From 1077fa4d772832f77a677ce7fb7c2d513b959e3f Mon Sep 17 00:00:00 2001
From: Eric Andersen <andersen@codepoet.org>
Date: Thu, 10 May 2001 00:40:28 +0000
Subject: uClibc now has a math library.  muahahahaha!  -Erik

---
 libm/float/psif.c | 153 ++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 153 insertions(+)
 create mode 100644 libm/float/psif.c

(limited to 'libm/float/psif.c')

diff --git a/libm/float/psif.c b/libm/float/psif.c
new file mode 100644
index 000000000..2d9187c67
--- /dev/null
+++ b/libm/float/psif.c
@@ -0,0 +1,153 @@
+/*							psif.c
+ *
+ *	Psi (digamma) function
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, psif();
+ *
+ * y = psif( x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ *              d      -
+ *   psi(x)  =  -- ln | (x)
+ *              dx
+ *
+ * is the logarithmic derivative of the gamma function.
+ * For integer x,
+ *                   n-1
+ *                    -
+ * psi(n) = -EUL  +   >  1/k.
+ *                    -
+ *                   k=1
+ *
+ * This formula is used for 0 < n <= 10.  If x is negative, it
+ * is transformed to a positive argument by the reflection
+ * formula  psi(1-x) = psi(x) + pi cot(pi x).
+ * For general positive x, the argument is made greater than 10
+ * using the recurrence  psi(x+1) = psi(x) + 1/x.
+ * Then the following asymptotic expansion is applied:
+ *
+ *                           inf.   B
+ *                            -      2k
+ * psi(x) = log(x) - 1/2x -   >   -------
+ *                            -        2k
+ *                           k=1   2k x
+ *
+ * where the B2k are Bernoulli numbers.
+ *
+ * ACCURACY:
+ *    Absolute error,  relative when |psi| > 1 :
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -33,0        30000      8.2e-7      1.2e-7
+ *    IEEE      0,33        100000      7.3e-7      7.7e-8
+ *
+ * ERROR MESSAGES:
+ *     message         condition      value returned
+ * psi singularity    x integer <=0      MAXNUMF
+ */
+
+/*
+Cephes Math Library Release 2.2:  June, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+
+static float A[] = {
+-4.16666666666666666667E-3,
+ 3.96825396825396825397E-3,
+-8.33333333333333333333E-3,
+ 8.33333333333333333333E-2
+};
+
+
+#define EUL 0.57721566490153286061
+
+extern float PIF, MAXNUMF;
+
+
+
+float floorf(float), logf(float), tanf(float);
+float polevlf(float, float *, int);
+
+float psif(float xx)
+{
+float p, q, nz, x, s, w, y, z;
+int i, n, negative;
+
+
+x = xx;
+nz = 0.0;
+negative = 0;
+if( x <= 0.0 )
+	{
+	negative = 1;
+	q = x;
+	p = floorf(q);
+	if( p == q )
+		{
+		mtherr( "psif", SING );
+		return( MAXNUMF );
+		}
+	nz = q - p;
+	if( nz != 0.5 )
+		{
+		if( nz > 0.5 )
+			{
+			p += 1.0;
+			nz = q - p;
+			}
+		nz = PIF/tanf(PIF*nz);
+		}
+	else
+		{
+		nz = 0.0;
+		}
+	x = 1.0 - x;
+	}
+
+/* check for positive integer up to 10 */
+if( (x <= 10.0) && (x == floorf(x)) )
+	{
+	y = 0.0;
+	n = x;
+	for( i=1; i<n; i++ )
+		{
+		w = i;
+		y += 1.0/w;
+		}
+	y -= EUL;
+	goto done;
+	}
+
+s = x;
+w = 0.0;
+while( s < 10.0 )
+	{
+	w += 1.0/s;
+	s += 1.0;
+	}
+
+if( s < 1.0e8 )
+	{
+	z = 1.0/(s * s);
+	y = z * polevlf( z, A, 3 );
+	}
+else
+	y = 0.0;
+
+y = logf(s)  -  (0.5/s)  -  y  -  w;
+
+done:
+if( negative )
+	{
+	y -= nz;
+	}
+return(y);
+}
-- 
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