|
__ecleazs( s );
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
if( exp < 0L )
|
||
|
|
{
|
||
|
|
if( exp > (long )(-NBITS-1) )
|
||
|
|
{
|
||
|
|
j = (int )exp;
|
||
|
|
i = __eshift( s, j );
|
||
|
|
if( i )
|
||
|
|
lost = 1;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
__ecleazs( s );
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
/* Round off, unless told not to by rcntrl. */
|
||
|
|
if( rcntrl == 0 )
|
||
|
|
goto mdfin;
|
||
|
|
if (rndprc == 64)
|
||
|
|
{
|
||
|
|
rw = 7;
|
||
|
|
re = 6;
|
||
|
|
rbit[NI-2] = 0;
|
||
|
|
rbit[6] = 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Shift down 1 temporarily if the data structure has an implied
|
||
|
|
* most significant bit and the number is denormal.
|
||
|
|
* For rndprc = 64 or NBITS, there is no implied bit.
|
||
|
|
* But Intel long double denormals lose one bit of significance even so.
|
||
|
|
*/
|
||
|
|
#if IBMPC
|
||
|
|
if( (exp <= 0) && (rndprc != NBITS) )
|
||
|
|
#else
|
||
|
|
if( (exp <= 0) && (rndprc != 64) && (rndprc != NBITS) )
|
||
|
|
#endif
|
||
|
|
{
|
||
|
|
lost |= s[NI-1] & 1;
|
||
|
|
__eshdn1(s);
|
||
|
|
}
|
||
|
|
/* Clear out all bits below the rounding bit,
|
||
|
|
* remembering in r if any were nonzero.
|
||
|
|
*/
|
||
|
|
r = s[rw] & rmsk;
|
||
|
|
if( rndprc < NBITS )
|
||
|
|
{
|
||
|
|
i = rw + 1;
|
||
|
|
while( i < NI )
|
||
|
|
{
|
||
|
|
if( s[i] )
|
||
|
|
r |= 1;
|
||
|
|
s[i] = 0;
|
||
|
|
++i;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
s[rw] &= ~rmsk;
|
||
|
|
if( (r & rmbit) != 0 )
|
||
|
|
{
|
||
|
|
if( r == rmbit )
|
||
|
|
{
|
||
|
|
if( lost == 0 )
|
||
|
|
{ /* round to even */
|
||
|
|
if( (s[re] & 1) == 0 )
|
||
|
|
goto mddone;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
if( subflg != 0 )
|
||
|
|
goto mddone;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
__eaddm( rbit, s );
|
||
|
|
}
|
||
|
|
mddone:
|
||
|
|
#if IBMPC
|
||
|
|
if( (exp <= 0) && (rndprc != NBITS) )
|
||
|
|
#else
|
||
|
|
if( (exp <= 0) && (rndprc != 64) && (rndprc != NBITS) )
|
||
|
|
#endif
|
||
|
|
{
|
||
|
|
__eshup1(s);
|
||
|
|
}
|
||
|
|
if( s[2] != 0 )
|
||
|
|
{ /* overflow on roundoff */
|
||
|
|
__eshdn1(s);
|
||
|
|
exp += 1;
|
||
|
|
}
|
||
|
|
mdfin:
|
||
|
|
s[NI-1] = 0;
|
||
|
|
if( exp >= 32767L )
|
||
|
|
{
|
||
|
|
#ifndef INFINITY
|
||
|
|
overf:
|
||
|
|
#endif
|
||
|
|
#ifdef INFINITY
|
||
|
|
s[1] = 32767;
|
||
|
|
for( i=2; i<NI-1; i++ )
|
||
|
|
s[i] = 0;
|
||
|
|
#else
|
||
|
|
s[1] = 32766;
|
||
|
|
s[2] = 0;
|
||
|
|
for( i=M+1; i<NI-1; i++ )
|
||
|
|
s[i] = 0xffff;
|
||
|
|
s[NI-1] = 0;
|
||
|
|
if( (rndprc < 64) || (rndprc == 113) )
|
||
|
|
s[rw] &= ~rmsk;
|
||
|
|
#endif
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
if( exp < 0 )
|
||
|
|
s[1] = 0;
|
||
|
|
else
|
||
|
|
s[1] = (unsigned short )exp;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
/*
|
||
|
|
; Multiply.
