sysdeps/libm-ieee754/s_exp2f.c

   1 /* Single-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, 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 TWO127 = 1.7014118346e+38;
  42
  43 float
  44 __ieee754_exp2f (float x)
  45 {
  46   static const float himark = (float) FLT_MAX_EXP;
  47   static const float lomark = (float) (FLT_MIN_EXP - FLT_MANT_DIG - 1) - 1.0;
  48
  49   /* Check for usual case.  */
  50   if (isless (x, himark) && isgreater (x, lomark))
  51     {
  52       static const float THREEp14 = 49152.0;
  53       int tval, unsafe;
  54       float rx, x22, result;
  55       union ieee754_float 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, -128 <= t < 128, and some real
  66          -1/512 <= x1 <= 1/512 so that
  67          x = ex + t/512 + x1.
  68
  69          First, calculate rx = ex + t/256.  */
  70       rx = x + THREEp14;
  71       rx -= THREEp14;
  72       x -= rx;  /* Compute x=x1. */
  73       /* Compute tval = (ex*256 + t)+128.
  74          Now, t = (tval mod 256)-128 and ex=tval/256  [that's mod, NOT %; and
  75          /-round-to-nearest not the usual c integer /].  */
  76       tval = (int) (rx * 256.0f + 128.0f);
  77
  78       /* 2. Adjust for accurate table entry.
  79          Find e so that
  80          x = ex + t/256 + e + x2
  81          where -7e-4 < e < 7e-4, and
  82          (float)(2^(t/256+e))
  83          is accurate to one part in 2^-64.  */
  84
  85       /* 'tval & 255' is the same as 'tval%256' except that it's always
  86          positive.
  87          Compute x = x2.  */
  88       x -= __exp2f_deltatable[tval & 255];
  89
  90       /* 3. Compute ex2 = 2^(t/255+e+ex).  */
  91       ex2_u.f = __exp2f_atable[tval & 255];
  92       tval >>= 8;
  93       unsafe = abs(tval) >= -FLT_MIN_EXP - 1;
  94       ex2_u.ieee.exponent += tval >> unsafe;
  95       scale_u.f = 1.0;
  96       scale_u.ieee.exponent += tval - (tval >> unsafe);
  97
  98       /* 4. Approximate 2^x2 - 1, using a second-degree polynomial,
  99          with maximum error in [-2^-9 - 2^-14, 2^-9 + 2^-14]
 100          less than 1.3e-10.  */
 101
 102       x22 = (.24022656679f * x + .69314736128f) * ex2_u.f;
 103
 104       /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex).  */
 105       fesetenv (&oldenv);
 106
 107       result = x22 * x + ex2_u.f;
 108
 109       if (!unsafe)
 110         return result;
 111       else
 112         return result * scale_u.f;
 113     }
 114   /* Exceptional cases:  */
 115   else if (isless (x, himark))
 116     {
 117       if (__isinff (x))
 118         /* e^-inf == 0, with no error.  */
 119         return 0;
 120       else
 121         /* Underflow */
 122         return TWOM100 * TWOM100;
 123     }
 124   else
 125     /* Return x, if x is a NaN or Inf; or overflow, otherwise.  */
 126     return TWO127*x;
 127 }