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annotate lib/expl.c @ 16578:5626e55f7f0b

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expl: Simplify computation. * lib/expl.c (expl): Simplify computation of exp_y. Fix comment.
author Bruno Haible <bruno@clisp.org>
date Tue, 06 Mar 2012 12:03:57 +0100
parents 6c7c671909d3
children 4a578c3945b8
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 /* Exponential function.
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2 Copyright (C) 2011-2012 Free Software Foundation, Inc.
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3
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4 This program is free software: you can redistribute it and/or modify
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5 it under the terms of the GNU General Public License as published by
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6 the Free Software Foundation; either version 3 of the License, or
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7 (at your option) any later version.
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8
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9 This program is distributed in the hope that it will be useful,
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10 but WITHOUT ANY WARRANTY; without even the implied warranty of
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11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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12 GNU General Public License for more details.
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13
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14 You should have received a copy of the GNU General Public License
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15 along with this program. If not, see <http://www.gnu.org/licenses/>. */
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16
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17 #include <config.h>
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18
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19 /* Specification. */
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20 #include <math.h>
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21
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22 #if HAVE_SAME_LONG_DOUBLE_AS_DOUBLE
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23
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24 long double
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25 expl (long double x)
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26 {
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27 return exp (x);
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28 }
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29
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30 #else
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31
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32 # include <float.h>
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33
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34 /* A value slightly larger than log(2). */
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35 #define LOG2_PLUS_EPSILON 0.6931471805599454L
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36
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37 /* Best possible approximation of log(2) as a 'long double'. */
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38 #define LOG2 0.693147180559945309417232121458176568075L
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39
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40 /* Best possible approximation of 1/log(2) as a 'long double'. */
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41 #define LOG2_INVERSE 1.44269504088896340735992468100189213743L
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42
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43 /* Best possible approximation of log(2)/256 as a 'long double'. */
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44 #define LOG2_BY_256 0.00270760617406228636491106297444600221904L
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45
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46 /* Best possible approximation of 256/log(2) as a 'long double'. */
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47 #define LOG2_BY_256_INVERSE 369.329930467574632284140718336484387181L
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48
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49 /* The upper 32 bits of log(2)/256. */
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50 #define LOG2_BY_256_HI_PART 0.0027076061733168899081647396087646484375L
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51 /* log(2)/256 - LOG2_HI_PART. */
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52 #define LOG2_BY_256_LO_PART \
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53 0.000000000000745396456746323365681353781544922399845L
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54
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55 long double
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56 expl (long double x)
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57 {
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58 if (isnanl (x))
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59 return x;
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60
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61 if (x >= (long double) LDBL_MAX_EXP * LOG2_PLUS_EPSILON)
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62 /* x > LDBL_MAX_EXP * log(2)
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63 hence exp(x) > 2^LDBL_MAX_EXP, overflows to Infinity. */
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64 return HUGE_VALL;
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65
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66 if (x <= (long double) (LDBL_MIN_EXP - 1 - LDBL_MANT_DIG) * LOG2_PLUS_EPSILON)
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67 /* x < (LDBL_MIN_EXP - 1 - LDBL_MANT_DIG) * log(2)
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68 hence exp(x) < 2^(LDBL_MIN_EXP-1-LDBL_MANT_DIG),
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69 underflows to zero. */
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70 return 0.0L;
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71
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72 /* Decompose x into
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73 x = n * log(2) + m * log(2)/256 + y
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74 where
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75 n is an integer,
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76 m is an integer, -128 <= m <= 128,
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77 y is a number, |y| <= log(2)/512 + epsilon = 0.00135...
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78 Then
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79 exp(x) = 2^n * exp(m * log(2)/256) * exp(y)
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80 The first factor is an ldexpl() call.
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81 The second factor is a table lookup.
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82 The third factor is computed
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83 - either as sinh(y) + cosh(y)
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84 where sinh(y) is computed through the power series:
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85 sinh(y) = y + y^3/3! + y^5/5! + ...
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86 and cosh(y) is computed as hypot(1, sinh(y)),
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87 - or as exp(2*z) = (1 + tanh(z)) / (1 - tanh(z))
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88 where z = y/2
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89 and tanh(z) is computed through its power series:
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90 tanh(z) = z
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91 - 1/3 * z^3
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92 + 2/15 * z^5
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93 - 17/315 * z^7
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94 + 62/2835 * z^9
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95 - 1382/155925 * z^11
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96 + 21844/6081075 * z^13
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97 - 929569/638512875 * z^15
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98 + ...
