Mercurial > cpython-lru_cache-weakref

annotate Modules/mathmodule.c @ 66978:aed2bbafa550 3.1

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Blocked revisions 87324 via svnmerge ........ r87324 | r.david.murray | 2010-12-16 14:08:51 -0500 (Thu, 16 Dec 2010) | 9 lines #10719: restore messages generated on invalid compileall args Before the introduction of filename arguments to compileall it gave semi useful messages about not being able to 'list' names that weren't valid directories. This fix restores that behavior. In addition to the test for this case, the patch also adds a test for the default behavior of compileall when no arguments are provided, and fixes a bug in one of the previously added tests. ........
author R. David Murray <rdmurray@bitdance.com>
date Thu, 16 Dec 2010 19:10:16 +0000
parents 0c87490767bf
children 3c9232a684ae
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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 * On some platforms (Ubuntu/ia64) it seems that errno can be
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87 * set to ERANGE for subnormal results that do *not* underflow
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88 * to zero. So to be safe, we'll ignore ERANGE whenever the
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89 * function result is less than one in absolute value.
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90 */
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91 if (fabs(x) < 1.0)
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92 result = 0;
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93 else
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94 PyErr_SetString(PyExc_OverflowError,
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95 "math range error");
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96 }
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97 else
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98 /* Unexpected math error */
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99 PyErr_SetFromErrno(PyExc_ValueError);
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100 return result;
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101 }
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102
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103 /*
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104 wrapper for atan2 that deals directly with special cases before
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105 delegating to the platform libm for the remaining cases. This
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106 is necessary to get consistent behaviour across platforms.
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107 Windows, FreeBSD and alpha Tru64 are amongst platforms that don't
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108 always follow C99.
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109 */
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110
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111 static double
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112 m_atan2(double y, double x)
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113 {
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114 if (Py_IS_NAN(x) || Py_IS_NAN(y))
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115 return Py_NAN;
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116 if (Py_IS_INFINITY(y)) {
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117 if (Py_IS_INFINITY(x)) {
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118 if (copysign(1., x) == 1.)
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119 /* atan2(+-inf, +inf) == +-pi/4 */
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120 return copysign(0.25*Py_MATH_PI, y);
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121 else
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122 /* atan2(+-inf, -inf) == +-pi*3/4 */
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123 return copysign(0.75*Py_MATH_PI, y);
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124 }
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125 /* atan2(+-inf, x) == +-pi/2 for finite x */
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126 return copysign(0.5*Py_MATH_PI, y);
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127 }
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128 if (Py_IS_INFINITY(x) || y == 0.) {
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129 if (copysign(1., x) == 1.)
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130 /* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
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131 return copysign(0., y);
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132 else
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133 /* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
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134 return copysign(Py_MATH_PI, y);
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135 }
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136 return atan2(y, x);
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137 }
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138
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139 /*
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140 Various platforms (Solaris, OpenBSD) do nonstandard things for log(0),
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141 log(-ve), log(NaN). Here are wrappers for log and log10 that deal with
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142 special values directly, passing positive non-special values through to
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143 the system log/log10.
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144 */
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145
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146 static double
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147 m_log(double x)
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148 {
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149 if (Py_IS_FINITE(x)) {
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150 if (x > 0.0)
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151 return log(x);
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152 errno = EDOM;
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153 if (x == 0.0)
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154 return -Py_HUGE_VAL; /* log(0) = -inf */
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155 else
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156 return Py_NAN; /* log(-ve) = nan */
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157 }
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158 else if (Py_IS_NAN(x))
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159 return x; /* log(nan) = nan */
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160 else if (x > 0.0)
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161 return x; /* log(inf) = inf */
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162 else {
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163 errno = EDOM;
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164 return Py_NAN; /* log(-inf) = nan */
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165 }
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166 }
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167
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168 static double
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169 m_log10(double x)
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170 {
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171 if (Py_IS_FINITE(x)) {
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172 if (x > 0.0)
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173 return log10(x);
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174 errno = EDOM;
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175 if (x == 0.0)
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176 return -Py_HUGE_VAL; /* log10(0) = -inf */
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177 else
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178 return Py_NAN; /* log10(-ve) = nan */
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179 }
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180 else if (Py_IS_NAN(x))
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181 return x; /* log10(nan) = nan */
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182 else if (x > 0.0)
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183 return x; /* log10(inf) = inf */
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184 else {
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185 errno = EDOM;
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186 return Py_NAN; /* log10(-inf) = nan */
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187 }
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188 }
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189
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190
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191 /*
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192 math_1 is used to wrap a libm function f that takes a double
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193 arguments and returns a double.
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194
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195 The error reporting follows these rules, which are designed to do
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196 the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
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197 platforms.
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198
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199 - a NaN result from non-NaN inputs causes ValueError to be raised
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200 - an infinite result from finite inputs causes OverflowError to be
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201 raised if can_overflow is 1, or raises ValueError if can_overflow
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202 is 0.
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203 - if the result is finite and errno == EDOM then ValueError is
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204 raised
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205 - if the result is finite and nonzero and errno == ERANGE then
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206 OverflowError is raised
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207
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208 The last rule is used to catch overflow on platforms which follow
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209 C89 but for which HUGE_VAL is not an infinity.
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210
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211 For the majority of one-argument functions these rules are enough
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212 to ensure that Python's functions behave as specified in 'Annex F'
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213 of the C99 standard, with the 'invalid' and 'divide-by-zero'
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214 floating-point exceptions mapping to Python's ValueError and the
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215 'overflow' floating-point exception mapping to OverflowError.
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216 math_1 only works for functions that don't have singularities *and*
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217 the possibility of overflow; fortunately, that covers everything we
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218 care about right now.
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219 */
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220
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221 static PyObject *
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222 math_1_to_whatever(PyObject *arg, double (*func) (double),
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223 PyObject *(*from_double_func) (double),
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224 int can_overflow)
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225 {
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226 double x, r;
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227 x = PyFloat_AsDouble(arg);
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228 if (x == -1.0 && PyErr_Occurred())
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229 return NULL;
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230 errno = 0;
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231 PyFPE_START_PROTECT("in math_1", return 0);
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232 r = (*func)(x);
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233 PyFPE_END_PROTECT(r);
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234 if (Py_IS_NAN(r) && !Py_IS_NAN(x)) {
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235 PyErr_SetString(PyExc_ValueError,
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236 "math domain error"); /* invalid arg */
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237 return NULL;
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238 }
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239 if (Py_IS_INFINITY(r) && Py_IS_FINITE(x)) {
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240 if (can_overflow)
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241 PyErr_SetString(PyExc_OverflowError,
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242 "math range error"); /* overflow */
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243 else
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244 PyErr_SetString(PyExc_ValueError,
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245 "math domain error"); /* singularity */
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246 return NULL;
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247 }
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248 if (Py_IS_FINITE(r) && errno && is_error(r))
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249 /* this branch unnecessary on most platforms */
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250 return NULL;
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251
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252 return (*from_double_func)(r);
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253 }
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254
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255 /*
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256 math_2 is used to wrap a libm function f that takes two double
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257 arguments and returns a double.
