sysdeps/ieee754/ldbl-128ibm/s_fmal.c

   1 /* Compute x * y + z as ternary operation.
   2    Copyright (C) 2011-2020 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4    Contributed by David Flaherty <flaherty@linux.vnet.ibm.com>.
   5
   6    The GNU C Library is free software; you can redistribute it and/or
   7    modify it under the terms of the GNU Lesser General Public
   8    License as published by the Free Software Foundation; either
   9    version 2.1 of the License, or (at your option) any later version.
  10
  11    The GNU C Library is distributed in the hope that it will be useful,
  12    but WITHOUT ANY WARRANTY; without even the implied warranty of
  13    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  14    Lesser General Public License for more details.
  15
  16    You should have received a copy of the GNU Lesser General Public
  17    License along with the GNU C Library; if not, see
  18    <https://www.gnu.org/licenses/>.  */
  19
  20 #include <fenv.h>
  21 #include <float.h>
  22 #include <math.h>
  23 #include <math-barriers.h>
  24 #include <math_private.h>
  25 #include <fenv_private.h>
  26 #include <math-underflow.h>
  27 #include <math_ldbl_opt.h>
  28 #include <mul_split.h>
  29 #include <stdlib.h>
  30
  31 /* Calculate X + Y exactly and store the result in *HI + *LO.  It is
  32    given that |X| >= |Y| and the values are small enough that no
  33    overflow occurs.  */
  34
  35 static void
  36 add_split (double *hi, double *lo, double x, double y)
  37 {
  38   /* Apply Dekker's algorithm.  */
  39   *hi = x + y;
  40   *lo = (x - *hi) + y;
  41 }
  42
  43 /* Value with extended range, used in intermediate computations.  */
  44 typedef struct
  45 {
  46   /* Value in [0.5, 1), as from frexp, or 0.  */
  47   double val;
  48   /* Exponent of power of 2 it is multiplied by, or 0 for zero.  */
  49   int exp;
  50 } ext_val;
  51
  52 /* Store D as an ext_val value.  */
  53
  54 static void
  55 store_ext_val (ext_val *v, double d)
  56 {
  57   v->val = __frexp (d, &v->exp);
  58 }
  59
  60 /* Store X * Y as ext_val values *V0 and *V1.  */
  61
  62 static void
  63 mul_ext_val (ext_val *v0, ext_val *v1, double x, double y)
  64 {
  65   int xexp, yexp;
  66   x = __frexp (x, &xexp);
  67   y = __frexp (y, &yexp);
  68   double hi, lo;
  69   mul_split (&hi, &lo, x, y);
  70   store_ext_val (v0, hi);
  71   if (hi != 0)
  72     v0->exp += xexp + yexp;
  73   store_ext_val (v1, lo);
  74   if (lo != 0)
  75     v1->exp += xexp + yexp;
  76 }
  77
  78 /* Compare absolute values of ext_val values pointed to by P and Q for
  79    qsort.  */
  80
  81 static int
  82 compare (const void *p, const void *q)
  83 {
  84   const ext_val *pe = p;
  85   const ext_val *qe = q;
  86   if (pe->val == 0)
  87     return qe->val == 0 ? 0 : -1;
  88   else if (qe->val == 0)
  89     return 1;
  90   else if (pe->exp < qe->exp)
  91     return -1;
  92   else if (pe->exp > qe->exp)
  93     return 1;
  94   else
  95     {
  96       double pd = fabs (pe->val);
  97       double qd = fabs (qe->val);
  98       if (pd < qd)
  99         return -1;
 100       else if (pd == qd)
 101         return 0;
 102       else
 103         return 1;
 104     }
 105 }
 106
 107 /* Calculate *X + *Y exactly, storing the high part in *X (rounded to
 108    nearest) and the low part in *Y.  It is given that |X| >= |Y|.  */
 109
 110 static void
 111 add_split_ext (ext_val *x, ext_val *y)
 112 {
 113   int xexp = x->exp, yexp = y->exp;
 114   if (y->val == 0 || xexp - yexp > 53)
 115     return;
 116   double hi = x->val;
 117   double lo = __scalbn (y->val, yexp - xexp);
 118   add_split (&hi, &lo, hi, lo);
 119   store_ext_val (x, hi);
 120   if (hi != 0)
 121     x->exp += xexp;
 122   store_ext_val (y, lo);
 123   if (lo != 0)
 124     y->exp += xexp;
 125 }
 126
 127 long double
 128 __fmal (long double x, long double y, long double z)
 129 {
 130   double xhi, xlo, yhi, ylo, zhi, zlo;
 131   int64_t hx, hy, hz;
 132   int xexp, yexp, zexp;
 133   double scale_val;
 134   int scale_exp;
 135   ldbl_unpack (x, &xhi, &xlo);
 136   EXTRACT_WORDS64 (hx, xhi);
 137   xexp = (hx & 0x7ff0000000000000LL) >> 52;
 138   ldbl_unpack (y, &yhi, &ylo);
 139   EXTRACT_WORDS64 (hy, yhi);
 140   yexp = (hy & 0x7ff0000000000000LL) >> 52;
 141   ldbl_unpack (z, &zhi, &zlo);
 142   EXTRACT_WORDS64 (hz, zhi);