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99 Since |z| <= log(2)/1024 < 0.0007, the relative error of the z^13 term
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100 is < 0.0007^12 < 2^-120 <= 2^-LDBL_MANT_DIG, therefore we can truncate
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101 the series after the z^11 term.
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102
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103 Given the usual bounds LDBL_MAX_EXP <= 16384, LDBL_MIN_EXP >= -16381,
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104 LDBL_MANT_DIG <= 120, we can estimate x: -11440 <= x <= 11357.
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105 This means, when dividing x by log(2), where we want x mod log(2)
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106 to be precise to LDBL_MANT_DIG bits, we have to use an approximation
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107 to log(2) that has 14+LDBL_MANT_DIG bits. */
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108
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109 {
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110 long double nm = roundl (x * LOG2_BY_256_INVERSE); /* = 256 * n + m */
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111 /* n has at most 15 bits, nm therefore has at most 23 bits, therefore
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112 n * LOG2_HI_PART is computed exactly, and n * LOG2_LO_PART is computed
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113 with an absolute error < 2^15 * 2e-10 * 2^-LDBL_MANT_DIG. */
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114 long double y_tmp = x - nm * LOG2_BY_256_HI_PART;
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115 long double y = y_tmp - nm * LOG2_BY_256_LO_PART;
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116 long double z = 0.5L * y;
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117
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118 /* Coefficients of the power series for tanh(z). */
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119 #define TANH_COEFF_1 1.0L
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120 #define TANH_COEFF_3 -0.333333333333333333333333333333333333334L
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121 #define TANH_COEFF_5 0.133333333333333333333333333333333333334L
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122 #define TANH_COEFF_7 -0.053968253968253968253968253968253968254L
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123 #define TANH_COEFF_9 0.0218694885361552028218694885361552028218L
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124 #define TANH_COEFF_11 -0.00886323552990219656886323552990219656886L
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125 #define TANH_COEFF_13 0.00359212803657248101692546136990581435026L
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126 #define TANH_COEFF_15 -0.00145583438705131826824948518070211191904L
6c7c671909d3 expl: Fix precision of computed result.
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127
6c7c671909d3 expl: Fix precision of computed result.
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diff changeset
128 long double z2 = z * z;
6c7c671909d3 expl: Fix precision of computed result.
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diff changeset
129 long double tanh_z =
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
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diff changeset
130 (((((TANH_COEFF_11
6c7c671909d3 expl: Fix precision of computed result.
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diff changeset
131 * z2 + TANH_COEFF_9)
6c7c671909d3 expl: Fix precision of computed result.
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diff changeset
132 * z2 + TANH_COEFF_7)
6c7c671909d3 expl: Fix precision of computed result.
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diff changeset
133 * z2 + TANH_COEFF_5)
6c7c671909d3 expl: Fix precision of computed result.
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diff changeset
134 * z2 + TANH_COEFF_3)
6c7c671909d3 expl: Fix precision of computed result.
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diff changeset
135 * z2 + TANH_COEFF_1)
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
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diff changeset
136 * z;
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
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diff changeset
137
16578
5626e55f7f0b expl: Simplify computation.
Bruno Haible <bruno@clisp.org>
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diff changeset
138 long double exp_y = (1.0L + tanh_z) / (1.0L - tanh_z);
16576
6c7c671909d3 expl: Fix precision of computed result.
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139
6c7c671909d3 expl: Fix precision of computed result.
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diff changeset
140 int n = (int) roundl (nm * (1.0L / 256.0L));
6c7c671909d3 expl: Fix precision of computed result.
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diff changeset
141 int m = (int) nm - 256 * n;
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
142
16576
6c7c671909d3 expl: Fix precision of computed result.
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diff changeset
143 /* expl_table[i] = exp((i - 128) * log(2)/256).
6c7c671909d3 expl: Fix precision of computed result.
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diff changeset
144 Computed in GNU clisp through
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
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diff changeset
145 (setf (long-float-digits) 128)
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
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diff changeset
146 (setq a 0L0)
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
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diff changeset
147 (setf (long-float-digits) 256)
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
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diff changeset
148 (dotimes (i 257)
6c7c671909d3 expl: Fix precision of computed result.
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diff changeset
149 (format t " ~D,~%"
16578
5626e55f7f0b expl: Simplify computation.
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diff changeset
150 (float (exp (* (/ (- i 128) 256) (log 2L0))) a))) */
16576
6c7c671909d3 expl: Fix precision of computed result.
