Mercurial > cpython-lru_cache-weakref

annotate Modules/cmathmodule.c @ 58973:db86bf39ccaa legacy-trunk

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Issue 7970: When email.Parser.Parser parses a MIME message of type message/rfc822 it turns it into an object whose body consists of a list containing a single Message object. HeaderParser, on the other hand, just copies the body as a string. Generator.flatten has a special handler for the message mime type that expected the body to be the one item list. This fails if the message was parsed by HeaderParser. So we now check to see if the body is a string first, and if so just we just emit it.
author R. David Murray <rdmurray@bitdance.com>
date Sun, 21 Feb 2010 04:23:00 +0000
parents 7f5cbc28f433
children fd25030223b0
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1 /* Complex math module */
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2
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3 /* much code borrowed from mathmodule.c */
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4
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5 #include "Python.h"
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6 #include "_math.h"
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7 /* we need DBL_MAX, DBL_MIN, DBL_EPSILON, DBL_MANT_DIG and FLT_RADIX from
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8 float.h. We assume that FLT_RADIX is either 2 or 16. */
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9 #include <float.h>
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10
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11 #if (FLT_RADIX != 2 && FLT_RADIX != 16)
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12 #error "Modules/cmathmodule.c expects FLT_RADIX to be 2 or 16"
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13 #endif
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14
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15 #ifndef M_LN2
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16 #define M_LN2 (0.6931471805599453094) /* natural log of 2 */
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17 #endif
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18
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19 #ifndef M_LN10
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20 #define M_LN10 (2.302585092994045684) /* natural log of 10 */
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21 #endif
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22
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23 /*
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24 CM_LARGE_DOUBLE is used to avoid spurious overflow in the sqrt, log,
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25 inverse trig and inverse hyperbolic trig functions. Its log is used in the
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26 evaluation of exp, cos, cosh, sin, sinh, tan, and tanh to avoid unecessary
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27 overflow.
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28 */
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29
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30 #define CM_LARGE_DOUBLE (DBL_MAX/4.)
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31 #define CM_SQRT_LARGE_DOUBLE (sqrt(CM_LARGE_DOUBLE))
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32 #define CM_LOG_LARGE_DOUBLE (log(CM_LARGE_DOUBLE))
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33 #define CM_SQRT_DBL_MIN (sqrt(DBL_MIN))
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34
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35 /*
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36 CM_SCALE_UP is an odd integer chosen such that multiplication by
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37 2**CM_SCALE_UP is sufficient to turn a subnormal into a normal.
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38 CM_SCALE_DOWN is (-(CM_SCALE_UP+1)/2). These scalings are used to compute
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39 square roots accurately when the real and imaginary parts of the argument
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40 are subnormal.
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41 */
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42
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43 #if FLT_RADIX==2
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44 #define CM_SCALE_UP (2*(DBL_MANT_DIG/2) + 1)
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45 #elif FLT_RADIX==16
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46 #define CM_SCALE_UP (4*DBL_MANT_DIG+1)
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47 #endif
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48 #define CM_SCALE_DOWN (-(CM_SCALE_UP+1)/2)
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49
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50 /* forward declarations */
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51 static Py_complex c_asinh(Py_complex);
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52 static Py_complex c_atanh(Py_complex);
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53 static Py_complex c_cosh(Py_complex);
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54 static Py_complex c_sinh(Py_complex);
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55 static Py_complex c_sqrt(Py_complex);
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56 static Py_complex c_tanh(Py_complex);
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57 static PyObject * math_error(void);
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58
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59 /* Code to deal with special values (infinities, NaNs, etc.). */
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60
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61 /* special_type takes a double and returns an integer code indicating
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62 the type of the double as follows:
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63 */
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64
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65 enum special_types {
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66 ST_NINF, /* 0, negative infinity */
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67 ST_NEG, /* 1, negative finite number (nonzero) */
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68 ST_NZERO, /* 2, -0. */
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69 ST_PZERO, /* 3, +0. */
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70 ST_POS, /* 4, positive finite number (nonzero) */
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71 ST_PINF, /* 5, positive infinity */
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72 ST_NAN /* 6, Not a Number */
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73 };
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74
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75 static enum special_types
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76 special_type(double d)
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77 {
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78 if (Py_IS_FINITE(d)) {
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79 if (d != 0) {
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80 if (copysign(1., d) == 1.)
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81 return ST_POS;
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82 else
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83 return ST_NEG;
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84 }
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85 else {
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86 if (copysign(1., d) == 1.)
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87 return ST_PZERO;
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88 else
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89 return ST_NZERO;
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90 }
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91 }
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92 if (Py_IS_NAN(d))
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93 return ST_NAN;
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94 if (copysign(1., d) == 1.)
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95 return ST_PINF;
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96 else
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97 return ST_NINF;
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98 }
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99
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100 #define SPECIAL_VALUE(z, table) \
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101 if (!Py_IS_FINITE((z).real) || !Py_IS_FINITE((z).imag)) { \
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102 errno = 0; \
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103 return table[special_type((z).real)] \
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104 [special_type((z).imag)]; \
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105 }
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106
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107 #define P Py_MATH_PI
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108 #define P14 0.25*Py_MATH_PI
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109 #define P12 0.5*Py_MATH_PI
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110 #define P34 0.75*Py_MATH_PI
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111 #define INF Py_HUGE_VAL
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112 #define N Py_NAN
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113 #define U -9.5426319407711027e33 /* unlikely value, used as placeholder */
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114
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115 /* First, the C functions that do the real work. Each of the c_*
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116 functions computes and returns the C99 Annex G recommended result
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117 and also sets errno as follows: errno = 0 if no floating-point
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118 exception is associated with the result; errno = EDOM if C99 Annex
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119 G recommends raising divide-by-zero or invalid for this result; and
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120 errno = ERANGE where the overflow floating-point signal should be
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121 raised.
