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/* @(#)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 <float.h> |
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#include <math.h> |
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#include "math_private.h" |
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static const double Zero[] = {0.0, -0.0,}; |
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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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* quotient, rounded to the nearest integer. We choose n=31 because |
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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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* 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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*/ |
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double |
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remquo(double x, double y, int *quo) |
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{ |
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int32_t n,hx,hy,hz,ix,iy,sx,i; |
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u_int32_t lx,ly,lz,q,sxy; |
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EXTRACT_WORDS(hx,lx,x); |
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EXTRACT_WORDS(hy,ly,y); |
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sxy = (hx ^ hy) & 0x80000000; |
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sx = hx&0x80000000; /* sign of x */ |
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hx ^=sx; /* |x| */ |
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hy &= 0x7fffffff; /* |y| */ |
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/* purge off exception values */ |
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if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ |
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((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ |
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return (x*y)/(x*y); |
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if(hx<=hy) { |
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if((hx<hy)||(lx<ly)) { |
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q = 0; |
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goto fixup; /* |x|<|y| return x or x-y */ |
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} |
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if(lx==ly) { |
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*quo = 1; |
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return Zero[(u_int32_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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if(hx<0x00100000) { /* subnormal x */ |
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if(hx==0) { |
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for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; |
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} else { |
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for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; |
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} |
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} else ix = (hx>>20)-1023; |
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/* determine iy = ilogb(y) */ |
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if(hy<0x00100000) { /* subnormal y */ |
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if(hy==0) { |
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for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; |
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} else { |
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for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; |
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} |
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} else iy = (hy>>20)-1023; |
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/* set up {hx,lx}, {hy,ly} and align y to x */ |
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if(ix >= -1022) |
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hx = 0x00100000|(0x000fffff&hx); |
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else { /* subnormal x, shift x to normal */ |
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n = -1022-ix; |
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if(n<=31) { |
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hx = (hx<<n)|(lx>>(32-n)); |
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lx <<= n; |
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} else { |
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hx = lx<<(n-32); |
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lx = 0; |
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} |
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} |
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if(iy >= -1022) |
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hy = 0x00100000|(0x000fffff&hy); |
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else { /* subnormal y, shift y to normal */ |
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n = -1022-iy; |
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if(n<=31) { |
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hy = (hy<<n)|(ly>>(32-n)); |
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ly <<= n; |
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} else { |
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hy = ly<<(n-32); |
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ly = 0; |
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} |
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} |
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/* fix point fmod */ |
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n = ix - iy; |
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q = 0; |
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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>>31); lx = lx+lx;} |
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else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;} |
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q <<= 1; |
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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;q++;} |
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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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*quo = (sxy ? -q : q); |
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return Zero[(u_int32_t)sx>>31]; |
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} |
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while(hx<0x00100000) { /* normalize x */ |
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hx = hx+hx+(lx>>31); lx = lx+lx; |
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iy -= 1; |
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} |
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if(iy>= -1022) { /* normalize output */ |
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hx = ((hx-0x00100000)|((iy+1023)<<20)); |
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} else { /* subnormal output */ |
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n = -1022 - iy; |
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if(n<=20) { |
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lx = (lx>>n)|((u_int32_t)hx<<(32-n)); |
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hx >>= n; |
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} else if (n<=31) { |
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lx = (hx<<(32-n))|(lx>>n); hx = sx; |
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} else { |
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lx = hx>>(n-32); hx = sx; |
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} |
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} |
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fixup: |
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INSERT_WORDS(x,hx,lx); |
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y = fabs(y); |
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if (y < 0x1p-1021) { |
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if (x+x>y || (x+x==y && (q & 1))) { |
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q++; |
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x-=y; |
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} |
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} else if (x>0.5*y || (x==0.5*y && (q & 1))) { |
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q++; |
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x-=y; |
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} |
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GET_HIGH_WORD(hx,x); |
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SET_HIGH_WORD(x,hx^sx); |
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q &= 0x7fffffff; |
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*quo = (sxy ? -q : q); |
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return x; |
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} |
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DEF_STD(remquo); |
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LDBL_MAYBE_CLONE(remquo); |