source: trunk/essentials/dev-lang/python/Modules/cmathmodule.c@ 3403

Last change on this file since 3403 was 3225, checked in by bird, 19 years ago

Python 2.5
File size: 8.0 KB
Line 
1/* Complex math module */
2
3/* much code borrowed from mathmodule.c */
4
5#include "Python.h"
6
7#ifndef M_PI
8#define M_PI (3.141592653589793239)
9#endif
10
11/* First, the C functions that do the real work */
12
13/* constants */
14static Py_complex c_one = {1., 0.};
15static Py_complex c_half = {0.5, 0.};
16static Py_complex c_i = {0., 1.};
17static Py_complex c_halfi = {0., 0.5};
18
19/* forward declarations */
20static Py_complex c_log(Py_complex);
21static Py_complex c_prodi(Py_complex);
22static Py_complex c_sqrt(Py_complex);
23static PyObject * math_error(void);
24
25
26static Py_complex
27c_acos(Py_complex x)
28{
29 return c_neg(c_prodi(c_log(c_sum(x,c_prod(c_i,
30 c_sqrt(c_diff(c_one,c_prod(x,x))))))));
31}
32
33PyDoc_STRVAR(c_acos_doc,
34"acos(x)\n"
35"\n"
36"Return the arc cosine of x.");
37
38
39static Py_complex
40c_acosh(Py_complex x)
41{
42 Py_complex z;
43 z = c_sqrt(c_half);
44 z = c_log(c_prod(z, c_sum(c_sqrt(c_sum(x,c_one)),
45 c_sqrt(c_diff(x,c_one)))));
46 return c_sum(z, z);
47}
48
49PyDoc_STRVAR(c_acosh_doc,
50"acosh(x)\n"
51"\n"
52"Return the hyperbolic arccosine of x.");
53
54
55static Py_complex
56c_asin(Py_complex x)
57{
58 /* -i * log[(sqrt(1-x**2) + i*x] */
59 const Py_complex squared = c_prod(x, x);
60 const Py_complex sqrt_1_minus_x_sq = c_sqrt(c_diff(c_one, squared));
61 return c_neg(c_prodi(c_log(
62 c_sum(sqrt_1_minus_x_sq, c_prodi(x))
63 ) ) );
64}
65
66PyDoc_STRVAR(c_asin_doc,
67"asin(x)\n"
68"\n"
69"Return the arc sine of x.");
70
71
72static Py_complex
73c_asinh(Py_complex x)
74{
75 Py_complex z;
76 z = c_sqrt(c_half);
77 z = c_log(c_prod(z, c_sum(c_sqrt(c_sum(x, c_i)),
78 c_sqrt(c_diff(x, c_i)))));
79 return c_sum(z, z);
80}
81
82PyDoc_STRVAR(c_asinh_doc,
83"asinh(x)\n"
84"\n"
85"Return the hyperbolic arc sine of x.");
86
87
88static Py_complex
89c_atan(Py_complex x)
90{
91 return c_prod(c_halfi,c_log(c_quot(c_sum(c_i,x),c_diff(c_i,x))));
92}
93
94PyDoc_STRVAR(c_atan_doc,
95"atan(x)\n"
96"\n"
97"Return the arc tangent of x.");
98
99
100static Py_complex
101c_atanh(Py_complex x)
102{
103 return c_prod(c_half,c_log(c_quot(c_sum(c_one,x),c_diff(c_one,x))));
104}
105
106PyDoc_STRVAR(c_atanh_doc,
107"atanh(x)\n"
108"\n"
109"Return the hyperbolic arc tangent of x.");
110
111
112static Py_complex
113c_cos(Py_complex x)
114{
115 Py_complex r;
116 r.real = cos(x.real)*cosh(x.imag);
117 r.imag = -sin(x.real)*sinh(x.imag);
118 return r;
119}
120
121PyDoc_STRVAR(c_cos_doc,
122"cos(x)\n"
123"n"
124"Return the cosine of x.");
125
126
127static Py_complex
128c_cosh(Py_complex x)
129{
130 Py_complex r;
131 r.real = cos(x.imag)*cosh(x.real);
132 r.imag = sin(x.imag)*sinh(x.real);
133 return r;
134}
135
136PyDoc_STRVAR(c_cosh_doc,
137"cosh(x)\n"
138"n"
139"Return the hyperbolic cosine of x.");
140
141
142static Py_complex
143c_exp(Py_complex x)
144{
145 Py_complex r;
146 double l = exp(x.real);
147 r.real = l*cos(x.imag);
148 r.imag = l*sin(x.imag);
149 return r;
150}
151
152PyDoc_STRVAR(c_exp_doc,
