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annotate Modules/mathmodule.c @ 70817:dd775b1561ba

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author Georg Brandl <georg@python.org>
date Tue, 14 Jun 2011 21:09:55 +0200
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children 7482d0e3476a
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1 /* Math module -- standard C math library functions, pi and e */
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2
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3 /* Here are some comments from Tim Peters, extracted from the
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4 discussion attached to http://bugs.python.org/issue1640. They
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5 describe the general aims of the math module with respect to
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6 special values, IEEE-754 floating-point exceptions, and Python
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7 exceptions.
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8
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9 These are the "spirit of 754" rules:
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10
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11 1. If the mathematical result is a real number, but of magnitude too
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12 large to approximate by a machine float, overflow is signaled and the
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13 result is an infinity (with the appropriate sign).
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14
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15 2. If the mathematical result is a real number, but of magnitude too
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16 small to approximate by a machine float, underflow is signaled and the
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17 result is a zero (with the appropriate sign).
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18
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19 3. At a singularity (a value x such that the limit of f(y) as y
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20 approaches x exists and is an infinity), "divide by zero" is signaled
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21 and the result is an infinity (with the appropriate sign). This is
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22 complicated a little by that the left-side and right-side limits may
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23 not be the same; e.g., 1/x approaches +inf or -inf as x approaches 0
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24 from the positive or negative directions. In that specific case, the
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25 sign of the zero determines the result of 1/0.
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26
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27 4. At a point where a function has no defined result in the extended
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28 reals (i.e., the reals plus an infinity or two), invalid operation is
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29 signaled and a NaN is returned.
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30
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31 And these are what Python has historically /tried/ to do (but not
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32 always successfully, as platform libm behavior varies a lot):
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33
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34 For #1, raise OverflowError.
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35
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36 For #2, return a zero (with the appropriate sign if that happens by
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37 accident ;-)).
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38
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39 For #3 and #4, raise ValueError. It may have made sense to raise
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40 Python's ZeroDivisionError in #3, but historically that's only been
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41 raised for division by zero and mod by zero.
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42
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43 */
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44
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45 /*
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46 In general, on an IEEE-754 platform the aim is to follow the C99
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47 standard, including Annex 'F', whenever possible. Where the
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48 standard recommends raising the 'divide-by-zero' or 'invalid'
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49 floating-point exceptions, Python should raise a ValueError. Where
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50 the standard recommends raising 'overflow', Python should raise an
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51 OverflowError. In all other circumstances a value should be
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52 returned.
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53 */
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54
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55 #include "Python.h"
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56 #include "_math.h"
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57
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58 /*
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59 sin(pi*x), giving accurate results for all finite x (especially x
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60 integral or close to an integer). This is here for use in the
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61 reflection formula for the gamma function. It conforms to IEEE
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62 754-2008 for finite arguments, but not for infinities or nans.
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63 */
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64
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65 static const double pi = 3.141592653589793238462643383279502884197;
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66 static const double sqrtpi = 1.772453850905516027298167483341145182798;
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67 static const double logpi = 1.144729885849400174143427351353058711647;
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68
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69 static double
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70 sinpi(double x)
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71 {
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72 double y, r;
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73 int n;
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74 /* this function should only ever be called for finite arguments */
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75 assert(Py_IS_FINITE(x));
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76 y = fmod(fabs(x), 2.0);
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77 n = (int)round(2.0*y);
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78 assert(0 <= n && n <= 4);
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79 switch (n) {
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80 case 0:
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81 r = sin(pi*y);
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82 break;
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83 case 1:
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84 r = cos(pi*(y-0.5));
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85 break;
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86 case 2:
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87 /* N.B. -sin(pi*(y-1.0)) is *not* equivalent: it would give
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88 -0.0 instead of 0.0 when y == 1.0. */
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89 r = sin(pi*(1.0-y));
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90 break;
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91 case 3:
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92 r = -cos(pi*(y-1.5));
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93 break;
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94 case 4:
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95 r = sin(pi*(y-2.0));
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96 break;
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97 default:
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98 assert(0); /* should never get here */
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99 r = -1.23e200; /* silence gcc warning */
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100 }
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101 return copysign(1.0, x)*r;
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102 }
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103
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104 /* Implementation of the real gamma function. In extensive but non-exhaustive
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105 random tests, this function proved accurate to within <= 10 ulps across the
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106 entire float domain. Note that accuracy may depend on the quality of the
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107 system math functions, the pow function in particular. Special cases
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108 follow C99 annex F. The parameters and method are tailored to platforms
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109 whose double format is the IEEE 754 binary64 format.
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110
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111 Method: for x > 0.0 we use the Lanczos approximation with parameters N=13
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112 and g=6.024680040776729583740234375; these parameters are amongst those
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113 used by the Boost library. Following Boost (again), we re-express the
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114 Lanczos sum as a rational function, and compute it that way. The
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115 coefficients below were computed independently using MPFR, and have been
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116 double-checked against the coefficients in the Boost source code.
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117
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118 For x < 0.0 we use the reflection formula.
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119
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120 There's one minor tweak that deserves explanation: Lanczos' formula for
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121 Gamma(x) involves computing pow(x+g-0.5, x-0.5) / exp(x+g-0.5). For many x
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122 values, x+g-0.5 can be represented exactly. However, in cases where it
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123 can't be represented exactly the small error in x+g-0.5 can be magnified
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124 significantly by the pow and exp calls, especially for large x. A cheap
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125 correction is to multiply by (1 + e*g/(x+g-0.5)), where e is the error
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126 involved in the computation of x+g-0.5 (that is, e = computed value of
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127 x+g-0.5 - exact value of x+g-0.5). Here's the proof:
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128
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129 Correction factor
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130 -----------------
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131 Write x+g-0.5 = y-e, where y is exactly representable as an IEEE 754
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132 double, and e is tiny. Then:
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133
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134 pow(x+g-0.5,x-0.5)/exp(x+g-0.5) = pow(y-e, x-0.5)/exp(y-e)
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135 = pow(y, x-0.5)/exp(y) * C,
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136
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137 where the correction_factor C is given by
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138
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139 C = pow(1-e/y, x-0.5) * exp(e)
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140
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141 Since e is tiny, pow(1-e/y, x-0.5) ~ 1-(x-0.5)*e/y, and exp(x) ~ 1+e, so:
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142
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143 C ~ (1-(x-0.5)*e/y) * (1+e) ~ 1 + e*(y-(x-0.5))/y
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144
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145 But y-(x-0.5) = g+e, and g+e ~ g. So we get C ~ 1 + e*g/y, and
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146
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147 pow(x+g-0.5,x-0.5)/exp(x+g-0.5) ~ pow(y, x-0.5)/exp(y) * (1 + e*g/y),
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148
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149 Note that for accuracy, when computing r*C it's better to do
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150
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151 r + e*g/y*r;
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152
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153 than
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154
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155 r * (1 + e*g/y);
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156
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157 since the addition in the latter throws away most of the bits of
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158 information in e*g/y.
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159 */
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160
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161 #define LANCZOS_N 13
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162 static const double lanczos_g = 6.024680040776729583740234375;
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163 static const double lanczos_g_minus_half = 5.524680040776729583740234375;
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164 static const double lanczos_num_coeffs[LANCZOS_N] = {
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165 23531376880.410759688572007674451636754734846804940,
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166 42919803642.649098768957899047001988850926355848959,
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167 35711959237.355668049440185451547166705960488635843,
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168 17921034426.037209699919755754458931112671403265390,
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169 6039542586.3520280050642916443072979210699388420708,
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170 1439720407.3117216736632230727949123939715485786772,
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171 248874557.86205415651146038641322942321632125127801,
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172 31426415.585400194380614231628318205362874684987640,
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173 2876370.6289353724412254090516208496135991145378768,
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174 186056.26539522349504029498971604569928220784236328,
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175 8071.6720023658162106380029022722506138218516325024,
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176 210.82427775157934587250973392071336271166969580291,
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177 2.5066282746310002701649081771338373386264310793408
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178 };
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179
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180 /* denominator is x*(x+1)*...*(x+LANCZOS_N-2) */
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181 static const double lanczos_den_coeffs[LANCZOS_N] = {
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182 0.0, 39916800.0, 120543840.0, 150917976.0, 105258076.0, 45995730.0,
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183 13339535.0, 2637558.0, 357423.0, 32670.0, 1925.0, 66.0, 1.0};
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184
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185 /* gamma values for small positive integers, 1 though NGAMMA_INTEGRAL */
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186 #define NGAMMA_INTEGRAL 23
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187 static const double gamma_integral[NGAMMA_INTEGRAL] = {
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188 1.0, 1.0, 2.0, 6.0, 24.0, 120.0, 720.0, 5040.0, 40320.0, 362880.0,
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189 3628800.0, 39916800.0, 479001600.0, 6227020800.0, 87178291200.0,
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190 1307674368000.0, 20922789888000.0, 355687428096000.0,
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191 6402373705728000.0, 121645100408832000.0, 2432902008176640000.0,
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192 51090942171709440000.0, 1124000727777607680000.0,
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193 };
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194
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195 /* Lanczos' sum L_g(x), for positive x */
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196
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197 static double
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198 lanczos_sum(double x)
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199 {
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200 double num = 0.0, den = 0.0;
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201 int i;
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202 assert(x > 0.0);
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203 /* evaluate the rational function lanczos_sum(x). For large
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204 x, the obvious algorithm risks overflow, so we instead
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205 rescale the denominator and numerator of the rational
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206 function by x**(1-LANCZOS_N) and treat this as a
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207 rational function in 1/x. This also reduces the error for
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208 larger x values. The choice of cutoff point (5.0 below) is
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209 somewhat arbitrary; in tests, smaller cutoff values than
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210 this resulted in lower accuracy. */
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211 if (x < 5.0) {
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212 for (i = LANCZOS_N; --i >= 0; ) {
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213 num = num * x + lanczos_num_coeffs[i];
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214 den = den * x + lanczos_den_coeffs[i];
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215 }
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216 }
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217 else {
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218 for (i = 0; i < LANCZOS_N; i++) {
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219 num = num / x + lanczos_num_coeffs[i];
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220 den = den / x + lanczos_den_coeffs[i];
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221 }
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222 }
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223 return num/den;
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224 }
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225
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226 static double
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227 m_tgamma(double x)
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228 {
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229 double absx, r, y, z, sqrtpow;
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230
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231 /* special cases */
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232 if (!Py_IS_FINITE(x)) {
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233 if (Py_IS_NAN(x) || x > 0.0)
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234 return x; /* tgamma(nan) = nan, tgamma(inf) = inf */
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235 else {
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236 errno = EDOM;
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237 return Py_NAN; /* tgamma(-inf) = nan, invalid */
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238 }
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239 }
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240 if (x == 0.0) {
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241 errno = EDOM;
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242 return 1.0/x; /* tgamma(+-0.0) = +-inf, divide-by-zero */
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243 }
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244
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245 /* integer arguments */
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246 if (x == floor(x)) {
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247 if (x < 0.0) {
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248 errno = EDOM; /* tgamma(n) = nan, invalid for */
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249 return Py_NAN; /* negative integers n */
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250 }
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251 if (x <= NGAMMA_INTEGRAL)
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252 return gamma_integral[(int)x - 1];
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253 }
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254 absx = fabs(x);
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255
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256 /* tiny arguments: tgamma(x) ~ 1/x for x near 0 */
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257 if (absx < 1e-20) {
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258 r = 1.0/x;
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259 if (Py_IS_INFINITY(r))
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260 errno = ERANGE;
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261 return r;
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262 }
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263
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264 /* large arguments: assuming IEEE 754 doubles, tgamma(x) overflows for
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265 x > 200, and underflows to +-0.0 for x < -200, not a negative
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266 integer. */
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267 if (absx > 200.0) {
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268 if (x < 0.0) {
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269 return 0.0/sinpi(x);
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270 }
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271 else {
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272 errno = ERANGE;
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273 return Py_HUGE_VAL;
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274 }
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275 }
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276
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277 y = absx + lanczos_g_minus_half;
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278 /* compute error in sum */
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279 if (absx > lanczos_g_minus_half) {
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280 /* note: the correction can be foiled by an optimizing
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281 compiler that (incorrectly) thinks that an expression like
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282 a + b - a - b can be optimized to 0.0. This shouldn't
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283 happen in a standards-conforming compiler. */
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284 double q = y - absx;
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285 z = q - lanczos_g_minus_half;
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286 }
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287 else {
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288 double q = y - lanczos_g_minus_half;
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289 z = q - absx;
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290 }
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291 z = z * lanczos_g / y;
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292 if (x < 0.0) {
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293 r = -pi / sinpi(absx) / absx * exp(y) / lanczos_sum(absx);
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294 r -= z * r;
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295 if (absx < 140.0) {
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296 r /= pow(y, absx - 0.5);
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297 }
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298 else {
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299 sqrtpow = pow(y, absx / 2.0 - 0.25);
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300 r /= sqrtpow;
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301 r /= sqrtpow;
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302 }
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303 }
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304 else {
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305 r = lanczos_sum(absx) / exp(y);
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306 r += z * r;
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307 if (absx < 140.0) {
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308 r *= pow(y, absx - 0.5);
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309 }
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310 else {
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311 sqrtpow = pow(y, absx / 2.0 - 0.25);
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312 r *= sqrtpow;
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313 r *= sqrtpow;
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314 }
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315 }
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316 if (Py_IS_INFINITY(r))
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317 errno = ERANGE;
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318 return r;
498
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319 }
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320
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321 /*
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322 lgamma: natural log of the absolute value of the Gamma function.