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258
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259 The error reporting follows these rules, which are designed to do
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260 the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
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261 platforms.
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262
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263 - a NaN result from non-NaN inputs causes ValueError to be raised
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264 - an infinite result from finite inputs causes OverflowError to be
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265 raised.
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266 - if the result is finite and errno == EDOM then ValueError is
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267 raised
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268 - if the result is finite and nonzero and errno == ERANGE then
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269 OverflowError is raised
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270
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271 The last rule is used to catch overflow on platforms which follow
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272 C89 but for which HUGE_VAL is not an infinity.
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273
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274 For most two-argument functions (copysign, fmod, hypot, atan2)
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275 these rules are enough to ensure that Python's functions behave as
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276 specified in 'Annex F' of the C99 standard, with the 'invalid' and
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277 'divide-by-zero' floating-point exceptions mapping to Python's
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278 ValueError and the 'overflow' floating-point exception mapping to
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279 OverflowError.
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280 */
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281
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282 static PyObject *
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283 math_1(PyObject *arg, double (*func) (double), int can_overflow)
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284 {
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285 return math_1_to_whatever(arg, func, PyFloat_FromDouble, can_overflow);
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286 }
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287
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288 static PyObject *
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289 math_1_to_int(PyObject *arg, double (*func) (double), int can_overflow)
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290 {
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291 return math_1_to_whatever(arg, func, PyLong_FromDouble, can_overflow);
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292 }
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293
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294 static PyObject *
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295 math_2(PyObject *args, double (*func) (double, double), char *funcname)
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296 {
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297 PyObject *ox, *oy;
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298 double x, y, r;
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299 if (! PyArg_UnpackTuple(args, funcname, 2, 2, &ox, &oy))
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300 return NULL;
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301 x = PyFloat_AsDouble(ox);
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302 y = PyFloat_AsDouble(oy);
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303 if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
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304 return NULL;
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305 errno = 0;
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306 PyFPE_START_PROTECT("in math_2", return 0);
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307 r = (*func)(x, y);
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308 PyFPE_END_PROTECT(r);
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309 if (Py_IS_NAN(r)) {
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310 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
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311 errno = EDOM;
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312 else
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313 errno = 0;
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314 }
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315 else if (Py_IS_INFINITY(r)) {
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316 if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
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317 errno = ERANGE;
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318 else
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319 errno = 0;
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320 }
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321 if (errno && is_error(r))
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322 return NULL;
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323 else
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324 return PyFloat_FromDouble(r);
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325 }
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326
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327 #define FUNC1(funcname, func, can_overflow, docstring) \
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328 static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
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329 return math_1(args, func, can_overflow); \
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330 }\
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331 PyDoc_STRVAR(math_##funcname##_doc, docstring);
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332
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333 #define FUNC2(funcname, func, docstring) \
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334 static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
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335 return math_2(args, func, #funcname); \
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336 }\
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337 PyDoc_STRVAR(math_##funcname##_doc, docstring);
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338
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339 FUNC1(acos, acos, 0,
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340 "acos(x)\n\nReturn the arc cosine (measured in radians) of x.")
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341 FUNC1(acosh, acosh, 0,
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342 "acosh(x)\n\nReturn the hyperbolic arc cosine (measured in radians) of x.")
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343 FUNC1(asin, asin, 0,
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344 "asin(x)\n\nReturn the arc sine (measured in radians) of x.")
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345 FUNC1(asinh, asinh, 0,
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346 "asinh(x)\n\nReturn the hyperbolic arc sine (measured in radians) of x.")
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347 FUNC1(atan, atan, 0,
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348 "atan(x)\n\nReturn the arc tangent (measured in radians) of x.")
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349 FUNC2(atan2, m_atan2,
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350 "atan2(y, x)\n\nReturn the arc tangent (measured in radians) of y/x.\n"
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351 "Unlike atan(y/x), the signs of both x and y are considered.")
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352 FUNC1(atanh, atanh, 0,
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353 "atanh(x)\n\nReturn the hyperbolic arc tangent (measured in radians) of x.")
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354
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355 static PyObject * math_ceil(PyObject *self, PyObject *number) {
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356 static PyObject *ceil_str = NULL;
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357 PyObject *method;
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358
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359 if (ceil_str == NULL) {
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360 ceil_str = PyUnicode_InternFromString("__ceil__");
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361 if (ceil_str == NULL)
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362 return NULL;
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363 }
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364
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365 method = _PyType_Lookup(Py_TYPE(number), ceil_str);
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366 if (method == NULL)
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367 return math_1_to_int(number, ceil, 0);
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368 else
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369 return PyObject_CallFunction(method, "O", number);
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370 }
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371
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372 PyDoc_STRVAR(math_ceil_doc,
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373 "ceil(x)\n\nReturn the ceiling of x as an int.\n"
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374 "This is the smallest integral value >= x.");
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375
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376 FUNC2(copysign, copysign,
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377 "copysign(x, y)\n\nReturn x with the sign of y.")
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378 FUNC1(cos, cos, 0,
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379 "cos(x)\n\nReturn the cosine of x (measured in radians).")
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380 FUNC1(cosh, cosh, 1,
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381 "cosh(x)\n\nReturn the hyperbolic cosine of x.")
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382 FUNC1(exp, exp, 1,
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383 "exp(x)\n\nReturn e raised to the power of x.")
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384 FUNC1(fabs, fabs, 0,
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385 "fabs(x)\n\nReturn the absolute value of the float x.")
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386
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387 static PyObject * math_floor(PyObject *self, PyObject *number) {
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388 static PyObject *floor_str = NULL;
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389 PyObject *method;
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390
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391 if (floor_str == NULL) {
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392 floor_str = PyUnicode_InternFromString("__floor__");
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393 if (floor_str == NULL)
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394 return NULL;
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395 }
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396
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397 method = _PyType_Lookup(Py_TYPE(number), floor_str);
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398 if (method == NULL)
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399 return math_1_to_int(number, floor, 0);
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400 else
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401 return PyObject_CallFunction(method, "O", number);
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402 }
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403
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404 PyDoc_STRVAR(math_floor_doc,
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405 "floor(x)\n\nReturn the floor of x as an int.\n"
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406 "This is the largest integral value <= x.");
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407
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408 FUNC1(log1p, log1p, 1,
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409 "log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n"
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410 "The result is computed in a way which is accurate for x near zero.")