|
||
|
|
;
|
||
|
|
; unsigned short a[NE], b[NE], c[NE];
|
||
|
|
; emul( a, b, c ); c = b * a
|
||
|
|
*/
|
||
|
|
void __emul(const short unsigned int *a,
|
||
|
|
const short unsigned int *b,
|
||
|
|
short unsigned int *c)
|
||
|
|
{
|
||
|
|
unsigned short ai[NI], bi[NI];
|
||
|
|
int i, j;
|
||
|
|
long lt, lta, ltb;
|
||
|
|
|
||
|
|
#ifdef NANS
|
||
|
|
/* NaN times anything is the same NaN. */
|
||
|
|
if( __eisnan(a) )
|
||
|
|
{
|
||
|
|
__emov(a,c);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
if( __eisnan(b) )
|
||
|
|
{
|
||
|
|
__emov(b,c);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
/* Zero times infinity is a NaN. */
|
||
|
|
if( (__eisinf(a) && __eiiszero(b))
|
||
|
|
|| (__eisinf(b) && __eiiszero(a)) )
|
||
|
|
{
|
||
|
|
mtherr( "emul", DOMAIN );
|
||
|
|
__enan_NBITS( c );
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
/* Infinity times anything else is infinity. */
|
||
|
|
#ifdef INFINITY
|
||
|
|
if( __eisinf(a) || __eisinf(b) )
|
||
|
|
{
|
||
|
|
if( __eisneg(a) ^ __eisneg(b) )
|
||
|
|
*(c+(NE-1)) = 0x8000;
|
||
|
|
else
|
||
|
|
*(c+(NE-1)) = 0;
|
||
|
|
__einfin(c);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
__emovi( a, ai );
|
||
|
|
__emovi( b, bi );
|
||
|
|
lta = ai[E];
|
||
|
|
ltb = bi[E];
|
||
|
|
if( ai[E] == 0 )
|
||
|
|
{
|
||
|
|
for( i=1; i<NI-1; i++ )
|
||
|
|
{
|
||
|
|
if( ai[i] != 0 )
|
||
|
|
{
|
||
|
|
lta -= __enormlz( ai );
|
||
|
|
goto mnzer1;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
__eclear(c);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
mnzer1:
|
||
|
|
|
||
|
|
if( bi[E] == 0 )
|
||
|
|
{
|
||
|
|
for( i=1; i<NI-1; i++ )
|
||
|
|
{
|
||
|
|
if( bi[i] != 0 )
|
||
|
|
{
|
||
|
|
ltb -= __enormlz( bi );
|
||
|
|
goto mnzer2;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
__eclear(c);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
mnzer2:
|
||
|
|
|
||
|
|
/* Multiply significands */
|
||
|
|
j = __emulm( ai, bi );
|
||
|
|
/* calculate exponent */
|
||
|
|
lt = lta + ltb - (EXONE - 1);
|
||
|
|
__emdnorm( bi, j, 0, lt, 64, NBITS );
|
||
|
|
/* calculate sign of product */
|
||
|
|
if( ai[0] == bi[0] )
|
||
|
|
bi[0] = 0;
|
||
|
|
else
|
||
|
|
bi[0] = 0xffff;
|
||
|
|
__emovo( bi, c );
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
/* move out internal format to ieee long double */
|
||
|
|
void __toe64(short unsigned int *a, short unsigned int *b)
|
||
|
|
{
|
||
|
|
register unsigned short *p, *q;
|
||
|
|
unsigned short i;
|
||
|
|
|
||
|
|
#ifdef NANS
|
||
|
|
if( __eiisnan(a) )
|
||
|
|
{
|
||
|
|
__enan_64( b );
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
#ifdef IBMPC
|
||
|
|
/* Shift Intel denormal significand down 1. */
|
||
|
|
if( a[E] == 0 )
|
||
|
|
__eshdn1(a);
|
||
|
|
#endif
|
||
|
|
p = a;
|
||
|
|
#ifdef MIEEE
|
||
|
|
q = b;
|
||
|
|
#else
|
||
|
|
q = b + 4; /* point to output exponent */
|
||
|
|
#if 1
