/* Adapted for Newlib, 2009. (Allow for int < 32 bits; return *quo=0 during
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/* Adapted for Newlib, 2009. (Allow for int < 32 bits; return *quo=0 during
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* errors to make test scripts easier.) */
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* errors to make test scripts easier.) */
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/* @(#)e_fmod.c 1.3 95/01/18 */
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/* @(#)e_fmod.c 1.3 95/01/18 */
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/*-
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/*-
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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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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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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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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* software is freely granted, provided that this notice
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* is preserved.
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* is preserved.
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* ====================================================
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* ====================================================
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*/
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*/
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#include <math.h>
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#include <math.h>
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#include "fdlibm.h"
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#include "fdlibm.h"
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/* For quotient, return either all 31 bits that can from calculation (using
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/* For quotient, return either all 31 bits that can from calculation (using
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* int32_t), or as many as can fit into an int that is smaller than 32 bits. */
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* int32_t), or as many as can fit into an int that is smaller than 32 bits. */
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#if INT_MAX > 0x7FFFFFFFL
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#if INT_MAX > 0x7FFFFFFFL
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#define QUO_MASK 0x7FFFFFFF
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#define QUO_MASK 0x7FFFFFFF
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# else
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# else
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#define QUO_MASK INT_MAX
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#define QUO_MASK INT_MAX
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#endif
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#endif
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static const float Zero[] = {0.0, -0.0,};
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static const float Zero[] = {0.0, -0.0,};
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/*
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/*
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* Return the IEEE remainder and set *quo to the last n bits of the
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* Return the IEEE remainder and set *quo to the last n bits of the
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* quotient, rounded to the nearest integer. We choose n=31--if that many fit--
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* quotient, rounded to the nearest integer. We choose n=31--if that many fit--
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* we wind up computing all the integer bits of the quotient anyway as
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* we wind up computing all the integer bits of the quotient anyway as
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* a side-effect of computing the remainder by the shift and subtract
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* a side-effect of computing the remainder by the shift and subtract
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* method. In practice, this is far more bits than are needed to use
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* method. In practice, this is far more bits than are needed to use
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* remquo in reduction algorithms.
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* remquo in reduction algorithms.
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*/
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*/
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float
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float
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remquof(float x, float y, int *quo)
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remquof(float x, float y, int *quo)
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{
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{
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__int32_t n,hx,hy,hz,ix,iy,sx,i;
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__int32_t n,hx,hy,hz,ix,iy,sx,i;
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__uint32_t q,sxy;
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__uint32_t q,sxy;
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|
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GET_FLOAT_WORD(hx,x);
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GET_FLOAT_WORD(hx,x);
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GET_FLOAT_WORD(hy,y);
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GET_FLOAT_WORD(hy,y);
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sxy = (hx ^ hy) & 0x80000000;
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sxy = (hx ^ hy) & 0x80000000;
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sx = hx&0x80000000; /* sign of x */
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sx = hx&0x80000000; /* sign of x */
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hx ^=sx; /* |x| */
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hx ^=sx; /* |x| */
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hy &= 0x7fffffff; /* |y| */
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hy &= 0x7fffffff; /* |y| */
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/* purge off exception values */
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/* purge off exception values */
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if(hy==0||hx>=0x7f800000||hy>0x7f800000) { /* y=0,NaN;or x not finite */
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if(hy==0||hx>=0x7f800000||hy>0x7f800000) { /* y=0,NaN;or x not finite */
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*quo = 0; /* Not necessary, but return consistent value */
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*quo = 0; /* Not necessary, but return consistent value */
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return (x*y)/(x*y);
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return (x*y)/(x*y);
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}
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}
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if(hx<hy) {
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if(hx<hy) {
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q = 0;
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q = 0;
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goto fixup; /* |x|<|y| return x or x-y */
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goto fixup; /* |x|<|y| return x or x-y */
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} else if(hx==hy) {
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} else if(hx==hy) {
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*quo = 1;
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*quo = 1;
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return Zero[(__uint32_t)sx>>31]; /* |x|=|y| return x*0*/
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return Zero[(__uint32_t)sx>>31]; /* |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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/* determine ix = ilogb(x) */
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if(hx<0x00800000) { /* subnormal x */
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if(hx<0x00800000) { /* subnormal x */
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for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1;
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for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1;
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} else ix = (hx>>23)-127;