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411 FUNC1(sin, sin, 0,
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412 "sin(x)\n\nReturn the sine of x (measured in radians).")
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413 FUNC1(sinh, sinh, 1,
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414 "sinh(x)\n\nReturn the hyperbolic sine of x.")
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415 FUNC1(sqrt, sqrt, 0,
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416 "sqrt(x)\n\nReturn the square root of x.")
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417 FUNC1(tan, tan, 0,
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418 "tan(x)\n\nReturn the tangent of x (measured in radians).")
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419 FUNC1(tanh, tanh, 0,
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420 "tanh(x)\n\nReturn the hyperbolic tangent of x.")
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421
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422 /* Precision summation function as msum() by Raymond Hettinger in
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423 <http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/393090>,
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424 enhanced with the exact partials sum and roundoff from Mark
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425 Dickinson's post at <http://bugs.python.org/file10357/msum4.py>.
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426 See those links for more details, proofs and other references.
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427
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428 Note 1: IEEE 754R floating point semantics are assumed,
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429 but the current implementation does not re-establish special
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430 value semantics across iterations (i.e. handling -Inf + Inf).
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431
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432 Note 2: No provision is made for intermediate overflow handling;
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433 therefore, sum([1e+308, 1e-308, 1e+308]) returns 1e+308 while
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434 sum([1e+308, 1e+308, 1e-308]) raises an OverflowError due to the
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435 overflow of the first partial sum.
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436
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437 Note 3: The intermediate values lo, yr, and hi are declared volatile so
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438 aggressive compilers won't algebraically reduce lo to always be exactly 0.0.
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439 Also, the volatile declaration forces the values to be stored in memory as
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440 regular doubles instead of extended long precision (80-bit) values. This
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441 prevents double rounding because any addition or subtraction of two doubles
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442 can be resolved exactly into double-sized hi and lo values. As long as the
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443 hi value gets forced into a double before yr and lo are computed, the extra
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444 bits in downstream extended precision operations (x87 for example) will be
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445 exactly zero and therefore can be losslessly stored back into a double,
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446 thereby preventing double rounding.
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447
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448 Note 4: A similar implementation is in Modules/cmathmodule.c.
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449 Be sure to update both when making changes.
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450
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451 Note 5: The signature of math.fsum() differs from __builtin__.sum()
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452 because the start argument doesn't make sense in the context of
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453 accurate summation. Since the partials table is collapsed before
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454 returning a result, sum(seq2, start=sum(seq1)) may not equal the
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455 accurate result returned by sum(itertools.chain(seq1, seq2)).
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456 */
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457
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458 #define NUM_PARTIALS 32 /* initial partials array size, on stack */
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459
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460 /* Extend the partials array p[] by doubling its size. */
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461 static int /* non-zero on error */
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462 _fsum_realloc(double **p_ptr, Py_ssize_t n,
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463 double *ps, Py_ssize_t *m_ptr)
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464 {
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465 void *v = NULL;
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466 Py_ssize_t m = *m_ptr;
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467
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468 m += m; /* double */
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469 if (n < m && m < (PY_SSIZE_T_MAX / sizeof(double))) {
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470 double *p = *p_ptr;
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471 if (p == ps) {
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472 v = PyMem_Malloc(sizeof(double) * m);
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473 if (v != NULL)
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474 memcpy(v, ps, sizeof(double) * n);
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475 }
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476 else
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477 v = PyMem_Realloc(p, sizeof(double) * m);
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478 }
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479 if (v == NULL) { /* size overflow or no memory */
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480 PyErr_SetString(PyExc_MemoryError, "math.fsum partials");
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481 return 1;
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482 }
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483 *p_ptr = (double*) v;
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484 *m_ptr = m;
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485 return 0;
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486 }
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487
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488 /* Full precision summation of a sequence of floats.
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489
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490 def msum(iterable):
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491 partials = [] # sorted, non-overlapping partial sums
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492 for x in iterable:
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493 i = 0
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494 for y in partials:
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495 if abs(x) < abs(y):
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496 x, y = y, x
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497 hi = x + y
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498 lo = y - (hi - x)
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499 if lo:
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500 partials[i] = lo
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501 i += 1
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502 x = hi
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503 partials[i:] = [x]
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504 return sum_exact(partials)
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505
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506 Rounded x+y stored in hi with the roundoff stored in lo. Together hi+lo
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507 are exactly equal to x+y. The inner loop applies hi/lo summation to each
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508 partial so that the list of partial sums remains exact.
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509
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510 Sum_exact() adds the partial sums exactly and correctly rounds the final
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511 result (using the round-half-to-even rule). The items in partials remain
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512 non-zero, non-special, non-overlapping and strictly increasing in
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513 magnitude, but possibly not all having the same sign.
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514
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515 Depends on IEEE 754 arithmetic guarantees and half-even rounding.