153"exp(x)\n"
154"\n"
155"Return the exponential value e**x.");
156
157
158static Py_complex
159c_log(Py_complex x)
160{
161 Py_complex r;
162 double l = hypot(x.real,x.imag);
163 r.imag = atan2(x.imag, x.real);
164 r.real = log(l);
165 return r;
166}
167
168
169static Py_complex
170c_log10(Py_complex x)
171{
172 Py_complex r;
173 double l = hypot(x.real,x.imag);
174 r.imag = atan2(x.imag, x.real)/log(10.);
175 r.real = log10(l);
176 return r;
177}
178
179PyDoc_STRVAR(c_log10_doc,
180"log10(x)\n"
181"\n"
182"Return the base-10 logarithm of x.");
183
184
185/* internal function not available from Python */
186static Py_complex
187c_prodi(Py_complex x)
188{
189 Py_complex r;
190 r.real = -x.imag;
191 r.imag = x.real;
192 return r;
193}
194
195
196static Py_complex
197c_sin(Py_complex x)
198{
199 Py_complex r;
200 r.real = sin(x.real) * cosh(x.imag);
201 r.imag = cos(x.real) * sinh(x.imag);
202 return r;
203}
204
205PyDoc_STRVAR(c_sin_doc,
206"sin(x)\n"
207"\n"
208"Return the sine of x.");
209
210
211static Py_complex
212c_sinh(Py_complex x)
213{
214 Py_complex r;
215 r.real = cos(x.imag) * sinh(x.real);
216 r.imag = sin(x.imag) * cosh(x.real);
217 return r;
218}
219
220PyDoc_STRVAR(c_sinh_doc,
221"sinh(x)\n"
222"\n"
223"Return the hyperbolic sine of x.");
224
225
226static Py_complex
227c_sqrt(Py_complex x)
228{
229 Py_complex r;
230 double s,d;
231 if (x.real == 0. && x.imag == 0.)
232 r = x;
233 else {
234 s = sqrt(0.5*(fabs(x.real) + hypot(x.real,x.imag)));
235 d = 0.5*x.imag/s;
236 if (x.real > 0.) {
237 r.real = s;
238 r.imag = d;
239 }
240 else if (x.imag >= 0.) {
241 r.real = d;
242 r.imag = s;
243 }
244 else {
245 r.real = -d;
246 r.imag = -s;
247 }
248 }
249 return r;
250}
251
252PyDoc_STRVAR(c_sqrt_doc,
253"sqrt(x)\n"
254"\n"
255"Return the square root of x.");
256
257
258static Py_complex
259c_tan(Py_complex x)
260{
261 Py_complex r;
262 double sr,cr,shi,chi;
263 double rs,is,rc,ic;
264 double d;
265 sr = sin(x.real);
266 cr = cos(x.real);
267 shi = sinh(x.imag);
268 chi = cosh(x.imag);
269 rs = sr * chi;
270 is = cr * shi;
271 rc = cr * chi;
272 ic = -sr * shi;
273 d = rc*rc + ic * ic;
274 r.real = (rs*rc + is*ic) / d;
275 r.imag = (is*rc - rs*ic) / d;
276 return r;
277}
278
279PyDoc_STRVAR(c_tan_doc,
280"tan(x)\n"
281"\n"
282"Return the tangent of x.");
283
284
285static Py_complex
286c_tanh(Py_complex x)
287{
288 Py_complex r;
289 double si,ci,shr,chr;
290 double rs,is,rc,ic;
291 double d;
292 si = sin(x.imag);
293 ci = cos(x.imag);
294 shr = sinh(x.real);
295 chr = cosh(x.real);
296 rs = ci * shr;
297 is = si * chr;
298 rc = ci * chr;
299 ic = si * shr;
300 d = rc*rc + ic*ic;
301 r.real = (rs*rc + is*ic) / d;
302 r.imag = (is*rc - rs*ic) / d;
303 return r;
304}
305
306PyDoc_STRVAR(c_tanh_doc,
307"tanh(x)\n"
308"\n"
309"Return the hyperbolic tangent of x.");
310
311static PyObject *
312cmath_log(PyObject *self, PyObject *args)
313{
314 Py_complex x;
315 Py_complex y;
316
317 if (!PyArg_ParseTuple(args, "D|D", &x, &y))
318 return NULL;
319
320 errno = 0;
321 PyFPE_START_PROTECT("complex function", return 0)
322 x = c_log(x);
323 if (PyTuple_GET_SIZE(args) == 2)
324 x = c_quot(x, c_log(y));
