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UT_Erf.h
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1 /*
2  * PROPRIETARY INFORMATION. This software is proprietary to
3  * Side Effects Software Inc., and is not to be reproduced,
4  * transmitted, or disclosed in any way without written permission.
5  *
6  * NAME: UT_Erf.h (UT Library, C++)
7  *
8  * COMMENTS:
9  * Functions for evaluating erf(), and related functions, in the complex
10  * plane.
11  */
12 
13 #ifndef __UT_Erf__
14 #define __UT_Erf__
15 
16 #include "UT_API.h"
17 
18 #include <SYS/SYS_Types.h>
19 
20 #include "UT_Complex.h"
21 
22 
23 /// Returns the value of Dawson's function:
24 ///
25 /// F(x) = exp(-x^2) * int(exp(y^2), y, 0, x).
26 ///
27 /// evaluated in the complex plane. Accuracy increases as niters increases.
28 /// Note that niters must be odd.
29 UT_API UT_Complex UTdawson(const UT_Complex &z, int niters = 35);
30 
31 /// Returns the evaluation of erf(x), where x is real-valued.
33 
34 /// Returns the evaluation of erf(z) given a very small number, eps, which
35 /// controls the accuracy of the result, and an upper bound on the number of
36 /// iterations allowed, niters. This function evaluates a continued fraction
37 /// representation of erf.
39  const UT_Complex &z,
40  fpreal eps = 1e-15,
41  int niters = 1000);
42 
43 /// Returns the evaluation of erfi(x).
45 
46 #endif
47 
UT_API UT_Complex UTdawson(const UT_Complex &z, int niters=35)
GLdouble GLdouble GLdouble z
Definition: glcorearb.h:847
#define UT_API
Definition: UT_API.h:12
UT_API fpreal UTerf(fpreal x)
Returns the evaluation of erf(x), where x is real-valued.
UT_API UT_Complex UTerfi(fpreal x)
Returns the evaluation of erfi(x).
double fpreal
Definition: SYS_Types.h:269
GLint GLenum GLint x
Definition: glcorearb.h:408