sysdeps/ieee754/flt-32/e_exp2f.c

   1 /* Single-precision floating point 2^x.
   2    Copyright (C) 1997,1998,2000,2001,2005,2006,2011
   3    Free Software Foundation, Inc.
   4    This file is part of the GNU C Library.
   5    Contributed by Geoffrey Keating <geoffk@ozemail.com.au>
   6
   7    The GNU C Library is free software; you can redistribute it and/or
   8    modify it under the terms of the GNU Lesser General Public
   9    License as published by the Free Software Foundation; either
  10    version 2.1 of the License, or (at your option) any later version.
  11
  12    The GNU C Library is distributed in the hope that it will be useful,
  13    but WITHOUT ANY WARRANTY; without even the implied warranty of
  14    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  15    Lesser General Public License for more details.
  16
  17    You should have received a copy of the GNU Lesser General Public
  18    License along with the GNU C Library; if not, see
  19    <http://www.gnu.org/licenses/>.  */
  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 <stdlib.h>
  32 #include <float.h>
  33 #include <ieee754.h>
  34 #include <math.h>
  35 #include <fenv.h>
  36 #include <inttypes.h>
  37 #include <math_private.h>
  38
  39 #include "t_exp2f.h"
  40
  41 static const volatile float TWOM100 = 7.88860905e-31;
  42 static const volatile float TWO127 = 1.7014118346e+38;
  43
  44 float
  45 __ieee754_exp2f (float x)
  46 {
  47   static const float himark = (float) FLT_MAX_EXP;
  48   static const float lomark = (float) (FLT_MIN_EXP - FLT_MANT_DIG - 1);
  49
  50   /* Check for usual case.  */
  51   if (isless (x, himark) && isgreaterequal (x, lomark))
  52     {
  53       static const float THREEp14 = 49152.0;
  54       int tval, unsafe;
  55       float rx, x22, result;
  56       union ieee754_float ex2_u, scale_u;
  57       fenv_t oldenv;
  58
  59       libc_feholdexcept_setroundf (&oldenv, FE_TONEAREST);
  60
  61       /* 1. Argument reduction.
  62          Choose integers ex, -128 <= t < 128, and some real
  63          -1/512 <= x1 <= 1/512 so that
  64          x = ex + t/512 + x1.
  65
  66          First, calculate rx = ex + t/256.  */
  67       rx = x + THREEp14;
  68       rx -= THREEp14;
  69       x -= rx;  /* Compute x=x1. */
  70       /* Compute tval = (ex*256 + t)+128.
  71          Now, t = (tval mod 256)-128 and ex=tval/256  [that's mod, NOT %; and
  72          /-round-to-nearest not the usual c integer /].  */
  73       tval = (int) (rx * 256.0f + 128.0f);
  74
  75       /* 2. Adjust for accurate table entry.
  76          Find e so that
  77          x = ex + t/256 + e + x2
  78          where -7e-4 < e < 7e-4, and
  79          (float)(2^(t/256+e))
  80          is accurate to one part in 2^-64.  */
  81
  82       /* 'tval & 255' is the same as 'tval%256' except that it's always
  83          positive.
  84          Compute x = x2.  */
  85       x -= __exp2f_deltatable[tval & 255];
  86
  87       /* 3. Compute ex2 = 2^(t/255+e+ex).  */
  88       ex2_u.f = __exp2f_atable[tval & 255];
  89       tval >>= 8;
  90       unsafe = abs(tval) >= -FLT_MIN_EXP - 1;
  91       ex2_u.ieee.exponent += tval >> unsafe;
  92       scale_u.f = 1.0;
  93       scale_u.ieee.exponent += tval - (tval >> unsafe);
  94
  95       /* 4. Approximate 2^x2 - 1, using a second-degree polynomial,
  96          with maximum error in [-2^-9 - 2^-14, 2^-9 + 2^-14]
  97          less than 1.3e-10.  */
  98
  99       x22 = (.24022656679f * x + .69314736128f) * ex2_u.f;
 100
 101       /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex).  */
 102       libc_fesetenv (&oldenv);
 103
 104       result = x22 * x + ex2_u.f;
 105
 106       if (!unsafe)
 107         return result;
 108       else
 109         return result * scale_u.f;
 110     }
 111   /* Exceptional cases:  */
 112   else if (isless (x, himark))
 113     {
 114       if (__isinf_nsf (x))
 115         /* e^-inf == 0, with no error.  */
 116         return 0;
 117       else
 118         /* Underflow */
 119         return TWOM100 * TWOM100;
 120     }
 121   else
 122     /* Return x, if x is a NaN or Inf; or overflow, otherwise.  */
 123     return TWO127*x;
 124 }
 125 strong_alias (__ieee754_exp2f, __exp2f_finite)