[2806] | 1 | /*************************************************************************
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| 2 | Cephes Math Library Release 2.8: June, 2000
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| 3 | Copyright by Stephen L. Moshier
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| 4 |
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| 5 | Contributors:
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| 6 | * Sergey Bochkanov (ALGLIB project). Translation from C to
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| 7 | pseudocode.
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| 8 |
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| 9 | See subroutines comments for additional copyrights.
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| 10 |
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| 11 | >>> SOURCE LICENSE >>>
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| 12 | This program is free software; you can redistribute it and/or modify
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| 13 | it under the terms of the GNU General Public License as published by
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| 14 | the Free Software Foundation (www.fsf.org); either version 2 of the
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| 15 | License, or (at your option) any later version.
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| 16 |
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| 17 | This program is distributed in the hope that it will be useful,
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| 18 | but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 19 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 20 | GNU General Public License for more details.
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| 21 |
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| 22 | A copy of the GNU General Public License is available at
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| 23 | http://www.fsf.org/licensing/licenses
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| 24 |
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| 25 | >>> END OF LICENSE >>>
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| 26 | *************************************************************************/
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| 27 |
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| 28 | using System;
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| 29 |
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| 30 | namespace alglib
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| 31 | {
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| 32 | public class fresnel
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| 33 | {
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| 34 | /*************************************************************************
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| 35 | Fresnel integral
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| 36 |
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| 37 | Evaluates the Fresnel integrals
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| 38 |
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| 39 | x
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| 40 | -
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| 41 | | |
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| 42 | C(x) = | cos(pi/2 t**2) dt,
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| 43 | | |
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| 44 | -
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| 45 | 0
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| 46 |
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| 47 | x
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| 48 | -
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| 49 | | |
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| 50 | S(x) = | sin(pi/2 t**2) dt.
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| 51 | | |
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| 52 | -
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| 53 | 0
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| 54 |
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| 55 |
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| 56 | The integrals are evaluated by a power series for x < 1.
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| 57 | For x >= 1 auxiliary functions f(x) and g(x) are employed
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| 58 | such that
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| 59 |
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| 60 | C(x) = 0.5 + f(x) sin( pi/2 x**2 ) - g(x) cos( pi/2 x**2 )
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| 61 | S(x) = 0.5 - f(x) cos( pi/2 x**2 ) - g(x) sin( pi/2 x**2 )
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| 62 |
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| 63 |
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| 64 |
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| 65 | ACCURACY:
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| 66 |
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| 67 | Relative error.
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| 68 |
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| 69 | Arithmetic function domain # trials peak rms
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| 70 | IEEE S(x) 0, 10 10000 2.0e-15 3.2e-16
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| 71 | IEEE C(x) 0, 10 10000 1.8e-15 3.3e-16
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| 72 |
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| 73 | Cephes Math Library Release 2.8: June, 2000
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| 74 | Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
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| 75 | *************************************************************************/
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| 76 | public static void fresnelintegral(double x,
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| 77 | ref double c,
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| 78 | ref double s)
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| 79 | {
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| 80 | double xxa = 0;
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| 81 | double f = 0;
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| 82 | double g = 0;
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| 83 | double cc = 0;
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| 84 | double ss = 0;
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| 85 | double t = 0;
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| 86 | double u = 0;
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| 87 | double x2 = 0;
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| 88 | double sn = 0;
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| 89 | double sd = 0;
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| 90 | double cn = 0;
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| 91 | double cd = 0;
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| 92 | double fn = 0;
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| 93 | double fd = 0;
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| 94 | double gn = 0;
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| 95 | double gd = 0;
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| 96 | double mpi = 0;
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| 97 | double mpio2 = 0;
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| 98 |
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| 99 | mpi = 3.14159265358979323846;
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| 100 | mpio2 = 1.57079632679489661923;
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| 101 | xxa = x;
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| 102 | x = Math.Abs(xxa);
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| 103 | x2 = x*x;
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| 104 | if( (double)(x2)<(double)(2.5625) )
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| 105 | {
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| 106 | t = x2*x2;
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| 107 | sn = -2.99181919401019853726E3;
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| 108 | sn = sn*t+7.08840045257738576863E5;