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122 */
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123
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124 static Py_complex acos_special_values[7][7];
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125
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126 static Py_complex
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127 c_acos(Py_complex z)
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128 {
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129 Py_complex s1, s2, r;
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130
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131 SPECIAL_VALUE(z, acos_special_values);
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132
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133 if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) {
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134 /* avoid unnecessary overflow for large arguments */
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135 r.real = atan2(fabs(z.imag), z.real);
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136 /* split into cases to make sure that the branch cut has the
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137 correct continuity on systems with unsigned zeros */
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138 if (z.real < 0.) {
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139 r.imag = -copysign(log(hypot(z.real/2., z.imag/2.)) +
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140 M_LN2*2., z.imag);
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141 } else {
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142 r.imag = copysign(log(hypot(z.real/2., z.imag/2.)) +
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143 M_LN2*2., -z.imag);
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144 }
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145 } else {
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146 s1.real = 1.-z.real;
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147 s1.imag = -z.imag;
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148 s1 = c_sqrt(s1);
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149 s2.real = 1.+z.real;
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150 s2.imag = z.imag;
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151 s2 = c_sqrt(s2);
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152 r.real = 2.*atan2(s1.real, s2.real);
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153 r.imag = m_asinh(s2.real*s1.imag - s2.imag*s1.real);
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154 }
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155 errno = 0;
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156 return r;
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157 }
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158
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159 PyDoc_STRVAR(c_acos_doc,
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160 "acos(x)\n"
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161 "\n"
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162 "Return the arc cosine of x.");
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163
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164
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165 static Py_complex acosh_special_values[7][7];
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166
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167 static Py_complex
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168 c_acosh(Py_complex z)
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169 {
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170 Py_complex s1, s2, r;
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171
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172 SPECIAL_VALUE(z, acosh_special_values);
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173
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174 if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) {
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175 /* avoid unnecessary overflow for large arguments */
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176 r.real = log(hypot(z.real/2., z.imag/2.)) + M_LN2*2.;
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177 r.imag = atan2(z.imag, z.real);
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178 } else {
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179 s1.real = z.real - 1.;
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180 s1.imag = z.imag;
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181 s1 = c_sqrt(s1);
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182 s2.real = z.real + 1.;
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183 s2.imag = z.imag;
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184 s2 = c_sqrt(s2);
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185 r.real = m_asinh(s1.real*s2.real + s1.imag*s2.imag);
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186 r.imag = 2.*atan2(s1.imag, s2.real);
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187 }
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188 errno = 0;
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189 return r;
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190 }
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191
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192 PyDoc_STRVAR(c_acosh_doc,
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193 "acosh(x)\n"
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194 "\n"
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195 "Return the hyperbolic arccosine of x.");
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196
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197
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198 static Py_complex
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199 c_asin(Py_complex z)
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200 {
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201 /* asin(z) = -i asinh(iz) */
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202 Py_complex s, r;
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203 s.real = -z.imag;
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204 s.imag = z.real;
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205 s = c_asinh(s);
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206 r.real = s.imag;
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207 r.imag = -s.real;
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208 return r;
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209 }
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210
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211 PyDoc_STRVAR(c_asin_doc,
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212 "asin(x)\n"
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213 "\n"
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214 "Return the arc sine of x.");
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215
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216
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217 static Py_complex asinh_special_values[7][7];
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218
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219 static Py_complex
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220 c_asinh(Py_complex z)
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221 {
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222 Py_complex s1, s2, r;
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223
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224 SPECIAL_VALUE(z, asinh_special_values);
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225
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226 if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) {
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227 if (z.imag >= 0.) {
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228 r.real = copysign(log(hypot(z.real/2., z.imag/2.)) +
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229 M_LN2*2., z.real);
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230 } else {
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231 r.real = -copysign(log(hypot(z.real/2., z.imag/2.)) +
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232 M_LN2*2., -z.real);
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233 }
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234 r.imag = atan2(z.imag, fabs(z.real));
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235 } else {
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236 s1.real = 1.+z.imag;
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237 s1.imag = -z.real;
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238 s1 = c_sqrt(s1);
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239 s2.real = 1.-z.imag;
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240 s2.imag = z.real;
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241 s2 = c_sqrt(s2);
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242 r.real = m_asinh(s1.real*s2.imag-s2.real*s1.imag);
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243 r.imag = atan2(z.imag, s1.real*s2.real-s1.imag*s2.imag);
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244 }
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245 errno = 0;
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246 return r;
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247 }
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248
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249 PyDoc_STRVAR(c_asinh_doc,
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250 "asinh(x)\n"
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251 "\n"
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252 "Return the hyperbolic arc sine of x.");
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253
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254
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255 static Py_complex
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256 c_atan(Py_complex z)
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257 {
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258 /* atan(z) = -i atanh(iz) */
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259 Py_complex s, r;
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260 s.real = -z.imag;
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261 s.imag = z.real;
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262 s = c_atanh(s);
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263 r.real = s.imag;
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264 r.imag = -s.real;
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265 return r;
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266 }
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267
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268 /* Windows screws up atan2 for inf and nan, and alpha Tru64 5.1 doesn't follow
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269 C99 for atan2(0., 0.). */
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270 static double
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271 c_atan2(Py_complex z)
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272 {
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273 if (Py_IS_NAN(z.real) || Py_IS_NAN(z.imag))
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274 return Py_NAN;
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275 if (Py_IS_INFINITY(z.imag)) {
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276 if (Py_IS_INFINITY(z.real)) {
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277 if (copysign(1., z.real) == 1.)
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278 /* atan2(+-inf, +inf) == +-pi/4 */
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279 return copysign(0.25*Py_MATH_PI, z.imag);
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280 else
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281 /* atan2(+-inf, -inf) == +-pi*3/4 */
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282 return copysign(0.75*Py_MATH_PI, z.imag);
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283 }
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284 /* atan2(+-inf, x) == +-pi/2 for finite x */
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285 return copysign(0.5*Py_MATH_PI, z.imag);
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286 }
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287 if (Py_IS_INFINITY(z.real) || z.imag == 0.) {
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288 if (copysign(1., z.real) == 1.)
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289 /* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
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290 return copysign(0., z.imag);
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291 else
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292 /* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
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293 return copysign(Py_MATH_PI, z.imag);
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294 }
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295 return atan2(z.imag, z.real);
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296 }
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297
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298 PyDoc_STRVAR(c_atan_doc,
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299 "atan(x)\n"
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300 "\n"
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301 "Return the arc tangent of x.");
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302
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303
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304 static Py_complex atanh_special_values[7][7];
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305
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306 static Py_complex
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307 c_atanh(Py_complex z)
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308 {
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309 Py_complex r;
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310 double ay, h;
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311
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312 SPECIAL_VALUE(z, atanh_special_values);
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313
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314 /* Reduce to case where z.real >= 0., using atanh(z) = -atanh(-z). */
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315 if (z.real < 0.) {
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316 return c_neg(c_atanh(c_neg(z)));
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317 }
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318
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319 ay = fabs(z.imag);
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320 if (z.real > CM_SQRT_LARGE_DOUBLE || ay > CM_SQRT_LARGE_DOUBLE) {
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321 /*
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322 if abs(z) is large then we use the approximation
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323 atanh(z) ~ 1/z +/- i*pi/2 (+/- depending on the sign
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324 of z.imag)
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325 */
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326 h = hypot(z.real/2., z.imag/2.); /* safe from overflow */
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327 r.real = z.real/4./h/h;
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328 /* the two negations in the next line cancel each other out
