mirror of
https://github.com/python/cpython.git
synced 2024-12-15 12:54:31 +08:00
427 lines
8.0 KiB
C
427 lines
8.0 KiB
C
/* Complex math module */
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/* much code borrowed from mathmodule.c */
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#include "Python.h"
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#ifndef M_PI
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#define M_PI (3.141592653589793239)
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#endif
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/* First, the C functions that do the real work */
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/* constants */
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static Py_complex c_one = {1., 0.};
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static Py_complex c_half = {0.5, 0.};
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static Py_complex c_i = {0., 1.};
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static Py_complex c_halfi = {0., 0.5};
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/* forward declarations */
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static Py_complex c_log(Py_complex);
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static Py_complex c_prodi(Py_complex);
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static Py_complex c_sqrt(Py_complex);
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static PyObject * math_error(void);
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static Py_complex
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c_acos(Py_complex x)
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{
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return c_neg(c_prodi(c_log(c_sum(x,c_prod(c_i,
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c_sqrt(c_diff(c_one,c_prod(x,x))))))));
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}
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PyDoc_STRVAR(c_acos_doc,
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"acos(x)\n"
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"\n"
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"Return the arc cosine of x.");
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static Py_complex
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c_acosh(Py_complex x)
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{
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Py_complex z;
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z = c_sqrt(c_half);
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z = c_log(c_prod(z, c_sum(c_sqrt(c_sum(x,c_one)),
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c_sqrt(c_diff(x,c_one)))));
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return c_sum(z, z);
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}
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PyDoc_STRVAR(c_acosh_doc,
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"acosh(x)\n"
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"\n"
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"Return the hyperbolic arccosine of x.");
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static Py_complex
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c_asin(Py_complex x)
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{
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/* -i * log[(sqrt(1-x**2) + i*x] */
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const Py_complex squared = c_prod(x, x);
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const Py_complex sqrt_1_minus_x_sq = c_sqrt(c_diff(c_one, squared));
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return c_neg(c_prodi(c_log(
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c_sum(sqrt_1_minus_x_sq, c_prodi(x))
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) ) );
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}
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PyDoc_STRVAR(c_asin_doc,
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"asin(x)\n"
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"\n"
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"Return the arc sine of x.");
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static Py_complex
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c_asinh(Py_complex x)
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{
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Py_complex z;
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z = c_sqrt(c_half);
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z = c_log(c_prod(z, c_sum(c_sqrt(c_sum(x, c_i)),
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c_sqrt(c_diff(x, c_i)))));
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return c_sum(z, z);
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}
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PyDoc_STRVAR(c_asinh_doc,
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"asinh(x)\n"
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"\n"
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"Return the hyperbolic arc sine of x.");
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static Py_complex
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c_atan(Py_complex x)
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{
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return c_prod(c_halfi,c_log(c_quot(c_sum(c_i,x),c_diff(c_i,x))));
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}
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PyDoc_STRVAR(c_atan_doc,
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"atan(x)\n"
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"\n"
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"Return the arc tangent of x.");
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static Py_complex
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c_atanh(Py_complex x)
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{
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return c_prod(c_half,c_log(c_quot(c_sum(c_one,x),c_diff(c_one,x))));
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}
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PyDoc_STRVAR(c_atanh_doc,
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"atanh(x)\n"
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"\n"
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"Return the hyperbolic arc tangent of x.");
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static Py_complex
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c_cos(Py_complex x)
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{
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Py_complex r;
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r.real = cos(x.real)*cosh(x.imag);
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r.imag = -sin(x.real)*sinh(x.imag);
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return r;
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}
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PyDoc_STRVAR(c_cos_doc,
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"cos(x)\n"
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"n"
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"Return the cosine of x.");
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static Py_complex
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c_cosh(Py_complex x)
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{
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Py_complex r;
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r.real = cos(x.imag)*cosh(x.real);
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r.imag = sin(x.imag)*sinh(x.real);
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return r;
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}
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PyDoc_STRVAR(c_cosh_doc,
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"cosh(x)\n"
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"n"
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"Return the hyperbolic cosine of x.");
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static Py_complex
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c_exp(Py_complex x)
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{
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Py_complex r;
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double l = exp(x.real);
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r.real = l*cos(x.imag);
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r.imag = l*sin(x.imag);
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return r;
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}
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PyDoc_STRVAR(c_exp_doc,
