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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 <sys/types.h> |
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#include <machine/ieee.h> |
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#include <float.h> |
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#include <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 Zero[] = {0.0L, -0.0L}; |
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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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* 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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remquol(long double x, long double y, int *quo) |
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{ |
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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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uint32_t esx, esy; |
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int ix,iy,n,q,sx,sxy; |
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GET_LDOUBLE_WORDS(esx,hx,lx,x); |
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GET_LDOUBLE_WORDS(esy,hy,ly,y); |
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sx = esx & 0x8000; |
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sxy = sx ^ (esy & 0x8000); |
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esx &= 0x7fff; /* |x| */ |
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esy &= 0x7fff; /* |y| */ |
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SET_LDOUBLE_EXP(x,esx); |
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SET_LDOUBLE_EXP(y,esy); |
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/* purge off exception values */ |
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if((esy|hy|ly)==0 || /* y=0 */ |
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(esx == BIAS + LDBL_MAX_EXP) || /* or x not finite */ |
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(esy == BIAS + LDBL_MAX_EXP && |
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((hy&~LDBL_NBIT)|ly)!=0)) /* or y is NaN */ |
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return (x*y)/(x*y); |
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if(esx<=esy) { |
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if((esx<esy) || |
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(hx<=hy && |
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(hx<hy || |
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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(hx==hy && lx==ly) { |
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*quo = 1; |
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return Zero[sx!=0]; /* |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(esx == 0) { /* subnormal x */ |
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x *= 0x1.0p512; |
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GET_LDOUBLE_WORDS(esx,hx,lx,x); |
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ix = esx - (BIAS + 512); |
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} else { |
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ix = esx - BIAS; |
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} |
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/* determine iy = ilogb(y) */ |
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if(esy == 0) { /* subnormal y */ |
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y *= 0x1.0p512; |
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GET_LDOUBLE_WORDS(esy,hy,ly,y); |
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iy = esy - (BIAS + 512); |
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} else { |
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iy = esy - 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(hx); |
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lx = SET_NBIT(lx); |
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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>>MANL_SHIFT); lx = lx+lx;} |
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else {hx = hz+hz+(lz>>MANL_SHIFT); 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[sx!=0]; |
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} |
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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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if (iy < LDBL_MIN_EXP) { |
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esx = (iy + BIAS + 512) & 0x7fff; |
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SET_LDOUBLE_WORDS(x,esx,hx,lx); |
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x *= 0x1p-512; |
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GET_LDOUBLE_WORDS(esx,hx,lx,x); |
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} else { |
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esx = (iy + BIAS) & 0x7fff; |
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} |
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SET_LDOUBLE_WORDS(x,esx,hx,lx); |
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fixup: |
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y = fabsl(y); |
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if (y < LDBL_MIN * 2) { |
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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_LDOUBLE_EXP(esx,x); |
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esx ^= sx; |
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SET_LDOUBLE_EXP(x,esx); |
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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(remquol); |