sysdeps/ieee754/dbl-64/e_exp2.c

   1 /* Double-precision floating point 2^x.
   2    Copyright (C) 1997,1998,2000,2001,2005,2006 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4    Contributed by Geoffrey Keating <geoffk@ozemail.com.au>
   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, write to the Free
  18    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
  19    02111-1307 USA.  */
  20
  21 /* The basic design here is from
  22    Shmuel Gal and Boris Bachelis, "An Accurate Elementary Mathematical
  23    Library for the IEEE Floating Point Standard", ACM Trans. Math. Soft.,
  24    17 (1), March 1991, pp. 26-45.
  25    It has been slightly modified to compute 2^x instead of e^x.
  26    */
  27 #ifndef _GNU_SOURCE
  28 #define _GNU_SOURCE
  29 #endif
  30 #include <stdlib.h>
  31 #include <float.h>
  32 #include <ieee754.h>
  33 #include <math.h>
  34 #include <fenv.h>
  35 #include <inttypes.h>
  36 #include <math_private.h>
  37
  38 #include "t_exp2.h"
  39
  40 /* XXX I know the assembler generates a warning about incorrect section
  41    attributes. But without the attribute here the compiler places the
  42    constants in the .data section.  Ideally the constant is placed in
  43    .rodata.cst8 so that it can be merged, but gcc sucks, it ICEs when
  44    we try to force this section on it.  --drepper  */
  45 static const volatile double TWO1023 = 8.988465674311579539e+307;
  46 static const volatile double TWOM1000 = 9.3326361850321887899e-302;
  47
  48 double
  49 __ieee754_exp2 (double x)
  50 {
  51   static const double himark = (double) DBL_MAX_EXP;
  52   static const double lomark = (double) (DBL_MIN_EXP - DBL_MANT_DIG - 1);
  53
  54   /* Check for usual case.  */
  55   if (isless (x, himark) && isgreaterequal (x, lomark))
  56     {
  57       static const double THREEp42 = 13194139533312.0;
  58       int tval, unsafe;
  59       double rx, x22, result;
  60       union ieee754_double ex2_u, scale_u;
  61       fenv_t oldenv;
  62
  63       feholdexcept (&oldenv);
  64 #ifdef FE_TONEAREST
  65       /* If we don't have this, it's too bad.  */
  66       fesetround (FE_TONEAREST);
  67 #endif
  68
  69       /* 1. Argument reduction.
  70          Choose integers ex, -256 <= t < 256, and some real
  71          -1/1024 <= x1 <= 1024 so that
  72          x = ex + t/512 + x1.
  73
  74          First, calculate rx = ex + t/512.  */
  75       rx = x + THREEp42;
  76       rx -= THREEp42;
  77       x -= rx;  /* Compute x=x1. */
  78       /* Compute tval = (ex*512 + t)+256.
  79          Now, t = (tval mod 512)-256 and ex=tval/512  [that's mod, NOT %; and
  80          /-round-to-nearest not the usual c integer /].  */
  81       tval = (int) (rx * 512.0 + 256.0);
  82
  83       /* 2. Adjust for accurate table entry.
  84          Find e so that
  85          x = ex + t/512 + e + x2
  86          where -1e6 < e < 1e6, and
  87          (double)(2^(t/512+e))
  88          is accurate to one part in 2^-64.  */
  89
  90       /* 'tval & 511' is the same as 'tval%512' except that it's always
  91          positive.
  92          Compute x = x2.  */
  93       x -= exp2_deltatable[tval & 511];
  94
  95       /* 3. Compute ex2 = 2^(t/512+e+ex).  */
  96       ex2_u.d = exp2_accuratetable[tval & 511];
  97       tval >>= 9;
  98       unsafe = abs(tval) >= -DBL_MIN_EXP - 1;
  99       ex2_u.ieee.exponent += tval >> unsafe;
 100       scale_u.d = 1.0;
 101       scale_u.ieee.exponent += tval - (tval >> unsafe);
 102
 103       /* 4. Approximate 2^x2 - 1, using a fourth-degree polynomial,
 104          with maximum error in [-2^-10-2^-30,2^-10+2^-30]
 105          less than 10^-19.  */
 106
 107       x22 = (((.0096181293647031180
 108                * x + .055504110254308625)
 109               * x + .240226506959100583)
 110              * x + .69314718055994495) * ex2_u.d;
 111
 112       /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex).  */
 113       fesetenv (&oldenv);
 114
 115       result = x22 * x + ex2_u.d;
 116
 117       if (!unsafe)
 118         return result;
 119       else
 120         return result * scale_u.d;
 121     }
 122   /* Exceptional cases:  */
 123   else if (isless (x, himark))
 124     {
 125       if (__isinf (x))
 126         /* e^-inf == 0, with no error.  */
 127         return 0;
 128       else
 129         /* Underflow */
 130         return TWOM1000 * TWOM1000;
 131     }
 132   else
 133     /* Return x, if x is a NaN or Inf; or overflow, otherwise.  */
 134     return TWO1023*x;
 135 }