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 uint32_t a_minf = 0xff800000;
  46   static const double himark = (double) DBL_MAX_EXP;
  47   static const double lomark = (double) (DBL_MIN_EXP - DBL_MANT_DIG - 1) - 1.0;
  48
  49   /* Check for usual case.  */
  50   if (isless (x, himark) && isgreater (x, lomark))
  51     {
  52       static const float TWO43 = 8796093022208.0;
  53       int tval, unsafe;
  54       double rx, x22, result;
  55       union ieee754_double ex2_u, scale_u;
  56       fenv_t oldenv;
  57
  58       feholdexcept (&oldenv);
  59 #ifdef FE_TONEAREST
  60       /* If we don't have this, it's too bad.  */
  61       fesetround (FE_TONEAREST);
  62 #endif
  63
  64       /* 1. Argument reduction.
  65          Choose integers ex, -256 <= t < 256, and some real
  66          -1/1024 <= x1 <= 1024 so that
  67          x = ex + t/512 + x1.
  68
  69          First, calculate rx = ex + t/512.  */
  70       if (x >= 0)
  71         {
  72           rx = x + TWO43;
  73           rx -= TWO43;
  74         }
  75       else
  76         {
  77           rx = x - TWO43;
  78           rx += TWO43;
  79         }
  80       x -= rx;  /* Compute x=x1. */
  81       /* Compute tval = (ex*512 + t)+256.
  82          Now, t = (tval mod 512)-256 and ex=tval/512  [that's mod, NOT %; and
  83          /-round-to-nearest not the usual c integer /].  */
  84       tval = (int) (rx * 512.0 + 256.0);
  85
  86       /* 2. Adjust for accurate table entry.
  87          Find e so that
  88          x = ex + t/512 + e + x2
  89          where -1e6 < e < 1e6, and
  90          (double)(2^(t/512+e))
  91          is accurate to one part in 2^-64.  */
  92
  93       /* 'tval & 511' is the same as 'tval%512' except that it's always
  94          positive.
  95          Compute x = x2.  */
  96       x -= exp2_deltatable[tval & 511];
  97
  98       /* 3. Compute ex2 = 2^(t/512+e+ex).  */
  99       ex2_u.d = exp2_accuratetable[tval & 511];
 100       tval >>= 9;
 101       unsafe = abs(tval) >= -DBL_MIN_EXP - 1;
 102       ex2_u.ieee.exponent += tval >> unsafe;
 103       scale_u.d = 1.0;
 104       scale_u.ieee.exponent += tval - (tval >> unsafe);
 105
 106       /* 4. Approximate 2^x2 - 1, using a fourth-degree polynomial,
 107          with maximum error in [-2^-10-2^-30,2^-10+2^-30]
 108          less than 10^-19.  */
 109
 110       x22 = (((.0096181293647031180
 111                * x + .055504110254308625)
 112               * x + .240226506959100583)
 113              * x + .69314718055994495) * ex2_u.d;
 114
 115       /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex).  */
 116       fesetenv (&oldenv);
 117
 118       result = x22 * x + ex2_u.d;
 119
 120       if (!unsafe)
 121         return result;
 122       else
 123         return result * scale_u.d;
 124     }
 125   /* Exceptional cases:  */
 126   else if (isless (x, himark))
 127     {
 128       if (x == *(const float *) &a_minf)
 129         /* e^-inf == 0, with no error.  */
 130         return 0;
 131       else
 132         /* Underflow */
 133         return TWOM1000 * TWOM1000;
 134     }
 135   else
 136     /* Return x, if x is a NaN or Inf; or overflow, otherwise.  */
 137     return TWO1023*x;
 138 }