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
|
/*
* Copyright (c) 1999
* Silicon Graphics Computer Systems, Inc.
*
* Copyright (c) 1999
* Boris Fomitchev
*
* This material is provided "as is", with absolutely no warranty expressed
* or implied. Any use is at your own risk.
*
* Permission to use or copy this software for any purpose is hereby granted
* without fee, provided the above notices are retained on all copies.
* Permission to modify the code and to distribute modified code is granted,
* provided the above notices are retained, and a notice that the code was
* modified is included with the above copyright notice.
*
*/
#include "stlport_prefix.h"
#include <numeric>
#include <cmath>
#include <complex>
#if defined (_STLP_MSVC_LIB) && (_STLP_MSVC_LIB >= 1400)
// hypot is deprecated.
# if defined (_STLP_MSVC)
# pragma warning (disable : 4996)
# elif defined (__ICL)
# pragma warning (disable : 1478)
# endif
#endif
_STLP_BEGIN_NAMESPACE
// Complex division and square roots.
// Absolute value
_STLP_TEMPLATE_NULL
_STLP_DECLSPEC float _STLP_CALL abs(const complex<float>& __z)
{ return ::hypot(__z._M_re, __z._M_im); }
_STLP_TEMPLATE_NULL
_STLP_DECLSPEC double _STLP_CALL abs(const complex<double>& __z)
{ return ::hypot(__z._M_re, __z._M_im); }
#if !defined (_STLP_NO_LONG_DOUBLE)
_STLP_TEMPLATE_NULL
_STLP_DECLSPEC long double _STLP_CALL abs(const complex<long double>& __z)
{ return ::hypot(__z._M_re, __z._M_im); }
#endif
// Phase
_STLP_TEMPLATE_NULL
_STLP_DECLSPEC float _STLP_CALL arg(const complex<float>& __z)
{ return ::atan2(__z._M_im, __z._M_re); }
_STLP_TEMPLATE_NULL
_STLP_DECLSPEC double _STLP_CALL arg(const complex<double>& __z)
{ return ::atan2(__z._M_im, __z._M_re); }
#if !defined (_STLP_NO_LONG_DOUBLE)
_STLP_TEMPLATE_NULL
_STLP_DECLSPEC long double _STLP_CALL arg(const complex<long double>& __z)
{ return ::atan2(__z._M_im, __z._M_re); }
#endif
// Construct a complex number from polar representation
_STLP_TEMPLATE_NULL
_STLP_DECLSPEC complex<float> _STLP_CALL polar(const float& __rho, const float& __phi)
{ return complex<float>(__rho * ::cos(__phi), __rho * ::sin(__phi)); }
_STLP_TEMPLATE_NULL
_STLP_DECLSPEC complex<double> _STLP_CALL polar(const double& __rho, const double& __phi)
{ return complex<double>(__rho * ::cos(__phi), __rho * ::sin(__phi)); }
#if !defined (_STLP_NO_LONG_DOUBLE)
_STLP_TEMPLATE_NULL
_STLP_DECLSPEC complex<long double> _STLP_CALL polar(const long double& __rho, const long double& __phi)
{ return complex<long double>(__rho * ::cos(__phi), __rho * ::sin(__phi)); }
#endif
// Division
template <class _Tp>
static void _divT(const _Tp& __z1_r, const _Tp& __z1_i,
const _Tp& __z2_r, const _Tp& __z2_i,
_Tp& __res_r, _Tp& __res_i) {
_Tp __ar = __z2_r >= 0 ? __z2_r : -__z2_r;
_Tp __ai = __z2_i >= 0 ? __z2_i : -__z2_i;
if (__ar <= __ai) {
_Tp __ratio = __z2_r / __z2_i;
_Tp __denom = __z2_i * (1 + __ratio * __ratio);
__res_r = (__z1_r * __ratio + __z1_i) / __denom;
__res_i = (__z1_i * __ratio - __z1_r) / __denom;
}
else {
_Tp __ratio = __z2_i / __z2_r;
_Tp __denom = __z2_r * (1 + __ratio * __ratio);
__res_r = (__z1_r + __z1_i * __ratio) / __denom;
__res_i = (__z1_i - __z1_r * __ratio) / __denom;
}
}
template <class _Tp>
static void _divT(const _Tp& __z1_r,
const _Tp& __z2_r, const _Tp& __z2_i,
_Tp& __res_r, _Tp& __res_i) {
_Tp __ar = __z2_r >= 0 ? __z2_r : -__z2_r;
_Tp __ai = __z2_i >= 0 ? __z2_i : -__z2_i;
if (__ar <= __ai) {
_Tp __ratio = __z2_r / __z2_i;
_Tp __denom = __z2_i * (1 + __ratio * __ratio);
