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

   1 /* Compute x * y + z as ternary operation.
   2    Copyright (C) 2011-2016 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    <http://www.gnu.org/licenses/>.  */
  19
  20 #include <fenv.h>
  21 #include <float.h>
  22 #include <math.h>
  23 #include <math_private.h>
  24 #include <math_ldbl_opt.h>
  25 #include <mul_split.h>
  26 #include <stdlib.h>
  27
  28 /* Calculate X + Y exactly and store the result in *HI + *LO.  It is
  29    given that |X| >= |Y| and the values are small enough that no
  30    overflow occurs.  */
  31
  32 static void
  33 add_split (double *hi, double *lo, double x, double y)
  34 {
  35   /* Apply Dekker's algorithm.  */
  36   *hi = x + y;
  37   *lo = (x - *hi) + y;
  38 }
  39
  40 /* Value with extended range, used in intermediate computations.  */
  41 typedef struct
  42 {
  43   /* Value in [0.5, 1), as from frexp, or 0.  */
  44   double val;
  45   /* Exponent of power of 2 it is multiplied by, or 0 for zero.  */
  46   int exp;
  47 } ext_val;
  48
  49 /* Store D as an ext_val value.  */
  50
  51 static void
  52 store_ext_val (ext_val *v, double d)
  53 {
  54   v->val = __frexp (d, &v->exp);
  55 }
  56
  57 /* Store X * Y as ext_val values *V0 and *V1.  */
  58
  59 static void
  60 mul_ext_val (ext_val *v0, ext_val *v1, double x, double y)
  61 {
  62   int xexp, yexp;
  63   x = __frexp (x, &xexp);
  64   y = __frexp (y, &yexp);
  65   double hi, lo;
  66   mul_split (&hi, &lo, x, y);
  67   store_ext_val (v0, hi);
  68   if (hi != 0)
  69     v0->exp += xexp + yexp;
  70   store_ext_val (v1, lo);
  71   if (lo != 0)
  72     v1->exp += xexp + yexp;
  73 }
  74
  75 /* Compare absolute values of ext_val values pointed to by P and Q for
  76    qsort.  */
  77
  78 static int
  79 compare (const void *p, const void *q)
  80 {
  81   const ext_val *pe = p;
  82   const ext_val *qe = q;
  83   if (pe->val == 0)
  84     return qe->val == 0 ? 0 : -1;
  85   else if (qe->val == 0)
  86     return 1;
  87   else if (pe->exp < qe->exp)
  88     return -1;
  89   else if (pe->exp > qe->exp)
  90     return 1;
  91   else
  92     {
  93       double pd = fabs (pe->val);
  94       double qd = fabs (qe->val);
  95       if (pd < qd)
  96         return -1;
  97       else if (pd == qd)
  98         return 0;
  99       else
 100         return 1;
 101     }
 102 }
 103
 104 /* Calculate *X + *Y exactly, storing the high part in *X (rounded to
 105    nearest) and the low part in *Y.  It is given that |X| >= |Y|.  */
 106
 107 static void
 108 add_split_ext (ext_val *x, ext_val *y)
 109 {
 110   int xexp = x->exp, yexp = y->exp;
 111   if (y->val == 0 || xexp - yexp > 53)
 112     return;
 113   double hi = x->val;
 114   double lo = __scalbn (y->val, yexp - xexp);
 115   add_split (&hi, &lo, hi, lo);
 116   store_ext_val (x, hi);
 117   if (hi != 0)
 118     x->exp += xexp;
 119   store_ext_val (y, lo);
 120   if (lo != 0)
 121     y->exp += xexp;
 122 }
 123
 124 long double
 125 __fmal (long double x, long double y, long double z)
 126 {
 127   double xhi, xlo, yhi, ylo, zhi, zlo;
 128   int64_t hx, hy, hz;
 129   int xexp, yexp, zexp;
 130   double scale_val;
 131   int scale_exp;
 132   ldbl_unpack (x, &xhi, &xlo);
 133   EXTRACT_WORDS64 (hx, xhi);
 134   xexp = (hx & 0x7ff0000000000000LL) >> 52;
 135   ldbl_unpack (y, &yhi, &ylo);
 136   EXTRACT_WORDS64 (hy, yhi);
 137   yexp = (hy & 0x7ff0000000000000LL) >> 52;
 138   ldbl_unpack (z, &zhi, &zlo);
 139   EXTRACT_WORDS64 (hz, zhi);
 140   zexp = (hz & 0x7ff0000000000000LL) >> 52;
 141
 142   /* If z is Inf or NaN, but x and y are finite, avoid any exceptions
 143      from computing x * y.  */
 144   if (zexp == 0x7ff && xexp != 0x7ff && yexp != 0x7ff)
 145     return (z + x) + y;
 146
 147   /* If z is zero and x are y are nonzero, compute the result as x * y
 148      to avoid the wrong sign of a zero result if x * y underflows to
 149      0.  */
