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annotate Modules/mathmodule.c @ 47426:4dedef4c0dfd

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Blocked revisions 63863 via svnmerge ........ r63863 | benjamin.peterson | 2008-06-01 14:01:25 -0500 (Sun, 01 Jun 2008) | 2 lines add a warning about bgen being removed ........
author Benjamin Peterson <benjamin@python.org>
date Sun, 01 Jun 2008 19:04:01 +0000
parents 3975ec2b0de2
children 2925b568aacc
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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 "longintrepr.h" /* just for SHIFT */
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57
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58 #ifdef _OSF_SOURCE
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59 /* OSF1 5.1 doesn't make this available with XOPEN_SOURCE_EXTENDED defined */
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60 extern double copysign(double, double);
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61 #endif
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62
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63 /* Call is_error when errno != 0, and where x is the result libm
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64 * returned. is_error will usually set up an exception and return
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65 * true (1), but may return false (0) without setting up an exception.
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66 */
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67 static int
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68 is_error(double x)
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69 {
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70 int result = 1; /* presumption of guilt */
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71 assert(errno); /* non-zero errno is a precondition for calling */
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72 if (errno == EDOM)
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73 PyErr_SetString(PyExc_ValueError, "math domain error");
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74
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75 else if (errno == ERANGE) {
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76 /* ANSI C generally requires libm functions to set ERANGE
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77 * on overflow, but also generally *allows* them to set
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78 * ERANGE on underflow too. There's no consistency about
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79 * the latter across platforms.
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80 * Alas, C99 never requires that errno be set.
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81 * Here we suppress the underflow errors (libm functions
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82 * should return a zero on underflow, and +- HUGE_VAL on
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83 * overflow, so testing the result for zero suffices to
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84 * distinguish the cases).
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85 */
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86 if (x)
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87 PyErr_SetString(PyExc_OverflowError,
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88 "math range error");
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89 else
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90 result = 0;
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91 }
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92 else
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93 /* Unexpected math error */
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94 PyErr_SetFromErrno(PyExc_ValueError);
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95 return result;
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96 }
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97
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98 /*
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99 wrapper for atan2 that deals directly with special cases before
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100 delegating to the platform libm for the remaining cases. This
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101 is necessary to get consistent behaviour across platforms.
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102 Windows, FreeBSD and alpha Tru64 are amongst platforms that don't
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103 always follow C99.
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104 */
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105
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106 static double
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107 m_atan2(double y, double x)
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108 {
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109 if (Py_IS_NAN(x) || Py_IS_NAN(y))
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110 return Py_NAN;
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111 if (Py_IS_INFINITY(y)) {
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112 if (Py_IS_INFINITY(x)) {
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113 if (copysign(1., x) == 1.)
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114 /* atan2(+-inf, +inf) == +-pi/4 */
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115 return copysign(0.25*Py_MATH_PI, y);
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116 else
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117 /* atan2(+-inf, -inf) == +-pi*3/4 */
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118 return copysign(0.75*Py_MATH_PI, y);
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119 }
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120 /* atan2(+-inf, x) == +-pi/2 for finite x */
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121 return copysign(0.5*Py_MATH_PI, y);
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122 }
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123 if (Py_IS_INFINITY(x) || y == 0.) {
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124 if (copysign(1., x) == 1.)
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125 /* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
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126 return copysign(0., y);
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127 else
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128 /* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
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129 return copysign(Py_MATH_PI, y);
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130 }
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131 return atan2(y, x);
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132 }
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133
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134 /*
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135 math_1 is used to wrap a libm function f that takes a double
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136 arguments and returns a double.
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137
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138 The error reporting follows these rules, which are designed to do
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139 the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
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140 platforms.
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141
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142 - a NaN result from non-NaN inputs causes ValueError to be raised
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143 - an infinite result from finite inputs causes OverflowError to be
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144 raised if can_overflow is 1, or raises ValueError if can_overflow
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145 is 0.
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146 - if the result is finite and errno == EDOM then ValueError is
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147 raised
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148 - if the result is finite and nonzero and errno == ERANGE then
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149 OverflowError is raised
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150
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151 The last rule is used to catch overflow on platforms which follow
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152 C89 but for which HUGE_VAL is not an infinity.
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153
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154 For the majority of one-argument functions these rules are enough
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155 to ensure that Python's functions behave as specified in 'Annex F'
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156 of the C99 standard, with the 'invalid' and 'divide-by-zero'
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157 floating-point exceptions mapping to Python's ValueError and the
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158 'overflow' floating-point exception mapping to OverflowError.
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159 math_1 only works for functions that don't have singularities *and*
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160 the possibility of overflow; fortunately, that covers everything we
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161 care about right now.
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162 */
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163
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164 static PyObject *
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165 math_1_to_whatever(PyObject *arg, double (*func) (double),
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166 PyObject *(*from_double_func) (double),
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167 int can_overflow)
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168 {
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169 double x, r;
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170 x = PyFloat_AsDouble(arg);
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171 if (x == -1.0 && PyErr_Occurred())
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172 return NULL;
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173 errno = 0;
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174 PyFPE_START_PROTECT("in math_1", return 0);
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175 r = (*func)(x);
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176 PyFPE_END_PROTECT(r);
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177 if (Py_IS_NAN(r) && !Py_IS_NAN(x)) {
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178 PyErr_SetString(PyExc_ValueError,
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179 "math domain error (invalid argument)");
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180 return NULL;
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181 }
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182 if (Py_IS_INFINITY(r) && Py_IS_FINITE(x)) {
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183 if (can_overflow)
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184 PyErr_SetString(PyExc_OverflowError,
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185 "math range error (overflow)");
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186 else
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187 PyErr_SetString(PyExc_ValueError,
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188 "math domain error (singularity)");
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189 return NULL;
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190 }
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191 if (Py_IS_FINITE(r) && errno && is_error(r))
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192 /* this branch unnecessary on most platforms */
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193 return NULL;
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194
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195 return (*from_double_func)(r);
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196 }
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197
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198 /*
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199 math_2 is used to wrap a libm function f that takes two double
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200 arguments and returns a double.