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323 For large arguments, Lanczos' formula works extremely well here.
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324 */
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325
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326 static double
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327 m_lgamma(double x)
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328 {
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329 double r, absx;
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330
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331 /* special cases */
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332 if (!Py_IS_FINITE(x)) {
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333 if (Py_IS_NAN(x))
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334 return x; /* lgamma(nan) = nan */
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335 else
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336 return Py_HUGE_VAL; /* lgamma(+-inf) = +inf */
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337 }
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338
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339 /* integer arguments */
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340 if (x == floor(x) && x <= 2.0) {
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341 if (x <= 0.0) {
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342 errno = EDOM; /* lgamma(n) = inf, divide-by-zero for */
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343 return Py_HUGE_VAL; /* integers n <= 0 */
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344 }
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345 else {
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346 return 0.0; /* lgamma(1) = lgamma(2) = 0.0 */
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347 }
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348 }
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349
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350 absx = fabs(x);
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351 /* tiny arguments: lgamma(x) ~ -log(fabs(x)) for small x */
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352 if (absx < 1e-20)
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353 return -log(absx);
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354
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355 /* Lanczos' formula. We could save a fraction of a ulp in accuracy by
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356 having a second set of numerator coefficients for lanczos_sum that
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357 absorbed the exp(-lanczos_g) term, and throwing out the lanczos_g
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358 subtraction below; it's probably not worth it. */
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359 r = log(lanczos_sum(absx)) - lanczos_g;
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360 r += (absx - 0.5) * (log(absx + lanczos_g - 0.5) - 1);
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361 if (x < 0.0)
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362 /* Use reflection formula to get value for negative x. */
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363 r = logpi - log(fabs(sinpi(absx))) - log(absx) - r;
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364 if (Py_IS_INFINITY(r))
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365 errno = ERANGE;
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366 return r;
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367 }
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368
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369 /*
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370 Implementations of the error function erf(x) and the complementary error
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371 function erfc(x).
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372
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373 Method: following 'Numerical Recipes' by Flannery, Press et. al. (2nd ed.,
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374 Cambridge University Press), we use a series approximation for erf for
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375 small x, and a continued fraction approximation for erfc(x) for larger x;
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376 combined with the relations erf(-x) = -erf(x) and erfc(x) = 1.0 - erf(x),
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377 this gives us erf(x) and erfc(x) for all x.
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378
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379 The series expansion used is:
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380
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381 erf(x) = x*exp(-x*x)/sqrt(pi) * [
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382 2/1 + 4/3 x**2 + 8/15 x**4 + 16/105 x**6 + ...]
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383
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384 The coefficient of x**(2k-2) here is 4**k*factorial(k)/factorial(2*k).
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385 This series converges well for smallish x, but slowly for larger x.
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386
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387 The continued fraction expansion used is:
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388
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389 erfc(x) = x*exp(-x*x)/sqrt(pi) * [1/(0.5 + x**2 -) 0.5/(2.5 + x**2 - )
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390 3.0/(4.5 + x**2 - ) 7.5/(6.5 + x**2 - ) ...]
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391
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392 after the first term, the general term has the form:
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393
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394 k*(k-0.5)/(2*k+0.5 + x**2 - ...).
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395
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396 This expansion converges fast for larger x, but convergence becomes
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397 infinitely slow as x approaches 0.0. The (somewhat naive) continued
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398 fraction evaluation algorithm used below also risks overflow for large x;
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399 but for large x, erfc(x) == 0.0 to within machine precision. (For
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400 example, erfc(30.0) is approximately 2.56e-393).
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401
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402 Parameters: use series expansion for abs(x) < ERF_SERIES_CUTOFF and
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403 continued fraction expansion for ERF_SERIES_CUTOFF <= abs(x) <
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404 ERFC_CONTFRAC_CUTOFF. ERFC_SERIES_TERMS and ERFC_CONTFRAC_TERMS are the
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405 numbers of terms to use for the relevant expansions. */
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406
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407 #define ERF_SERIES_CUTOFF 1.5
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408 #define ERF_SERIES_TERMS 25
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409 #define ERFC_CONTFRAC_CUTOFF 30.0
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410 #define ERFC_CONTFRAC_TERMS 50
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411
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412 /*
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413 Error function, via power series.
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414
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415 Given a finite float x, return an approximation to erf(x).
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416 Converges reasonably fast for small x.
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417 */
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418
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419 static double
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420 m_erf_series(double x)
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421 {
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422 double x2, acc, fk, result;
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423 int i, saved_errno;
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424
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425 x2 = x * x;
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426 acc = 0.0;
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427 fk = (double)ERF_SERIES_TERMS + 0.5;
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428 for (i = 0; i < ERF_SERIES_TERMS; i++) {
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429 acc = 2.0 + x2 * acc / fk;
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430 fk -= 1.0;
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431 }
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432 /* Make sure the exp call doesn't affect errno;
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433 see m_erfc_contfrac for more. */
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434 saved_errno = errno;
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435 result = acc * x * exp(-x2) / sqrtpi;
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436 errno = saved_errno;
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437 return result;
498
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438 }
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439
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440 /*
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441 Complementary error function, via continued fraction expansion.
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442
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443 Given a positive float x, return an approximation to erfc(x). Converges
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444 reasonably fast for x large (say, x > 2.0), and should be safe from
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445 overflow if x and nterms are not too large. On an IEEE 754 machine, with x
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446 <= 30.0, we're safe up to nterms = 100. For x >= 30.0, erfc(x) is smaller
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447 than the smallest representable nonzero float. */
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448
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449 static double
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450 m_erfc_contfrac(double x)
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451 {
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452 double x2, a, da, p, p_last, q, q_last, b, result;
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453 int i, saved_errno;
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454
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455 if (x >= ERFC_CONTFRAC_CUTOFF)
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456 return 0.0;
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457
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458 x2 = x*x;
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459 a = 0.0;
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460 da = 0.5;
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461 p = 1.0; p_last = 0.0;
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462 q = da + x2; q_last = 1.0;
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463 for (i = 0; i < ERFC_CONTFRAC_TERMS; i++) {
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464 double temp;
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465 a += da;
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466 da += 2.0;
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467 b = da + x2;
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468 temp = p; p = b*p - a*p_last; p_last = temp;
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469 temp = q; q = b*q - a*q_last; q_last = temp;
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470 }
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471 /* Issue #8986: On some platforms, exp sets errno on underflow to zero;
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472 save the current errno value so that we can restore it later. */
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473 saved_errno = errno;
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474 result = p / q * x * exp(-x2) / sqrtpi;
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475 errno = saved_errno;
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476 return result;
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477 }
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478
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479 /* Error function erf(x), for general x */
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480
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481 static double
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482 m_erf(double x)
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483 {
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484 double absx, cf;
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485
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486 if (Py_IS_NAN(x))
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487 return x;
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488 absx = fabs(x);
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489 if (absx < ERF_SERIES_CUTOFF)
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490 return m_erf_series(x);
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491 else {
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492 cf = m_erfc_contfrac(absx);
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493 return x > 0.0 ? 1.0 - cf : cf - 1.0;
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494 }
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495 }
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496
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497 /* Complementary error function erfc(x), for general x. */
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498
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499 static double
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500 m_erfc(double x)
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501 {
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502 double absx, cf;
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503
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504 if (Py_IS_NAN(x))
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505 return x;
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506 absx = fabs(x);
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507 if (absx < ERF_SERIES_CUTOFF)
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508 return 1.0 - m_erf_series(x);
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509 else {
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510 cf = m_erfc_contfrac(absx);
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511 return x > 0.0 ? cf : 2.0 - cf;
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512 }
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513 }
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514
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515 /*
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516 wrapper for atan2 that deals directly with special cases before
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517 delegating to the platform libm for the remaining cases. This
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518 is necessary to get consistent behaviour across platforms.
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519 Windows, FreeBSD and alpha Tru64 are amongst platforms that don't
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520 always follow C99.
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521 */
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522
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523 static double
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524 m_atan2(double y, double x)
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525 {
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526 if (Py_IS_NAN(x) || Py_IS_NAN(y))
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527 return Py_NAN;
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528 if (Py_IS_INFINITY(y)) {
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529 if (Py_IS_INFINITY(x)) {
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530 if (copysign(1., x) == 1.)
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531 /* atan2(+-inf, +inf) == +-pi/4 */
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532 return copysign(0.25*Py_MATH_PI, y);
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533 else
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534 /* atan2(+-inf, -inf) == +-pi*3/4 */
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535 return copysign(0.75*Py_MATH_PI, y);
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536 }
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537 /* atan2(+-inf, x) == +-pi/2 for finite x */
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538 return copysign(0.5*Py_MATH_PI, y);
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539 }
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540 if (Py_IS_INFINITY(x) || y == 0.) {
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541 if (copysign(1., x) == 1.)
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542 /* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
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543 return copysign(0., y);
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544 else
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545 /* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
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546 return copysign(Py_MATH_PI, y);
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547 }
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548 return atan2(y, x);
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549 }
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550
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551 /*
50123
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552 Various platforms (Solaris, OpenBSD) do nonstandard things for log(0),
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553 log(-ve), log(NaN). Here are wrappers for log and log10 that deal with
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554 special values directly, passing positive non-special values through to
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555 the system log/log10.
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556 */
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557
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558 static double
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559 m_log(double x)
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560 {
61467
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561 if (Py_IS_FINITE(x)) {
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562 if (x > 0.0)
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563 return log(x);
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564 errno = EDOM;
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565 if (x == 0.0)
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566 return -Py_HUGE_VAL; /* log(0) = -inf */
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567 else
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568 return Py_NAN; /* log(-ve) = nan */
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569 }
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570 else if (Py_IS_NAN(x))
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571 return x; /* log(nan) = nan */
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572 else if (x > 0.0)
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573 return x; /* log(inf) = inf */
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574 else {
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575 errno = EDOM;
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576 return Py_NAN; /* log(-inf) = nan */
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577 }
50123
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578 }
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579
69946
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
580 /*
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
581 log2: log to base 2.
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
582
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Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
583 Uses an algorithm that should:
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627780933948 Grammatical fix for a comment for log2, to avoid referring to an *algorithm* as monotonic.
Mark Dickinson <mdickinson@enthought.com>
parents: 69971
diff changeset
584
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Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
585 (a) produce exact results for powers of 2, and
69973
627780933948 Grammatical fix for a comment for log2, to avoid referring to an *algorithm* as monotonic.
Mark Dickinson <mdickinson@enthought.com>
parents: 69971
diff changeset
586 (b) give a monotonic log2 (for positive finite floats),
627780933948 Grammatical fix for a comment for log2, to avoid referring to an *algorithm* as monotonic.
Mark Dickinson <mdickinson@enthought.com>
parents: 69971
diff changeset
587 assuming that the system log is monotonic.