|
||
|
|
/* NOTE: if data type is 96 bits wide, clear the last word here. */
|
||
|
|
*(q+1)= 0;
|
||
|
|
#endif
|
||
|
|
#endif
|
||
|
|
|
||
|
|
/* combine sign and exponent */
|
||
|
|
i = *p++;
|
||
|
|
#ifdef MIEEE
|
||
|
|
if( i )
|
||
|
|
*q++ = *p++ | 0x8000;
|
||
|
|
else
|
||
|
|
*q++ = *p++;
|
||
|
|
*q++ = 0;
|
||
|
|
#else
|
||
|
|
if( i )
|
||
|
|
*q-- = *p++ | 0x8000;
|
||
|
|
else
|
||
|
|
*q-- = *p++;
|
||
|
|
#endif
|
||
|
|
/* skip over guard word */
|
||
|
|
++p;
|
||
|
|
/* move the significand */
|
||
|
|
#ifdef MIEEE
|
||
|
|
for( i=0; i<4; i++ )
|
||
|
|
*q++ = *p++;
|
||
|
|
#else
|
||
|
|
#ifdef INFINITY
|
||
|
|
if (__eiisinf (a))
|
||
|
|
{
|
||
|
|
/* Intel long double infinity. */
|
||
|
|
*q-- = 0x8000;
|
||
|
|
*q-- = 0;
|
||
|
|
*q-- = 0;
|
||
|
|
*q = 0;
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
for( i=0; i<4; i++ )
|
||
|
|
*q-- = *p++;
|
||
|
|
#endif
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
/* Compare two e type numbers.
|
||
|
|
*
|
||
|
|
* unsigned short a[NE], b[NE];
|
||
|
|
* ecmp( a, b );
|
||
|
|
*
|
||
|
|
* returns +1 if a > b
|
||
|
|
* 0 if a == b
|
||
|
|
* -1 if a < b
|
||
|
|
* -2 if either a or b is a NaN.
|
||
|
|
*/
|
||
|
|
int __ecmp(const short unsigned int * __restrict__ a,
|
||
|
|
const short unsigned int * __restrict__ 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.
|
||
|
|
*/
|
||
|
|
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.
|
||
|
|
*/
|
||
|
|
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 );
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
/* Move internal format number out,
|
||
|
|
* converting it to external format.
|
||
|
|
*/
|
||
|
|
void __emovo(const short unsigned int * __restrict__ a,
|
||
|
|
short unsigned int * __restrict__ b)
|
||
|
|
{
|
||
|
|
register const unsigned short *p;
|
||
|
|
register unsigned short *q;
|
||
|
|
unsigned short i;
|
||
|
|
|
||
|
|
p = a;
|
||
|
|
q = b + (NE-1); /* point to output exponent */
|
||
|
|
/* combine sign and exponent */
|
||
|
|
i = *p++;
|
||
|
|
if( i )
|
||
|
|
*q-- = *p++ | 0x8000;
|
||
|
|
else
|
||
|
|
*q-- = *p++;
|
||
|
|
#ifdef INFINITY
|
||
|
|
if( *(p-1) == 0x7fff )
|
||
|
|
{
|
||
|
|
#ifdef NANS
|
||
|
|
if( __eiisnan(a) )
|
||
|
|
{
|
||
|
|
__enan_NBITS( b );
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
__einfin(b);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
/* skip over guard word */
|
||
|
|
++p;
|
||
|
|
/* move the significand */
|
||
|
|
for( i=0; i<NE-1; i++ )
|
||
|
|
*q-- = *p++;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
#if USE_LDTOA
|
||
|
|
|
||
|
|
|
||
|
|
void __eiremain(short unsigned int *den, short unsigned int *num,
|
||
|
|
short unsigned int *equot )
|
||
|
|
{
|
||
|
|
long ld, ln;
|
||
|
|
unsigned short j;
|
||
|
|
|
||
|
|
ld = den[E];
|
||
|
|
ld -= __enormlz( den );
|
||
|
|
ln = num[E];
|
||
|
|
ln -= __enormlz( num );