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516 */
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517
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518 static PyObject*
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519 math_fsum(PyObject *self, PyObject *seq)
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520 {
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521 PyObject *item, *iter, *sum = NULL;
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522 Py_ssize_t i, j, n = 0, m = NUM_PARTIALS;
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523 double x, y, t, ps[NUM_PARTIALS], *p = ps;
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524 double xsave, special_sum = 0.0, inf_sum = 0.0;
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525 volatile double hi, yr, lo;
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526
61467
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527 iter = PyObject_GetIter(seq);
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528 if (iter == NULL)
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529 return NULL;
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530
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531 PyFPE_START_PROTECT("fsum", Py_DECREF(iter); return NULL)
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532
61467
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533 for(;;) { /* for x in iterable */
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534 assert(0 <= n && n <= m);
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535 assert((m == NUM_PARTIALS && p == ps) ||
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536 (m > NUM_PARTIALS && p != NULL));
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537
61467
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538 item = PyIter_Next(iter);
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539 if (item == NULL) {
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540 if (PyErr_Occurred())
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541 goto _fsum_error;
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542 break;
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543 }
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544 x = PyFloat_AsDouble(item);
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545 Py_DECREF(item);
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546 if (PyErr_Occurred())
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547 goto _fsum_error;
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548
61467
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549 xsave = x;
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550 for (i = j = 0; j < n; j++) { /* for y in partials */
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551 y = p[j];
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552 if (fabs(x) < fabs(y)) {
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553 t = x; x = y; y = t;
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554 }
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555 hi = x + y;
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556 yr = hi - x;
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557 lo = y - yr;
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558 if (lo != 0.0)
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559 p[i++] = lo;
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560 x = hi;
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561 }
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562
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563 n = i; /* ps[i:] = [x] */
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564 if (x != 0.0) {
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565 if (! Py_IS_FINITE(x)) {
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566 /* a nonfinite x could arise either as
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567 a result of intermediate overflow, or
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568 as a result of a nan or inf in the
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569 summands */
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570 if (Py_IS_FINITE(xsave)) {
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571 PyErr_SetString(PyExc_OverflowError,
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572 "intermediate overflow in fsum");
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573 goto _fsum_error;
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574 }
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575 if (Py_IS_INFINITY(xsave))
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576 inf_sum += xsave;
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577 special_sum += xsave;
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578 /* reset partials */
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579 n = 0;
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580 }
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581 else if (n >= m && _fsum_realloc(&p, n, ps, &m))
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582 goto _fsum_error;
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583 else
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584 p[n++] = x;
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585 }
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586 }
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587
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588 if (special_sum != 0.0) {
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589 if (Py_IS_NAN(inf_sum))
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590 PyErr_SetString(PyExc_ValueError,
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591 "-inf + inf in fsum");
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592 else
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593 sum = PyFloat_FromDouble(special_sum);
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594 goto _fsum_error;
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595 }
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596
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597 hi = 0.0;
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598 if (n > 0) {
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599 hi = p[--n];
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600 /* sum_exact(ps, hi) from the top, stop when the sum becomes
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601 inexact. */
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602 while (n > 0) {
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603 x = hi;
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604 y = p[--n];
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605 assert(fabs(y) < fabs(x));
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606 hi = x + y;
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607 yr = hi - x;
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608 lo = y - yr;
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609 if (lo != 0.0)
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610 break;
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611 }
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612 /* Make half-even rounding work across multiple partials.
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613 Needed so that sum([1e-16, 1, 1e16]) will round-up the last
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614 digit to two instead of down to zero (the 1e-16 makes the 1
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615 slightly closer to two). With a potential 1 ULP rounding
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616 error fixed-up, math.fsum() can guarantee commutativity. */
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617 if (n > 0 && ((lo < 0.0 && p[n-1] < 0.0) ||
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618 (lo > 0.0 && p[n-1] > 0.0))) {
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619 y = lo * 2.0;
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620 x = hi + y;
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621 yr = x - hi;
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622 if (y == yr)
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623 hi = x;
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624 }
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625 }
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626 sum = PyFloat_FromDouble(hi);
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627
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628 _fsum_error:
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629 PyFPE_END_PROTECT(hi)
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630 Py_DECREF(iter);
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631 if (p != ps)
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632 PyMem_Free(p);
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633 return sum;
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634 }
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635
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636 #undef NUM_PARTIALS
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637
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638 PyDoc_STRVAR(math_fsum_doc,
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639 "fsum(iterable)\n\n\
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640 Return an accurate floating point sum of values in the iterable.\n\
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641 Assumes IEEE-754 floating point arithmetic.");
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642
4635
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643 static PyObject *
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644 math_factorial(PyObject *self, PyObject *arg)
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645 {
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646 long i, x;
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647 PyObject *result, *iobj, *newresult;
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648
61467
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649 if (PyFloat_Check(arg)) {
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650 double dx = PyFloat_AS_DOUBLE((PyFloatObject *)arg);
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651 if (dx != floor(dx)) {
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652 PyErr_SetString(PyExc_ValueError,
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653 "factorial() only accepts integral values");
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654 return NULL;
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655 }
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656 }
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657
61467
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658 x = PyLong_AsLong(arg);
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659 if (x == -1 && PyErr_Occurred())
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660 return NULL;
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661 if (x < 0) {
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662 PyErr_SetString(PyExc_ValueError,
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663 "factorial() not defined for negative values");
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664 return NULL;
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665 }
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666
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667 result = (PyObject *)PyLong_FromLong(1);
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668 if (result == NULL)
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669 return NULL;
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670 for (i=1 ; i<=x ; i++) {
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671 iobj = (PyObject *)PyLong_FromLong(i);
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672 if (iobj == NULL)
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673 goto error;
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674 newresult = PyNumber_Multiply(result, iobj);
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675 Py_DECREF(iobj);
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676 if (newresult == NULL)
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677 goto error;
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678 Py_DECREF(result);
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679 result = newresult;
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680 }
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681 return result;
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682
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683 error:
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684 Py_DECREF(result);
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685 return NULL;
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686 }
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687
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688 PyDoc_STRVAR(math_factorial_doc,
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689 "factorial(x) -> Integral\n"
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690 "\n"
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691 "Find x!. Raise a ValueError if x is negative or non-integral.");
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692
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693 static PyObject *
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694 math_trunc(PyObject *self, PyObject *number)
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695 {
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696 static PyObject *trunc_str = NULL;
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697 PyObject *trunc;
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698
61467
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699 if (Py_TYPE(number)->tp_dict == NULL) {
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700 if (PyType_Ready(Py_TYPE(number)) < 0)
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701 return NULL;
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702 }
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703
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704 if (trunc_str == NULL) {
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705 trunc_str = PyUnicode_InternFromString("__trunc__");
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706 if (trunc_str == NULL)
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707 return NULL;
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708 }
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709
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710 trunc = _PyType_Lookup(Py_TYPE(number), trunc_str);
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711 if (trunc == NULL) {
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712 PyErr_Format(PyExc_TypeError,
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713 "type %.100s doesn't define __trunc__ method",
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714 Py_TYPE(number)->tp_name);
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715 return NULL;
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716 }
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717 return PyObject_CallFunctionObjArgs(trunc, number, NULL);
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718 }
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719
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720 PyDoc_STRVAR(math_trunc_doc,
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721 "trunc(x:Real) -> Integral\n"
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722 "\n"
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723 "Truncates x to the nearest Integral toward 0. Uses the __trunc__ magic method.");
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724
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725 static PyObject *
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
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726 math_frexp(PyObject *self, PyObject *arg)
407
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Guido van Rossum <guido@python.org>
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727 {
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728 int i;
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729 double x = PyFloat_AsDouble(arg);
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730 if (x == -1.0 && PyErr_Occurred())
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731 return NULL;
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732 /* deal with special cases directly, to sidestep platform
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733 differences */
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734 if (Py_IS_NAN(x) || Py_IS_INFINITY(x) || !x) {
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735 i = 0;
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736 }
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737 else {
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738 PyFPE_START_PROTECT("in math_frexp", return 0);
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739 x = frexp(x, &i);
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740 PyFPE_END_PROTECT(x);
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741 }
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742 return Py_BuildValue("(di)", x, i);
407
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Guido van Rossum <guido@python.org>
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diff changeset
743 }
9b3d557665a9 Added frexp, ldexp, modf, fmod.
