ref: e6b4528626528c2bf11f760bfc660375195e6055
dir: /sys/src/cmd/python/Modules/cmathmodule.c/
/* Complex math module */ /* much code borrowed from mathmodule.c */ #include "Python.h" #ifndef M_PI #define M_PI (3.141592653589793239) #endif /* First, the C functions that do the real work */ /* constants */ static Py_complex c_one = {1., 0.}; static Py_complex c_half = {0.5, 0.}; static Py_complex c_i = {0., 1.}; static Py_complex c_halfi = {0., 0.5}; /* forward declarations */ static Py_complex c_log(Py_complex); static Py_complex c_prodi(Py_complex); static Py_complex c_sqrt(Py_complex); static PyObject * math_error(void); static Py_complex c_acos(Py_complex x) { return c_neg(c_prodi(c_log(c_sum(x,c_prod(c_i, c_sqrt(c_diff(c_one,c_prod(x,x)))))))); } PyDoc_STRVAR(c_acos_doc, "acos(x)\n" "\n" "Return the arc cosine of x."); static Py_complex c_acosh(Py_complex x) { Py_complex z; z = c_sqrt(c_half); z = c_log(c_prod(z, c_sum(c_sqrt(c_sum(x,c_one)), c_sqrt(c_diff(x,c_one))))); return c_sum(z, z); } PyDoc_STRVAR(c_acosh_doc, "acosh(x)\n" "\n" "Return the hyperbolic arccosine of x."); static Py_complex c_asin(Py_complex x) { /* -i * log[(sqrt(1-x**2) + i*x] */ const Py_complex squared = c_prod(x, x); const Py_complex sqrt_1_minus_x_sq = c_sqrt(c_diff(c_one, squared)); return c_neg(c_prodi(c_log( c_sum(sqrt_1_minus_x_sq, c_prodi(x)) ) ) ); } PyDoc_STRVAR(c_asin_doc, "asin(x)\n" "\n" "Return the arc sine of x."); static Py_complex c_asinh(Py_complex x) { Py_complex z; z = c_sqrt(c_half); z = c_log(c_prod(z, c_sum(c_sqrt(c_sum(x, c_i)), c_sqrt(c_diff(x, c_i))))); return c_sum(z, z); } PyDoc_STRVAR(c_asinh_doc, "asinh(x)\n" "\n" "Return the hyperbolic arc sine of x."); static Py_complex c_atan(Py_complex x) { return c_prod(c_halfi,c_log(c_quot(c_sum(c_i,x),c_diff(c_i,x)))); } PyDoc_STRVAR(c_atan_doc, "atan(x)\n" "\n" "Return the arc tangent of x."); static Py_complex c_atanh(Py_complex x) { return c_prod(c_half,c_log(c_quot(c_sum(c_one,x),c_diff(c_one,x)))); } PyDoc_STRVAR(c_atanh_doc, "atanh(x)\n" "\n" "Return the hyperbolic arc tangent of x."); static Py_complex c_cos(Py_complex x) { Py_complex r; r.real = cos(x.real)*cosh(x.imag); r.imag = -sin(x.real)*sinh(x.imag); return r; } PyDoc_STRVAR(c_cos_doc, "cos(x)\n" "n" "Return the cosine of x."); static Py_complex c_cosh(Py_complex x) { Py_complex r; r.real = cos(x.imag)*cosh(x.real); r.imag = sin(x.imag)*sinh(x.real); return r; } PyDoc_STRVAR(c_cosh_doc, "cosh(x)\n" "n" "Return the hyperbolic cosine of x."); static Py_complex c_exp(Py_complex x) { Py_complex r; double l = exp(x.real); r.real = l*cos(x.imag); r.imag = l*sin(x.imag); return r; } PyDoc_STRVAR(c_exp_doc, "exp(x)\n" "\n" "Return the exponential value e**x."); static Py_complex c_log(Py_complex x) { Py_complex r; double l = hypot(x.real,x.imag); r.imag = atan2(x.imag, x.real); r.real = log(l); return r; } static Py_complex c_log10(Py_complex x) { Py_complex r; double l = hypot(x.real,x.imag); r.imag = atan2(x.imag, x.real)/log(10.); r.real = log10(l); return r; } PyDoc_STRVAR(c_log10_doc, "log10(x)\n" "\n" "Return the base-10 logarithm of x."); /* internal function not available from Python */ static Py_complex c_prodi(Py_complex x) { Py_complex r; r.real = -x.imag; r.imag = x.real; return r; } static Py_complex c_sin(Py_complex x) { Py_complex r; r.real = sin(x.real) * cosh(x.imag); r.imag = cos(x.real) * sinh(x.imag); return r; } PyDoc_STRVAR(c_sin_doc, "sin(x)\n" "\n" "Return the sine of x."); static Py_complex c_sinh(Py_complex x) { Py_complex r; r.real = cos(x.imag) * sinh(x.real); r.imag = sin(x.imag) * cosh(x.real); return r; } PyDoc_STRVAR(c_sinh_doc, "sinh(x)\n" "\n" "Return the hyperbolic sine of x."); static Py_complex c_sqrt(Py_complex x) { Py_complex r; double s,d; if (x.real == 0. && x.imag == 0.) r = x; else { s = sqrt(0.5*(fabs(x.real) + hypot(x.real,x.imag))); d = 0.5*x.imag/s; if (x.real > 0.) { r.real = s; r.imag = d; } else if (x.imag >= 0.) { r.real = d; r.imag = s; } else { r.real = -d; r.imag = -s; } } return r; } PyDoc_STRVAR(c_sqrt_doc, "sqrt(x)\n" "\n" "Return the square root of x."); static Py_complex c_tan(Py_complex x) { Py_complex r; double sr,cr,shi,chi; double rs,is,rc,ic; double d; sr = sin(x.real); cr = cos(x.real); shi = sinh(x.imag); chi = cosh(x.imag); rs = sr * chi; is = cr * shi; rc = cr * chi; ic = -sr * shi; d = rc*rc + ic * ic; r.real = (rs*rc + is*ic) / d; r.imag = (is*rc - rs*ic) / d; return r; } PyDoc_STRVAR(c_tan_doc, "tan(x)\n" "\n" "Return the tangent of x."); static Py_complex c_tanh(Py_complex x) { Py_complex r; double si,ci,shr,chr; double rs,is,rc,ic; double d; si = sin(x.imag); ci = cos(x.imag); shr = sinh(x.real); chr = cosh(x.real); rs = ci * shr; is = si * chr; rc = ci * chr; ic = si * shr; d = rc*rc + ic*ic; r.real = (rs*rc + is*ic) / d; r.imag = (is*rc - rs*ic) / d; return r; } PyDoc_STRVAR(c_tanh_doc, "tanh(x)\n" "\n" "Return the hyperbolic tangent of x."); static PyObject * cmath_log(PyObject *self, PyObject *args) { Py_complex x; Py_complex y; if (!PyArg_ParseTuple(args, "D|D", &x, &y)) return NULL; errno = 0; PyFPE_START_PROTECT("complex function", return 0) x = c_log(x); if (PyTuple_GET_SIZE(args) == 2) x = c_quot(x, c_log(y)); PyFPE_END_PROTECT(x) if (errno != 0) return math_error(); Py_ADJUST_ERANGE2(x.real, x.imag); return PyComplex_FromCComplex(x); } PyDoc_STRVAR(cmath_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."); /* And now the glue to make them available from Python: */ static PyObject * math_error(void) { if (errno == EDOM) PyErr_SetString(PyExc_ValueError, "math domain error"); else if (errno == ERANGE) PyErr_SetString(PyExc_OverflowError, "math range error"); else /* Unexpected math error */ PyErr_SetFromErrno(PyExc_ValueError); return NULL; } static PyObject * math_1(PyObject *args, Py_complex (*func)(Py_complex)) { Py_complex x; if (!PyArg_ParseTuple(args, "D", &x)) return NULL; errno = 0; PyFPE_START_PROTECT("complex function", return 0) x = (*func)(x); PyFPE_END_PROTECT(x) Py_ADJUST_ERANGE2(x.real, x.imag); if (errno != 0) return math_error(); else return PyComplex_FromCComplex(x); } #define FUNC1(stubname, func) \ static PyObject * stubname(PyObject *self, PyObject *args) { \ return math_1(args, func); \ } FUNC1(cmath_acos, c_acos) FUNC1(cmath_acosh, c_acosh) FUNC1(cmath_asin, c_asin) FUNC1(cmath_asinh, c_asinh) FUNC1(cmath_atan, c_atan) FUNC1(cmath_atanh, c_atanh) FUNC1(cmath_cos, c_cos) FUNC1(cmath_cosh, c_cosh) FUNC1(cmath_exp, c_exp) FUNC1(cmath_log10, c_log10) FUNC1(cmath_sin, c_sin) FUNC1(cmath_sinh, c_sinh) FUNC1(cmath_sqrt, c_sqrt) FUNC1(cmath_tan, c_tan) FUNC1(cmath_tanh, c_tanh) PyDoc_STRVAR(module_doc, "This module is always available. It provides access to mathematical\n" "functions for complex numbers."); static PyMethodDef cmath_methods[] = { {"acos", cmath_acos, METH_VARARGS, c_acos_doc}, {"acosh", cmath_acosh, METH_VARARGS, c_acosh_doc}, {"asin", cmath_asin, METH_VARARGS, c_asin_doc}, {"asinh", cmath_asinh, METH_VARARGS, c_asinh_doc}, {"atan", cmath_atan, METH_VARARGS, c_atan_doc}, {"atanh", cmath_atanh, METH_VARARGS, c_atanh_doc}, {"cos", cmath_cos, METH_VARARGS, c_cos_doc}, {"cosh", cmath_cosh, METH_VARARGS, c_cosh_doc}, {"exp", cmath_exp, METH_VARARGS, c_exp_doc}, {"log", cmath_log, METH_VARARGS, cmath_log_doc}, {"log10", cmath_log10, METH_VARARGS, c_log10_doc}, {"sin", cmath_sin, METH_VARARGS, c_sin_doc}, {"sinh", cmath_sinh, METH_VARARGS, c_sinh_doc}, {"sqrt", cmath_sqrt, METH_VARARGS, c_sqrt_doc}, {"tan", cmath_tan, METH_VARARGS, c_tan_doc}, {"tanh", cmath_tanh, METH_VARARGS, c_tanh_doc}, {NULL, NULL} /* sentinel */ }; PyMODINIT_FUNC initcmath(void) { PyObject *m; m = Py_InitModule3("cmath", cmath_methods, module_doc); if (m == NULL) return; PyModule_AddObject(m, "pi", PyFloat_FromDouble(atan(1.0) * 4.0)); PyModule_AddObject(m, "e", PyFloat_FromDouble(exp(1.0))); }