|
||
|
|
__ecleaz( equot );
|
||
|
|
while( ln >= ld )
|
||
|
|
{
|
||
|
|
if( __ecmpm(den,num) <= 0 )
|
||
|
|
{
|
||
|
|
__esubm(den, num);
|
||
|
|
j = 1;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
j = 0;
|
||
|
|
}
|
||
|
|
__eshup1(equot);
|
||
|
|
equot[NI-1] |= j;
|
||
|
|
__eshup1(num);
|
||
|
|
ln -= 1;
|
||
|
|
}
|
||
|
|
__emdnorm( num, 0, 0, ln, 0, NBITS );
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
void __eadd1(const short unsigned int * __restrict__ a,
|
||
|
|
const short unsigned int * __restrict__ b,
|
||
|
|
short unsigned int * __restrict__ c,
|
||
|
|
int subflg)
|
||
|
|
{
|
||
|
|
unsigned short ai[NI], bi[NI], ci[NI];
|
||
|
|
int i, lost, j, k;
|
||
|
|
long lt, lta, ltb;
|
||
|
|
|
||
|
|
#ifdef INFINITY
|
||
|
|
if( __eisinf(a) )
|
||
|
|
{
|
||
|
|
__emov(a,c);
|
||
|
|
if( subflg )
|
||
|
|
__eneg(c);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
if( __eisinf(b) )
|
||
|
|
{
|
||
|
|
__emov(b,c);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
__emovi( a, ai );
|
||
|
|
__emovi( b, bi );
|
||
|
|
if( sub )
|
||
|
|
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, NBITS);
|
||
|
|
|
||
|
|
done:
|
||
|
|
__emovo( bi, c );
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
/* y = largest integer not greater than x
|
||
|
|
* (truncated toward minus infinity)
|
||
|
|
*
|
||
|
|
* unsigned short x[NE], y[NE]
|
||
|
|
*
|
||
|
|
* efloor( x, y );
|
||
|
|
*/
|
||
|
|
|
||
|
|
|
||
|
|
void __efloor(short unsigned int *x, short unsigned int *y)
|
||
|
|
{
|
||
|
|
register unsigned short *p;
|
||
|
|
int e, expon, i;
|
||
|
|
unsigned short f[NE];
|
||
|
|
const unsigned short bmask[] = {
|
||
|
|
0xffff,
|
||
|
|
0xfffe,
|
||
|
|
0xfffc,
|
||
|
|
0xfff8,
|
||
|
|
0xfff0,
|
||
|
|
0xffe0,
|
||
|
|
0xffc0,
|
||
|
|
0xff80,
|
||
|
|
0xff00,
|
||
|
|
0xfe00,
|
||
|
|
0xfc00,
|
||
|
|
0xf800,
|
||
|
|
0xf000,
|
||
|
|
0xe000,
|
||
|
|
0xc000,
|
||
|
|
0x8000,
|
||
|
|
0x0000,
|
||
|
|
};
|
||
|
|
|
||
|
|
__emov( x, f ); /* leave in external format */
|
||
|
|
expon = (int )f[NE-1];
|
||
|
|
e = (expon & 0x7fff) - (EXONE - 1);
|
||
|
|
if( e <= 0 )
|
||
|
|
{
|
||
|
|
__eclear(y);
|
||
|
|
goto isitneg;
|
||
|
|
}
|
||
|
|
/* number of bits to clear out */
|
||
|
|
e = NBITS - e;
|
||
|
|
__emov( f, y );
|
||
|
|
if( e <= 0 )
|
||
|
|
return;
|
||
|
|
|
||
|
|
p = &y[0];
|
||
|
|
while( e >= 16 )
|
||
|
|
{
|
||
|
|
*p++ = 0;
|
||
|
|
e -= 16;
|
||
|
|
}
|
||
|
|
/* clear the remaining bits */
|
||
|
|
*p &= bmask[e];
|
||
|
|
/* truncate negatives toward minus infinity */
|
||
|
|
isitneg:
|
||
|
|
|
||
|
|
if( (unsigned short )expon & (unsigned short )0x8000 )
|
||
|
|
{
|
||
|
|
for( i=0; i<NE-1; i++ )
|
||
|
|
{
|
||
|
|
if( f[i] != y[i] )
|
||
|
|
{
|
||
|
|
__esub( __eone, y, y );
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/*
|
||
|
|
; Subtract external format numbers.