Guido van Rossum <guido@python.org>
parents: 320
diff changeset
744
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745 PyDoc_STRVAR(math_frexp_doc,
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diff changeset
746 "frexp(x)\n"
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diff changeset
747 "\n"
b4521436e8f8 Mechanical fiddling to make this easier to work with in my editor.
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parents: 19048
diff changeset
748 "Return the mantissa and exponent of x, as pair (m, e).\n"
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diff changeset
749 "m is a float and e is an int, such that x = m * 2.**e.\n"
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diff changeset
750 "If x is 0, m and e are both 0. Else 0.5 <= abs(m) < 1.0.");
9593
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Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
751
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Barry Warsaw <barry@python.org>
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diff changeset
752 static PyObject *
13326
24717405dd89 ANSI-fication, remove Py_PROTO, etc.
Fred Drake <fdrake@acm.org>
parents: 13309
diff changeset
753 math_ldexp(PyObject *self, PyObject *args)
407
9b3d557665a9 Added frexp, ldexp, modf, fmod.
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diff changeset
754 {
61467
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755 double x, r;
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756 PyObject *oexp;
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757 long exp;
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758 if (! PyArg_ParseTuple(args, "dO:ldexp", &x, &oexp))
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759 return NULL;
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760
61467
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761 if (PyLong_Check(oexp)) {
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762 /* on overflow, replace exponent with either LONG_MAX
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763 or LONG_MIN, depending on the sign. */
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764 exp = PyLong_AsLong(oexp);
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765 if (exp == -1 && PyErr_Occurred()) {
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766 if (PyErr_ExceptionMatches(PyExc_OverflowError)) {
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767 if (Py_SIZE(oexp) < 0) {
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768 exp = LONG_MIN;
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769 }
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770 else {
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771 exp = LONG_MAX;
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772 }
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773 PyErr_Clear();
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774 }
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775 else {
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776 /* propagate any unexpected exception */
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777 return NULL;
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778 }
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779 }
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780 }
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781 else {
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782 PyErr_SetString(PyExc_TypeError,
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783 "Expected an int or long as second argument "
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diff changeset
784 "to ldexp.");
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785 return NULL;
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786 }
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787
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788 if (x == 0. || !Py_IS_FINITE(x)) {
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diff changeset
789 /* NaNs, zeros and infinities are returned unchanged */
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790 r = x;
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791 errno = 0;
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792 } else if (exp > INT_MAX) {
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793 /* overflow */
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794 r = copysign(Py_HUGE_VAL, x);
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795 errno = ERANGE;
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796 } else if (exp < INT_MIN) {
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797 /* underflow to +-0 */
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798 r = copysign(0., x);
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799 errno = 0;
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800 } else {
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801 errno = 0;
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802 PyFPE_START_PROTECT("in math_ldexp", return 0);
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803 r = ldexp(x, (int)exp);
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804 PyFPE_END_PROTECT(r);
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805 if (Py_IS_INFINITY(r))
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806 errno = ERANGE;
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807 }
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808
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809 if (errno && is_error(r))
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810 return NULL;
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811 return PyFloat_FromDouble(r);
407
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Guido van Rossum <guido@python.org>
parents: 320
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812 }
9b3d557665a9 Added frexp, ldexp, modf, fmod.
Guido van Rossum <guido@python.org>
parents: 320
diff changeset
813
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diff changeset
814 PyDoc_STRVAR(math_ldexp_doc,
57210
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parents: 50250
diff changeset
815 "ldexp(x, i)\n\n\
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parents: 50250
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816 Return x * (2**i).");
9593
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Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
817
4635
49745ddb4f69 Renamed
Barry Warsaw <barry@python.org>
parents: 4503
diff changeset
818 static PyObject *
40450
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Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
819 math_modf(PyObject *self, PyObject *arg)
407
9b3d557665a9 Added frexp, ldexp, modf, fmod.
Guido van Rossum <guido@python.org>
parents: 320
diff changeset
820 {
61467
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821 double y, x = PyFloat_AsDouble(arg);
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822 if (x == -1.0 && PyErr_Occurred())
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823 return NULL;
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824 /* some platforms don't do the right thing for NaNs and
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825 infinities, so we take care of special cases directly. */
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826 if (!Py_IS_FINITE(x)) {
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827 if (Py_IS_INFINITY(x))
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828 return Py_BuildValue("(dd)", copysign(0., x), x);
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829 else if (Py_IS_NAN(x))
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830 return Py_BuildValue("(dd)", x, x);
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831 }
46505
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832
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833 errno = 0;
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834 PyFPE_START_PROTECT("in math_modf", return 0);
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835 x = modf(x, &y);
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836 PyFPE_END_PROTECT(x);
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837 return Py_BuildValue("(dd)", x, y);
407
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diff changeset
838 }
6
fc6fcd7df4f7 Initial revision
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diff changeset
839
23832
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840 PyDoc_STRVAR(math_modf_doc,
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841 "modf(x)\n"
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842 "\n"
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843 "Return the fractional and integer parts of x. Both results carry the sign\n"
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diff changeset
844 "of x and are floats.");
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845
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846 /* A decent logarithm is easy to compute even for huge longs, but libm can't
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847 do that by itself -- loghelper can. func is log or log10, and name is
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848 "log" or "log10". Note that overflow isn't possible: a long can contain
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diff changeset
849 no more than INT_MAX * SHIFT bits, so has value certainly less than
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parents: 19712
diff changeset
850 2**(2**64 * 2**16) == 2**2**80, and log2 of that is 2**80, which is
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851 small enough to fit in an IEEE single. log and log10 are even smaller.
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852 */
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853
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diff changeset
854 static PyObject*
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855 loghelper(PyObject* arg, double (*func)(double), char *funcname)
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856 {
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857 /* If it is long, do it ourselves. */
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858 if (PyLong_Check(arg)) {
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859 double x;
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860 int e;
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diff changeset
861 x = _PyLong_AsScaledDouble(arg, &e);
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diff changeset
862 if (x <= 0.0) {
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diff changeset
863 PyErr_SetString(PyExc_ValueError,
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diff changeset
864 "math domain error");
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diff changeset
865 return NULL;
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diff changeset
866 }
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diff changeset
867 /* Value is ~= x * 2**(e*PyLong_SHIFT), so the log ~=
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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parents: 57210
diff changeset
868 log(x) + log(2) * e * PyLong_SHIFT.
