summaryrefslogtreecommitdiff
path: root/libm/float/psif.c
diff options
context:
space:
mode:
Diffstat (limited to 'libm/float/psif.c')
-rw-r--r--libm/float/psif.c153
1 files changed, 0 insertions, 153 deletions
diff --git a/libm/float/psif.c b/libm/float/psif.c
deleted file mode 100644
index 2d9187c67..000000000
--- a/libm/float/psif.c
+++ /dev/null
@@ -1,153 +0,0 @@
-/* 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);
-}