/
CalculusFieldElement.java
489 lines (423 loc) · 14.9 KB
/
CalculusFieldElement.java
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
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/*
* This is not the original file distributed by the Apache Software Foundation
* It has been modified by the Hipparchus project
*/
package org.hipparchus;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.FieldSinCos;
import org.hipparchus.util.FieldSinhCosh;
/**
* Interface representing a <a href="http://mathworld.wolfram.com/Field.html">field</a>
* with calculus capabilities (sin, cos, ...).
* @param <T> the type of the field elements
* @see FieldElement
* @since 1.7
*/
public interface CalculusFieldElement<T extends FieldElement<T>> extends FieldElement<T> {
/** Degrees to radians conversion factor. */
double DEG_TO_RAD = FastMath.PI / 180.0;
/** Radians to degrees conversion factor. */
double RAD_TO_DEG = 180.0 / FastMath.PI;
/** Create an instance corresponding to a constant real value.
* @param value constant real value
* @return instance corresponding to a constant real value
*/
T newInstance(final double value);
/** '+' operator.
* @param a right hand side parameter of the operator
* @return this+a
*/
T add(double a);
/** '-' operator.
* @param a right hand side parameter of the operator
* @return this-a
*/
T subtract(double a);
/** '×' operator.
* @param a right hand side parameter of the operator
* @return this×a
*/
T multiply(double a);
/** '÷' operator.
* @param a right hand side parameter of the operator
* @return this÷a
*/
T divide(double a);
/**
* Return the exponent of the instance, removing the bias.
* <p>
* For double numbers of the form 2<sup>x</sup>, the unbiased
* exponent is exactly x.
* </p>
* @return exponent for the instance, without bias
*/
default int getExponent() {
return FastMath.getExponent(getReal());
}
/**
* Multiply the instance by a power of 2.
* @param n power of 2
* @return this × 2<sup>n</sup>
*/
T scalb(int n);
/**
* Compute least significant bit (Unit in Last Position) for a number.
* @return ulp(this)
* @since 2.0
*/
T ulp();
/**
* Returns the hypotenuse of a triangle with sides {@code this} and {@code y}
* - sqrt(<i>this</i><sup>2</sup> +<i>y</i><sup>2</sup>)
* avoiding intermediate overflow or underflow.
*
* <ul>
* <li> If either argument is infinite, then the result is positive infinity.</li>
* <li> else, if either argument is NaN then the result is NaN.</li>
* </ul>
*
* @param y a value
* @return sqrt(<i>this</i><sup>2</sup> +<i>y</i><sup>2</sup>)
* @exception MathIllegalArgumentException if number of free parameters or orders are inconsistent
*/
T hypot(T y)
throws MathIllegalArgumentException;
/** {@inheritDoc} */
@Override
T reciprocal();
/** Square root.
* @return square root of the instance
*/
T sqrt();
/** Cubic root.
* @return cubic root of the instance
*/
T cbrt();
/** N<sup>th</sup> root.
* @param n order of the root
* @return n<sup>th</sup> root of the instance
*/
T rootN(int n);
/** Power operation.
* @param p power to apply
* @return this<sup>p</sup>
*/
T pow(double p);
/** Integer power operation.
* @param n power to apply
* @return this<sup>n</sup>
*/
T pow(int n);
/** Power operation.
* @param e exponent
* @return this<sup>e</sup>
* @exception MathIllegalArgumentException if number of free parameters or orders are inconsistent
*/
T pow(T e)
throws MathIllegalArgumentException;
/** Exponential.
* @return exponential of the instance
*/
T exp();
/** Exponential minus 1.
* @return exponential minus one of the instance
*/
T expm1();
/** Natural logarithm.
* @return logarithm of the instance
*/
T log();
/** Shifted natural logarithm.
* @return logarithm of one plus the instance
*/
T log1p();
/** Base 10 logarithm.
* @return base 10 logarithm of the instance
*/
T log10();
/** Cosine operation.
* @return cos(this)
*/
T cos();
/** Sine operation.
* @return sin(this)
*/
T sin();
/** Combined Sine and Cosine operation.
* @return [sin(this), cos(this)]
* @since 1.4
*/
FieldSinCos<T> sinCos();
/** Tangent operation.