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329 except when working with unsigned zeros: they're there to
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330 ensure that the branch cut has the correct continuity on
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331 systems that don't support signed zeros */
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332 r.imag = -copysign(Py_MATH_PI/2., -z.imag);
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333 errno = 0;
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334 } else if (z.real == 1. && ay < CM_SQRT_DBL_MIN) {
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335 /* C99 standard says: atanh(1+/-0.) should be inf +/- 0i */
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336 if (ay == 0.) {
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337 r.real = INF;
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338 r.imag = z.imag;
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339 errno = EDOM;
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340 } else {
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341 r.real = -log(sqrt(ay)/sqrt(hypot(ay, 2.)));
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342 r.imag = copysign(atan2(2., -ay)/2, z.imag);
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343 errno = 0;
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344 }
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345 } else {
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346 r.real = m_log1p(4.*z.real/((1-z.real)*(1-z.real) + ay*ay))/4.;
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347 r.imag = -atan2(-2.*z.imag, (1-z.real)*(1+z.real) - ay*ay)/2.;
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348 errno = 0;
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349 }
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350 return r;
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351 }
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352
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353 PyDoc_STRVAR(c_atanh_doc,
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354 "atanh(x)\n"
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355 "\n"
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356 "Return the hyperbolic arc tangent of x.");
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357
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358
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359 static Py_complex
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360 c_cos(Py_complex z)
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361 {
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362 /* cos(z) = cosh(iz) */
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363 Py_complex r;
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364 r.real = -z.imag;
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365 r.imag = z.real;
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366 r = c_cosh(r);
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367 return r;
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368 }
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369
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370 PyDoc_STRVAR(c_cos_doc,
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371 "cos(x)\n"
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372 "\n"
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373 "Return the cosine of x.");
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374
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375
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376 /* cosh(infinity + i*y) needs to be dealt with specially */
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377 static Py_complex cosh_special_values[7][7];
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378
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379 static Py_complex
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380 c_cosh(Py_complex z)
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381 {
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382 Py_complex r;
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383 double x_minus_one;
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384
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385 /* special treatment for cosh(+/-inf + iy) if y is not a NaN */
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386 if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
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387 if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag) &&
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388 (z.imag != 0.)) {
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389 if (z.real > 0) {
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390 r.real = copysign(INF, cos(z.imag));
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391 r.imag = copysign(INF, sin(z.imag));
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392 }
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393 else {
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394 r.real = copysign(INF, cos(z.imag));
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395 r.imag = -copysign(INF, sin(z.imag));
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396 }
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397 }
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398 else {
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399 r = cosh_special_values[special_type(z.real)]
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400 [special_type(z.imag)];
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401 }
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402 /* need to set errno = EDOM if y is +/- infinity and x is not
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403 a NaN */
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404 if (Py_IS_INFINITY(z.imag) && !Py_IS_NAN(z.real))
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405 errno = EDOM;
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406 else
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407 errno = 0;
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408 return r;
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409 }
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410
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411 if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
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412 /* deal correctly with cases where cosh(z.real) overflows but
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413 cosh(z) does not. */
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414 x_minus_one = z.real - copysign(1., z.real);
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415 r.real = cos(z.imag) * cosh(x_minus_one) * Py_MATH_E;
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416 r.imag = sin(z.imag) * sinh(x_minus_one) * Py_MATH_E;
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417 } else {
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418 r.real = cos(z.imag) * cosh(z.real);
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419 r.imag = sin(z.imag) * sinh(z.real);
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420 }
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421 /* detect overflow, and set errno accordingly */
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422 if (Py_IS_INFINITY(r.real) || Py_IS_INFINITY(r.imag))
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423 errno = ERANGE;
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424 else
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425 errno = 0;
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426 return r;
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427 }
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428
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429 PyDoc_STRVAR(c_cosh_doc,
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430 "cosh(x)\n"
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431 "\n"
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432 "Return the hyperbolic cosine of x.");
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433
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434
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435 /* exp(infinity + i*y) and exp(-infinity + i*y) need special treatment for
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436 finite y */
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437 static Py_complex exp_special_values[7][7];
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438
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439 static Py_complex
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440 c_exp(Py_complex z)
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441 {
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442 Py_complex r;
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443 double l;
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444
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445 if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
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446 if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
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447 && (z.imag != 0.)) {
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448 if (z.real > 0) {
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449 r.real = copysign(INF, cos(z.imag));
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450 r.imag = copysign(INF, sin(z.imag));
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451 }
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452 else {
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453 r.real = copysign(0., cos(z.imag));
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454 r.imag = copysign(0., sin(z.imag));
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455 }
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456 }
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457 else {
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458 r = exp_special_values[special_type(z.real)]
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459 [special_type(z.imag)];
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460 }
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461 /* need to set errno = EDOM if y is +/- infinity and x is not
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462 a NaN and not -infinity */
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463 if (Py_IS_INFINITY(z.imag) &&
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464 (Py_IS_FINITE(z.real) ||
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465 (Py_IS_INFINITY(z.real) && z.real > 0)))
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466 errno = EDOM;
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467 else
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468 errno = 0;
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469 return r;
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470 }
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471
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472 if (z.real > CM_LOG_LARGE_DOUBLE) {
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473 l = exp(z.real-1.);
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474 r.real = l*cos(z.imag)*Py_MATH_E;
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475 r.imag = l*sin(z.imag)*Py_MATH_E;
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476 } else {
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477 l = exp(z.real);
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478 r.real = l*cos(z.imag);
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479 r.imag = l*sin(z.imag);
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480 }
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481 /* detect overflow, and set errno accordingly */
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482 if (Py_IS_INFINITY(r.real) || Py_IS_INFINITY(r.imag))
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483 errno = ERANGE;
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484 else
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485 errno = 0;
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486 return r;
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487 }
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488
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489 PyDoc_STRVAR(c_exp_doc,
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490 "exp(x)\n"
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491 "\n"
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492 "Return the exponential value e**x.");
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493
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494
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495 static Py_complex log_special_values[7][7];
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496
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497 static Py_complex
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498 c_log(Py_complex z)
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499 {
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500 /*
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501 The usual formula for the real part is log(hypot(z.real, z.imag)).
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502 There are four situations where this formula is potentially
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503 problematic:
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504
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505 (1) the absolute value of z is subnormal. Then hypot is subnormal,
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506 so has fewer than the usual number of bits of accuracy, hence may
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507 have large relative error. This then gives a large absolute error
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508 in the log. This can be solved by rescaling z by a suitable power
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parents: 36324
diff changeset
509 of 2.
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parents: 36324
diff changeset
510
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511 (2) the absolute value of z is greater than DBL_MAX (e.g. when both
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512 z.real and z.imag are within a factor of 1/sqrt(2) of DBL_MAX)
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diff changeset
513 Again, rescaling solves this.
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parents: 36324
diff changeset
514
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515 (3) the absolute value of z is close to 1. In this case it's
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516 difficult to achieve good accuracy, at least in part because a
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517 change of 1ulp in the real or imaginary part of z can result in a
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518 change of billions of ulps in the correctly rounded answer.
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diff changeset
519
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520 (4) z = 0. The simplest thing to do here is to call the
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521 floating-point log with an argument of 0, and let its behaviour
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522 (returning -infinity, signaling a floating-point exception, setting
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523 errno, or whatever) determine that of c_log. So the usual formula
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diff changeset
524 is fine here.
