Repository navigation
Expand file tree
/
Copy pathcmath.cs
More file actions
435 lines (338 loc) · 14.1 KB
/
Copy pathcmath.cs
File metadata and controls
435 lines (338 loc) · 14.1 KB
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
// Licensed to the .NET Foundation under one or more agreements.
// The .NET Foundation licenses this file to you under the Apache 2.0 License.
// See the LICENSE file in the project root for more information.
using System;
using System.Numerics;
using IronPython.Runtime;
using IronPython.Runtime.Operations;
using Microsoft.Scripting.Utils;
[assembly: PythonModule("cmath", typeof(IronPython.Modules.ComplexMath))]
namespace IronPython.Modules {
public class ComplexMath {
public const double pi = Math.PI;
public const double e = Math.E;
public const string __doc__ = "Provides access to functions for operating on complex numbers";
//cos(a+ ib) = cosa*coshb - i*sina*sinhb
public static Complex cos(object x) {
Complex num = GetComplexNum(x);
// magnitude is always NaN
if (double.IsNaN(num.Imaginary())) {
return new Complex(double.NaN, double.NaN);
}
// can't take sin or cos of +/-Infinity
if (double.IsInfinity(num.Real)) {
throw PythonOps.ValueError("math domain error");
}
double real, imag;
real = Math.Cos(num.Real) * Math.Cosh(num.Imaginary());
imag = -(Math.Sin(num.Real) * Math.Sinh(num.Imaginary()));
return new Complex(real, imag);
}
//sin(a+ ib) = sina*coshb + i*cosa*sinhb
public static Complex sin(object x) {
Complex num = GetComplexNum(x);
// magnitude is always NaN
if (double.IsNaN(num.Imaginary())) {
return new Complex(double.NaN, double.NaN);
}
// can't take sin or cos of +/-Infinity
if (double.IsInfinity(num.Real)) {
throw PythonOps.ValueError("math domain error");
}
double real, imag;
real = Math.Sin(num.Real) * Math.Cosh(num.Imaginary());
imag = Math.Cos(num.Real) * Math.Sinh(num.Imaginary());
return new Complex(real, imag);
}
public static Complex tan(object x) {
Complex num = GetComplexNum(x);
// limit as num.Imaginary() -> Infinity
if (double.IsPositiveInfinity(num.Imaginary())) {
return Complex.ImaginaryOne;
}
// limit as num.Imaginary() -> -Infinity
if (double.IsNegativeInfinity(num.Imaginary())) {
return new Complex(0.0, -1.0);
}
return sin(num) / cos(num);
}
//cosh(a+ ib) = cosha*cosb + i*sinha*sinb
public static Complex cosh(object x) {
Complex num = GetComplexNum(x);
// magnitude is always NaN
if (double.IsNaN(num.Real)) {
return new Complex(double.NaN, double.NaN);
}
// can't take sin or cos of +/-Infinity
if (double.IsInfinity(num.Imaginary())) {
throw PythonOps.ValueError("math domain error");
}
double real, imag;
real = Math.Cosh(num.Real) * Math.Cos(num.Imaginary());
imag = Math.Sinh(num.Real) * Math.Sin(num.Imaginary());
return new Complex(real, imag);
}
//sin(a+ ib) = sinha*cosb + i*cosha*sinb
public static Complex sinh(object x) {
Complex num = GetComplexNum(x);
// magnitude is always NaN
if (double.IsNaN(num.Real)) {
return new Complex(double.NaN, double.NaN);
}
// can't take sin or cos of +/-Infinity
if (double.IsInfinity(num.Imaginary())) {
throw PythonOps.ValueError("math domain error");
}
double real, imag;
real = Math.Sinh(num.Real) * Math.Cos(num.Imaginary());
imag = Math.Cosh(num.Real) * Math.Sin(num.Imaginary());
return new Complex(real, imag);
}
public static Complex tanh(object x) {
Complex num = GetComplexNum(x);
// limit as num.Real -> Infinity
if (double.IsPositiveInfinity(num.Real)) {
return Complex.One;
}
// limit as num.Real -> -Infinity
if (double.IsNegativeInfinity(num.Real)) {
return new Complex(-1.0, 0.0);
