自由度 df1, df2 のＦ分布において，x 以上の値をとる確率を与える関数です。

# Ｆ分布の上側確率　<a name="fxp">fxp.awk</a>

function fxp(f, df1, df2,     i1, i2, c, p, s, w, y, m2pi)
{
   m2pi = 0.636619772367581343076
   m_pi = 3.14159265358979323846
   i1 = 2-(df1%2)
   i2 = 2-(df2%2)
   w = df2/(df2+df1*f)
   y = 1.0-w
   p = sqrt(w)
   s = sqrt(y)
   if (2*i1-i2 == 0) {
       p = 1.0-s
       c = s*w/2.0
   }
   else if (2*i1-i2 == 1) {
       c = s*p/m_pi
       p = 1.0-atan2(s, p)*m2pi
   }
   else if (2*i1-i2 == 2) {
       p = w
       c = w*y
   }
   else {
       c = y*p/2.0
   }
   for (; df2 > i2; i2 += 2) {
       p -= 2.0/i2*c
       c *= w*(i1+i2)/i2
   }
   for (; df1 > i1; i1 += 2) {
       p += 2.0/i1*c
       c *= y*(i1+i2)/i1
   }
   return (p < 0.0 && abs(p) < 1e-10) ? 0.0 : p
}