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diff changeset
151 static const long double expl_table[257] =
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
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diff changeset
152 {
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
153 0.707106781186547524400844362104849039284L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
154 0.709023942160207598920563322257676190836L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
155 0.710946301084582779904674297352120049962L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
156 0.71287387205274715340350157671438300618L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
157 0.714806669195985005617532889137569953044L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
158 0.71674470668389442125974978427737336719L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
159 0.71868799872449116280161304224785251353L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
160 0.720636559564312831364255957304947586072L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
161 0.72259040348852331001850312073583545284L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
162 0.724549544821017490259402705487111270714L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
163 0.726513997924526282423036245842287293786L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
164 0.728483777200721910815451524818606761737L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
165 0.730458897090323494325651445155310766577L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
166 0.732439372073202913296664682112279175616L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
167 0.734425216668490963430822513132890712652L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
168 0.736416445434683797507470506133110286942L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
169 0.738413072969749655693453740187024961962L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
170 0.740415113911235885228829945155951253966L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
171 0.742422582936376250272386395864403155277L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
172 0.744435494762198532693663597314273242753L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
173 0.746453864145632424600321765743336770838L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
174 0.748477705883617713391824861712720862423L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
175 0.750507034813212760132561481529764324813L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
176 0.752541865811703272039672277899716132493L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
177 0.75458221379671136988300977551659676571L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
178 0.756628093726304951096818488157633113612L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
179 0.75867952059910734940489114658718937343L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
180 0.760736509454407291763130627098242426467L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
181 0.762799075372269153425626844758470477304L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
182 0.76486723347364351194254345936342587308L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
183 0.766940998920478000900300751753859329456L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
184 0.769020386915828464216738479594307884331L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
185 0.771105412703970411806145931045367420652L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
186 0.773196091570510777431255778146135325272L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
187 0.77529243884249997956151370535341912283L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
188 0.777394469888544286059157168801667390437L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
189 0.779502200118918483516864044737428940745L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
190 0.781615644985678852072965367573877941354L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
191 0.783734819982776446532455855478222575498L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
192 0.78585974064617068462428149076570281356L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
193 0.787990422553943243227635080090952504452L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
194 0.790126881326412263402248482007960521995L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
195 0.79226913262624686505993407346567890838L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
196 0.794417192158581972116898048814333564685L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
197 0.796571075671133448968624321559534367934L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
198 0.798730798954313549131410147104316569576L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
199 0.800896377841346676896923120795476813684L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
200 0.803067828208385462848443946517563571584L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
201 0.805245165974627154089760333678700291728L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
202 0.807428407102430320039984581575729114268L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
203 0.809617567597431874649880866726368203972L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
204 0.81181266350866441589760797777344082227L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
205 0.814013710928673883424109261007007338614L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
206 0.816220725993637535170713864466769240053L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
207 0.818433724883482243883852017078007231025L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
208 0.82065272382200311435413206848451310067L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
209 0.822877739076982422259378362362911222833L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
210 0.825108786960308875483586738272485101678L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
211 0.827345883828097198786118571797909120834L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
212 0.829589046080808042697824787210781231927L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
213 0.831838290163368217523168228488195222638L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
214 0.834093632565291253329796170708536192903L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
215 0.836355089820798286809404612069230711295L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
216 0.83862267850893927589613232455870870518L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
217 0.84089641525371454303112547623321489504L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
218 0.84317631672419664796432298771385230143L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
219 0.84546239963465259098692866759361830709L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
220 0.84775468074466634749045860363936420312L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
221 0.850053176859261734750681286748751167545L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
222 0.852357904829025611837203530384718316326L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
223 0.854668881550231413551897437515331498025L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
224 0.856986123964963019301812477839166009452L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
225 0.859309649061238957814672188228156252257L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
226 0.861639473873136948607517116872358729753L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
227 0.863975615480918781121524414614366207052L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
228 0.866318091011155532438509953514163469652L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
229 0.868666917636853124497101040936083380124L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
230 0.871022112577578221729056715595464682243L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
231 0.873383693099584470038708278290226842228L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
232 0.875751676515939078050995142767930296012L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
233 0.878126080186649741556080309687656610647L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
234 0.880506921518791912081045787323636256171L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
235 0.882894217966636410521691124969260937028L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
236 0.885287987031777386769987907431242017412L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
237 0.88768824626326062627527960009966160388L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