 150   if (z == 0 && x != 0 && y != 0)
 151     return x * y;
 152
 153   /* If x or y or z is Inf/NaN, or if x * y is zero, compute as x * y
 154      + z.  */
 155   if (xexp == 0x7ff || yexp == 0x7ff || zexp == 0x7ff
 156       || x == 0 || y == 0)
 157     return (x * y) + z;
 158
 159   {
 160     SET_RESTORE_ROUND (FE_TONEAREST);
 161
 162     ext_val vals[10];
 163     store_ext_val (&vals[0], zhi);
 164     store_ext_val (&vals[1], zlo);
 165     mul_ext_val (&vals[2], &vals[3], xhi, yhi);
 166     mul_ext_val (&vals[4], &vals[5], xhi, ylo);
 167     mul_ext_val (&vals[6], &vals[7], xlo, yhi);
 168     mul_ext_val (&vals[8], &vals[9], xlo, ylo);
 169     qsort (vals, 10, sizeof (ext_val), compare);
 170     /* Add up the values so that each element of VALS has absolute
 171        value at most equal to the last set bit of the next nonzero
 172        element.  */
 173     for (size_t i = 0; i <= 8; i++)
 174       {
 175         add_split_ext (&vals[i + 1], &vals[i]);
 176         qsort (vals + i + 1, 9 - i, sizeof (ext_val), compare);
 177       }
 178     /* Add up the values in the other direction, so that each element
 179        of VALS has absolute value less than 5ulp of the next
 180        value.  */
 181     size_t dstpos = 9;
 182     for (size_t i = 1; i <= 9; i++)
 183       {
 184         if (vals[dstpos].val == 0)
 185           {
 186             vals[dstpos] = vals[9 - i];
 187             vals[9 - i].val = 0;
 188             vals[9 - i].exp = 0;
 189           }
 190         else
 191           {
 192             add_split_ext (&vals[dstpos], &vals[9 - i]);
 193             if (vals[9 - i].val != 0)
 194               {
 195                 if (9 - i < dstpos - 1)
 196                   {
 197                     vals[dstpos - 1] = vals[9 - i];
 198                     vals[9 - i].val = 0;
 199                     vals[9 - i].exp = 0;
 200                   }
 201                 dstpos--;
 202               }
 203           }
 204       }
 205     /* If the result is an exact zero, it results from adding two
 206        values with opposite signs; recompute in the original rounding
 207        mode.  */
 208     if (vals[9].val == 0)
 209       goto zero_out;
 210     /* Adding the top three values will now give a result as accurate
 211        as the underlying long double arithmetic.  */
 212     add_split_ext (&vals[9], &vals[8]);
 213     if (compare (&vals[8], &vals[7]) < 0)
 214       {
 215         ext_val tmp = vals[7];
 216         vals[7] = vals[8];
 217         vals[8] = tmp;
 218       }
 219     add_split_ext (&vals[8], &vals[7]);
 220     add_split_ext (&vals[9], &vals[8]);
 221     if (vals[9].exp > DBL_MAX_EXP || vals[9].exp < DBL_MIN_EXP)
 222       {
 223         /* Overflow or underflow, with the result depending on the
 224            original rounding mode, but not on the low part computed
 225            here.  */
 226         scale_val = vals[9].val;
 227         scale_exp = vals[9].exp;
 228         goto scale_out;
 229       }
 230     double hi = __scalbn (vals[9].val, vals[9].exp);
 231     double lo = __scalbn (vals[8].val, vals[8].exp);
 232     /* It is possible that the low part became subnormal and was
 233        rounded so that the result is no longer canonical.  */
 234     ldbl_canonicalize (&hi, &lo);
 235     long double ret = ldbl_pack (hi, lo);
 236     math_check_force_underflow (ret);
 237     return ret;
 238   }
 239
 240  scale_out:
 241   scale_val = math_opt_barrier (scale_val);
 242   scale_val = __scalbn (scale_val, scale_exp);
 243   if (fabs (scale_val) == DBL_MAX)
 244     return __copysignl (LDBL_MAX, scale_val);
 245   math_check_force_underflow (scale_val);
 246   return scale_val;
 247
 248  zero_out:;
 249   double zero = 0.0;
 250   zero = math_opt_barrier (zero);
 251   return zero - zero;
 252 }
 253 #if IS_IN (libm)
 254 long_double_symbol (libm, __fmal, fmal);
 255 #else
 256 long_double_symbol (libc, __fmal, fmal);
 257 #endif