/*
* Asymptotic expansion for ln(|B(a, b)|) for a > ASYMP_FACTOR*max(|b|, 1).
*/
static double lbeta_asymp(double a, double b, int *sgn)
{
double r = lgam_sgn(b, sgn);
r -= b * log(a);
r += b*(1-b)/(2*a);
r += b*(1-b)*(1-2*b)/(12*a*a);
r += - b*b*(1-b)*(1-b)/(12*a*a*a);
return r;
}
static double jvs(double n, double x)
{
double t, u, y, z, k;
int ex, sgngam;
z = -x * x / 4.0;
u = 1.0;
y = u;
k = 1.0;
t = 1.0;
while (t > MACHEP) {
u *= z / (k * (n + k));
y += u;
k += 1.0;
if (y != 0)
t = fabs(u / y);
}
#if CEPHES_DEBUG
printf("power series=%.5e ", y);
#endif
t = frexp(0.5 * x, &ex);
ex = ex * n;
if ((ex > -1023)
&& (ex < 1023)
&& (n > 0.0)
&& (n < (MAXGAM - 1.0))) {
t = pow(0.5 * x, n) / gamma(n + 1.0);
#if CEPHES_DEBUG
printf("pow(.5*x, %.4e)/gamma(n+1)=%.5e\n", n, t);
#endif
y *= t;
}
else {
#if CEPHES_DEBUG
z = n * log(0.5 * x);
k = lgam(n + 1.0);
t = z - k;
printf("log pow=%.5e, lgam(%.4e)=%.5e\n", z, n + 1.0, k);
#else
t = n * log(0.5 * x) - lgam_sgn(n + 1.0, &sgngam);
#endif
if (y < 0) {
sgngam = -sgngam;
y = -y;
}
t += log(y);
#if CEPHES_DEBUG
printf("log y=%.5e\n", log(y));
#endif
if (t < -MAXLOG) {
return (0.0);
}
if (t > MAXLOG) {
mtherr("Jv", OVERFLOW);
return (NPY_INFINITY);
}
y = sgngam * exp(t);
}
return (y);
}
double beta(double a, double b)
{
double y;
int sign = 1;
if (a <= 0.0) {
if (a == floor(a)) {
if (a == (int)a) {
return beta_negint((int)a, b);
}
else {
goto overflow;
}
}
}
if (b <= 0.0) {
if (b == floor(b)) {
if (b == (int)b) {
return beta_negint((int)b, a);
}
else {
goto overflow;
}
}
}
if (fabs(a) < fabs(b)) {
y = a; a = b; b = y;
}
if (fabs(a) > ASYMP_FACTOR * fabs(b) && a > ASYMP_FACTOR) {
/* Avoid loss of precision in lgam(a + b) - lgam(a) */
y = lbeta_asymp(a, b, &sign);
return sign * exp(y);
}
y = a + b;
if (fabs(y) > MAXGAM || fabs(a) > MAXGAM || fabs(b) > MAXGAM) {
int sgngam;
y = lgam_sgn(y, &sgngam);
sign *= sgngam; /* keep track of the sign */
y = lgam_sgn(b, &sgngam) - y;
sign *= sgngam;
y = lgam_sgn(a, &sgngam) + y;
sign *= sgngam;
if (y > MAXLOG) {
goto overflow;
}
return (sign * exp(y));
}
y = Gamma(y);
a = Gamma(a);
b = Gamma(b);
if (y == 0.0)
goto overflow;
if (fabs(fabs(a) - fabs(y)) > fabs(fabs(b) - fabs(y))) {
y = b / y;
y *= a;
}
else {
y = a / y;
y *= b;
}
return (y);
overflow:
mtherr("beta", OVERFLOW);
return (sign * CEPHES_INFINITY);
}