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201
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202 The error reporting follows these rules, which are designed to do
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203 the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
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204 platforms.
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205
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206 - a NaN result from non-NaN inputs causes ValueError to be raised
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207 - an infinite result from finite inputs causes OverflowError to be
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208 raised.
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209 - if the result is finite and errno == EDOM then ValueError is
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210 raised
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211 - if the result is finite and nonzero and errno == ERANGE then
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212 OverflowError is raised
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213
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214 The last rule is used to catch overflow on platforms which follow
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215 C89 but for which HUGE_VAL is not an infinity.
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216
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217 For most two-argument functions (copysign, fmod, hypot, atan2)
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218 these rules are enough to ensure that Python's functions behave as
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219 specified in 'Annex F' of the C99 standard, with the 'invalid' and
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220 'divide-by-zero' floating-point exceptions mapping to Python's
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221 ValueError and the 'overflow' floating-point exception mapping to
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222 OverflowError.
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223 */
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224
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225 static PyObject *
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226 math_1(PyObject *arg, double (*func) (double), int can_overflow)
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227 {
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228 return math_1_to_whatever(arg, func, PyFloat_FromDouble, can_overflow);
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229 }
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230
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231 static PyObject *
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232 math_1_to_int(PyObject *arg, double (*func) (double), int can_overflow)
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233 {
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234 return math_1_to_whatever(arg, func, PyLong_FromDouble, can_overflow);
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235 }
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236
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237 static PyObject *
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238 math_2(PyObject *args, double (*func) (double, double), char *funcname)
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239 {
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240 PyObject *ox, *oy;
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241 double x, y, r;
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242 if (! PyArg_UnpackTuple(args, funcname, 2, 2, &ox, &oy))
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243 return NULL;
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244 x = PyFloat_AsDouble(ox);
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245 y = PyFloat_AsDouble(oy);
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246 if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
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247 return NULL;
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248 errno = 0;
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249 PyFPE_START_PROTECT("in math_2", return 0);
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250 r = (*func)(x, y);
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251 PyFPE_END_PROTECT(r);
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252 if (Py_IS_NAN(r)) {
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253 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
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254 errno = EDOM;
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255 else
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256 errno = 0;
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257 }
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258 else if (Py_IS_INFINITY(r)) {
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259 if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
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260 errno = ERANGE;
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261 else
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262 errno = 0;
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263 }
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264 if (errno && is_error(r))
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265 return NULL;
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266 else
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267 return PyFloat_FromDouble(r);
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268 }
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269
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270 #define FUNC1(funcname, func, can_overflow, docstring) \
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271 static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
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272 return math_1(args, func, can_overflow); \
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273 }\
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274 PyDoc_STRVAR(math_##funcname##_doc, docstring);
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275
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276 #define FUNC2(funcname, func, docstring) \
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277 static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
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278 return math_2(args, func, #funcname); \
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279 }\
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280 PyDoc_STRVAR(math_##funcname##_doc, docstring);
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281
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282 FUNC1(acos, acos, 0,
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283 "acos(x)\n\nReturn the arc cosine (measured in radians) of x.")
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284 FUNC1(acosh, acosh, 0,
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285 "acosh(x)\n\nReturn the hyperbolic arc cosine (measured in radians) of x.")
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286 FUNC1(asin, asin, 0,
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287 "asin(x)\n\nReturn the arc sine (measured in radians) of x.")
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288 FUNC1(asinh, asinh, 0,
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289 "asinh(x)\n\nReturn the hyperbolic arc sine (measured in radians) of x.")
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290 FUNC1(atan, atan, 0,
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291 "atan(x)\n\nReturn the arc tangent (measured in radians) of x.")
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292 FUNC2(atan2, m_atan2,
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293 "atan2(y, x)\n\nReturn the arc tangent (measured in radians) of y/x.\n"
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294 "Unlike atan(y/x), the signs of both x and y are considered.")
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295 FUNC1(atanh, atanh, 0,
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296 "atanh(x)\n\nReturn the hyperbolic arc tangent (measured in radians) of x.")
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297
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298 static PyObject * math_ceil(PyObject *self, PyObject *number) {
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299 static PyObject *ceil_str = NULL;
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300 PyObject *method;
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301
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302 if (ceil_str == NULL) {
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303 ceil_str = PyUnicode_InternFromString("__ceil__");
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304 if (ceil_str == NULL)
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305 return NULL;
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306 }
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307
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308 method = _PyType_Lookup(Py_TYPE(number), ceil_str);
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309 if (method == NULL)
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310 return math_1_to_int(number, ceil, 0);
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311 else
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312 return PyObject_CallFunction(method, "O", number);
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313 }
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314
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315 PyDoc_STRVAR(math_ceil_doc,
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316 "ceil(x)\n\nReturn the ceiling of x as an int.\n"
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317 "This is the smallest integral value >= x.");
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318
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319 FUNC2(copysign, copysign,
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320 "copysign(x,y)\n\nReturn x with the sign of y.")
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321 FUNC1(cos, cos, 0,
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322 "cos(x)\n\nReturn the cosine of x (measured in radians).")
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323 FUNC1(cosh, cosh, 1,
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324 "cosh(x)\n\nReturn the hyperbolic cosine of x.")
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325 FUNC1(exp, exp, 1,
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326 "exp(x)\n\nReturn e raised to the power of x.")
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327 FUNC1(fabs, fabs, 0,
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328 "fabs(x)\n\nReturn the absolute value of the float x.")