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525
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526 */
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527
3771
d0988318b756 complex -> Py_complex
Guido van Rossum <guido@python.org>
parents: 3615
diff changeset
528 Py_complex r;
46477
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diff changeset
529 double ax, ay, am, an, h;
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530
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531 SPECIAL_VALUE(z, log_special_values);
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532
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diff changeset
533 ax = fabs(z.real);
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diff changeset
534 ay = fabs(z.imag);
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535
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diff changeset
536 if (ax > CM_LARGE_DOUBLE || ay > CM_LARGE_DOUBLE) {
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diff changeset
537 r.real = log(hypot(ax/2., ay/2.)) + M_LN2;
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parents: 36324
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538 } else if (ax < DBL_MIN && ay < DBL_MIN) {
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parents: 36324
diff changeset
539 if (ax > 0. || ay > 0.) {
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540 /* catch cases where hypot(ax, ay) is subnormal */
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parents: 36324
diff changeset
541 r.real = log(hypot(ldexp(ax, DBL_MANT_DIG),
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
542 ldexp(ay, DBL_MANT_DIG))) - DBL_MANT_DIG*M_LN2;
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543 }
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544 else {
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parents: 36324
diff changeset
545 /* log(+/-0. +/- 0i) */
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546 r.real = -INF;
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547 r.imag = atan2(z.imag, z.real);
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548 errno = EDOM;
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549 return r;
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550 }
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Christian Heimes <christian@cheimes.de>
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551 } else {
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552 h = hypot(ax, ay);
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553 if (0.71 <= h && h <= 1.73) {
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554 am = ax > ay ? ax : ay; /* max(ax, ay) */
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555 an = ax > ay ? ay : ax; /* min(ax, ay) */
57864
7f5cbc28f433 Issue #7518: Move substitute definitions of C99 math functions from
Mark Dickinson <dickinsm@gmail.com>
parents: 55539
diff changeset
556 r.real = m_log1p((am-1)*(am+1)+an*an)/2.;
46477
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557 } else {
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558 r.real = log(h);
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559 }
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560 }
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561 r.imag = atan2(z.imag, z.real);
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562 errno = 0;
3334
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Guido van Rossum <guido@python.org>
parents:
diff changeset
563 return r;
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
564 }
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
565
9593
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
566
16707
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
567 static Py_complex
46477
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568 c_log10(Py_complex z)
3334
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Guido van Rossum <guido@python.org>
parents:
diff changeset
569 {
3771
d0988318b756 complex -> Py_complex
Guido van Rossum <guido@python.org>
parents: 3615
diff changeset
570 Py_complex r;
46477
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571 int errno_save;
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572
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573 r = c_log(z);
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parents: 36324
diff changeset
574 errno_save = errno; /* just in case the divisions affect errno */
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575 r.real = r.real / M_LN10;
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576 r.imag = r.imag / M_LN10;
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577 errno = errno_save;
3334
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Guido van Rossum <guido@python.org>
parents:
diff changeset
578 return r;
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
579 }
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
580
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 22722
diff changeset
581 PyDoc_STRVAR(c_log10_doc,
16707
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
582 "log10(x)\n"
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
583 "\n"
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 22722
diff changeset
584 "Return the base-10 logarithm of x.");
9593
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
585
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
586
16707
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
587 static Py_complex
46477
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diff changeset
588 c_sin(Py_complex z)
3334
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Guido van Rossum <guido@python.org>
parents:
diff changeset
589 {
46477
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diff changeset
590 /* sin(z) = -i sin(iz) */
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
591 Py_complex s, r;
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diff changeset
592 s.real = -z.imag;
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parents: 36324
diff changeset
593 s.imag = z.real;
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parents: 36324
diff changeset
594 s = c_sinh(s);
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parents: 36324
diff changeset
595 r.real = s.imag;
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diff changeset
596 r.imag = -s.real;
3334
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Guido van Rossum <guido@python.org>
parents:
diff changeset
597 return r;
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
598 }
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
599
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 22722
diff changeset
600 PyDoc_STRVAR(c_sin_doc,
16707
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
601 "sin(x)\n"
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
602 "\n"
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 22722
diff changeset
603 "Return the sine of x.");
9593
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
604
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
605
46477
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diff changeset
606 /* sinh(infinity + i*y) needs to be dealt with specially */
46505
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parents: 46477
diff changeset
607 static Py_complex sinh_special_values[7][7];
46477
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608
16707
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
609 static Py_complex
46477
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diff changeset
610 c_sinh(Py_complex z)
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
611 {
3771
d0988318b756 complex -> Py_complex
Guido van Rossum <guido@python.org>
parents: 3615
diff changeset
612 Py_complex r;
46477
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parents: 36324
diff changeset
613 double x_minus_one;
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
614
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parents: 36324
diff changeset
615 /* special treatment for sinh(+/-inf + iy) if y is finite and
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parents: 36324
diff changeset
616 nonzero */
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parents: 36324
diff changeset
617 if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
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618 if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
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parents: 36324
diff changeset
619 && (z.imag != 0.)) {
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parents: 36324
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620 if (z.real > 0) {
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parents: 36324
diff changeset
621 r.real = copysign(INF, cos(z.imag));
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diff changeset
622 r.imag = copysign(INF, sin(z.imag));
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parents: 36324
diff changeset
623 }
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624 else {
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parents: 36324
diff changeset
625 r.real = -copysign(INF, cos(z.imag));
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parents: 36324
diff changeset
626 r.imag = copysign(INF, sin(z.imag));
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parents: 36324
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627 }
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628 }
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parents: 36324
diff changeset
629 else {
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parents: 36324
diff changeset
630 r = sinh_special_values[special_type(z.real)]
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parents: 36324
diff changeset
631 [special_type(z.imag)];
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parents: 36324
diff changeset
632 }
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parents: 36324
diff changeset
633 /* need to set errno = EDOM if y is +/- infinity and x is not
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diff changeset
634 a NaN */
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diff changeset
635 if (Py_IS_INFINITY(z.imag) && !Py_IS_NAN(z.real))
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diff changeset
636 errno = EDOM;
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
637 else
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
638 errno = 0;
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
639 return r;
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
640 }
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
641
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
642 if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
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diff changeset
643 x_minus_one = z.real - copysign(1., z.real);
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parents: 36324
diff changeset
644 r.real = cos(z.imag) * sinh(x_minus_one) * Py_MATH_E;
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
645 r.imag = sin(z.imag) * cosh(x_minus_one) * Py_MATH_E;
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diff changeset
646 } else {
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647 r.real = cos(z.imag) * sinh(z.real);
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parents: 36324
diff changeset
648 r.imag = sin(z.imag) * cosh(z.real);
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
649 }
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parents: 36324
diff changeset
650 /* detect overflow, and set errno accordingly */
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parents: 36324
diff changeset
651 if (Py_IS_INFINITY(r.real) || Py_IS_INFINITY(r.imag))
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diff changeset
652 errno = ERANGE;
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diff changeset
653 else
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diff changeset
654 errno = 0;
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
655 return r;
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
656 }
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
657
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 22722
diff changeset
658 PyDoc_STRVAR(c_sinh_doc,
16707
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
659 "sinh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
660 "\n"
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 22722
diff changeset
661 "Return the hyperbolic sine of x.");
9593
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
662
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
663
46505
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 46477
diff changeset
664 static Py_complex sqrt_special_values[7][7];
46477
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
665
16707
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
666 static Py_complex
46477
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Christian Heimes <christian@cheimes.de>
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diff changeset
667 c_sqrt(Py_complex z)
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
668 {
46477
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
669 /*
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parents: 36324
diff changeset
670 Method: use symmetries to reduce to the case when x = z.real and y
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parents: 36324
diff changeset
671 = z.imag are nonnegative. Then the real part of the result is
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
672 given by
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
673
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
674 s = sqrt((x + hypot(x, y))/2)
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
675
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
676 and the imaginary part is
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
677
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
678 d = (y/2)/s
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
679
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
680 If either x or y is very large then there's a risk of overflow in
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
681 computation of the expression x + hypot(x, y). We can avoid this
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parents: 36324
diff changeset
682 by rewriting the formula for s as:
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
683
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
684 s = 2*sqrt(x/8 + hypot(x/8, y/8))
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parents: 36324
diff changeset
685
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
686 This costs us two extra multiplications/divisions, but avoids the
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
687 overhead of checking for x and y large.
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
688
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
689 If both x and y are subnormal then hypot(x, y) may also be
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
690 subnormal, so will lack full precision. We solve this by rescaling
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
691 x and y by a sufficiently large power of 2 to ensure that x and y
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
692 are normal.
