sysdeps/libm-ieee754/s_exp2.c

   1 /* Double-precision floating point 2^x.
   2    Copyright (C) 1997, 1998 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 Library General Public License as
   8    published by the Free Software Foundation; either version 2 of the
   9    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    Library General Public License for more details.
  15
  16    You should have received a copy of the GNU Library General Public
  17    License along with the GNU C Library; see the file COPYING.LIB.  If not,
  18    write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
  19    Boston, MA 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 <float.h>
  31 #include <ieee754.h>
  32 #include <math.h>
  33 #include <fenv.h>
  34 #include <inttypes.h>
  35 #include <math_private.h>
  36
  37 #include "t_exp2.h"
  38
  39 static const volatile double TWO1023 = 8.988465674311579539e+307;
  40 static const volatile double TWOM1000 = 9.3326361850321887899e-302;
  41
  42 double
  43 __ieee754_exp2 (double x)
  44 {
  45   static const double himark = (double) DBL_MAX_EXP;
  46   static const double lomark = (double) (DBL_MIN_EXP - DBL_MANT_DIG - 1) - 1.0;
  47
  48   /* Check for usual case.  */
  49   if (isless (x, himark) && isgreater (x, lomark))
  50     {
  51       static const double THREEp42 = 13194139533312.0;
  52       int tval, unsafe;
  53       double rx, x22, result;
  54       union ieee754_double ex2_u, scale_u;
  55       fenv_t oldenv;
  56
  57       feholdexcept (&oldenv);
  58 #ifdef FE_TONEAREST
  59       /* If we don't have this, it's too bad.  */
  60       fesetround (FE_TONEAREST);
  61 #endif
  62
  63       /* 1. Argument reduction.
  64          Choose integers ex, -256 <= t < 256, and some real
  65          -1/1024 <= x1 <= 1024 so that
  66          x = ex + t/512 + x1.
  67
  68          First, calculate rx = ex + t/512.  */
  69       rx = x + THREEp42;
  70       rx -= THREEp42;
  71       x -= rx;  /* Compute x=x1. */
  72       /* Compute tval = (ex*512 + t)+256.
  73          Now, t = (tval mod 512)-256 and ex=tval/512  [that's mod, NOT %; and
  74          /-round-to-nearest not the usual c integer /].  */
  75       tval = (int) (rx * 512.0 + 256.0);
  76
  77       /* 2. Adjust for accurate table entry.
  78          Find e so that
  79          x = ex + t/512 + e + x2
  80          where -1e6 < e < 1e6, and
  81          (double)(2^(t/512+e))
  82          is accurate to one part in 2^-64.  */
  83
  84       /* 'tval & 511' is the same as 'tval%512' except that it's always
  85          positive.
  86          Compute x = x2.  */
  87       x -= exp2_deltatable[tval & 511];
  88
  89       /* 3. Compute ex2 = 2^(t/512+e+ex).  */
  90       ex2_u.d = exp2_accuratetable[tval & 511];
  91       tval >>= 9;
  92       unsafe = abs(tval) >= -DBL_MIN_EXP - 1;
  93       ex2_u.ieee.exponent += tval >> unsafe;
  94       scale_u.d = 1.0;
  95       scale_u.ieee.exponent += tval - (tval >> unsafe);
  96
  97       /* 4. Approximate 2^x2 - 1, using a fourth-degree polynomial,
  98          with maximum error in [-2^-10-2^-30,2^-10+2^-30]
  99          less than 10^-19.  */
 100
 101       x22 = (((.0096181293647031180
 102                * x + .055504110254308625)
 103               * x + .240226506959100583)
 104              * x + .69314718055994495) * ex2_u.d;
 105
 106       /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex).  */
 107       fesetenv (&oldenv);
 108
 109       result = x22 * x + ex2_u.d;
 110
 111       if (!unsafe)
 112         return result;
 113       else
 114         return result * scale_u.d;
 115     }
 116   /* Exceptional cases:  */
 117   else if (isless (x, himark))
 118     {
 119       if (__isinf (x))
 120         /* e^-inf == 0, with no error.  */
 121         return 0;
 122       else
 123         /* Underflow */
 124         return TWOM1000 * TWOM1000;
 125     }
 126   else
 127     /* Return x, if x is a NaN or Inf; or overflow, otherwise.  */
 128     return TWO1023*x;
 129 }