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329
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330 static PyObject * math_floor(PyObject *self, PyObject *number) {
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331 static PyObject *floor_str = NULL;
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332 PyObject *method;
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333
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334 if (floor_str == NULL) {
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335 floor_str = PyUnicode_InternFromString("__floor__");
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336 if (floor_str == NULL)
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337 return NULL;
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338 }
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339
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340 method = _PyType_Lookup(Py_TYPE(number), floor_str);
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341 if (method == NULL)
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342 return math_1_to_int(number, floor, 0);
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343 else
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344 return PyObject_CallFunction(method, "O", number);
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345 }
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346
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347 PyDoc_STRVAR(math_floor_doc,
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348 "floor(x)\n\nReturn the floor of x as an int.\n"
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349 "This is the largest integral value <= x.");
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350
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351 FUNC1(log1p, log1p, 1,
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352 "log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n\
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353 The result is computed in a way which is accurate for x near zero.")
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354 FUNC1(sin, sin, 0,
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355 "sin(x)\n\nReturn the sine of x (measured in radians).")
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356 FUNC1(sinh, sinh, 1,
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357 "sinh(x)\n\nReturn the hyperbolic sine of x.")
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358 FUNC1(sqrt, sqrt, 0,
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359 "sqrt(x)\n\nReturn the square root of x.")
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360 FUNC1(tan, tan, 0,
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361 "tan(x)\n\nReturn the tangent of x (measured in radians).")
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362 FUNC1(tanh, tanh, 0,
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363 "tanh(x)\n\nReturn the hyperbolic tangent of x.")
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364
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365 /* Precision summation function as msum() by Raymond Hettinger in
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366 <http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/393090>,
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367 enhanced with the exact partials sum and roundoff from Mark
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368 Dickinson's post at <http://bugs.python.org/file10357/msum4.py>.
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369 See those links for more details, proofs and other references.
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370
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371 Note 1: IEEE 754R floating point semantics are assumed,
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372 but the current implementation does not re-establish special
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373 value semantics across iterations (i.e. handling -Inf + Inf).
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374
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375 Note 2: No provision is made for intermediate overflow handling;
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376 therefore, sum([1e+308, 1e-308, 1e+308]) returns result 1e+308 while
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377 sum([1e+308, 1e+308, 1e-308]) raises an OverflowError due to the
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378 overflow of the first partial sum.
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379
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380 Note 3: Aggressively optimizing compilers can potentially eliminate the
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381 residual values needed for accurate summation. For instance, the statements
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382 "hi = x + y; lo = y - (hi - x);" could be mis-transformed to
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383 "hi = x + y; lo = 0.0;" which defeats the computation of residuals.
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384
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385 Note 4: A similar implementation is in Modules/cmathmodule.c.
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386 Be sure to update both when making changes.
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387
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388 Note 5: The signature of math.sum() differs from __builtin__.sum()
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389 because the start argument doesn't make sense in the context of
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390 accurate summation. Since the partials table is collapsed before
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391 returning a result, sum(seq2, start=sum(seq1)) may not equal the
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392 accurate result returned by sum(itertools.chain(seq1, seq2)).
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393 */
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394
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395 #define NUM_PARTIALS 32 /* initial partials array size, on stack */
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396
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397 /* Extend the partials array p[] by doubling its size. */
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398 static int /* non-zero on error */
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399 _sum_realloc(double **p_ptr, Py_ssize_t n,
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400 double *ps, Py_ssize_t *m_ptr)
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401 {
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402 void *v = NULL;
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403 Py_ssize_t m = *m_ptr;
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404
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405 m += m; /* double */
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406 if (n < m && m < (PY_SSIZE_T_MAX / sizeof(double))) {
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407 double *p = *p_ptr;
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408 if (p == ps) {
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409 v = PyMem_Malloc(sizeof(double) * m);
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410 if (v != NULL)
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411 memcpy(v, ps, sizeof(double) * n);
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412 }
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413 else
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414 v = PyMem_Realloc(p, sizeof(double) * m);
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415 }
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416 if (v == NULL) { /* size overflow or no memory */
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417 PyErr_SetString(PyExc_MemoryError, "math sum partials");
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418 return 1;
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419 }
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420 *p_ptr = (double*) v;
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421 *m_ptr = m;
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422 return 0;
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423 }
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424
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425 /* Full precision summation of a sequence of floats.
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426
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427 def msum(iterable):
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428 partials = [] # sorted, non-overlapping partial sums
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429 for x in iterable:
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430 i = 0
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431 for y in partials:
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432 if abs(x) < abs(y):
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433 x, y = y, x
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434 hi = x + y
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435 lo = y - (hi - x)
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436 if lo:
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437 partials[i] = lo
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438 i += 1
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439 x = hi
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440 partials[i:] = [x]
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441 return sum_exact(partials)
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442
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443 Rounded x+y stored in hi with the roundoff stored in lo. Together hi+lo
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444 are exactly equal to x+y. The inner loop applies hi/lo summation to each
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445 partial so that the list of partial sums remains exact.
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446
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447 Sum_exact() adds the partial sums exactly and correctly rounds the final
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448 result (using the round-half-to-even rule). The items in partials remain
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449 non-zero, non-special, non-overlapping and strictly increasing in
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450 magnitude, but possibly not all having the same sign.
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451
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452 Depends on IEEE 754 arithmetic guarantees and half-even rounding.