69946
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Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
588 */
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
589
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Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
590 static double
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Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
591 m_log2(double x)
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
592 {
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
593 if (!Py_IS_FINITE(x)) {
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
594 if (Py_IS_NAN(x))
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Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
595 return x; /* log2(nan) = nan */
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
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parents: 68457
diff changeset
596 else if (x > 0.0)
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
597 return x; /* log2(+inf) = +inf */
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Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
598 else {
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Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
599 errno = EDOM;
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
600 return Py_NAN; /* log2(-inf) = nan, invalid-operation */
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Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
601 }
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Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
602 }
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Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
603
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Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
604 if (x > 0.0) {
69975
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Victor Stinner <victor.stinner@haypocalc.com>
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diff changeset
605 #ifdef HAVE_LOG2
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Victor Stinner <victor.stinner@haypocalc.com>
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606 return log2(x);
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Victor Stinner <victor.stinner@haypocalc.com>
parents: 69973
diff changeset
607 #else
69946
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Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
608 double m;
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
609 int e;
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Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
610 m = frexp(x, &e);
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
611 /* We want log2(m * 2**e) == log(m) / log(2) + e. Care is needed when
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
612 * x is just greater than 1.0: in that case e is 1, log(m) is negative,
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
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parents: 68457
diff changeset
613 * and we get significant cancellation error from the addition of
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parents: 68457
diff changeset
614 * log(m) / log(2) to e. The slight rewrite of the expression below
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Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
615 * avoids this problem.
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diff changeset
616 */
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
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617 if (x >= 1.0) {
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
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parents: 68457
diff changeset
618 return log(2.0 * m) / log(2.0) + (e - 1);
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Victor Stinner <victor.stinner@haypocalc.com>
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619 }
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Victor Stinner <victor.stinner@haypocalc.com>
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620 else {
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Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
621 return log(m) / log(2.0) + e;
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
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622 }
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diff changeset
623 #endif
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Victor Stinner <victor.stinner@haypocalc.com>
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diff changeset
624 }
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
625 else if (x == 0.0) {
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
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parents: 68457
diff changeset
626 errno = EDOM;
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Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
627 return -Py_HUGE_VAL; /* log2(0) = -inf, divide-by-zero */
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
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628 }
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diff changeset
629 else {
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630 errno = EDOM;
69971
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parents: 69946
diff changeset
631 return Py_NAN; /* log2(-inf) = nan, invalid-operation */
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632 }
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Victor Stinner <victor.stinner@haypocalc.com>
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diff changeset
633 }
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Victor Stinner <victor.stinner@haypocalc.com>
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diff changeset
634
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635 static double
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636 m_log10(double x)
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637 {
61467
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638 if (Py_IS_FINITE(x)) {
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639 if (x > 0.0)
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640 return log10(x);
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641 errno = EDOM;
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642 if (x == 0.0)
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643 return -Py_HUGE_VAL; /* log10(0) = -inf */
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644 else
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645 return Py_NAN; /* log10(-ve) = nan */
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646 }
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647 else if (Py_IS_NAN(x))
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648 return x; /* log10(nan) = nan */
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649 else if (x > 0.0)
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650 return x; /* log10(inf) = inf */
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651 else {
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652 errno = EDOM;
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653 return Py_NAN; /* log10(-inf) = nan */
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654 }
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655 }
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656
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657
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658 /* Call is_error when errno != 0, and where x is the result libm
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659 * returned. is_error will usually set up an exception and return
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660 * true (1), but may return false (0) without setting up an exception.
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661 */
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662 static int
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663 is_error(double x)
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664 {
61466
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665 int result = 1; /* presumption of guilt */
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666 assert(errno); /* non-zero errno is a precondition for calling */
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667 if (errno == EDOM)
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668 PyErr_SetString(PyExc_ValueError, "math domain error");
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669
61466
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670 else if (errno == ERANGE) {
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671 /* ANSI C generally requires libm functions to set ERANGE
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672 * on overflow, but also generally *allows* them to set
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673 * ERANGE on underflow too. There's no consistency about
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674 * the latter across platforms.
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675 * Alas, C99 never requires that errno be set.
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676 * Here we suppress the underflow errors (libm functions
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677 * should return a zero on underflow, and +- HUGE_VAL on
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678 * overflow, so testing the result for zero suffices to
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679 * distinguish the cases).
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680 *
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681 * On some platforms (Ubuntu/ia64) it seems that errno can be
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682 * set to ERANGE for subnormal results that do *not* underflow
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683 * to zero. So to be safe, we'll ignore ERANGE whenever the
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684 * function result is less than one in absolute value.
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685 */
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686 if (fabs(x) < 1.0)
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687 result = 0;
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688 else
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689 PyErr_SetString(PyExc_OverflowError,
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690 "math range error");
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691 }
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692 else
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693 /* Unexpected math error */
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694 PyErr_SetFromErrno(PyExc_ValueError);
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695 return result;
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696 }
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697
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698 /*
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699 math_1 is used to wrap a libm function f that takes a double
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700 arguments and returns a double.
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701
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702 The error reporting follows these rules, which are designed to do
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703 the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
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704 platforms.
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705
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706 - a NaN result from non-NaN inputs causes ValueError to be raised
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707 - an infinite result from finite inputs causes OverflowError to be
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708 raised if can_overflow is 1, or raises ValueError if can_overflow
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709 is 0.
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710 - if the result is finite and errno == EDOM then ValueError is
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711 raised
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712 - if the result is finite and nonzero and errno == ERANGE then
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713 OverflowError is raised
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714
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715 The last rule is used to catch overflow on platforms which follow
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716 C89 but for which HUGE_VAL is not an infinity.
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717
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718 For the majority of one-argument functions these rules are enough
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719 to ensure that Python's functions behave as specified in 'Annex F'
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720 of the C99 standard, with the 'invalid' and 'divide-by-zero'
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721 floating-point exceptions mapping to Python's ValueError and the
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722 'overflow' floating-point exception mapping to OverflowError.
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723 math_1 only works for functions that don't have singularities *and*
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724 the possibility of overflow; fortunately, that covers everything we
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725 care about right now.
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726 */
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727
4635
49745ddb4f69 Renamed
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728 static PyObject *
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729 math_1_to_whatever(PyObject *arg, double (*func) (double),
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730 PyObject *(*from_double_func) (double),
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731 int can_overflow)
6
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diff changeset
732 {
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733 double x, r;
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734 x = PyFloat_AsDouble(arg);
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735 if (x == -1.0 && PyErr_Occurred())
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736 return NULL;
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737 errno = 0;
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738 PyFPE_START_PROTECT("in math_1", return 0);
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739 r = (*func)(x);
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740 PyFPE_END_PROTECT(r);
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741 if (Py_IS_NAN(r) && !Py_IS_NAN(x)) {
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742 PyErr_SetString(PyExc_ValueError,
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743 "math domain error"); /* invalid arg */
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744 return NULL;
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745 }
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746 if (Py_IS_INFINITY(r) && Py_IS_FINITE(x)) {
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747 if (can_overflow)
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748 PyErr_SetString(PyExc_OverflowError,
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749 "math range error"); /* overflow */
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750 else
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751 PyErr_SetString(PyExc_ValueError,
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752 "math domain error"); /* singularity */
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753 return NULL;
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754 }
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755 if (Py_IS_FINITE(r) && errno && is_error(r))
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756 /* this branch unnecessary on most platforms */
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757 return NULL;
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758
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759 return (*from_double_func)(r);
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760 }
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761
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762 /* variant of math_1, to be used when the function being wrapped is known to
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763 set errno properly (that is, errno = EDOM for invalid or divide-by-zero,
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764 errno = ERANGE for overflow). */
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765
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766 static PyObject *
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767 math_1a(PyObject *arg, double (*func) (double))
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768 {
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769 double x, r;
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770 x = PyFloat_AsDouble(arg);
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771 if (x == -1.0 && PyErr_Occurred())
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772 return NULL;
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773 errno = 0;
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774 PyFPE_START_PROTECT("in math_1a", return 0);
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775 r = (*func)(x);
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776 PyFPE_END_PROTECT(r);
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777 if (errno && is_error(r))
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778 return NULL;
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779 return PyFloat_FromDouble(r);
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780 }
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781
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782 /*
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783 math_2 is used to wrap a libm function f that takes two double
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784 arguments and returns a double.
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785
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786 The error reporting follows these rules, which are designed to do
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787 the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
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788 platforms.
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diff changeset
789
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790 - a NaN result from non-NaN inputs causes ValueError to be raised
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791 - an infinite result from finite inputs causes OverflowError to be
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diff changeset
792 raised.
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793 - if the result is finite and errno == EDOM then ValueError is
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diff changeset
794 raised
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795 - if the result is finite and nonzero and errno == ERANGE then
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796 OverflowError is raised
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797
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798 The last rule is used to catch overflow on platforms which follow
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799 C89 but for which HUGE_VAL is not an infinity.
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800
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801 For most two-argument functions (copysign, fmod, hypot, atan2)
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802 these rules are enough to ensure that Python's functions behave as
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803 specified in 'Annex F' of the C99 standard, with the 'invalid' and
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804 'divide-by-zero' floating-point exceptions mapping to Python's
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805 ValueError and the 'overflow' floating-point exception mapping to
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806 OverflowError.
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807 */
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808
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809 static PyObject *
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810 math_1(PyObject *arg, double (*func) (double), int can_overflow)
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811 {
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812 return math_1_to_whatever(arg, func, PyFloat_FromDouble, can_overflow);
44499
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813 }
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814
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815 static PyObject *
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816 math_1_to_int(PyObject *arg, double (*func) (double), int can_overflow)
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817 {
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818 return math_1_to_whatever(arg, func, PyLong_FromDouble, can_overflow);
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819 }
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820
4635
49745ddb4f69 Renamed
Barry Warsaw <barry@python.org>
parents: 4503
diff changeset
821 static PyObject *
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
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822 math_2(PyObject *args, double (*func) (double, double), char *funcname)
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823 {
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824 PyObject *ox, *oy;
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825 double x, y, r;
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826 if (! PyArg_UnpackTuple(args, funcname, 2, 2, &ox, &oy))
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827 return NULL;
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828 x = PyFloat_AsDouble(ox);
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829 y = PyFloat_AsDouble(oy);
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830 if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
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831 return NULL;
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832 errno = 0;
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833 PyFPE_START_PROTECT("in math_2", return 0);
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834 r = (*func)(x, y);
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835 PyFPE_END_PROTECT(r);
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836 if (Py_IS_NAN(r)) {
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837 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
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838 errno = EDOM;
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839 else
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840 errno = 0;
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841 }
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842 else if (Py_IS_INFINITY(r)) {
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843 if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
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844 errno = ERANGE;
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845 else
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846 errno = 0;
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847 }
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848 if (errno && is_error(r))
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849 return NULL;
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850 else
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851 return PyFloat_FromDouble(r);
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852 }
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853
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854 #define FUNC1(funcname, func, can_overflow, docstring) \
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855 static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
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856 return math_1(args, func, can_overflow); \
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857 }\
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858 PyDoc_STRVAR(math_##funcname##_doc, docstring);
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859
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860 #define FUNC1A(funcname, func, docstring) \
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861 static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
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862 return math_1a(args, func); \
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863 }\
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864 PyDoc_STRVAR(math_##funcname##_doc, docstring);
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865
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24717405dd89 ANSI-fication, remove Py_PROTO, etc.
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parents: 13309
diff changeset
866 #define FUNC2(funcname, func, docstring) \
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867 static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
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diff changeset
868 return math_2(args, func, #funcname); \
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869 }\
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870 PyDoc_STRVAR(math_##funcname##_doc, docstring);
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871
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872 FUNC1(acos, acos, 0,
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873 "acos(x)\n\nReturn the arc cosine (measured in radians) of x.")
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874 FUNC1(acosh, m_acosh, 0,
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875 "acosh(x)\n\nReturn the hyperbolic arc cosine (measured in radians) of x.")
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876 FUNC1(asin, asin, 0,
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877 "asin(x)\n\nReturn the arc sine (measured in radians) of x.")
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878 FUNC1(asinh, m_asinh, 0,
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diff changeset
879 "asinh(x)\n\nReturn the hyperbolic arc sine (measured in radians) of x.")
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880 FUNC1(atan, atan, 0,
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881 "atan(x)\n\nReturn the arc tangent (measured in radians) of x.")
46516
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882 FUNC2(atan2, m_atan2,
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parents: 18066
diff changeset
883 "atan2(y, x)\n\nReturn the arc tangent (measured in radians) of y/x.\n"
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parents: 18066
diff changeset
884 "Unlike atan(y/x), the signs of both x and y are considered.")
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885 FUNC1(atanh, m_atanh, 0,
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diff changeset
886 "atanh(x)\n\nReturn the hyperbolic arc tangent (measured in radians) of x.")
