inline long double ibeta(long double a, long double b, long double x)
{
#ifdef BOOST_MSVC
return incbet((double)a, (double)b, (double)x);
#else
return incbetl(a, b);
#endif
}
double fdtrc(double a, double b, double x)
{
double w;
if ((a <= 0.0) || (b <= 0.0) || (x < 0.0)) {
mtherr("fdtrc", DOMAIN);
return CEPHES_NAN;
}
w = b / (b + a * x);
return incbet(0.5 * b, 0.5 * a, w);
}
double fdtr(double a, double b, double x)
{
double w;
if ((a <= 0.0) || (b <= 0.0) || (x < 0.0)) {
mtherr("fdtr", DOMAIN);
return CEPHES_NAN;
}
w = a * x;
w = w / (b + w);
return incbet(0.5 * a, 0.5 * b, w);
}
double fdtri(double a, double b, double y)
{
double w, x;
if ((a <= 0.0) || (b <= 0.0) || (y <= 0.0) || (y > 1.0)) {
mtherr("fdtri", DOMAIN);
return CEPHES_NAN;
}
y = 1.0 - y;
/* Compute probability for x = 0.5. */
w = incbet(0.5 * b, 0.5 * a, 0.5);
/* If that is greater than y, then the solution w < .5.
* Otherwise, solve at 1-y to remove cancellation in (b - b*w). */
if (w > y || y < 0.001) {
w = incbi(0.5 * b, 0.5 * a, y);
x = (b - b * w) / (a * w);
}
else {
w = incbi(0.5 * a, 0.5 * b, 1.0 - y);
x = b * w / (a * (1.0 - w));
}
return x;
}
double btdtr( double a, double b, double x )
{
return( incbet( a, b, x ) );
}
inline double ibeta(double a, double b, double x)
{ return incbet(a, b, x); }
double stdtr (double rk, double t)
{
double x, z, f, tz, p, xsqk;
int k, j, is_int;
if (rk <= 0) {
mtherr("stdtr", CEPHES_DOMAIN);
return 0.0;
} else {
k = (int) rk;
is_int = (rk - k) == 0.0;
}
if (t == 0) {
return 0.5;
}
if (t < -2.0) {
z = rk / (rk + t * t);
p = 0.5 * incbet(0.5*rk, 0.5, z);
return p;
}
if (is_int) {
/* integer df */
/* compute integral from -t to +t */
if (t < 0) {
x = -t;
} else {
x = t;
}
z = 1.0 + (x * x)/rk;
/* test if k is odd or even */
if ((k & 1) != 0) {
/* computation for odd k */
xsqk = x/sqrt(rk);
p = atan(xsqk);
if (k > 1) {
f = 1.0;
tz = 1.0;
j = 3;
while ((j <= (k-2)) && ((tz/f) > MACHEP)) {
tz *= (j - 1)/(z * j);
f += tz;
j += 2;
}
p += f * xsqk/z;
}
p *= 2.0/PI;
} else {
/* computation for even k */
f = 1.0;
tz = 1.0;
j = 2;
while ((j <= (k-2)) && ((tz/f) > MACHEP)) {
tz *= (j - 1)/(z * j);
f += tz;
j += 2;
}
p = f * x/sqrt(z*rk);
}
/* common exit */
if (t < 0) {
p = -p; /* note destruction of relative accuracy */
}
p = 0.5 + 0.5 * p;
} else {
/* non-integer df */
z = rk / (rk + t * t);
p = 0.5 * incbet(0.5*rk, 0.5, z);
if (t > 0) {
p = 1-p;
}
}
return p;
}