* @return tan(this)
*/
T tan();
/** Arc cosine operation.
* @return acos(this)
*/
T acos();
/** Arc sine operation.
* @return asin(this)
*/
T asin();
/** Arc tangent operation.
* @return atan(this)
*/
T atan();
/** Two arguments arc tangent operation.
* @param x second argument of the arc tangent
* @return atan2(this, x)
* @exception MathIllegalArgumentException if number of free parameters or orders are inconsistent
*/
T atan2(T x)
throws MathIllegalArgumentException;
/** Hyperbolic cosine operation.
* @return cosh(this)
*/
T cosh();
/** Hyperbolic sine operation.
* @return sinh(this)
*/
T sinh();
/** Combined hyperbolic sine and sosine operation.
* @return [sinh(this), cosh(this)]
* @since 2.0
*/
FieldSinhCosh<T> sinhCosh();
/** Hyperbolic tangent operation.
* @return tanh(this)
*/
T tanh();
/** Inverse hyperbolic cosine operation.
* @return acosh(this)
*/
T acosh();
/** Inverse hyperbolic sine operation.
* @return asin(this)
*/
T asinh();
/** Inverse hyperbolic tangent operation.
* @return atanh(this)
*/
T atanh();
/** Convert radians to degrees, with error of less than 0.5 ULP
* @return instance converted into degrees
*/
default T toDegrees() {
return multiply(RAD_TO_DEG);
}
/** Convert degrees to radians, with error of less than 0.5 ULP
* @return instance converted into radians
*/
default T toRadians() {
return multiply(DEG_TO_RAD);
}
/**
* Compute a linear combination.
* @param a Factors.
* @param b Factors.
* @return <code>Σ<sub>i</sub> a<sub>i</sub> b<sub>i</sub></code>.
* @throws MathIllegalArgumentException if arrays dimensions don't match
*/
T linearCombination(T[] a, T[] b)
throws MathIllegalArgumentException;
/**
* Compute a linear combination.
* @param a Factors.
* @param b Factors.
* @return <code>Σ<sub>i</sub> a<sub>i</sub> b<sub>i</sub></code>.
* @throws MathIllegalArgumentException if arrays dimensions don't match
*/
T linearCombination(double[] a, T[] b)
throws MathIllegalArgumentException;
/**
* Compute a linear combination.
* @param a1 first factor of the first term
* @param b1 second factor of the first term
* @param a2 first factor of the second term
* @param b2 second factor of the second term
* @return a<sub>1</sub>×b<sub>1</sub> +
* a<sub>2</sub>×b<sub>2</sub>
* @see #linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
* @see #linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
*/
T linearCombination(T a1, T b1, T a2, T b2);
/**
* Compute a linear combination.
* @param a1 first factor of the first term
* @param b1 second factor of the first term
* @param a2 first factor of the second term
* @param b2 second factor of the second term
* @return a<sub>1</sub>×b<sub>1</sub> +
* a<sub>2</sub>×b<sub>2</sub>
* @see #linearCombination(double, FieldElement, double, FieldElement, double, FieldElement)
* @see #linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)
*/
T linearCombination(double a1, T b1, double a2, T b2);
/**
* Compute a linear combination.
* @param a1 first factor of the first term
* @param b1 second factor of the first term
* @param a2 first factor of the second term
* @param b2 second factor of the second term
* @param a3 first factor of the third term
* @param b3 second factor of the third term
* @return a<sub>1</sub>×b<sub>1</sub> +
* a<sub>2</sub>×b<sub>2</sub> + a<sub>3</sub>×b<sub>3</sub>
* @see #linearCombination(FieldElement, FieldElement, FieldElement, FieldElement)
* @see #linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
*/
T linearCombination(T a1, T b1, T a2, T b2, T a3, T b3);
/**
* Compute a linear combination.
