1 files changed, 154 insertions, 0 deletions
diff --git a/libm/float/stdtrf.c b/libm/float/stdtrf.c
new file mode 100644
index 000000000..76b14c1f6
--- /dev/null
+++ b/libm/float/stdtrf.c
@@ -0,0 +1,154 @@
+/*							stdtrf.c
+ *
+ *	Student's t distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float t, stdtrf();
+ * short k;
+ *
+ * y = stdtrf( k, t );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the integral from minus infinity to t of the Student
+ * t distribution with integer k > 0 degrees of freedom:
+ *
+ *                                      t
+ *                                      -
+ *                                     | |
+ *              -                      |         2   -(k+1)/2
+ *             | ( (k+1)/2 )           |  (     x   )
+ *       ----------------------        |  ( 1 + --- )        dx
+ *                     -               |  (      k  )
+ *       sqrt( k pi ) | ( k/2 )        |
+ *                                   | |
+ *                                    -
+ *                                   -inf.
+ * 
+ * Relation to incomplete beta integral:
+ *
+ *        1 - stdtr(k,t) = 0.5 * incbet( k/2, 1/2, z )
+ * where
+ *        z = k/(k + t**2).
+ *
+ * For t < -1, this is the method of computation.  For higher t,
+ * a direct method is derived from integration by parts.
+ * Since the function is symmetric about t=0, the area under the
+ * right tail of the density is found by calling the function
+ * with -t instead of t.
+ * 
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      +/- 100      5000       2.3e-5      2.9e-6
+ */
+
+
+/*
+Cephes Math Library Release 2.2:  July, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+extern float PIF, MACHEPF;
+
+#ifdef ANSIC
+float sqrtf(float), atanf(float), incbetf(float, float, float);
+#else
+float sqrtf(), atanf(), incbetf();
+#endif
+
+
+
+float stdtrf( int k, float tt )
+{
+float t, x, rk, z, f, tz, p, xsqk;
+int j;
+
+t = tt;
+if( k <= 0 )
+	{
+	mtherr( "stdtrf", DOMAIN );
+	return(0.0);
+	}
+
+if( t == 0 )
+	return( 0.5 );
+
+if( t < -1.0 )
+	{
+	rk = k;
+	z = rk / (rk + t * t);
+	p = 0.5 * incbetf( 0.5*rk, 0.5, z );
+	return( p );
+	}
+
+/*	compute integral from -t to + t */
+
+if( t < 0 )
+	x = -t;
+else
+	x = t;
+
+rk = k;	/* degrees of freedom */
+z = 1.0 + ( x * x )/rk;
+
+/* test if k is odd or even */
+if( (k & 1) != 0)
+	{
+
+	/*	computation for odd k	*/
+
+	xsqk = x/sqrtf(rk);
+	p = atanf( xsqk );
+	if( k > 1 )
+		{
+		f = 1.0;
+		tz = 1.0;
+		j = 3;
+		while(  (j<=(k-2)) && ( (tz/f) > MACHEPF )  )
+			{
+			tz *= (j-1)/( z * j );
+			f += tz;
+			j += 2;
+			}
+		p += f * xsqk/z;
+		}
+	p *= 2.0/PIF;
+	}
+
+
+else
+	{
+
+	/*	computation for even k	*/
+
+	f = 1.0;
+	tz = 1.0;
+	j = 2;
+
+	while(  ( j <= (k-2) ) && ( (tz/f) > MACHEPF )  )
+		{
+		tz *= (j - 1)/( z * j );
+		f += tz;
+		j += 2;
+		}
+	p = f * x/sqrtf(z*rk);
+	}
+
+/*	common exit	*/
+
+
+if( t < 0 )
+	p = -p;	/* note destruction of relative accuracy */
+
+	p = 0.5 + 0.5 * p;
+return(p);
+}