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source: branches/HeuristicLab.Problems.GaussianProcessTuning/ILNumerics.2.14.4735.573/Misc/ILFComplex.cs @ 9793

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Last change on this file since 9793 was 9102, checked in by gkronber, 12 years ago
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1	///
2	/// This file is part of ILNumerics Community Edition.
3	///
4	/// ILNumerics Community Edition - high performance computing for applications.
5	/// Copyright (C) 2006 - 2012 Haymo Kutschbach, http://ilnumerics.net
6	///
7	/// ILNumerics Community Edition is free software: you can redistribute it and/or modify
8	/// it under the terms of the GNU General Public License version 3 as published by
9	/// the Free Software Foundation.
10	///
11	/// ILNumerics Community Edition is distributed in the hope that it will be useful,
12	/// but WITHOUT ANY WARRANTY; without even the implied warranty of
13	/// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14	/// GNU General Public License for more details.
15	///
16	/// You should have received a copy of the GNU General Public License
17	/// along with ILNumerics Community Edition. See the file License.txt in the root
18	/// of your distribution package. If not, see <http://www.gnu.org/licenses/>.
19	///
20	/// In addition this software uses the following components and/or licenses:
21	///
22	/// =================================================================================
23	/// The Open Toolkit Library License
24	///
25	/// Copyright (c) 2006 - 2009 the Open Toolkit library.
26	///
27	/// Permission is hereby granted, free of charge, to any person obtaining a copy
28	/// of this software and associated documentation files (the "Software"), to deal
29	/// in the Software without restriction, including without limitation the rights to
30	/// use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
31	/// the Software, and to permit persons to whom the Software is furnished to do
32	/// so, subject to the following conditions:
33	///
34	/// The above copyright notice and this permission notice shall be included in all
35	/// copies or substantial portions of the Software.
36	///
37	/// =================================================================================
38	///
39
40	#pragma warning disable 162
41	using System;
42	using System.Collections.Generic;
43	using System.Text;
44	using System.Runtime.InteropServices;
45
46
47
48	namespace ILNumerics {
49	/// <summary>
50	/// Floating point complex value data type of float (single) precision
51	/// </summary>
52	/// <remarks>This class extends the system value types for real numbers to complex float
53	/// values. Besides the publicly available members 'real' and 'imag' it provides all the
54	/// basis functionality the floating point System.double brings (abs, log, sqrt, tan etc.) for
55	/// float precision complex,
56	/// as well as it overrides the basic unary and binary operators for all common system value
57	/// types including rarely used types (e.g. UInt16). This includes the basic numerical operations
58	/// like '+','-','/','*' and the relational operators: '==','>','>=' etc. Also there are some
59	/// explicit and some implicit casting operators from / to fcomplex values into system
60	/// value types. </remarks>
61	[Serializable]
62	[StructLayout(LayoutKind.Sequential)]
63	public struct fcomplex : IEquatable<fcomplex> {
64	/// <summary>
65	/// Real part of this complex number
66	/// </summary>
67	public float real;
68	/// <summary>
69	/// Imaginary part of this complex number
70	/// </summary>
71	public float imag;
72	/// <summary>
73	/// Imaginary unit
74	/// </summary>
75	public static readonly fcomplex i = new fcomplex(0.0f,1.0f);
76
77	/// <summary>
78	/// Construct new float complex number
79	/// </summary>
80	/// <param name="real">Real part</param>
81	/// <param name="imag">Imaginary part</param>
82	public fcomplex(float real, float imag) {
83	this.real = real;
84	this.imag = imag;
85	}
86
87	/// <summary>
88	/// Complex conjugate
89	/// </summary>
90	public fcomplex conj {
91	get{
92	return new fcomplex(real,imag * (-1.0f));
93	}
94	}
95
96	/// <summary>
97	/// Positive infinity for real and imag part of complex value
98	/// </summary>
99	public static fcomplex INF {
100	get {
101	return new fcomplex(
102	float.PositiveInfinity,
103	float.PositiveInfinity
104	);
105	}
106	}
107
108	/// <summary>
109	/// New fcomplex, real and imaginary parts are zero
110	/// </summary>
111	public static fcomplex Zero {
112	get {
113	return new fcomplex(0f,0f);
114	}
115	}
116
117	/// <summary>
118	/// fcomplex quantity, marked as being "not a number"
119	/// </summary>
120	public static fcomplex NaN {
121	get {
122	return new fcomplex(float.NaN,float.NaN);
123	}
124	}
125
126	/// <summary>
127	/// Are obj's real and imaginary part identical to the real and imaginary parts of this fcomplex
128	/// </summary>
129	/// <param name="obj">fcomplex object to determine the equality for</param>
130	/// <returns>true if obj is of fcomplex type and its real and imag part has the same
131	/// values as the real and imaginary part of this array.</returns>
132	public override bool Equals(object obj) {
133	if (obj is fcomplex && ((fcomplex)obj) == this)
134	return true;
135	return false;
136	}
137
138	/// <summary>
139	/// Check if a fcomplex number equals this fcomplex number
140	/// </summary>
141	/// <param name="other">other complex number</param>
142	/// <returns>true if both, real and imaginary parts of both complex number are (binary) equal, false otherwise</returns>
143	public bool Equals(fcomplex other) {
144	return real.Equals(other.real) && imag.Equals(other.imag);
145	}
146
147	/// <summary>
148	/// Give HashCode of this fcomplex number
149	/// </summary>
150	/// <returns>HashCode of this fcomplex number</returns>
151	public override int GetHashCode() {
152	return 31 * real.GetHashCode() + imag.GetHashCode();
153	}
154
155
156
157
158	#region HYCALPER AUTO GENERATED CODE
159
160
161	/// <summary>
162	/// Add two complex numbers
163	/// </summary>
164	/// <param name="A">First summand</param>
165	/// <param name="B">Second summand</param>
166	/// <returns>result</returns>
167	public static complex operator +( fcomplex A, complex B) {
168	complex ret;
169	ret.real = (double) (A.real + B.real );
170	ret.imag = (double) (A.imag + B.imag );
171	return ret;
172	}
173	/// <summary>
174	/// Subtract two complex values
175	/// </summary>
176	/// <param name="A">Minuend</param>
177	/// <param name="B">Subtrahend</param>
178	/// <returns>result</returns>
179	public static complex operator -( fcomplex A, complex B) {
180	complex ret;
181	ret.real = (double) (A.real - B.real );
182	ret.imag = (double) (A.imag - B.imag );
183	return ret;
184	}
185	/// <summary>
186	/// Multiply two complex values
187	/// </summary>
188	/// <param name="A">First factor</param>
189	/// <param name="B">Second factor</param>
190	/// <returns>result</returns>
191	public static complex operator *( fcomplex A, complex B) {
192	complex ret;
193	ret.real = (double) ((A.real * B.real ) - (A.imag * B.imag ));
194	ret.imag = (double) ((A.real * B.imag ) + (A.imag * B.real ));
195	return ret;
196	}
197	/// <summary>
198	/// Divide two numbers
199	/// </summary>
200	/// <param name="A">Divident</param>
201	/// <param name="B">Divisor</param>
202	/// <returns>Result</returns>
203	/// <remarks><para>Unless the operator must handle special inputs (Inf or 0 values),
204	/// the algorithm described in [1] is used for division. This is considered to be
205	/// more robust against floating point overflow than the naive approach of simple
206	/// cartesian division.</para>
207	/// <para>References: [1]: Smith, R.L., Algorithm 116: Complex division. Commun.ACM 5,8 (1962),435 <br />
208	/// [2]: Stewart, G.W., A note on complex division, ACM trans.on math software, Vol.11, N.3 (1985)</para></remarks>
209	public static complex operator /( fcomplex A, complex B) {
210	if (B.imag == 0) return A / B.real;
211	return A * (1 / B);
212	if (IsNaN(A) \|\| complex .IsNaN(B)) return NaN;
213	//if ( complex .IsInfinity(B)) return NaN;
214	//if (A.real == 0 && A.imag == 0) return ( complex )0;
215	complex ret;
216	if (B.real == 0) {
217	ret.imag = (double) -(A.real / B.imag);
218	ret.real = (double) (A.imag / B.imag);
219	return ret;
220	}
221	// this would be the naive approach. But it come with to little robustness against overflow
222	//double norm2 = B.real * B.real + B.imag * B.imag;
223	//if (norm2 == 0) return INF; // this may be removed, since division by 0 results in inf anyway ?
224	//ret.real = (double) (((A.real * B.real ) + (A.imag * B.imag )) / norm2);
225	//ret.imag = (double) (((A.imag * B.real ) - (A.real * B.imag )) / norm2);
226
227	// this algorithm is taken from [1]. The one described in [2] was not taken. Tests
228	// did not show any advantage when using double precision floating point arithmetic.