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"exp(x)\n"
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"\n"
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"Return the exponential value e**x.");
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static Py_complex
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c_log(Py_complex x)
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{
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Py_complex r;
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double l = hypot(x.real,x.imag);
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r.imag = atan2(x.imag, x.real);
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r.real = log(l);
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return r;
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}
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static Py_complex
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c_log10(Py_complex x)
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{
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Py_complex r;
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double l = hypot(x.real,x.imag);
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r.imag = atan2(x.imag, x.real)/log(10.);
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r.real = log10(l);
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return r;
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}
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PyDoc_STRVAR(c_log10_doc,
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"log10(x)\n"
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"\n"
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"Return the base-10 logarithm of x.");
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/* internal function not available from Python */
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static Py_complex
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c_prodi(Py_complex x)
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{
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Py_complex r;
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r.real = -x.imag;
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r.imag = x.real;
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return r;
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}
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static Py_complex
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c_sin(Py_complex x)
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{
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Py_complex r;
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r.real = sin(x.real) * cosh(x.imag);
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r.imag = cos(x.real) * sinh(x.imag);
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return r;
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}
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PyDoc_STRVAR(c_sin_doc,
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"sin(x)\n"
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"\n"
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"Return the sine of x.");
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static Py_complex
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c_sinh(Py_complex x)
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{
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Py_complex r;
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r.real = cos(x.imag) * sinh(x.real);
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r.imag = sin(x.imag) * cosh(x.real);
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return r;
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}
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PyDoc_STRVAR(c_sinh_doc,
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"sinh(x)\n"
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"\n"
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"Return the hyperbolic sine of x.");
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static Py_complex
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c_sqrt(Py_complex x)
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{
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Py_complex r;
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double s,d;
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if (x.real == 0. && x.imag == 0.)
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r = x;
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else {
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s = sqrt(0.5*(fabs(x.real) + hypot(x.real,x.imag)));
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d = 0.5*x.imag/s;
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if (x.real > 0.) {
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r.real = s;
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r.imag = d;
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}
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else if (x.imag >= 0.) {
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r.real = d;
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r.imag = s;
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}
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else {
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r.real = -d;
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r.imag = -s;
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}
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}
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return r;
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}
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PyDoc_STRVAR(c_sqrt_doc,
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"sqrt(x)\n"
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"\n"
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"Return the square root of x.");
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static Py_complex
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c_tan(Py_complex x)
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{
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Py_complex r;
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double sr,cr,shi,chi;
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double rs,is,rc,ic;
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double d;
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sr = sin(x.real);
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cr = cos(x.real);
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shi = sinh(x.imag);
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chi = cosh(x.imag);
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rs = sr * chi;
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is = cr * shi;
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rc = cr * chi;
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ic = -sr * shi;
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d = rc*rc + ic * ic;
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r.real = (rs*rc + is*ic) / d;
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r.imag = (is*rc - rs*ic) / d;
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return r;
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}
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PyDoc_STRVAR(c_tan_doc,
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"tan(x)\n"
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"\n"
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"Return the tangent of x.");
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static Py_complex
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c_tanh(Py_complex x)
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{
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Py_complex r;
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double si,ci,shr,chr;
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double rs,is,rc,ic;
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double d;
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si = sin(x.imag);
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ci = cos(x.imag);
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shr = sinh(x.real);
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chr = cosh(x.real);
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rs = ci * shr;
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is = si * chr;
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rc = ci * chr;
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ic = si * shr;
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d = rc*rc + ic*ic;
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r.real = (rs*rc + is*ic) / d;