|
||
|
|
;
|
||
|
|
; unsigned short a[NE], b[NE], c[NE];
|
||
|
|
; esub( a, b, c ); c = b - a
|
||
|
|
*/
|
||
|
|
|
||
|
|
|
||
|
|
void __esub(const short unsigned int * a,
|
||
|
|
const short unsigned int * b,
|
||
|
|
short unsigned int * c)
|
||
|
|
{
|
||
|
|
|
||
|
|
#ifdef NANS
|
||
|
|
if( __eisnan(a) )
|
||
|
|
{
|
||
|
|
__emov (a, c);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
if( __eisnan(b) )
|
||
|
|
{
|
||
|
|
__emov(b,c);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
/* Infinity minus infinity is a NaN.
|
||
|
|
* Test for subtracting infinities of the same sign.
|
||
|
|
*/
|
||
|
|
if( __eisinf(a) && __eisinf(b) && ((__eisneg (a) ^ __eisneg (b)) == 0))
|
||
|
|
{
|
||
|
|
mtherr( "esub", DOMAIN );
|
||
|
|
__enan_NBITS( c );
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
__eadd1( a, b, c, 1 );
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
/*
|
||
|
|
; Divide.
|
||
|
|
;
|
||
|
|
; unsigned short a[NI], b[NI], c[NI];
|
||
|
|
; ediv( a, b, c ); c = b / a
|
||
|
|
*/
|
||
|
|
|
||
|
|
void __ediv(const short unsigned int *a,
|
||
|
|
const short unsigned int *b,
|
||
|
|
short unsigned int *c)
|
||
|
|
{
|
||
|
|
unsigned short ai[NI], bi[NI];
|
||
|
|
int i;
|
||
|
|
long lt, lta, ltb;
|
||
|
|
|
||
|
|
#ifdef NANS
|
||
|
|
/* Return any NaN input. */
|
||
|
|
if( __eisnan(a) )
|
||
|
|
{
|
||
|
|
__emov(a,c);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
if( __eisnan(b) )
|
||
|
|
{
|
||
|
|
__emov(b,c);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
/* Zero over zero, or infinity over infinity, is a NaN. */
|
||
|
|
if( (__eiszero(a) && __eiszero(b))
|
||
|
|
|| (__eisinf (a) && __eisinf (b)) )
|
||
|
|
{
|
||
|
|
mtherr( "ediv", DOMAIN );
|
||
|
|
__enan_NBITS( c );
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
/* Infinity over anything else is infinity. */
|
||
|
|
#ifdef INFINITY
|
||
|
|
if( __eisinf(b) )
|
||
|
|
{
|
||
|
|
if( __eisneg(a) ^ __eisneg(b) )
|
||
|
|
*(c+(NE-1)) = 0x8000;
|
||
|
|
else
|
||
|
|
*(c+(NE-1)) = 0;
|
||
|
|
__einfin(c);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
if( __eisinf(a) )
|
||
|
|
{
|
||
|
|
__eclear(c);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
__emovi( a, ai );
|
||
|
|
__emovi( b, bi );
|
||
|
|
lta = ai[E];
|
||
|
|
ltb = bi[E];
|
||
|
|
if( bi[E] == 0 )
|
||
|
|
{ /* See if numerator is zero. */
|
||
|
|
for( i=1; i<NI-1; i++ )
|
||
|
|
{
|
||
|
|
if( bi[i] != 0 )
|
||
|
|
{
|
||
|
|
ltb -= __enormlz( bi );
|
||
|
|
goto dnzro1;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
__eclear(c);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
dnzro1:
|
||
|
|
|
||
|
|
if( ai[E] == 0 )