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
693 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
694
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
695
3771
d0988318b756 complex -> Py_complex
Guido van Rossum <guido@python.org>
parents: 3615
diff changeset
696 Py_complex r;
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
697 double s,d;
46477
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
698 double ax, ay;
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
699
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
700 SPECIAL_VALUE(z, sqrt_special_values);
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
701
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
702 if (z.real == 0. && z.imag == 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
703 r.real = 0.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
704 r.imag = z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
705 return r;
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
706 }
46477
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
707
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
708 ax = fabs(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
709 ay = fabs(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
710
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
711 if (ax < DBL_MIN && ay < DBL_MIN && (ax > 0. || ay > 0.)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
712 /* here we catch cases where hypot(ax, ay) is subnormal */
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
713 ax = ldexp(ax, CM_SCALE_UP);
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
714 s = ldexp(sqrt(ax + hypot(ax, ldexp(ay, CM_SCALE_UP))),
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
715 CM_SCALE_DOWN);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
716 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
717 ax /= 8.;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
718 s = 2.*sqrt(ax + hypot(ax, ay/8.));
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
719 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
720 d = ay/(2.*s);
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
721
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
722 if (z.real >= 0.) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
723 r.real = s;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
724 r.imag = copysign(d, z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
725 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
726 r.real = d;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
727 r.imag = copysign(s, z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
728 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
729 errno = 0;
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
730 return r;
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
731 }
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
732
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 22722
diff changeset
733 PyDoc_STRVAR(c_sqrt_doc,
16707
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
734 "sqrt(x)\n"
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
735 "\n"
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 22722
diff changeset
736 "Return the square root of x.");
9593
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
737
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
738
16707
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
739 static Py_complex
46477
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
740 c_tan(Py_complex z)
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
741 {
46477
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
742 /* tan(z) = -i tanh(iz) */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
743 Py_complex s, r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
744 s.real = -z.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
745 s.imag = z.real;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
746 s = c_tanh(s);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
747 r.real = s.imag;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
748 r.imag = -s.real;
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
749 return r;
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
750 }
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
751
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 22722
diff changeset
752 PyDoc_STRVAR(c_tan_doc,
16707
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
753 "tan(x)\n"
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
754 "\n"
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 22722
diff changeset
755 "Return the tangent of x.");
9593
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
756
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
757
46477
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
758 /* tanh(infinity + i*y) needs to be dealt with specially */
46505
63965327b3ef Merged revisions 62386-62387,62389-62393,62396,62400-62402,62407,62409-62410,62412-62414,62418-62419 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 46477
diff changeset
759 static Py_complex tanh_special_values[7][7];
46477
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
760
16707
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
761 static Py_complex
46477
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
762 c_tanh(Py_complex z)
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
763 {
46477
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
764 /* Formula:
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
765
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
766 tanh(x+iy) = (tanh(x)(1+tan(y)^2) + i tan(y)(1-tanh(x))^2) /
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
767 (1+tan(y)^2 tanh(x)^2)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
768
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
769 To avoid excessive roundoff error, 1-tanh(x)^2 is better computed
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
770 as 1/cosh(x)^2. When abs(x) is large, we approximate 1-tanh(x)^2
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
771 by 4 exp(-2*x) instead, to avoid possible overflow in the
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
772 computation of cosh(x).
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
773
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
774 */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
775
3771
d0988318b756 complex -> Py_complex
Guido van Rossum <guido@python.org>
parents: 3615
diff changeset
776 Py_complex r;
46477
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
777 double tx, ty, cx, txty, denom;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
778
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
779 /* special treatment for tanh(+/-inf + iy) if y is finite and
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
780 nonzero */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
781 if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
782 if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
783 && (z.imag != 0.)) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
784 if (z.real > 0) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
785 r.real = 1.0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
786 r.imag = copysign(0.,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
787 2.*sin(z.imag)*cos(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
788 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
789 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
790 r.real = -1.0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
791 r.imag = copysign(0.,
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
792 2.*sin(z.imag)*cos(z.imag));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
793 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
794 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
795 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
796 r = tanh_special_values[special_type(z.real)]
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
797 [special_type(z.imag)];
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
798 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
799 /* need to set errno = EDOM if z.imag is +/-infinity and
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
800 z.real is finite */
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
801 if (Py_IS_INFINITY(z.imag) && Py_IS_FINITE(z.real))
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
802 errno = EDOM;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
803 else
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
804 errno = 0;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
805 return r;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
806 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
807
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
808 /* danger of overflow in 2.*z.imag !*/
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
809 if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
810 r.real = copysign(1., z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
811 r.imag = 4.*sin(z.imag)*cos(z.imag)*exp(-2.*fabs(z.real));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
812 } else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
813 tx = tanh(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
814 ty = tan(z.imag);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
815 cx = 1./cosh(z.real);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
816 txty = tx*ty;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
817 denom = 1. + txty*txty;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
818 r.real = tx*(1.+ty*ty)/denom;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
819 r.imag = ((ty/denom)*cx)*cx;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
820 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
821 errno = 0;
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
822 return r;
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
823 }
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
824
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 22722
diff changeset
825 PyDoc_STRVAR(c_tanh_doc,
16707
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
826 "tanh(x)\n"
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
827 "\n"
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 22722
diff changeset
828 "Return the hyperbolic tangent of x.");
9593
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
829
46477
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
830
32350
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
831 static PyObject *
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
832 cmath_log(PyObject *self, PyObject *args)
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
833 {
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
834 Py_complex x;
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
835 Py_complex y;
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
836
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
837 if (!PyArg_ParseTuple(args, "D|D", &x, &y))
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
838 return NULL;
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
839
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
840 errno = 0;
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
841 PyFPE_START_PROTECT("complex function", return 0)
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
842 x = c_log(x);
47890
f772476ad90d Minor rewrite of cmath_log to work around a Sun compiler bug. See issue
Mark Dickinson <dickinsm@gmail.com>
parents: 47093
diff changeset
843 if (PyTuple_GET_SIZE(args) == 2) {
f772476ad90d Minor rewrite of cmath_log to work around a Sun compiler bug. See issue
Mark Dickinson <dickinsm@gmail.com>
parents: 47093
diff changeset
844 y = c_log(y);
f772476ad90d Minor rewrite of cmath_log to work around a Sun compiler bug. See issue
Mark Dickinson <dickinsm@gmail.com>
parents: 47093
diff changeset
845 x = c_quot(x, y);
f772476ad90d Minor rewrite of cmath_log to work around a Sun compiler bug. See issue
