summaryrefslogtreecommitdiffstats
path: root/Objects/complexobject.c
blob: 05649428451eed0f0316c13e8f9c22aad508d593 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
/***********************************************************
Copyright 1991-1995 by Stichting Mathematisch Centrum, Amsterdam,
The Netherlands.

                        All Rights Reserved

Permission to use, copy, modify, and distribute this software and its
documentation for any purpose and without fee is hereby granted,
provided that the above copyright notice appear in all copies and that
both that copyright notice and this permission notice appear in
supporting documentation, and that the names of Stichting Mathematisch
Centrum or CWI or Corporation for National Research Initiatives or
CNRI not be used in advertising or publicity pertaining to
distribution of the software without specific, written prior
permission.

While CWI is the initial source for this software, a modified version
is made available by the Corporation for National Research Initiatives
(CNRI) at the Internet address ftp://ftp.python.org.

STICHTING MATHEMATISCH CENTRUM AND CNRI DISCLAIM ALL WARRANTIES WITH
REGARD TO THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS, IN NO EVENT SHALL STICHTING MATHEMATISCH
CENTRUM OR CNRI BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL
DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR
PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER
TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR
PERFORMANCE OF THIS SOFTWARE.

******************************************************************/

/* Complex object implementation */

/* Borrows heavily from floatobject.c */

/* Submitted by Jim Hugunin */

#ifndef WITHOUT_COMPLEX

#include "Python.h"
#include "mymath.h"

#ifdef HAVE_LIMITS_H
#include <limits.h>
#endif


/* elementary operations on complex numbers */

static Py_complex c_1 = {1., 0.};

Py_complex c_sum(a,b)
	Py_complex a,b;
{
	Py_complex r;
	r.real = a.real + b.real;
	r.imag = a.imag + b.imag;
	return r;
}

Py_complex c_diff(a,b)
	Py_complex a,b;
{
	Py_complex r;
	r.real = a.real - b.real;
	r.imag = a.imag - b.imag;
	return r;
}

Py_complex c_neg(a)
	Py_complex a;
{
	Py_complex r;
	r.real = -a.real;
	r.imag = -a.imag;
	return r;
}

Py_complex c_prod(a,b)
	Py_complex a,b;
{
	Py_complex r;
	r.real = a.real*b.real - a.imag*b.imag;
	r.imag = a.real*b.imag + a.imag*b.real;
	return r;
}

Py_complex c_quot(a,b)
	Py_complex a,b;
{
	Py_complex r;
	double d = b.real*b.real + b.imag*b.imag;
	if (d == 0.)
		errno = EDOM;
	r.real = (a.real*b.real + a.imag*b.imag)/d;
	r.imag = (a.imag*b.real - a.real*b.imag)/d;
	return r;
}

Py_complex c_pow(a,b)
	Py_complex a,b;
{
	Py_complex r;
	double vabs,len,at,phase;
	if (b.real == 0. && b.imag == 0.) {
		r.real = 1.;
		r.imag = 0.;
	}
	else if (a.real == 0. && a.imag == 0.) {
		if (b.imag != 0. || b.real < 0.)
			errno = ERANGE;
		r.real = 0.;
		r.imag = 0.;
	}
	else {
		vabs = hypot(a.real,a.imag);
		len = pow(vabs,b.real);
		at = atan2(a.imag, a.real);
		phase = at*b.real;
		if (b.imag != 0.0) {
			len /= exp(at*b.imag);
			phase += b.imag*log(vabs);
		}
		r.real = len*cos(phase);
		r.imag = len*sin(phase);
	}
	return r;
}

static Py_complex c_powu(x, n)
	Py_complex x;
	long n;
{
	Py_complex r, p;
	long mask = 1;
	r = c_1;
	p = x;
	while (mask > 0 && n >= mask) {
		if (n & mask)
			r = c_prod(r,p);
		mask <<= 1;
		p = c_prod(p,p);
	}
	return r;
}

static Py_complex c_powi(x, n)
	Py_complex x;
	long n;
{
	Py_complex cn;

	if (n > 100 || n < -100) {
		cn.real = (double) n;
		cn.imag = 0.;
		return c_pow(x,cn);
	}
	else if (n > 0)
		return c_powu(x,n);
	else
		return c_quot(c_1,c_powu(x,-n));

}

PyObject *
PyComplex_FromCComplex(cval)
	Py_complex cval;
{
	register PyComplexObject *op =
		(PyComplexObject *) malloc(sizeof(PyComplexObject));
	if (op == NULL)
		return PyErr_NoMemory();
	op->ob_type = &PyComplex_Type;
	op->cval = cval;
	_Py_NewReference((PyObject *)op);
	return (PyObject *) op;
}