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453 */
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454
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455 static PyObject*
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456 math_sum(PyObject *self, PyObject *seq)
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457 {
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458 PyObject *item, *iter, *sum = NULL;
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459 Py_ssize_t i, j, n = 0, m = NUM_PARTIALS;
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460 double x, y, hi, lo=0.0, ps[NUM_PARTIALS], *p = ps;
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461
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462 iter = PyObject_GetIter(seq);
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463 if (iter == NULL)
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464 return NULL;
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465
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466 PyFPE_START_PROTECT("sum", Py_DECREF(iter); return NULL)
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467
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468 for(;;) { /* for x in iterable */
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469 assert(0 <= n && n <= m);
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470 assert((m == NUM_PARTIALS && p == ps) ||
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471 (m > NUM_PARTIALS && p != NULL));
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472
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473 item = PyIter_Next(iter);
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474 if (item == NULL) {
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475 if (PyErr_Occurred())
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476 goto _sum_error;
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477 break;
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478 }
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479 x = PyFloat_AsDouble(item);
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480 Py_DECREF(item);
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481 if (PyErr_Occurred())
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482 goto _sum_error;
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483
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484 for (i = j = 0; j < n; j++) { /* for y in partials */
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485 y = p[j];
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486 hi = x + y;
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487 lo = fabs(x) < fabs(y)
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488 ? x - (hi - y)
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489 : y - (hi - x);
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490 if (lo != 0.0)
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491 p[i++] = lo;
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492 x = hi;
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493 }
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494
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495 n = i; /* ps[i:] = [x] */
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496 if (x != 0.0) {
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497 /* If non-finite, reset partials, effectively
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498 adding subsequent items without roundoff
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499 and yielding correct non-finite results,
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500 provided IEEE 754 rules are observed */
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501 if (! Py_IS_FINITE(x))
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502 n = 0;
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503 else if (n >= m && _sum_realloc(&p, n, ps, &m))
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504 goto _sum_error;
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505 p[n++] = x;
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506 }
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507 }
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508
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509 if (n > 0) {
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510 hi = p[--n];
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511 if (Py_IS_FINITE(hi)) {
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512 /* sum_exact(ps, hi) from the top, stop when the sum becomes inexact. */
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513 while (n > 0) {
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514 x = p[--n];
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515 y = hi;
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516 hi = x + y;
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517 assert(fabs(x) < fabs(y));
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518 lo = x - (hi - y);
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519 if (lo != 0.0)
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520 break;
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521 }
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522 /* Little dance to allow half-even rounding across multiple partials.
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523 Needed so that sum([1e-16, 1, 1e16]) will round-up to two instead
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524 of down to zero (the 1e16 makes the 1 slightly closer to two). */
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525 if (n > 0 && ((lo < 0.0 && p[n-1] < 0.0) ||
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526 (lo > 0.0 && p[n-1] > 0.0))) {
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527 y = lo * 2.0;
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528 x = hi + y;
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529 if (y == (x - hi))
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530 hi = x;
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531 }
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532 }
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533 else { /* raise corresponding error */
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534 errno = Py_IS_NAN(hi) ? EDOM : ERANGE;
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535 if (is_error(hi))
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536 goto _sum_error;
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537 }
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538 }
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539 else /* default */
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540 hi = 0.0;
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541 sum = PyFloat_FromDouble(hi);
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542
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543 _sum_error:
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544 PyFPE_END_PROTECT(hi)
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545 Py_DECREF(iter);
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546 if (p != ps)
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547 PyMem_Free(p);
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548 return sum;
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549 }
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550
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551 #undef NUM_PARTIALS
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552
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553 PyDoc_STRVAR(math_sum_doc,
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554 "sum(iterable)\n\n\
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555 Return an accurate floating point sum of values in the iterable.\n\
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556 Assumes IEEE-754 floating point arithmetic.");
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557
4635
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558 static PyObject *
45082
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559 math_trunc(PyObject *self, PyObject *number)
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560 {
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561 static PyObject *trunc_str = NULL;
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562 PyObject *trunc;
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563
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564 if (Py_TYPE(number)->tp_dict == NULL) {
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565 if (PyType_Ready(Py_TYPE(number)) < 0)
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566 return NULL;
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567 }
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568
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569 if (trunc_str == NULL) {
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570 trunc_str = PyUnicode_InternFromString("__trunc__");
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571 if (trunc_str == NULL)
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572 return NULL;
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573 }
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574
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575 trunc = _PyType_Lookup(Py_TYPE(number), trunc_str);
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576 if (trunc == NULL) {
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577 PyErr_Format(PyExc_TypeError,
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578 "type %.100s doesn't define __trunc__ method",
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579 Py_TYPE(number)->tp_name);
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580 return NULL;
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581 }
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582 return PyObject_CallFunctionObjArgs(trunc, number, NULL);
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583 }
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584
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585 PyDoc_STRVAR(math_trunc_doc,
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586 "trunc(x:Real) -> Integral\n"
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587 "\n"
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588 "Truncates x to the nearest Integral toward 0. Uses the __trunc__ magic method.");
45082
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589
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590 static PyObject *
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591 math_frexp(PyObject *self, PyObject *arg)
407
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592 {
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593 int i;
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594 double x = PyFloat_AsDouble(arg);
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595 if (x == -1.0 && PyErr_Occurred())
407
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596 return NULL;
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597 /* deal with special cases directly, to sidestep platform
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598 differences */
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599 if (Py_IS_NAN(x) || Py_IS_INFINITY(x) || !x) {
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600 i = 0;
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601 }
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602 else {
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603 PyFPE_START_PROTECT("in math_frexp", return 0);
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604 x = frexp(x, &i);
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605 PyFPE_END_PROTECT(x);
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606 }
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607 return Py_BuildValue("(di)", x, i);
407
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608 }
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609
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610 PyDoc_STRVAR(math_frexp_doc,
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611 "frexp(x)\n"
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612 "\n"
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613 "Return the mantissa and exponent of x, as pair (m, e).\n"
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614 "m is a float and e is an int, such that x = m * 2.**e.\n"
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615 "If x is 0, m and e are both 0. Else 0.5 <= abs(m) < 1.0.");
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616
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617 static PyObject *
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618 math_ldexp(PyObject *self, PyObject *args)
407
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619 {
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620 double x, r;
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621 PyObject *oexp;
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622 long exp;
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623 if (! PyArg_ParseTuple(args, "dO:ldexp", &x, &oexp))
407
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624 return NULL;
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625
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626 if (PyLong_Check(oexp)) {
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627 /* on overflow, replace exponent with either LONG_MAX
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628 or LONG_MIN, depending on the sign. */
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629 exp = PyLong_AsLong(oexp);
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630 if (exp == -1 && PyErr_Occurred()) {
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631 if (PyErr_ExceptionMatches(PyExc_OverflowError)) {
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632 if (Py_SIZE(oexp) < 0) {
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633 exp = LONG_MIN;
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634 }
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635 else {
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636 exp = LONG_MAX;
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637 }
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638 PyErr_Clear();
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639 }
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640 else {
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641 /* propagate any unexpected exception */
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642 return NULL;
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643 }
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644 }
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645 }
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646 else {
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647 PyErr_SetString(PyExc_TypeError,
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648 "Expected an int or long as second argument "
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649 "to ldexp.");
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650 return NULL;
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651 }
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652
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653 if (x == 0. || !Py_IS_FINITE(x)) {
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654 /* NaNs, zeros and infinities are returned unchanged */
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655 r = x;
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656 errno = 0;
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657 } else if (exp > INT_MAX) {
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658 /* overflow */
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659 r = copysign(Py_HUGE_VAL, x);
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660 errno = ERANGE;
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661 } else if (exp < INT_MIN) {
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662 /* underflow to +-0 */
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663 r = copysign(0., x);
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664 errno = 0;
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665 } else {
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666 errno = 0;
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667 PyFPE_START_PROTECT("in math_ldexp", return 0);
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668 r = ldexp(x, (int)exp);
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669 PyFPE_END_PROTECT(r);
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diff changeset
670 if (Py_IS_INFINITY(r))
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
671 errno = ERANGE;
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
672 }
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
673
46477
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
674 if (errno && is_error(r))
15170
09c7ac188ce2 Stop raising OverflowError on underflows reported by libm (errno==ERANGE and
Tim Peters <tim.peters@gmail.com>
parents: 14616
diff changeset
675 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
676 return PyFloat_FromDouble(r);
407
9b3d557665a9 Added frexp, ldexp, modf, fmod.