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diff changeset
869 CAUTION: e*PyLong_SHIFT may overflow using int arithmetic,
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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parents: 57210
diff changeset
870 so force use of double. */
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diff changeset
871 x = func(x) + (e * (double)PyLong_SHIFT) * func(2.0);
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diff changeset
872 return PyFloat_FromDouble(x);
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parents: 57210
diff changeset
873 }
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
874
61467
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diff changeset
875 /* Else let libm handle it by itself. */
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parents: 57210
diff changeset
876 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
877 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
878
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
879 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
880 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
881 {
61467
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parents: 57210
diff changeset
882 PyObject *arg;
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diff changeset
883 PyObject *base = NULL;
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parents: 57210
diff changeset
884 PyObject *num, *den;
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Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
885 PyObject *ans;
26661
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
886
61467
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diff changeset
887 if (!PyArg_UnpackTuple(args, "log", 1, 2, &arg, &base))
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diff changeset
888 return NULL;
26661
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
889
61467
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diff changeset
890 num = loghelper(arg, m_log, "log");
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parents: 57210
diff changeset
891 if (num == NULL || base == NULL)
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parents: 57210
diff changeset
892 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
893
61467
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diff changeset
894 den = loghelper(base, m_log, "log");
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parents: 57210
diff changeset
895 if (den == NULL) {
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Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
896 Py_DECREF(num);
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parents: 57210
diff changeset
897 return NULL;
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Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
898 }
26661
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
899
61467
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diff changeset
900 ans = PyNumber_TrueDivide(num, den);
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parents: 57210
diff changeset
901 Py_DECREF(num);
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parents: 57210
diff changeset
902 Py_DECREF(den);
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Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
903 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
904 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
905
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
906 PyDoc_STRVAR(math_log_doc,
57210
a0951f11be3d Merged revisions 76235 via svnmerge from
Benjamin Peterson <benjamin@python.org>
parents: 50250
diff changeset
907 "log(x[, base])\n\n\
a0951f11be3d Merged revisions 76235 via svnmerge from
Benjamin Peterson <benjamin@python.org>
parents: 50250
diff changeset
908 Return the logarithm of x to the given base.\n\
26661
b12e326b4ea2 Apply SF patch 652930: Add optional base argument to math.log(x[, base]).
Raymond Hettinger <python@rcn.com>
parents: 24471
diff changeset
909 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
910
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
911 static PyObject *
40450
cc992d75d5b3 Four months of trunk changes (including a few releases...)
Thomas Wouters <thomas@python.org>
parents: 37191
diff changeset
912 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
913 {
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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parents: 57210
diff changeset
914 return loghelper(arg, m_log10, "log10");
19713
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
915 }
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
916
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
917 PyDoc_STRVAR(math_log10_doc,
57210
a0951f11be3d Merged revisions 76235 via svnmerge from
Benjamin Peterson <benjamin@python.org>
parents: 50250
diff changeset
918 "log10(x)\n\nReturn the base 10 logarithm of x.");
19713
9433dd3c197e Return reasonable results for math.log(long) and math.log10(long) (we were
Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
919
46477
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Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
920 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
921 math_fmod(PyObject *self, PyObject *args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
922 {
61467
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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parents: 57210
diff changeset
923 PyObject *ox, *oy;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
924 double r, x, y;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
925 if (! PyArg_UnpackTuple(args, "fmod", 2, 2, &ox, &oy))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
926 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
927 x = PyFloat_AsDouble(ox);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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parents: 57210
diff changeset
928 y = PyFloat_AsDouble(oy);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
929 if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
930 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
931 /* fmod(x, +/-Inf) returns x for finite x. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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parents: 57210
diff changeset
932 if (Py_IS_INFINITY(y) && Py_IS_FINITE(x))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
933 return PyFloat_FromDouble(x);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
934 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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parents: 57210
diff changeset
935 PyFPE_START_PROTECT("in math_fmod", return 0);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
936 r = fmod(x, y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
937 PyFPE_END_PROTECT(r);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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parents: 57210
diff changeset
938 if (Py_IS_NAN(r)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
939 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
940 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
941 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
942 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
943 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
944 if (errno && is_error(r))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
945 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
946 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
947 return PyFloat_FromDouble(r);
46477
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
948 }
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
949
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
950 PyDoc_STRVAR(math_fmod_doc,
57210
a0951f11be3d Merged revisions 76235 via svnmerge from
Benjamin Peterson <benjamin@python.org>
parents: 50250
diff changeset
951 "fmod(x, y)\n\nReturn fmod(x, y), according to platform C."
46477
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
952 " x % y may differ.");
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
953
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
954 static PyObject *
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
955 math_hypot(PyObject *self, PyObject *args)
b69f443ef480 Merged revisions 62380,62382-62383 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 45134
diff changeset
956 {
61467
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diff changeset
957 PyObject *ox, *oy;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
958 double r, x, y;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
959 if (! PyArg_UnpackTuple(args, "hypot", 2, 2, &ox, &oy))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
960 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
961 x = PyFloat_AsDouble(ox);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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parents: 57210
diff changeset
962 y = PyFloat_AsDouble(oy);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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parents: 57210
diff changeset
963 if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
964 return NULL;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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parents: 57210
diff changeset
965 /* hypot(x, +/-Inf) returns Inf, even if x is a NaN. */
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
966 if (Py_IS_INFINITY(x))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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diff changeset
967 return PyFloat_FromDouble(fabs(x));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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parents: 57210
diff changeset
968 if (Py_IS_INFINITY(y))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
969 return PyFloat_FromDouble(fabs(y));
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
970 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
971 PyFPE_START_PROTECT("in math_hypot", return 0);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
972 r = hypot(x, y);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
973 PyFPE_END_PROTECT(r);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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parents: 57210
diff changeset
974 if (Py_IS_NAN(r)) {
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
975 if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
976 errno = EDOM;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
977 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
978 errno = 0;
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
979 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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diff changeset
980 else if (Py_IS_INFINITY(r)) {
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parents: 57210
diff changeset
981 if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
982 errno = ERANGE;
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Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
983 else
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
984 errno = 0;
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Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
985 }
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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diff changeset
986 if (errno && is_error(r))
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987 return NULL;
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988 else
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989 return PyFloat_FromDouble(r);
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990 }
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991
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992 PyDoc_STRVAR(math_hypot_doc,
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993 "hypot(x, y)\n\nReturn the Euclidean distance, sqrt(x*x + y*y).");
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994
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995 /* pow can't use math_2, but needs its own wrapper: the problem is
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996 that an infinite result can arise either as a result of overflow
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997 (in which case OverflowError should be raised) or as a result of
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998 e.g. 0.**-5. (for which ValueError needs to be raised.)