Mark Dickinson <dickinsm@gmail.com>
parents: 47093
diff changeset
846 }
32350
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
847 PyFPE_END_PROTECT(x)
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
848 if (errno != 0)
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
849 return math_error();
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
850 return PyComplex_FromCComplex(x);
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
851 }
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
852
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
853 PyDoc_STRVAR(cmath_log_doc,
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
854 "log(x[, base]) -> the logarithm of x to the given base.\n\
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
855 If the base not specified, returns the natural logarithm (base e) of x.");
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
856
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
857
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
858 /* And now the glue to make them available from Python: */
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
859
4639
97ec9dfbb2b6 Renamed Grandly
Roger E. Masse <rmasse@newcnri.cnri.reston.va.us>
parents: 4600
diff changeset
860 static PyObject *
13651
8a063423e0b7 Bunch of minor ANSIfications: 'void initfunc()' -> 'void initfunc(void)',
Thomas Wouters <thomas@python.org>
parents: 13493
diff changeset
861 math_error(void)
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
862 {
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
863 if (errno == EDOM)
4639
97ec9dfbb2b6 Renamed Grandly
Roger E. Masse <rmasse@newcnri.cnri.reston.va.us>
parents: 4600
diff changeset
864 PyErr_SetString(PyExc_ValueError, "math domain error");
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
865 else if (errno == ERANGE)
4639
97ec9dfbb2b6 Renamed Grandly
Roger E. Masse <rmasse@newcnri.cnri.reston.va.us>
parents: 4600
diff changeset
866 PyErr_SetString(PyExc_OverflowError, "math range error");
97ec9dfbb2b6 Renamed Grandly
Roger E. Masse <rmasse@newcnri.cnri.reston.va.us>
parents: 4600
diff changeset
867 else /* Unexpected math error */
16707
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
868 PyErr_SetFromErrno(PyExc_ValueError);
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
869 return NULL;
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
870 }
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
871
4639
97ec9dfbb2b6 Renamed Grandly
Roger E. Masse <rmasse@newcnri.cnri.reston.va.us>
parents: 4600
diff changeset
872 static PyObject *
13493
8bacf8631a11 ANSI-fication
Peter Schneider-Kamp <nowonder@nowonder.de>
parents: 13447
diff changeset
873 math_1(PyObject *args, Py_complex (*func)(Py_complex))
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
874 {
46477
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
875 Py_complex x,r ;
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
876 if (!PyArg_ParseTuple(args, "D", &x))
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
877 return NULL;
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
878 errno = 0;
46477
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
879 PyFPE_START_PROTECT("complex function", return 0);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
880 r = (*func)(x);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
881 PyFPE_END_PROTECT(r);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
882 if (errno == EDOM) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
883 PyErr_SetString(PyExc_ValueError, "math domain error");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
884 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
885 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
886 else if (errno == ERANGE) {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
887 PyErr_SetString(PyExc_OverflowError, "math range error");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
888 return NULL;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
889 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
890 else {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
891 return PyComplex_FromCComplex(r);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
892 }
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
893 }
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
894
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
895 #define FUNC1(stubname, func) \
13493
8bacf8631a11 ANSI-fication
Peter Schneider-Kamp <nowonder@nowonder.de>
parents: 13447
diff changeset
896 static PyObject * stubname(PyObject *self, PyObject *args) { \
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
897 return math_1(args, func); \
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
898 }
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
899
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
900 FUNC1(cmath_acos, c_acos)
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
901 FUNC1(cmath_acosh, c_acosh)
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
902 FUNC1(cmath_asin, c_asin)
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
903 FUNC1(cmath_asinh, c_asinh)
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
904 FUNC1(cmath_atan, c_atan)
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
905 FUNC1(cmath_atanh, c_atanh)
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
906 FUNC1(cmath_cos, c_cos)
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
907 FUNC1(cmath_cosh, c_cosh)
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
908 FUNC1(cmath_exp, c_exp)
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
909 FUNC1(cmath_log10, c_log10)
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
910 FUNC1(cmath_sin, c_sin)
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
911 FUNC1(cmath_sinh, c_sinh)
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
912 FUNC1(cmath_sqrt, c_sqrt)
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
913 FUNC1(cmath_tan, c_tan)
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
914 FUNC1(cmath_tanh, c_tanh)
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
915
46477
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916 static PyObject *
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917 cmath_phase(PyObject *self, PyObject *args)
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diff changeset
918 {
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919 Py_complex z;
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920 double phi;
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921 if (!PyArg_ParseTuple(args, "D:phase", &z))
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922 return NULL;
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923 errno = 0;
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924 PyFPE_START_PROTECT("arg function", return 0)
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925 phi = c_atan2(z);
47093
54fd0458550c Following Amaury's advice
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diff changeset
926 PyFPE_END_PROTECT(phi)
46477
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927 if (errno != 0)
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928 return math_error();
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929 else
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930 return PyFloat_FromDouble(phi);
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931 }
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932
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933 PyDoc_STRVAR(cmath_phase_doc,
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934 "phase(z) -> float\n\n\
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935 Return argument, also known as the phase angle, of a complex.");
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936
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937 static PyObject *
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938 cmath_polar(PyObject *self, PyObject *args)
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939 {
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940 Py_complex z;
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941 double r, phi;
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942 if (!PyArg_ParseTuple(args, "D:polar", &z))
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943 return NULL;
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944 PyFPE_START_PROTECT("polar function", return 0)
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945 phi = c_atan2(z); /* should not cause any exception */
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diff changeset
946 r = c_abs(z); /* sets errno to ERANGE on overflow; otherwise 0 */
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diff changeset
947 PyFPE_END_PROTECT(r)
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diff changeset
948 if (errno != 0)
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949 return math_error();
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950 else
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951 return Py_BuildValue("dd", r, phi);
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952 }
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953
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954 PyDoc_STRVAR(cmath_polar_doc,
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955 "polar(z) -> r: float, phi: float\n\n\
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956 Convert a complex from rectangular coordinates to polar coordinates. r is\n\
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957 the distance from 0 and phi the phase angle.");
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958
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959 /*
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960 rect() isn't covered by the C99 standard, but it's not too hard to
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961 figure out 'spirit of C99' rules for special value handing:
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diff changeset
962
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diff changeset
963 rect(x, t) should behave like exp(log(x) + it) for positive-signed x
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diff changeset
964 rect(x, t) should behave like -exp(log(-x) + it) for negative-signed x
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diff changeset
965 rect(nan, t) should behave like exp(nan + it), except that rect(nan, 0)
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diff changeset
966 gives nan +- i0 with the sign of the imaginary part unspecified.
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967
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968 */
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diff changeset
969
46505
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970 static Py_complex rect_special_values[7][7];
46477
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diff changeset
971
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972 static PyObject *
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973 cmath_rect(PyObject *self, PyObject *args)
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diff changeset
974 {
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diff changeset
975 Py_complex z;
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diff changeset
976 double r, phi;
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diff changeset
977 if (!PyArg_ParseTuple(args, "dd:rect", &r, &phi))
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978 return NULL;
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979 errno = 0;
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980 PyFPE_START_PROTECT("rect function", return 0)
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diff changeset
981
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diff changeset
982 /* deal with special values */
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diff changeset
983 if (!Py_IS_FINITE(r) || !Py_IS_FINITE(phi)) {