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} else ix = (hx>>23)-127;
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/* determine iy = ilogb(y) */
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/* determine iy = ilogb(y) */
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if(hy<0x00800000) { /* subnormal y */
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if(hy<0x00800000) { /* subnormal y */
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for (iy = -126,i=(hy<<8); i>0; i<<=1) iy -=1;
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for (iy = -126,i=(hy<<8); i>0; i<<=1) iy -=1;
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} else iy = (hy>>23)-127;
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} else iy = (hy>>23)-127;
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|
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/* set up {hx,lx}, {hy,ly} and align y to x */
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/* set up {hx,lx}, {hy,ly} and align y to x */
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if(ix >= -126)
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if(ix >= -126)
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hx = 0x00800000|(0x007fffff&hx);
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hx = 0x00800000|(0x007fffff&hx);
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else { /* subnormal x, shift x to normal */
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else { /* subnormal x, shift x to normal */
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n = -126-ix;
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n = -126-ix;
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hx <<= n;
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hx <<= n;
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}
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}
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if(iy >= -126)
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if(iy >= -126)
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hy = 0x00800000|(0x007fffff&hy);
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hy = 0x00800000|(0x007fffff&hy);
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else { /* subnormal y, shift y to normal */
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else { /* subnormal y, shift y to normal */
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n = -126-iy;
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n = -126-iy;
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hy <<= n;
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hy <<= n;
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}
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}
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|
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/* fix point fmod */
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/* fix point fmod */
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n = ix - iy;
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n = ix - iy;
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q = 0;
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q = 0;
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while(n--) {
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while(n--) {
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hz=hx-hy;
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hz=hx-hy;
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if(hz<0) hx = hx << 1;
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if(hz<0) hx = hx << 1;
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else {hx = hz << 1; q++;}
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else {hx = hz << 1; q++;}
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q <<= 1;
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q <<= 1;
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}
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}
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hz=hx-hy;
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hz=hx-hy;
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if(hz>=0) {hx=hz;q++;}
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if(hz>=0) {hx=hz;q++;}
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|
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/* convert back to floating value and restore the sign */
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/* convert back to floating value and restore the sign */
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if(hx==0) { /* return sign(x)*0 */
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if(hx==0) { /* return sign(x)*0 */
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*quo = (sxy ? -q : q);
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*quo = (sxy ? -q : q);
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return Zero[(__uint32_t)sx>>31];
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return Zero[(__uint32_t)sx>>31];
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}
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}
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while(hx<0x00800000) { /* normalize x */
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while(hx<0x00800000) { /* normalize x */
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hx <<= 1;
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hx <<= 1;
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iy -= 1;
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iy -= 1;
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}
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}
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if(iy>= -126) { /* normalize output */
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if(iy>= -126) { /* normalize output */
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hx = ((hx-0x00800000)|((iy+127)<<23));
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hx = ((hx-0x00800000)|((iy+127)<<23));
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} else { /* subnormal output */
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} else { /* subnormal output */
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n = -126 - iy;
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n = -126 - iy;
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hx >>= n;
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hx >>= n;
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}
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}
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fixup:
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fixup:
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SET_FLOAT_WORD(x,hx);
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SET_FLOAT_WORD(x,hx);
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y = fabsf(y);
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y = fabsf(y);
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if (y < 0x1p-125f) {
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if (y < 0x1p-125f) {
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if (x+x>y || (x+x==y && (q & 1))) {
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if (x+x>y || (x+x==y && (q & 1))) {
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q++;
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q++;
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x-=y;
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x-=y;
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}
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}
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} else if (x>0.5f*y || (x==0.5f*y && (q & 1))) {
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} else if (x>0.5f*y || (x==0.5f*y && (q & 1))) {
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q++;
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q++;
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x-=y;
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x-=y;
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}
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}
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GET_FLOAT_WORD(hx,x);
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GET_FLOAT_WORD(hx,x);
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SET_FLOAT_WORD(x,hx^sx);
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SET_FLOAT_WORD(x,hx^sx);
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q &= 0x7fffffff;
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q &= 0x7fffffff;
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*quo = (sxy ? -q : q);
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*quo = (sxy ? -q : q);
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return x;
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return x;
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}
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}
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