229	double tmp1, tmp2;
230	if (Math.Abs(B.real) >= Math.Abs(B.imag)) {
231	tmp1 = (double) (B.imag * (1/B.real));
232	tmp2 = (double) (B.real + B.imag*tmp1);
233	ret.real = (double) (A.real + A.imag*tmp1)/tmp2;
234	ret.imag = (double) (A.imag - A.real*tmp1)/tmp2;
235	} else {
236	tmp1 = (double) (B.real * (1/B.imag));
237	tmp2 = (double) (B.imag + B.real*tmp1);
238	ret.real = (double) (A.imag + A.real*tmp1)/tmp2;
239	ret.imag = - (double) (A.real - A.imag*tmp1)/tmp2;
240	}
241	return ret;
242	}
243	/// <summary>
244	/// Equality comparison for complex numbers
245	/// </summary>
246	/// <param name="A">Left side</param>
247	/// <param name="B">Right side</param>
248	/// <returns>true, if real and imaginary part are identical</returns>
249	public static bool operator ==( fcomplex A, complex B) {
250	return (A.imag == B.imag ) && (A.real == B.real );
251	}
252	/// <summary>
253	/// Unequality comparison for complex numbers
254	/// </summary>
255	/// <param name="A">Left side</param>
256	/// <param name="B">Right side</param>
257	/// <returns>true if real and imaginary parts of A and B are not equal, false otherwise</returns>
258	public static bool operator !=( fcomplex A, complex B) {
259	return (A.imag != B.imag ) \|\| (A.real != B.real );
260	}
261	/// <summary>
262	/// Greater than comparison for complex numbers
263	/// </summary>
264	/// <param name="A">Left side</param>
265	/// <param name="B">Right side</param>
266	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
267	/// <remarks>Only the real parts are compared!</remarks>
268	public static bool operator > ( fcomplex A, complex B) {
269	return (A.real > B.real );
270	}
271	/// <summary>
272	/// Lower than comparison for complex numbers
273	/// </summary>
274	/// <param name="A">Left side</param>
275	/// <param name="B">Right side</param>
276	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
277	/// <remarks>Only the real parts are compared!</remarks>
278	public static bool operator < ( fcomplex A, complex B) {
279	return (A.real < B.real );
280	}
281	/// <summary>
282	/// Greater than or equal to comparison for complex numbers
283	/// </summary>
284	/// <param name="A">Left side</param>
285	/// <param name="B">Right side</param>
286	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
287	/// <remarks>Only the real parts are compared!</remarks>
288	public static bool operator >=( fcomplex A, complex B) {
289	return (A.real >= B.real );
290	}
291	/// <summary>
292	/// Lower than or equal to comparison for complex numbers
293	/// </summary>
294	/// <param name="A">Left side</param>
295	/// <param name="B">Right side</param>
296	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
297	/// <remarks>Only the real parts are compared!</remarks>
298	public static bool operator <=( fcomplex A, complex B) {
299	return (A.real <= B.real );
300	}
301
302	/// <summary>
303	/// Add two complex numbers
304	/// </summary>
305	/// <param name="A">First summand</param>
306	/// <param name="B">Second summand</param>
307	/// <returns>result</returns>
308	public static fcomplex operator +( fcomplex A, fcomplex B) {
309	fcomplex ret;
310	ret.real = (float) (A.real + B.real );
311	ret.imag = (float) (A.imag + B.imag );
312	return ret;
313	}
314	/// <summary>
315	/// Subtract two complex values
316	/// </summary>
317	/// <param name="A">Minuend</param>
318	/// <param name="B">Subtrahend</param>
319	/// <returns>result</returns>
320	public static fcomplex operator -( fcomplex A, fcomplex B) {
321	fcomplex ret;
322	ret.real = (float) (A.real - B.real );
323	ret.imag = (float) (A.imag - B.imag );
324	return ret;
325	}
326	/// <summary>
327	/// Multiply two complex values
328	/// </summary>
329	/// <param name="A">First factor</param>
330	/// <param name="B">Second factor</param>
331	/// <returns>result</returns>
332	public static fcomplex operator *( fcomplex A, fcomplex B) {
333	fcomplex ret;
334	ret.real = (float) ((A.real * B.real ) - (A.imag * B.imag ));
335	ret.imag = (float) ((A.real * B.imag ) + (A.imag * B.real ));
336	return ret;
337	}
338	/// <summary>
339	/// Divide two numbers
340	/// </summary>
341	/// <param name="A">Divident</param>
342	/// <param name="B">Divisor</param>
343	/// <returns>Result</returns>
344	/// <remarks><para>Unless the operator must handle special inputs (Inf or 0 values),
345	/// the algorithm described in [1] is used for division. This is considered to be
346	/// more robust against floating point overflow than the naive approach of simple
347	/// cartesian division.</para>
348	/// <para>References: [1]: Smith, R.L., Algorithm 116: Complex division. Commun.ACM 5,8 (1962),435 <br />
349	/// [2]: Stewart, G.W., A note on complex division, ACM trans.on math software, Vol.11, N.3 (1985)</para></remarks>
350	public static fcomplex operator /( fcomplex A, fcomplex B) {
351	if (B.imag == 0) return A / B.real;
352	return A * (1 / B);
353	if (IsNaN(A) \|\| fcomplex .IsNaN(B)) return NaN;
354	//if ( fcomplex .IsInfinity(B)) return NaN;
355	//if (A.real == 0 && A.imag == 0) return ( fcomplex )0;
356	fcomplex ret;
357	if (B.real == 0) {
358	ret.imag = (float) -(A.real / B.imag);
359	ret.real = (float) (A.imag / B.imag);
360	return ret;
361	}
362	// this would be the naive approach. But it come with to little robustness against overflow
363	//double norm2 = B.real * B.real + B.imag * B.imag;
364	//if (norm2 == 0) return INF; // this may be removed, since division by 0 results in inf anyway ?
365	//ret.real = (float) (((A.real * B.real ) + (A.imag * B.imag )) / norm2);
366	//ret.imag = (float) (((A.imag * B.real ) - (A.real * B.imag )) / norm2);
367
368	// this algorithm is taken from [1]. The one described in [2] was not taken. Tests
369	// did not show any advantage when using double precision floating point arithmetic.
370	float tmp1, tmp2;
371	if (Math.Abs(B.real) >= Math.Abs(B.imag)) {
372	tmp1 = (float) (B.imag * (1/B.real));
373	tmp2 = (float) (B.real + B.imag*tmp1);
374	ret.real = (float) (A.real + A.imag*tmp1)/tmp2;
375	ret.imag = (float) (A.imag - A.real*tmp1)/tmp2;
376	} else {
377	tmp1 = (float) (B.real * (1/B.imag));
378	tmp2 = (float) (B.imag + B.real*tmp1);
379	ret.real = (float) (A.imag + A.real*tmp1)/tmp2;
380	ret.imag = - (float) (A.real - A.imag*tmp1)/tmp2;
381	}
382	return ret;
383	}
384	/// <summary>
385	/// Equality comparison for complex numbers
386	/// </summary>
387	/// <param name="A">Left side</param>
388	/// <param name="B">Right side</param>
389	/// <returns>true, if real and imaginary part are identical</returns>
390	public static bool operator ==( fcomplex A, fcomplex B) {
391	return (A.imag == B.imag ) && (A.real == B.real );
392	}
393	/// <summary>
394	/// Unequality comparison for complex numbers
395	/// </summary>
396	/// <param name="A">Left side</param>
397	/// <param name="B">Right side</param>
398	/// <returns>true if real and imaginary parts of A and B are not equal, false otherwise</returns>
399	public static bool operator !=( fcomplex A, fcomplex B) {
400	return (A.imag != B.imag ) \|\| (A.real != B.real );
401	}
402	/// <summary>
403	/// Greater than comparison for complex numbers
404	/// </summary>
405	/// <param name="A">Left side</param>
406	/// <param name="B">Right side</param>
407	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
408	/// <remarks>Only the real parts are compared!</remarks>
409	public static bool operator > ( fcomplex A, fcomplex B) {
410	return (A.real > B.real );
411	}
412	/// <summary>
413	/// Lower than comparison for complex numbers
414	/// </summary>
415	/// <param name="A">Left side</param>
416	/// <param name="B">Right side</param>
417	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
418	/// <remarks>Only the real parts are compared!</remarks>
419	public static bool operator < ( fcomplex A, fcomplex B) {
420	return (A.real < B.real );
421	}
422	/// <summary>
423	/// Greater than or equal to comparison for complex numbers
424	/// </summary>
425	/// <param name="A">Left side</param>
426	/// <param name="B">Right side</param>
427	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
428	/// <remarks>Only the real parts are compared!</remarks>
429	public static bool operator >=( fcomplex A, fcomplex B) {
430	return (A.real >= B.real );
431	}
432	/// <summary>
433	/// Lower than or equal to comparison for complex numbers
434	/// </summary>
435	/// <param name="A">Left side</param>
436	/// <param name="B">Right side</param>
437	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
438	/// <remarks>Only the real parts are compared!</remarks>
439	public static bool operator <=( fcomplex A, fcomplex B) {
440	return (A.real <= B.real );
441	}
442
443	#endregion HYCALPER AUTO GENERATED CODE
444
445
446
447
448	#region HYCALPER AUTO GENERATED CODE
449
450
451	/// <summary>
452	/// Add two complex numbers
453	/// </summary>
454	/// <param name="A">First summand</param>
455	/// <param name="B">Second summand</param>
456	/// <returns>Result</returns>
457	public static fcomplex operator +( fcomplex A, Int64 B) {
458	fcomplex ret;
459	ret.real = (float) (A.real + B);
460	ret.imag = (float) A.imag;
461	return ret;
462	}
463	/// <summary>
464	/// Subtract two values
465	/// </summary>
466	/// <param name="A">Minuend</param>
467	/// <param name="B">Subtrahend</param>
468	/// <returns>result</returns>
469	public static fcomplex operator -( fcomplex A, Int64 B) {
470	fcomplex ret;
471	ret.real = (float) (A.real - B);
472	ret.imag = (float) A.imag;
473	return ret;
474	}
475	/// <summary>
476	/// Multiply two values
477	/// </summary>
478	/// <param name="A">First factor</param>
479	/// <param name="B">Second factor</param>
480	/// <returns>result</returns>
481	public static fcomplex operator *( fcomplex A, Int64 B) {
482	fcomplex ret;
483	ret.real = (float) (A.real * B);
484	ret.imag = (float) (A.imag * B);
485	return ret;
486	}
487	/// <summary>
488	/// Divide two numbers
489	/// </summary>
490	/// <param name="A">Divident</param>
491	/// <param name="B">Divisor</param>
492	/// <returns>result</returns>
493	public static fcomplex operator /( fcomplex A, Int64 B) {
494	if (IsNaN(A)) return NaN;
495
496	if (A.real == 0 && A.imag == 0) {
497	if (B == 0) return NaN;
498	return ( fcomplex )0;
499	} else {
500	if (false)
501	{
502	if (IsInfinity(A)) {
503	return NaN;
504	} else {
505	return ( fcomplex )0;
506	}
507	}
508	}
509	fcomplex ret;
510	if (B == 0) return INF ;
511	ret.real = (float) (A.real / B);
512	ret.imag = (float) (A.imag / B);
513	return ret;
514	}
515	/// <summary>
516	/// Equality comparison for complex numbers
517	/// </summary>
518	/// <param name="A">Left side</param>
519	/// <param name="B">Right side</param>
520	/// <returns>result</returns>
521	/// <remarks>Real inputs are converted to a complex number and the result is compared to the complex input.</remarks>
522	public static bool operator ==( fcomplex A, Int64 B) {
523	return (A.real == B && A.imag == 0.0);
524	}
525	/// <summary>
526	/// Unequality comparison for complex numbers
527	/// </summary>
528	/// <param name="A">Left side</param>
529	/// <param name="B">Right side</param>
530	/// <returns>true if real and imaginary parts of A and B are not equal, false otherwise</returns>
531	/// <remarks>Real inputs are converted to a complex number and the result is compared to the complex input.</remarks>
532	public static bool operator !=( fcomplex A, Int64 B) {
533	return (A.imag != 0.0) \|\| (A.real != B);
534	}
535	/// <summary>
536	/// Freater than comparison for complex numbers
537	/// </summary>
538	/// <param name="A">Left side</param>
539	/// <param name="B">Right side</param>
540	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
541	/// <remarks>Only the real parts are compared!</remarks>
542	public static bool operator > ( fcomplex A, Int64 B) {
543	return (A.real > B);
544	}
545	/// <summary>
546	/// Lower than comparison for complex numbers
547	/// </summary>
548	/// <param name="A">Left side</param>
549	/// <param name="B">Right side</param>
550	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
551	/// <remarks>Only the real parts are compared!</remarks>
552	public static bool operator <( fcomplex A, Int64 B) {
553	return (A.real < B);
554	}
555	/// <summary>