Guido van Rossum <guido@python.org>
parents: 320
diff changeset
677 }
9b3d557665a9 Added frexp, ldexp, modf, fmod.
Guido van Rossum <guido@python.org>
parents: 320
diff changeset
678
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
679 PyDoc_STRVAR(math_ldexp_doc,
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
680 "ldexp(x, i) -> x * (2**i)");
9593
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
681
4635
49745ddb4f69 Renamed
Barry Warsaw <barry@python.org>
parents: 4503
diff changeset
682 static PyObject *
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
683 math_modf(PyObject *self, PyObject *arg)
407
9b3d557665a9 Added frexp, ldexp, modf, fmod.
Guido van Rossum <guido@python.org>
parents: 320
diff changeset
684 {
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
685 double y, x = PyFloat_AsDouble(arg);
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
686 if (x == -1.0 && PyErr_Occurred())
407
9b3d557665a9 Added frexp, ldexp, modf, fmod.
Guido van Rossum <guido@python.org>
parents: 320
diff changeset
687 return NULL;
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
688 /* some platforms don't do the right thing for NaNs and
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
689 infinities, so we take care of special cases directly. */
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
690 if (!Py_IS_FINITE(x)) {
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
691 if (Py_IS_INFINITY(x))
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
692 return Py_BuildValue("(dd)", copysign(0., x), x);
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
693 else if (Py_IS_NAN(x))
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
694 return Py_BuildValue("(dd)", x, x);
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
695 }
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
696
407
9b3d557665a9 Added frexp, ldexp, modf, fmod.
Guido van Rossum <guido@python.org>
parents: 320
diff changeset
697 errno = 0;
46477
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
698 PyFPE_START_PROTECT("in math_modf", return 0);
407
9b3d557665a9 Added frexp, ldexp, modf, fmod.
Guido van Rossum <guido@python.org>
parents: 320
diff changeset
699 x = modf(x, &y);
46477
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
700 PyFPE_END_PROTECT(x);
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
701 return Py_BuildValue("(dd)", x, y);
407
9b3d557665a9 Added frexp, ldexp, modf, fmod.
Guido van Rossum <guido@python.org>
parents: 320
diff changeset
702 }
6
fc6fcd7df4f7 Initial revision
Guido van Rossum <guido@python.org>
parents:
diff changeset
703
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
704 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
705 "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
706 "\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor.
Tim Peters <tim.peters@gmail.com>
parents: 19048
diff changeset
707 "Return the fractional and integer parts of x. Both results carry the sign\n"
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
708 "of x. The integer part is returned as a real.");
9593
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
709
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
710 /* 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
711 do that by itself -- loghelper can. func is log or log10, and name is
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
712 "log" or "log10". Note that overflow isn't possible: a long can contain
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
713 no more than INT_MAX * SHIFT bits, so has value certainly less than
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
714 2**(2**64 * 2**16) == 2**2**80, and log2 of that is 2**80, which is
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
715 small enough to fit in an IEEE single. log and log10 are even smaller.
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
716 */
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
717
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
718 static PyObject*
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
719 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
720 {
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
721 /* If it is long, do it ourselves. */
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
722 if (PyLong_Check(arg)) {
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
723 double x;
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
724 int e;
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
725 x = _PyLong_AsScaledDouble(arg, &e);
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
726 if (x <= 0.0) {
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
727 PyErr_SetString(PyExc_ValueError,
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
728 "math domain error");
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
729 return NULL;
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
730 }
44999
7c02182e2979 Merged revisions 60284-60349 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 44943
diff changeset
731 /* Value is ~= x * 2**(e*PyLong_SHIFT), so the log ~=
7c02182e2979 Merged revisions 60284-60349 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 44943
diff changeset
732 log(x) + log(2) * e * PyLong_SHIFT.
7c02182e2979 Merged revisions 60284-60349 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 44943
diff changeset
733 CAUTION: e*PyLong_SHIFT may overflow using int arithmetic,
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
734 so force use of double. */
42334
e70cdce0e8b2 Merged revisions 56467-56482 via svnmerge from
Martin v. Löwis <martin@v.loewis.de>
parents: 40450
diff changeset
735 x = func(x) + (e * (double)PyLong_SHIFT) * func(2.0);
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
736 return PyFloat_FromDouble(x);
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
737 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
738
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
739 /* Else let libm handle it by itself. */
46477
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
740 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
741 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
742
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
743 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
744 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
745 {
26661
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
746 PyObject *arg;
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
747 PyObject *base = NULL;
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
748 PyObject *num, *den;
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
749 PyObject *ans;
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
750
26818
e094a03a80ff SF patch #659536: Use PyArg_UnpackTuple where possible.
