src/math/remquol.c

   1 /* origin: FreeBSD /usr/src/lib/msun/src/s_remquol.c */
   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 #include "libm.h"
  14
  15 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
  16 long double remquol(long double x, long double y, int *quo)
  17 {
  18         return remquo(x, y, quo);
  19 }
  20 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
  21
  22 #define BIAS (LDBL_MAX_EXP - 1)
  23
  24 #if LDBL_MANL_SIZE > 32
  25 typedef uint64_t manl_t;
  26 #else
  27 typedef uint32_t manl_t;
  28 #endif
  29
  30 #if LDBL_MANH_SIZE > 32
  31 typedef uint64_t manh_t;
  32 #else
  33 typedef uint32_t manh_t;
  34 #endif
  35
  36 /*
  37  * These macros add and remove an explicit integer bit in front of the
  38  * fractional mantissa, if the architecture doesn't have such a bit by
  39  * default already.
  40  */
  41 #ifdef LDBL_IMPLICIT_NBIT
  42 #define SET_NBIT(hx)    ((hx) | (1ULL << LDBL_MANH_SIZE))
  43 #define HFRAC_BITS      LDBL_MANH_SIZE
  44 #else
  45 #define SET_NBIT(hx)    (hx)
  46 #define HFRAC_BITS      (LDBL_MANH_SIZE - 1)
  47 #endif
  48
  49 #define MANL_SHIFT      (LDBL_MANL_SIZE - 1)
  50
  51 static const long double Zero[] = {0.0, -0.0};
  52
  53 /*
  54  * Return the IEEE remainder and set *quo to the last n bits of the
  55  * quotient, rounded to the nearest integer.  We choose n=31 because
  56  * we wind up computing all the integer bits of the quotient anyway as
  57  * a side-effect of computing the remainder by the shift and subtract
  58  * method.  In practice, this is far more bits than are needed to use
  59  * remquo in reduction algorithms.
  60  *
  61  * Assumptions:
  62  * - The low part of the mantissa fits in a manl_t exactly.
  63  * - The high part of the mantissa fits in an int64_t with enough room
  64  *   for an explicit integer bit in front of the fractional bits.
  65  */
  66 long double 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;
 130                 lz = lx - ly;
 131                 if (lx < ly)
 132                         hz -= 1;
 133                 if (hz < 0) {
 134                         hx = hx + hx + (lx>>MANL_SHIFT);
 135                         lx = lx + lx;
 136                 } else {
 137                         hx = hz + hz + (lz>>MANL_SHIFT);
 138                         lx = lz + lz;
 139                         q++;
 140                 }
 141                 q <<= 1;
 142         }
 143         hz = hx - hy;
 144         lz = lx - ly;
 145         if (lx < ly)
 146                 hz -= 1;
 147         if (hz >= 0) {
 148                 hx = hz;
 149                 lx = lz;
 150                 q++;
 151         }
 152
 153         /* convert back to floating value and restore the sign */
 154         if ((hx|lx) == 0) {  /* return sign(x)*0 */
 155                 q &= 0x7fffffff;
 156                 *quo = sxy ? -q : q;
 157                 return Zero[sx];
 158         }
 159         while (hx < (1ULL<<HFRAC_BITS)) {  /* normalize x */
 160                 hx = hx + hx + (lx>>MANL_SHIFT);
 161                 lx = lx + lx;
 162                 iy -= 1;
 163         }
 164         ux.bits.manh = hx; /* The integer bit is truncated here if needed. */
 165         ux.bits.manl = lx;
 166         if (iy < LDBL_MIN_EXP) {
 167                 ux.bits.exp = iy + (BIAS + 512);
 168                 ux.e *= 0x1p-512;
 169         } else {
 170                 ux.bits.exp = iy + BIAS;
 171         }
 172         ux.bits.sign = 0;
 173         x = ux.e;
 174 fixup:
 175         y = fabsl(y);
 176         if (y < LDBL_MIN * 2) {
 177                 if (x + x > y || (x + x == y && (q & 1))) {
 178                         q++;
 179                         x-=y;
 180                 }
 181         } else if (x > 0.5*y || (x == 0.5*y && (q & 1))) {
 182                 q++;
 183                 x-=y;
 184         }
 185
 186         ux.e = x;
 187         ux.bits.sign ^= sx;
 188         x = ux.e;
 189
 190         q &= 0x7fffffff;
 191         *quo = sxy ? -q : q;
 192         return x;
 193 }
 194 #endif