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| 109 | sn = sn*t-6.29741486205862506537E7;
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| 110 | sn = sn*t+2.54890880573376359104E9;
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| 111 | sn = sn*t-4.42979518059697779103E10;
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| 112 | sn = sn*t+3.18016297876567817986E11;
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| 113 | sd = 1.00000000000000000000E0;
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| 114 | sd = sd*t+2.81376268889994315696E2;
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| 115 | sd = sd*t+4.55847810806532581675E4;
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| 116 | sd = sd*t+5.17343888770096400730E6;
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| 117 | sd = sd*t+4.19320245898111231129E8;
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| 118 | sd = sd*t+2.24411795645340920940E10;
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| 119 | sd = sd*t+6.07366389490084639049E11;
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| 120 | cn = -4.98843114573573548651E-8;
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| 121 | cn = cn*t+9.50428062829859605134E-6;
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| 122 | cn = cn*t-6.45191435683965050962E-4;
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| 123 | cn = cn*t+1.88843319396703850064E-2;
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| 124 | cn = cn*t-2.05525900955013891793E-1;
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| 125 | cn = cn*t+9.99999999999999998822E-1;
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| 126 | cd = 3.99982968972495980367E-12;
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| 127 | cd = cd*t+9.15439215774657478799E-10;
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| 128 | cd = cd*t+1.25001862479598821474E-7;
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| 129 | cd = cd*t+1.22262789024179030997E-5;
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| 130 | cd = cd*t+8.68029542941784300606E-4;
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| 131 | cd = cd*t+4.12142090722199792936E-2;
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| 132 | cd = cd*t+1.00000000000000000118E0;
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| 133 | s = Math.Sign(xxa)*x*x2*sn/sd;
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| 134 | c = Math.Sign(xxa)*x*cn/cd;
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| 135 | return;
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| 136 | }
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| 137 | if( (double)(x)>(double)(36974.0) )
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| 138 | {
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| 139 | c = Math.Sign(xxa)*0.5;
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| 140 | s = Math.Sign(xxa)*0.5;
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| 141 | return;
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| 142 | }
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| 143 | x2 = x*x;
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| 144 | t = mpi*x2;
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| 145 | u = 1/(t*t);
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| 146 | t = 1/t;
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| 147 | fn = 4.21543555043677546506E-1;
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| 148 | fn = fn*u+1.43407919780758885261E-1;
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| 149 | fn = fn*u+1.15220955073585758835E-2;
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| 150 | fn = fn*u+3.45017939782574027900E-4;
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| 151 | fn = fn*u+4.63613749287867322088E-6;
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| 152 | fn = fn*u+3.05568983790257605827E-8;
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| 153 | fn = fn*u+1.02304514164907233465E-10;
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| 154 | fn = fn*u+1.72010743268161828879E-13;
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| 155 | fn = fn*u+1.34283276233062758925E-16;
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| 156 | fn = fn*u+3.76329711269987889006E-20;
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| 157 | fd = 1.00000000000000000000E0;
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| 158 | fd = fd*u+7.51586398353378947175E-1;
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| 159 | fd = fd*u+1.16888925859191382142E-1;
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| 160 | fd = fd*u+6.44051526508858611005E-3;
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| 161 | fd = fd*u+1.55934409164153020873E-4;
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| 162 | fd = fd*u+1.84627567348930545870E-6;
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| 163 | fd = fd*u+1.12699224763999035261E-8;
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| 164 | fd = fd*u+3.60140029589371370404E-11;
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| 165 | fd = fd*u+5.88754533621578410010E-14;
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| 166 | fd = fd*u+4.52001434074129701496E-17;
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| 167 | fd = fd*u+1.25443237090011264384E-20;
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| 168 | gn = 5.04442073643383265887E-1;
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| 169 | gn = gn*u+1.97102833525523411709E-1;
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| 170 | gn = gn*u+1.87648584092575249293E-2;
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| 171 | gn = gn*u+6.84079380915393090172E-4;
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| 172 | gn = gn*u+1.15138826111884280931E-5;
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| 173 | gn = gn*u+9.82852443688422223854E-8;
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| 174 | gn = gn*u+4.45344415861750144738E-10;
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| 175 | gn = gn*u+1.08268041139020870318E-12;
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| 176 | gn = gn*u+1.37555460633261799868E-15;
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| 177 | gn = gn*u+8.36354435630677421531E-19;
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| 178 | gn = gn*u+1.86958710162783235106E-22;
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| 179 | gd = 1.00000000000000000000E0;
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| 180 | gd = gd*u+1.47495759925128324529E0;
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| 181 | gd = gd*u+3.37748989120019970451E-1;
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| 182 | gd = gd*u+2.53603741420338795122E-2;
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| 183 | gd = gd*u+8.14679107184306179049E-4;
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| 184 | gd = gd*u+1.27545075667729118702E-5;
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| 185 | gd = gd*u+1.04314589657571990585E-7;
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| 186 | gd = gd*u+4.60680728146520428211E-10;
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| 187 | gd = gd*u+1.10273215066240270757E-12;
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| 188 | gd = gd*u+1.38796531259578871258E-15;
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| 189 | gd = gd*u+8.39158816283118707363E-19;
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| 190 | gd = gd*u+1.86958710162783236342E-22;
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| 191 | f = 1-u*fn/fd;
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| 192 | g = t*gn/gd;
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| 193 | t = mpio2*x2;
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| 194 | cc = Math.Cos(t);
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| 195 | ss = Math.Sin(t);
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| 196 | t = mpi*x;
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| 197 | c = 0.5+(f*ss-g*cc)/t;
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| 198 | s = 0.5-(f*cc+g*ss)/t;
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| 199 | c = c*Math.Sign(xxa);
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| 200 | s = s*Math.Sign(xxa);
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| 201 | }
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| 202 | }
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| 203 | }
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