* @param a1 first factor of the first term
* @param b1 second factor of the first term
* @param a2 first factor of the second term
* @param b2 second factor of the second term
* @param a3 first factor of the third term
* @param b3 second factor of the third term
* @return a<sub>1</sub>×b<sub>1</sub> +
* a<sub>2</sub>×b<sub>2</sub> + a<sub>3</sub>×b<sub>3</sub>
* @see #linearCombination(double, FieldElement, double, FieldElement)
* @see #linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)
*/
T linearCombination(double a1, T b1, double a2, T b2, double a3, T b3);
/**
* Compute a linear combination.
* @param a1 first factor of the first term
* @param b1 second factor of the first term
* @param a2 first factor of the second term
* @param b2 second factor of the second term
* @param a3 first factor of the third term
* @param b3 second factor of the third term
* @param a4 first factor of the fourth term
* @param b4 second factor of the fourth term
* @return a<sub>1</sub>×b<sub>1</sub> +
* a<sub>2</sub>×b<sub>2</sub> + a<sub>3</sub>×b<sub>3</sub> +
* a<sub>4</sub>×b<sub>4</sub>
* @see #linearCombination(FieldElement, FieldElement, FieldElement, FieldElement)
* @see #linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
*/
T linearCombination(T a1, T b1, T a2, T b2, T a3, T b3, T a4, T b4);
/**
* Compute a linear combination.
* @param a1 first factor of the first term
* @param b1 second factor of the first term
* @param a2 first factor of the second term
* @param b2 second factor of the second term
* @param a3 first factor of the third term
* @param b3 second factor of the third term
* @param a4 first factor of the fourth term
* @param b4 second factor of the fourth term
* @return a<sub>1</sub>×b<sub>1</sub> +
* a<sub>2</sub>×b<sub>2</sub> + a<sub>3</sub>×b<sub>3</sub> +
* a<sub>4</sub>×b<sub>4</sub>
* @see #linearCombination(double, FieldElement, double, FieldElement)
* @see #linearCombination(double, FieldElement, double, FieldElement, double, FieldElement)
*/
T linearCombination(double a1, T b1, double a2, T b2, double a3, T b3, double a4, T b4);
/** Get the smallest whole number larger than instance.
* @return ceil(this)
*/
T ceil();
/** Get the largest whole number smaller than instance.
* @return floor(this)
*/
T floor();
/** Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.
* @return a double number r such that r is an integer r - 0.5 ≤ this ≤ r + 0.5
*/
T rint();
/** IEEE remainder operator.
* @param a right hand side parameter of the operator
* @return this - n × a where n is the closest integer to this/a
*/
T remainder(double a);
/** IEEE remainder operator.
* @param a right hand side parameter of the operator
* @return this - n × a where n is the closest integer to this/a
*/
T remainder(T a);
/** Compute the sign of the instance.
* The sign is -1 for negative numbers, +1 for positive numbers and 0 otherwise,
* for Complex number, it is extended on the unit circle (equivalent to z/|z|,
* with special handling for 0 and NaN)
* @return -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a
*/
T sign();
/**
* Returns the instance with the sign of the argument.
* A NaN {@code sign} argument is treated as positive.
*
* @param sign the sign for the returned value
* @return the instance with the same sign as the {@code sign} argument
*/
T copySign(T sign);
/**
* Returns the instance with the sign of the argument.
* A NaN {@code sign} argument is treated as positive.
*
* @param sign the sign for the returned value
* @return the instance with the same sign as the {@code sign} argument
*/
T copySign(double sign);
/**
* Check if the instance is infinite.
* @return true if the instance is infinite
*/
default boolean isInfinite() {
return Double.isInfinite(getReal());
}
/**
* Check if the instance is finite (neither infinite nor NaN).
* @return true if the instance is finite (neither infinite nor NaN)
* @since 2.0
*/
default boolean isFinite() {
return Double.isFinite(getReal());
}
/**
* Check if the instance is Not a Number.
* @return true if the instance is Not a Number
*/
default boolean isNaN() {
return Double.isNaN(getReal());
}
/** norm.
* @return norm(this)
* @since 2.0
*/
default double norm() {
return abs().getReal();
}
/** absolute value.
* <p>
* Just another name for {@link #norm()}
* </p>
* @return abs(this)
*/
T abs();
/** Get the closest long to instance real value.
* @return closest long to {@link #getReal()}
*/
default long round() {
return FastMath.round(getReal());
}
}