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984 /* if r is +/-infinity and phi is finite but nonzero then
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diff changeset
985 result is (+-INF +-INF i), but we need to compute cos(phi)
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diff changeset
986 and sin(phi) to figure out the signs. */
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diff changeset
987 if (Py_IS_INFINITY(r) && (Py_IS_FINITE(phi)
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988 && (phi != 0.))) {
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989 if (r > 0) {
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990 z.real = copysign(INF, cos(phi));
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991 z.imag = copysign(INF, sin(phi));
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992 }
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993 else {
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994 z.real = -copysign(INF, cos(phi));
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995 z.imag = -copysign(INF, sin(phi));
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diff changeset
996 }
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997 }
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998 else {
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diff changeset
999 z = rect_special_values[special_type(r)]
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1000 [special_type(phi)];
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1001 }
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1002 /* need to set errno = EDOM if r is a nonzero number and phi
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1003 is infinite */
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1004 if (r != 0. && !Py_IS_NAN(r) && Py_IS_INFINITY(phi))
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1005 errno = EDOM;
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1006 else
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1007 errno = 0;
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1008 }
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1009 else {
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1010 z.real = r * cos(phi);
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1011 z.imag = r * sin(phi);
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1012 errno = 0;
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1013 }
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1014
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1015 PyFPE_END_PROTECT(z)
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1016 if (errno != 0)
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1017 return math_error();
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1018 else
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1019 return PyComplex_FromCComplex(z);
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1020 }
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1021
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1022 PyDoc_STRVAR(cmath_rect_doc,
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1023 "rect(r, phi) -> z: complex\n\n\
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1024 Convert from polar coordinates to rectangular coordinates.");
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1025
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1026 static PyObject *
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1027 cmath_isnan(PyObject *self, PyObject *args)
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parents: 36324
diff changeset
1028 {
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Christian Heimes <christian@cheimes.de>
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diff changeset
1029 Py_complex z;
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1030 if (!PyArg_ParseTuple(args, "D:isnan", &z))
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1031 return NULL;
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parents: 36324
diff changeset
1032 return PyBool_FromLong(Py_IS_NAN(z.real) || Py_IS_NAN(z.imag));
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Christian Heimes <christian@cheimes.de>
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diff changeset
1033 }
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1034
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1035 PyDoc_STRVAR(cmath_isnan_doc,
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1036 "isnan(z) -> bool\n\
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1037 Checks if the real or imaginary part of z not a number (NaN)");
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1038
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1039 static PyObject *
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1040 cmath_isinf(PyObject *self, PyObject *args)
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1041 {
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1042 Py_complex z;
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1043 if (!PyArg_ParseTuple(args, "D:isnan", &z))
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1044 return NULL;
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1045 return PyBool_FromLong(Py_IS_INFINITY(z.real) ||
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1046 Py_IS_INFINITY(z.imag));
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1047 }
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1048
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1049 PyDoc_STRVAR(cmath_isinf_doc,
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1050 "isinf(z) -> bool\n\
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1051 Checks if the real or imaginary part of z is infinite.");
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1052
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
1053
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 22722
diff changeset
1054 PyDoc_STRVAR(module_doc,
16707
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
1055 "This module is always available. It provides access to mathematical\n"
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 22722
diff changeset
1056 "functions for complex numbers.");
9593
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
1057
4639
97ec9dfbb2b6 Renamed Grandly
Roger E. Masse <rmasse@newcnri.cnri.reston.va.us>
parents: 4600
diff changeset
1058 static PyMethodDef cmath_methods[] = {
16707
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
1059 {"acos", cmath_acos, METH_VARARGS, c_acos_doc},
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
1060 {"acosh", cmath_acosh, METH_VARARGS, c_acosh_doc},
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
1061 {"asin", cmath_asin, METH_VARARGS, c_asin_doc},
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
1062 {"asinh", cmath_asinh, METH_VARARGS, c_asinh_doc},
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
1063 {"atan", cmath_atan, METH_VARARGS, c_atan_doc},
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
1064 {"atanh", cmath_atanh, METH_VARARGS, c_atanh_doc},
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
1065 {"cos", cmath_cos, METH_VARARGS, c_cos_doc},
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
1066 {"cosh", cmath_cosh, METH_VARARGS, c_cosh_doc},
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
1067 {"exp", cmath_exp, METH_VARARGS, c_exp_doc},
46477
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parents: 36324
diff changeset
1068 {"isinf", cmath_isinf, METH_VARARGS, cmath_isinf_doc},
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1069 {"isnan", cmath_isnan, METH_VARARGS, cmath_isnan_doc},
32350
11c31a98dfd6 Patch #826074: cmath.log optional base argument, fixes #823209
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
1070 {"log", cmath_log, METH_VARARGS, cmath_log_doc},
16707
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
1071 {"log10", cmath_log10, METH_VARARGS, c_log10_doc},
46477
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parents: 36324
diff changeset
1072 {"phase", cmath_phase, METH_VARARGS, cmath_phase_doc},
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1073 {"polar", cmath_polar, METH_VARARGS, cmath_polar_doc},
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1074 {"rect", cmath_rect, METH_VARARGS, cmath_rect_doc},
16707
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
1075 {"sin", cmath_sin, METH_VARARGS, c_sin_doc},
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
1076 {"sinh", cmath_sinh, METH_VARARGS, c_sinh_doc},
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
1077 {"sqrt", cmath_sqrt, METH_VARARGS, c_sqrt_doc},
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
1078 {"tan", cmath_tan, METH_VARARGS, c_tan_doc},
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
1079 {"tanh", cmath_tanh, METH_VARARGS, c_tanh_doc},
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
1080 {NULL, NULL} /* sentinel */
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
1081 };
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
1082
24471
f66b3a3509c7 Excise DL_EXPORT/DL_IMPORT from Modules/*. Required adding a prototype
Mark Hammond <mhammond@skippinet.com.au>
parents: 24280
diff changeset
1083 PyMODINIT_FUNC
13651
8a063423e0b7 Bunch of minor ANSIfications: 'void initfunc()' -> 'void initfunc(void)',
Thomas Wouters <thomas@python.org>
parents: 13493
diff changeset
1084 initcmath(void)
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
parents:
diff changeset
1085 {
22722
ba68dda15df0 Use the PyModule_*() API instead of manipulating the module dictionary
Fred Drake <fdrake@acm.org>
parents: 22227
diff changeset
1086 PyObject *m;
16707
9696c95d09b7 Mechanical edits just so I can read it.
Tim Peters <tim.peters@gmail.com>
parents: 13817
diff changeset
1087
9593
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
1088 m = Py_InitModule3("cmath", cmath_methods, module_doc);
36324
1af7f719ed28 Check return result from Py_InitModule*(). This API can fail.
Neal Norwitz <nnorwitz@gmail.com>
parents: 32350
diff changeset
1089 if (m == NULL)
1af7f719ed28 Check return result from Py_InitModule*(). This API can fail.
Neal Norwitz <nnorwitz@gmail.com>
parents: 32350
diff changeset
1090 return;
22722
ba68dda15df0 Use the PyModule_*() API instead of manipulating the module dictionary
Fred Drake <fdrake@acm.org>
parents: 22227
diff changeset
1091
ba68dda15df0 Use the PyModule_*() API instead of manipulating the module dictionary
Fred Drake <fdrake@acm.org>
parents: 22227
diff changeset
1092 PyModule_AddObject(m, "pi",
46477
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1093 PyFloat_FromDouble(Py_MATH_PI));
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Christian Heimes <christian@cheimes.de>
parents: 36324
diff changeset
1094 PyModule_AddObject(m, "e", PyFloat_FromDouble(Py_MATH_E));
46505
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parents: 46477
diff changeset
1095
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parents: 46477
diff changeset
1096 /* initialize special value tables */
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parents: 46477
diff changeset
1097
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Christian Heimes <christian@cheimes.de>
parents: 46477
diff changeset
1098 #define INIT_SPECIAL_VALUES(NAME, BODY) { Py_complex* p = (Py_complex*)NAME; BODY }
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parents: 46477
diff changeset
1099 #define C(REAL, IMAG) p->real = REAL; p->imag = IMAG; ++p;
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diff changeset
1100
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diff changeset
1101 INIT_SPECIAL_VALUES(acos_special_values, {
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Christian Heimes <christian@cheimes.de>
parents: 46477
diff changeset
1102 C(P34,INF) C(P,INF) C(P,INF) C(P,-INF) C(P,-INF) C(P34,-INF) C(N,INF)
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parents: 46477
diff changeset
1103 C(P12,INF) C(U,U) C(U,U) C(U,U) C(U,U) C(P12,-INF) C(N,N)
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Christian Heimes <christian@cheimes.de>