556	/// Greater than or equal to comparison for complex numbers
557	/// </summary>
558	/// <param name="A">Left side</param>
559	/// <param name="B">Right side</param>
560	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
561	/// <remarks>Only the real parts are compared!</remarks>
562	public static bool operator >=( fcomplex A, Int64 B) {
563	return (A.real >= B);
564	}
565	/// <summary>
566	/// Lower than or equal to comparison for complex numbers
567	/// </summary>
568	/// <param name="A">Left side</param>
569	/// <param name="B">Right side</param>
570	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
571	/// <remarks>Only the real parts are compared!</remarks>
572	public static bool operator <=( fcomplex A, Int64 B) {
573	return (A.real <= B);
574	}
575
576	/// <summary>
577	/// Add two complex numbers
578	/// </summary>
579	/// <param name="A">First summand</param>
580	/// <param name="B">Second summand</param>
581	/// <returns>Result</returns>
582	public static fcomplex operator +( fcomplex A, Int32 B) {
583	fcomplex ret;
584	ret.real = (float) (A.real + B);
585	ret.imag = (float) A.imag;
586	return ret;
587	}
588	/// <summary>
589	/// Subtract two values
590	/// </summary>
591	/// <param name="A">Minuend</param>
592	/// <param name="B">Subtrahend</param>
593	/// <returns>result</returns>
594	public static fcomplex operator -( fcomplex A, Int32 B) {
595	fcomplex ret;
596	ret.real = (float) (A.real - B);
597	ret.imag = (float) A.imag;
598	return ret;
599	}
600	/// <summary>
601	/// Multiply two values
602	/// </summary>
603	/// <param name="A">First factor</param>
604	/// <param name="B">Second factor</param>
605	/// <returns>result</returns>
606	public static fcomplex operator *( fcomplex A, Int32 B) {
607	fcomplex ret;
608	ret.real = (float) (A.real * B);
609	ret.imag = (float) (A.imag * B);
610	return ret;
611	}
612	/// <summary>
613	/// Divide two numbers
614	/// </summary>
615	/// <param name="A">Divident</param>
616	/// <param name="B">Divisor</param>
617	/// <returns>result</returns>
618	public static fcomplex operator /( fcomplex A, Int32 B) {
619	if (IsNaN(A)) return NaN;
620
621	if (A.real == 0 && A.imag == 0) {
622	if (B == 0) return NaN;
623	return ( fcomplex )0;
624	} else {
625	if (false)
626	{
627	if (IsInfinity(A)) {
628	return NaN;
629	} else {
630	return ( fcomplex )0;
631	}
632	}
633	}
634	fcomplex ret;
635	if (B == 0) return INF ;
636	ret.real = (float) (A.real / B);
637	ret.imag = (float) (A.imag / B);
638	return ret;
639	}
640	/// <summary>
641	/// Equality comparison for complex numbers
642	/// </summary>
643	/// <param name="A">Left side</param>
644	/// <param name="B">Right side</param>
645	/// <returns>result</returns>
646	/// <remarks>Real inputs are converted to a complex number and the result is compared to the complex input.</remarks>
647	public static bool operator ==( fcomplex A, Int32 B) {
648	return (A.real == B && A.imag == 0.0);
649	}
650	/// <summary>
651	/// Unequality comparison for complex numbers
652	/// </summary>
653	/// <param name="A">Left side</param>
654	/// <param name="B">Right side</param>
655	/// <returns>true if real and imaginary parts of A and B are not equal, false otherwise</returns>
656	/// <remarks>Real inputs are converted to a complex number and the result is compared to the complex input.</remarks>
657	public static bool operator !=( fcomplex A, Int32 B) {
658	return (A.imag != 0.0) \|\| (A.real != B);
659	}
660	/// <summary>
661	/// Freater than comparison for complex numbers
662	/// </summary>
663	/// <param name="A">Left side</param>
664	/// <param name="B">Right side</param>
665	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
666	/// <remarks>Only the real parts are compared!</remarks>
667	public static bool operator > ( fcomplex A, Int32 B) {
668	return (A.real > B);
669	}
670	/// <summary>
671	/// Lower than comparison for complex numbers
672	/// </summary>
673	/// <param name="A">Left side</param>
674	/// <param name="B">Right side</param>
675	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
676	/// <remarks>Only the real parts are compared!</remarks>
677	public static bool operator <( fcomplex A, Int32 B) {
678	return (A.real < B);
679	}
680	/// <summary>
681	/// Greater than or equal to comparison for complex numbers
682	/// </summary>
683	/// <param name="A">Left side</param>
684	/// <param name="B">Right side</param>
685	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
686	/// <remarks>Only the real parts are compared!</remarks>
687	public static bool operator >=( fcomplex A, Int32 B) {
688	return (A.real >= B);
689	}
690	/// <summary>
691	/// Lower than or equal to comparison for complex numbers
692	/// </summary>
693	/// <param name="A">Left side</param>
694	/// <param name="B">Right side</param>
695	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
696	/// <remarks>Only the real parts are compared!</remarks>
697	public static bool operator <=( fcomplex A, Int32 B) {
698	return (A.real <= B);
699	}
700
701	/// <summary>
702	/// Add two complex numbers
703	/// </summary>
704	/// <param name="A">First summand</param>
705	/// <param name="B">Second summand</param>
706	/// <returns>Result</returns>
707	public static fcomplex operator +( fcomplex A, float B) {
708	fcomplex ret;
709	ret.real = (float) (A.real + B);
710	ret.imag = (float) A.imag;
711	return ret;
712	}
713	/// <summary>
714	/// Subtract two values
715	/// </summary>
716	/// <param name="A">Minuend</param>
717	/// <param name="B">Subtrahend</param>
718	/// <returns>result</returns>
719	public static fcomplex operator -( fcomplex A, float B) {
720	fcomplex ret;
721	ret.real = (float) (A.real - B);
722	ret.imag = (float) A.imag;
723	return ret;
724	}
725	/// <summary>
726	/// Multiply two values
727	/// </summary>
728	/// <param name="A">First factor</param>
729	/// <param name="B">Second factor</param>
730	/// <returns>result</returns>
731	public static fcomplex operator *( fcomplex A, float B) {
732	fcomplex ret;
733	ret.real = (float) (A.real * B);
734	ret.imag = (float) (A.imag * B);
735	return ret;
736	}
737	/// <summary>
738	/// Divide two numbers
739	/// </summary>
740	/// <param name="A">Divident</param>
741	/// <param name="B">Divisor</param>
742	/// <returns>result</returns>
743	public static fcomplex operator /( fcomplex A, float B) {
744	if (IsNaN(A)) return NaN;
745	if (float.IsNaN(B)) return NaN;
746	if (A.real == 0 && A.imag == 0) {
747	if (B == 0) return NaN;
748	return ( fcomplex )0;
749	} else {
750	if (float.IsInfinity(B))
751	{
752	if (IsInfinity(A)) {
753	return NaN;
754	} else {
755	return ( fcomplex )0;
756	}
757	}
758	}
759	fcomplex ret;
760	if (B == 0) return INF ;
761	ret.real = (float) (A.real / B);
762	ret.imag = (float) (A.imag / B);
763	return ret;
764	}
765	/// <summary>
766	/// Equality comparison for complex numbers
767	/// </summary>
768	/// <param name="A">Left side</param>
769	/// <param name="B">Right side</param>
770	/// <returns>result</returns>
771	/// <remarks>Real inputs are converted to a complex number and the result is compared to the complex input.</remarks>
772	public static bool operator ==( fcomplex A, float B) {
773	return (A.real == B && A.imag == 0.0);
774	}
775	/// <summary>
776	/// Unequality comparison for complex numbers
777	/// </summary>
778	/// <param name="A">Left side</param>
779	/// <param name="B">Right side</param>
780	/// <returns>true if real and imaginary parts of A and B are not equal, false otherwise</returns>
781	/// <remarks>Real inputs are converted to a complex number and the result is compared to the complex input.</remarks>
782	public static bool operator !=( fcomplex A, float B) {
783	return (A.imag != 0.0) \|\| (A.real != B);
784	}
785	/// <summary>
786	/// Freater than comparison for complex numbers
787	/// </summary>
788	/// <param name="A">Left side</param>
789	/// <param name="B">Right side</param>
790	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
791	/// <remarks>Only the real parts are compared!</remarks>
792	public static bool operator > ( fcomplex A, float B) {
793	return (A.real > B);
794	}
795	/// <summary>
796	/// Lower than comparison for complex numbers
797	/// </summary>
798	/// <param name="A">Left side</param>
799	/// <param name="B">Right side</param>
800	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
801	/// <remarks>Only the real parts are compared!</remarks>
802	public static bool operator <( fcomplex A, float B) {
803	return (A.real < B);
804	}
805	/// <summary>
806	/// Greater than or equal to comparison for complex numbers
807	/// </summary>
808	/// <param name="A">Left side</param>
809	/// <param name="B">Right side</param>
810	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
811	/// <remarks>Only the real parts are compared!</remarks>
812	public static bool operator >=( fcomplex A, float B) {
813	return (A.real >= B);
814	}
815	/// <summary>
816	/// Lower than or equal to comparison for complex numbers
817	/// </summary>
818	/// <param name="A">Left side</param>
819	/// <param name="B">Right side</param>
820	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
821	/// <remarks>Only the real parts are compared!</remarks>
822	public static bool operator <=( fcomplex A, float B) {
823	return (A.real <= B);
824	}
825
826	/// <summary>
827	/// Add two complex numbers
828	/// </summary>
829	/// <param name="A">First summand</param>
830	/// <param name="B">Second summand</param>
831	/// <returns>Result</returns>
832	public static fcomplex operator +( fcomplex A, byte B) {
833	fcomplex ret;
834	ret.real = (float) (A.real + B);
835	ret.imag = (float) A.imag;
836	return ret;
837	}
838	/// <summary>
839	/// Subtract two values
840	/// </summary>
841	/// <param name="A">Minuend</param>
842	/// <param name="B">Subtrahend</param>
843	/// <returns>result</returns>
844	public static fcomplex operator -( fcomplex A, byte B) {
845	fcomplex ret;
846	ret.real = (float) (A.real - B);
847	ret.imag = (float) A.imag;
848	return ret;
849	}
850	/// <summary>
851	/// Multiply two values
852	/// </summary>
853	/// <param name="A">First factor</param>
854	/// <param name="B">Second factor</param>
855	/// <returns>result</returns>
856	public static fcomplex operator *( fcomplex A, byte B) {
857	fcomplex ret;
858	ret.real = (float) (A.real * B);
859	ret.imag = (float) (A.imag * B);
860	return ret;
861	}
862	/// <summary>
863	/// Divide two numbers
864	/// </summary>
865	/// <param name="A">Divident</param>
866	/// <param name="B">Divisor</param>
867	/// <returns>result</returns>
868	public static fcomplex operator /( fcomplex A, byte B) {
869	if (IsNaN(A)) return NaN;
870
871	if (A.real == 0 && A.imag == 0) {
872	if (B == 0) return NaN;
873	return ( fcomplex )0;
874	} else {
875	if (false)
876	{
877	if (IsInfinity(A)) {
878	return NaN;
879	} else {
880	return ( fcomplex )0;
881	}
882	}
883	}
884	fcomplex ret;
885	if (B == 0) return INF ;
886	ret.real = (float) (A.real / B);
887	ret.imag = (float) (A.imag / B);
888	return ret;
889	}
890	/// <summary>
891	/// Equality comparison for complex numbers
892	/// </summary>
893	/// <param name="A">Left side</param>
894	/// <param name="B">Right side</param>
895	/// <returns>result</returns>
896	/// <remarks>Real inputs are converted to a complex number and the result is compared to the complex input.</remarks>
897	public static bool operator ==( fcomplex A, byte B) {
898	return (A.real == B && A.imag == 0.0);
899	}
900	/// <summary>
901	/// Unequality comparison for complex numbers
902	/// </summary>
903	/// <param name="A">Left side</param>
904	/// <param name="B">Right side</param>
905	/// <returns>true if real and imaginary parts of A and B are not equal, false otherwise</returns>
906	/// <remarks>Real inputs are converted to a complex number and the result is compared to the complex input.</remarks>
907	public static bool operator !=( fcomplex A, byte B) {
908	return (A.imag != 0.0) \|\| (A.real != B);
909	}
910	/// <summary>
911	/// Freater than comparison for complex numbers
912	/// </summary>
913	/// <param name="A">Left side</param>
914	/// <param name="B">Right side</param>
915	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
916	/// <remarks>Only the real parts are compared!</remarks>