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Guido van Rossum <guido@python.org>
parents: 42334
diff changeset
887
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__
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diff changeset
888 static PyObject * math_ceil(PyObject *self, PyObject *number) {
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889 static PyObject *ceil_str = NULL;
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diff changeset
890 PyObject *method, *result;
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Guido van Rossum <guido@python.org>
parents: 42334
diff changeset
891
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Benjamin Peterson <benjamin@python.org>
parents: 62679
diff changeset
892 method = _PyObject_LookupSpecial(number, "__ceil__", &ceil_str);
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893 if (method == NULL) {
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894 if (PyErr_Occurred())
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895 return NULL;
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896 return math_1_to_int(number, ceil, 0);
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897 }
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diff changeset
898 result = PyObject_CallFunctionObjArgs(method, NULL);
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diff changeset
899 Py_DECREF(method);
3304dc56dda4 Style/consistency nit: make math_floor and math_ceil code look the same.
Mark Dickinson <dickinsm@gmail.com>
parents: 62680
diff changeset
900 return result;
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diff changeset
901 }
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902
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diff changeset
903 PyDoc_STRVAR(math_ceil_doc,
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904 "ceil(x)\n\nReturn the ceiling of x as an int.\n"
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diff changeset
905 "This is the smallest integral value >= x.");
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Guido van Rossum <guido@python.org>
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906
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907 FUNC2(copysign, copysign,
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908 "copysign(x, y)\n\nReturn x with the sign of y.")
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909 FUNC1(cos, cos, 0,
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910 "cos(x)\n\nReturn the cosine of x (measured in radians).")
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911 FUNC1(cosh, cosh, 1,
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912 "cosh(x)\n\nReturn the hyperbolic cosine of x.")
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913 FUNC1A(erf, m_erf,
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914 "erf(x)\n\nError function at x.")
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915 FUNC1A(erfc, m_erfc,
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diff changeset
916 "erfc(x)\n\nComplementary error function at x.")
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917 FUNC1(exp, exp, 1,
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diff changeset
918 "exp(x)\n\nReturn e raised to the power of x.")
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919 FUNC1(expm1, m_expm1, 1,
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920 "expm1(x)\n\nReturn exp(x)-1.\n"
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921 "This function avoids the loss of precision involved in the direct "
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922 "evaluation of exp(x)-1 for small x.")
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923 FUNC1(fabs, fabs, 0,
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Tim Peters <tim.peters@gmail.com>
parents: 18066
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924 "fabs(x)\n\nReturn the absolute value of the float x.")
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Guido van Rossum <guido@python.org>
parents: 42334
diff changeset
925
1c98b445d847 Fix math.ceil() and math.floor() to fall back to __ceil__ and __floor__
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926 static PyObject * math_floor(PyObject *self, PyObject *number) {
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927 static PyObject *floor_str = NULL;
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928 PyObject *method, *result;
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Guido van Rossum <guido@python.org>
parents: 42334
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929
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930 method = _PyObject_LookupSpecial(number, "__floor__", &floor_str);
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931 if (method == NULL) {
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932 if (PyErr_Occurred())
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933 return NULL;
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934 return math_1_to_int(number, floor, 0);
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935 }
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936 result = PyObject_CallFunctionObjArgs(method, NULL);
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937 Py_DECREF(method);
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938 return result;
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Guido van Rossum <guido@python.org>
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939 }
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940
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941 PyDoc_STRVAR(math_floor_doc,
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942 "floor(x)\n\nReturn the floor of x as an int.\n"
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943 "This is the largest integral value <= x.");
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944
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945 FUNC1A(gamma, m_tgamma,
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946 "gamma(x)\n\nGamma function at x.")
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947 FUNC1A(lgamma, m_lgamma,
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diff changeset
948 "lgamma(x)\n\nNatural logarithm of absolute value of Gamma function at x.")
62844
87555f45cd6b Issue #9186: log1p(-1.0) should raise ValueError, not OverflowError.
Mark Dickinson <dickinsm@gmail.com>
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diff changeset
949 FUNC1(log1p, m_log1p, 0,
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950 "log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n"
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951 "The result is computed in a way which is accurate for x near zero.")
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952 FUNC1(sin, sin, 0,
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953 "sin(x)\n\nReturn the sine of x (measured in radians).")
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954 FUNC1(sinh, sinh, 1,
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955 "sinh(x)\n\nReturn the hyperbolic sine of x.")
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956 FUNC1(sqrt, sqrt, 0,
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957 "sqrt(x)\n\nReturn the square root of x.")
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958 FUNC1(tan, tan, 0,
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959 "tan(x)\n\nReturn the tangent of x (measured in radians).")
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960 FUNC1(tanh, tanh, 0,
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diff changeset
961 "tanh(x)\n\nReturn the hyperbolic tangent of x.")
6
fc6fcd7df4f7 Initial revision
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diff changeset
962
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963 /* Precision summation function as msum() by Raymond Hettinger in
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964 <http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/393090>,
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965 enhanced with the exact partials sum and roundoff from Mark
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966 Dickinson's post at <http://bugs.python.org/file10357/msum4.py>.
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967 See those links for more details, proofs and other references.
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968
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969 Note 1: IEEE 754R floating point semantics are assumed,
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970 but the current implementation does not re-establish special
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971 value semantics across iterations (i.e. handling -Inf + Inf).
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972
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973 Note 2: No provision is made for intermediate overflow handling;
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974 therefore, sum([1e+308, 1e-308, 1e+308]) returns 1e+308 while
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975 sum([1e+308, 1e+308, 1e-308]) raises an OverflowError due to the
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976 overflow of the first partial sum.
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977
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978 Note 3: The intermediate values lo, yr, and hi are declared volatile so
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979 aggressive compilers won't algebraically reduce lo to always be exactly 0.0.
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980 Also, the volatile declaration forces the values to be stored in memory as
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981 regular doubles instead of extended long precision (80-bit) values. This
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982 prevents double rounding because any addition or subtraction of two doubles
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983 can be resolved exactly into double-sized hi and lo values. As long as the
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984 hi value gets forced into a double before yr and lo are computed, the extra
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985 bits in downstream extended precision operations (x87 for example) will be
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986 exactly zero and therefore can be losslessly stored back into a double,
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987 thereby preventing double rounding.
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988
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989 Note 4: A similar implementation is in Modules/cmathmodule.c.
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990 Be sure to update both when making changes.
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991
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992 Note 5: The signature of math.fsum() differs from __builtin__.sum()
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993 because the start argument doesn't make sense in the context of
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994 accurate summation. Since the partials table is collapsed before
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995 returning a result, sum(seq2, start=sum(seq1)) may not equal the
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996 accurate result returned by sum(itertools.chain(seq1, seq2)).
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997 */
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998
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999 #define NUM_PARTIALS 32 /* initial partials array size, on stack */
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1000
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1001 /* Extend the partials array p[] by doubling its size. */
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1002 static int /* non-zero on error */
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1003 _fsum_realloc(double **p_ptr, Py_ssize_t n,
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1004 double *ps, Py_ssize_t *m_ptr)
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1005 {
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1006 void *v = NULL;
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1007 Py_ssize_t m = *m_ptr;
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1008
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1009 m += m; /* double */
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1010 if (n < m && m < (PY_SSIZE_T_MAX / sizeof(double))) {
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1011 double *p = *p_ptr;
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1012 if (p == ps) {
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1013 v = PyMem_Malloc(sizeof(double) * m);
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1014 if (v != NULL)
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1015 memcpy(v, ps, sizeof(double) * n);
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1016 }
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1017 else
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1018 v = PyMem_Realloc(p, sizeof(double) * m);
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1019 }
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1020 if (v == NULL) { /* size overflow or no memory */
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1021 PyErr_SetString(PyExc_MemoryError, "math.fsum partials");
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1022 return 1;
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1023 }
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1024 *p_ptr = (double*) v;
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diff changeset
1025 *m_ptr = m;
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1026 return 0;
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1027 }
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diff changeset
1028
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diff changeset
1029 /* Full precision summation of a sequence of floats.
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diff changeset
1030
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diff changeset
1031 def msum(iterable):
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1032 partials = [] # sorted, non-overlapping partial sums
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1033 for x in iterable:
62496
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1034 i = 0
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1035 for y in partials:
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1036 if abs(x) < abs(y):
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1037 x, y = y, x
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1038 hi = x + y
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1039 lo = y - (hi - x)
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1040 if lo:
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diff changeset
1041 partials[i] = lo
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1042 i += 1
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1043 x = hi
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1044 partials[i:] = [x]
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1045 return sum_exact(partials)
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1046
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diff changeset
1047 Rounded x+y stored in hi with the roundoff stored in lo. Together hi+lo
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diff changeset
1048 are exactly equal to x+y. The inner loop applies hi/lo summation to each
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diff changeset
1049 partial so that the list of partial sums remains exact.
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diff changeset
1050
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diff changeset
1051 Sum_exact() adds the partial sums exactly and correctly rounds the final
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diff changeset
1052 result (using the round-half-to-even rule). The items in partials remain
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1053 non-zero, non-special, non-overlapping and strictly increasing in
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1054 magnitude, but possibly not all having the same sign.
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diff changeset
1055
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diff changeset
1056 Depends on IEEE 754 arithmetic guarantees and half-even rounding.
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1057 */
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diff changeset
1058
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diff changeset
1059 static PyObject*
48606
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1060 math_fsum(PyObject *self, PyObject *seq)
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1061 {
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1062 PyObject *item, *iter, *sum = NULL;
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1063 Py_ssize_t i, j, n = 0, m = NUM_PARTIALS;
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1064 double x, y, t, ps[NUM_PARTIALS], *p = ps;
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1065 double xsave, special_sum = 0.0, inf_sum = 0.0;
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1066 volatile double hi, yr, lo;
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1067
61467
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1068 iter = PyObject_GetIter(seq);
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1069 if (iter == NULL)
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1070 return NULL;
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1071
61467
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1072 PyFPE_START_PROTECT("fsum", Py_DECREF(iter); return NULL)
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diff changeset
1073
61467
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1074 for(;;) { /* for x in iterable */
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1075 assert(0 <= n && n <= m);
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1076 assert((m == NUM_PARTIALS && p == ps) ||
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1077 (m > NUM_PARTIALS && p != NULL));
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diff changeset
1078
61467
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1079 item = PyIter_Next(iter);
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1080 if (item == NULL) {
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1081 if (PyErr_Occurred())
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1082 goto _fsum_error;
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diff changeset
1083 break;
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1084 }
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1085 x = PyFloat_AsDouble(item);
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1086 Py_DECREF(item);
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1087 if (PyErr_Occurred())
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1088 goto _fsum_error;
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diff changeset
1089
61467
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1090 xsave = x;
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diff changeset
1091 for (i = j = 0; j < n; j++) { /* for y in partials */
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diff changeset
1092 y = p[j];
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1093 if (fabs(x) < fabs(y)) {
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1094 t = x; x = y; y = t;
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1095 }
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diff changeset
1096 hi = x + y;
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1097 yr = hi - x;
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1098 lo = y - yr;
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1099 if (lo != 0.0)
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1100 p[i++] = lo;
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1101 x = hi;
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1102 }
48606
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1103
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1104 n = i; /* ps[i:] = [x] */
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1105 if (x != 0.0) {
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1106 if (! Py_IS_FINITE(x)) {
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1107 /* a nonfinite x could arise either as
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1108 a result of intermediate overflow, or
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1109 as a result of a nan or inf in the
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1110 summands */
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1111 if (Py_IS_FINITE(xsave)) {
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1112 PyErr_SetString(PyExc_OverflowError,
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1113 "intermediate overflow in fsum");
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1114 goto _fsum_error;
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1115 }
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1116 if (Py_IS_INFINITY(xsave))
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1117 inf_sum += xsave;
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1118 special_sum += xsave;
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1119 /* reset partials */
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1120 n = 0;
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1121 }
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1122 else if (n >= m && _fsum_realloc(&p, n, ps, &m))
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1123 goto _fsum_error;
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1124 else
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1125 p[n++] = x;
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1126 }
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1127 }
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1128
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1129 if (special_sum != 0.0) {
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1130 if (Py_IS_NAN(inf_sum))
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1131 PyErr_SetString(PyExc_ValueError,
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1132 "-inf + inf in fsum");
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1133 else
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1134 sum = PyFloat_FromDouble(special_sum);
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1135 goto _fsum_error;
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1136 }
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1137
61467
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1138 hi = 0.0;
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1139 if (n > 0) {
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1140 hi = p[--n];
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1141 /* sum_exact(ps, hi) from the top, stop when the sum becomes
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1142 inexact. */
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1143 while (n > 0) {
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1144 x = hi;
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1145 y = p[--n];
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1146 assert(fabs(y) < fabs(x));
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1147 hi = x + y;
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1148 yr = hi - x;
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1149 lo = y - yr;
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1150 if (lo != 0.0)
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1151 break;
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1152 }
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1153 /* Make half-even rounding work across multiple partials.