PyObject *
PyComplex_FromDoubles(real, imag)
	double real, imag;
{
	Py_complex c;
	c.real = real;
	c.imag = imag;
	return PyComplex_FromCComplex(c);
}

double
PyComplex_RealAsDouble(op)
	PyObject *op;
{
	if (PyComplex_Check(op)) {
		return ((PyComplexObject *)op)->cval.real;
	} else {
		return PyFloat_AsDouble(op);
	}
}

double
PyComplex_ImagAsDouble(op)
	PyObject *op;
{
	if (PyComplex_Check(op)) {
		return ((PyComplexObject *)op)->cval.imag;
	} else {
		return 0.0;
	}
}

Py_complex
PyComplex_AsCComplex(op)
	PyObject *op;
{
	Py_complex cv;
	if (PyComplex_Check(op)) {
		return ((PyComplexObject *)op)->cval;
	} else {
		cv.real = PyFloat_AsDouble(op);
		cv.imag = 0.;
		return cv;
	}   
}

static void
complex_dealloc(op)
	PyObject *op;
{
	PyMem_DEL(op);
}


static void
complex_buf_repr(buf, v)
	char *buf;
	PyComplexObject *v;
{
	if (v->cval.real == 0.)
		sprintf(buf, "%.12gj", v->cval.imag);
	else
		sprintf(buf, "(%.12g%+.12gj)", v->cval.real, v->cval.imag);
}

static int
complex_print(v, fp, flags)
	PyComplexObject *v;
	FILE *fp;
	int flags; /* Not used but required by interface */
{
	char buf[100];
	complex_buf_repr(buf, v);
	fputs(buf, fp);
	return 0;
}

static PyObject *
complex_repr(v)
	PyComplexObject *v;
{
	char buf[100];
	complex_buf_repr(buf, v);
	return PyString_FromString(buf);
}

static int
complex_compare(v, w)
	PyComplexObject *v, *w;
{
/* Note: "greater" and "smaller" have no meaning for complex numbers,
   but Python requires that they be defined nevertheless. */
	Py_complex i, j;
	i = v->cval;
	j = w->cval;
	if (i.real == j.real && i.imag == j.imag)
	   return 0;
	else if (i.real != j.real)
	   return (i.real < j.real) ? -1 : 1;
	else
	   return (i.imag < j.imag) ? -1 : 1;
}

static long
complex_hash(v)
	PyComplexObject *v;
{
	double intpart, fractpart;
	int expo;
	long hipart, x;
	/* This is designed so that Python numbers with the same
	   value hash to the same value, otherwise comparisons
	   of mapping keys will turn out weird */

#ifdef MPW /* MPW C modf expects pointer to extended as second argument */
{
	extended e;
	fractpart = modf(v->cval.real, &e);
	intpart = e;
}
#else
	fractpart = modf(v->cval.real, &intpart);
#endif

	if (fractpart == 0.0 && v->cval.imag == 0.0) {
		if (intpart > 0x7fffffffL || -intpart > 0x7fffffffL) {
			/* Convert to long int and use its hash... */
			PyObject *w = PyLong_FromDouble(v->cval.real);
			if (w == NULL)
				return -1;
			x = PyObject_Hash(w);
			Py_DECREF(w);
			return x;
		}
		x = (long)intpart;
	}
	else {
		fractpart = frexp(fractpart, &expo);
		fractpart = fractpart * 2147483648.0; /* 2**31 */
		hipart = (long)fractpart; /* Take the top 32 bits */
		fractpart = (fractpart - (double)hipart) * 2147483648.0;
						/* Get the next 32 bits */
		x = hipart + (long)fractpart + (long)intpart + (expo << 15);
						/* Combine everything */

		if (v->cval.imag != 0.0) { /* Hash the imaginary part */
			/* XXX Note that this hashes complex(x, y)
			   to the same value as complex(y, x).
			   Still better than it used to be :-) */
#ifdef MPW
			{
				extended e;
				fractpart = modf(v->cval.imag, &e);
				intpart = e;
			}
#else
			fractpart = modf(v->cval.imag, &intpart);
#endif
			fractpart = frexp(fractpart, &expo);
			fractpart = fractpart * 2147483648.0; /* 2**31 */
			hipart = (long)fractpart; /* Take the top 32 bits */
			fractpart =
				(fractpart - (double)hipart) * 2147483648.0;
						/* Get the next 32 bits */
			x ^= hipart + (long)fractpart +
				(long)intpart + (expo << 15);
						/* Combine everything */
		}
	}
	if (x == -1)
		x = -2;
	return x;
}

