| /* Math module -- standard C math library functions, pi and e */ |
| |
| #include "Python.h" |
| #include "longintrepr.h" /* just for SHIFT */ |
| |
| #ifndef _MSC_VER |
| #ifndef __STDC__ |
| extern double fmod (double, double); |
| extern double frexp (double, int *); |
| extern double ldexp (double, int); |
| extern double modf (double, double *); |
| #endif /* __STDC__ */ |
| #endif /* _MSC_VER */ |
| |
| /* Call is_error when errno != 0, and where x is the result libm |
| * returned. is_error will usually set up an exception and return |
| * true (1), but may return false (0) without setting up an exception. |
| */ |
| static int |
| is_error(double x) |
| { |
| int result = 1; /* presumption of guilt */ |
| assert(errno); /* non-zero errno is a precondition for calling */ |
| if (errno == EDOM) |
| PyErr_SetString(PyExc_ValueError, "math domain error"); |
| |
| else if (errno == ERANGE) { |
| /* ANSI C generally requires libm functions to set ERANGE |
| * on overflow, but also generally *allows* them to set |
| * ERANGE on underflow too. There's no consistency about |
| * the latter across platforms. |
| * Alas, C99 never requires that errno be set. |
| * Here we suppress the underflow errors (libm functions |
| * should return a zero on underflow, and +- HUGE_VAL on |
| * overflow, so testing the result for zero suffices to |
| * distinguish the cases). |
| */ |
| if (x) |
| PyErr_SetString(PyExc_OverflowError, |
| "math range error"); |
| else |
| result = 0; |
| } |
| else |
| /* Unexpected math error */ |
| PyErr_SetFromErrno(PyExc_ValueError); |
| return result; |
| } |
| |
| static PyObject * |
| math_1(PyObject *args, double (*func) (double), char *argsfmt) |
| { |
| double x; |
| if (! PyArg_ParseTuple(args, argsfmt, &x)) |
| return NULL; |
| errno = 0; |
| PyFPE_START_PROTECT("in math_1", return 0) |
| x = (*func)(x); |
| PyFPE_END_PROTECT(x) |
| Py_SET_ERRNO_ON_MATH_ERROR(x); |
| if (errno && is_error(x)) |
| return NULL; |
| else |
| return PyFloat_FromDouble(x); |
| } |
| |
| static PyObject * |
| math_2(PyObject *args, double (*func) (double, double), char *argsfmt) |
| { |
| double x, y; |
| if (! PyArg_ParseTuple(args, argsfmt, &x, &y)) |
| return NULL; |
| errno = 0; |
| PyFPE_START_PROTECT("in math_2", return 0) |
| x = (*func)(x, y); |
| PyFPE_END_PROTECT(x) |
| Py_SET_ERRNO_ON_MATH_ERROR(x); |
| if (errno && is_error(x)) |
| return NULL; |
| else |
| return PyFloat_FromDouble(x); |
| } |
| |
| #define FUNC1(funcname, func, docstring) \ |
| static PyObject * math_##funcname(PyObject *self, PyObject *args) { \ |
| return math_1(args, func, "d:" #funcname); \ |
| }\ |
| PyDoc_STRVAR(math_##funcname##_doc, docstring); |
| |
| #define FUNC2(funcname, func, docstring) \ |
| static PyObject * math_##funcname(PyObject *self, PyObject *args) { \ |
| return math_2(args, func, "dd:" #funcname); \ |
| }\ |
| PyDoc_STRVAR(math_##funcname##_doc, docstring); |
| |
| FUNC1(acos, acos, |
| "acos(x)\n\nReturn the arc cosine (measured in radians) of x.") |
| FUNC1(asin, asin, |
| "asin(x)\n\nReturn the arc sine (measured in radians) of x.") |
| FUNC1(atan, atan, |
| "atan(x)\n\nReturn the arc tangent (measured in radians) of x.") |
| FUNC2(atan2, atan2, |
| "atan2(y, x)\n\nReturn the arc tangent (measured in radians) of y/x.\n" |
| "Unlike atan(y/x), the signs of both x and y are considered.") |
| FUNC1(ceil, ceil, |
| "ceil(x)\n\nReturn the ceiling of x as a float.\n" |
| "This is the smallest integral value >= x.") |
| FUNC1(cos, cos, |
| "cos(x)\n\nReturn the cosine of x (measured in radians).") |
| FUNC1(cosh, cosh, |
| "cosh(x)\n\nReturn the hyperbolic cosine of x.") |
| FUNC1(exp, exp, |
| "exp(x)\n\nReturn e raised to the power of x.") |
| FUNC1(fabs, fabs, |
| "fabs(x)\n\nReturn the absolute value of the float x.") |
| FUNC1(floor, floor, |
| "floor(x)\n\nReturn the floor of x as a float.\n" |