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1154 Needed so that sum([1e-16, 1, 1e16]) will round-up the last
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1155 digit to two instead of down to zero (the 1e-16 makes the 1
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1156 slightly closer to two). With a potential 1 ULP rounding
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1157 error fixed-up, math.fsum() can guarantee commutativity. */
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1158 if (n > 0 && ((lo < 0.0 && p[n-1] < 0.0) ||
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1159 (lo > 0.0 && p[n-1] > 0.0))) {
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1160 y = lo * 2.0;
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1161 x = hi + y;
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1162 yr = x - hi;
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1163 if (y == yr)
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1164 hi = x;
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1165 }
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1166 }
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1167 sum = PyFloat_FromDouble(hi);
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1168
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1169 _fsum_error:
61467
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1170 PyFPE_END_PROTECT(hi)
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1171 Py_DECREF(iter);
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1172 if (p != ps)
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1173 PyMem_Free(p);
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1174 return sum;
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1175 }
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1176
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diff changeset
1177 #undef NUM_PARTIALS
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1178
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1179 PyDoc_STRVAR(math_fsum_doc,
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1180 "fsum(iterable)\n\n\
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1181 Return an accurate floating point sum of values in the iterable.\n\
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1182 Assumes IEEE-754 floating point arithmetic.");
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diff changeset
1183
61599
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1184 /* Return the smallest integer k such that n < 2**k, or 0 if n == 0.
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1185 * Equivalent to floor(lg(x))+1. Also equivalent to: bitwidth_of_type -
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1186 * count_leading_zero_bits(x)
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1187 */
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
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1188
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1189 /* XXX: This routine does more or less the same thing as
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1190 * bits_in_digit() in Objects/longobject.c. Someday it would be nice to
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1191 * consolidate them. On BSD, there's a library function called fls()
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1192 * that we could use, and GCC provides __builtin_clz().
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
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1193 */
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
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1194
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
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1195 static unsigned long
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1196 bit_length(unsigned long n)
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1197 {
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1198 unsigned long len = 0;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1199 while (n != 0) {
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1200 ++len;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1201 n >>= 1;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1202 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1203 return len;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1204 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1205
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1206 static unsigned long
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1207 count_set_bits(unsigned long n)
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1208 {
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1209 unsigned long count = 0;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1210 while (n != 0) {
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1211 ++count;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1212 n &= n - 1; /* clear least significant bit */
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1213 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1214 return count;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1215 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1216
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1217 /* Divide-and-conquer factorial algorithm
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1218 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1219 * Based on the formula and psuedo-code provided at:
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1220 * http://www.luschny.de/math/factorial/binarysplitfact.html
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1221 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1222 * Faster algorithms exist, but they're more complicated and depend on
62859
ca05371cff10 Fix typo in a comment in mathmodule.c.
Ezio Melotti <ezio.melotti@gmail.com>
parents: 62844
diff changeset
1223 * a fast prime factorization algorithm.
61599
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1224 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1225 * Notes on the algorithm
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1226 * ----------------------
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1227 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1228 * factorial(n) is written in the form 2**k * m, with m odd. k and m are
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1229 * computed separately, and then combined using a left shift.
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1230 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1231 * The function factorial_odd_part computes the odd part m (i.e., the greatest
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1232 * odd divisor) of factorial(n), using the formula:
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1233 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1234 * factorial_odd_part(n) =
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1235 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1236 * product_{i >= 0} product_{0 < j <= n / 2**i, j odd} j
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1237 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1238 * Example: factorial_odd_part(20) =
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1239 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1240 * (1) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1241 * (1) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
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parents: 61466
diff changeset
1242 * (1 * 3 * 5) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1243 * (1 * 3 * 5 * 7 * 9)
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1244 * (1 * 3 * 5 * 7 * 9 * 11 * 13 * 15 * 17 * 19)
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1245 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1246 * Here i goes from large to small: the first term corresponds to i=4 (any
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1247 * larger i gives an empty product), and the last term corresponds to i=0.
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1248 * Each term can be computed from the last by multiplying by the extra odd
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1249 * numbers required: e.g., to get from the penultimate term to the last one,
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1250 * we multiply by (11 * 13 * 15 * 17 * 19).
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1251 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1252 * To see a hint of why this formula works, here are the same numbers as above
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1253 * but with the even parts (i.e., the appropriate powers of 2) included. For
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1254 * each subterm in the product for i, we multiply that subterm by 2**i:
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1255 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1256 * factorial(20) =
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1257 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1258 * (16) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1259 * (8) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1260 * (4 * 12 * 20) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1261 * (2 * 6 * 10 * 14 * 18) *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1262 * (1 * 3 * 5 * 7 * 9 * 11 * 13 * 15 * 17 * 19)
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1263 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1264 * The factorial_partial_product function computes the product of all odd j in
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1265 * range(start, stop) for given start and stop. It's used to compute the
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1266 * partial products like (11 * 13 * 15 * 17 * 19) in the example above. It
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1267 * operates recursively, repeatedly splitting the range into two roughly equal
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1268 * pieces until the subranges are small enough to be computed using only C
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1269 * integer arithmetic.
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1270 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1271 * The two-valuation k (i.e., the exponent of the largest power of 2 dividing
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1272 * the factorial) is computed independently in the main math_factorial
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1273 * function. By standard results, its value is:
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1274 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1275 * two_valuation = n//2 + n//4 + n//8 + ....
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1276 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1277 * It can be shown (e.g., by complete induction on n) that two_valuation is
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1278 * equal to n - count_set_bits(n), where count_set_bits(n) gives the number of
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1279 * '1'-bits in the binary expansion of n.
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1280 */
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1281
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1282 /* factorial_partial_product: Compute product(range(start, stop, 2)) using
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1283 * divide and conquer. Assumes start and stop are odd and stop > start.
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1284 * max_bits must be >= bit_length(stop - 2). */
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1285
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1286 static PyObject *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1287 factorial_partial_product(unsigned long start, unsigned long stop,
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1288 unsigned long max_bits)
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1289 {
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1290 unsigned long midpoint, num_operands;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1291 PyObject *left = NULL, *right = NULL, *result = NULL;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1292
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1293 /* If the return value will fit an unsigned long, then we can
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1294 * multiply in a tight, fast loop where each multiply is O(1).
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1295 * Compute an upper bound on the number of bits required to store
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1296 * the answer.
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1297 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1298 * Storing some integer z requires floor(lg(z))+1 bits, which is
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1299 * conveniently the value returned by bit_length(z). The
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1300 * product x*y will require at most
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1301 * bit_length(x) + bit_length(y) bits to store, based
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1302 * on the idea that lg product = lg x + lg y.
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1303 *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1304 * We know that stop - 2 is the largest number to be multiplied. From
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1305 * there, we have: bit_length(answer) <= num_operands *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1306 * bit_length(stop - 2)
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1307 */
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1308
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1309 num_operands = (stop - start) / 2;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1310 /* The "num_operands <= 8 * SIZEOF_LONG" check guards against the
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1311 * unlikely case of an overflow in num_operands * max_bits. */
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1312 if (num_operands <= 8 * SIZEOF_LONG &&
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1313 num_operands * max_bits <= 8 * SIZEOF_LONG) {
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1314 unsigned long j, total;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1315 for (total = start, j = start + 2; j < stop; j += 2)
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1316 total *= j;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1317 return PyLong_FromUnsignedLong(total);
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1318 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1319
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1320 /* find midpoint of range(start, stop), rounded up to next odd number. */
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1321 midpoint = (start + num_operands) | 1;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1322 left = factorial_partial_product(start, midpoint,
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1323 bit_length(midpoint - 2));
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1324 if (left == NULL)
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1325 goto error;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1326 right = factorial_partial_product(midpoint, stop, max_bits);
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1327 if (right == NULL)
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1328 goto error;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1329 result = PyNumber_Multiply(left, right);
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1330
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1331 error:
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1332 Py_XDECREF(left);
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1333 Py_XDECREF(right);
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1334 return result;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1335 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1336
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1337 /* factorial_odd_part: compute the odd part of factorial(n). */
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1338
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1339 static PyObject *
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1340 factorial_odd_part(unsigned long n)
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1341 {
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1342 long i;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1343 unsigned long v, lower, upper;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1344 PyObject *partial, *tmp, *inner, *outer;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1345
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1346 inner = PyLong_FromLong(1);
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1347 if (inner == NULL)
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1348 return NULL;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1349 outer = inner;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1350 Py_INCREF(outer);
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1351
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1352 upper = 3;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1353 for (i = bit_length(n) - 2; i >= 0; i--) {
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1354 v = n >> i;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1355 if (v <= 2)
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1356 continue;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1357 lower = upper;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1358 /* (v + 1) | 1 = least odd integer strictly larger than n / 2**i */
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1359 upper = (v + 1) | 1;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1360 /* Here inner is the product of all odd integers j in the range (0,
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1361 n/2**(i+1)]. The factorial_partial_product call below gives the
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1362 product of all odd integers j in the range (n/2**(i+1), n/2**i]. */
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1363 partial = factorial_partial_product(lower, upper, bit_length(upper-2));
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1364 /* inner *= partial */
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1365 if (partial == NULL)
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1366 goto error;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1367 tmp = PyNumber_Multiply(inner, partial);
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1368 Py_DECREF(partial);
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1369 if (tmp == NULL)
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1370 goto error;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1371 Py_DECREF(inner);
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1372 inner = tmp;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1373 /* Now inner is the product of all odd integers j in the range (0,
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1374 n/2**i], giving the inner product in the formula above. */
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1375
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1376 /* outer *= inner; */
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1377 tmp = PyNumber_Multiply(outer, inner);
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1378 if (tmp == NULL)
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1379 goto error;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1380 Py_DECREF(outer);
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1381 outer = tmp;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1382 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1383
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1384 goto done;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1385
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1386 error:
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1387 Py_DECREF(outer);
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1388 done:
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1389 Py_DECREF(inner);
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1390 return outer;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1391 }
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1392
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1393 /* Lookup table for small factorial values */
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1394
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1395 static const unsigned long SmallFactorials[] = {
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1396 1, 1, 2, 6, 24, 120, 720, 5040, 40320,
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1397 362880, 3628800, 39916800, 479001600,
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1398 #if SIZEOF_LONG >= 8
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1399 6227020800, 87178291200, 1307674368000,
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1400 20922789888000, 355687428096000, 6402373705728000,
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1401 121645100408832000, 2432902008176640000
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1402 #endif
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1403 };
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1404
4635
49745ddb4f69 Renamed
Barry Warsaw <barry@python.org>
parents: 4503
diff changeset
1405 static PyObject *
47562
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Georg Brandl <georg@python.org>
parents: 47559
diff changeset
1406 math_factorial(PyObject *self, PyObject *arg)
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from
Georg Brandl <georg@python.org>
parents: 47559
diff changeset
1407 {
61599
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1408 long x;
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1409 PyObject *result, *odd_part, *two_valuation;
47562
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parents: 47559
diff changeset
1410
61467
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Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1411 if (PyFloat_Check(arg)) {
61466
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Antoine Pitrou <solipsis@pitrou.net>
parents: 58125
diff changeset
1412 PyObject *lx;
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1413 double dx = PyFloat_AS_DOUBLE((PyFloatObject *)arg);
61466
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 58125
diff changeset
1414 if (!(Py_IS_FINITE(dx) && dx == floor(dx))) {
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1415 PyErr_SetString(PyExc_ValueError,
61599
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1416 "factorial() only accepts integral values");
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1417 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1418 }
61466
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 58125
diff changeset
1419 lx = PyLong_FromDouble(dx);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 58125
diff changeset
1420 if (lx == NULL)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 58125
diff changeset
1421 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 58125
diff changeset
1422 x = PyLong_AsLong(lx);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 58125
diff changeset
1423 Py_DECREF(lx);
61467
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Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1424 }
61466
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 58125
diff changeset
1425 else
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 58125
diff changeset
1426 x = PyLong_AsLong(arg);
47562
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Georg Brandl <georg@python.org>
parents: 47559
diff changeset
1427
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1428 if (x == -1 && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1429 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1430 if (x < 0) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1431 PyErr_SetString(PyExc_ValueError,
61599
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1432 "factorial() not defined for negative values");
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1433 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1434 }
47562
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Georg Brandl <georg@python.org>
parents: 47559
diff changeset
1435
61599
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1436 /* use lookup table if x is small */
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1437 if (x < (long)(sizeof(SmallFactorials)/sizeof(SmallFactorials[0])))
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1438 return PyLong_FromUnsignedLong(SmallFactorials[x]);
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1439
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1440 /* else express in the form odd_part * 2**two_valuation, and compute as
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1441 odd_part << two_valuation. */
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1442 odd_part = factorial_odd_part(x);
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1443 if (odd_part == NULL)
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1444 return NULL;
61599
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1445 two_valuation = PyLong_FromLong(x - count_set_bits(x));
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1446 if (two_valuation == NULL) {
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1447 Py_DECREF(odd_part);
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1448 return NULL;
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1449 }
61599
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1450 result = PyNumber_Lshift(odd_part, two_valuation);
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1451 Py_DECREF(two_valuation);
1e149b50aca6 Issue #8692: Improve performance of math.factorial:
Mark Dickinson <dickinsm@gmail.com>
parents: 61466
diff changeset
1452 Py_DECREF(odd_part);
61467
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Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1453 return result;
47562
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Georg Brandl <georg@python.org>
parents: 47559
diff changeset
1454 }
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from
Georg Brandl <georg@python.org>
parents: 47559
diff changeset
1455
50250
1adfabcbe073 Merged revisions 67886-67887 via svnmerge from
Benjamin Peterson <benjamin@python.org>
parents: 50123
diff changeset
1456 PyDoc_STRVAR(math_factorial_doc,
1adfabcbe073 Merged revisions 67886-67887 via svnmerge from
Benjamin Peterson <benjamin@python.org>
parents: 50123
diff changeset
1457 "factorial(x) -> Integral\n"
1adfabcbe073 Merged revisions 67886-67887 via svnmerge from
Benjamin Peterson <benjamin@python.org>
parents: 50123
diff changeset
1458 "\n"
1adfabcbe073 Merged revisions 67886-67887 via svnmerge from
Benjamin Peterson <benjamin@python.org>
parents: 50123
diff changeset
1459 "Find x!. Raise a ValueError if x is negative or non-integral.");
47562
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Georg Brandl <georg@python.org>
parents: 47559
diff changeset
1460
bd584f121c4b Merged revisions 64002-64003,64012,64036-64037,64047,64050-64052,64054-64055,64066,64071 via svnmerge from
Georg Brandl <georg@python.org>
parents: 47559
diff changeset
1461 static PyObject *
45082
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45029
diff changeset
1462 math_trunc(PyObject *self, PyObject *number)
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45029
diff changeset
1463 {
61467
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Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1464 static PyObject *trunc_str = NULL;
62679
4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial
Benjamin Peterson <benjamin@python.org>
parents: 62668
diff changeset
1465 PyObject *trunc, *result;
45082
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Christian Heimes <christian@cheimes.de>
parents: 45029
diff changeset
1466
61467
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Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1467 if (Py_TYPE(number)->tp_dict == NULL) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1468 if (PyType_Ready(Py_TYPE(number)) < 0)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1469 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1470 }
45082
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45029
diff changeset
1471
62668
a89a3d92f8ae correctly lookup __trunc__ and __floor__
Benjamin Peterson <benjamin@python.org>
parents: 62495
diff changeset
1472 trunc = _PyObject_LookupSpecial(number, "__trunc__", &trunc_str);
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1473 if (trunc == NULL) {
62668
a89a3d92f8ae correctly lookup __trunc__ and __floor__
Benjamin Peterson <benjamin@python.org>
parents: 62495
diff changeset
1474 if (!PyErr_Occurred())
a89a3d92f8ae correctly lookup __trunc__ and __floor__
Benjamin Peterson <benjamin@python.org>
parents: 62495
diff changeset
1475 PyErr_Format(PyExc_TypeError,
a89a3d92f8ae correctly lookup __trunc__ and __floor__
Benjamin Peterson <benjamin@python.org>
parents: 62495
diff changeset
1476 "type %.100s doesn't define __trunc__ method",
a89a3d92f8ae correctly lookup __trunc__ and __floor__
Benjamin Peterson <benjamin@python.org>
parents: 62495
diff changeset
1477 Py_TYPE(number)->tp_name);
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1478 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1479 }
62679
4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial
Benjamin Peterson <benjamin@python.org>
parents: 62668
diff changeset
1480 result = PyObject_CallFunctionObjArgs(trunc, NULL);
4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial
Benjamin Peterson <benjamin@python.org>
parents: 62668
diff changeset
1481 Py_DECREF(trunc);
4b0c88275f3b account for different ref counting semantics of _PyObject_LookupSpecial
Benjamin Peterson <benjamin@python.org>
parents: 62668
diff changeset
1482 return result;
45082
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45029
diff changeset
1483 }
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45029
diff changeset
1484
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45029
diff changeset
1485 PyDoc_STRVAR(math_trunc_doc,
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45029
diff changeset
1486 "trunc(x:Real) -> Integral\n"
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45029
diff changeset
1487 "\n"
45134
bdcf40d1b38e Merged revisions 60481,60485,60489-60520,60523-60527,60530-60533,60535-60538,60540-60551 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45082
diff changeset
1488 "Truncates x to the nearest Integral toward 0. Uses the __trunc__ magic method.");
45082
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45029
diff changeset
1489
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45029
diff changeset
1490 static PyObject *
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1491 math_frexp(PyObject *self, PyObject *arg)
407
9b3d557665a9 Added frexp, ldexp, modf, fmod.
Guido van Rossum <guido@python.org>
parents: 320
diff changeset
1492 {
61467
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Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1493 int i;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1494 double x = PyFloat_AsDouble(arg);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1495 if (x == -1.0 && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1496 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1497 /* deal with special cases directly, to sidestep platform
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1498 differences */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1499 if (Py_IS_NAN(x) || Py_IS_INFINITY(x) || !x) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1500 i = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1501 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1502 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1503 PyFPE_START_PROTECT("in math_frexp", return 0);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1504 x = frexp(x, &i);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1505 PyFPE_END_PROTECT(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1506 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1507 return Py_BuildValue("(di)", x, i);
407
9b3d557665a9 Added frexp, ldexp, modf, fmod.
Guido van Rossum <guido@python.org>
parents: 320
diff changeset
1508 }
9b3d557665a9 Added frexp, ldexp, modf, fmod.
Guido van Rossum <guido@python.org>
parents: 320
diff changeset
1509
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
1510 PyDoc_STRVAR(math_frexp_doc,
19712
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor.
Tim Peters <tim.peters@gmail.com>
parents: 19048
diff changeset
1511 "frexp(x)\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor.
Tim Peters <tim.peters@gmail.com>
parents: 19048
diff changeset
1512 "\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor.
Tim Peters <tim.peters@gmail.com>
parents: 19048
diff changeset
1513 "Return the mantissa and exponent of x, as pair (m, e).\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor.
Tim Peters <tim.peters@gmail.com>
parents: 19048
diff changeset
1514 "m is a float and e is an int, such that x = m * 2.**e.\n"
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
1515 "If x is 0, m and e are both 0. Else 0.5 <= abs(m) < 1.0.");
9593
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
1516
4635
49745ddb4f69 Renamed
Barry Warsaw <barry@python.org>
parents: 4503
diff changeset
1517 static PyObject *
13326
24717405dd89 ANSI-fication, remove Py_PROTO, etc.
Fred Drake <fdrake@acm.org>
parents: 13309
diff changeset
1518 math_ldexp(PyObject *self, PyObject *args)
407
9b3d557665a9 Added frexp, ldexp, modf, fmod.
Guido van Rossum <guido@python.org>
parents: 320
diff changeset
1519 {
61467
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Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1520 double x, r;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1521 PyObject *oexp;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1522 long exp;
61466
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Antoine Pitrou <solipsis@pitrou.net>
parents: 58125
diff changeset
1523 int overflow;
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1524 if (! PyArg_ParseTuple(args, "dO:ldexp", &x, &oexp))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1525 return NULL;
47063
081c15806e28 Merged revisions 62914-62916,62918-62919,62921-62922,62924-62942,62944-62945,62947-62949 via svnmerge from
Alexandre Vassalotti <alexandre@peadrop.com>
parents: 46791
diff changeset
1526
61467
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Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1527 if (PyLong_Check(oexp)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1528 /* on overflow, replace exponent with either LONG_MAX
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1529 or LONG_MIN, depending on the sign. */
61466
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 58125
diff changeset
1530 exp = PyLong_AsLongAndOverflow(oexp, &overflow);
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 58125
diff changeset
1531 if (exp == -1 && PyErr_Occurred())
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 58125
diff changeset
1532 return NULL;
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 58125
diff changeset
1533 if (overflow)
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 58125
diff changeset
1534 exp = overflow < 0 ? LONG_MIN : LONG_MAX;
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1535 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1536 else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1537 PyErr_SetString(PyExc_TypeError,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1538 "Expected an int or long as second argument "
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1539 "to ldexp.");
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1540 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1541 }
47063
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Alexandre Vassalotti <alexandre@peadrop.com>
parents: 46791
diff changeset
1542
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1543 if (x == 0. || !Py_IS_FINITE(x)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1544 /* NaNs, zeros and infinities are returned unchanged */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1545 r = x;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1546 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1547 } else if (exp > INT_MAX) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1548 /* overflow */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1549 r = copysign(Py_HUGE_VAL, x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1550 errno = ERANGE;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1551 } else if (exp < INT_MIN) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1552 /* underflow to +-0 */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1553 r = copysign(0., x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1554 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1555 } else {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1556 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1557 PyFPE_START_PROTECT("in math_ldexp", return 0);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1558 r = ldexp(x, (int)exp);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1559 PyFPE_END_PROTECT(r);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1560 if (Py_IS_INFINITY(r))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1561 errno = ERANGE;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1562 }
47063
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Alexandre Vassalotti <alexandre@peadrop.com>
parents: 46791
diff changeset
1563
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1564 if (errno && is_error(r))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1565 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1566 return PyFloat_FromDouble(r);
407
9b3d557665a9 Added frexp, ldexp, modf, fmod.
Guido van Rossum <guido@python.org>
parents: 320
diff changeset
1567 }
9b3d557665a9 Added frexp, ldexp, modf, fmod.
Guido van Rossum <guido@python.org>
parents: 320
diff changeset
1568
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
1569 PyDoc_STRVAR(math_ldexp_doc,
57210
a0951f11be3d Merged revisions 76235 via svnmerge from
Benjamin Peterson <benjamin@python.org>
parents: 50250
diff changeset
1570 "ldexp(x, i)\n\n\
a0951f11be3d Merged revisions 76235 via svnmerge from
Benjamin Peterson <benjamin@python.org>
parents: 50250
diff changeset
1571 Return x * (2**i).");
9593
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
1572
4635
49745ddb4f69 Renamed
Barry Warsaw <barry@python.org>
parents: 4503
diff changeset
1573 static PyObject *
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1574 math_modf(PyObject *self, PyObject *arg)
407
9b3d557665a9 Added frexp, ldexp, modf, fmod.
Guido van Rossum <guido@python.org>
parents: 320
diff changeset
1575 {
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1576 double y, x = PyFloat_AsDouble(arg);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1577 if (x == -1.0 && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1578 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1579 /* some platforms don't do the right thing for NaNs and
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1580 infinities, so we take care of special cases directly. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1581 if (!Py_IS_FINITE(x)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1582 if (Py_IS_INFINITY(x))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1583 return Py_BuildValue("(dd)", copysign(0., x), x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1584 else if (Py_IS_NAN(x))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1585 return Py_BuildValue("(dd)", x, x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1586 }
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
1587
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1588 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1589 PyFPE_START_PROTECT("in math_modf", return 0);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1590 x = modf(x, &y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1591 PyFPE_END_PROTECT(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1592 return Py_BuildValue("(dd)", x, y);
407
9b3d557665a9 Added frexp, ldexp, modf, fmod.
