143 lines
3.8 KiB
C
143 lines
3.8 KiB
C
/* @(#)e_fmod.c 1.3 95/01/18 */
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/*-
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include <sys/types.h>
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//#include <machine/ieee.h>
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#include <float.h>
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#include <openlibm_math.h>
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#include <stdint.h>
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#include "math_private.h"
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#define BIAS (LDBL_MAX_EXP - 1)
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/*
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* These macros add and remove an explicit integer bit in front of the
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* fractional mantissa, if the architecture doesn't have such a bit by
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* default already.
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*/
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#ifdef LDBL_IMPLICIT_NBIT
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#define LDBL_NBIT 0
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#define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE))
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#define HFRAC_BITS EXT_FRACHBITS
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#else
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#define LDBL_NBIT 0x80000000
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#define SET_NBIT(hx) (hx)
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#define HFRAC_BITS (EXT_FRACHBITS - 1)
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#endif
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#define MANL_SHIFT (EXT_FRACLBITS - 1)
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static const long double one = 1.0, Zero[] = {0.0, -0.0,};
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/*
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* fmodl(x,y)
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* Return x mod y in exact arithmetic
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* Method: shift and subtract
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*
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* Assumptions:
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* - The low part of the mantissa fits in a manl_t exactly.
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* - The high part of the mantissa fits in an int64_t with enough room
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* for an explicit integer bit in front of the fractional bits.
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*/
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long double
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fmodl(long double x, long double y)
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{
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union {
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long double e;
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struct ieee_ext bits;
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} ux, uy;
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int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
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uint32_t hy;
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uint32_t lx,ly,lz;
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int ix,iy,n,sx;
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ux.e = x;
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uy.e = y;
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sx = ux.bits.ext_sign;
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/* purge off exception values */
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if((uy.bits.ext_exp|uy.bits.ext_frach|uy.bits.ext_fracl)==0 || /* y=0 */
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(ux.bits.ext_exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */
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(uy.bits.ext_exp == BIAS + LDBL_MAX_EXP &&
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((uy.bits.ext_frach&~LDBL_NBIT)|uy.bits.ext_fracl)!=0)) /* or y is NaN */
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return (x*y)/(x*y);
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if(ux.bits.ext_exp<=uy.bits.ext_exp) {
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if((ux.bits.ext_exp<uy.bits.ext_exp) ||
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(ux.bits.ext_frach<=uy.bits.ext_frach &&
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(ux.bits.ext_frach<uy.bits.ext_frach ||
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ux.bits.ext_fracl<uy.bits.ext_fracl))) {
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return x; /* |x|<|y| return x or x-y */
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}
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if(ux.bits.ext_frach==uy.bits.ext_frach &&
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ux.bits.ext_fracl==uy.bits.ext_fracl) {
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return Zero[sx]; /* |x|=|y| return x*0*/
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}
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}
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/* determine ix = ilogb(x) */
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if(ux.bits.ext_exp == 0) { /* subnormal x */
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ux.e *= 0x1.0p512;
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ix = ux.bits.ext_exp - (BIAS + 512);
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} else {
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ix = ux.bits.ext_exp - BIAS;
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}
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/* determine iy = ilogb(y) */
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if(uy.bits.ext_exp == 0) { /* subnormal y */
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uy.e *= 0x1.0p512;
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iy = uy.bits.ext_exp - (BIAS + 512);
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} else {
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iy = uy.bits.ext_exp - BIAS;
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}
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/* set up {hx,lx}, {hy,ly} and align y to x */
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hx = SET_NBIT(ux.bits.ext_frach);
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hy = SET_NBIT(uy.bits.ext_frach);
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lx = ux.bits.ext_fracl;
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ly = uy.bits.ext_fracl;
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/* fix point fmod */
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n = ix - iy;
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while(n--) {
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hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
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if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
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else {
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if ((hz|lz)==0) /* return sign(x)*0 */
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return Zero[sx];
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hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz;
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}
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}
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hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
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if(hz>=0) {hx=hz;lx=lz;}
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/* convert back to floating value and restore the sign */
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if((hx|lx)==0) /* return sign(x)*0 */
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return Zero[sx];
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while(hx<(1ULL<<HFRAC_BITS)) { /* normalize x */
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hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
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iy -= 1;
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}
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ux.bits.ext_frach = hx; /* The mantissa is truncated here if needed. */
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ux.bits.ext_fracl = lx;
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if (iy < LDBL_MIN_EXP) {
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ux.bits.ext_exp = iy + (BIAS + 512);
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ux.e *= 0x1p-512;
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} else {
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ux.bits.ext_exp = iy + BIAS;
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}
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x = ux.e * one; /* create necessary signal */
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return x; /* exact output */
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}
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