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       xh = z + zz;
 121
 122       if (nonfinite (xh))
 123         return xh;
 124
 125       x.dval[0] = xh;
 126       x.dval[1] = z - xh + zz;
 127     }
 128   return x.ldval;
 129 }
 130
 131 long double
 132 __gcc_qsub (double a, double b, double c, double d)
 133 {
 134   return __gcc_qadd (a, b, -c, -d);
 135 }
 136
 137 long double
 138 __gcc_qmul (double a, double b, double c, double d)
 139 {
 140   longDblUnion z;
 141   double t, tau, u, v, w;
 142
 143   t = a * c;                    /* Highest order double term.  */
 144
 145   if (unlikely (t == 0)         /* Preserve -0.  */
 146       || nonfinite (t))
 147     return t;
 148
 149   /* Sum terms of two highest orders. */
 150
 151   /* Use fused multiply-add to get low part of a * c.  */
 152   asm ("fmsub %0,%1,%2,%3" : "=f"(tau) : "f"(a), "f"(c), "f"(t));
 153   v = a*d;
 154   w = b*c;
 155   tau += v + w;     /* Add in other second-order terms.  */
 156   u = t + tau;
 157
 158   /* Construct long double result.  */
 159   if (nonfinite (u))
 160     return u;
 161   z.dval[0] = u;
 162   z.dval[1] = (t - u) + tau;
 163   return z.ldval;
 164 }
 165
 166 long double
 167 __gcc_qdiv (double a, double b, double c, double d)
 168 {
 169   longDblUnion z;
 170   double s, sigma, t, tau, u, v, w;
 171
 172   t = a / c;                    /* highest order double term */
 173
 174   if (unlikely (t == 0)         /* Preserve -0.  */
 175       || nonfinite (t))
 176     return t;
 177
 178   /* Finite nonzero result requires corrections to the highest order term.  */
 179
 180   s = c * t;                    /* (s,sigma) = c*t exactly.  */
 181   w = -(-b + d * t);    /* Written to get fnmsub for speed, but not
 182                            numerically necessary.  */
 183
 184   /* Use fused multiply-add to get low part of c * t.    */
 185   asm ("fmsub %0,%1,%2,%3" : "=f"(sigma) : "f"(c), "f"(t), "f"(s));
 186   v = a - s;
 187
 188   tau = ((v-sigma)+w)/c;   /* Correction to t.  */
 189   u = t + tau;
 190
 191   /* Construct long double result.  */
 192   if (nonfinite (u))
 193     return u;
 194   z.dval[0] = u;
 195   z.dval[1] = (t - u) + tau;
 196   return z.ldval;
 197 }
 198
 199 #endif