sysdeps/libm-ieee754/s_exp2f.c

   1 /* Single-precision floating point 2^x.
   2    Copyright (C) 1997 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, and for
  26    single-precision.
  27    */
  28 #ifndef _GNU_SOURCE
  29 # define _GNU_SOURCE
  30 #endif
  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_exp2f.h"
  39
  40 static const volatile float TWOM100 = 7.88860905e-31;
  41 static const volatile float huge = 1e+30;
  42
  43 float
  44 __ieee754_exp2f (float x)
  45 {
  46   static const uint32_t a_inf = 0x7f800000;
  47   /* Check for usual case.  */
  48   if (isless (x, (float) FLT_MAX_EXP)
  49       && isgreater (x, (float) (FLT_MIN_EXP - 1)))
  50     {
  51       static const float TWO16 = 65536.0;
  52       int tval;
  53       float rx, x22;
  54       union ieee754_float ex2_u;
  55       fenv_t oldenv;
  56
  57       feholdexcept (&oldenv);
  58       fesetround (FE_TONEAREST);
  59
  60       /* 1. Argument reduction.
  61          Choose integers ex, -128 <= t < 128, and some real
  62          -1/512 <= x1 <= 1/512 so that
  63          x = ex + t/512 + x1.
  64
  65          First, calculate rx = ex + t/256.  */
  66       if (x >= 0)
  67         {
  68           rx = x + TWO16;
  69           rx -= TWO16;
  70         }
  71       else
  72         {
  73           rx = x - TWO16;
  74           rx += TWO16;
  75         }
  76       x -= rx;  /* Compute x=x1. */
  77       /* Compute tval = (ex*256 + t)+128.
  78          Now, t = (tval mod 256)-128 and ex=tval/256  [that's mod, NOT %; and
  79          /-round-to-nearest not the usual c integer /].  */
  80       tval = (int) (rx * 256.0f + 128.0f);
  81
  82       /* 2. Adjust for accurate table entry.
  83          Find e so that
  84          x = ex + t/256 + e + x2
  85          where -7e-4 < e < 7e-4, and
  86          (float)(2^(t/256+e))
  87          is accurate to one part in 2^-64.  */
  88
  89       /* 'tval & 255' is the same as 'tval%256' except that it's always
  90          positive.
  91          Compute x = x2.  */
  92       x -= exp2_deltatable[tval & 255];
  93
  94       /* 3. Compute ex2 = 2^(t/255+e+ex).  */
  95       ex2_u.f = exp2_accuratetable[tval & 255];
  96       ex2_u.ieee.exponent += tval >> 8;
  97
  98       /* 4. Approximate 2^x2 - 1, using a second-degree polynomial,
  99          2^x2 ~= sum(k=0..2 | (x2 * ln(2))^k / k! ) +
 100          so
 101          2^x2 - 1 ~= sum(k=1..4 | (x2 * ln(2))^k / k! )
 102          with error less than 2^(1/512+7e-4) * (x2 * ln(2))^3 / 3! < 1.2e-18.  */
 103
 104       x22 = (.240226507f * x + .6931471806f) * ex2_u.f;
 105
 106       /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex).  */
 107       fesetenv (&oldenv);
 108
 109       /* Need to check: does this set FE_INEXACT correctly? */
 110       return x22 * x + ex2_u.f;
 111     }
 112   /* 2^inf == inf, with no error.  */
 113   else if (x == *(const float *)&a_inf)
 114     {
 115       return x;
 116     }
 117   /* Check for overflow.  */
 118   else if (isgreaterequal (x, (float) FLT_MAX_EXP))
 119     return huge * huge;
 120   /* And underflow (including -inf).  */
 121   else if (isless (x, (float) (FLT_MIN_EXP - FLT_MANT_DIG)))
 122     return TWOM100 * TWOM100;
 123   /* Maybe the result needs to be a denormalised number...  */
 124   else if (!isnan (x))
 125     return __ieee754_exp2f (x + 100.0) * TWOM100;
 126   else /* isnan(x) */
 127     return x + x;
 128 }