__res_r = (__z1_r * __ratio) / __denom;
__res_i = - __z1_r / __denom;
}
else {
_Tp __ratio = __z2_i / __z2_r;
_Tp __denom = __z2_r * (1 + __ratio * __ratio);
__res_r = __z1_r / __denom;
__res_i = - (__z1_r * __ratio) / __denom;
}
}
void _STLP_CALL
complex<float>::_div(const float& __z1_r, const float& __z1_i,
const float& __z2_r, const float& __z2_i,
float& __res_r, float& __res_i)
{ _divT(__z1_r, __z1_i, __z2_r, __z2_i, __res_r, __res_i); }
void _STLP_CALL
complex<float>::_div(const float& __z1_r,
const float& __z2_r, const float& __z2_i,
float& __res_r, float& __res_i)
{ _divT(__z1_r, __z2_r, __z2_i, __res_r, __res_i); }
void _STLP_CALL
complex<double>::_div(const double& __z1_r, const double& __z1_i,
const double& __z2_r, const double& __z2_i,
double& __res_r, double& __res_i)
{ _divT(__z1_r, __z1_i, __z2_r, __z2_i, __res_r, __res_i); }
void _STLP_CALL
complex<double>::_div(const double& __z1_r,
const double& __z2_r, const double& __z2_i,
double& __res_r, double& __res_i)
{ _divT(__z1_r, __z2_r, __z2_i, __res_r, __res_i); }
#if !defined (_STLP_NO_LONG_DOUBLE)
void _STLP_CALL
complex<long double>::_div(const long double& __z1_r, const long double& __z1_i,
const long double& __z2_r, const long double& __z2_i,
long double& __res_r, long double& __res_i)
{ _divT(__z1_r, __z1_i, __z2_r, __z2_i, __res_r, __res_i); }
void _STLP_CALL
complex<long double>::_div(const long double& __z1_r,
const long double& __z2_r, const long double& __z2_i,
long double& __res_r, long double& __res_i)
{ _divT(__z1_r, __z2_r, __z2_i, __res_r, __res_i); }
#endif
//----------------------------------------------------------------------
// Square root
template <class _Tp>
static complex<_Tp> sqrtT(const complex<_Tp>& z) {
_Tp re = z._M_re;
_Tp im = z._M_im;
_Tp mag = ::hypot(re, im);
complex<_Tp> result;
if (mag == 0.f) {
result._M_re = result._M_im = 0.f;
} else if (re > 0.f) {
result._M_re = ::sqrt(0.5f * (mag + re));
result._M_im = im/result._M_re/2.f;
} else {
result._M_im = ::sqrt(0.5f * (mag - re));
if (im < 0.f)
result._M_im = - result._M_im;
result._M_re = im/result._M_im/2.f;
}
return result;
}
complex<float> _STLP_CALL
sqrt(const complex<float>& z) { return sqrtT(z); }
complex<double> _STLP_CALL
sqrt(const complex<double>& z) { return sqrtT(z); }
#if !defined (_STLP_NO_LONG_DOUBLE)
complex<long double> _STLP_CALL
sqrt(const complex<long double>& z) { return sqrtT(z); }
#endif
// exp, log, pow for complex<float>, complex<double>, and complex<long double>
//----------------------------------------------------------------------
// exp
template <class _Tp>
static complex<_Tp> expT(const complex<_Tp>& z) {
_Tp expx = ::exp(z._M_re);
return complex<_Tp>(expx * ::cos(z._M_im),
expx * ::sin(z._M_im));
}
_STLP_DECLSPEC complex<float> _STLP_CALL exp(const complex<float>& z)
{ return expT(z); }
_STLP_DECLSPEC complex<double> _STLP_CALL exp(const complex<double>& z)
{ return expT(z); }
#if !defined (_STLP_NO_LONG_DOUBLE)
_STLP_DECLSPEC complex<long double> _STLP_CALL exp(const complex<long double>& z)
{ return expT(z); }
#endif
//----------------------------------------------------------------------
// log10
template <class _Tp>
static complex<_Tp> log10T(const complex<_Tp>& z, const _Tp& ln10_inv) {
complex<_Tp> r;
r._M_im = ::atan2(z._M_im, z._M_re) * ln10_inv;
r._M_re = ::log10(::hypot(z._M_re, z._M_im));
return r;
}
_STLP_DECLSPEC complex<float> _STLP_CALL log10(const complex<float>& z)
{
const float LN10_INVF = 1.f / ::log(10.f);
return log10T(z, LN10_INVF);
}