}
return sinh(num) / cosh(num);
}
//acos(x) = -i*ln( x + i*(1-x*x)^1/2)
public static Complex acos(object x) {
Complex num = GetComplexNum(x);
double a = MathUtils.Hypot(num.Real + 1.0, num.Imaginary());
double b = MathUtils.Hypot(num.Real - 1.0, num.Imaginary());
double c = 0.5 * (a + b);
double real = Math.Acos(0.5 * (a - b));
double imag = Math.Log(c + Math.Sqrt(c + 1) * Math.Sqrt(c - 1));
return new Complex(real, num.Imaginary() >= 0 ? imag : -imag);
}
//asin(x) = -i*ln( i*x + (1-x*x)^1/2)
public static Complex asin(object x) {
Complex num = GetComplexNum(x);
double a = MathUtils.Hypot(num.Real + 1.0, num.Imaginary());
double b = MathUtils.Hypot(num.Real - 1.0, num.Imaginary());
double c = 0.5 * (a + b);
double real = Math.Asin(0.5 * (a - b));
double imag = Math.Log(c + Math.Sqrt(c + 1) * Math.Sqrt(c - 1));
return new Complex(real, num.Imaginary() >= 0 ? imag : -imag);
}
//atan(x) = i/2*ln( (i+x)/ (i-x))
public static Complex atan(object x) {
Complex num = GetComplexNum(x);
Complex i = Complex.ImaginaryOne;
return i * 0.5 * (log(i + num) - log(i - num));
}
//acosh(x) = ln( x + (x*x -1)^1/2)
public static Complex acosh(object x) {
Complex num = GetComplexNum(x);
return log(num + sqrt(num + 1) * sqrt(num - 1));
}
//asin(x) = ln( x + (x*x +1)^1/2)
public static Complex asinh(object x) {
Complex num = GetComplexNum(x);
if (num.IsZero()) {
// preserve -0.0 imag component
return MathUtils.MakeImaginary(num.Imaginary());
}
Complex recip = 1 / num;
return log(num) + log(1 + sqrt(recip * recip + 1));
}
//atanh(x) = (ln(1 +x) - ln(1-x))/2
public static Complex atanh(object x) {
Complex num = GetComplexNum(x);
return (log(1 + num) - log(1 - num)) * 0.5;
}
//ln(re^iO) = ln(r) + iO
public static Complex log(object x) {
Complex num = GetComplexNum(x);
if (num.IsZero()) {
throw PythonOps.ValueError("math domain error");
}
double r, theta;
r = num.Abs();
theta = GetAngle(num);
return new Complex(Math.Log(r), theta);
}
//log b to base a = ln b / ln a
public static Complex log(object x, object logBase) {
return log(x) / log(logBase);
}
public static Complex log10(object x) {
return log(x, 10);
}
public static Complex exp(object x) {
Complex num = GetComplexNum(x);
// degenerate case: num is real
if (num.Imaginary() == 0.0) {
if (double.IsPositiveInfinity(num.Real)) {
return new Complex(double.PositiveInfinity, 0.0);
}
double expt = Math.Exp(num.Real);
if (double.IsInfinity(expt)) {
throw PythonOps.OverflowError("math range error");
}
return new Complex(expt, 0.0);
}
// magnitude is always 0
if (double.IsNegativeInfinity(num.Real)) {
return Complex.Zero;
}
// magnitude is always NaN
if (double.IsNaN(num.Real)) {
return new Complex(double.NaN, double.NaN);
}
// angle is always NaN
if (double.IsNaN(num.Imaginary())) {
return new Complex(double.IsInfinity(num.Real) ? double.PositiveInfinity : double.NaN, double.NaN);
}
// can't take sin or cos of +/-infinity
if (double.IsInfinity(num.Imaginary())) {
throw PythonOps.ValueError("math domain error");
}
// use c*(e^x) = (sign(c))*e^(x+log(abs(c))) for fewer overflows in corner cases
double real;
double cosImag = Math.Cos(num.Imaginary());
if (cosImag > 0.0) {
real = Math.Exp(num.Real + Math.Log(cosImag));
} else if (cosImag < 0.0) {
real = -Math.Exp(num.Real + Math.Log(-cosImag));
} else {
real = 0.0;
}
// use c*(e^x) = (sign(c))*e^(x+log(abs(c))) for fewer overflows in corner cases
double imag;
double sinImag = Math.Sin(num.Imaginary());
if (sinImag > 0.0) {
imag = Math.Exp(num.Real + Math.Log(sinImag));
} else if (sinImag < 0.0) {
