| Pré. | Proc. |
fresnl
Fresnel integral.SYNOPSIS:
double x, S, C;
void fresnl();
fresnl(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 a power series for x < 1. 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 10000 2.0e-15 3.2e-16
IEEE C(x) 0, 10 10000 1.8e-15 3.3e-16
DEC S(x) 0, 10 6000 2.2e-16 3.9e-17
DEC C(x) 0, 10 5000 2.3e-16 3.9e-17
JavaScript:
var x= 2.5625;
var r = cephes.fresnl(x);
Session,Output(r.result);
Session,Output(r.ssa);
Session,Output(r.csa);
Return value: Object
Format: JSON
{
"result" : int,
"ssa" : double,
"cca" : double
}