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annotate lib/tanl.c @ 10001:facc928673d7

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Declare rpmatch.
author Bruno Haible <bruno@clisp.org>
date Tue, 29 Apr 2008 02:55:59 +0200
parents 810b08d769f8
children 678640901735
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1 /* s_tanl.c -- long double version of s_tan.c.
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2 * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
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3 */
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4
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5 /* @(#)s_tan.c 5.1 93/09/24 */
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6 /*
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7 * ====================================================
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8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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9 *
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10 * Developed at SunPro, a Sun Microsystems, Inc. business.
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11 * Permission to use, copy, modify, and distribute this
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12 * software is freely granted, provided that this notice
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13 * is preserved.
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14 * ====================================================
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15 */
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16
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17 #include <config.h>
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18
c115624bf99a New module 'math'. <math.h> replaces mathl.h.
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19 /* Specification. */
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20 #include <math.h>
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21
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22 /* tanl(x)
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23 * Return tangent function of x.
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24 *
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25 * kernel function:
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26 * __kernel_tanl ... tangent function on [-pi/4,pi/4]
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27 * __ieee754_rem_pio2l ... argument reduction routine
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28 *
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29 * Method.
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30 * Let S,C and T denote the sin, cos and tan respectively on
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31 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
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32 * in [-pi/4 , +pi/4], and let n = k mod 4.
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33 * We have
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34 *
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35 * n sin(x) cos(x) tan(x)
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36 * ----------------------------------------------------------
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37 * 0 S C T
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38 * 1 C -S -1/T
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39 * 2 -S -C T
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40 * 3 -C S -1/T
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41 * ----------------------------------------------------------
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42 *
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43 * Special cases:
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44 * Let trig be any of sin, cos, or tan.
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45 * trig(+-INF) is NaN, with signals;
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46 * trig(NaN) is that NaN;
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47 *
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48 * Accuracy:
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49 * TRIG(x) returns trig(x) nearly rounded
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50 */
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51
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52 #include "trigl.h"
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53 #ifdef HAVE_SINL
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54 #ifdef HAVE_COSL
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55 #include "trigl.c"
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56 #endif
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57 #endif
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c3d334708928 Better support of signalling NaNs.
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58 #include "isnanl.h"
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59
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60 /*
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61 * ====================================================
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62 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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63 *
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64 * Developed at SunPro, a Sun Microsystems, Inc. business.
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65 * Permission to use, copy, modify, and distribute this
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66 * software is freely granted, provided that this notice
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67 * is preserved.
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68 * ====================================================
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69 */
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70
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71 /*
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72 Long double expansions contributed by
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73 Stephen L. Moshier <moshier@na-net.ornl.gov>
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74 */
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75
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76 /* __kernel_tanl( x, y, k )
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77 * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
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78 * Input x is assumed to be bounded by ~pi/4 in magnitude.
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79 * Input y is the tail of x.
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80 * Input k indicates whether tan (if k=1) or
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81 * -1/tan (if k= -1) is returned.
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82 *
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83 * Algorithm
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84 * 1. Since tan(-x) = -tan(x), we need only to consider positive x.
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85 * 2. if x < 2^-57, return x with inexact if x!=0.
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86 * 3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2)
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87 * on [0,0.67433].
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88 *
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89 * Note: tan(x+y) = tan(x) + tan'(x)*y
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90 * ~ tan(x) + (1+x*x)*y
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91 * Therefore, for better accuracy in computing tan(x+y), let
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92 * r = x^3 * R(x^2)
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93 * then
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94 * tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y))
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95 *
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96 * 4. For x in [0.67433,pi/4], let y = pi/4 - x, then
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97 * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
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98 * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
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99 */
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100
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101
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102 static const long double
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103 pio4hi = 7.8539816339744830961566084581987569936977E-1L,
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104 pio4lo = 2.1679525325309452561992610065108379921906E-35L,
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105
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106 /* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2)
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107 0 <= x <= 0.6743316650390625
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108 Peak relative error 8.0e-36 */
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109 TH = 3.333333333333333333333333333333333333333E-1L,
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110 T0 = -1.813014711743583437742363284336855889393E7L,
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111 T1 = 1.320767960008972224312740075083259247618E6L,
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112 T2 = -2.626775478255838182468651821863299023956E4L,
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113 T3 = 1.764573356488504935415411383687150199315E2L,
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114 T4 = -3.333267763822178690794678978979803526092E-1L,
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115
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116 U0 = -1.359761033807687578306772463253710042010E8L,
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117 U1 = 6.494370630656893175666729313065113194784E7L,
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118 U2 = -4.180787672237927475505536849168729386782E6L,
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119 U3 = 8.031643765106170040139966622980914621521E4L,
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120 U4 = -5.323131271912475695157127875560667378597E2L;
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121 /* 1.000000000000000000000000000000000000000E0 */
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122
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123
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124 long double
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125 kernel_tanl (long double x, long double y, int iy)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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diff changeset
126 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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127 long double z, r, v, w, s, u, u1;
9923
810b08d769f8 fix typos in mathl
Paolo Bonzini <bonzini@gnu.org>
parents: 8563
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128 int invert = 0, sign;
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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129
8544
245a3653b197 Fix indentation.