_STLP_DECLSPEC complex<double> _STLP_CALL log10(const complex<double>& z)
{
const double LN10_INV = 1. / ::log10(10.);
return log10T(z, LN10_INV);
}
#if !defined (_STLP_NO_LONG_DOUBLE)
_STLP_DECLSPEC complex<long double> _STLP_CALL log10(const complex<long double>& z)
{
const long double LN10_INVL = 1.l / ::log(10.l);
return log10T(z, LN10_INVL);
}
#endif
//----------------------------------------------------------------------
// log
template <class _Tp>
static complex<_Tp> logT(const complex<_Tp>& z) {
complex<_Tp> r;
r._M_im = ::atan2(z._M_im, z._M_re);
r._M_re = ::log(::hypot(z._M_re, z._M_im));
return r;
}
_STLP_DECLSPEC complex<float> _STLP_CALL log(const complex<float>& z)
{ return logT(z); }
_STLP_DECLSPEC complex<double> _STLP_CALL log(const complex<double>& z)
{ return logT(z); }
#ifndef _STLP_NO_LONG_DOUBLE
_STLP_DECLSPEC complex<long double> _STLP_CALL log(const complex<long double>& z)
{ return logT(z); }
# endif
//----------------------------------------------------------------------
// pow
template <class _Tp>
static complex<_Tp> powT(const _Tp& a, const complex<_Tp>& b) {
_Tp logr = ::log(a);
_Tp x = ::exp(logr * b._M_re);
_Tp y = logr * b._M_im;
return complex<_Tp>(x * ::cos(y), x * ::sin(y));
}
template <class _Tp>
static complex<_Tp> powT(const complex<_Tp>& z_in, int n) {
complex<_Tp> z = z_in;
z = _STLP_PRIV __power(z, (n < 0 ? -n : n), multiplies< complex<_Tp> >());
if (n < 0)
return _Tp(1.0) / z;
else
return z;
}
template <class _Tp>
static complex<_Tp> powT(const complex<_Tp>& a, const _Tp& b) {
_Tp logr = ::log(::hypot(a._M_re,a._M_im));
_Tp logi = ::atan2(a._M_im, a._M_re);
_Tp x = ::exp(logr * b);
_Tp y = logi * b;
return complex<_Tp>(x * ::cos(y), x * ::sin(y));
}
template <class _Tp>
static complex<_Tp> powT(const complex<_Tp>& a, const complex<_Tp>& b) {
_Tp logr = ::log(::hypot(a._M_re,a._M_im));
_Tp logi = ::atan2(a._M_im, a._M_re);
_Tp x = ::exp(logr * b._M_re - logi * b._M_im);
_Tp y = logr * b._M_im + logi * b._M_re;
return complex<_Tp>(x * ::cos(y), x * ::sin(y));
}
_STLP_DECLSPEC complex<float> _STLP_CALL pow(const float& a, const complex<float>& b)
{ return powT(a, b); }
_STLP_DECLSPEC complex<float> _STLP_CALL pow(const complex<float>& z_in, int n)
{ return powT(z_in, n); }
_STLP_DECLSPEC complex<float> _STLP_CALL pow(const complex<float>& a, const float& b)
{ return powT(a, b); }
_STLP_DECLSPEC complex<float> _STLP_CALL pow(const complex<float>& a, const complex<float>& b)
{ return powT(a, b); }
_STLP_DECLSPEC complex<double> _STLP_CALL pow(const double& a, const complex<double>& b)
{ return powT(a, b); }
_STLP_DECLSPEC complex<double> _STLP_CALL pow(const complex<double>& z_in, int n)
{ return powT(z_in, n); }
_STLP_DECLSPEC complex<double> _STLP_CALL pow(const complex<double>& a, const double& b)
{ return powT(a, b); }
_STLP_DECLSPEC complex<double> _STLP_CALL pow(const complex<double>& a, const complex<double>& b)
{ return powT(a, b); }
#if !defined (_STLP_NO_LONG_DOUBLE)
_STLP_DECLSPEC complex<long double> _STLP_CALL pow(const long double& a,
const complex<long double>& b)
{ return powT(a, b); }
_STLP_DECLSPEC complex<long double> _STLP_CALL pow(const complex<long double>& z_in, int n)
{ return powT(z_in, n); }
_STLP_DECLSPEC complex<long double> _STLP_CALL pow(const complex<long double>& a,
const long double& b)
{ return powT(a, b); }
_STLP_DECLSPEC complex<long double> _STLP_CALL pow(const complex<long double>& a,
const complex<long double>& b)
{ return powT(a, b); }
#endif
_STLP_END_NAMESPACE
|