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999 */
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1000
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1001 static PyObject *
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1002 math_pow(PyObject *self, PyObject *args)
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1003 {
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1004 PyObject *ox, *oy;
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1005 double r, x, y;
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1006 int odd_y;
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1007
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1008 if (! PyArg_UnpackTuple(args, "pow", 2, 2, &ox, &oy))
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1009 return NULL;
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1010 x = PyFloat_AsDouble(ox);
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1011 y = PyFloat_AsDouble(oy);
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1012 if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
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1013 return NULL;
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1014
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1015 /* deal directly with IEEE specials, to cope with problems on various
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1016 platforms whose semantics don't exactly match C99 */
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1017 r = 0.; /* silence compiler warning */
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1018 if (!Py_IS_FINITE(x) || !Py_IS_FINITE(y)) {
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1019 errno = 0;
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1020 if (Py_IS_NAN(x))
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1021 r = y == 0. ? 1. : x; /* NaN**0 = 1 */
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1022 else if (Py_IS_NAN(y))
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1023 r = x == 1. ? 1. : y; /* 1**NaN = 1 */
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1024 else if (Py_IS_INFINITY(x)) {
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1025 odd_y = Py_IS_FINITE(y) && fmod(fabs(y), 2.0) == 1.0;
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1026 if (y > 0.)
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1027 r = odd_y ? x : fabs(x);
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1028 else if (y == 0.)
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1029 r = 1.;
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1030 else /* y < 0. */
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1031 r = odd_y ? copysign(0., x) : 0.;
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1032 }
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1033 else if (Py_IS_INFINITY(y)) {
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1034 if (fabs(x) == 1.0)
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1035 r = 1.;
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1036 else if (y > 0. && fabs(x) > 1.0)
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1037 r = y;
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1038 else if (y < 0. && fabs(x) < 1.0) {
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1039 r = -y; /* result is +inf */
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1040 if (x == 0.) /* 0**-inf: divide-by-zero */
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1041 errno = EDOM;
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1042 }
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1043 else
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1044 r = 0.;
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1045 }
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1046 }
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1047 else {
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1048 /* let libm handle finite**finite */
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1049 errno = 0;
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1050 PyFPE_START_PROTECT("in math_pow", return 0);
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1051 r = pow(x, y);
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1052 PyFPE_END_PROTECT(r);
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1053 /* a NaN result should arise only from (-ve)**(finite
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1054 non-integer); in this case we want to raise ValueError. */
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1055 if (!Py_IS_FINITE(r)) {
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1056 if (Py_IS_NAN(r)) {
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1057 errno = EDOM;
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1058 }
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1059 /*
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1060 an infinite result here arises either from:
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1061 (A) (+/-0.)**negative (-> divide-by-zero)
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1062 (B) overflow of x**y with x and y finite
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1063 */
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1064 else if (Py_IS_INFINITY(r)) {
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1065 if (x == 0.)
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1066 errno = EDOM;
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1067 else
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1068 errno = ERANGE;
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1069 }
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1070 }
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1071 }
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1072
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1073 if (errno && is_error(r))
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1074 return NULL;
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1075 else
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1076 return PyFloat_FromDouble(r);
46477
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1077 }
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1078
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1079 PyDoc_STRVAR(math_pow_doc,
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1080 "pow(x, y)\n\nReturn x**y (x to the power of y).");
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1081
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1082 static const double degToRad = Py_MATH_PI / 180.0;
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1083 static const double radToDeg = 180.0 / Py_MATH_PI;
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parents: 19758
diff changeset
1084
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and
Raymond Hettinger <python@rcn.com>
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diff changeset
1085 static PyObject *
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1086 math_degrees(PyObject *self, PyObject *arg)
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1087 {
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1088 double x = PyFloat_AsDouble(arg);
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1089 if (x == -1.0 && PyErr_Occurred())
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1090 return NULL;
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1091 return PyFloat_FromDouble(x * radToDeg);
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1092 }
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1093
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1094 PyDoc_STRVAR(math_degrees_doc,
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1095 "degrees(x)\n\n\
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diff changeset
1096 Convert angle x from radians to degrees.");
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diff changeset
1097
a4d675b8b53c Added degrees() and radians() to mathmodule. Closes patch 552452 and
Raymond Hettinger <python@rcn.com>
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diff changeset
1098 static PyObject *
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1099 math_radians(PyObject *self, PyObject *arg)
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1100 {
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1101 double x = PyFloat_AsDouble(arg);
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1102 if (x == -1.0 && PyErr_Occurred())
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1103 return NULL;
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1104 return PyFloat_FromDouble(x * degToRad);
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parents: 19758
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1105 }
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parents: 19758
diff changeset
1106
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1107 PyDoc_STRVAR(math_radians_doc,
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1108 "radians(x)\n\n\
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1109 Convert angle x from degrees to radians.");
19713
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Tim Peters <tim.peters@gmail.com>
parents: 19712
diff changeset
1110
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1111 static PyObject *
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1112 math_isnan(PyObject *self, PyObject *arg)
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1113 {
61467
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diff changeset
1114 double x = PyFloat_AsDouble(arg);
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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diff changeset
1115 if (x == -1.0 && PyErr_Occurred())
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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diff changeset
1116 return NULL;
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diff changeset
1117 return PyBool_FromLong((long)Py_IS_NAN(x));
44441
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 44351
diff changeset
1118 }
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Christian Heimes <christian@cheimes.de>
parents: 44351
diff changeset
1119
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parents: 44351
diff changeset
