| 1 | /* Math module -- standard C math library functions, pi and e */
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| 2 |
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| 3 | #include "Python.h"
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| 4 | #include "longintrepr.h" /* just for SHIFT */
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| 5 |
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| 6 | #ifndef _MSC_VER
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| 7 | #ifndef __STDC__
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| 8 | extern double fmod (double, double);
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| 9 | extern double frexp (double, int *);
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| 10 | extern double ldexp (double, int);
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| 11 | extern double modf (double, double *);
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| 12 | #endif /* __STDC__ */
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| 13 | #endif /* _MSC_VER */
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| 14 |
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| 15 | /* Call is_error when errno != 0, and where x is the result libm
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| 16 | * returned. is_error will usually set up an exception and return
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| 17 | * true (1), but may return false (0) without setting up an exception.
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| 18 | */
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| 19 | static int
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| 20 | is_error(double x)
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| 21 | {
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| 22 | int result = 1; /* presumption of guilt */
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| 23 | assert(errno); /* non-zero errno is a precondition for calling */
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| 24 | if (errno == EDOM)
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| 25 | PyErr_SetString(PyExc_ValueError, "math domain error");
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| 26 |
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| 27 | else if (errno == ERANGE) {
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| 28 | /* ANSI C generally requires libm functions to set ERANGE
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| 29 | * on overflow, but also generally *allows* them to set
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| 30 | * ERANGE on underflow too. There's no consistency about
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| 31 | * the latter across platforms.
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| 32 | * Alas, C99 never requires that errno be set.
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| 33 | * Here we suppress the underflow errors (libm functions
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| 34 | * should return a zero on underflow, and +- HUGE_VAL on
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| 35 | * overflow, so testing the result for zero suffices to
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| 36 | * distinguish the cases).
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| 37 | */
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| 38 | if (x)
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| 39 | PyErr_SetString(PyExc_OverflowError,
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| 40 | "math range error");
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| 41 | else
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| 42 | result = 0;
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| 43 | }
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| 44 | else
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| 45 | /* Unexpected math error */
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| 46 | PyErr_SetFromErrno(PyExc_ValueError);
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| 47 | return result;
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| 48 | }
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| 49 |
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| 50 | static PyObject *
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| 51 | math_1(PyObject *args, double (*func) (double), char *argsfmt)
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| 52 | {
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| 53 | double x;
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| 54 | if (! PyArg_ParseTuple(args, argsfmt, &x))
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| 55 | return NULL;
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| 56 | errno = 0;
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| 57 | PyFPE_START_PROTECT("in math_1", return 0)
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| 58 | x = (*func)(x);
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| 59 | PyFPE_END_PROTECT(x)
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| 60 | Py_SET_ERRNO_ON_MATH_ERROR(x);
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| 61 | if (errno && is_error(x))
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| 62 | return NULL;
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| 63 | else
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| 64 | return PyFloat_FromDouble(x);
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| 65 | }
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| 66 |
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| 67 | static PyObject *
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| 68 | math_2(PyObject *args, double (*func) (double, double), char *argsfmt)
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| 69 | {
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| 70 | double x, y;
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| 71 | if (! PyArg_ParseTuple(args, argsfmt, &x, &y))
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| 72 | return NULL;
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| 73 | errno = 0;
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| 74 | PyFPE_START_PROTECT("in math_2", return 0)
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| 75 | x = (*func)(x, y);
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| 76 | PyFPE_END_PROTECT(x)
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| 77 | Py_SET_ERRNO_ON_MATH_ERROR(x);
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| 78 | if (errno && is_error(x))
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| 79 | return NULL;
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| 80 | else
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| 81 | return PyFloat_FromDouble(x);
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| 82 | }
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| 83 |
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| 84 | #define FUNC1(funcname, func, docstring) \
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| 85 | static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
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| 86 | return math_1(args, func, "d:" #funcname); \
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| 87 | }\
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| 88 | PyDoc_STRVAR(math_##funcname##_doc, docstring);
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| 89 |
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| 90 | #define FUNC2(funcname, func, docstring) \
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| 91 | static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
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| 92 | return math_2(args, func, "dd:" #funcname); \
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| 93 | }\
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| 94 | PyDoc_STRVAR(math_##funcname##_doc, docstring);
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| 95 |
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| 96 | FUNC1(acos, acos,
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| 97 | "acos(x)\n\nReturn the arc cosine (measured in radians) of x.")
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| 98 | FUNC1(asin, asin,
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| 99 | "asin(x)\n\nReturn the arc sine (measured in radians) of x.")
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| 100 | FUNC1(atan, atan,
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| 101 | "atan(x)\n\nReturn the arc tangent (measured in radians) of x.")