|
||
|
|
{ /* possible divide by zero */
|
||
|
|
for( i=1; i<NI-1; i++ )
|
||
|
|
{
|
||
|
|
if( ai[i] != 0 )
|
||
|
|
{
|
||
|
|
lta -= __enormlz( ai );
|
||
|
|
goto dnzro2;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if( ai[0] == bi[0] )
|
||
|
|
*(c+(NE-1)) = 0;
|
||
|
|
else
|
||
|
|
*(c+(NE-1)) = 0x8000;
|
||
|
|
__einfin(c);
|
||
|
|
mtherr( "ediv", SING );
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
dnzro2:
|
||
|
|
|
||
|
|
i = __edivm( ai, bi );
|
||
|
|
/* calculate exponent */
|
||
|
|
lt = ltb - lta + EXONE;
|
||
|
|
__emdnorm( bi, i, 0, lt, 64, NBITS );
|
||
|
|
/* set the sign */
|
||
|
|
if( ai[0] == bi[0] )
|
||
|
|
bi[0] = 0;
|
||
|
|
else
|
||
|
|
bi[0] = 0Xffff;
|
||
|
|
__emovo( bi, c );
|
||
|
|
}
|
||
|
|
|
||
|
|
void __e64toe(short unsigned int *pe, short unsigned int *y)
|
||
|
|
{
|
||
|
|
unsigned short yy[NI];
|
||
|
|
unsigned short *p, *q, *e;
|
||
|
|
int i;
|
||
|
|
|
||
|
|
e = pe;
|
||
|
|
p = yy;
|
||
|
|
for( i=0; i<NE-5; i++ )
|
||
|
|
*p++ = 0;
|
||
|
|
#ifdef IBMPC
|
||
|
|
for( i=0; i<5; i++ )
|
||
|
|
*p++ = *e++;
|
||
|
|
#endif
|
||
|
|
#ifdef DEC
|
||
|
|
for( i=0; i<5; i++ )
|
||
|
|
*p++ = *e++;
|
||
|
|
#endif
|
||
|
|
#ifdef MIEEE
|
||
|
|
p = &yy[0] + (NE-1);
|
||
|
|
*p-- = *e++;
|
||
|
|
++e;
|
||
|
|
for( i=0; i<4; i++ )
|
||
|
|
*p-- = *e++;
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#ifdef IBMPC
|
||
|
|
/* For Intel long double, shift denormal significand up 1
|
||
|
|
-- but only if the top significand bit is zero. */
|
||
|
|
if((yy[NE-1] & 0x7fff) == 0 && (yy[NE-2] & 0x8000) == 0)
|
||
|
|
{
|
||
|
|
unsigned short temp[NI+1];
|
||
|
|
__emovi(yy, temp);
|
||
|
|
__eshup1(temp);
|
||
|
|
__emovo(temp,y);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
#ifdef INFINITY
|
||
|
|
/* Point to the exponent field. */
|
||
|
|
p = &yy[NE-1];
|
||
|
|
if( *p == 0x7fff )
|
||
|
|
{
|
||
|
|
#ifdef NANS
|
||
|
|
#ifdef IBMPC
|
||
|
|
for( i=0; i<4; i++ )
|
||
|
|
{
|
||
|
|
if((i != 3 && pe[i] != 0)
|
||
|
|
/* Check for Intel long double infinity pattern. */
|
||
|
|
|| (i == 3 && pe[i] != 0x8000))
|
||
|
|
{
|
||
|
|
__enan_NBITS( y );
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
#else
|
||
|
|
for( i=1; i<=4; i++ )
|
||
|
|
{
|
||
|
|
if( pe[i] != 0 )
|
||
|
|
{
|
||
|
|
__enan_NBITS( y );
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
#endif /* NANS */
|
||
|
|
__eclear( y );
|
||
|
|
__einfin( y );
|
||
|
|
if( *p & 0x8000 )
|
||
|
|
__eneg(y);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
p = yy;
|
||
|
|
q = y;
|
||
|
|
for( i=0; i<NE; i++ )
|
||
|
|
*q++ = *p++;
|
||
|
|
}
|
||
|
|
|
||
|
|
#endif /* USE_LDTOA */
|