static PyObject *
complex_add(v, w)
	PyComplexObject *v;
	PyComplexObject *w;
{
	Py_complex result;
	PyFPE_START_PROTECT("complex_add", return 0)
	result = c_sum(v->cval,w->cval);
	PyFPE_END_PROTECT(result)
	return PyComplex_FromCComplex(result);
}

static PyObject *
complex_sub(v, w)
	PyComplexObject *v;
	PyComplexObject *w;
{
	Py_complex result;
	PyFPE_START_PROTECT("complex_sub", return 0)
	result = c_diff(v->cval,w->cval);
	PyFPE_END_PROTECT(result)
	return PyComplex_FromCComplex(result);
}

static PyObject *
complex_mul(v, w)
	PyComplexObject *v;
	PyComplexObject *w;
{
	Py_complex result;
	PyFPE_START_PROTECT("complex_mul", return 0)
	result = c_prod(v->cval,w->cval);
	PyFPE_END_PROTECT(result)
	return PyComplex_FromCComplex(result);
}

static PyObject *
complex_div(v, w)
	PyComplexObject *v;
	PyComplexObject *w;
{
	Py_complex quot;
	PyFPE_START_PROTECT("complex_div", return 0)
	errno = 0;
	quot = c_quot(v->cval,w->cval);
	PyFPE_END_PROTECT(quot)
	if (errno == EDOM) {
		PyErr_SetString(PyExc_ZeroDivisionError, "complex division");
		return NULL;
	}
	return PyComplex_FromCComplex(quot);
}

static PyObject *
complex_remainder(v, w)
	PyComplexObject *v;
	PyComplexObject *w;
{
        Py_complex div, mod;
	errno = 0;
	div = c_quot(v->cval,w->cval); /* The raw divisor value. */
	if (errno == EDOM) {
		PyErr_SetString(PyExc_ZeroDivisionError, "complex remainder");
		return NULL;
	}
	div.real = floor(div.real); /* Use the floor of the real part. */
	div.imag = 0.0;
	mod = c_diff(v->cval, c_prod(w->cval, div));

	return PyComplex_FromCComplex(mod);
}


static PyObject *
complex_divmod(v, w)
	PyComplexObject *v;
	PyComplexObject *w;
{
        Py_complex div, mod;
	PyObject *d, *m, *z;
	errno = 0;
	div = c_quot(v->cval,w->cval); /* The raw divisor value. */
	if (errno == EDOM) {
		PyErr_SetString(PyExc_ZeroDivisionError, "complex divmod()");
		return NULL;
	}
	div.real = floor(div.real); /* Use the floor of the real part. */
	div.imag = 0.0;
	mod = c_diff(v->cval, c_prod(w->cval, div));
	d = PyComplex_FromCComplex(div);
	m = PyComplex_FromCComplex(mod);
	z = Py_BuildValue("(OO)", d, m);
	Py_XDECREF(d);
	Py_XDECREF(m);
	return z;
}

static PyObject *
complex_pow(v, w, z)
	PyComplexObject *v;
	PyObject *w;
	PyComplexObject *z;
{
	Py_complex p;
	Py_complex exponent;
	long int_exponent;

 	if ((PyObject *)z!=Py_None) {
		PyErr_SetString(PyExc_ValueError, "complex modulo");
		return NULL;
	}

	PyFPE_START_PROTECT("complex_pow", return 0)
	errno = 0;
	exponent = ((PyComplexObject*)w)->cval;
	int_exponent = (long)exponent.real;
	if (exponent.imag == 0. && exponent.real == int_exponent)
		p = c_powi(v->cval,int_exponent);
	else
		p = c_pow(v->cval,exponent);

	PyFPE_END_PROTECT(p)
	if (errno == ERANGE) {
		PyErr_SetString(PyExc_ValueError,
				"0.0 to a negative or complex power");
		return NULL;
	}

	return PyComplex_FromCComplex(p);
}

static PyObject *
complex_neg(v)
	PyComplexObject *v;
{
	Py_complex neg;
	neg.real = -v->cval.real;
	neg.imag = -v->cval.imag;
	return PyComplex_FromCComplex(neg);
}

static PyObject *
complex_pos(v)
	PyComplexObject *v;
{
	Py_INCREF(v);
	return (PyObject *)v;
}

static PyObject *
complex_abs(v)
	PyComplexObject *v;
{
	double result;
	PyFPE_START_PROTECT("complex_abs", return 0)
	result = hypot(v->cval.real,v->cval.imag);
	PyFPE_END_PROTECT(result)
	return PyFloat_FromDouble(result);
}