238 0.89009501325771220447985955243623523504L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
239 0.892508305659467490072110281986409916153L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
240 0.8949281411607004980029443898876582985L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
241 0.897354537501553593213851621063890907178L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
242 0.899787512470267546027427696662514569756L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
243 0.902227083903311940153838631655504844215L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
244 0.904673269685515934269259325789226871994L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
245 0.907126087750199378124917300181170171233L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
246 0.909585556079304284147971563828178746372L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
247 0.91205169270352665549806275316460097744L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
248 0.914524515702448671545983912696158354092L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
249 0.91700404320467123174354159479414442804L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
250 0.919490293387946858856304371174663918816L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
251 0.921983284479312962533570386670938449637L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
252 0.92448303475522546419252726694739603678L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
253 0.92698956254169278419622653516884831976L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
254 0.929502886214410192307650717745572682403L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
255 0.932023024198894522404814545597236289343L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
256 0.934549994970619252444512104439799143264L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
257 0.93708381705514995066499947497722326722L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
258 0.93962450902828008902058735120448448827L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
259 0.942172089516167224843810351983745154882L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
260 0.944726577195469551733539267378681531548L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
261 0.947287990793482820670109326713462307376L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
262 0.949856349088277632361251759806996099924L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
263 0.952431670908837101825337466217860725517L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
264 0.955013975135194896221170529572799135168L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
265 0.957603280698573646936305635147915443924L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
266 0.960199606581523736948607188887070611744L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
267 0.962802971818062464478519115091191368377L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
268 0.965413395493813583952272948264534783197L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
269 0.968030896746147225299027952283345762418L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
270 0.970655494764320192607710617437589705184L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
271 0.973287208789616643172102023321302921373L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
272 0.97592605811548914795551023340047499377L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
273 0.978572062087700134509161125813435745597L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
274 0.981225240104463713381244885057070325016L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
275 0.983885611616587889056366801238014683926L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
276 0.98655319612761715646797006813220671315L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
277 0.989228013193975484129124959065583667775L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
278 0.99191008242510968492991311132615581644L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
279 0.994599423483633175652477686222166314457L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
280 0.997296056085470126257659913847922601123L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
281 1.0L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
282 1.00271127505020248543074558845036204047L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
283 1.0054299011128028213513839559347998147L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
284 1.008155898118417515783094890817201039276L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
285 1.01088928605170046002040979056186052439L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
286 1.013630084951489438840258929063939929597L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
287 1.01637831491095303794049311378629406276L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
288 1.0191339960777379496848780958207928794L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
289 1.02189714865411667823448013478329943978L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
290 1.02466779289713564514828907627081492763L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
291 1.0274459491187636965388611939222137815L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
292 1.030231637686041012871707902453904567093L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
293 1.033024879021228422500108283970460918086L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
294 1.035825693601957120029983209018081371844L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
295 1.03863410196137879061243669795463973258L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
296 1.04145012468831614126454607901189312648L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
297 1.044273782427413840321966478739929008784L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
298 1.04710509587928986612990725022711224056L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
299 1.04994408580068726608203812651590790906L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
300 1.05279077300462632711989120298074630319L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
301 1.05564517836055715880834132515293865216L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
302 1.058507322794512690105772109683716645074L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
303 1.061377227289262080950567678003883726294L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
304 1.06425491288446454978861125700158022068L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
305 1.06714040067682361816952112099280916261L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
306 1.0700337118202417735424119367576235685L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
307 1.072934867525975551385035450873827585343L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
308 1.075843889062791037803228648476057074063L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
309 1.07876079775711979374068003743848295849L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
310 1.081685614993215201942115594422531125643L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
311 1.08461836221330923781610517190661434161L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
312 1.087559060917769665346797830944039707867L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
313 1.09050773266525765920701065576070797899L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
314 1.09346439907288585422822014625044716208L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
315 1.096429081816376823386138295859248481766L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
316 1.09940180263022198546369696823882990404L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
317 1.10238258330784094355641420942564685751L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
318 1.10537144570174125558827469625695031104L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
319 1.108368411723678638009423649426619850137L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
320 1.111373503344817603850149254228916637444L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
321 1.1143867425958925363088129569196030678L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
322 1.11740815156736919905457996308578026665L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
323 1.12043775240960668442900387986631301277L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
324 1.123475567333019800733729739775321431954L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
325 1.12652161860824189979479864378703477763L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
326 1.129575928566288145997264988840249825907L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