917	public static bool operator > ( fcomplex A, byte B) {
918	return (A.real > B);
919	}
920	/// <summary>
921	/// Lower than comparison for complex numbers
922	/// </summary>
923	/// <param name="A">Left side</param>
924	/// <param name="B">Right side</param>
925	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
926	/// <remarks>Only the real parts are compared!</remarks>
927	public static bool operator <( fcomplex A, byte B) {
928	return (A.real < B);
929	}
930	/// <summary>
931	/// Greater than or equal to comparison for complex numbers
932	/// </summary>
933	/// <param name="A">Left side</param>
934	/// <param name="B">Right side</param>
935	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
936	/// <remarks>Only the real parts are compared!</remarks>
937	public static bool operator >=( fcomplex A, byte B) {
938	return (A.real >= B);
939	}
940	/// <summary>
941	/// Lower than or equal to comparison for complex numbers
942	/// </summary>
943	/// <param name="A">Left side</param>
944	/// <param name="B">Right side</param>
945	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
946	/// <remarks>Only the real parts are compared!</remarks>
947	public static bool operator <=( fcomplex A, byte B) {
948	return (A.real <= B);
949	}
950
951	/// <summary>
952	/// Add two complex numbers
953	/// </summary>
954	/// <param name="A">First summand</param>
955	/// <param name="B">Second summand</param>
956	/// <returns>Result</returns>
957	public static fcomplex operator +( fcomplex A, double B) {
958	fcomplex ret;
959	ret.real = (float) (A.real + B);
960	ret.imag = (float) A.imag;
961	return ret;
962	}
963	/// <summary>
964	/// Subtract two values
965	/// </summary>
966	/// <param name="A">Minuend</param>
967	/// <param name="B">Subtrahend</param>
968	/// <returns>result</returns>
969	public static fcomplex operator -( fcomplex A, double B) {
970	fcomplex ret;
971	ret.real = (float) (A.real - B);
972	ret.imag = (float) A.imag;
973	return ret;
974	}
975	/// <summary>
976	/// Multiply two values
977	/// </summary>
978	/// <param name="A">First factor</param>
979	/// <param name="B">Second factor</param>
980	/// <returns>result</returns>
981	public static fcomplex operator *( fcomplex A, double B) {
982	fcomplex ret;
983	ret.real = (float) (A.real * B);
984	ret.imag = (float) (A.imag * B);
985	return ret;
986	}
987	/// <summary>
988	/// Divide two numbers
989	/// </summary>
990	/// <param name="A">Divident</param>
991	/// <param name="B">Divisor</param>
992	/// <returns>result</returns>
993	public static fcomplex operator /( fcomplex A, double B) {
994	if (IsNaN(A)) return NaN;
995	if (double.IsNaN(B)) return NaN;
996	if (A.real == 0 && A.imag == 0) {
997	if (B == 0) return NaN;
998	return ( fcomplex )0;
999	} else {
1000	if (double.IsInfinity(B))
1001	{
1002	if (IsInfinity(A)) {
1003	return NaN;
1004	} else {
1005	return ( fcomplex )0;
1006	}
1007	}
1008	}
1009	fcomplex ret;
1010	if (B == 0) return INF ;
1011	ret.real = (float) (A.real / B);
1012	ret.imag = (float) (A.imag / B);
1013	return ret;
1014	}
1015	/// <summary>
1016	/// Equality comparison for complex numbers
1017	/// </summary>
1018	/// <param name="A">Left side</param>
1019	/// <param name="B">Right side</param>
1020	/// <returns>result</returns>
1021	/// <remarks>Real inputs are converted to a complex number and the result is compared to the complex input.</remarks>
1022	public static bool operator ==( fcomplex A, double B) {
1023	return (A.real == B && A.imag == 0.0);
1024	}
1025	/// <summary>
1026	/// Unequality comparison for complex numbers
1027	/// </summary>
1028	/// <param name="A">Left side</param>
1029	/// <param name="B">Right side</param>
1030	/// <returns>true if real and imaginary parts of A and B are not equal, false otherwise</returns>
1031	/// <remarks>Real inputs are converted to a complex number and the result is compared to the complex input.</remarks>
1032	public static bool operator !=( fcomplex A, double B) {
1033	return (A.imag != 0.0) \|\| (A.real != B);
1034	}
1035	/// <summary>
1036	/// Freater than comparison for complex numbers
1037	/// </summary>
1038	/// <param name="A">Left side</param>
1039	/// <param name="B">Right side</param>
1040	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
1041	/// <remarks>Only the real parts are compared!</remarks>
1042	public static bool operator > ( fcomplex A, double B) {
1043	return (A.real > B);
1044	}
1045	/// <summary>
1046	/// Lower than comparison for complex numbers
1047	/// </summary>
1048	/// <param name="A">Left side</param>
1049	/// <param name="B">Right side</param>
1050	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
1051	/// <remarks>Only the real parts are compared!</remarks>
1052	public static bool operator <( fcomplex A, double B) {
1053	return (A.real < B);
1054	}
1055	/// <summary>
1056	/// Greater than or equal to comparison for complex numbers
1057	/// </summary>
1058	/// <param name="A">Left side</param>
1059	/// <param name="B">Right side</param>
1060	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
1061	/// <remarks>Only the real parts are compared!</remarks>
1062	public static bool operator >=( fcomplex A, double B) {
1063	return (A.real >= B);
1064	}
1065	/// <summary>
1066	/// Lower than or equal to comparison for complex numbers
1067	/// </summary>
1068	/// <param name="A">Left side</param>
1069	/// <param name="B">Right side</param>
1070	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
1071	/// <remarks>Only the real parts are compared!</remarks>
1072	public static bool operator <=( fcomplex A, double B) {
1073	return (A.real <= B);
1074	}
1075
1076	#endregion HYCALPER AUTO GENERATED CODE
1077
1078
1079
1080
1081	#region HYCALPER AUTO GENERATED CODE
1082
1083
1084	/// <summary>
1085	/// Add two complex values
1086	/// </summary>
1087	/// <param name="A">First summand</param>
1088	/// <param name="B">Second summand</param>
1089	/// <returns>Result</returns>
1090	public static fcomplex operator +( Int64 A, fcomplex B) {
1091	fcomplex ret;
1092	ret.real = (float) (A + B.real);
1093	ret.imag = (float) B.imag;
1094	return ret;
1095	}
1096	/// <summary>
1097	/// Subtract two values
1098	/// </summary>
1099	/// <param name="A">Minuend</param>
1100	/// <param name="B">Subtrahend</param>
1101	/// <returns>Result</returns>
1102	public static fcomplex operator -( Int64 A, fcomplex B) {
1103	fcomplex ret;
1104	ret.real = (float) (A - B.real);
1105	ret.imag = - (float) B.imag;
1106	return ret;
1107	}
1108	/// <summary>
1109	/// Multiply two values
1110	/// </summary>
1111	/// <param name="A">First factor</param>
1112	/// <param name="B">Second factor</param>
1113	/// <returns>Result</returns>
1114	public static fcomplex operator *( Int64 A, fcomplex B) {
1115	fcomplex ret;
1116	ret.real = (float) (A * B.real);
1117	ret.imag = (float) (A * B.imag);
1118	return ret;
1119	}
1120	/// <summary>
1121	/// Divide two values
1122	/// </summary>
1123	/// <param name="A">Divident</param>
1124	/// <param name="B">Divisor</param>
1125	/// <returns>Result</returns>
1126	public static fcomplex operator /( Int64 A, fcomplex B) {
1127	fcomplex ret;
1128	if (A == 0) {
1129	if (IsInfinity(B)) return NaN;
1130	} else {
1131	if (IsInfinity(B)) return ( fcomplex )0;
1132	}
1133	if (B.real == 0 && B.imag == 0) {
1134	return INF;
1135	}
1136	// this algorithm is taken from [1]. The one described in [2] was not taken. Tests
1137	// did not show any advantage when using double precision floating point arithmetic.
1138	double tmp;
1139	if (Math.Abs(B.real) >= Math.Abs(B.imag)) {
1140	tmp = (float) (B.imag * (1/B.real));
1141	ret.imag = (float) (B.real + B.imag*tmp);
1142	ret.real = (float) A/ret.imag;
1143	ret.imag = - (float) (A*tmp)/ret.imag;
1144	} else {
1145	tmp = (float) (B.real * (1/B.imag));
1146	ret.imag = (float) (B.imag + B.real*tmp);
1147	ret.real = (float) (A*tmp)/ret.imag;
1148	ret.imag = - (float) A/ret.imag;
1149	}
1150	return ret;
1151	}
1152	/// <summary>
1153	/// Equality comparison for complex numbers
1154	/// </summary>
1155	/// <param name="A">Left side</param>
1156	/// <param name="B">Right side</param>
1157	/// <returns>Result</returns>
1158	/// <remarks>Real inputs are converted to a complex number and the result is compared to the complex input.</remarks>
1159	public static bool operator ==( Int64 A, fcomplex B) {
1160	return (B.real == A && B.imag == 0.0);
1161	}
1162	/// <summary>
1163	/// Unequality comparison for complex numbers
1164	/// </summary>
1165	/// <param name="A">Left side</param>
1166	/// <param name="B">Right side</param>
1167	/// <returns>true if real and imaginary parts of A and B are not equal, false otherwise</returns>
1168	/// <remarks>Real inputs are converted to a complex number and the result is compared to the complex input.</remarks>
1169	public static bool operator !=( Int64 A, fcomplex B) {
1170	return (B.imag != 0.0) \|\| (B.real != A);
1171	}
1172	/// <summary>
1173	/// Greater than comparison for complex numbers
1174	/// </summary>
1175	/// <param name="A">Left side</param>
1176	/// <param name="B">Right side</param>
1177	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
1178	/// <remarks>Only the real parts are compared!</remarks>
1179	public static bool operator > ( Int64 A, fcomplex B) {
1180	return (A > B.real);
1181	}
1182	/// <summary>
1183	/// Lower than comparison for complex numbers
1184	/// </summary>
1185	/// <param name="A">Left side</param>
1186	/// <param name="B">Right side</param>
1187	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
1188	/// <remarks>Only the real parts are compared!</remarks>
1189	public static bool operator < ( Int64 A, fcomplex B) {
1190	return (A < B.real);
1191	}
1192	/// <summary>
1193	/// Greater than or equal to comparison for complex numbers
1194	/// </summary>
1195	/// <param name="A">Left side</param>
1196	/// <param name="B">Right side</param>
1197	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
1198	/// <remarks>Only the real parts are compared!</remarks>
1199	public static bool operator >=( Int64 A, fcomplex B) {
1200	return (A >= B.real);
1201	}
1202	/// <summary>
1203	/// Lower than or equal to comparison for complex numbers
1204	/// </summary>
1205	/// <param name="A">Left side</param>
1206	/// <param name="B">Right side</param>
1207	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
1208	/// <remarks>Only the real parts are compared!</remarks>
1209	public static bool operator <=( Int64 A, fcomplex B) {
1210	return (A <= B.real);
1211	}
1212
1213	/// <summary>
1214	/// Add two complex values
1215	/// </summary>
1216	/// <param name="A">First summand</param>
1217	/// <param name="B">Second summand</param>
1218	/// <returns>Result</returns>
1219	public static fcomplex operator +( Int32 A, fcomplex B) {
1220	fcomplex ret;
1221	ret.real = (float) (A + B.real);
1222	ret.imag = (float) B.imag;
1223	return ret;
1224	}
1225	/// <summary>
1226	/// Subtract two values
1227	/// </summary>
1228	/// <param name="A">Minuend</param>
1229	/// <param name="B">Subtrahend</param>
1230	/// <returns>Result</returns>
1231	public static fcomplex operator -( Int32 A, fcomplex B) {
1232	fcomplex ret;
1233	ret.real = (float) (A - B.real);
1234	ret.imag = - (float) B.imag;
1235	return ret;
1236	}
1237	/// <summary>
1238	/// Multiply two values
1239	/// </summary>
1240	/// <param name="A">First factor</param>
1241	/// <param name="B">Second factor</param>
1242	/// <returns>Result</returns>
1243	public static fcomplex operator *( Int32 A, fcomplex B) {
1244	fcomplex ret;
1245	ret.real = (float) (A * B.real);
1246	ret.imag = (float) (A * B.imag);
1247	return ret;
1248	}
1249	/// <summary>
1250	/// Divide two values
1251	/// </summary>
1252	/// <param name="A">Divident</param>
1253	/// <param name="B">Divisor</param>
1254	/// <returns>Result</returns>
1255	public static fcomplex operator /( Int32 A, fcomplex B) {
1256	fcomplex ret;
1257	if (A == 0) {
1258	if (IsInfinity(B)) return NaN;
1259	} else {
1260	if (IsInfinity(B)) return ( fcomplex )0;
1261	}
1262	if (B.real == 0 && B.imag == 0) {
1263	return INF;
1264	}
1265	// this algorithm is taken from [1]. The one described in [2] was not taken. Tests
1266	// did not show any advantage when using double precision floating point arithmetic.
