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
40static const volatile double TWO1023 = 8.988465674311579539e+307;
41static const volatile double TWOM1000 = 9.3326361850321887899e-302;
42
43double
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}
131