diff options
Diffstat (limited to 'newlib/libm/common/s_remquo.c')
| -rw-r--r-- | newlib/libm/common/s_remquo.c | 219 |
1 files changed, 194 insertions, 25 deletions
diff --git a/newlib/libm/common/s_remquo.c b/newlib/libm/common/s_remquo.c index bd52f39fc..9e18ab132 100644 --- a/newlib/libm/common/s_remquo.c +++ b/newlib/libm/common/s_remquo.c @@ -1,39 +1,208 @@ -/* Copyright (C) 2002 by Red Hat, Incorporated. All rights reserved. +/* 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. * - * Permission to use, copy, modify, and distribute this software - * is freely granted, provided that this notice is preserved. + * 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 -#include "fdlibm.h" +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]>. -#ifndef _DOUBLE_IS_32BITS +BUGS +IEEE754-2008 calls for <<remquo>>(subnormal, inf) to cause the "underflow" +floating-point exception. This implementation does not. -#ifdef __STDC__ - double remquo(double x, double y, int *quo) /* wrapper remquo */ -#else - double remquo(x,y,quo) /* wrapper remquo */ - double x,y; - int *quo; +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) { - int signx, signy, signres; - int mswx; - int mswy; - double x_over_y; + __int32_t n,hx,hy,hz,ix,iy,sx,i; + __uint32_t lx,ly,lz,q,sxy; - GET_HIGH_WORD(mswx, x); - GET_HIGH_WORD(mswy, y); + 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| */ - signx = (mswx & 0x80000000) >> 31; - signy = (mswy & 0x80000000) >> 31; + /* 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 = 1; + return Zero[(__uint32_t)sx>>31]; /* |x|=|y| return x*0*/ + } + } - signres = (signx ^ signy) ? -1 : 1; + /* 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; - x_over_y = fabs(x / y); + /* 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; - *quo = signres * (lrint(x_over_y) & 0x7f); + /* 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; + } + } - return remainder(x,y); -} + /* 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++;} -#endif /* defined(_DOUBLE_IS_32BITS) */ + /* 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; +} |