Raymond Hettinger <python@rcn.com>
parents: 26661
diff changeset
751 if (!PyArg_UnpackTuple(args, "log", 1, 2, &arg, &base))
26661
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
752 return NULL;
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
753
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
754 num = loghelper(arg, log, "log");
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
755 if (num == NULL || base == NULL)
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
756 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
757
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
758 den = loghelper(base, log, "log");
26661
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
759 if (den == NULL) {
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
760 Py_DECREF(num);
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
761 return NULL;
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
762 }
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
763
37191
4bfe8afe8f65 Get rid of remnants of integer division
Neal Norwitz <nnorwitz@gmail.com>
parents: 36324
diff changeset
764 ans = PyNumber_TrueDivide(num, den);
26661
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
765 Py_DECREF(num);
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
766 Py_DECREF(den);
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
767 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
768 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
769
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
770 PyDoc_STRVAR(math_log_doc,
26661
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
771 "log(x[, base]) -> the logarithm of x to the given base.\n\
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
772 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
773
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
774 static PyObject *
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
775 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
776 {
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
777 return loghelper(arg, 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
778 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
779
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
780 PyDoc_STRVAR(math_log10_doc,
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
781 "log10(x) -> 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
782
46477
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
783 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
784 math_fmod(PyObject *self, PyObject *args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
785 {
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
786 PyObject *ox, *oy;
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
787 double r, x, y;
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788 if (! PyArg_UnpackTuple(args, "fmod", 2, 2, &ox, &oy))
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789 return NULL;
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790 x = PyFloat_AsDouble(ox);
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791 y = PyFloat_AsDouble(oy);
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792 if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
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793 return NULL;
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794 /* fmod(x, +/-Inf) returns x for finite x. */
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795 if (Py_IS_INFINITY(y) && Py_IS_FINITE(x))
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796 return PyFloat_FromDouble(x);
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797 errno = 0;
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798 PyFPE_START_PROTECT("in math_fmod", return 0);
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799 r = fmod(x, y);
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800 PyFPE_END_PROTECT(r);
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801 if (Py_IS_NAN(r)) {
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802 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
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803 errno = EDOM;
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804 else
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805 errno = 0;
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806 }
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807 if (errno && is_error(r))
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808 return NULL;
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809 else
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810 return PyFloat_FromDouble(r);
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811 }
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812
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813 PyDoc_STRVAR(math_fmod_doc,
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814 "fmod(x,y)\n\nReturn fmod(x, y), according to platform C."
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815 " x % y may differ.");
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816
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817 static PyObject *
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818 math_hypot(PyObject *self, PyObject *args)
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819 {
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820 PyObject *ox, *oy;
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821 double r, x, y;
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822 if (! PyArg_UnpackTuple(args, "hypot", 2, 2, &ox, &oy))
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823 return NULL;
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824 x = PyFloat_AsDouble(ox);
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825 y = PyFloat_AsDouble(oy);
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826 if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
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827 return NULL;
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828 /* hypot(x, +/-Inf) returns Inf, even if x is a NaN. */
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829 if (Py_IS_INFINITY(x))
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830 return PyFloat_FromDouble(fabs(x));
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831 if (Py_IS_INFINITY(y))
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832 return PyFloat_FromDouble(fabs(y));
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833 errno = 0;
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834 PyFPE_START_PROTECT("in math_hypot", return 0);
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835 r = hypot(x, y);
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836 PyFPE_END_PROTECT(r);
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837 if (Py_IS_NAN(r)) {
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838 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
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839 errno = EDOM;
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840 else
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841 errno = 0;
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842 }
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843 else if (Py_IS_INFINITY(r)) {
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844 if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
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845 errno = ERANGE;
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846 else
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847 errno = 0;
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848 }
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849 if (errno && is_error(r))
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850 return NULL;
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851 else
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852 return PyFloat_FromDouble(r);
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853 }
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854
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855 PyDoc_STRVAR(math_hypot_doc,
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856 "hypot(x,y)\n\nReturn the Euclidean distance, sqrt(x*x + y*y).");
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857
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858 /* pow can't use math_2, but needs its own wrapper: the problem is
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859 that an infinite result can arise either as a result of overflow
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860 (in which case OverflowError should be raised) or as a result of
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861 e.g. 0.**-5. (for which ValueError needs to be raised.)
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862 */
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863
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864 static PyObject *
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865 math_pow(PyObject *self, PyObject *args)
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866 {
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867 PyObject *ox, *oy;
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868 double r, x, y;
46505
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869 int odd_y;
46477
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870
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871 if (! PyArg_UnpackTuple(args, "pow", 2, 2, &ox, &oy))
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872 return NULL;
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873 x = PyFloat_AsDouble(ox);
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874 y = PyFloat_AsDouble(oy);
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875 if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
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876 return NULL;
46505
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877
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878 /* deal directly with IEEE specials, to cope with problems on various
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879 platforms whose semantics don't exactly match C99 */
46664
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880 r = 0.; /* silence compiler warning */
46505
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881 if (!Py_IS_FINITE(x) || !Py_IS_FINITE(y)) {
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882 errno = 0;
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883 if (Py_IS_NAN(x))
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884 r = y == 0. ? 1. : x; /* NaN**0 = 1 */
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885 else if (Py_IS_NAN(y))
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886 r = x == 1. ? 1. : y; /* 1**NaN = 1 */
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887 else if (Py_IS_INFINITY(x)) {
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888 odd_y = Py_IS_FINITE(y) && fmod(fabs(y), 2.0) == 1.0;
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889 if (y > 0.)
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890 r = odd_y ? x : fabs(x);
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891 else if (y == 0.)