1120 PyDoc_STRVAR(math_isnan_doc,
57210
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Benjamin Peterson <benjamin@python.org>
parents: 50250
diff changeset
1121 "isnan(x) -> bool\n\n\
a0951f11be3d Merged revisions 76235 via svnmerge from
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parents: 50250
diff changeset
1122 Check if float x is not a number (NaN).");
44441
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Christian Heimes <christian@cheimes.de>
parents: 44351
diff changeset
1123
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parents: 44351
diff changeset
1124 static PyObject *
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parents: 44351
diff changeset
1125 math_isinf(PyObject *self, PyObject *arg)
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Christian Heimes <christian@cheimes.de>
parents: 44351
diff changeset
1126 {
61467
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diff changeset
1127 double x = PyFloat_AsDouble(arg);
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diff changeset
1128 if (x == -1.0 && PyErr_Occurred())
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diff changeset
1129 return NULL;
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diff changeset
1130 return PyBool_FromLong((long)Py_IS_INFINITY(x));
44441
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Christian Heimes <christian@cheimes.de>
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diff changeset
1131 }
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Christian Heimes <christian@cheimes.de>
parents: 44351
diff changeset
1132
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 44351
diff changeset
1133 PyDoc_STRVAR(math_isinf_doc,
57210
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Benjamin Peterson <benjamin@python.org>
parents: 50250
diff changeset
1134 "isinf(x) -> bool\n\n\
a0951f11be3d Merged revisions 76235 via svnmerge from
Benjamin Peterson <benjamin@python.org>
parents: 50250
diff changeset
1135 Check if float x is infinite (positive or negative).");
44441
b91ca87e6f32 Merged revisions 59666-59679 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents: 44351
diff changeset
1136
4635
49745ddb4f69 Renamed
Barry Warsaw <barry@python.org>
parents: 4503
diff changeset
1137 static PyMethodDef math_methods[] = {
61467
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diff changeset
1138 {"acos", math_acos, METH_O, math_acos_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
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diff changeset
1139 {"acosh", math_acosh, METH_O, math_acosh_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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parents: 57210
diff changeset
1140 {"asin", math_asin, METH_O, math_asin_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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diff changeset
1141 {"asinh", math_asinh, METH_O, math_asinh_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
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diff changeset
1142 {"atan", math_atan, METH_O, math_atan_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
Antoine Pitrou <solipsis@pitrou.net>
parents: 57210
diff changeset
1143 {"atan2", math_atan2, METH_VARARGS, math_atan2_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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diff changeset
1144 {"atanh", math_atanh, METH_O, math_atanh_doc},
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diff changeset
1145 {"ceil", math_ceil, METH_O, math_ceil_doc},
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diff changeset
1146 {"copysign", math_copysign, METH_VARARGS, math_copysign_doc},
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diff changeset
1147 {"cos", math_cos, METH_O, math_cos_doc},
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diff changeset
1148 {"cosh", math_cosh, METH_O, math_cosh_doc},
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diff changeset
1149 {"degrees", math_degrees, METH_O, math_degrees_doc},
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parents: 57210
diff changeset
1150 {"exp", math_exp, METH_O, math_exp_doc},
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diff changeset
1151 {"fabs", math_fabs, METH_O, math_fabs_doc},
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Antoine Pitrou <solipsis@pitrou.net>
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diff changeset
1152 {"factorial", math_factorial, METH_O, math_factorial_doc},
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diff changeset
1153 {"floor", math_floor, METH_O, math_floor_doc},
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diff changeset
1154 {"fmod", math_fmod, METH_VARARGS, math_fmod_doc},
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diff changeset
1155 {"frexp", math_frexp, METH_O, math_frexp_doc},
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diff changeset
1156 {"fsum", math_fsum, METH_O, math_fsum_doc},
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diff changeset
1157 {"hypot", math_hypot, METH_VARARGS, math_hypot_doc},
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diff changeset
1158 {"isinf", math_isinf, METH_O, math_isinf_doc},
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diff changeset
1159 {"isnan", math_isnan, METH_O, math_isnan_doc},
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diff changeset
1160 {"ldexp", math_ldexp, METH_VARARGS, math_ldexp_doc},
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diff changeset
1161 {"log", math_log, METH_VARARGS, math_log_doc},
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diff changeset
1162 {"log1p", math_log1p, METH_O, math_log1p_doc},
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diff changeset
1163 {"log10", math_log10, METH_O, math_log10_doc},
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diff changeset
1164 {"modf", math_modf, METH_O, math_modf_doc},
f197407bdba2 Recorded merge of revisions 81032 via svnmerge from
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diff changeset
1165 {"pow", math_pow, METH_VARARGS, math_pow_doc},
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diff changeset
1166 {"radians", math_radians, METH_O, math_radians_doc},
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diff changeset
1167 {"sin", math_sin, METH_O, math_sin_doc},
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diff changeset
1168 {"sinh", math_sinh, METH_O, math_sinh_doc},
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diff changeset
1169 {"sqrt", math_sqrt, METH_O, math_sqrt_doc},
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diff changeset
1170 {"tan", math_tan, METH_O, math_tan_doc},
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diff changeset
1171 {"tanh", math_tanh, METH_O, math_tanh_doc},
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diff changeset
1172 {"trunc", math_trunc, METH_O, math_trunc_doc},
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diff changeset
1173 {NULL, NULL} /* sentinel */
6
fc6fcd7df4f7 Initial revision
Guido van Rossum <guido@python.org>
parents:
diff changeset
1174 };
fc6fcd7df4f7 Initial revision
Guido van Rossum <guido@python.org>
parents:
diff changeset
1175
9593
f22f769bf3d9 Added Doc strings -- by Chris Petrilli.
Guido van Rossum <guido@python.org>
parents: 9588
diff changeset
1176
23832
ed1ba37a46b7 Patch #568124: Add doc string macros.
Martin v. Löwis <martin@v.loewis.de>
parents: 23427
diff changeset
1177 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
1178 "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
1179 "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
1180
47580
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API.
Martin v. Löwis <martin@v.loewis.de>
parents: 47562
diff changeset
1181
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API.
Martin v. Löwis <martin@v.loewis.de>
parents: 47562
diff changeset
1182 static struct PyModuleDef mathmodule = {
61467
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1183 PyModuleDef_HEAD_INIT,
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diff changeset
1184 "math",
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diff changeset
1185 module_doc,
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diff changeset
1186 -1,
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1187 math_methods,
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1188 NULL,
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diff changeset
1189 NULL,
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1190 NULL,
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1191 NULL
47580
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API.
Martin v. Löwis <martin@v.loewis.de>
parents: 47562
diff changeset
1192 };
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API.
Martin v. Löwis <martin@v.loewis.de>
parents: 47562
diff changeset
1193
24471
f66b3a3509c7 Excise DL_EXPORT/DL_IMPORT from Modules/*. Required adding a prototype
Mark Hammond <mhammond@skippinet.com.au>
parents: 23832
diff changeset
1194 PyMODINIT_FUNC
47580
94f64f11fdd0 Implement PEP 3121: new module initialization and finalization API.
Martin v. Löwis <martin@v.loewis.de>
parents: 47562
diff changeset
1195 PyInit_math(void)
6
fc6fcd7df4f7 Initial revision
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parents:
diff changeset
1196 {
61467
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1197 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
1198
61467
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1199 m = PyModule_Create(&mathmodule);
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1200 if (m == NULL)
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1201 goto finally;
4752
7367fb107108 Better error checking in initmath().
Barry Warsaw <barry@python.org>
parents: 4635
diff changeset
1202
61467
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1203 PyModule_AddObject(m, "pi", PyFloat_FromDouble(Py_MATH_PI));
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diff changeset
1204 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
1205
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diff changeset
1206 finally:
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1207 return m;
6
fc6fcd7df4f7 Initial revision
Guido van Rossum <guido@python.org>
parents:
diff changeset
1208 }