1267	double tmp;
1268	if (Math.Abs(B.real) >= Math.Abs(B.imag)) {
1269	tmp = (float) (B.imag * (1/B.real));
1270	ret.imag = (float) (B.real + B.imag*tmp);
1271	ret.real = (float) A/ret.imag;
1272	ret.imag = - (float) (A*tmp)/ret.imag;
1273	} else {
1274	tmp = (float) (B.real * (1/B.imag));
1275	ret.imag = (float) (B.imag + B.real*tmp);
1276	ret.real = (float) (A*tmp)/ret.imag;
1277	ret.imag = - (float) A/ret.imag;
1278	}
1279	return ret;
1280	}
1281	/// <summary>
1282	/// Equality comparison for complex numbers
1283	/// </summary>
1284	/// <param name="A">Left side</param>
1285	/// <param name="B">Right side</param>
1286	/// <returns>Result</returns>
1287	/// <remarks>Real inputs are converted to a complex number and the result is compared to the complex input.</remarks>
1288	public static bool operator ==( Int32 A, fcomplex B) {
1289	return (B.real == A && B.imag == 0.0);
1290	}
1291	/// <summary>
1292	/// Unequality comparison for complex numbers
1293	/// </summary>
1294	/// <param name="A">Left side</param>
1295	/// <param name="B">Right side</param>
1296	/// <returns>true if real and imaginary parts of A and B are not equal, false otherwise</returns>
1297	/// <remarks>Real inputs are converted to a complex number and the result is compared to the complex input.</remarks>
1298	public static bool operator !=( Int32 A, fcomplex B) {
1299	return (B.imag != 0.0) \|\| (B.real != A);
1300	}
1301	/// <summary>
1302	/// Greater than comparison for complex numbers
1303	/// </summary>
1304	/// <param name="A">Left side</param>
1305	/// <param name="B">Right side</param>
1306	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
1307	/// <remarks>Only the real parts are compared!</remarks>
1308	public static bool operator > ( Int32 A, fcomplex B) {
1309	return (A > B.real);
1310	}
1311	/// <summary>
1312	/// Lower than comparison for complex numbers
1313	/// </summary>
1314	/// <param name="A">Left side</param>
1315	/// <param name="B">Right side</param>
1316	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
1317	/// <remarks>Only the real parts are compared!</remarks>
1318	public static bool operator < ( Int32 A, fcomplex B) {
1319	return (A < B.real);
1320	}
1321	/// <summary>
1322	/// Greater than or equal to comparison for complex numbers
1323	/// </summary>
1324	/// <param name="A">Left side</param>
1325	/// <param name="B">Right side</param>
1326	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
1327	/// <remarks>Only the real parts are compared!</remarks>
1328	public static bool operator >=( Int32 A, fcomplex B) {
1329	return (A >= B.real);
1330	}
1331	/// <summary>
1332	/// Lower than or equal to comparison for complex numbers
1333	/// </summary>
1334	/// <param name="A">Left side</param>
1335	/// <param name="B">Right side</param>
1336	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
1337	/// <remarks>Only the real parts are compared!</remarks>
1338	public static bool operator <=( Int32 A, fcomplex B) {
1339	return (A <= B.real);
1340	}
1341
1342	/// <summary>
1343	/// Add two complex values
1344	/// </summary>
1345	/// <param name="A">First summand</param>
1346	/// <param name="B">Second summand</param>
1347	/// <returns>Result</returns>
1348	public static fcomplex operator +( float A, fcomplex B) {
1349	fcomplex ret;
1350	ret.real = (float) (A + B.real);
1351	ret.imag = (float) B.imag;
1352	return ret;
1353	}
1354	/// <summary>
1355	/// Subtract two values
1356	/// </summary>
1357	/// <param name="A">Minuend</param>
1358	/// <param name="B">Subtrahend</param>
1359	/// <returns>Result</returns>
1360	public static fcomplex operator -( float A, fcomplex B) {
1361	fcomplex ret;
1362	ret.real = (float) (A - B.real);
1363	ret.imag = - (float) B.imag;
1364	return ret;
1365	}
1366	/// <summary>
1367	/// Multiply two values
1368	/// </summary>
1369	/// <param name="A">First factor</param>
1370	/// <param name="B">Second factor</param>
1371	/// <returns>Result</returns>
1372	public static fcomplex operator *( float A, fcomplex B) {
1373	fcomplex ret;
1374	ret.real = (float) (A * B.real);
1375	ret.imag = (float) (A * B.imag);
1376	return ret;
1377	}
1378	/// <summary>
1379	/// Divide two values
1380	/// </summary>
1381	/// <param name="A">Divident</param>
1382	/// <param name="B">Divisor</param>
1383	/// <returns>Result</returns>
1384	public static fcomplex operator /( float A, fcomplex B) {
1385	fcomplex ret;
1386	if (A == 0) {
1387	if (IsInfinity(B)) return NaN;
1388	} else {
1389	if (IsInfinity(B)) return ( fcomplex )0;
1390	}
1391	if (B.real == 0 && B.imag == 0) {
1392	return INF;
1393	}
1394	// this algorithm is taken from [1]. The one described in [2] was not taken. Tests
1395	// did not show any advantage when using double precision floating point arithmetic.
1396	double tmp;
1397	if (Math.Abs(B.real) >= Math.Abs(B.imag)) {
1398	tmp = (float) (B.imag * (1/B.real));
1399	ret.imag = (float) (B.real + B.imag*tmp);
1400	ret.real = (float) A/ret.imag;
1401	ret.imag = - (float) (A*tmp)/ret.imag;
1402	} else {
1403	tmp = (float) (B.real * (1/B.imag));
1404	ret.imag = (float) (B.imag + B.real*tmp);
1405	ret.real = (float) (A*tmp)/ret.imag;
1406	ret.imag = - (float) A/ret.imag;
1407	}
1408	return ret;
1409	}
1410	/// <summary>
1411	/// Equality comparison for complex numbers
1412	/// </summary>
1413	/// <param name="A">Left side</param>
1414	/// <param name="B">Right side</param>
1415	/// <returns>Result</returns>
1416	/// <remarks>Real inputs are converted to a complex number and the result is compared to the complex input.</remarks>
1417	public static bool operator ==( float A, fcomplex B) {
1418	return (B.real == A && B.imag == 0.0);
1419	}
1420	/// <summary>
1421	/// Unequality comparison for complex numbers
1422	/// </summary>
1423	/// <param name="A">Left side</param>
1424	/// <param name="B">Right side</param>
1425	/// <returns>true if real and imaginary parts of A and B are not equal, false otherwise</returns>
1426	/// <remarks>Real inputs are converted to a complex number and the result is compared to the complex input.</remarks>
1427	public static bool operator !=( float A, fcomplex B) {
1428	return (B.imag != 0.0) \|\| (B.real != A);
1429	}
1430	/// <summary>
1431	/// Greater than comparison for complex numbers
1432	/// </summary>
1433	/// <param name="A">Left side</param>
1434	/// <param name="B">Right side</param>
1435	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
1436	/// <remarks>Only the real parts are compared!</remarks>
1437	public static bool operator > ( float A, fcomplex B) {
1438	return (A > B.real);
1439	}
1440	/// <summary>
1441	/// Lower than comparison for complex numbers
1442	/// </summary>
1443	/// <param name="A">Left side</param>
1444	/// <param name="B">Right side</param>
1445	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
1446	/// <remarks>Only the real parts are compared!</remarks>
1447	public static bool operator < ( float A, fcomplex B) {
1448	return (A < B.real);
1449	}
1450	/// <summary>
1451	/// Greater than or equal to comparison for complex numbers
1452	/// </summary>
1453	/// <param name="A">Left side</param>
1454	/// <param name="B">Right side</param>
1455	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
1456	/// <remarks>Only the real parts are compared!</remarks>
1457	public static bool operator >=( float A, fcomplex B) {
1458	return (A >= B.real);
1459	}
1460	/// <summary>
1461	/// Lower than or equal to comparison for complex numbers
1462	/// </summary>
1463	/// <param name="A">Left side</param>
1464	/// <param name="B">Right side</param>
1465	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
1466	/// <remarks>Only the real parts are compared!</remarks>
1467	public static bool operator <=( float A, fcomplex B) {
1468	return (A <= B.real);
1469	}
1470
1471	/// <summary>
1472	/// Add two complex values
1473	/// </summary>
1474	/// <param name="A">First summand</param>
1475	/// <param name="B">Second summand</param>
1476	/// <returns>Result</returns>
1477	public static fcomplex operator +( byte A, fcomplex B) {
1478	fcomplex ret;
1479	ret.real = (float) (A + B.real);
1480	ret.imag = (float) B.imag;
1481	return ret;
1482	}
1483	/// <summary>
1484	/// Subtract two values
1485	/// </summary>
1486	/// <param name="A">Minuend</param>
1487	/// <param name="B">Subtrahend</param>
1488	/// <returns>Result</returns>
1489	public static fcomplex operator -( byte A, fcomplex B) {
1490	fcomplex ret;
1491	ret.real = (float) (A - B.real);
1492	ret.imag = - (float) B.imag;
1493	return ret;
1494	}
1495	/// <summary>
1496	/// Multiply two values
1497	/// </summary>
1498	/// <param name="A">First factor</param>
1499	/// <param name="B">Second factor</param>
1500	/// <returns>Result</returns>
1501	public static fcomplex operator *( byte A, fcomplex B) {
1502	fcomplex ret;
1503	ret.real = (float) (A * B.real);
1504	ret.imag = (float) (A * B.imag);
1505	return ret;
1506	}
1507	/// <summary>
1508	/// Divide two values
1509	/// </summary>
1510	/// <param name="A">Divident</param>
1511	/// <param name="B">Divisor</param>
1512	/// <returns>Result</returns>
1513	public static fcomplex operator /( byte A, fcomplex B) {
1514	fcomplex ret;
1515	if (A == 0) {
1516	if (IsInfinity(B)) return NaN;
1517	} else {
1518	if (IsInfinity(B)) return ( fcomplex )0;
1519	}
1520	if (B.real == 0 && B.imag == 0) {
1521	return INF;
1522	}
1523	// this algorithm is taken from [1]. The one described in [2] was not taken. Tests
1524	// did not show any advantage when using double precision floating point arithmetic.