static int
complex_nonzero(v)
	PyComplexObject *v;
{
	return v->cval.real != 0.0 || v->cval.imag != 0.0;
}

static int
complex_coerce(pv, pw)
	PyObject **pv;
	PyObject **pw;
{
	Py_complex cval;
	cval.imag = 0.;
	if (PyInt_Check(*pw)) {
		cval.real = (double)PyInt_AsLong(*pw);
		*pw = PyComplex_FromCComplex(cval);
		Py_INCREF(*pv);
		return 0;
	}
	else if (PyLong_Check(*pw)) {
		cval.real = PyLong_AsDouble(*pw);
		*pw = PyComplex_FromCComplex(cval);
		Py_INCREF(*pv);
		return 0;
	}
	else if (PyFloat_Check(*pw)) {
		cval.real = PyFloat_AsDouble(*pw);
		*pw = PyComplex_FromCComplex(cval);
		Py_INCREF(*pv);
		return 0;
	}
	return 1; /* Can't do it */
}

static PyObject *
complex_int(v)
	PyObject *v;
{
	PyErr_SetString(PyExc_TypeError,
		   "can't convert complex to int; use e.g. int(abs(z))");
	return NULL;
}

static PyObject *
complex_long(v)
	PyObject *v;
{
	PyErr_SetString(PyExc_TypeError,
		   "can't convert complex to long; use e.g. long(abs(z))");
	return NULL;
}

static PyObject *
complex_float(v)
	PyObject *v;
{
	PyErr_SetString(PyExc_TypeError,
		   "can't convert complex to float; use e.g. abs(z)");
	return NULL;
}

static PyObject *
complex_conjugate(self, args)
	PyObject *self;
	PyObject *args;
{
	Py_complex c;
	if (!PyArg_ParseTuple(args, ":conjugate"))
		return NULL;
	c = ((PyComplexObject *)self)->cval;
	c.imag = -c.imag;
	return PyComplex_FromCComplex(c);
}

static PyMethodDef complex_methods[] = {
	{"conjugate",	complex_conjugate,	1},
	{NULL,		NULL}		/* sentinel */
};


static PyObject *
complex_getattr(self, name)
	PyComplexObject *self;
	char *name;
{
	if (strcmp(name, "real") == 0)
		return (PyObject *)PyFloat_FromDouble(self->cval.real);
	else if (strcmp(name, "imag") == 0)
		return (PyObject *)PyFloat_FromDouble(self->cval.imag);
	else if (strcmp(name, "__members__") == 0)
		return Py_BuildValue("[ss]", "imag", "real");
	return Py_FindMethod(complex_methods, (PyObject *)self, name);
}

static PyNumberMethods complex_as_number = {
	(binaryfunc)complex_add, /*nb_add*/
	(binaryfunc)complex_sub, /*nb_subtract*/
	(binaryfunc)complex_mul, /*nb_multiply*/
	(binaryfunc)complex_div, /*nb_divide*/
	(binaryfunc)complex_remainder,	/*nb_remainder*/
	(binaryfunc)complex_divmod,	/*nb_divmod*/
	(ternaryfunc)complex_pow, /*nb_power*/
	(unaryfunc)complex_neg, /*nb_negative*/
	(unaryfunc)complex_pos, /*nb_positive*/
	(unaryfunc)complex_abs, /*nb_absolute*/
	(inquiry)complex_nonzero, /*nb_nonzero*/
	0,		/*nb_invert*/
	0,		/*nb_lshift*/
	0,		/*nb_rshift*/
	0,		/*nb_and*/
	0,		/*nb_xor*/
	0,		/*nb_or*/
	(coercion)complex_coerce, /*nb_coerce*/
	(unaryfunc)complex_int, /*nb_int*/
	(unaryfunc)complex_long, /*nb_long*/
	(unaryfunc)complex_float, /*nb_float*/
	0,		/*nb_oct*/
	0,		/*nb_hex*/
};

PyTypeObject PyComplex_Type = {
	PyObject_HEAD_INIT(&PyType_Type)
	0,
	"complex",
	sizeof(PyComplexObject),
	0,
	(destructor)complex_dealloc,	/*tp_dealloc*/
	(printfunc)complex_print,	/*tp_print*/
	(getattrfunc)complex_getattr,	/*tp_getattr*/
	0,				/*tp_setattr*/
	(cmpfunc)complex_compare,	/*tp_compare*/
	(reprfunc)complex_repr,		/*tp_repr*/
	&complex_as_number,    		/*tp_as_number*/
	0,				/*tp_as_sequence*/
	0,				/*tp_as_mapping*/
	(hashfunc)complex_hash, 	/*tp_hash*/
};

#endif