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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 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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} |