fresnel.cpp File Reference

#include "math-precomp.h"
#include <mrpt/math/fresnel.h>
#include <cfloat>
#include <cmath>

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Macros
#define	NUM_ASYMPTOTIC_TERMS   35
#define	NUM_ASYMPTOTIC_TERMS   35

Functions
static long double	Power_Series_S (long double x)
static long double	xFresnel_Auxiliary_Cosine_Integral (long double x)
static long double	xFresnel_Auxiliary_Sine_Integral (long double x)
static long double	Power_Series_C (long double x)
static long double	xChebyshev_Tn_Series (long double x, const long double a[], int degree)
long double	lfresnel_sin_alt (long double x)
long double	lfresnel_cos_alt (long double x)
double	Fresnel_Sine_Integral (double x)
long double	xFresnel_Sine_Integral (long double x)
double	Fresnel_Auxiliary_Sine_Integral (double x)
static long double	sin_Chebyshev_Expansion_0_1 (long double x)
static long double	sin_Chebyshev_Expansion_1_3 (long double x)
static long double	sin_Chebyshev_Expansion_3_5 (long double x)
static long double	sin_Chebyshev_Expansion_5_7 (long double x)
static long double	sin_Asymptotic_Series (long double x)
double	Fresnel_Auxiliary_Cosine_Integral (double x)
static long double	cos_Chebyshev_Expansion_0_1 (long double x)
static long double	cos_Chebyshev_Expansion_1_3 (long double x)
static long double	cos_Chebyshev_Expansion_3_5 (long double x)
static long double	cos_Chebyshev_Expansion_5_7 (long double x)
static long double	cos_Asymptotic_Series (long double x)
double	Fresnel_Cosine_Integral (double x)
long double	xFresnel_Cosine_Integral (long double x)

Variables
static long double const	sqrt_2pi = 2.506628274631000502415765284811045253006L

Macro Definition Documentation

NUM_ASYMPTOTIC_TERMS [1/2]

#define NUM_ASYMPTOTIC_TERMS   35

Definition at line 981 of file fresnel.cpp.

Referenced by cos_Asymptotic_Series(), and sin_Asymptotic_Series().

NUM_ASYMPTOTIC_TERMS [2/2]

#define NUM_ASYMPTOTIC_TERMS   35

Definition at line 981 of file fresnel.cpp.

Function Documentation

cos_Asymptotic_Series()

static long double cos_Asymptotic_Series ( long double  x )

static

Definition at line 982 of file fresnel.cpp.

References mrpt::math::factorial(), NUM_ASYMPTOTIC_TERMS, and sqrt_2pi.

Referenced by xFresnel_Auxiliary_Cosine_Integral().

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cos_Chebyshev_Expansion_0_1()

static long double cos_Chebyshev_Expansion_0_1 ( long double  x )

static

Definition at line 802 of file fresnel.cpp.

References xChebyshev_Tn_Series().

Referenced by xFresnel_Auxiliary_Cosine_Integral().

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cos_Chebyshev_Expansion_1_3()

static long double cos_Chebyshev_Expansion_1_3 ( long double  x )

static

Definition at line 847 of file fresnel.cpp.

References xChebyshev_Tn_Series().

Referenced by xFresnel_Auxiliary_Cosine_Integral().

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cos_Chebyshev_Expansion_3_5()

static long double cos_Chebyshev_Expansion_3_5 ( long double  x )

static

Definition at line 893 of file fresnel.cpp.

References xChebyshev_Tn_Series().

Referenced by xFresnel_Auxiliary_Cosine_Integral().

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cos_Chebyshev_Expansion_5_7()

static long double cos_Chebyshev_Expansion_5_7 ( long double  x )

static

Definition at line 937 of file fresnel.cpp.

References xChebyshev_Tn_Series().

Referenced by xFresnel_Auxiliary_Cosine_Integral().

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Fresnel_Auxiliary_Cosine_Integral()

double Fresnel_Auxiliary_Cosine_Integral

(

double

x

)

Definition at line 545 of file fresnel.cpp.

References xFresnel_Auxiliary_Cosine_Integral().

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Fresnel_Auxiliary_Sine_Integral()

double Fresnel_Auxiliary_Sine_Integral

(

double

x

)

Definition at line 232 of file fresnel.cpp.

References xFresnel_Auxiliary_Sine_Integral().

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Fresnel_Cosine_Integral()

double Fresnel_Cosine_Integral

(

double

x

)

Definition at line 619 of file fresnel.cpp.

References xFresnel_Cosine_Integral().

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Fresnel_Sine_Integral()

double Fresnel_Sine_Integral

(

double

x

)

Definition at line 105 of file fresnel.cpp.

References xFresnel_Sine_Integral().

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lfresnel_cos_alt()

long double lfresnel_cos_alt

(

long double

x

)

Definition at line 43 of file fresnel.cpp.

References Power_Series_C(), xFresnel_Auxiliary_Cosine_Integral(), and xFresnel_Auxiliary_Sine_Integral().

Referenced by mrpt::math::lfresnel_cos_integral().