1525	double tmp;
1526	if (Math.Abs(B.real) >= Math.Abs(B.imag)) {
1527	tmp = (float) (B.imag * (1/B.real));
1528	ret.imag = (float) (B.real + B.imag*tmp);
1529	ret.real = (float) A/ret.imag;
1530	ret.imag = - (float) (A*tmp)/ret.imag;
1531	} else {
1532	tmp = (float) (B.real * (1/B.imag));
1533	ret.imag = (float) (B.imag + B.real*tmp);
1534	ret.real = (float) (A*tmp)/ret.imag;
1535	ret.imag = - (float) A/ret.imag;
1536	}
1537	return ret;
1538	}
1539	/// <summary>
1540	/// Equality comparison for complex numbers
1541	/// </summary>
1542	/// <param name="A">Left side</param>
1543	/// <param name="B">Right side</param>
1544	/// <returns>Result</returns>
1545	/// <remarks>Real inputs are converted to a complex number and the result is compared to the complex input.</remarks>
1546	public static bool operator ==( byte A, fcomplex B) {
1547	return (B.real == A && B.imag == 0.0);
1548	}
1549	/// <summary>
1550	/// Unequality comparison for complex numbers
1551	/// </summary>
1552	/// <param name="A">Left side</param>
1553	/// <param name="B">Right side</param>
1554	/// <returns>true if real and imaginary parts of A and B are not equal, false otherwise</returns>
1555	/// <remarks>Real inputs are converted to a complex number and the result is compared to the complex input.</remarks>
1556	public static bool operator !=( byte A, fcomplex B) {
1557	return (B.imag != 0.0) \|\| (B.real != A);
1558	}
1559	/// <summary>
1560	/// Greater than comparison for complex numbers
1561	/// </summary>
1562	/// <param name="A">Left side</param>
1563	/// <param name="B">Right side</param>
1564	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
1565	/// <remarks>Only the real parts are compared!</remarks>
1566	public static bool operator > ( byte A, fcomplex B) {
1567	return (A > B.real);
1568	}
1569	/// <summary>
1570	/// Lower than comparison for complex numbers
1571	/// </summary>
1572	/// <param name="A">Left side</param>
1573	/// <param name="B">Right side</param>
1574	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
1575	/// <remarks>Only the real parts are compared!</remarks>
1576	public static bool operator < ( byte A, fcomplex B) {
1577	return (A < B.real);
1578	}
1579	/// <summary>
1580	/// Greater than or equal to comparison for complex numbers
1581	/// </summary>
1582	/// <param name="A">Left side</param>
1583	/// <param name="B">Right side</param>
1584	/// <returns>true if real part of A is greater than real part of B, false otherwise</returns>
1585	/// <remarks>Only the real parts are compared!</remarks>
1586	public static bool operator >=( byte A, fcomplex B) {
1587	return (A >= B.real);
1588	}
1589	/// <summary>
1590	/// Lower than or equal to comparison for complex numbers
1591	/// </summary>
1592	/// <param name="A">Left side</param>
1593	/// <param name="B">Right side</param>
1594	/// <returns>true if real part of A is lower then real part of B, false otherwise</returns>
1595	/// <remarks>Only the real parts are compared!</remarks>
1596	public static bool operator <=( byte A, fcomplex B) {
1597	return (A <= B.real);
1598	}
1599
1600	#endregion HYCALPER AUTO GENERATED CODE
1601
1602	#region unary minus
1603	/// <summary>
1604	/// Unary minus operator
1605	/// </summary>
1606	/// <param name="in1">fcomplex input</param>
1607	/// <returns>fcomplex number similar to in1, having real and imag part negated</returns>
1608	public static fcomplex operator -( fcomplex in1) {
1609	fcomplex ret = new fcomplex();
1610	ret.imag = -in1.imag;
1611	ret.real = -in1.real;
1612	return ret;
1613	}
1614	#endregion
1615
1616	/// <summary>
1617	/// Magnitude value of float complex number
1618	/// </summary>
1619	/// <param name="input">fcomplex number</param>
1620	/// <returns>Magnitude of input</returns>
1621	public static float Abs(fcomplex input) {
1622	return (float) Math.Sqrt ( input.real * input.real + input.imag * input.imag );
1623	}
1624	/// <summary>
1625	/// Angle of complex number
1626	/// </summary>
1627	/// <param name="input">fcomplex number to compute angle of</param>
1628	/// <returns>Angle of input</returns>
1629	public static double Angle(fcomplex input) {
1630	return (float) Math.Atan2 ( input.imag, input.real );
1631	}
1632	/// <summary>
1633	/// Arcus cosinus for float complex number
1634	/// </summary>
1635	/// <param name="input">fcomplex input</param>
1636	/// <returns>Arcus cosinus of input</returns>
1637	/// <remarks>The arcus cosinus of a complex number is computed by
1638	/// <para>Log(Sqrt(input^2 - 1) + input) * i </para></remarks>
1639	public static fcomplex Acos(fcomplex input) {
1640	fcomplex ret = new fcomplex ( 0, -1 );
1641	return fcomplex.Log ( fcomplex.Sqrt ( input * input - 1 )
1642	+ input ) * ret;
1643	}
1644	/// <summary>
1645	/// Arcus cosinus of real number
1646	/// </summary>
1647	/// <param name="input">float input</param>
1648	/// <returns>Arcus cosinus of input</returns>
1649	/// <remarks>For input > 1.0, <see cref="ILNumerics.fcomplex.Acos(fcomplex)"/> will be used. </remarks>
1650	public static fcomplex Acos(float input) {
1651	if (Math.Abs(input) <= 1.0)
1652	return new fcomplex((float)Math.Acos(input), 0.0f);
1653	else {
1654	return Acos((fcomplex)input);
1655	}
1656	}
1657	/// <summary>
1658	/// Arcus sinus of real number
1659	/// </summary>
1660	/// <param name="input">float input</param>
1661	/// <returns>Arcus sinus of input</returns>
1662	/// <remarks>For input > 1.0, <see cref="ILNumerics.fcomplex.Asin(fcomplex)"/> will be used. </remarks>
1663	public static fcomplex Asin(float input) {
1664	if (Math.Abs(input) <= 1.0)
1665	return new fcomplex((float)Math.Asin(input), 0.0f);
1666	else {
1667	return Asin((fcomplex)input);
1668	}
1669	}
1670	/// <summary>
1671	/// Arcus sinus for complex number
1672	/// </summary>
1673	/// <param name="input">fcomplex input</param>
1674	/// <returns>Arcus sinus of input</returns>
1675	public static fcomplex Asin(fcomplex input) {
1676	fcomplex ret = Acos ( input );
1677	ret.real = (float) (Math.PI / 2 - ret.real);
1678	return ret;
1679	}
1680	/// <summary>
1681	/// Power of base e for float complex number
1682	/// </summary>
1683	/// <param name="input">fcomplex input</param>
1684	/// <returns>Result of Exp(input)</returns>
1685	public static fcomplex Exp(fcomplex input) {
1686	return fcomplex.FromPol ( (float) Math.Exp ( input.real ), input.imag );
1687	}
1688	/// <summary>
1689	/// fcomplex power real exponent
1690	/// </summary>
1691	/// <param name="input">Basis </param>
1692	/// <param name="exponent">Exponent</param>
1693	/// <returns>New fcomplex number with result</returns>
1694	public static fcomplex Pow(fcomplex input, double exponent) {
1695	fcomplex ret = input.Log ();
1696	ret.imag *= (float) exponent;
1697	ret.real *= (float) exponent;
1698	return ret.Exp ();
1699	}
1700	/// <summary>
1701	/// Complex power - real basis, real exponent
1702	/// </summary>
1703	/// <param name="basis">Basis</param>
1704	/// <param name="exponent">Exponent</param>
1705	/// <returns>fcomplex number.</returns>
1706	/// <remarks>The result will be a fcomplex number. For negative basis
1707	/// the basis will be converted to a fcomplex number and the power
1708	/// will be computed in the fcomplex plane.</remarks>
1709	public static fcomplex Pow(double basis, double exponent) {
1710	if (basis < 0) {
1711	return Pow((fcomplex)basis, exponent);
1712	} else {
1713	return (fcomplex)Math.Pow(basis, exponent);
1714	}
1715	}
1716	/// <summary>
1717	/// Power: complex base, complex exponent
1718	/// </summary>
1719	/// <param name="basis">Basis</param>
1720	/// <param name="exponent">Exponent</param>
1721	/// <returns>result of basis^exponent</returns>
1722	public static fcomplex Pow(fcomplex basis, fcomplex exponent) {
1723	fcomplex ret = ( basis.Log () * exponent );
1724	return ret.Exp ();
1725	}
1726	/// <summary>
1727	/// Square root of real input
1728	/// </summary>
1729	/// <param name="input">float input</param>
1730	/// <returns>Square root of input</returns>
1731	public static fcomplex Sqrt(float input) {
1732	if (input > 0)
1733	return new fcomplex((float)Math.Sqrt(input), 0.0f);
1734	else
1735	return Sqrt((fcomplex)input);
1736	}
1737	/// <summary>
1738	/// Square root of complex number
1739	/// </summary>
1740	/// <param name="input">fcomplex input</param>
1741	/// <returns>Square root of input</returns>
1742	public static fcomplex Sqrt(fcomplex input) {
1743	// Reference : numerical recipes in C: Appendix C
1744	fcomplex ret = new fcomplex ();
1745	double x, y, w, r;
1746	if (input.real == 0.0 && input.imag == 0.0)
1747	return ret;
1748	else {
1749	x = (float) Math.Abs ( input.real );
1750	y = (float) Math.Abs ( input.imag );
1751	if (x >= y) {
1752	r = y / x;
1753	w = Math.Sqrt ( x ) * Math.Sqrt ( 0.5 * ( 1.0 + Math.Sqrt ( 1.0 + r * r ) ) );
1754	} else {
1755	r = x / y;
1756	w = Math.Sqrt ( y ) * Math.Sqrt ( 0.5 * ( r + Math.Sqrt ( 1.0 + r * r ) ) );
1757	}
1758	if (input.real >= 0.0) {
1759	ret.real = (float) w;
1760	ret.imag = (float) (input.imag / ( 2.0 * w ));
1761	} else {
1762	ret.imag = (float) (( input.imag >= 0 ) ? w : -w);
1763	ret.real = (float) (input.imag / ( 2.0 * ret.imag ));
1764	}
1765	return ret;
1766	}
1767	}
1768	/// <summary>
1769	/// Tangens of float complex number
1770	/// </summary>
1771	/// <param name="input">fcomplex input</param>
1772	/// <returns>Tangens of input</returns>
1773	public static fcomplex Tan(fcomplex input) {
1774	fcomplex ci = Cos(input);
1775	if (ci.real == (float)0.0 && ci.imag == (float)0.0)
1776	return INF;
1777	return (Sin(input) / ci);
1778	}
1779	/// <summary>
1780	/// Tangens hyperbolicus of float complex input
1781	/// </summary>
1782	/// <param name="input">fcomplex input</param>
1783	/// <returns>Tangens hyperbolicus</returns>
1784	public static fcomplex Tanh(fcomplex input) {
1785	fcomplex si = Sin(input);
1786	if (si.real == (float)0.0 && si.imag == (float)0.0)
1787	return INF;
1788	return (Cos(input) / si);
1789	}
1790	/// <summary>
1791	/// Logarithm of complex input
1792	/// </summary>
1793	/// <param name="input">fcomplex input</param>
1794	/// <returns>Logarithm of input</returns>
