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annotate lib/expl.c @ 11224:5aa57cee93aa

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avoid gcc 3.4.3 bug on long double NaN on Irix 6.5 * tests/nan.h (NaNl): Rewrite as function on Irix, to avoid compilation bug by using runtime conversion. * m4/isfinite.m4 (gl_ISFINITE): Likewise. * m4/isnanl.m4 (gl_FUNC_ISNANL): Likewise. * modules/ceill-tests (Files): Use nan.h. * modules/floorl-tests (Files): Likewise. * modules/frexpl-tests (Files): Likewise. * modules/isnanl-tests (Files): Likewise. * modules/ldexpl-tests (Files): Likewise. * modules/roundl-tests (Files): Likewise. * modules/truncl-tests (Files): Likewise. * tests/test-ceill.c (main): Use a working NaN. * tests/test-floorl.c (main): Likewise. * tests/test-frexpl.c (main): Likewise. * tests/test-isnan.c (test_long_double): Likewise. * tests/test-isnanl.h (main): Likewise. * tests/test-ldexpl.h (main): Likewise. * tests/test-roundl.h (main): Likewise. * tests/test-truncl.h (main): Likewise. See http://lists.gnu.org/archive/html/bug-gnulib/2009-02/msg00190.html. Signed-off-by: Eric Blake <ebb9@byu.net>
author Eric Blake <ebb9@byu.net>
date Thu, 26 Feb 2009 20:18:42 -0700
parents bbbbbf4cd1c5
children e8d2c6fc33ad
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1 /* Emulation for expl.
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2 Contributed by Paolo Bonzini
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3
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4 Copyright 2002, 2003, 2007 Free Software Foundation, Inc.
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5
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6 This file is part of gnulib.
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7
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8 This program is free software: you can redistribute it and/or modify
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9 it under the terms of the GNU General Public License as published by
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10 the Free Software Foundation; either version 3 of the License, or
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11 (at your option) any later version.
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12
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13 This program is distributed in the hope that it will be useful,
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14 but WITHOUT ANY WARRANTY; without even the implied warranty of
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15 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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16 GNU General Public License for more details.
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17
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18 You should have received a copy of the GNU General Public License
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19 along with this program. If not, see <http://www.gnu.org/licenses/>. */
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20
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21 #include <config.h>
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22
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23 /* Specification. */
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24 #include <math.h>
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25
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26 #include <float.h>
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27
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28 static const long double C[] = {
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29 /* Chebyshev polynom coeficients for (exp(x)-1)/x */
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30 #define P1 C[0]
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31 #define P2 C[1]
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32 #define P3 C[2]
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33 #define P4 C[3]
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34 #define P5 C[4]
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35 #define P6 C[5]
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36 0.5L,
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37 1.66666666666666666666666666666666683E-01L,
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38 4.16666666666666666666654902320001674E-02L,
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39 8.33333333333333333333314659767198461E-03L,
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40 1.38888888889899438565058018857254025E-03L,
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41 1.98412698413981650382436541785404286E-04L,
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42
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43 /* Smallest integer x for which e^x overflows. */
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44 #define himark C[6]
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45 11356.523406294143949491931077970765L,
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46
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47 /* Largest integer x for which e^x underflows. */
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48 #define lomark C[7]
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49 -11433.4627433362978788372438434526231L,
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50
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51 /* very small number */
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52 #define TINY C[8]
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53 1.0e-4900L,
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54
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55 /* 2^16383 */
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56 #define TWO16383 C[9]
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57 5.94865747678615882542879663314003565E+4931L};
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58
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59 long double
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60 expl (long double x)
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61 {
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62 /* Check for usual case. */
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63 if (x < himark && x > lomark)
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64 {
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65 int exponent;
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66 long double t, x22;
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67 int k = 1;
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68 long double result = 1.0;
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69
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70 /* Compute an integer power of e with a granularity of 0.125. */
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71 exponent = (int) floorl (x * 8.0L);
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72 x -= exponent / 8.0L;
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73
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74 if (x > 0.0625)
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75 {
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76 exponent++;
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77 x -= 0.125L;
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78 }
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79
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80 if (exponent < 0)
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81 {
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82 t = 0.8824969025845954028648921432290507362220L; /* e^-0.25 */
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83 exponent = -exponent;
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84 }
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85 else
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86 t = 1.1331484530668263168290072278117938725655L; /* e^0.25 */
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87
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88 while (exponent)
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89 {
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90 if (exponent & k)
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91 {
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92 result *= t;
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93 exponent ^= k;
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94 }
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95 t *= t;
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96 k <<= 1;
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97 }
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98
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99 /* Approximate (e^x - 1)/x, using a seventh-degree polynomial,
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100 with maximum error in [-2^-16-2^-53,2^-16+2^-53]
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101 less than 4.8e-39. */
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102 x22 = x + x*x*(P1+x*(P2+x*(P3+x*(P4+x*(P5+x*P6)))));
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103
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104 return result + result * x22;
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105 }
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106 /* Exceptional cases: */
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107 else if (x < himark)
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108 {
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109 if (x + x == x)
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110 /* e^-inf == 0, with no error. */
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111 return 0;
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112 else
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113 /* Underflow */
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114 return TINY * TINY;
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115 }
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116 else
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117 /* Return x, if x is a NaN or Inf; or overflow, otherwise. */
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118 return TWO16383*x;
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119 }
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120
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121 #if 0
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122 int
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123 main (void)
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124 {
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125 printf ("%.16Lg\n", expl(1.0L));
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126 printf ("%.16Lg\n", expl(-1.0L));
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127 printf ("%.16Lg\n", expl(2.0L));
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128 printf ("%.16Lg\n", expl(4.0L));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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129 printf ("%.16Lg\n", expl(-2.0L));
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130 printf ("%.16Lg\n", expl(-4.0L));
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131 printf ("%.16Lg\n", expl(0.0625L));
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132 printf ("%.16Lg\n", expl(0.3L));
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133 printf ("%.16Lg\n", expl(0.6L));
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134 }
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135 #endif