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130 sign = 1;
245a3653b197 Fix indentation.
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131 if (x < 0)
245a3653b197 Fix indentation.
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132 {
245a3653b197 Fix indentation.
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133 x = -x;
245a3653b197 Fix indentation.
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134 y = -y;
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135 sign = -1;
245a3653b197 Fix indentation.
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136 }
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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137
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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138 if (x < 0.000000000000000006938893903907228377647697925567626953125L) /* x < 2**-57 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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parents:
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139 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
140 if ((int) x == 0)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
141 { /* generate inexact */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
142 if (iy == -1 && x == 0.0)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
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143 return 1.0L / fabs (x);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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diff changeset
144 else
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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145 return (iy == 1) ? x : -1.0L / x;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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146 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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diff changeset
147 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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diff changeset
148 if (x >= 0.6743316650390625) /* |x| >= 0.6743316650390625 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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149 {
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810b08d769f8 fix typos in mathl
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parents: 8563
diff changeset
150 invert = 1;
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b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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diff changeset
151
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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diff changeset
152 z = pio4hi - x;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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diff changeset
153 w = pio4lo - y;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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154 x = z + w;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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155 y = 0.0;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
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156 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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157 z = x * x;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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158 r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4)));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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159 v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z))));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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160 r = r / v;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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diff changeset
161
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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162 s = z * x;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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163 r = y + z * (s * r + y);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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164 r += TH * s;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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165 w = x + r;
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Paolo Bonzini <bonzini@gnu.org>
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diff changeset
166 if (invert)
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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167 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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168 v = (long double) iy;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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169 w = (v - 2.0 * (x - (w * w / (w + v) - r)));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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170 if (sign < 0)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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171 w = -w;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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172 return w;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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173 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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174 if (iy == 1)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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175 return w;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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176 else
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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diff changeset
177 { /* if allow error up to 2 ulp,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
178 simply return -1.0/(x+r) here */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
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179 /* compute -1.0/(x+r) accurately */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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180 u1 = (double) w;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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181 v = r - (u1 - x);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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182 z = -1.0 / w;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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183 u = (double) z;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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184 s = 1.0 + u * u1;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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parents:
diff changeset
185 return u + z * (s + u * v);
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diff changeset
186 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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diff changeset
187 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
188
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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189 long double
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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190 tanl (long double x)
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Bruno Haible <bruno@clisp.org>
parents:
diff changeset
191 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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diff changeset
192 long double y[2], z = 0.0L;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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diff changeset
193 int n;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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194
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195 /* tanl(NaN) is NaN */
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196 if (isnanl (x))
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197 return x;
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diff changeset
198
4239
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199 /* |x| ~< pi/4 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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diff changeset
200 if (x >= -0.7853981633974483096156608458198757210492 &&
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
201 x <= 0.7853981633974483096156608458198757210492)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
202 return kernel_tanl (x, z, 1);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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parents:
diff changeset
203
8563
c3d334708928 Better support of signalling NaNs.
Bruno Haible <bruno@clisp.org>
parents: 8544
diff changeset
204 /* tanl(Inf) is NaN, tanl(0) is 0 */
c3d334708928 Better support of signalling NaNs.
Bruno Haible <bruno@clisp.org>
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diff changeset
205 else if (x + x == x)
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
206 return x - x; /* NaN */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
207
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
208 /* argument reduction needed */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
209 else
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
210 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
211 n = ieee754_rem_pio2l (x, y);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
212 /* 1 -- n even, -1 -- n odd */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
213 return kernel_tanl (y[0], y[1], 1 - ((n & 1) << 1));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
214 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
215 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
216
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
217 #if 0
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
218 int
4652
b09c3f1225b6 Remove K&R cruft.
Paul Eggert <eggert@cs.ucla.edu>
parents: 4239
diff changeset
219 main (void)
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
220 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
221 printf ("%.16Lg\n", tanl(0.7853981633974483096156608458198757210492));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
222 printf ("%.16Lg\n", tanl(-0.7853981633974483096156608458198757210492));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
223 printf ("%.16Lg\n", tanl(0.7853981633974483096156608458198757210492 *3));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
224 printf ("%.16Lg\n", tanl(-0.7853981633974483096156608458198757210492 *31));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
225 printf ("%.16Lg\n", tanl(0.7853981633974483096156608458198757210492 / 2));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
226 printf ("%.16Lg\n", tanl(0.7853981633974483096156608458198757210492 * 3/2));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
227 printf ("%.16Lg\n", tanl(0.7853981633974483096156608458198757210492 * 5/2));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
228 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
229 #endif