Guido van Rossum <guido@python.org>
parents: 320
diff changeset
1593 }
6
fc6fcd7df4f7 Initial revision
Guido van Rossum <guido@python.org>
parents:
diff changeset
1594
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
1595 PyDoc_STRVAR(math_modf_doc,
19712
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor.
Tim Peters <tim.peters@gmail.com>
parents: 19048
diff changeset
1596 "modf(x)\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor.
Tim Peters <tim.peters@gmail.com>
parents: 19048
diff changeset
1597 "\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor.
Tim Peters <tim.peters@gmail.com>
parents: 19048
diff changeset
1598 "Return the fractional and integer parts of x. Both results carry the sign\n"
50250
1adfabcbe073 Merged revisions 67886-67887 via svnmerge from
Benjamin Peterson <benjamin@python.org>
parents: 50123
diff changeset
1599 "of x and are floats.");
9593
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
1600
19713
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1601 /* A decent logarithm is easy to compute even for huge longs, but libm can't
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1602 do that by itself -- loghelper can. func is log or log10, and name is
58088
46d60e5ff103 Merged revisions 77234 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents: 57866
diff changeset
1603 "log" or "log10". Note that overflow of the result isn't possible: a long
46d60e5ff103 Merged revisions 77234 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents: 57866
diff changeset
1604 can contain no more than INT_MAX * SHIFT bits, so has value certainly less
46d60e5ff103 Merged revisions 77234 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents: 57866
diff changeset
1605 than 2**(2**64 * 2**16) == 2**2**80, and log2 of that is 2**80, which is
19713
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1606 small enough to fit in an IEEE single. log and log10 are even smaller.
58088
46d60e5ff103 Merged revisions 77234 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents: 57866
diff changeset
1607 However, intermediate overflow is possible for a long if the number of bits
46d60e5ff103 Merged revisions 77234 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents: 57866
diff changeset
1608 in that long is larger than PY_SSIZE_T_MAX. */
19713
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1609
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1610 static PyObject*
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1611 loghelper(PyObject* arg, double (*func)(double), char *funcname)
19713
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1612 {
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1613 /* If it is long, do it ourselves. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1614 if (PyLong_Check(arg)) {
65026
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1615 double x, result;
61466
cab14be0ada1 Recorded merge of revisions 81029 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 58125
diff changeset
1616 Py_ssize_t e;
65026
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1617
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1618 /* Negative or zero inputs give a ValueError. */
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1619 if (Py_SIZE(arg) <= 0) {
61467
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Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1620 PyErr_SetString(PyExc_ValueError,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1621 "math domain error");
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1622 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1623 }
64969
c8dc4b5e54fb Issue #9599: Tweak loghelper algorithm to return slightly improved results for powers of 2.
Mark Dickinson <dickinsm@gmail.com>
parents: 62970
diff changeset
1624
65026
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1625 x = PyLong_AsDouble(arg);
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1626 if (x == -1.0 && PyErr_Occurred()) {
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1627 if (!PyErr_ExceptionMatches(PyExc_OverflowError))
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1628 return NULL;
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1629 /* Here the conversion to double overflowed, but it's possible
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1630 to compute the log anyway. Clear the exception and continue. */
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1631 PyErr_Clear();
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1632 x = _PyLong_Frexp((PyLongObject *)arg, &e);
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1633 if (x == -1.0 && PyErr_Occurred())
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1634 return NULL;
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1635 /* Value is ~= x * 2**e, so the log ~= log(x) + log(2) * e. */
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1636 result = func(x) + func(2.0) * e;
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1637 }
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1638 else
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1639 /* Successfully converted x to a double. */
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1640 result = func(x);
a9349fd3d0f7 Issue #9599: Further accuracy tweaks to loghelper. For an integer n that's small enough to be converted to a float without overflow, log(n) is now computed as log(float(n)), and similarly for log10.
Mark Dickinson <dickinsm@gmail.com>
parents: 64969
diff changeset
1641 return PyFloat_FromDouble(result);
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1642 }
19713
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1643
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1644 /* Else let libm handle it by itself. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1645 return math_1(arg, func, 0);
19713
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1646 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1647
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1648 static PyObject *
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1649 math_log(PyObject *self, PyObject *args)
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1650 {
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1651 PyObject *arg;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1652 PyObject *base = NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1653 PyObject *num, *den;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1654 PyObject *ans;
26661
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
1655
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1656 if (!PyArg_UnpackTuple(args, "log", 1, 2, &arg, &base))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1657 return NULL;
26661
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
1658
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1659 num = loghelper(arg, m_log, "log");
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1660 if (num == NULL || base == NULL)
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1661 return num;
26661
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
1662
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1663 den = loghelper(base, m_log, "log");
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1664 if (den == NULL) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1665 Py_DECREF(num);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1666 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1667 }
26661
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
1668
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1669 ans = PyNumber_TrueDivide(num, den);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1670 Py_DECREF(num);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1671 Py_DECREF(den);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1672 return ans;
19713
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1673 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1674
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
1675 PyDoc_STRVAR(math_log_doc,
57210
a0951f11be3d Merged revisions 76235 via svnmerge from
Benjamin Peterson <benjamin@python.org>
parents: 50250
diff changeset
1676 "log(x[, base])\n\n\
a0951f11be3d Merged revisions 76235 via svnmerge from
Benjamin Peterson <benjamin@python.org>
parents: 50250
diff changeset
1677 Return the logarithm of x to the given base.\n\
26661
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
1678 If the base not specified, returns the natural logarithm (base e) of x.");
19713
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1679
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1680 static PyObject *
69946
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
1681 math_log2(PyObject *self, PyObject *arg)
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
1682 {
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
1683 return loghelper(arg, m_log2, "log2");
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
1684 }
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
1685
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
1686 PyDoc_STRVAR(math_log2_doc,
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
1687 "log2(x)\n\nReturn the base 2 logarithm of x.");
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
1688
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
diff changeset
1689 static PyObject *
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1690 math_log10(PyObject *self, PyObject *arg)
19713
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1691 {
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1692 return loghelper(arg, m_log10, "log10");
19713
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1693 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1694
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
1695 PyDoc_STRVAR(math_log10_doc,
57210
a0951f11be3d Merged revisions 76235 via svnmerge from
Benjamin Peterson <benjamin@python.org>
parents: 50250
diff changeset
1696 "log10(x)\n\nReturn the base 10 logarithm of x.");
19713
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1697
46477
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
1698 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
1699 math_fmod(PyObject *self, PyObject *args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
1700 {
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1701 PyObject *ox, *oy;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1702 double r, x, y;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1703 if (! PyArg_UnpackTuple(args, "fmod", 2, 2, &ox, &oy))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1704 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1705 x = PyFloat_AsDouble(ox);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1706 y = PyFloat_AsDouble(oy);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1707 if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1708 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1709 /* fmod(x, +/-Inf) returns x for finite x. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1710 if (Py_IS_INFINITY(y) && Py_IS_FINITE(x))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1711 return PyFloat_FromDouble(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1712 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1713 PyFPE_START_PROTECT("in math_fmod", return 0);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1714 r = fmod(x, y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1715 PyFPE_END_PROTECT(r);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1716 if (Py_IS_NAN(r)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1717 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1718 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1719 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1720 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1721 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1722 if (errno && is_error(r))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1723 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1724 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1725 return PyFloat_FromDouble(r);
46477
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
1726 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
1727
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
1728 PyDoc_STRVAR(math_fmod_doc,
57210
a0951f11be3d Merged revisions 76235 via svnmerge from
Benjamin Peterson <benjamin@python.org>
parents: 50250
diff changeset
1729 "fmod(x, y)\n\nReturn fmod(x, y), according to platform C."
46477
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
1730 " x % y may differ.");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
1731
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
1732 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
1733 math_hypot(PyObject *self, PyObject *args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
1734 {
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1735 PyObject *ox, *oy;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1736 double r, x, y;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1737 if (! PyArg_UnpackTuple(args, "hypot", 2, 2, &ox, &oy))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1738 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1739 x = PyFloat_AsDouble(ox);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1740 y = PyFloat_AsDouble(oy);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1741 if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1742 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1743 /* hypot(x, +/-Inf) returns Inf, even if x is a NaN. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1744 if (Py_IS_INFINITY(x))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1745 return PyFloat_FromDouble(fabs(x));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1746 if (Py_IS_INFINITY(y))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1747 return PyFloat_FromDouble(fabs(y));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1748 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1749 PyFPE_START_PROTECT("in math_hypot", return 0);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1750 r = hypot(x, y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1751 PyFPE_END_PROTECT(r);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1752 if (Py_IS_NAN(r)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1753 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1754 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1755 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1756 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1757 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1758 else if (Py_IS_INFINITY(r)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1759 if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1760 errno = ERANGE;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1761 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1762 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1763 }
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1764 if (errno && is_error(r))
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diff changeset
1765 return NULL;
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diff changeset
1766 else
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1767 return PyFloat_FromDouble(r);
46477
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diff changeset
1768 }
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diff changeset
1769
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diff changeset
1770 PyDoc_STRVAR(math_hypot_doc,
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diff changeset
1771 "hypot(x, y)\n\nReturn the Euclidean distance, sqrt(x*x + y*y).");
46477
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diff changeset
1772
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diff changeset
1773 /* pow can't use math_2, but needs its own wrapper: the problem is
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1774 that an infinite result can arise either as a result of overflow
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diff changeset
1775 (in which case OverflowError should be raised) or as a result of
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1776 e.g. 0.**-5. (for which ValueError needs to be raised.)
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diff changeset
1777 */
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diff changeset
1778
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1779 static PyObject *
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1780 math_pow(PyObject *self, PyObject *args)
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diff changeset
1781 {
61467
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1782 PyObject *ox, *oy;
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diff changeset
1783 double r, x, y;
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diff changeset
1784 int odd_y;
46477
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1785
61467
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1786 if (! PyArg_UnpackTuple(args, "pow", 2, 2, &ox, &oy))
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1787 return NULL;
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1788 x = PyFloat_AsDouble(ox);
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1789 y = PyFloat_AsDouble(oy);
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diff changeset
1790 if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
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1791 return NULL;
46505
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1792
61467
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1793 /* deal directly with IEEE specials, to cope with problems on various
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diff changeset
1794 platforms whose semantics don't exactly match C99 */
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diff changeset
1795 r = 0.; /* silence compiler warning */
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diff changeset
1796 if (!Py_IS_FINITE(x) || !Py_IS_FINITE(y)) {
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1797 errno = 0;
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1798 if (Py_IS_NAN(x))
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diff changeset
1799 r = y == 0. ? 1. : x; /* NaN**0 = 1 */
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1800 else if (Py_IS_NAN(y))
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diff changeset
1801 r = x == 1. ? 1. : y; /* 1**NaN = 1 */
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1802 else if (Py_IS_INFINITY(x)) {
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1803 odd_y = Py_IS_FINITE(y) && fmod(fabs(y), 2.0) == 1.0;
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1804 if (y > 0.)
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1805 r = odd_y ? x : fabs(x);
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1806 else if (y == 0.)
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1807 r = 1.;
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1808 else /* y < 0. */
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1809 r = odd_y ? copysign(0., x) : 0.;
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1810 }
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1811 else if (Py_IS_INFINITY(y)) {
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1812 if (fabs(x) == 1.0)
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1813 r = 1.;
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1814 else if (y > 0. && fabs(x) > 1.0)
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1815 r = y;
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1816 else if (y < 0. && fabs(x) < 1.0) {
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diff changeset
1817 r = -y; /* result is +inf */
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diff changeset
1818 if (x == 0.) /* 0**-inf: divide-by-zero */
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1819 errno = EDOM;
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1820 }
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1821 else
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diff changeset
1822 r = 0.;
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1823 }
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1824 }
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diff changeset
1825 else {
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diff changeset
1826 /* let libm handle finite**finite */
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diff changeset
1827 errno = 0;
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diff changeset
1828 PyFPE_START_PROTECT("in math_pow", return 0);
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diff changeset
1829 r = pow(x, y);
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diff changeset
1830 PyFPE_END_PROTECT(r);
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diff changeset
1831 /* a NaN result should arise only from (-ve)**(finite
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diff changeset
1832 non-integer); in this case we want to raise ValueError. */
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1833 if (!Py_IS_FINITE(r)) {
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1834 if (Py_IS_NAN(r)) {
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1835 errno = EDOM;
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diff changeset
1836 }
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diff changeset
1837 /*
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diff changeset
1838 an infinite result here arises either from:
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diff changeset
1839 (A) (+/-0.)**negative (-> divide-by-zero)
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1840 (B) overflow of x**y with x and y finite
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diff changeset
1841 */
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1842 else if (Py_IS_INFINITY(r)) {
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diff changeset
1843 if (x == 0.)
