1 | |
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2 | /* @(#)z_sineh.c 1.0 98/08/13 */ |
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3 | /****************************************************************** |
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4 | * The following routines are coded directly from the algorithms |
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5 | * and coefficients given in "Software Manual for the Elementary |
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6 | * Functions" by William J. Cody, Jr. and William Waite, Prentice |
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7 | * Hall, 1980. |
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8 | ******************************************************************/ |
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9 | |
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10 | /* |
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11 | FUNCTION |
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12 | <<sinh>>, <<sinhf>>, <<cosh>>, <<coshf>>, <<sineh>>---hyperbolic sine or cosine |
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13 | |
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14 | INDEX |
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15 | sinh |
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16 | INDEX |
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17 | sinhf |
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18 | INDEX |
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19 | cosh |
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20 | INDEX |
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21 | coshf |
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22 | |
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23 | SYNOPSIS |
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24 | #include <math.h> |
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25 | double sinh(double <[x]>); |
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26 | float sinhf(float <[x]>); |
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27 | double cosh(double <[x]>); |
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28 | float coshf(float <[x]>); |
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29 | |
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30 | DESCRIPTION |
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31 | <<sinh>> and <<cosh>> compute the hyperbolic sine or cosine |
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32 | of the argument <[x]>. |
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33 | Angles are specified in radians. <<sinh>>(<[x]>) is defined as |
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34 | @ifnottex |
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35 | . (exp(<[x]>) - exp(-<[x]>))/2 |
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36 | @end ifnottex |
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37 | @tex |
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38 | $${e^x - e^{-x}}\over 2$$ |
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39 | @end tex |
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40 | <<cosh>> is defined as |
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41 | @ifnottex |
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42 | . (exp(<[x]>) - exp(-<[x]>))/2 |
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43 | @end ifnottex |
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44 | @tex |
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45 | $${e^x + e^{-x}}\over 2$$ |
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46 | @end tex |
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47 | |
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48 | <<sinhf>> and <<coshf>> are identical, save that they take |
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49 | and returns <<float>> values. |
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50 | |
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51 | RETURNS |
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52 | The hyperbolic sine or cosine of <[x]> is returned. |
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53 | |
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54 | When the correct result is too large to be representable (an |
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55 | overflow), the functions return <<HUGE_VAL>> with the |
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56 | appropriate sign, and sets the global value <<errno>> to |
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57 | <<ERANGE>>. |
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58 | |
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59 | PORTABILITY |
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60 | <<sinh>> is ANSI C. |
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61 | <<sinhf>> is an extension. |
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62 | <<cosh>> is ANSI C. |
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63 | <<coshf>> is an extension. |
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64 | |
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65 | */ |
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66 | |
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67 | /****************************************************************** |
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68 | * Hyperbolic Sine |
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69 | * |
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70 | * Input: |
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71 | * x - floating point value |
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72 | * |
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73 | * Output: |
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74 | * hyperbolic sine of x |
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75 | * |
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76 | * Description: |
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77 | * This routine calculates hyperbolic sines. |
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78 | * |
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79 | *****************************************************************/ |
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80 | |
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81 | #include <float.h> |
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82 | #include "fdlibm.h" |
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83 | #include "zmath.h" |
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84 | |
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85 | static const double q[] = { -0.21108770058106271242e+7, |
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86 | 0.36162723109421836460e+5, |
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87 | -0.27773523119650701667e+3 }; |
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88 | static const double p[] = { -0.35181283430177117881e+6, |
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89 | -0.11563521196851768270e+5, |
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90 | -0.16375798202630751372e+3, |
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91 | -0.78966127417357099479 }; |
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92 | static const double LNV = 0.6931610107421875000; |
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93 | static const double INV_V2 = 0.24999308500451499336; |
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94 | static const double V_OVER2_MINUS1 = 0.13830277879601902638e-4; |
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95 | |
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96 | double |
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97 | sineh (double x, |
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98 | int cosineh) |
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99 | { |
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100 | double y, f, P, Q, R, res, z, w; |
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101 | int sgn = 1; |
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102 | double WBAR = 18.55; |
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103 | |
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104 | /* Check for special values. */ |
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105 | switch (numtest (x)) |
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106 | { |
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107 | case NAN: |
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108 | errno = EDOM; |
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109 | return (x); |
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110 | case INF: |
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111 | errno = ERANGE; |
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112 | return (ispos (x) ? z_infinity.d : -z_infinity.d); |
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113 | } |
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114 | |
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115 | y = fabs (x); |
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116 | |
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117 | if (!cosineh && x < 0.0) |
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118 | sgn = -1; |
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119 | |
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120 | if ((y > 1.0 && !cosineh) || cosineh) |
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121 | { |
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122 | if (y > BIGX) |
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123 | { |
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124 | w = y - LNV; |
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125 | |
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126 | /* Check for w > maximum here. */ |
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127 | if (w > BIGX) |
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128 | { |
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129 | errno = ERANGE; |
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130 | return (x); |
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131 | } |
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132 | |
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133 | z = exp (w); |
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134 | |
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135 | if (w > WBAR) |
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136 | res = z * (V_OVER2_MINUS1 + 1.0); |
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137 | } |
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138 | |
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139 | else |
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140 | { |
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141 | z = exp (y); |
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142 | if (cosineh) |
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143 | res = (z + 1 / z) / 2.0; |
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144 | else |
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145 | res = (z - 1 / z) / 2.0; |
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146 | } |
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147 | |
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148 | if (sgn < 0) |
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149 | res = -res; |
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150 | } |
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151 | else |
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152 | { |
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153 | /* Check for y being too small. */ |
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154 | if (y < z_rooteps) |
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155 | { |
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156 | res = x; |
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157 | } |
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158 | /* Calculate the Taylor series. */ |
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159 | else |
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160 | { |
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161 | f = x * x; |
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162 | Q = ((f + q[2]) * f + q[1]) * f + q[0]; |
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163 | P = ((p[3] * f + p[2]) * f + p[1]) * f + p[0]; |
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164 | R = f * (P / Q); |
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165 | |
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166 | res = x + x * R; |
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167 | } |
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168 | } |
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169 | |
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170 | return (res); |
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171 | } |
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