sysdeps/ieee754/flt-32/e_exp2f.c

   1 /* Single-precision floating point 2^x.
   2    Copyright (C) 1997-2014 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, see
  18    <http://www.gnu.org/licenses/>.  */
  19
  20 /* The basic design here is from
  21    Shmuel Gal and Boris Bachelis, "An Accurate Elementary Mathematical
  22    Library for the IEEE Floating Point Standard", ACM Trans. Math. Soft.,
  23    17 (1), March 1991, pp. 26-45.
  24    It has been slightly modified to compute 2^x instead of e^x, and for
  25    single-precision.
  26    */
  27 #ifndef _GNU_SOURCE
  28 # define _GNU_SOURCE
  29 #endif
  30 #include <stdlib.h>
  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);
  48
  49   /* Check for usual case.  */
  50   if (isless (x, himark) && isgreaterequal (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
  57       {
  58         SET_RESTORE_ROUND_NOEXF (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         rx = x + THREEp14;
  67         rx -= THREEp14;
  68         x -= rx;  /* Compute x=x1. */
  69         /* Compute tval = (ex*256 + t)+128.
  70            Now, t = (tval mod 256)-128 and ex=tval/256  [that's mod, NOT %;
  71            and /-round-to-nearest not the usual c integer /].  */
  72         tval = (int) (rx * 256.0f + 128.0f);
  73
  74         /* 2. Adjust for accurate table entry.
  75            Find e so that
  76            x = ex + t/256 + e + x2
  77            where -7e-4 < e < 7e-4, and
  78            (float)(2^(t/256+e))
  79            is accurate to one part in 2^-64.  */
  80
  81         /* 'tval & 255' is the same as 'tval%256' except that it's always
  82            positive.
  83            Compute x = x2.  */
  84         x -= __exp2f_deltatable[tval & 255];
  85
  86         /* 3. Compute ex2 = 2^(t/255+e+ex).  */
  87         ex2_u.f = __exp2f_atable[tval & 255];
  88         tval >>= 8;
  89         unsafe = abs(tval) >= -FLT_MIN_EXP - 1;
  90         ex2_u.ieee.exponent += tval >> unsafe;
  91         scale_u.f = 1.0;
  92         scale_u.ieee.exponent += tval - (tval >> unsafe);
  93
  94         /* 4. Approximate 2^x2 - 1, using a second-degree polynomial,
  95            with maximum error in [-2^-9 - 2^-14, 2^-9 + 2^-14]
  96            less than 1.3e-10.  */
  97
  98         x22 = (.24022656679f * x + .69314736128f) * ex2_u.f;
  99       }
 100
 101       /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex).  */
 102       result = x22 * x + ex2_u.f;
 103
 104       if (!unsafe)
 105         return result;
 106       else
 107         return result * scale_u.f;
 108     }
 109   /* Exceptional cases:  */
 110   else if (isless (x, himark))
 111     {
 112       if (__isinf_nsf (x))
 113         /* e^-inf == 0, with no error.  */
 114         return 0;
 115       else
 116         /* Underflow */
 117         return TWOM100 * TWOM100;
 118     }
 119   else
 120     /* Return x, if x is a NaN or Inf; or overflow, otherwise.  */
 121     return TWO127*x;
 122 }
 123 strong_alias (__ieee754_exp2f, __exp2f_finite)