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892 r = 1.;
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893 else /* y < 0. */
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894 r = odd_y ? copysign(0., x) : 0.;
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895 }
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896 else if (Py_IS_INFINITY(y)) {
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897 if (fabs(x) == 1.0)
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898 r = 1.;
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899 else if (y > 0. && fabs(x) > 1.0)
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900 r = y;
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901 else if (y < 0. && fabs(x) < 1.0) {
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902 r = -y; /* result is +inf */
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903 if (x == 0.) /* 0**-inf: divide-by-zero */
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904 errno = EDOM;
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905 }
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diff changeset
906 else
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907 r = 0.;
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908 }
46477
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909 }
46505
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910 else {
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911 /* let libm handle finite**finite */
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912 errno = 0;
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913 PyFPE_START_PROTECT("in math_pow", return 0);
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914 r = pow(x, y);
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915 PyFPE_END_PROTECT(r);
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916 /* a NaN result should arise only from (-ve)**(finite
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917 non-integer); in this case we want to raise ValueError. */
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918 if (!Py_IS_FINITE(r)) {
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diff changeset
919 if (Py_IS_NAN(r)) {
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920 errno = EDOM;
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921 }
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diff changeset
922 /*
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diff changeset
923 an infinite result here arises either from:
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diff changeset
924 (A) (+/-0.)**negative (-> divide-by-zero)
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diff changeset
925 (B) overflow of x**y with x and y finite
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diff changeset
926 */
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diff changeset
927 else if (Py_IS_INFINITY(r)) {
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parents: 46477
diff changeset
928 if (x == 0.)
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diff changeset
929 errno = EDOM;
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diff changeset
930 else
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diff changeset
931 errno = ERANGE;
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diff changeset
932 }
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diff changeset
933 }
46477
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diff changeset
934 }
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diff changeset
935
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diff changeset
936 if (errno && is_error(r))
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diff changeset
937 return NULL;
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diff changeset
938 else
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diff changeset
939 return PyFloat_FromDouble(r);
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diff changeset
940 }
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diff changeset
941
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942 PyDoc_STRVAR(math_pow_doc,
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diff changeset
943 "pow(x,y)\n\nReturn x**y (x to the power of y).");
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944
44441
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945 static const double degToRad = Py_MATH_PI / 180.0;
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diff changeset
946 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
947
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and
Raymond Hettinger <python@rcn.com>
parents: 19758
diff changeset
948 static PyObject *
40450
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diff changeset
949 math_degrees(PyObject *self, PyObject *arg)
23427
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Raymond Hettinger <python@rcn.com>
parents: 19758
diff changeset
950 {
40450
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951 double x = PyFloat_AsDouble(arg);
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952 if (x == -1.0 && PyErr_Occurred())
23427
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and
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diff changeset
953 return NULL;
44441
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954 return PyFloat_FromDouble(x * radToDeg);
23427
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Raymond Hettinger <python@rcn.com>
parents: 19758
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955 }
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and
Raymond Hettinger <python@rcn.com>
parents: 19758
diff changeset
956
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
957 PyDoc_STRVAR(math_degrees_doc,
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
958 "degrees(x) -> converts angle x from radians to degrees");
23427
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and
Raymond Hettinger <python@rcn.com>
parents: 19758
diff changeset
959
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and
Raymond Hettinger <python@rcn.com>
parents: 19758
diff changeset
960 static PyObject *
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diff changeset
961 math_radians(PyObject *self, PyObject *arg)
23427
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Raymond Hettinger <python@rcn.com>
parents: 19758
diff changeset
962 {
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963 double x = PyFloat_AsDouble(arg);
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diff changeset
964 if (x == -1.0 && PyErr_Occurred())
23427
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and
Raymond Hettinger <python@rcn.com>
parents: 19758
diff changeset
965 return NULL;
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and
Raymond Hettinger <python@rcn.com>
parents: 19758
diff changeset
966 return PyFloat_FromDouble(x * degToRad);
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and
Raymond Hettinger <python@rcn.com>
parents: 19758
diff changeset
967 }
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and
Raymond Hettinger <python@rcn.com>
parents: 19758
diff changeset
968
23832
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Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
969 PyDoc_STRVAR(math_radians_doc,
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
970 "radians(x) -> converts 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
971
44441
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972 static PyObject *
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diff changeset
973 math_isnan(PyObject *self, PyObject *arg)
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diff changeset
974 {
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975 double x = PyFloat_AsDouble(arg);
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diff changeset
976 if (x == -1.0 && PyErr_Occurred())
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diff changeset
977 return NULL;
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978 return PyBool_FromLong((long)Py_IS_NAN(x));
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979 }
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980
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diff changeset
981 PyDoc_STRVAR(math_isnan_doc,
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diff changeset
982 "isnan(x) -> bool\n\
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diff changeset
983 Checks if float x is not a number (NaN)");
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diff changeset
984
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985 static PyObject *
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diff changeset
986 math_isinf(PyObject *self, PyObject *arg)
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diff changeset
987 {
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988 double x = PyFloat_AsDouble(arg);
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989 if (x == -1.0 && PyErr_Occurred())
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990 return NULL;
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991 return PyBool_FromLong((long)Py_IS_INFINITY(x));
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992 }
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993
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994 PyDoc_STRVAR(math_isinf_doc,
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diff changeset
995 "isinf(x) -> bool\n\
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996 Checks if float x is infinite (positive or negative)");
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diff changeset
997
4635
49745ddb4f69 Renamed
Barry Warsaw <barry@python.org>
parents: 4503
diff changeset
998 static PyMethodDef math_methods[] = {
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diff changeset
999 {"acos", math_acos, METH_O, math_acos_doc},
46477
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diff changeset
1000 {"acosh", math_acosh, METH_O, math_acosh_doc},
40450
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diff changeset
1001 {"asin", math_asin, METH_O, math_asin_doc},
46477
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diff changeset
1002 {"asinh", math_asinh, METH_O, math_asinh_doc},
40450
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diff changeset
1003 {"atan", math_atan, METH_O, math_atan_doc},
13326
24717405dd89 ANSI-fication, remove Py_PROTO, etc.
