gcc/config/rs6000/darwin-ldouble.c

   1 /* 128-bit long double support routines for Darwin.
   2    Copyright (C) 1993, 2003, 2004, 2005, 2006
   3    Free Software Foundation, Inc.
   4
   5 This file is part of GCC.
   6
   7 GCC is free software; you can redistribute it and/or modify it under
   8 the terms of the GNU General Public License as published by the Free
   9 Software Foundation; either version 2, or (at your option) any later
  10 version.
  11
  12 In addition to the permissions in the GNU General Public License, the
  13 Free Software Foundation gives you unlimited permission to link the
  14 compiled version of this file into combinations with other programs,
  15 and to distribute those combinations without any restriction coming
  16 from the use of this file.  (The General Public License restrictions
  17 do apply in other respects; for example, they cover modification of
  18 the file, and distribution when not linked into a combine
  19 executable.)
  20
  21 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
  22 WARRANTY; without even the implied warranty of MERCHANTABILITY or
  23 FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  24 for more details.
  25
  26 You should have received a copy of the GNU General Public License
  27 along with GCC; see the file COPYING.  If not, write to the Free
  28 Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
  29 02110-1301, USA.  */
  30
  31 /* Implementations of floating-point long double basic arithmetic
  32    functions called by the IBM C compiler when generating code for
  33    PowerPC platforms.  In particular, the following functions are
  34    implemented: __gcc_qadd, __gcc_qsub, __gcc_qmul, and __gcc_qdiv.
  35    Double-double algorithms are based on the paper "Doubled-Precision
  36    IEEE Standard 754 Floating-Point Arithmetic" by W. Kahan, February 26,
  37    1987.  An alternative published reference is "Software for
  38    Doubled-Precision Floating-Point Computations", by Seppo Linnainmaa,
  39    ACM TOMS vol 7 no 3, September 1981, pages 272-283.  */
  40
  41 /* Each long double is made up of two IEEE doubles.  The value of the
  42    long double is the sum of the values of the two parts.  The most
  43    significant part is required to be the value of the long double
  44    rounded to the nearest double, as specified by IEEE.  For Inf
  45    values, the least significant part is required to be one of +0.0 or
  46    -0.0.  No other requirements are made; so, for example, 1.0 may be
  47    represented as (1.0, +0.0) or (1.0, -0.0), and the low part of a
  48    NaN is don't-care.
  49
  50    This code currently assumes big-endian.  */
  51
  52 #if !_SOFT_FLOAT && (defined (__MACH__) || defined (__powerpc64__) || defined (__powerpc__) || defined (_AIX))
  53
  54 #define fabs(x) __builtin_fabs(x)
  55 #define isless(x, y) __builtin_isless (x, y)
  56 #define inf() __builtin_inf()
  57
  58 #define unlikely(x) __builtin_expect ((x), 0)
  59
  60 #define nonfinite(a) unlikely (! isless (fabs (a), inf ()))
  61
  62 /* All these routines actually take two long doubles as parameters,
  63    but GCC currently generates poor code when a union is used to turn
  64    a long double into a pair of doubles.  */
  65
  66 extern long double __gcc_qadd (double, double, double, double);
  67 extern long double __gcc_qsub (double, double, double, double);
  68 extern long double __gcc_qmul (double, double, double, double);
  69 extern long double __gcc_qdiv (double, double, double, double);
  70
  71 #if defined __ELF__ && defined SHARED \
  72     && (defined __powerpc64__ || !(defined __linux__ || defined __gnu_hurd__))
  73 /* Provide definitions of the old symbol names to satisfy apps and
  74    shared libs built against an older libgcc.  To access the _xlq