imag = -Math.Exp(num.Real + Math.Log(-sinImag));
} else {
imag = 0.0;
}
// check for overflow
if ((double.IsInfinity(real) || double.IsInfinity(imag)) && !double.IsInfinity(num.Real)) {
throw PythonOps.OverflowError("math range error");
}
return new Complex(real, imag);
}
public static Complex sqrt(object x) {
Complex num = GetComplexNum(x);
if (num.Imaginary() == 0.0) {
if (num.Real >= 0.0) {
return MathUtils.MakeReal(Math.Sqrt(num.Real));
} else {
return MathUtils.MakeImaginary(Math.Sqrt(-num.Real));
}
}
double c = num.Abs() + num.Real;
double real = Math.Sqrt(0.5 * c);
double imag = num.Imaginary() / Math.Sqrt(2 * c);
return new Complex(real, imag);
}
public static double phase(object x) {
Complex num = GetComplexNum(x);
return GetAngle(num);
}
public static PythonTuple polar(object x) {
Complex num = GetComplexNum(x);
double[] res = new double[] { num.Abs(), GetAngle(num) };
// check for overflow
if (double.IsInfinity(res[0]) && !IsInfinity(num)) {
throw PythonOps.OverflowError("math range error");
}
return new PythonTuple(res);
}
public static Complex rect(double r, double theta) {
// magnitude is always 0
if (r == 0.0) {
return Complex.Zero;
}
// angle is always 0
if (theta == 0.0) {
return new Complex(r, 0.0);
}
// magnitude is always NaN
if (double.IsNaN(r)) {
return new Complex(double.NaN, double.NaN);
}
// angle is always NaN
if (double.IsNaN(theta)) {
return new Complex(double.IsInfinity(r) ? double.PositiveInfinity : double.NaN, double.NaN);
}
// can't take sin or cos of +/-Infinity
if (double.IsInfinity(theta)) {
throw PythonOps.ValueError("math domain error");
}
return new Complex(r * Math.Cos(theta), r * Math.Sin(theta));
}
public static bool isinf(object x) {
Complex num = GetComplexNum(x);
return IsInfinity(num);
}
public static bool isnan(object x) {
Complex num = GetComplexNum(x);
return IsNaN(num);
}
public static bool isfinite(object x) {
Complex num = GetComplexNum(x);
return IsFinite(num);
}
#region Helpers
private static bool IsInfinity(Complex num) {
return double.IsInfinity(num.Real) || double.IsInfinity(num.Imaginary());
}
private static bool IsNaN(Complex num) {
return double.IsNaN(num.Real) || double.IsNaN(num.Imaginary());
}
private static bool IsFinite(Complex num) {
// double.IsFinite is not available in .NET Framework 4.5 and was added to .NET Core in 2.1
return !double.IsInfinity(num.Real) && !double.IsNaN(num.Real)
&& !double.IsInfinity(num.Imaginary) && !double.IsNaN(num.Imaginary);
}
private static double GetAngle(Complex num) {
if (IsNaN(num)) {
return double.NaN;
}
if (double.IsPositiveInfinity(num.Real)) {
if (double.IsPositiveInfinity(num.Imaginary())) {
return Math.PI * 0.25;
} else if (double.IsNegativeInfinity(num.Imaginary())) {
return Math.PI * -0.25;
} else {
return 0.0;
}
}
if (double.IsNegativeInfinity(num.Real)) {
if (double.IsPositiveInfinity(num.Imaginary())) {
return Math.PI * 0.75;
} else if (double.IsNegativeInfinity(num.Imaginary())) {
return Math.PI * -0.75;
} else {
return DoubleOps.Sign(num.Imaginary()) * Math.PI;
}
}
if (num.Real == 0.0) {
if (num.Imaginary() != 0.0) {
return Math.PI * 0.5 * Math.Sign(num.Imaginary());
} else {
return (DoubleOps.IsPositiveZero(num.Real) ? 0.0 : Math.PI) * DoubleOps.Sign(num.Imaginary());
}
}
return Math.Atan2(num.Imaginary(), num.Real);
}
private static Complex GetComplexNum(object num) {
Complex complexNum;
if (num != null) {
complexNum = Converter.ConvertToComplex(num);
} else {
throw new NullReferenceException("The input was null");
}
return complexNum;
}
#endregion
}
}