325 PyFPE_END_PROTECT(x)
326 if (errno != 0)
327 return math_error();
328 Py_ADJUST_ERANGE2(x.real, x.imag);
329 return PyComplex_FromCComplex(x);
330}
331
332PyDoc_STRVAR(cmath_log_doc,
333"log(x[, base]) -> the logarithm of x to the given base.\n\
334If the base not specified, returns the natural logarithm (base e) of x.");
335
336
337/* And now the glue to make them available from Python: */
338
339static PyObject *
340math_error(void)
341{
342 if (errno == EDOM)
343 PyErr_SetString(PyExc_ValueError, "math domain error");
344 else if (errno == ERANGE)
345 PyErr_SetString(PyExc_OverflowError, "math range error");
346 else /* Unexpected math error */
347 PyErr_SetFromErrno(PyExc_ValueError);
348 return NULL;
349}
350
351static PyObject *
352math_1(PyObject *args, Py_complex (*func)(Py_complex))
353{
354 Py_complex x;
355 if (!PyArg_ParseTuple(args, "D", &x))
356 return NULL;
357 errno = 0;
358 PyFPE_START_PROTECT("complex function", return 0)
359 x = (*func)(x);
360 PyFPE_END_PROTECT(x)
361 Py_ADJUST_ERANGE2(x.real, x.imag);
362 if (errno != 0)
363 return math_error();
364 else
365 return PyComplex_FromCComplex(x);
366}
367
368#define FUNC1(stubname, func) \
369 static PyObject * stubname(PyObject *self, PyObject *args) { \
370 return math_1(args, func); \
371 }
372
373FUNC1(cmath_acos, c_acos)
374FUNC1(cmath_acosh, c_acosh)
375FUNC1(cmath_asin, c_asin)
376FUNC1(cmath_asinh, c_asinh)
377FUNC1(cmath_atan, c_atan)
378FUNC1(cmath_atanh, c_atanh)
379FUNC1(cmath_cos, c_cos)
380FUNC1(cmath_cosh, c_cosh)
381FUNC1(cmath_exp, c_exp)
382FUNC1(cmath_log10, c_log10)
383FUNC1(cmath_sin, c_sin)
384FUNC1(cmath_sinh, c_sinh)
385FUNC1(cmath_sqrt, c_sqrt)
386FUNC1(cmath_tan, c_tan)
387FUNC1(cmath_tanh, c_tanh)
388
389
390PyDoc_STRVAR(module_doc,
391"This module is always available. It provides access to mathematical\n"
392"functions for complex numbers.");
393
394static PyMethodDef cmath_methods[] = {
395 {"acos", cmath_acos, METH_VARARGS, c_acos_doc},
396 {"acosh", cmath_acosh, METH_VARARGS, c_acosh_doc},
397 {"asin", cmath_asin, METH_VARARGS, c_asin_doc},
398 {"asinh", cmath_asinh, METH_VARARGS, c_asinh_doc},
399 {"atan", cmath_atan, METH_VARARGS, c_atan_doc},
400 {"atanh", cmath_atanh, METH_VARARGS, c_atanh_doc},
401 {"cos", cmath_cos, METH_VARARGS, c_cos_doc},
402 {"cosh", cmath_cosh, METH_VARARGS, c_cosh_doc},
403 {"exp", cmath_exp, METH_VARARGS, c_exp_doc},
404 {"log", cmath_log, METH_VARARGS, cmath_log_doc},
405 {"log10", cmath_log10, METH_VARARGS, c_log10_doc},
406 {"sin", cmath_sin, METH_VARARGS, c_sin_doc},
407 {"sinh", cmath_sinh, METH_VARARGS, c_sinh_doc},
408 {"sqrt", cmath_sqrt, METH_VARARGS, c_sqrt_doc},
409 {"tan", cmath_tan, METH_VARARGS, c_tan_doc},
410 {"tanh", cmath_tanh, METH_VARARGS, c_tanh_doc},
411 {NULL, NULL} /* sentinel */
412};
413
414PyMODINIT_FUNC
415initcmath(void)
416{
417 PyObject *m;
418
419 m = Py_InitModule3("cmath", cmath_methods, module_doc);
420 if (m == NULL)
421 return;
422
423 PyModule_AddObject(m, "pi",
424 PyFloat_FromDouble(atan(1.0) * 4.0));
425 PyModule_AddObject(m, "e", PyFloat_FromDouble(exp(1.0)));
426}
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