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r.imag = (is*rc - rs*ic) / d;
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return r;
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}
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PyDoc_STRVAR(c_tanh_doc,
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"tanh(x)\n"
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"\n"
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"Return the hyperbolic tangent of x.");
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static PyObject *
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cmath_log(PyObject *self, PyObject *args)
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{
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Py_complex x;
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Py_complex y;
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if (!PyArg_ParseTuple(args, "D|D", &x, &y))
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return NULL;
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errno = 0;
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PyFPE_START_PROTECT("complex function", return 0)
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x = c_log(x);
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if (PyTuple_GET_SIZE(args) == 2)
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x = c_quot(x, c_log(y));
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PyFPE_END_PROTECT(x)
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if (errno != 0)
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return math_error();
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Py_ADJUST_ERANGE2(x.real, x.imag);
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return PyComplex_FromCComplex(x);
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}
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PyDoc_STRVAR(cmath_log_doc,
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"log(x[, base]) -> the logarithm of x to the given base.\n\
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If the base not specified, returns the natural logarithm (base e) of x.");
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/* And now the glue to make them available from Python: */
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static PyObject *
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math_error(void)
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{
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if (errno == EDOM)
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PyErr_SetString(PyExc_ValueError, "math domain error");
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else if (errno == ERANGE)
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PyErr_SetString(PyExc_OverflowError, "math range error");
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else /* Unexpected math error */
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PyErr_SetFromErrno(PyExc_ValueError);
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return NULL;
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}
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static PyObject *
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math_1(PyObject *args, Py_complex (*func)(Py_complex))
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{
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Py_complex x;
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if (!PyArg_ParseTuple(args, "D", &x))
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return NULL;
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errno = 0;
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PyFPE_START_PROTECT("complex function", return 0)
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x = (*func)(x);
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PyFPE_END_PROTECT(x)
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Py_ADJUST_ERANGE2(x.real, x.imag);
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if (errno != 0)
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return math_error();
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else
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return PyComplex_FromCComplex(x);
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}
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#define FUNC1(stubname, func) \
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static PyObject * stubname(PyObject *self, PyObject *args) { \
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return math_1(args, func); \
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}
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FUNC1(cmath_acos, c_acos)
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FUNC1(cmath_acosh, c_acosh)
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FUNC1(cmath_asin, c_asin)
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FUNC1(cmath_asinh, c_asinh)
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FUNC1(cmath_atan, c_atan)
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FUNC1(cmath_atanh, c_atanh)
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FUNC1(cmath_cos, c_cos)
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FUNC1(cmath_cosh, c_cosh)
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FUNC1(cmath_exp, c_exp)
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FUNC1(cmath_log10, c_log10)
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FUNC1(cmath_sin, c_sin)
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FUNC1(cmath_sinh, c_sinh)
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FUNC1(cmath_sqrt, c_sqrt)
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FUNC1(cmath_tan, c_tan)
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FUNC1(cmath_tanh, c_tanh)
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PyDoc_STRVAR(module_doc,
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"This module is always available. It provides access to mathematical\n"
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"functions for complex numbers.");
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static PyMethodDef cmath_methods[] = {
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{"acos", cmath_acos, METH_VARARGS, c_acos_doc},
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{"acosh", cmath_acosh, METH_VARARGS, c_acosh_doc},
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{"asin", cmath_asin, METH_VARARGS, c_asin_doc},
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{"asinh", cmath_asinh, METH_VARARGS, c_asinh_doc},
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{"atan", cmath_atan, METH_VARARGS, c_atan_doc},
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{"atanh", cmath_atanh, METH_VARARGS, c_atanh_doc},
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{"cos", cmath_cos, METH_VARARGS, c_cos_doc},
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{"cosh", cmath_cosh, METH_VARARGS, c_cosh_doc},
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{"exp", cmath_exp, METH_VARARGS, c_exp_doc},
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{"log", cmath_log, METH_VARARGS, cmath_log_doc},
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{"log10", cmath_log10, METH_VARARGS, c_log10_doc},
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{"sin", cmath_sin, METH_VARARGS, c_sin_doc},
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{"sinh", cmath_sinh, METH_VARARGS, c_sinh_doc},
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{"sqrt", cmath_sqrt, METH_VARARGS, c_sqrt_doc},
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{"tan", cmath_tan, METH_VARARGS, c_tan_doc},
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{"tanh", cmath_tanh, METH_VARARGS, c_tanh_doc},
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{NULL, NULL} /* sentinel */
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};
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PyMODINIT_FUNC
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initcmath(void)
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{
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PyObject *m;
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m = Py_InitModule3("cmath", cmath_methods, module_doc);
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if (m == NULL)
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return;
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PyModule_AddObject(m, "pi",
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PyFloat_FromDouble(atan(1.0) * 4.0));
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PyModule_AddObject(m, "e", PyFloat_FromDouble(exp(1.0)));
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}
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