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| 102 | FUNC2(atan2, atan2,
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| 103 | "atan2(y, x)\n\nReturn the arc tangent (measured in radians) of y/x.\n"
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| 104 | "Unlike atan(y/x), the signs of both x and y are considered.")
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| 105 | FUNC1(ceil, ceil,
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| 106 | "ceil(x)\n\nReturn the ceiling of x as a float.\n"
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| 107 | "This is the smallest integral value >= x.")
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| 108 | FUNC1(cos, cos,
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| 109 | "cos(x)\n\nReturn the cosine of x (measured in radians).")
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| 110 | FUNC1(cosh, cosh,
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| 111 | "cosh(x)\n\nReturn the hyperbolic cosine of x.")
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| 112 | FUNC1(exp, exp,
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| 113 | "exp(x)\n\nReturn e raised to the power of x.")
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| 114 | FUNC1(fabs, fabs,
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| 115 | "fabs(x)\n\nReturn the absolute value of the float x.")
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| 116 | FUNC1(floor, floor,
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| 117 | "floor(x)\n\nReturn the floor of x as a float.\n"
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| 118 | "This is the largest integral value <= x.")
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| 119 | FUNC2(fmod, fmod,
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| 120 | "fmod(x,y)\n\nReturn fmod(x, y), according to platform C."
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| 121 | " x % y may differ.")
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| 122 | FUNC2(hypot, hypot,
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| 123 | "hypot(x,y)\n\nReturn the Euclidean distance, sqrt(x*x + y*y).")
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| 124 | FUNC2(pow, pow,
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| 125 | "pow(x,y)\n\nReturn x**y (x to the power of y).")
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| 126 | FUNC1(sin, sin,
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| 127 | "sin(x)\n\nReturn the sine of x (measured in radians).")
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| 128 | FUNC1(sinh, sinh,
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| 129 | "sinh(x)\n\nReturn the hyperbolic sine of x.")
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| 130 | FUNC1(sqrt, sqrt,
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| 131 | "sqrt(x)\n\nReturn the square root of x.")
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| 132 | FUNC1(tan, tan,
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| 133 | "tan(x)\n\nReturn the tangent of x (measured in radians).")
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| 134 | FUNC1(tanh, tanh,
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| 135 | "tanh(x)\n\nReturn the hyperbolic tangent of x.")
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| 136 |
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| 137 | static PyObject *
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| 138 | math_frexp(PyObject *self, PyObject *args)
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| 139 | {
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| 140 | double x;
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| 141 | int i;
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| 142 | if (! PyArg_ParseTuple(args, "d:frexp", &x))
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| 143 | return NULL;
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| 144 | errno = 0;
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| 145 | x = frexp(x, &i);
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| 146 | Py_SET_ERRNO_ON_MATH_ERROR(x);
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| 147 | if (errno && is_error(x))
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| 148 | return NULL;
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| 149 | else
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| 150 | return Py_BuildValue("(di)", x, i);
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| 151 | }
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| 152 |
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| 153 | PyDoc_STRVAR(math_frexp_doc,
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| 154 | "frexp(x)\n"
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| 155 | "\n"
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| 156 | "Return the mantissa and exponent of x, as pair (m, e).\n"
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| 157 | "m is a float and e is an int, such that x = m * 2.**e.\n"
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| 158 | "If x is 0, m and e are both 0. Else 0.5 <= abs(m) < 1.0.");
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| 159 |
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| 160 | static PyObject *
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| 161 | math_ldexp(PyObject *self, PyObject *args)
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| 162 | {
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| 163 | double x;
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| 164 | int exp;
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| 165 | if (! PyArg_ParseTuple(args, "di:ldexp", &x, &exp))
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| 166 | return NULL;
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| 167 | errno = 0;
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| 168 | PyFPE_START_PROTECT("ldexp", return 0)
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| 169 | x = ldexp(x, exp);
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| 170 | PyFPE_END_PROTECT(x)
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| 171 | Py_SET_ERRNO_ON_MATH_ERROR(x);
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| 172 | if (errno && is_error(x))
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| 173 | return NULL;
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| 174 | else
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| 175 | return PyFloat_FromDouble(x);
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| 176 | }
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| 177 |
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| 178 | PyDoc_STRVAR(math_ldexp_doc,
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| 179 | "ldexp(x, i) -> x * (2**i)");
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| 180 |
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| 181 | static PyObject *
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| 182 | math_modf(PyObject *self, PyObject *args)
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| 183 | {
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| 184 | double x, y;
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| 185 | if (! PyArg_ParseTuple(args, "d:modf", &x))
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| 186 | return NULL;
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| 187 | errno = 0;
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| 188 | x = modf(x, &y);
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| 189 | Py_SET_ERRNO_ON_MATH_ERROR(x);
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| 190 | if (errno && is_error(x))
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| 191 | return NULL;
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| 192 | else
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| 193 | return Py_BuildValue("(dd)", x, y);
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| 194 | }
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| 195 |
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| 196 | PyDoc_STRVAR(math_modf_doc,
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| 197 | "modf(x)\n"
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| 198 | "\n"
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| 199 | "Return the fractional and integer parts of x. Both results carry the sign\n"
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| 200 | "of x. The integer part is returned as a real.");
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| 201 |
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| 202 | /* A decent logarithm is easy to compute even for huge longs, but libm can't
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| 203 | do that by itself -- loghelper can. func is log or log10, and name is
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| 204 | "log" or "log10". Note that overflow isn't possible: a long can contain
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| 205 | no more than INT_MAX * SHIFT bits, so has value certainly less than
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| 206 | 2**(2**64 * 2**16) == 2**2**80, and log2 of that is 2**80, which is
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| 207 | small enough to fit in an IEEE single. log and log10 are even smaller.
