1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
|
/* fresnlf.c
*
* Fresnel integral
*
*
*
* SYNOPSIS:
*
* float x, S, C;
* void fresnlf();
*
* fresnlf( x, _&S, _&C );
*
*
* DESCRIPTION:
*
* Evaluates the Fresnel integrals
*
* x
* -
* | |
* C(x) = | cos(pi/2 t**2) dt,
* | |
* -
* 0
*
* x
* -
* | |
* S(x) = | sin(pi/2 t**2) dt.
* | |
* -
* 0
*
*
* The integrals are evaluated by power series for small x.
* For x >= 1 auxiliary functions f(x) and g(x) are employed
* such that
*
* C(x) = 0.5 + f(x) sin( pi/2 x**2 ) - g(x) cos( pi/2 x**2 )
* S(x) = 0.5 - f(x) cos( pi/2 x**2 ) - g(x) sin( pi/2 x**2 )
*
*
*
* ACCURACY:
*
* Relative error.
*
* Arithmetic function domain # trials peak rms
* IEEE S(x) 0, 10 30000 1.1e-6 1.9e-7
* IEEE C(x) 0, 10 30000 1.1e-6 2.0e-7
*/
/*
Cephes Math Library Release 2.1: January, 1989
Copyright 1984, 1987, 1989 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
#include <math.h>
/* S(x) for small x */
static float sn[7] = {
1.647629463788700E-009,
-1.522754752581096E-007,
8.424748808502400E-006,
-3.120693124703272E-004,
7.244727626597022E-003,
-9.228055941124598E-002,
5.235987735681432E-001
};
/* C(x) for small x */
static float cn[7] = {
1.416802502367354E-008,
-1.157231412229871E-006,
5.387223446683264E-005,
-1.604381798862293E-003,
2.818489036795073E-002,
-2.467398198317899E-001,
9.999999760004487E-001
};
/* Auxiliary function f(x) */
static float fn[8] = {
-1.903009855649792E+012,
1.355942388050252E+011,
-4.158143148511033E+009,
7.343848463587323E+007,
-8.732356681548485E+005,
8.560515466275470E+003,
-1.032877601091159E+002,
2.999401847870011E+000
};
/* Auxiliary function g(x) */
static float gn[8] = {
-1.860843997624650E+011,
1.278350673393208E+010,
-3.779387713202229E+008,
6.492611570598858E+006,
-7.787789623358162E+004,
8.602931494734327E+002,
-1.493439396592284E+001,
9.999841934744914E-001
};
extern float PIF, PIO2F;
#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
#ifdef ANSIC
float polevlf( float, float *, int );
float cosf(float), sinf(float);
#else
float polevlf(), cosf(), sinf();
#endif
void fresnlf( float xxa, float *ssa, float *cca )
{
float f, g, cc, ss, c, s, t, u, x, x2;
x = xxa;
x = fabsf(x);
x2 = x * x;
if( x2 < 2.5625 )
{
t = x2 * x2;
ss = x * x2 * polevlf( t, sn, 6);
cc = x * polevlf( t, cn, 6);
goto done;
}
if( x > 36974.0 )
{
cc = 0.5;
ss = 0.5;
goto done;
}
/* Asymptotic power series auxiliary functions
* for large argument
*/
x2 = x * x;
t = PIF * x2;
u = 1.0/(t * t);
t = 1.0/t;
f = 1.0 - u * polevlf( u, fn, 7);
g = t * polevlf( u, gn, 7);
t = PIO2F * x2;
c = cosf(t);
s = sinf(t);
t = PIF * x;
cc = 0.5 + (f * s - g * c)/t;
ss = 0.5 - (f * c + g * s)/t;
done:
if( xxa < 0.0 )
{
cc = -cc;
ss = -ss;
}
*cca = cc;
*ssa = ss;
#if !ANSIC
return 0;
#endif
}
|