 143   zexp = (hz & 0x7ff0000000000000LL) >> 52;
 144
 145   /* If z is Inf or NaN, but x and y are finite, avoid any exceptions
 146      from computing x * y.  */
 147   if (zexp == 0x7ff && xexp != 0x7ff && yexp != 0x7ff)
 148     return (z + x) + y;
 149
 150   /* If z is zero and x are y are nonzero, compute the result as x * y
 151      to avoid the wrong sign of a zero result if x * y underflows to
 152      0.  */
 153   if (z == 0 && x != 0 && y != 0)
 154     return x * y;
 155
 156   /* If x or y or z is Inf/NaN, or if x * y is zero, compute as x * y
 157      + z.  */
 158   if (xexp == 0x7ff || yexp == 0x7ff || zexp == 0x7ff
 159       || x == 0 || y == 0)
 160     return (x * y) + z;
 161
 162   {
 163     SET_RESTORE_ROUND (FE_TONEAREST);
 164
 165     ext_val vals[10];
 166     store_ext_val (&vals[0], zhi);
 167     store_ext_val (&vals[1], zlo);
 168     mul_ext_val (&vals[2], &vals[3], xhi, yhi);
 169     mul_ext_val (&vals[4], &vals[5], xhi, ylo);
 170     mul_ext_val (&vals[6], &vals[7], xlo, yhi);
 171     mul_ext_val (&vals[8], &vals[9], xlo, ylo);
 172     qsort (vals, 10, sizeof (ext_val), compare);
 173     /* Add up the values so that each element of VALS has absolute
 174        value at most equal to the last set bit of the next nonzero
 175        element.  */
 176     for (size_t i = 0; i <= 8; i++)
 177       {
 178         add_split_ext (&vals[i + 1], &vals[i]);
 179         qsort (vals + i + 1, 9 - i, sizeof (ext_val), compare);
 180       }
 181     /* Add up the values in the other direction, so that each element
 182        of VALS has absolute value less than 5ulp of the next
 183        value.  */
 184     size_t dstpos = 9;
 185     for (size_t i = 1; i <= 9; i++)
 186       {
 187         if (vals[dstpos].val == 0)
 188           {
 189             vals[dstpos] = vals[9 - i];
 190             vals[9 - i].val = 0;
 191             vals[9 - i].exp = 0;
 192           }
 193         else
 194           {
 195             add_split_ext (&vals[dstpos], &vals[9 - i]);
 196             if (vals[9 - i].val != 0)
 197               {
 198                 if (9 - i < dstpos - 1)
 199                   {
 200                     vals[dstpos - 1] = vals[9 - i];
 201                     vals[9 - i].val = 0;
 202                     vals[9 - i].exp = 0;
 203                   }
 204                 dstpos--;
 205               }
 206           }
 207       }
 208     /* If the result is an exact zero, it results from adding two
 209        values with opposite signs; recompute in the original rounding
 210        mode.  */
 211     if (vals[9].val == 0)
 212       goto zero_out;
 213     /* Adding the top three values will now give a result as accurate
 214        as the underlying long double arithmetic.  */
 215     add_split_ext (&vals[9], &vals[8]);
 216     if (compare (&vals[8], &vals[7]) < 0)
 217       {
 218         ext_val tmp = vals[7];
 219         vals[7] = vals[8];
 220         vals[8] = tmp;
 221       }
 222     add_split_ext (&vals[8], &vals[7]);
 223     add_split_ext (&vals[9], &vals[8]);
 224     if (vals[9].exp > DBL_MAX_EXP || vals[9].exp < DBL_MIN_EXP)
 225       {
 226         /* Overflow or underflow, with the result depending on the
 227            original rounding mode, but not on the low part computed
 228            here.  */
 229         scale_val = vals[9].val;
 230         scale_exp = vals[9].exp;
 231         goto scale_out;
 232       }
 233     double hi = __scalbn (vals[9].val, vals[9].exp);
 234     double lo = __scalbn (vals[8].val, vals[8].exp);
 235     /* It is possible that the low part became subnormal and was
 236        rounded so that the result is no longer canonical.  */
 237     ldbl_canonicalize (&hi, &lo);
 238     long double ret = ldbl_pack (hi, lo);
 239     math_check_force_underflow (ret);
 240     return ret;
 241   }
 242
 243  scale_out:
 244   scale_val = math_opt_barrier (scale_val);
 245   scale_val = __scalbn (scale_val, scale_exp);
 246   if (fabs (scale_val) == DBL_MAX)
 247     return copysignl (LDBL_MAX, scale_val);
 248   math_check_force_underflow (scale_val);
 249   return scale_val;
 250
 251  zero_out:;
 252   double zero = 0.0;
 253   zero = math_opt_barrier (zero);
 254   return zero - zero;
 255 }
 256 #if IS_IN (libm)
 257 long_double_symbol (libm, __fmal, fmal);
 258 #else
 259 long_double_symbol (libc, __fmal, fmal);
 260 #endif