| "This is the largest integral value <= x.") |
| FUNC2(fmod, fmod, |
| "fmod(x,y)\n\nReturn fmod(x, y), according to platform C." |
| " x % y may differ.") |
| FUNC2(hypot, hypot, |
| "hypot(x,y)\n\nReturn the Euclidean distance, sqrt(x*x + y*y).") |
| FUNC2(pow, pow, |
| "pow(x,y)\n\nReturn x**y (x to the power of y).") |
| FUNC1(sin, sin, |
| "sin(x)\n\nReturn the sine of x (measured in radians).") |
| FUNC1(sinh, sinh, |
| "sinh(x)\n\nReturn the hyperbolic sine of x.") |
| FUNC1(sqrt, sqrt, |
| "sqrt(x)\n\nReturn the square root of x.") |
| FUNC1(tan, tan, |
| "tan(x)\n\nReturn the tangent of x (measured in radians).") |
| FUNC1(tanh, tanh, |
| "tanh(x)\n\nReturn the hyperbolic tangent of x.") |
| |
| static PyObject * |
| math_frexp(PyObject *self, PyObject *args) |
| { |
| double x; |
| int i; |
| if (! PyArg_ParseTuple(args, "d:frexp", &x)) |
| return NULL; |
| errno = 0; |
| x = frexp(x, &i); |
| Py_SET_ERRNO_ON_MATH_ERROR(x); |
| if (errno && is_error(x)) |
| return NULL; |
| else |
| return Py_BuildValue("(di)", x, i); |
| } |
| |
| PyDoc_STRVAR(math_frexp_doc, |
| "frexp(x)\n" |
| "\n" |
| "Return the mantissa and exponent of x, as pair (m, e).\n" |
| "m is a float and e is an int, such that x = m * 2.**e.\n" |
| "If x is 0, m and e are both 0. Else 0.5 <= abs(m) < 1.0."); |
| |
| static PyObject * |
| math_ldexp(PyObject *self, PyObject *args) |
| { |
| double x; |
| int exp; |
| if (! PyArg_ParseTuple(args, "di:ldexp", &x, &exp)) |
| return NULL; |
| errno = 0; |
| PyFPE_START_PROTECT("ldexp", return 0) |
| x = ldexp(x, exp); |
| PyFPE_END_PROTECT(x) |
| Py_SET_ERRNO_ON_MATH_ERROR(x); |
| if (errno && is_error(x)) |
| return NULL; |
| else |
| return PyFloat_FromDouble(x); |
| } |
| |
| PyDoc_STRVAR(math_ldexp_doc, |
| "ldexp(x, i) -> x * (2**i)"); |
| |
| static PyObject * |
| math_modf(PyObject *self, PyObject *args) |
| { |
| double x, y; |
| if (! PyArg_ParseTuple(args, "d:modf", &x)) |
| return NULL; |
| errno = 0; |
| x = modf(x, &y); |
| Py_SET_ERRNO_ON_MATH_ERROR(x); |
| if (errno && is_error(x)) |
| return NULL; |
| else |
| return Py_BuildValue("(dd)", x, y); |
| } |
| |
| PyDoc_STRVAR(math_modf_doc, |
| "modf(x)\n" |
| "\n" |
| "Return the fractional and integer parts of x. Both results carry the sign\n" |
| "of x. The integer part is returned as a real."); |
| |
| /* A decent logarithm is easy to compute even for huge longs, but libm can't |
| do that by itself -- loghelper can. func is log or log10, and name is |
| "log" or "log10". Note that overflow isn't possible: a long can contain |
| no more than INT_MAX * SHIFT bits, so has value certainly less than |
| 2**(2**64 * 2**16) == 2**2**80, and log2 of that is 2**80, which is |
| small enough to fit in an IEEE single. log and log10 are even smaller. |
| */ |
| |
| static PyObject* |
| loghelper(PyObject* args, double (*func)(double), char *format, PyObject *arg) |
| { |
| /* If it is long, do it ourselves. */ |
| if (PyLong_Check(arg)) { |
| double x; |
| int e; |
| x = _PyLong_AsScaledDouble(arg, &e); |
| if (x <= 0.0) { |
| PyErr_SetString(PyExc_ValueError, |
| "math domain error"); |
| return NULL; |
| } |
| /* Value is ~= x * 2**(e*SHIFT), so the log ~= |
| log(x) + log(2) * e * SHIFT. |
| CAUTION: e*SHIFT may overflow using int arithmetic, |
| so force use of double. */ |
| x = func(x) + (e * (double)SHIFT) * func(2.0); |
| return PyFloat_FromDouble(x); |
| } |
| |
| /* Else let libm handle it by itself. */ |
| return math_1(args, func, format); |
| } |
| |
| static PyObject * |
| math_log(PyObject *self, PyObject *args) |
| { |
| PyObject *arg; |
| PyObject *base = NULL; |
| PyObject *num, *den; |
| PyObject *ans; |
| PyObject *newargs; |
| |
| if (!PyArg_UnpackTuple(args, "log", 1, 2, &arg, &base)) |
| return NULL; |
| if (base == NULL) |
| return loghelper(args, log, "d:log", arg); |
| |
| newargs = PyTuple_Pack(1, arg); |