parents: 46477
diff changeset
1104 C(P12,INF) C(U,U) C(P12,0.) C(P12,-0.) C(U,U) C(P12,-INF) C(P12,N)
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parents: 46477
diff changeset
1105 C(P12,INF) C(U,U) C(P12,0.) C(P12,-0.) C(U,U) C(P12,-INF) C(P12,N)
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Christian Heimes <christian@cheimes.de>
parents: 46477
diff changeset
1106 C(P12,INF) C(U,U) C(U,U) C(U,U) C(U,U) C(P12,-INF) C(N,N)
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Christian Heimes <christian@cheimes.de>
parents: 46477
diff changeset
1107 C(P14,INF) C(0.,INF) C(0.,INF) C(0.,-INF) C(0.,-INF) C(P14,-INF) C(N,INF)
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Christian Heimes <christian@cheimes.de>
parents: 46477
diff changeset
1108 C(N,INF) C(N,N) C(N,N) C(N,N) C(N,N) C(N,-INF) C(N,N)
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parents: 46477
diff changeset
1109 })
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parents: 46477
diff changeset
1110
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parents: 46477
diff changeset
1111 INIT_SPECIAL_VALUES(acosh_special_values, {
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parents: 46477
diff changeset
1112 C(INF,-P34) C(INF,-P) C(INF,-P) C(INF,P) C(INF,P) C(INF,P34) C(INF,N)
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parents: 46477
diff changeset
1113 C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
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parents: 46477
diff changeset
1114 C(INF,-P12) C(U,U) C(0.,-P12) C(0.,P12) C(U,U) C(INF,P12) C(N,N)
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parents: 46477
diff changeset
1115 C(INF,-P12) C(U,U) C(0.,-P12) C(0.,P12) C(U,U) C(INF,P12) C(N,N)
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parents: 46477
diff changeset
1116 C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
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Christian Heimes <christian@cheimes.de>
parents: 46477
diff changeset
1117 C(INF,-P14) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,P14) C(INF,N)
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parents: 46477
diff changeset
1118 C(INF,N) C(N,N) C(N,N) C(N,N) C(N,N) C(INF,N) C(N,N)
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diff changeset
1119 })
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diff changeset
1120
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parents: 46477
diff changeset
1121 INIT_SPECIAL_VALUES(asinh_special_values, {
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parents: 46477
diff changeset
1122 C(-INF,-P14) C(-INF,-0.) C(-INF,-0.) C(-INF,0.) C(-INF,0.) C(-INF,P14) C(-INF,N)
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parents: 46477
diff changeset
1123 C(-INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(-INF,P12) C(N,N)
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parents: 46477
diff changeset
1124 C(-INF,-P12) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(-INF,P12) C(N,N)
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1125 C(INF,-P12) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(INF,P12) C(N,N)
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1126 C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
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1127 C(INF,-P14) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,P14) C(INF,N)
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1128 C(INF,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(INF,N) C(N,N)
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1129 })
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1130
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1131 INIT_SPECIAL_VALUES(atanh_special_values, {
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1132 C(-0.,-P12) C(-0.,-P12) C(-0.,-P12) C(-0.,P12) C(-0.,P12) C(-0.,P12) C(-0.,N)
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1133 C(-0.,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(-0.,P12) C(N,N)
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1134 C(-0.,-P12) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(-0.,P12) C(-0.,N)
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1135 C(0.,-P12) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,P12) C(0.,N)
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1136 C(0.,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(0.,P12) C(N,N)
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1137 C(0.,-P12) C(0.,-P12) C(0.,-P12) C(0.,P12) C(0.,P12) C(0.,P12) C(0.,N)
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1138 C(0.,-P12) C(N,N) C(N,N) C(N,N) C(N,N) C(0.,P12) C(N,N)
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1139 })
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1140
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1141 INIT_SPECIAL_VALUES(cosh_special_values, {
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1142 C(INF,N) C(U,U) C(INF,0.) C(INF,-0.) C(U,U) C(INF,N) C(INF,N)
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1143 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
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1144 C(N,0.) C(U,U) C(1.,0.) C(1.,-0.) C(U,U) C(N,0.) C(N,0.)
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1145 C(N,0.) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(N,0.) C(N,0.)
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1146 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
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1147 C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N)
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1148 C(N,N) C(N,N) C(N,0.) C(N,0.) C(N,N) C(N,N) C(N,N)
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1149 })
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1150
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1151 INIT_SPECIAL_VALUES(exp_special_values, {
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1152 C(0.,0.) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,0.) C(0.,0.)
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1153 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
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1154 C(N,N) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(N,N) C(N,N)
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1155 C(N,N) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(N,N) C(N,N)
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1156 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
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1157 C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N)
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1158 C(N,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(N,N) C(N,N)
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1159 })
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1160
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1161 INIT_SPECIAL_VALUES(log_special_values, {
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1162 C(INF,-P34) C(INF,-P) C(INF,-P) C(INF,P) C(INF,P) C(INF,P34) C(INF,N)
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1163 C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
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1164 C(INF,-P12) C(U,U) C(-INF,-P) C(-INF,P) C(U,U) C(INF,P12) C(N,N)
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1165 C(INF,-P12) C(U,U) C(-INF,-0.) C(-INF,0.) C(U,U) C(INF,P12) C(N,N)
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1166 C(INF,-P12) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,P12) C(N,N)
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1167 C(INF,-P14) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,P14) C(INF,N)
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1168 C(INF,N) C(N,N) C(N,N) C(N,N) C(N,N) C(INF,N) C(N,N)
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1169 })
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1170
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1171 INIT_SPECIAL_VALUES(sinh_special_values, {
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1172 C(INF,N) C(U,U) C(-INF,-0.) C(-INF,0.) C(U,U) C(INF,N) C(INF,N)
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1173 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
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1174 C(0.,N) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(0.,N) C(0.,N)
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1175 C(0.,N) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,N) C(0.,N)
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1176 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
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1177 C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N)
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1178 C(N,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(N,N) C(N,N)
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1179 })
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1181 INIT_SPECIAL_VALUES(sqrt_special_values, {
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1182 C(INF,-INF) C(0.,-INF) C(0.,-INF) C(0.,INF) C(0.,INF) C(INF,INF) C(N,INF)
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1183 C(INF,-INF) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,INF) C(N,N)
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1184 C(INF,-INF) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(INF,INF) C(N,N)
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1185 C(INF,-INF) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(INF,INF) C(N,N)
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1186 C(INF,-INF) C(U,U) C(U,U) C(U,U) C(U,U) C(INF,INF) C(N,N)
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1187 C(INF,-INF) C(INF,-0.) C(INF,-0.) C(INF,0.) C(INF,0.) C(INF,INF) C(INF,N)
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1188 C(INF,-INF) C(N,N) C(N,N) C(N,N) C(N,N) C(INF,INF) C(N,N)
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1189 })
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1191 INIT_SPECIAL_VALUES(tanh_special_values, {
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1192 C(-1.,0.) C(U,U) C(-1.,-0.) C(-1.,0.) C(U,U) C(-1.,0.) C(-1.,0.)
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1193 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
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1194 C(N,N) C(U,U) C(-0.,-0.) C(-0.,0.) C(U,U) C(N,N) C(N,N)
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1195 C(N,N) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(N,N) C(N,N)
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1196 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
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1197 C(1.,0.) C(U,U) C(1.,-0.) C(1.,0.) C(U,U) C(1.,0.) C(1.,0.)
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1198 C(N,N) C(N,N) C(N,-0.) C(N,0.) C(N,N) C(N,N) C(N,N)
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1199 })
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1200
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1201 INIT_SPECIAL_VALUES(rect_special_values, {
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1202 C(INF,N) C(U,U) C(-INF,0.) C(-INF,-0.) C(U,U) C(INF,N) C(INF,N)
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1203 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
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1204 C(0.,0.) C(U,U) C(-0.,0.) C(-0.,-0.) C(U,U) C(0.,0.) C(0.,0.)
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1205 C(0.,0.) C(U,U) C(0.,-0.) C(0.,0.) C(U,U) C(0.,0.) C(0.,0.)
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1206 C(N,N) C(U,U) C(U,U) C(U,U) C(U,U) C(N,N) C(N,N)
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1207 C(INF,N) C(U,U) C(INF,-0.) C(INF,0.) C(U,U) C(INF,N) C(INF,N)
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1208 C(N,N) C(N,N) C(N,0.) C(N,0.) C(N,N) C(N,N) C(N,N)
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1209 })
3334
969bd911e114 complex math
Guido van Rossum <guido@python.org>
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1210 }