newlib/libm/common/s_remquo.c

   1 /* Adapted for Newlib, 2009.  (Allow for int < 32 bits; return *quo=0 during
   2  * errors to make test scripts easier.)  */
   3 /* @(#)e_fmod.c 1.3 95/01/18 */
   4 /*-
   5  * ====================================================
   6  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   7  *
   8  * Developed at SunSoft, a Sun Microsystems, Inc. business.
   9  * Permission to use, copy, modify, and distribute this
  10  * software is freely granted, provided that this notice
  11  * is preserved.
  12  * ====================================================
  13  */
  14 /*
  15 FUNCTION
  16 <<remquo>>, <<remquof>>---remainder and part of quotient
  17 INDEX
  18         remquo
  19 INDEX
  20         remquof
  21
  22 SYNOPSIS
  23         #include <math.h>
  24         double remquo(double <[x]>, double <[y]>, int *<[quo]>);
  25         float remquof(float <[x]>, float <[y]>, int *<[quo]>);
  26
  27 DESCRIPTION
  28 The <<remquo>> functions compute the same remainder as the <<remainder>>
  29 functions; this value is in the range -<[y]>/2 ... +<[y]>/2.  In the object
  30 pointed to by <<quo>> they store a value whose sign is the sign of <<x>>/<<y>>
  31 and whose magnitude is congruent modulo 2**n to the magnitude of the integral
  32 quotient of <<x>>/<<y>>.  (That is, <<quo>> is given the n lsbs of the
  33 quotient, not counting the sign.)  This implementation uses n=31 if int is 32
  34 bits or more, otherwise, n is 1 less than the width of int.
  35
  36 For example:
  37 .       remquo(-29.0, 3.0, &<[quo]>)
  38 returns -1.0 and sets <[quo]>=10, and
  39 .       remquo(-98307.0, 3.0, &<[quo]>)
  40 returns -0.0 and sets <[quo]>=-32769, although for 16-bit int, <[quo]>=-1.  In
  41 the latter case, the actual quotient of -(32769=0x8001) is reduced to -1
  42 because of the 15-bit limitation for the quotient.
  43
  44 RETURNS
  45 When either argument is NaN, NaN is returned.  If <[y]> is 0 or <[x]> is
  46 infinite (and neither is NaN), a domain error occurs (i.e. the "invalid"
  47 floating point exception is raised or errno is set to EDOM), and NaN is
  48 returned.
  49 Otherwise, the <<remquo>> functions return <[x]> REM <[y]>.
  50
  51 BUGS
  52 IEEE754-2008 calls for <<remquo>>(subnormal, inf) to cause the "underflow"
  53 floating-point exception.  This implementation does not.
  54
  55 PORTABILITY
  56 C99, POSIX.
  57
  58 */
  59
  60 #include <limits.h>
  61 #include <math.h>
  62 #include "fdlibm.h"
  63
  64 /* For quotient, return either all 31 bits that can from calculation (using
  65  * int32_t), or as many as can fit into an int that is smaller than 32 bits.  */
  66 #if INT_MAX > 0x7FFFFFFFL
  67   #define QUO_MASK 0x7FFFFFFF
  68 # else
  69   #define QUO_MASK INT_MAX
  70 #endif
  71
  72 static const double Zero[] = {0.0, -0.0,};
  73
  74 /*
  75  * Return the IEEE remainder and set *quo to the last n bits of the
  76  * quotient, rounded to the nearest integer.  We choose n=31--if that many fit--
  77  * because we wind up computing all the integer bits of the quotient anyway as
  78  * a side-effect of computing the remainder by the shift and subtract
  79  * method.  In practice, this is far more bits than are needed to use
  80  * remquo in reduction algorithms.