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1844 errno = EDOM;
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1845 else
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1846 errno = ERANGE;
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diff changeset
1847 }
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diff changeset
1848 }
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1849 }
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1850
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1851 if (errno && is_error(r))
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1852 return NULL;
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1853 else
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1854 return PyFloat_FromDouble(r);
46477
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1855 }
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diff changeset
1856
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1857 PyDoc_STRVAR(math_pow_doc,
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diff changeset
1858 "pow(x, y)\n\nReturn x**y (x to the power of y).");
46477
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diff changeset
1859
44441
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1860 static const double degToRad = Py_MATH_PI / 180.0;
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diff changeset
1861 static const double radToDeg = 180.0 / Py_MATH_PI;
23427
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and
Raymond Hettinger <python@rcn.com>
parents: 19758
diff changeset
1862
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and
Raymond Hettinger <python@rcn.com>
parents: 19758
diff changeset
1863 static PyObject *
40450
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Thomas Wouters <thomas@python.org>
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1864 math_degrees(PyObject *self, PyObject *arg)
23427
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and
Raymond Hettinger <python@rcn.com>
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1865 {
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1866 double x = PyFloat_AsDouble(arg);
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1867 if (x == -1.0 && PyErr_Occurred())
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1868 return NULL;
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1869 return PyFloat_FromDouble(x * radToDeg);
23427
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and
Raymond Hettinger <python@rcn.com>
parents: 19758
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1870 }
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and
Raymond Hettinger <python@rcn.com>
parents: 19758
diff changeset
1871
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
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diff changeset
1872 PyDoc_STRVAR(math_degrees_doc,
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1873 "degrees(x)\n\n\
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diff changeset
1874 Convert angle x from radians to degrees.");
23427
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Raymond Hettinger <python@rcn.com>
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diff changeset
1875
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and
Raymond Hettinger <python@rcn.com>
parents: 19758
diff changeset
1876 static PyObject *
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1877 math_radians(PyObject *self, PyObject *arg)
23427
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Raymond Hettinger <python@rcn.com>
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diff changeset
1878 {
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1879 double x = PyFloat_AsDouble(arg);
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1880 if (x == -1.0 && PyErr_Occurred())
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1881 return NULL;
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1882 return PyFloat_FromDouble(x * degToRad);
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Raymond Hettinger <python@rcn.com>
parents: 19758
diff changeset
1883 }
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and
Raymond Hettinger <python@rcn.com>
parents: 19758
diff changeset
1884
23832
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Martin v. Löwis <martin@v.loewis.de>
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diff changeset
1885 PyDoc_STRVAR(math_radians_doc,
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1886 "radians(x)\n\n\
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1887 Convert angle x from degrees to radians.");
19713
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1888
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1889 static PyObject *
62968
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Mark Dickinson <dickinsm@gmail.com>
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diff changeset
1890 math_isfinite(PyObject *self, PyObject *arg)
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Mark Dickinson <dickinsm@gmail.com>
parents: 62859
diff changeset
1891 {
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite.
Mark Dickinson <dickinsm@gmail.com>
parents: 62859
diff changeset
1892 double x = PyFloat_AsDouble(arg);
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite.
Mark Dickinson <dickinsm@gmail.com>
parents: 62859
diff changeset
1893 if (x == -1.0 && PyErr_Occurred())
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite.
Mark Dickinson <dickinsm@gmail.com>
parents: 62859
diff changeset
1894 return NULL;
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite.
Mark Dickinson <dickinsm@gmail.com>
parents: 62859
diff changeset
1895 return PyBool_FromLong((long)Py_IS_FINITE(x));
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite.
Mark Dickinson <dickinsm@gmail.com>
parents: 62859
diff changeset
1896 }
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite.
Mark Dickinson <dickinsm@gmail.com>
parents: 62859
diff changeset
1897
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite.
Mark Dickinson <dickinsm@gmail.com>
parents: 62859
diff changeset
1898 PyDoc_STRVAR(math_isfinite_doc,
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite.
Mark Dickinson <dickinsm@gmail.com>
parents: 62859
diff changeset
1899 "isfinite(x) -> bool\n\n\
62970
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Mark Dickinson <dickinsm@gmail.com>
parents: 62968
diff changeset
1900 Return True if x is neither an infinity nor a NaN, and False otherwise.");
62968
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Mark Dickinson <dickinsm@gmail.com>
parents: 62859
diff changeset
1901
53e7ae8ca039 Issue #9165: Add math.isfinite and cmath.isfinite.
Mark Dickinson <dickinsm@gmail.com>
parents: 62859
diff changeset
1902 static PyObject *
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diff changeset
1903 math_isnan(PyObject *self, PyObject *arg)
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Christian Heimes <christian@cheimes.de>
parents: 44351
diff changeset
1904 {
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diff changeset
1905 double x = PyFloat_AsDouble(arg);
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1906 if (x == -1.0 && PyErr_Occurred())
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1907 return NULL;
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1908 return PyBool_FromLong((long)Py_IS_NAN(x));
44441
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Christian Heimes <christian@cheimes.de>
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diff changeset
1909 }
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diff changeset
1910
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1911 PyDoc_STRVAR(math_isnan_doc,
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diff changeset
1912 "isnan(x) -> bool\n\n\
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Mark Dickinson <dickinsm@gmail.com>
parents: 62968
diff changeset
1913 Return True if x is a NaN (not a number), and False otherwise.");
44441
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diff changeset
1914
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diff changeset
1915 static PyObject *
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diff changeset
1916 math_isinf(PyObject *self, PyObject *arg)
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diff changeset
1917 {
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1918 double x = PyFloat_AsDouble(arg);
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1919 if (x == -1.0 && PyErr_Occurred())
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1920 return NULL;
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1921 return PyBool_FromLong((long)Py_IS_INFINITY(x));
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1922 }
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1923
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1924 PyDoc_STRVAR(math_isinf_doc,
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1925 "isinf(x) -> bool\n\n\
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Mark Dickinson <dickinsm@gmail.com>
parents: 62968
diff changeset
1926 Return True if x is a positive or negative infinity, and False otherwise.");
44441
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1927
4635
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Barry Warsaw <barry@python.org>
parents: 4503
diff changeset
1928 static PyMethodDef math_methods[] = {
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1929 {"acos", math_acos, METH_O, math_acos_doc},
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1930 {"acosh", math_acosh, METH_O, math_acosh_doc},
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1931 {"asin", math_asin, METH_O, math_asin_doc},
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1932 {"asinh", math_asinh, METH_O, math_asinh_doc},
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1933 {"atan", math_atan, METH_O, math_atan_doc},
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1934 {"atan2", math_atan2, METH_VARARGS, math_atan2_doc},
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1935 {"atanh", math_atanh, METH_O, math_atanh_doc},
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1936 {"ceil", math_ceil, METH_O, math_ceil_doc},
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1937 {"copysign", math_copysign, METH_VARARGS, math_copysign_doc},
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1938 {"cos", math_cos, METH_O, math_cos_doc},
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1939 {"cosh", math_cosh, METH_O, math_cosh_doc},
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1940 {"degrees", math_degrees, METH_O, math_degrees_doc},
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1941 {"erf", math_erf, METH_O, math_erf_doc},
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1942 {"erfc", math_erfc, METH_O, math_erfc_doc},
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1943 {"exp", math_exp, METH_O, math_exp_doc},
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1944 {"expm1", math_expm1, METH_O, math_expm1_doc},
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1945 {"fabs", math_fabs, METH_O, math_fabs_doc},
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1946 {"factorial", math_factorial, METH_O, math_factorial_doc},
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1947 {"floor", math_floor, METH_O, math_floor_doc},
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1948 {"fmod", math_fmod, METH_VARARGS, math_fmod_doc},
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1949 {"frexp", math_frexp, METH_O, math_frexp_doc},
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1950 {"fsum", math_fsum, METH_O, math_fsum_doc},
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1951 {"gamma", math_gamma, METH_O, math_gamma_doc},
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1952 {"hypot", math_hypot, METH_VARARGS, math_hypot_doc},
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1953 {"isfinite", math_isfinite, METH_O, math_isfinite_doc},
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1954 {"isinf", math_isinf, METH_O, math_isinf_doc},
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1955 {"isnan", math_isnan, METH_O, math_isnan_doc},
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1956 {"ldexp", math_ldexp, METH_VARARGS, math_ldexp_doc},
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1957 {"lgamma", math_lgamma, METH_O, math_lgamma_doc},
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1958 {"log", math_log, METH_VARARGS, math_log_doc},
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1959 {"log1p", math_log1p, METH_O, math_log1p_doc},
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1960 {"log10", math_log10, METH_O, math_log10_doc},
69946
6d1cbfcee45a Issue #11888: Add log2 function to math module. Patch written by Mark
Victor Stinner <victor.stinner@haypocalc.com>
parents: 68457
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1961 {"log2", math_log2, METH_O, math_log2_doc},
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1962 {"modf", math_modf, METH_O, math_modf_doc},
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1963 {"pow", math_pow, METH_VARARGS, math_pow_doc},
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1964 {"radians", math_radians, METH_O, math_radians_doc},
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1965 {"sin", math_sin, METH_O, math_sin_doc},
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1966 {"sinh", math_sinh, METH_O, math_sinh_doc},
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1967 {"sqrt", math_sqrt, METH_O, math_sqrt_doc},
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1968 {"tan", math_tan, METH_O, math_tan_doc},
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1969 {"tanh", math_tanh, METH_O, math_tanh_doc},
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1970 {"trunc", math_trunc, METH_O, math_trunc_doc},
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1971 {NULL, NULL} /* sentinel */
6
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parents:
diff changeset
1972 };
fc6fcd7df4f7 Initial revision
Guido van Rossum <guido@python.org>
parents:
diff changeset
1973
9593
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
1974
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
1975 PyDoc_STRVAR(module_doc,
19712
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor.
Tim Peters <tim.peters@gmail.com>
parents: 19048
diff changeset
1976 "This module is always available. It provides access to the\n"
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
1977 "mathematical functions defined by the C standard.");
9593
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Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
1978
47580
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API.
Martin v. Löwis <martin@v.loewis.de>
parents: 47562
diff changeset
1979
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API.
Martin v. Löwis <martin@v.loewis.de>
parents: 47562
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1980 static struct PyModuleDef mathmodule = {
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1981 PyModuleDef_HEAD_INIT,
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1982 "math",
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1983 module_doc,
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1984 -1,
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1985 math_methods,
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1986 NULL,
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1987 NULL,
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1988 NULL,
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1989 NULL
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Martin v. Löwis <martin@v.loewis.de>
parents: 47562
diff changeset
1990 };
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API.
Martin v. Löwis <martin@v.loewis.de>
parents: 47562
diff changeset
1991
24471
f66b3a3509c7 Excise DL_EXPORT/DL_IMPORT from Modules/*. Required adding a prototype
Mark Hammond <mhammond@skippinet.com.au>
parents: 23832
diff changeset
1992 PyMODINIT_FUNC
47580
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API.
Martin v. Löwis <martin@v.loewis.de>
parents: 47562
diff changeset
1993 PyInit_math(void)
6
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parents:
diff changeset
1994 {
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1995 PyObject *m;
19048
e282d6b2b758 Part of SF patch [#431848] mathmodule.c: doc strings & conversion, from
Tim Peters <tim.peters@gmail.com>
parents: 18066
diff changeset
1996
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1997 m = PyModule_Create(&mathmodule);
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1998 if (m == NULL)
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1999 goto finally;
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2000
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2001 PyModule_AddObject(m, "pi", PyFloat_FromDouble(Py_MATH_PI));
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2002 PyModule_AddObject(m, "e", PyFloat_FromDouble(Py_MATH_E));
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Barry Warsaw <barry@python.org>
parents: 4635
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2003
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2004 finally:
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2005 return m;
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2006 }