#include "functions.h"

static const double pi2=pi*2;
static const double pi_sur2=pi/2;
// cos (0<x<pi/2)


static double reducted_cos(const double& a)
{
    double u=1.0;
    double a2=a*a;
    // p doit toujours être un nombre impair >1
    for(int p=13;p>=1;p-=2)
        u=1-a2/(p*p+p)*u;
    return u;
}

static void modulo_2pi(double& a)
{
    while (a<=-pi2) a+=pi2;
    while (a>pi2) a-=pi2;
    return a;
}

double FE_cos(double angle)
{
    modulo_2pi(angle);
    int angle_arrondi=(int)(angle/pi_sur2);
    switch (angle_arrondi)
    {
        case -2:
        case 1:
        return -reducted_cos(angle);
        case -1:
        case 0:
        return reducted_cos(angle);
    }
}

double FE_sin(double angle)
{
    return FE_cos(angle-pi_sur2);
}