327 1.13263851959871922798707372367762308438L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
328 1.13570941415780551424039033067611701343L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
329 1.13878863475669165370383028384151125472L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
330 1.14187620396956162271229760828788093894L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
331 1.14497214443180421939441388822291589579L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
332 1.14807647884017900677879966269734268003L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
333 1.15118922995298270581775963520198253612L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
334 1.154310420590216039548221528724806960684L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
335 1.157440073633751029613085766293796821106L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
336 1.16057821202749874636945947257609098625L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
337 1.16372485877757751381357359909218531234L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
338 1.166880036952481570555516298414089287834L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
339 1.170043769683250188080259035792738573L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
340 1.17321608016363724753480435451324538889L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
341 1.176396991650281276284645728483848641054L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
342 1.17958652746287594548610056676944051898L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
343 1.182784710984341029924457204693850757966L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
344 1.18599156566099383137126564953421556374L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
345 1.18920711500272106671749997056047591529L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
346 1.19243138258315122214272755814543101148L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
347 1.195664392039827374583837049865451975705L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
348 1.19890616707438048177030255797630020695L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
349 1.202156731452703142096396957497765876003L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
350 1.205416109005123825604211432558411335666L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
351 1.208684323626581577354792255889216998484L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
352 1.21196139927680119446816891773249304545L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
353 1.215247359980468878116520251338798457624L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
354 1.218542229827408361758207148117394510724L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
355 1.221846032972757516903891841911570785836L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
356 1.225158793637145437709464594384845353707L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
357 1.22848053610687000569400895779278184036L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
358 1.2318112847340759358845566532127948166L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
359 1.235151063936933305692912507415415760294L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
360 1.238499898199816567833368865859612431545L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
361 1.24185781207348404859367746872659560551L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
362 1.24522483017525793277520496748615267417L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
363 1.24860097718920473662176609730249554519L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
364 1.25198627786631627006020603178920359732L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
365 1.255380757024691089579390657442301194595L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
366 1.25878443954971644307786044181516261876L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
367 1.26219735039425070801401025851841645967L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
368 1.265619514578806324196273999873453036296L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
369 1.26905095719173322255441908103233800472L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
370 1.27249170338940275123669204418460217677L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
371 1.27594177839639210038120243475928938891L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
372 1.27940120750566922691358797002785254596L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
373 1.28287001607877828072666978102151405111L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
374 1.286348229546025533601482208069738348355L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
375 1.28983587340666581223274729549155218968L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
376 1.293332973229089436725559789048704304684L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
377 1.296839554651009665933754117792451159835L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
378 1.30035564337965065101414056707091779129L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
379 1.30388126519193589857452364895199736833L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
380 1.30741644593467724479715157747196172848L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
381 1.310961211524764341922991786330755849366L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
382 1.314515587949354658485983613383997794965L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
383 1.318079601266063994690185647066116617664L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
384 1.32165327760315751432651181233060922616L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
385 1.32523664315974129462953709549872167411L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
386 1.32882972420595439547865089632866510792L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
387 1.33243254708316144935164337949073577407L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
388 1.33604513820414577344262790437186975929L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
389 1.33966752405330300536003066972435257602L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
390 1.34329973118683526382421714618163087542L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
391 1.346941786232945835788173713229537282075L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
392 1.35059371589203439140852219606013396004L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
393 1.35425554693689272829801474014070280434L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
394 1.357927306212901046494536695671766697446L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
395 1.36160902063822475558553593883194147464L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
396 1.36530071720401181543069836033754285543L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
397 1.36900242297459061192960113298219283217L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
398 1.37271416508766836928499785714471721579L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
399 1.37643597075453010021632280551868696026L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
400 1.380167867260238095581945274358283464697L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
401 1.383909881963831954872659527265192818L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
402 1.387662042298529159042861017950775988896L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
403 1.39142437577192618714983552956624344668L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
404 1.395196909966200178275574599249220994716L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
405 1.398979672538311140209528136715194969206L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
406 1.40277269122020470637471352433337881711L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
407 1.40657599381901544248361973255451684411L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
408 1.410389608217270704414375128268675481145L,
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
409 1.41421356237309504880168872420969807857L
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
410 };
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
411
16576
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
412 return ldexpl (expl_table[128 + m] * exp_y, n);
6c7c671909d3 expl: Fix precision of computed result.
Bruno Haible <bruno@clisp.org>
parents: 16511
diff changeset
413 }
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
414 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
415
15937
16cba28a5e86 expl: Simplify for platforms where 'long double' == 'double'.
Bruno Haible <bruno@clisp.org>
parents: 14079
diff changeset
416 #endif