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[/] [openrisc/] [trunk/] [gnu-src/] [newlib-1.18.0/] [newlib/] [libm/] [common/] [s_remquo.c] - Rev 207
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/* Adapted for Newlib, 2009. (Allow for int < 32 bits; return *quo=0 during * errors to make test scripts easier.) */ /* @(#)e_fmod.c 1.3 95/01/18 */ /*- * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* FUNCTION <<remquo>>, <<remquof>>--remainder and part of quotient INDEX remquo INDEX remquof ANSI_SYNOPSIS #include <math.h> double remquo(double <[x]>, double <[y]>, int *<[quo]>); float remquof(float <[x]>, float <[y]>, int *<[quo]>); DESCRIPTION The <<remquo>> functions compute the same remainder as the <<remainder>> functions; this value is in the range -<[y]>/2 ... +<[y]>/2. In the object pointed to by <<quo>> they store a value whose sign is the sign of <<x>>/<<y>> and whose magnitude is congruent modulo 2**n to the magnitude of the integral quotient of <<x>>/<<y>>. (That is, <<quo>> is given the n lsbs of the quotient, not counting the sign.) This implementation uses n=31 if int is 32 bits or more, otherwise, n is 1 less than the width of int. For example: . remquo(-29.0, 3.0, &<[quo]>) returns -1.0 and sets <[quo]>=10, and . remquo(-98307.0, 3.0, &<[quo]>) returns -0.0 and sets <[quo]>=-32769, although for 16-bit int, <[quo]>=-1. In the latter case, the actual quotient of -(32769=0x8001) is reduced to -1 because of the 15-bit limitation for the quotient. RETURNS When either argument is NaN, NaN is returned. If <[y]> is 0 or <[x]> is infinite (and neither is NaN), a domain error occurs (i.e. the "invalid" floating point exception is raised or errno is set to EDOM), and NaN is returned. Otherwise, the <<remquo>> functions return <[x]> REM <[y]>. BUGS IEEE754-2008 calls for <<remquo>>(subnormal, inf) to cause the "underflow" floating-point exception. This implementation does not. PORTABILITY C99, POSIX. */ #include <limits.h> #include <math.h> #include "fdlibm.h" /* For quotient, return either all 31 bits that can from calculation (using * int32_t), or as many as can fit into an int that is smaller than 32 bits. */ #if INT_MAX > 0x7FFFFFFFL #define QUO_MASK 0x7FFFFFFF # else #define QUO_MASK INT_MAX #endif static const double Zero[] = {0.0, -0.0,}; /* * Return the IEEE remainder and set *quo to the last n bits of the * quotient, rounded to the nearest integer. We choose n=31--if that many fit-- * because we wind up computing all the integer bits of the quotient anyway as * a side-effect of computing the remainder by the shift and subtract * method. In practice, this is far more bits than are needed to use * remquo in reduction algorithms. */ double remquo(double x, double y, int *quo) { __int32_t n,hx,hy,hz,ix,iy,sx,i; __uint32_t lx,ly,lz,q,sxy; EXTRACT_WORDS(hx,lx,x); EXTRACT_WORDS(hy,ly,y); sxy = (hx ^ hy) & 0x80000000; sx = hx&0x80000000; /* sign of x */ hx ^=sx; /* |x| */ hy &= 0x7fffffff; /* |y| */ /* purge off exception values */ if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ ((hy|((ly|-ly)>>31))>0x7ff00000)) { /* or y is NaN */ *quo = 0; /* Not necessary, but return consistent value */ return (x*y)/(x*y); } if(hx<=hy) { if((hx<hy)||(lx<ly)) { q = 0; goto fixup; /* |x|<|y| return x or x-y */ } if(lx==ly) { *quo = (sxy ? -1 : 1); return Zero[(__uint32_t)sx>>31]; /* |x|=|y| return x*0 */ } } /* determine ix = ilogb(x) */ if(hx<0x00100000) { /* subnormal x */ if(hx==0) { for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; } else { for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; } } else ix = (hx>>20)-1023; /* determine iy = ilogb(y) */ if(hy<0x00100000) { /* subnormal y */ if(hy==0) { for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; } else { for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; } } else iy = (hy>>20)-1023; /* set up {hx,lx}, {hy,ly} and align y to x */ if(ix >= -1022) hx = 0x00100000|(0x000fffff&hx); else { /* subnormal x, shift x to normal */ n = -1022-ix; if(n<=31) { hx = (hx<<n)|(lx>>(32-n)); lx <<= n; } else { hx = lx<<(n-32); lx = 0; } } if(iy >= -1022) hy = 0x00100000|(0x000fffff&hy); else { /* subnormal y, shift y to normal */ n = -1022-iy; if(n<=31) { hy = (hy<<n)|(ly>>(32-n)); ly <<= n; } else { hy = ly<<(n-32); ly = 0; } } /* fix point fmod */ n = ix - iy; q = 0; while(n--) { hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;} else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;} q <<= 1; } hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; if(hz>=0) {hx=hz;lx=lz;q++;} /* convert back to floating value and restore the sign */ if((hx|lx)==0) { /* return sign(x)*0 */ q &= QUO_MASK; *quo = (sxy ? -q : q); return Zero[(__uint32_t)sx>>31]; } while(hx<0x00100000) { /* normalize x */ hx = hx+hx+(lx>>31); lx = lx+lx; iy -= 1; } if(iy>= -1022) { /* normalize output */ hx = ((hx-0x00100000)|((iy+1023)<<20)); } else { /* subnormal output */ n = -1022 - iy; if(n<=20) { lx = (lx>>n)|((__uint32_t)hx<<(32-n)); hx >>= n; } else if (n<=31) { lx = (hx<<(32-n))|(lx>>n); hx = sx; } else { lx = hx>>(n-32); hx = sx; } } fixup: INSERT_WORDS(x,hx,lx); y = fabs(y); if (y < 0x1p-1021) { if (x+x>y || (x+x==y && (q & 1))) { q++; x-=y; } } else if (x>0.5*y || (x==0.5*y && (q & 1))) { q++; x-=y; } GET_HIGH_WORD(hx,x); SET_HIGH_WORD(x,hx^sx); q &= QUO_MASK; *quo = (sxy ? -q : q); return x; }