1 | /* origin: FreeBSD /usr/src/lib/msun/src/s_atanl.c */
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2 | /*
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3 | * ====================================================
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4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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5 | *
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6 | * Developed at SunPro, a Sun Microsystems, Inc. business.
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7 | * Permission to use, copy, modify, and distribute this
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8 | * software is freely granted, provided that this notice
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9 | * is preserved.
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10 | * ====================================================
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11 | */
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12 | /*
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13 | * See comments in atan.c.
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14 | * Converted to long double by David Schultz <das@FreeBSD.ORG>.
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15 | */
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16 |
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17 | #include "libm.h"
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18 |
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19 | #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
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20 | long double atanl(long double x)
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21 | {
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22 | return atan(x);
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23 | }
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24 | #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
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25 |
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26 | #if LDBL_MANT_DIG == 64
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27 | #define EXPMAN(u) ((u.i.se & 0x7fff)<<8 | (u.i.m>>55 & 0xff))
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28 |
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29 | static const long double atanhi[] = {
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30 | 4.63647609000806116202e-01L,
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31 | 7.85398163397448309628e-01L,
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32 | 9.82793723247329067960e-01L,
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33 | 1.57079632679489661926e+00L,
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34 | };
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35 |
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36 | static const long double atanlo[] = {
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37 | 1.18469937025062860669e-20L,
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38 | -1.25413940316708300586e-20L,
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39 | 2.55232234165405176172e-20L,
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40 | -2.50827880633416601173e-20L,
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41 | };
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42 |
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43 | static const long double aT[] = {
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44 | 3.33333333333333333017e-01L,
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45 | -1.99999999999999632011e-01L,
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46 | 1.42857142857046531280e-01L,
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47 | -1.11111111100562372733e-01L,
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48 | 9.09090902935647302252e-02L,
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49 | -7.69230552476207730353e-02L,
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50 | 6.66661718042406260546e-02L,
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51 | -5.88158892835030888692e-02L,
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52 | 5.25499891539726639379e-02L,
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53 | -4.70119845393155721494e-02L,
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54 | 4.03539201366454414072e-02L,
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55 | -2.91303858419364158725e-02L,
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56 | 1.24822046299269234080e-02L,
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57 | };
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58 |
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59 | static long double T_even(long double x)
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60 | {
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61 | return aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] +
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62 | x * (aT[8] + x * (aT[10] + x * aT[12])))));
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63 | }
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64 |
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65 | static long double T_odd(long double x)
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66 | {
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67 | return aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] +
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68 | x * (aT[9] + x * aT[11]))));
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69 | }
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70 | #elif LDBL_MANT_DIG == 113
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71 | #define EXPMAN(u) ((u.i.se & 0x7fff)<<8 | u.i.top>>8)
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72 |
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73 | const long double atanhi[] = {
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74 | 4.63647609000806116214256231461214397e-01L,
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75 | 7.85398163397448309615660845819875699e-01L,
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76 | 9.82793723247329067985710611014666038e-01L,
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77 | 1.57079632679489661923132169163975140e+00L,
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78 | };
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79 |
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80 | const long double atanlo[] = {
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81 | 4.89509642257333492668618435220297706e-36L,
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82 | 2.16795253253094525619926100651083806e-35L,
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83 | -2.31288434538183565909319952098066272e-35L,
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84 | 4.33590506506189051239852201302167613e-35L,
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85 | };
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86 |
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87 | const long double aT[] = {
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88 | 3.33333333333333333333333333333333125e-01L,
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89 | -1.99999999999999999999999999999180430e-01L,
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90 | 1.42857142857142857142857142125269827e-01L,
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91 | -1.11111111111111111111110834490810169e-01L,
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92 | 9.09090909090909090908522355708623681e-02L,
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93 | -7.69230769230769230696553844935357021e-02L,
