sysdeps/ieee754/flt-32/e_exp2f.c

   1 /* Single-precision floating point 2^x.
   2    Copyright (C) 1997, 1998, 2000, 2001 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 Lesser General Public
   8    License as published by the Free Software Foundation; either
   9    version 2.1 of the 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    Lesser General Public License for more details.
  15
  16    You should have received a copy of the GNU Lesser General Public
  17    License along with the GNU C Library; if not, write to the Free
  18    Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
  19    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 <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       feholdexcept (&oldenv);
  60 #ifdef FE_TONEAREST
  61       /* If we don't have this, it's too bad.  */
  62       fesetround (FE_TONEAREST);
  63 #endif
  64
  65       /* 1. Argument reduction.
  66          Choose integers ex, -128 <= t < 128, and some real
  67          -1/512 <= x1 <= 1/512 so that
  68          x = ex + t/512 + x1.
  69
  70          First, calculate rx = ex + t/256.  */
  71       rx = x + THREEp14;
  72       rx -= THREEp14;
  73       x -= rx;  /* Compute x=x1. */
  74       /* Compute tval = (ex*256 + t)+128.
  75          Now, t = (tval mod 256)-128 and ex=tval/256  [that's mod, NOT %; and
  76          /-round-to-nearest not the usual c integer /].  */
  77       tval = (int) (rx * 256.0f + 128.0f);
  78
  79       /* 2. Adjust for accurate table entry.
  80          Find e so that
  81          x = ex + t/256 + e + x2
  82          where -7e-4 < e < 7e-4, and
  83          (float)(2^(t/256+e))
  84          is accurate to one part in 2^-64.  */
  85
  86       /* 'tval & 255' is the same as 'tval%256' except that it's always
  87          positive.
  88          Compute x = x2.  */
  89       x -= __exp2f_deltatable[tval & 255];
  90
  91       /* 3. Compute ex2 = 2^(t/255+e+ex).  */
  92       ex2_u.f = __exp2f_atable[tval & 255];
  93       tval >>= 8;
  94       unsafe = abs(tval) >= -FLT_MIN_EXP - 1;
  95       ex2_u.ieee.exponent += tval >> unsafe;
  96       scale_u.f = 1.0;
  97       scale_u.ieee.exponent += tval - (tval >> unsafe);
  98
  99       /* 4. Approximate 2^x2 - 1, using a second-degree polynomial,
 100          with maximum error in [-2^-9 - 2^-14, 2^-9 + 2^-14]
 101          less than 1.3e-10.  */
 102
 103       x22 = (.24022656679f * x + .69314736128f) * ex2_u.f;
 104
 105       /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex).  */
 106       fesetenv (&oldenv);
 107
 108       result = x22 * x + ex2_u.f;
 109
 110       if (!unsafe)
 111         return result;
 112       else
 113         return result * scale_u.f;
 114     }
 115   /* Exceptional cases:  */
 116   else if (isless (x, himark))
 117     {
 118       if (__isinff (x))
 119         /* e^-inf == 0, with no error.  */
 120         return 0;
 121       else
 122         /* Underflow */
 123         return TWOM100 * TWOM100;
 124     }
 125   else
 126     /* Return x, if x is a NaN or Inf; or overflow, otherwise.  */
 127     return TWO127*x;
 128 }