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| 208 | */
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| 209 |
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| 210 | static PyObject*
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| 211 | loghelper(PyObject* args, double (*func)(double), char *format, PyObject *arg)
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| 212 | {
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| 213 | /* If it is long, do it ourselves. */
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| 214 | if (PyLong_Check(arg)) {
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| 215 | double x;
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| 216 | int e;
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| 217 | x = _PyLong_AsScaledDouble(arg, &e);
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| 218 | if (x <= 0.0) {
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| 219 | PyErr_SetString(PyExc_ValueError,
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| 220 | "math domain error");
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| 221 | return NULL;
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| 222 | }
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| 223 | /* Value is ~= x * 2**(e*SHIFT), so the log ~=
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| 224 | log(x) + log(2) * e * SHIFT.
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| 225 | CAUTION: e*SHIFT may overflow using int arithmetic,
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| 226 | so force use of double. */
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| 227 | x = func(x) + (e * (double)SHIFT) * func(2.0);
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| 228 | return PyFloat_FromDouble(x);
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| 229 | }
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| 230 |
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| 231 | /* Else let libm handle it by itself. */
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| 232 | return math_1(args, func, format);
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| 233 | }
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| 234 |
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| 235 | static PyObject *
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| 236 | math_log(PyObject *self, PyObject *args)
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| 237 | {
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| 238 | PyObject *arg;
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| 239 | PyObject *base = NULL;
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| 240 | PyObject *num, *den;
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| 241 | PyObject *ans;
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| 242 | PyObject *newargs;
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| 243 |
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| 244 | if (!PyArg_UnpackTuple(args, "log", 1, 2, &arg, &base))
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| 245 | return NULL;
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| 246 | if (base == NULL)
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| 247 | return loghelper(args, log, "d:log", arg);
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| 248 |
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| 249 | newargs = PyTuple_Pack(1, arg);
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| 250 | if (newargs == NULL)
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| 251 | return NULL;
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| 252 | num = loghelper(newargs, log, "d:log", arg);
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| 253 | Py_DECREF(newargs);
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| 254 | if (num == NULL)
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| 255 | return NULL;
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| 256 |
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| 257 | newargs = PyTuple_Pack(1, base);
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| 258 | if (newargs == NULL) {
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| 259 | Py_DECREF(num);
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| 260 | return NULL;
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| 261 | }
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| 262 | den = loghelper(newargs, log, "d:log", base);
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| 263 | Py_DECREF(newargs);
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| 264 | if (den == NULL) {
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| 265 | Py_DECREF(num);
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| 266 | return NULL;
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| 267 | }
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| 268 |
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| 269 | ans = PyNumber_Divide(num, den);
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| 270 | Py_DECREF(num);
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| 271 | Py_DECREF(den);
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| 272 | return ans;
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| 273 | }
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| 274 |
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| 275 | PyDoc_STRVAR(math_log_doc,
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| 276 | "log(x[, base]) -> the logarithm of x to the given base.\n\
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| 277 | If the base not specified, returns the natural logarithm (base e) of x.");
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| 278 |
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| 279 | static PyObject *
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| 280 | math_log10(PyObject *self, PyObject *args)
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| 281 | {
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| 282 | PyObject *arg;
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| 283 |
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| 284 | if (!PyArg_UnpackTuple(args, "log10", 1, 1, &arg))
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| 285 | return NULL;
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| 286 | return loghelper(args, log10, "d:log10", arg);
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| 287 | }
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| 288 |
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| 289 | PyDoc_STRVAR(math_log10_doc,
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| 290 | "log10(x) -> the base 10 logarithm of x.");
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| 291 |
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| 292 | static const double degToRad = 3.141592653589793238462643383 / 180.0;
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| 293 |
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| 294 | static PyObject *
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| 295 | math_degrees(PyObject *self, PyObject *args)
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| 296 | {
