static long double ___jn(int n, double *x)
{
long double Sum;
long double Fact;
long double y;
register int i;
double xx;
long double Xi;
int My;
if (n < 0)
return n & 1 ? ___jn(-n, x) : -___jn(-n, x);
if ((x[0] >= 17.7 + 0.0144 * (n * n))) {
Xi = x[0] - M_PI * (n * 0.5 + 0.25);
My = n * n << 2;
return sqrt(M_2_PI / x[0]) * (P(My, x) * cos(Xi) - Q(My, x) * sin(Xi));
}
xx = x[0] * 0.5;
Sum = 0.;
Fact = 1.;
y = -xx * xx;
for (i = 1; i <= n; i++)
Fact *= xx / i;
for (i = 1; ; i++) {
Sum += Fact;
Fact *= y / (i * (n + i));
if (EXPL(Sum) - EXPL(Fact) > 53 || !EXPL(Fact))
break;
}
return Sum;
}
static long double ___yn(int n, double *x)
{
long double Sum1;
long double Sum2;
long double Fact1;
long double Fact2;
long double F1;
long double F2;
long double y;
register int i;
double xx;
long double Xi;
unsigned int My;
if (EXPD(x[0]) == 0)
return -1. / 0.; /* ignore the gcc warning, this is intentional */
if ((x[0] >= (n >= 32 ? 25.8 : (n < 8 ? 17.4 + 0.1 * n : 16.2 + 0.3 * n)))) {
Xi = x[0] - M_PI * (n * 0.5 + 0.25);
My = n * n << 2;
return sqrt(M_2_PI / x[0]) * (P(My, x) * sin(Xi) + Q(My, x) * cos(Xi));
}
Sum1 = Sum2 = F1 = F2 = 0;
Fact1 = 1. / (xx = x[0] * 0.5);
Fact2 = 1.;
y = xx * xx;
for (i = 1; i < n; i++)
Fact1 *= (n - i) / xx;
for (i = 1; i <= n; i++) {
Sum1 += Fact1;
if (i == n)
break;
Fact1 *= y / (i * (n - i));
}
for (i = 1; i <= n; i++) {
Fact2 *= xx / i;
F1 += 1. / i;
}
for (i = 1; ; i++) {
Sum2 += Fact2 * (F1 + F2);
Fact2 *= -y / (i * (n + i));
if (EXPL(Sum2) - EXPL(Fact2) > 53 || !EXPL(Fact2))
break;
F1 += 1. / (n + i);
F2 += 1. / i;
}
return M_1_PI * (2. * (M_C + log(xx)) * ___jn(n, x) - Sum1 - Sum2);
}
/* private */
static double _logfact(long double x)
{
static unsigned char list [] = { 6, 4, 3, 3, 2, 2 };
long double z = 2. * M_PI * x;
register int e = EXPL (x);
return (log(x) - 1) * x + 0.5 * log(z) + _poly(1. / (x * x),
e < 0x4003 ? 10 : (e > 0x4008 ? 1 : list[e - 0x4003]),
_coeff) / x;
}
static long double Q(int My, double *x)
{
long double Fact = (My - 1) / x[0] * 0.125;
long double Sum = Fact;
long double z182 = -0.015625 / (x[0] * x[0]);
register int i;
for (i = 2; ; i += 2) {
Fact *= SQUARE(i + i - 1) * SQUARE(i + i + 1) * z182 / (i * (i + 1));
if (EXPL(Fact) < 0x3FFF - 53)
break;
Sum += Fact;
}
return Sum;
}
static long double P(int My, double *x)
{
long double Sum = 0.;
long double Fact = 1.;
long double z182 = -0.015625 / (x[0] * x[0]);
register int i;
for (i = 1; ; i += 2) {
Fact *= SQUARE(i + i - 1) * SQUARE(i + i + 1) * z182 / (i * (i + 1));
if (EXPL(Fact) < 0x3FFF - 53)
break;
Sum += Fact;
}
return 1. + Sum;
}