1795	public static fcomplex Log(fcomplex input) {
1796	fcomplex ret = new fcomplex ();
1797	ret.real = (float) Math.Log ( Math.Sqrt ( input.real * input.real + input.imag * input.imag ) );
1798	ret.imag = (float) Math.Atan2 ( input.imag, input.real );
1799	return ret;
1800	}
1801	/// <summary>
1802	/// Logarithm to base 10
1803	/// </summary>
1804	/// <param name="input">fcomplex input</param>
1805	/// <returns>Logarithm of input</returns>
1806	public static fcomplex Log10(fcomplex input) {
1807	return Log(input) / 2.30258509299405f;
1808	}
1809	/// <summary>
1810	/// Logarithm of base 2
1811	/// </summary>
1812	/// <param name="input">fcomplex input</param>
1813	/// <returns>Logarithm of input</returns>
1814	public static fcomplex Log2(fcomplex input) {
1815	return Log(input) / 0.693147180559945f;
1816	}
1817	/// <summary>
1818	/// Logarithm of real input
1819	/// </summary>
1820	/// <param name="input">float input - may be negative</param>
1821	/// <returns>Complex logarithm</returns>
1822	public static fcomplex Log(float input) {
1823	return Log (new fcomplex(input,0.0f));
1824	}
1825	/// <summary>
1826	/// Logarithm of base 10 of real input
1827	/// </summary>
1828	/// <param name="input">float input - may be negative</param>
1829	/// <returns>Complex logarithm of base 10</returns>
1830	public static fcomplex Log10(float input) {
1831	return Log(new fcomplex(input,0.0f)) / 2.30258509299405f;
1832	}
1833	/// <summary>
1834	/// Logarithm of base 2
1835	/// </summary>
1836	/// <param name="input">float input - may be negative</param>
1837	/// <returns>Complex logarithm of base 2</returns>
1838	public static fcomplex Log2(float input) {
1839	return Log(new fcomplex(input,0.0f)) / 0.693147180559945f;
1840	}
1841	/// <summary>
1842	/// Convert from polar to cartesian form
1843	/// </summary>
1844	/// <param name="magnitude">Magnitude</param>
1845	/// <param name="angle">Angle</param>
1846	/// <returns>fcomplex number with magnitude <c>magnitude</c>
1847	/// and phase <c>angle</c></returns>
1848	public static fcomplex FromPol(float magnitude, float angle) {
1849	return new fcomplex (
1850	(magnitude * (float)Math.Cos ( angle )),
1851	(magnitude * (float)Math.Sin ( angle ))
1852	);
1853	}
1854	/// <summary>
1855	/// Convert this float complex number to string
1856	/// </summary>
1857	/// <returns>String representation of this float complex number</returns>
1858	public override String ToString() {
1859	if (imag>=0)
1860	return String.Format("{0} + {1}i",real,imag);
1861	else
1862	return String.Format("{0} {1}i",real,imag);
1863	}
1864	private static string m_precSpecI = "";
1865	private static string m_precSpecR = "";
1866	private static int m_lastDigits = 0;
1867	/// <summary>
1868	/// Print formated output of this number, determine number of digits
1869	/// </summary>
1870	/// <param name="digits">Number of digits</param>
1871	/// <returns>Formatted output</returns>
1872	public string ToString(int digits) {
1873	if (digits < 1) return "";
1874	if (digits != m_lastDigits) {
1875	m_lastDigits = digits;
1876	m_precSpecR = String.Format("{{0:f{0}}}",digits);
1877	m_precSpecI = String.Format("{{1:f{0}}}i",digits);
1878	}
1879	if (imag >= 0) {
1880	return String.Format(m_precSpecR+"+"+m_precSpecI,real,imag);
1881	} else {
1882	return String.Format(m_precSpecR+m_precSpecI,real,imag);
1883	}
1884	}
1885	/// <summary>
1886	/// Magnitude of this float complex number
1887	/// </summary>
1888	/// <returns>Magnitude</returns>
1889	public float Abs() {
1890	return (float)Math.Sqrt(real * real + imag * imag);
1891	}
1892	/// <summary>
1893	/// Phase angle of this float complex number
1894	/// </summary>
1895	/// <returns>Phase angle </returns>
1896	public double Angle() {
1897	return (float)Math.Atan2(imag, real);
1898	}
1899	/// <summary>
1900	/// Arcus cosinus of this float complex number
1901	/// </summary>
1902	/// <returns>Arcus cosinus</returns>
1903	public fcomplex Acos() {
1904	fcomplex ret = new fcomplex(0, -1);
1905	return fcomplex.Log(fcomplex.Sqrt(this * this - 1)
1906	+ this) * ret;
1907	}
1908	/// <summary>
1909	/// Arcus sinus of this float complex number
1910	/// </summary>
1911	/// <returns>Arcus sinus</returns>
1912	public fcomplex Asin() {
1913	fcomplex ret = Acos(this);
1914	ret.real = (float)(Math.PI / 2 - ret.real);
1915	return ret;
1916	}
1917	/// <summary>
1918	/// Arcus tangens of float complex number
1919	/// </summary>
1920	/// <param name="input">fcomplex input</param>
1921	/// <returns>Arcus tangens of input</returns>
1922	public static fcomplex Atan(fcomplex input) {
1923	fcomplex ret = new fcomplex(0, (float)0.5);
1924	return (ret * Log((fcomplex.i + input) / (fcomplex.i - input)));
1925	}
1926	/// <summary>
1927	/// Round towards next greater integer
1928	/// </summary>
1929	/// <param name="input">fcomplex input</param>
1930	/// <returns>Rounded float complex number</returns>
1931	/// <remarks>Real and imaginary parts are independently rounded
1932	/// towards the next integer value towards positive infinity.</remarks>
1933	public static fcomplex Ceiling (fcomplex input){
1934	return new fcomplex(
1935	(float)Math.Ceiling(input.real),
1936	(float)Math.Ceiling(input.imag)
1937	);
1938	}
1939	/// <summary>
1940	/// Round towards next lower integer
1941	/// </summary>
1942	/// <param name="input">fcomplex input</param>
1943	/// <returns>Rounded float complex number</returns>
1944	/// <remarks>Real and imaginary parts are independently rounded
1945	/// towards the next integer value towards negative infinity.</remarks>
1946	public static fcomplex Floor (fcomplex input){
1947	return new fcomplex(
1948	(float)Math.Floor(input.real),
1949	(float)Math.Floor(input.imag)
1950	);
1951	}
1952	/// <summary>
1953	/// Round mercantilistic
1954	/// </summary>
1955	/// <param name="input">fcomplex number</param>
1956	/// <returns>Rounded number</returns>
1957	/// <remarks>Real and imaginaty parts are rounded independently. </remarks>
1958	public static fcomplex Round (fcomplex input){
1959	return new fcomplex(
1960	(float)Math.Round(input.real),
1961	(float)Math.Round(input.imag)
1962	);
1963	}
1964	/// <summary>
1965	/// Signum function
1966	/// </summary>
1967	/// <param name="input">fcomplex input</param>
1968	/// <returns> Signum of input</returns>
1969	/// <remarks>
1970	/// For numbers a = 0.0 + 0.0i, sign(a)'s real and imag parts are 0.0.
1971	/// For all other numbers sign(a) is the projection onto the unit circle.</remarks>
1972	public static fcomplex Sign(fcomplex input){
1973	if (input.real == 0.0 && input.imag == 0.0)
1974	return new fcomplex();
1975	else {
1976	float mag = (float)Math.Sqrt(input.real * input.real + input.imag * input.imag);
1977	return new fcomplex(
1978	input.real / mag,
1979	input.imag / mag);
1980	}
1981	}
1982	/// <summary>
1983	/// Truncate a floating point complex value
1984	/// </summary>
1985	/// <param name="input">fcomplex input</param>
1986	/// <returns>Integer part of input</returns>
1987	/// <remarks>Operates on real and imaginary parts seperately.</remarks>
1988	public static fcomplex Truncate (fcomplex input){
1989	return new fcomplex(
1990	(float)Math.Truncate(input.real),
1991	(float)Math.Truncate(input.imag)
1992	);
1993	}
1994	/// <summary>
1995	/// Cosinus
1996	/// </summary>
1997	/// <param name="input">fcomplex input</param>
1998	/// <returns>Cosinus of input</returns>
1999	/// <remarks><para>The cosinus is computed by the trigonometric euler equation: </para>
2000	/// <para>0.5 * [exp(i input) + exp(-i input)]</para></remarks>
2001	public static fcomplex Cos(fcomplex input) {
2002	fcomplex i = new fcomplex(0, 1.0f);
2003	fcomplex ni = new fcomplex(0, -1.0f);
2004	return (Exp(i * input) + Exp(ni * input)) / 2.0f;
2005	}
2006	/// <summary>
2007	/// Cosinus hyperbolicus
2008	/// </summary>
2009	/// <param name="input">fcomplex input</param>
2010	/// <returns>Cosinus hyperbolicus of input</returns>
2011	/// <remarks><para>The cosinus is computed by the trigonometric euler equation: </para>
2012	/// <para>(Exp(input) + Exp(-1.0 * input)) / 2.0</para></remarks>
2013	public static fcomplex Cosh(fcomplex input) {
2014	return (Exp(input) + Exp(-1.0f * input)) / 2.0f;
2015	}
2016	/// <summary>
2017	/// Sinus
2018	/// </summary>
2019	/// <param name="input">fcomplex input</param>
2020	/// <returns>Sinus of input</returns>
2021	/// <remarks><para>The sinus is computed by the trigonometric euler equation: </para>
2022	/// <para>(Exp(i * input) - Exp(-1.0 * i * input)) / (2.0 * i)</para></remarks>
2023	public static fcomplex Sin(fcomplex input) {
2024	fcomplex i = new fcomplex(0, (float)1.0);
2025	fcomplex mi = new fcomplex(0, (float)-1.0);
2026	return (Exp(i * input) - Exp(mi * input)) / (2.0 * i);
2027	}
2028	/// <summary>
2029	/// Sinus hyperbolicus
2030	/// </summary>
2031	/// <param name="input">fcomplex input</param>
2032	/// <returns>Sinus hyperbolicus of input</returns>
2033	/// <remarks><para>The sinus hyperbolicus is computed by the trigonometric euler equation: </para>
2034	/// <para>(Exp(input) - Exp(-1.0 * input)) / 2.0</para></remarks>
2035	public static fcomplex Sinh(fcomplex input) {
2036	fcomplex ret = new fcomplex(0, 2);
2037	fcomplex i = new fcomplex(0, (float)1.0);
2038	fcomplex mi = new fcomplex(0, (float)-1.0);
2039	return (Exp(input) - Exp(-1.0 * input)) / 2.0;
2040	}
2041	/// <summary>
2042	/// Exponential / power of base e
2043	/// </summary>
2044	/// <returns>Power of base e</returns>
2045	public fcomplex Exp() {
2046	return fcomplex.FromPol((float)Math.Exp(real), imag);
2047	}
2048	/// <summary>
2049	/// Power of fcomplex number, real exponent
2050	/// </summary>
2051	/// <param name="exponent">Exponent</param>
2052	/// <returns>New fcomplex number with result</returns>
2053	public fcomplex Pow(double exponent) {
2054	fcomplex ret = Log();
2055	ret.imag *= (float)exponent;
2056	ret.real *= (float)exponent;
2057	return ret.Exp();
2058	}
2059	/// <summary>
2060	/// Power of fcomplex number, complex exponent
2061	/// </summary>
2062	/// <param name="exponent">Exponent</param>
