compiler/stdc/math/s_remquol.c

   1 /* @(#)e_fmod.c 1.3 95/01/18 */
   2 /*-
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunSoft, a Sun Microsystems, Inc. business.
   7  * Permission to use, copy, modify, and distribute this
   8  * software is freely granted, provided that this notice
   9  * is preserved.
  10  * ====================================================
  11  */
  12
  13 __FBSDID("$FreeBSD: src/lib/msun/src/s_remquol.c,v 1.2 2008/07/31 20:09:47 das Exp $");
  14
  15 #include <float.h>
  16
  17 #include "math.h"
  18 #include "fpmath.h"
  19 #include "math_private.h"
  20
  21 #define BIAS (LDBL_MAX_EXP - 1)
  22
  23 #if LDBL_MANL_SIZE > 32
  24 typedef uint64_t manl_t;
  25 #else
  26 typedef uint32_t manl_t;
  27 #endif
  28
  29 #if LDBL_MANH_SIZE > 32
  30 typedef uint64_t manh_t;
  31 #else
  32 typedef uint32_t manh_t;
  33 #endif
  34
  35 /*
  36  * These macros add and remove an explicit integer bit in front of the
  37  * fractional mantissa, if the architecture doesn't have such a bit by
  38  * default already.
  39  */
  40 #ifdef LDBL_IMPLICIT_NBIT
  41 #define SET_NBIT(hx)    ((hx) | (1ULL << LDBL_MANH_SIZE))
  42 #define HFRAC_BITS      LDBL_MANH_SIZE
  43 #else
  44 #define SET_NBIT(hx)    (hx)
  45 #define HFRAC_BITS      (LDBL_MANH_SIZE - 1)
  46 #endif
  47
  48 #define MANL_SHIFT      (LDBL_MANL_SIZE - 1)
  49
  50 static const long double Zero[] = {0.0L, -0.0L};
  51
  52 /*
  53  * Return the IEEE remainder and set *quo to the last n bits of the
  54  * quotient, rounded to the nearest integer.  We choose n=31 because
  55  * we wind up computing all the integer bits of the quotient anyway as
  56  * a side-effect of computing the remainder by the shift and subtract
  57  * method.  In practice, this is far more bits than are needed to use
  58  * remquo in reduction algorithms.
  59  *
  60  * Assumptions:
  61  * - The low part of the mantissa fits in a manl_t exactly.
  62  * - The high part of the mantissa fits in an int64_t with enough room
  63  *   for an explicit integer bit in front of the fractional bits.
  64  */
  65 long double
  66 remquol(long double x, long double y, int *quo)
  67 {
  68         union IEEEl2bits ux, uy;
  69         int64_t hx,hz;  /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
  70         manh_t hy;
  71         manl_t lx,ly,lz;
  72         int ix,iy,n,q,sx,sxy;
  73
  74         ux.e = x;
  75         uy.e = y;
  76         sx = ux.bits.sign;
  77         sxy = sx ^ uy.bits.sign;
  78         ux.bits.sign = 0;       /* |x| */
  79         uy.bits.sign = 0;       /* |y| */
  80         x = ux.e;
  81
  82     /* purge off exception values */
  83         if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */
  84            (ux.bits.exp == BIAS + LDBL_MAX_EXP) ||       /* or x not finite */
  85            (uy.bits.exp == BIAS + LDBL_MAX_EXP &&
  86             ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */
  87             return (x*y)/(x*y);
  88         if(ux.bits.exp<=uy.bits.exp) {
  89             if((ux.bits.exp<uy.bits.exp) ||
  90                (ux.bits.manh<=uy.bits.manh &&
  91                 (ux.bits.manh<uy.bits.manh ||
  92                  ux.bits.manl<uy.bits.manl))) {
  93                 q = 0;
  94                 goto fixup;     /* |x|<|y| return x or x-y */
  95             }
  96             if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) {
  97                 *quo = (sxy ? -1 : 1);
  98                 return Zero[sx];        /* |x|=|y| return x*0*/
  99             }
 100         }
 101
 102     /* determine ix = ilogb(x) */
 103         if(ux.bits.exp == 0) {  /* subnormal x */
 104             ux.e *= 0x1.0p512;
 105             ix = ux.bits.exp - (BIAS + 512);
 106         } else {
 107             ix = ux.bits.exp - BIAS;
 108         }
 109
 110     /* determine iy = ilogb(y) */
 111         if(uy.bits.exp == 0) {  /* subnormal y */
 112             uy.e *= 0x1.0p512;
 113             iy = uy.bits.exp - (BIAS + 512);
 114         } else {
 115             iy = uy.bits.exp - BIAS;
 116         }
 117
 118     /* set up {hx,lx}, {hy,ly} and align y to x */
 119         hx = SET_NBIT(ux.bits.manh);
 120         hy = SET_NBIT(uy.bits.manh);
 121         lx = ux.bits.manl;
 122         ly = uy.bits.manl;
 123
 124     /* fix point fmod */
 125         n = ix - iy;
 126         q = 0;
 127
 128         while(n--) {
 129             hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 130             if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
 131             else {hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; q++;}
 132             q <<= 1;
 133         }
 134         hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 135         if(hz>=0) {hx=hz;lx=lz;q++;}
 136
 137     /* convert back to floating value and restore the sign */
 138         if((hx|lx)==0) {                        /* return sign(x)*0 */
 139             q &= 0x7fffffff;
 140             *quo = (sxy ? -q : q);
 141             return Zero[sx];
 142         }
 143         while(hx<(1ULL<<HFRAC_BITS)) {  /* normalize x */
 144             hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
 145             iy -= 1;
 146         }
 147         ux.bits.manh = hx; /* The integer bit is truncated here if needed. */
 148         ux.bits.manl = lx;
 149         if (iy < LDBL_MIN_EXP) {
 150             ux.bits.exp = iy + (BIAS + 512);
 151             ux.e *= 0x1p-512;
 152         } else {
 153             ux.bits.exp = iy + BIAS;
 154         }
 155         ux.bits.sign = 0;
 156         x = ux.e;
 157 fixup:
 158         y = fabsl(y);
 159         if (y < LDBL_MIN * 2) {
 160             if (x+x>y || (x+x==y && (q & 1))) {
 161                 q++;
 162                 x-=y;
 163             }
 164         } else if (x>0.5*y || (x==0.5*y && (q & 1))) {
 165             q++;
 166             x-=y;
 167         }
 168
 169         ux.e = x;
 170         ux.bits.sign ^= sx;
 171         x = ux.e;
 172
 173         q &= 0x7fffffff;
 174         *quo = (sxy ? -q : q);
 175         return x;
 176 }