| if (newargs == NULL) |
| return NULL; |
| num = loghelper(newargs, log, "d:log", arg); |
| Py_DECREF(newargs); |
| if (num == NULL) |
| return NULL; |
| |
| newargs = PyTuple_Pack(1, base); |
| if (newargs == NULL) { |
| Py_DECREF(num); |
| return NULL; |
| } |
| den = loghelper(newargs, log, "d:log", base); |
| Py_DECREF(newargs); |
| if (den == NULL) { |
| Py_DECREF(num); |
| return NULL; |
| } |
| |
| ans = PyNumber_TrueDivide(num, den); |
| Py_DECREF(num); |
| Py_DECREF(den); |
| return ans; |
| } |
| |
| PyDoc_STRVAR(math_log_doc, |
| "log(x[, base]) -> the logarithm of x to the given base.\n\ |
| If the base not specified, returns the natural logarithm (base e) of x."); |
| |
| static PyObject * |
| math_log10(PyObject *self, PyObject *args) |
| { |
| PyObject *arg; |
| |
| if (!PyArg_UnpackTuple(args, "log10", 1, 1, &arg)) |
| return NULL; |
| return loghelper(args, log10, "d:log10", arg); |
| } |
| |
| PyDoc_STRVAR(math_log10_doc, |
| "log10(x) -> the base 10 logarithm of x."); |
| |
| static const double degToRad = 3.141592653589793238462643383 / 180.0; |
| |
| static PyObject * |
| math_degrees(PyObject *self, PyObject *args) |
| { |
| double x; |
| if (! PyArg_ParseTuple(args, "d:degrees", &x)) |
| return NULL; |
| return PyFloat_FromDouble(x / degToRad); |
| } |
| |
| PyDoc_STRVAR(math_degrees_doc, |
| "degrees(x) -> converts angle x from radians to degrees"); |
| |
| static PyObject * |
| math_radians(PyObject *self, PyObject *args) |
| { |
| double x; |
| if (! PyArg_ParseTuple(args, "d:radians", &x)) |
| return NULL; |
| return PyFloat_FromDouble(x * degToRad); |
| } |
| |
| PyDoc_STRVAR(math_radians_doc, |
| "radians(x) -> converts angle x from degrees to radians"); |
| |
| static PyMethodDef math_methods[] = { |
| {"acos", math_acos, METH_VARARGS, math_acos_doc}, |
| {"asin", math_asin, METH_VARARGS, math_asin_doc}, |
| {"atan", math_atan, METH_VARARGS, math_atan_doc}, |
| {"atan2", math_atan2, METH_VARARGS, math_atan2_doc}, |
| {"ceil", math_ceil, METH_VARARGS, math_ceil_doc}, |
| {"cos", math_cos, METH_VARARGS, math_cos_doc}, |
| {"cosh", math_cosh, METH_VARARGS, math_cosh_doc}, |
| {"degrees", math_degrees, METH_VARARGS, math_degrees_doc}, |
| {"exp", math_exp, METH_VARARGS, math_exp_doc}, |
| {"fabs", math_fabs, METH_VARARGS, math_fabs_doc}, |
| {"floor", math_floor, METH_VARARGS, math_floor_doc}, |
| {"fmod", math_fmod, METH_VARARGS, math_fmod_doc}, |
| {"frexp", math_frexp, METH_VARARGS, math_frexp_doc}, |
| {"hypot", math_hypot, METH_VARARGS, math_hypot_doc}, |
| {"ldexp", math_ldexp, METH_VARARGS, math_ldexp_doc}, |
| {"log", math_log, METH_VARARGS, math_log_doc}, |
| {"log10", math_log10, METH_VARARGS, math_log10_doc}, |
| {"modf", math_modf, METH_VARARGS, math_modf_doc}, |
| {"pow", math_pow, METH_VARARGS, math_pow_doc}, |
| {"radians", math_radians, METH_VARARGS, math_radians_doc}, |
| {"sin", math_sin, METH_VARARGS, math_sin_doc}, |
| {"sinh", math_sinh, METH_VARARGS, math_sinh_doc}, |
| {"sqrt", math_sqrt, METH_VARARGS, math_sqrt_doc}, |
| {"tan", math_tan, METH_VARARGS, math_tan_doc}, |
| {"tanh", math_tanh, METH_VARARGS, math_tanh_doc}, |
| {NULL, NULL} /* sentinel */ |
| }; |
| |
| |
| PyDoc_STRVAR(module_doc, |
| "This module is always available. It provides access to the\n" |
| "mathematical functions defined by the C standard."); |
| |
| PyMODINIT_FUNC |
| initmath(void) |
| { |
| PyObject *m, *d, *v; |
| |
| m = Py_InitModule3("math", math_methods, module_doc); |
| if (m == NULL) |
| goto finally; |
| d = PyModule_GetDict(m); |
| |
| if (!(v = PyFloat_FromDouble(atan(1.0) * 4.0))) |
| goto finally; |
| if (PyDict_SetItemString(d, "pi", v) < 0) |
| goto finally; |
| Py_DECREF(v); |
| |
| if (!(v = PyFloat_FromDouble(exp(1.0)))) |
| goto finally; |
| if (PyDict_SetItemString(d, "e", v) < 0) |
| goto finally; |
| Py_DECREF(v); |
| |
| finally: |
| return; |
| } |