  75    symbols an explicit version reference is needed, so these won't
  76    satisfy an unadorned reference like _xlqadd.  If dot symbols are
  77    not needed, the assembler will remove the aliases from the symbol
  78    table.  */
  79 __asm__ (".symver __gcc_qadd,_xlqadd@GCC_3.4\n\t"
  80          ".symver __gcc_qsub,_xlqsub@GCC_3.4\n\t"
  81          ".symver __gcc_qmul,_xlqmul@GCC_3.4\n\t"
  82          ".symver __gcc_qdiv,_xlqdiv@GCC_3.4\n\t"
  83          ".symver .__gcc_qadd,._xlqadd@GCC_3.4\n\t"
  84          ".symver .__gcc_qsub,._xlqsub@GCC_3.4\n\t"
  85          ".symver .__gcc_qmul,._xlqmul@GCC_3.4\n\t"
  86          ".symver .__gcc_qdiv,._xlqdiv@GCC_3.4");
  87 #endif
  88
  89 typedef union
  90 {
  91   long double ldval;
  92   double dval[2];
  93 } longDblUnion;
  94
  95 /* Add two 'long double' values and return the result.  */
  96 long double
  97 __gcc_qadd (double a, double aa, double c, double cc)
  98 {
  99   longDblUnion x;
 100   double z, q, zz, xh;
 101
 102   z = a + c;
 103
 104   if (nonfinite (z))
 105     {
 106       z = cc + aa + c + a;
 107       if (nonfinite (z))
 108         return z;
 109       x.dval[0] = z;  /* Will always be DBL_MAX.  */
 110       zz = aa + cc;
 111       if (fabs(a) > fabs(c))
 112         x.dval[1] = a - z + c + zz;
 113       else
 114         x.dval[1] = c - z + a + zz;
 115     }
 116   else
 117     {
 118       q = a - z;
 119       zz = q + c + (a - (q + z)) + aa + cc;
 120
 121       /* Keep -0 result.  */
 122       if (zz == 0.0)
 123         return z;
 124
 125       xh = z + zz;
 126       if (nonfinite (xh))
 127         return xh;
 128
 129       x.dval[0] = xh;
 130       x.dval[1] = z - xh + zz;
 131     }
 132   return x.ldval;
 133 }
 134
 135 long double
 136 __gcc_qsub (double a, double b, double c, double d)
 137 {
 138   return __gcc_qadd (a, b, -c, -d);
 139 }
 140
 141 long double
 142 __gcc_qmul (double a, double b, double c, double d)
 143 {
 144   longDblUnion z;
 145   double t, tau, u, v, w;
 146
 147   t = a * c;                    /* Highest order double term.  */
 148
 149   if (unlikely (t == 0)         /* Preserve -0.  */
 150       || nonfinite (t))
 151     return t;
 152
 153   /* Sum terms of two highest orders. */
 154
 155   /* Use fused multiply-add to get low part of a * c.  */
 156   asm ("fmsub %0,%1,%2,%3" : "=f"(tau) : "f"(a), "f"(c), "f"(t));
 157   v = a*d;
 158   w = b*c;
 159   tau += v + w;     /* Add in other second-order terms.  */
 160   u = t + tau;
 161
 162   /* Construct long double result.  */
 163   if (nonfinite (u))
 164     return u;
 165   z.dval[0] = u;
 166   z.dval[1] = (t - u) + tau;
 167   return z.ldval;
 168 }
 169
 170 long double
 171 __gcc_qdiv (double a, double b, double c, double d)
 172 {
 173   longDblUnion z;
 174   double s, sigma, t, tau, u, v, w;
 175
 176   t = a / c;                    /* highest order double term */
 177
 178   if (unlikely (t == 0)         /* Preserve -0.  */
 179       || nonfinite (t))
 180     return t;
 181
 182   /* Finite nonzero result requires corrections to the highest order term.  */
 183
 184   s = c * t;                    /* (s,sigma) = c*t exactly.  */
 185   w = -(-b + d * t);    /* Written to get fnmsub for speed, but not
 186                            numerically necessary.  */
 187
 188   /* Use fused multiply-add to get low part of c * t.    */
 189   asm ("fmsub %0,%1,%2,%3" : "=f"(sigma) : "f"(c), "f"(t), "f"(s));
 190   v = a - s;
 191
 192   tau = ((v-sigma)+w)/c;   /* Correction to t.  */
 193   u = t + tau;
 194
 195   /* Construct long double result.  */
 196   if (nonfinite (u))
 197     return u;
 198   z.dval[0] = u;
 199   z.dval[1] = (t - u) + tau;
 200   return z.ldval;
 201 }
 202
 203 #endif