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94 | 6.66666666666666660390096773046256096e-02L,
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95 | -5.88235294117646671706582985209643694e-02L,
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96 | 5.26315789473666478515847092020327506e-02L,
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97 | -4.76190476189855517021024424991436144e-02L,
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98 | 4.34782608678695085948531993458097026e-02L,
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99 | -3.99999999632663469330634215991142368e-02L,
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100 | 3.70370363987423702891250829918659723e-02L,
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101 | -3.44827496515048090726669907612335954e-02L,
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102 | 3.22579620681420149871973710852268528e-02L,
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103 | -3.03020767654269261041647570626778067e-02L,
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104 | 2.85641979882534783223403715930946138e-02L,
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105 | -2.69824879726738568189929461383741323e-02L,
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106 | 2.54194698498808542954187110873675769e-02L,
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107 | -2.35083879708189059926183138130183215e-02L,
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108 | 2.04832358998165364349957325067131428e-02L,
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109 | -1.54489555488544397858507248612362957e-02L,
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110 | 8.64492360989278761493037861575248038e-03L,
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111 | -2.58521121597609872727919154569765469e-03L,
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112 | };
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113 |
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114 | static long double T_even(long double x)
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115 | {
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116 | return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * (aT[8] +
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117 | x * (aT[10] + x * (aT[12] + x * (aT[14] + x * (aT[16] +
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118 | x * (aT[18] + x * (aT[20] + x * aT[22])))))))))));
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119 | }
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120 |
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121 | static long double T_odd(long double x)
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122 | {
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123 | return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * (aT[9] +
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124 | x * (aT[11] + x * (aT[13] + x * (aT[15] + x * (aT[17] +
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125 | x * (aT[19] + x * (aT[21] + x * aT[23])))))))))));
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126 | }
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127 | #endif
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128 |
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129 | long double atanl(long double x)
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130 | {
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131 | union ldshape u = {x};
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132 | long double w, s1, s2, z;
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133 | int id;
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134 | unsigned e = u.i.se & 0x7fff;
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135 | unsigned sign = u.i.se >> 15;
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136 | unsigned expman;
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137 |
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138 | if (e >= 0x3fff + LDBL_MANT_DIG + 1) { /* if |x| is large, atan(x)~=pi/2 */
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139 | if (isnan(x))
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140 | return x;
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141 | return sign ? -atanhi[3] : atanhi[3];
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142 | }
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143 | /* Extract the exponent and the first few bits of the mantissa. */
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144 | expman = EXPMAN(u);
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145 | if (expman < ((0x3fff - 2) << 8) + 0xc0) { /* |x| < 0.4375 */
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146 | if (e < 0x3fff - (LDBL_MANT_DIG+1)/2) { /* if |x| is small, atanl(x)~=x */
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147 | /* raise underflow if subnormal */
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148 | if (e == 0)
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149 | FORCE_EVAL((float)x);
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150 | return x;
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151 | }
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152 | id = -1;
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153 | } else {
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154 | x = fabsl(x);
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155 | if (expman < (0x3fff << 8) + 0x30) { /* |x| < 1.1875 */
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156 | if (expman < ((0x3fff - 1) << 8) + 0x60) { /* 7/16 <= |x| < 11/16 */
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157 | id = 0;
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158 | x = (2.0*x-1.0)/(2.0+x);
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159 | } else { /* 11/16 <= |x| < 19/16 */
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160 | id = 1;
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161 | x = (x-1.0)/(x+1.0);
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162 | }
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163 | } else {
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164 | if (expman < ((0x3fff + 1) << 8) + 0x38) { /* |x| < 2.4375 */
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165 | id = 2;
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166 | x = (x-1.5)/(1.0+1.5*x);
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167 | } else { /* 2.4375 <= |x| */
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168 | id = 3;
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169 | x = -1.0/x;
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170 | }
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171 | }
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172 | }
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173 | /* end of argument reduction */
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174 | z = x*x;
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175 | w = z*z;
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176 | /* break sum aT[i]z**(i+1) into odd and even poly */
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177 | s1 = z*T_even(w);
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178 | s2 = w*T_odd(w);
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179 | if (id < 0)
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180 | return x - x*(s1+s2);
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181 | z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
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182 | return sign ? -z : z;
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183 | }
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184 | #endif
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