2063	/// <returns>New fcomplex number with result</returns>
2064	public fcomplex Pow(fcomplex exponent) {
2065	fcomplex ret = (Log() * exponent);
2066	return ret.Exp();
2067	}
2068	/// <summary>
2069	/// Square root of fcomplex number
2070	/// </summary>
2071	/// <returns>Square root</returns>
2072	public fcomplex Sqrt() {
2073	// Reference : numerical recipes in C: Appendix C
2074	fcomplex ret = new fcomplex();
2075	double x, y, w, r;
2076	if ( real == 0.0 && imag == 0.0)
2077	return ret;
2078	else {
2079	x = (float)Math.Abs(real);
2080	y = (float)Math.Abs( imag);
2081	if (x >= y) {
2082	r = y / x;
2083	w = Math.Sqrt(x) * Math.Sqrt(0.5 * (1.0 + Math.Sqrt(1.0 + r * r)));
2084	} else {
2085	r = x / y;
2086	w = Math.Sqrt(y) * Math.Sqrt(0.5 * (r + Math.Sqrt(1.0 + r * r)));
2087	}
2088	if ( real >= 0.0) {
2089	ret.real = (float)w;
2090	ret.imag = (float)( imag / (2.0 * w));
2091	} else {
2092	ret.imag = (float)(( imag >= 0) ? w : -w);
2093	ret.real = (float)( imag / (2.0 * ret.imag));
2094	}
2095	return ret;
2096	}
2097	}
2098	/// <summary>
2099	/// Logarithm of fcomplex number
2100	/// </summary>
2101	/// <returns>Natural logarithm</returns>
2102	/// <remarks>The logarithm of a complex number A is defined as follows: <br />
2103	/// <list type="none"><item>real part: log(abs(A))</item>
2104	/// <item>imag part: Atan2(imag(A),real(A))</item></list>
2105	/// </remarks>
2106	public fcomplex Log() {
2107	fcomplex ret = new fcomplex();
2108	ret.real = (float)Math.Log(Math.Sqrt( real * real + imag * imag));
2109	ret.imag = (float)Math.Atan2( imag, real);
2110	return ret;
2111	}
2112	/// <summary>
2113	/// Test if any of real or imaginary parts are NAN's
2114	/// </summary>
2115	/// <param name="input">fcomplex input</param>
2116	/// <returns>true if any of real or imag part is not a number</returns>
2117	public static bool IsNaN(fcomplex input) {
2118	if (Single.IsNaN(input.real) \|\| Single.IsNaN(input.imag))
2119	return true;
2120	else
2121	return false;
2122	}
2123	/// <summary>
2124	/// Test if any of real or imaginary parts are infinite
2125	/// </summary>
2126	/// <param name="input">fcomplex input</param>
2127	/// <returns>true if any of real or imag part is infinite</returns>
2128	public static bool IsInfinity(fcomplex input) {
2129	if (Single.IsInfinity(input.real) \|\| Single.IsInfinity(input.imag))
2130	return true;
2131	else
2132	return false;
2133	}
2134	/// <summary>
2135	/// Test if any of real or imaginary parts are pos. infinite
2136	/// </summary>
2137	/// <param name="input">fcomplex input</param>
2138	/// <returns>true if any of real or imag part is positive infinite</returns>
2139	public static bool IsPositiveInfinity(fcomplex input) {
2140	if (Single.IsPositiveInfinity(input.real) \|\| Single.IsPositiveInfinity(input.imag))
2141	return true;
2142	else
2143	return false;
2144	}
2145	/// <summary>
2146	/// Test if any of real or imaginary parts are neg. infinite
2147	/// </summary>
2148	/// <param name="input">fcomplex input</param>
2149	/// <returns>true if any of real or imag part is negative infinite</returns>
2150	public static bool IsNegativeInfinity(fcomplex input) {
2151	if (Single.IsNegativeInfinity(input.real) \|\| Single.IsNegativeInfinity(input.imag))
2152	return true;
2153	else
2154	return false;
2155	}
2156	/// <summary>
2157	/// Test if any of real or imaginary parts are finite
2158	/// </summary>
2159	/// <param name="input">fcomplex input</param>
2160	/// <returns>true if any of real and imag part is finite</returns>
2161	public static bool IsFinite (fcomplex input) {
2162	if (ILMath.isfinite(input.real) && ILMath.isfinite(input.imag))
2163	return true;
2164	else
2165	return false;
2166	}
2167
2168	#region CAST_OPERATORS
2169	/// <summary>
2170	/// Implicit cast real number into complex number
2171	/// </summary>
2172	/// <param name="a">double</param>
2173	/// <returns>fcomplex number with real part equals a</returns>
2174	public static implicit operator fcomplex(double a) {
2175	return new fcomplex((float)a, 0.0F);
2176	}
2177	/// <summary>
2178	/// Implicit cast real number into complex number
2179	/// </summary>
2180	/// <param name="a">float</param>
2181	/// <returns>fcomplex number with real part equals a</returns>
2182	public static implicit operator fcomplex(float a) {
2183	return new fcomplex(a, 0.0F);
2184	}
2185	/// <summary>
2186	/// Implicit cast real number into complex number
2187	/// </summary>
2188	/// <param name="a">byte</param>
2189	/// <returns>fcomplex number with real part equals a</returns>
2190	public static implicit operator fcomplex(byte a) {
2191	return new fcomplex(a, 0.0F);
2192	}
2193	/// <summary>
2194	/// Implicit cast real number into complex number
2195	/// </summary>
2196	/// <param name="a">char</param>
2197	/// <returns>fcomplex number with real part equals a</returns>
2198	public static implicit operator fcomplex(char a) {
2199	return new fcomplex(a, 0.0F);
2200	}
2201	/// <summary>
2202	/// Implicit cast real number into complex number
2203	/// </summary>
2204	/// <param name="a">Int16</param>
2205	/// <returns>fcomplex number with real part equals a</returns>
2206	public static implicit operator fcomplex(Int16 a) {
2207	return new fcomplex(a, 0.0F);
2208	}
2209	/// <summary>
2210	/// Implicit cast real number into complex number
2211	/// </summary>
2212	/// <param name="a">Int32</param>
2213	/// <returns>fcomplex number with real part equals a</returns>
2214	public static implicit operator fcomplex(Int32 a) {
2215	return new fcomplex((float)a, 0.0F);
2216	}
2217	/// <summary>
2218	/// Implicit cast real number into complex number
2219	/// </summary>
2220	/// <param name="a">Int64</param>
2221	/// <returns>fcomplex number with real part equals a</returns>
2222	public static implicit operator fcomplex(Int64 a) {
2223	return new fcomplex((float)a, 0.0F);
2224	}
2225	/// <summary>
2226	/// Implicit cast real number into complex number
2227	/// </summary>
2228	/// <param name="a">UInt16</param>
2229	/// <returns>fcomplex number with real part equals a</returns>
2230	public static implicit operator fcomplex(UInt16 a) {
2231	return new fcomplex((float)a, 0.0F);
2232	}
2233	/// <summary>
2234	/// Implicit cast real number into complex number
2235	/// </summary>
2236	/// <param name="a">UInt32</param>
2237	/// <returns>fcomplex number with real part equals a</returns>
2238	public static implicit operator fcomplex(UInt32 a) {
2239	return new fcomplex((float)a, 0.0F);
2240	}
2241	/// <summary>
2242	/// Implicit cast real number into complex number
2243	/// </summary>
2244	/// <param name="a">UInt64</param>
2245	/// <returns>fcomplex number with real part equals a</returns>
2246	public static implicit operator fcomplex(UInt64 a) {
2247	return new fcomplex((float)a, 0.0F);
2248	}
2249
2250	/// <summary>
2251	/// Explicit cast complex number into real number
2252	/// </summary>
2253	/// <param name="a">fcomplex number</param>
2254	/// <returns>Real number with real part of a</returns>
2255	public static explicit operator double(fcomplex a) {
2256	return a.real;
2257	}
2258	/// <summary>
2259	/// Explicit cast complex number into real number
2260	/// </summary>
2261	/// <param name="a">fcomplex number</param>
2262	/// <returns>Real number with real part of a</returns>
2263	public static explicit operator float(fcomplex a) {
2264	return (float)a.real;
2265	}
2266	/// <summary>
2267	/// Explicit cast complex number into real number
2268	/// </summary>
2269	/// <param name="a">fcomplex number</param>
2270	/// <returns>Real number with real part of a</returns>
2271	public static explicit operator byte(fcomplex a) {
2272	return (byte) a.real;
2273	}
2274	/// <summary>
2275	/// Explicit cast complex number into real number
2276	/// </summary>
2277	/// <param name="a">fcomplex number</param>
2278	/// <returns>Real number with real part of a</returns>
2279	public static explicit operator char(fcomplex a) {
2280	return (char) a.real;
2281	}
2282	/// <summary>
2283	/// Explicit cast complex number into real number
2284	/// </summary>
2285	/// <param name="a">fcomplex number</param>
2286	/// <returns>Real number with real part of a</returns>
2287	public static explicit operator Int16(fcomplex a) {
2288	return (Int16) a.real;
2289	}
2290	/// <summary>
2291	/// Explicit cast complex number into real number
2292	/// </summary>
2293	/// <param name="a">complex number</param>
2294	/// <returns>Real number with real part of a</returns>
2295	public static explicit operator Int32(fcomplex a) {
2296	return (Int32) a.real;
2297	}
2298	/// <summary>
2299	/// Explicit cast complex number into real number
2300	/// </summary>
2301	/// <param name="a">fcomplex number</param>
2302	/// <returns>Real number with real part of a</returns>
2303	public static explicit operator Int64(fcomplex a) {
2304	return (Int64) a.real;
2305	}
2306	/// <summary>
2307	/// Explicit cast complex number into real number
2308	/// </summary>
2309	/// <param name="a">fcomplex number</param>
2310	/// <returns>Real number with real part of a</returns>
2311	public static explicit operator UInt16(fcomplex a) {
2312	return (UInt16) a.real;
2313	}
2314	/// <summary>
2315	/// Explicit cast complex number into real number
2316	/// </summary>
2317	/// <param name="a">fcomplex number</param>
2318	/// <returns>Real number with real part of a</returns>
2319	public static explicit operator UInt32(fcomplex a) {
2320	return (UInt32) a.real;
2321	}
2322	/// <summary>
2323	/// Explicit cast complex number into real number
2324	/// </summary>
2325	/// <param name="a">fcomplex number</param>
2326	/// <returns>Real number with real part of a</returns>
2327	public static explicit operator UInt64(fcomplex a) {
2328	return (UInt64) a.real;
2329	}
2330	/// <summary>
2331	/// Test if real and imag part are zero
2332	/// </summary>
2333	/// <returns>true if real and imag parts are zero, false else</returns>
2334	public bool iszero() {
2335	if (real == 0.0f && imag == 0.0f)
2336	return true;
2337	else
2338	return false;
2339	}
2340	#endregion CAST_OPERATORS
2341
2342	}
2343
2344	}

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