sysdeps/ieee754/dbl-64/e_exp2.c

   1 /* Double-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.
  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_exp2.h"
  39
  40 static const volatile double TWO1023 = 8.988465674311579539e+307;
  41 static const volatile double TWOM1000 = 9.3326361850321887899e-302;
  42
  43 double
  44 __ieee754_exp2 (double x)
  45 {
  46   static const double himark = (double) DBL_MAX_EXP;
  47   static const double lomark = (double) (DBL_MIN_EXP - DBL_MANT_DIG - 1);
  48
  49   /* Check for usual case.  */
  50   if (isless (x, himark) && isgreaterequal (x, lomark))
  51     {
  52       static const double THREEp42 = 13194139533312.0;
  53       int tval, unsafe;
  54       double rx, x22, result;
  55       union ieee754_double 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, -256 <= t < 256, and some real
  66          -1/1024 <= x1 <= 1024 so that
  67          x = ex + t/512 + x1.
  68
  69          First, calculate rx = ex + t/512.  */
  70       rx = x + THREEp42;
  71       rx -= THREEp42;
  72       x -= rx;  /* Compute x=x1. */
  73       /* Compute tval = (ex*512 + t)+256.
  74          Now, t = (tval mod 512)-256 and ex=tval/512  [that's mod, NOT %; and
  75          /-round-to-nearest not the usual c integer /].  */
  76       tval = (int) (rx * 512.0 + 256.0);
  77
  78       /* 2. Adjust for accurate table entry.
  79          Find e so that
  80          x = ex + t/512 + e + x2
  81          where -1e6 < e < 1e6, and
  82          (double)(2^(t/512+e))
  83          is accurate to one part in 2^-64.  */
  84
  85       /* 'tval & 511' is the same as 'tval%512' except that it's always
  86          positive.
  87          Compute x = x2.  */
  88       x -= exp2_deltatable[tval & 511];
  89
  90       /* 3. Compute ex2 = 2^(t/512+e+ex).  */
  91       ex2_u.d = exp2_accuratetable[tval & 511];
  92       tval >>= 9;
  93       unsafe = abs(tval) >= -DBL_MIN_EXP - 1;
  94       ex2_u.ieee.exponent += tval >> unsafe;
  95       scale_u.d = 1.0;
  96       scale_u.ieee.exponent += tval - (tval >> unsafe);
  97
  98       /* 4. Approximate 2^x2 - 1, using a fourth-degree polynomial,
  99          with maximum error in [-2^-10-2^-30,2^-10+2^-30]
 100          less than 10^-19.  */
 101
 102       x22 = (((.0096181293647031180
 103                * x + .055504110254308625)
 104               * x + .240226506959100583)
 105              * x + .69314718055994495) * ex2_u.d;
 106
 107       /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex).  */
 108       fesetenv (&oldenv);
 109
 110       result = x22 * x + ex2_u.d;
 111
 112       if (!unsafe)
 113         return result;
 114       else
 115         return result * scale_u.d;
 116     }
 117   /* Exceptional cases:  */
 118   else if (isless (x, himark))
 119     {
 120       if (__isinf (x))
 121         /* e^-inf == 0, with no error.  */
 122         return 0;
 123       else
 124         /* Underflow */
 125         return TWOM1000 * TWOM1000;
 126     }
 127   else
 128     /* Return x, if x is a NaN or Inf; or overflow, otherwise.  */
 129     return TWO1023*x;
 130 }