  81  */
  82 double
  83 remquo(double x, double y, int *quo)
  84 {
  85         __int32_t n,hx,hy,hz,ix,iy,sx,i;
  86         __uint32_t lx,ly,lz,q,sxy;
  87
  88         EXTRACT_WORDS(hx,lx,x);
  89         EXTRACT_WORDS(hy,ly,y);
  90         sxy = (hx ^ hy) & 0x80000000;
  91         sx = hx&0x80000000;             /* sign of x */
  92         hx ^=sx;                /* |x| */
  93         hy &= 0x7fffffff;       /* |y| */
  94
  95     /* purge off exception values */
  96         if((hy|ly)==0||(hx>=0x7ff00000)||       /* y=0,or x not finite */
  97           ((hy|((ly|-ly)>>31))>0x7ff00000))  {  /* or y is NaN */
  98             *quo = 0;   /* Not necessary, but return consistent value */
  99             return (x*y)/(x*y);
 100         }
 101         if(hx<=hy) {
 102             if((hx<hy)||(lx<ly)) {
 103                 q = 0;
 104                 goto fixup;     /* |x|<|y| return x or x-y */
 105             }
 106             if(lx==ly) {
 107                 *quo = (sxy ? -1 : 1);
 108                 return Zero[(__uint32_t)sx>>31];        /* |x|=|y| return x*0 */
 109             }
 110         }
 111
 112     /* determine ix = ilogb(x) */
 113         if(hx<0x00100000) {     /* subnormal x */
 114             if(hx==0) {
 115                 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
 116             } else {
 117                 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
 118             }
 119         } else ix = (hx>>20)-1023;
 120
 121     /* determine iy = ilogb(y) */
 122         if(hy<0x00100000) {     /* subnormal y */
 123             if(hy==0) {
 124                 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
 125             } else {
 126                 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
 127             }
 128         } else iy = (hy>>20)-1023;
 129
 130     /* set up {hx,lx}, {hy,ly} and align y to x */
 131         if(ix >= -1022)
 132             hx = 0x00100000|(0x000fffff&hx);
 133         else {          /* subnormal x, shift x to normal */
 134             n = -1022-ix;
 135             if(n<=31) {
 136                 hx = (hx<<n)|(lx>>(32-n));
 137                 lx <<= n;
 138             } else {
 139                 hx = lx<<(n-32);
 140                 lx = 0;
 141             }
 142         }
 143         if(iy >= -1022)
 144             hy = 0x00100000|(0x000fffff&hy);
 145         else {          /* subnormal y, shift y to normal */
 146             n = -1022-iy;
 147             if(n<=31) {
 148                 hy = (hy<<n)|(ly>>(32-n));
 149                 ly <<= n;
 150             } else {
 151                 hy = ly<<(n-32);
 152                 ly = 0;
 153             }
 154         }
 155
 156     /* fix point fmod */
 157         n = ix - iy;
 158         q = 0;
 159         while(n--) {
 160             hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 161             if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
 162             else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;}
 163             q <<= 1;
 164         }
 165         hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 166         if(hz>=0) {hx=hz;lx=lz;q++;}
 167
 168     /* convert back to floating value and restore the sign */
 169         if((hx|lx)==0) {                        /* return sign(x)*0 */
 170             q &= QUO_MASK;
 171             *quo = (sxy ? -q : q);
 172             return Zero[(__uint32_t)sx>>31];
 173         }
 174         while(hx<0x00100000) {          /* normalize x */
 175             hx = hx+hx+(lx>>31); lx = lx+lx;
 176             iy -= 1;
 177         }
 178         if(iy>= -1022) {        /* normalize output */
 179             hx = ((hx-0x00100000)|((iy+1023)<<20));
 180         } else {                /* subnormal output */
 181             n = -1022 - iy;
 182             if(n<=20) {
 183                 lx = (lx>>n)|((__uint32_t)hx<<(32-n));
 184                 hx >>= n;
 185             } else if (n<=31) {
 186                 lx = (hx<<(32-n))|(lx>>n); hx = sx;
 187             } else {
 188                 lx = hx>>(n-32); hx = sx;
 189             }
 190         }
 191 fixup:
 192         INSERT_WORDS(x,hx,lx);
 193         y = fabs(y);
 194         if (y < 0x1p-1021) {
 195             if (x+x>y || (x+x==y && (q & 1))) {
 196                 q++;
 197                 x-=y;
 198             }
 199         } else if (x>0.5*y || (x==0.5*y && (q & 1))) {
 200             q++;
 201             x-=y;
 202         }
 203         GET_HIGH_WORD(hx,x);
 204         SET_HIGH_WORD(x,hx^sx);
 205         q &= QUO_MASK;
 206         *quo = (sxy ? -q : q);
 207         return x;
 208 }