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| 297 | double x;
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| 298 | if (! PyArg_ParseTuple(args, "d:degrees", &x))
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| 299 | return NULL;
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| 300 | return PyFloat_FromDouble(x / degToRad);
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| 301 | }
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| 302 |
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| 303 | PyDoc_STRVAR(math_degrees_doc,
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| 304 | "degrees(x) -> converts angle x from radians to degrees");
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| 305 |
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| 306 | static PyObject *
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| 307 | math_radians(PyObject *self, PyObject *args)
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| 308 | {
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| 309 | double x;
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| 310 | if (! PyArg_ParseTuple(args, "d:radians", &x))
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| 311 | return NULL;
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| 312 | return PyFloat_FromDouble(x * degToRad);
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| 313 | }
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| 314 |
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| 315 | PyDoc_STRVAR(math_radians_doc,
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| 316 | "radians(x) -> converts angle x from degrees to radians");
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| 317 |
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| 318 | static PyMethodDef math_methods[] = {
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| 319 | {"acos", math_acos, METH_VARARGS, math_acos_doc},
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| 320 | {"asin", math_asin, METH_VARARGS, math_asin_doc},
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| 321 | {"atan", math_atan, METH_VARARGS, math_atan_doc},
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| 322 | {"atan2", math_atan2, METH_VARARGS, math_atan2_doc},
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| 323 | {"ceil", math_ceil, METH_VARARGS, math_ceil_doc},
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| 324 | {"cos", math_cos, METH_VARARGS, math_cos_doc},
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| 325 | {"cosh", math_cosh, METH_VARARGS, math_cosh_doc},
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| 326 | {"degrees", math_degrees, METH_VARARGS, math_degrees_doc},
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| 327 | {"exp", math_exp, METH_VARARGS, math_exp_doc},
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| 328 | {"fabs", math_fabs, METH_VARARGS, math_fabs_doc},
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| 329 | {"floor", math_floor, METH_VARARGS, math_floor_doc},
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| 330 | {"fmod", math_fmod, METH_VARARGS, math_fmod_doc},
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| 331 | {"frexp", math_frexp, METH_VARARGS, math_frexp_doc},
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| 332 | {"hypot", math_hypot, METH_VARARGS, math_hypot_doc},
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| 333 | {"ldexp", math_ldexp, METH_VARARGS, math_ldexp_doc},
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| 334 | {"log", math_log, METH_VARARGS, math_log_doc},
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| 335 | {"log10", math_log10, METH_VARARGS, math_log10_doc},
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| 336 | {"modf", math_modf, METH_VARARGS, math_modf_doc},
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| 337 | {"pow", math_pow, METH_VARARGS, math_pow_doc},
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| 338 | {"radians", math_radians, METH_VARARGS, math_radians_doc},
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| 339 | {"sin", math_sin, METH_VARARGS, math_sin_doc},
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| 340 | {"sinh", math_sinh, METH_VARARGS, math_sinh_doc},
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| 341 | {"sqrt", math_sqrt, METH_VARARGS, math_sqrt_doc},
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| 342 | {"tan", math_tan, METH_VARARGS, math_tan_doc},
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| 343 | {"tanh", math_tanh, METH_VARARGS, math_tanh_doc},
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| 344 | {NULL, NULL} /* sentinel */
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| 345 | };
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| 346 |
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| 347 |
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| 348 | PyDoc_STRVAR(module_doc,
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| 349 | "This module is always available. It provides access to the\n"
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| 350 | "mathematical functions defined by the C standard.");
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| 351 |
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| 352 | PyMODINIT_FUNC
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| 353 | initmath(void)
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| 354 | {
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| 355 | PyObject *m, *d, *v;
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| 356 |
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| 357 | m = Py_InitModule3("math", math_methods, module_doc);
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| 358 | if (m == NULL)
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| 359 | goto finally;
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| 360 | d = PyModule_GetDict(m);
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| 361 |
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| 362 | if (!(v = PyFloat_FromDouble(atan(1.0) * 4.0)))
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| 363 | goto finally;
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| 364 | if (PyDict_SetItemString(d, "pi", v) < 0)
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| 365 | goto finally;
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| 366 | Py_DECREF(v);
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| 367 |
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| 368 | if (!(v = PyFloat_FromDouble(exp(1.0))))
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| 369 | goto finally;
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| 370 | if (PyDict_SetItemString(d, "e", v) < 0)
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| 371 | goto finally;
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| 372 | Py_DECREF(v);
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| 373 |
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| 374 | finally:
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| 375 | return;
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| 376 | }
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