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lfresnel_sin_alt()

long double lfresnel_sin_alt

(

long double

x

)

Definition at line 29 of file fresnel.cpp.

References Power_Series_S(), xFresnel_Auxiliary_Cosine_Integral(), and xFresnel_Auxiliary_Sine_Integral().

Referenced by mrpt::math::lfresnel_sin_integral().

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Power_Series_C()

static long double Power_Series_C ( long double  x )

static

Definition at line 686 of file fresnel.cpp.

References mrpt::math::factorial().

Referenced by lfresnel_cos_alt(), and xFresnel_Cosine_Integral().

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Power_Series_S()

static long double Power_Series_S ( long double  x )

static

Definition at line 172 of file fresnel.cpp.

References mrpt::math::factorial().

Referenced by lfresnel_sin_alt(), and xFresnel_Sine_Integral().

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sin_Asymptotic_Series()

static long double sin_Asymptotic_Series ( long double  x )

static

Definition at line 484 of file fresnel.cpp.

References mrpt::math::factorial(), NUM_ASYMPTOTIC_TERMS, and sqrt_2pi.

Referenced by xFresnel_Auxiliary_Sine_Integral().

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sin_Chebyshev_Expansion_0_1()

static long double sin_Chebyshev_Expansion_0_1 ( long double  x )

static

Definition at line 301 of file fresnel.cpp.

References xChebyshev_Tn_Series().

Referenced by xFresnel_Auxiliary_Sine_Integral().

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sin_Chebyshev_Expansion_1_3()

static long double sin_Chebyshev_Expansion_1_3 ( long double  x )

static

Definition at line 346 of file fresnel.cpp.

References xChebyshev_Tn_Series().

Referenced by xFresnel_Auxiliary_Sine_Integral().

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sin_Chebyshev_Expansion_3_5()

static long double sin_Chebyshev_Expansion_3_5 ( long double  x )

static

Definition at line 393 of file fresnel.cpp.

References xChebyshev_Tn_Series().

Referenced by xFresnel_Auxiliary_Sine_Integral().

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sin_Chebyshev_Expansion_5_7()

static long double sin_Chebyshev_Expansion_5_7 ( long double  x )

static

Definition at line 438 of file fresnel.cpp.

References xChebyshev_Tn_Series().

Referenced by xFresnel_Auxiliary_Sine_Integral().

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xChebyshev_Tn_Series()

static long double xChebyshev_Tn_Series ( long double  x, const long double  a[], int  degree  )

static

Definition at line 756 of file fresnel.cpp.

Referenced by cos_Chebyshev_Expansion_0_1(), cos_Chebyshev_Expansion_1_3(), cos_Chebyshev_Expansion_3_5(), cos_Chebyshev_Expansion_5_7(), sin_Chebyshev_Expansion_0_1(), sin_Chebyshev_Expansion_1_3(), sin_Chebyshev_Expansion_3_5(), and sin_Chebyshev_Expansion_5_7().

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xFresnel_Auxiliary_Cosine_Integral()

long double xFresnel_Auxiliary_Cosine_Integral ( long double  x )

static

Definition at line 580 of file fresnel.cpp.

References cos_Asymptotic_Series(), cos_Chebyshev_Expansion_0_1(), cos_Chebyshev_Expansion_1_3(), cos_Chebyshev_Expansion_3_5(), and cos_Chebyshev_Expansion_5_7().

Referenced by Fresnel_Auxiliary_Cosine_Integral(), lfresnel_cos_alt(), lfresnel_sin_alt(), xFresnel_Cosine_Integral(), and xFresnel_Sine_Integral().

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xFresnel_Auxiliary_Sine_Integral()

long double xFresnel_Auxiliary_Sine_Integral ( long double  x )

static

Definition at line 268 of file fresnel.cpp.

References sin_Asymptotic_Series(), sin_Chebyshev_Expansion_0_1(), sin_Chebyshev_Expansion_1_3(), sin_Chebyshev_Expansion_3_5(), and sin_Chebyshev_Expansion_5_7().

Referenced by Fresnel_Auxiliary_Sine_Integral(), lfresnel_cos_alt(), lfresnel_sin_alt(), xFresnel_Cosine_Integral(), and xFresnel_Sine_Integral().

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xFresnel_Cosine_Integral()

long double xFresnel_Cosine_Integral

(

long double

x

)

Definition at line 646 of file fresnel.cpp.

References Power_Series_C(), xFresnel_Auxiliary_Cosine_Integral(), and xFresnel_Auxiliary_Sine_Integral().

Referenced by Fresnel_Cosine_Integral().

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xFresnel_Sine_Integral()

long double xFresnel_Sine_Integral

(

long double

x

)

Definition at line 132 of file fresnel.cpp.

References Power_Series_S(), xFresnel_Auxiliary_Cosine_Integral(), and xFresnel_Auxiliary_Sine_Integral().

Referenced by Fresnel_Sine_Integral().

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Variable Documentation

sqrt_2pi

long double const sqrt_2pi = 2.506628274631000502415765284811045253006L

static

Definition at line 206 of file fresnel.cpp.

Referenced by cos_Asymptotic_Series(), and sin_Asymptotic_Series().