Fred Drake <fdrake@acm.org>
parents: 13309
diff changeset
1004 {"atan2", math_atan2, METH_VARARGS, math_atan2_doc},
46477
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Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
1005 {"atanh", math_atanh, METH_O, math_atanh_doc},
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1006 {"ceil", math_ceil, METH_O, math_ceil_doc},
44441
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 44351
diff changeset
1007 {"copysign", math_copysign, METH_VARARGS, math_copysign_doc},
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1008 {"cos", math_cos, METH_O, math_cos_doc},
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1009 {"cosh", math_cosh, METH_O, math_cosh_doc},
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1010 {"degrees", math_degrees, METH_O, math_degrees_doc},
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1011 {"exp", math_exp, METH_O, math_exp_doc},
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1012 {"fabs", math_fabs, METH_O, math_fabs_doc},
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1013 {"floor", math_floor, METH_O, math_floor_doc},
13326
24717405dd89 ANSI-fication, remove Py_PROTO, etc.
Fred Drake <fdrake@acm.org>
parents: 13309
diff changeset
1014 {"fmod", math_fmod, METH_VARARGS, math_fmod_doc},
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1015 {"frexp", math_frexp, METH_O, math_frexp_doc},
13326
24717405dd89 ANSI-fication, remove Py_PROTO, etc.
Fred Drake <fdrake@acm.org>
parents: 13309
diff changeset
1016 {"hypot", math_hypot, METH_VARARGS, math_hypot_doc},
44441
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 44351
diff changeset
1017 {"isinf", math_isinf, METH_O, math_isinf_doc},
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 44351
diff changeset
1018 {"isnan", math_isnan, METH_O, math_isnan_doc},
13326
24717405dd89 ANSI-fication, remove Py_PROTO, etc.
Fred Drake <fdrake@acm.org>
parents: 13309
diff changeset
1019 {"ldexp", math_ldexp, METH_VARARGS, math_ldexp_doc},
24717405dd89 ANSI-fication, remove Py_PROTO, etc.
Fred Drake <fdrake@acm.org>
parents: 13309
diff changeset
1020 {"log", math_log, METH_VARARGS, math_log_doc},
46477
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
1021 {"log1p", math_log1p, METH_O, math_log1p_doc},
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1022 {"log10", math_log10, METH_O, math_log10_doc},
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1023 {"modf", math_modf, METH_O, math_modf_doc},
13326
24717405dd89 ANSI-fication, remove Py_PROTO, etc.
Fred Drake <fdrake@acm.org>
parents: 13309
diff changeset
1024 {"pow", math_pow, METH_VARARGS, math_pow_doc},
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1025 {"radians", math_radians, METH_O, math_radians_doc},
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1026 {"sin", math_sin, METH_O, math_sin_doc},
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1027 {"sinh", math_sinh, METH_O, math_sinh_doc},
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1028 {"sqrt", math_sqrt, METH_O, math_sqrt_doc},
47320
3975ec2b0de2 Merged revisions 63542-63544,63546,63553,63563-63564,63567,63569,63576 via svnmerge from
Benjamin Peterson <benjamin@python.org>
parents: 47175
diff changeset
1029 {"sum", math_sum, METH_O, math_sum_doc},
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1030 {"tan", math_tan, METH_O, math_tan_doc},
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
1031 {"tanh", math_tanh, METH_O, math_tanh_doc},
45082
d7540031b959 Merged revisions 60475-60479,60481-60488 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45029
diff changeset
1032 {"trunc", math_trunc, METH_O, math_trunc_doc},
6
fc6fcd7df4f7 Initial revision
Guido van Rossum <guido@python.org>
parents:
diff changeset
1033 {NULL, NULL} /* sentinel */
fc6fcd7df4f7 Initial revision
Guido van Rossum <guido@python.org>
parents:
diff changeset
1034 };
fc6fcd7df4f7 Initial revision
Guido van Rossum <guido@python.org>
parents:
diff changeset
1035
9593
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
1036
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
1037 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
1038 "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
1039 "mathematical functions defined by the C standard.");
9593
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
1040
24471
f66b3a3509c7 Excise DL_EXPORT/DL_IMPORT from Modules/*. Required adding a prototype
Mark Hammond <mhammond@skippinet.com.au>
parents: 23832
diff changeset
1041 PyMODINIT_FUNC
13651
8a063423e0b7 Bunch of minor ANSIfications: 'void initfunc()' -> 'void initfunc(void)',
Thomas Wouters <thomas@python.org>
parents: 13331
diff changeset
1042 initmath(void)
6
fc6fcd7df4f7 Initial revision
Guido van Rossum <guido@python.org>
parents:
diff changeset
1043 {
46477
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Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
1044 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
1045
9593
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Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
1046 m = Py_InitModule3("math", math_methods, module_doc);
36324
1af7f719ed28 Check return result from Py_InitModule*(). This API can fail.
Neal Norwitz <nnorwitz@gmail.com>
parents: 34872
diff changeset
1047 if (m == NULL)
1af7f719ed28 Check return result from Py_InitModule*(). This API can fail.
Neal Norwitz <nnorwitz@gmail.com>
parents: 34872
diff changeset
1048 goto finally;
4752
7367fb107108 Better error checking in initmath().
Barry Warsaw <barry@python.org>
parents: 4635
diff changeset
1049
46477
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Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
1050 PyModule_AddObject(m, "pi", PyFloat_FromDouble(Py_MATH_PI));
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
1051 PyModule_AddObject(m, "e", PyFloat_FromDouble(Py_MATH_E));
4752
7367fb107108 Better error checking in initmath().
Barry Warsaw <barry@python.org>
parents: 4635
diff changeset
1052
46477
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Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
1053 finally:
14346
5397fdf88ec2 Do the absolute minimal amount of modifications to eradicate
Barry Warsaw <barry@python.org>
parents: 13912
diff changeset
1054 return;
6
fc6fcd7df4f7 Initial revision
Guido van Rossum <guido@python.org>
parents:
diff changeset
1055 }