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/*							psi.c
 *
 *	Psi (digamma) function
 *
 *
 * SYNOPSIS:
 *
 * double x, y, psi();
 *
 * y = psi( x );
 *
 *
 * DESCRIPTION:
 *
 *              d      -
 *   psi(x)  =  -- ln | (x)
 *              dx
 *
 * is the logarithmic derivative of the md_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) = md_log(x) - 1/2x -   >   -------
 *                            -        2k
 *                           k=1   2k x
 *
 * where the B2k are Bernoulli numbers.
 *
 * ACCURACY:
 *    Relative error (except absolute when |psi| < 1):
 * arithmetic   domain     # trials      peak         rms
 *    DEC       0,30         2500       1.7e-16     2.0e-17
 *    IEEE      0,30        30000       1.3e-15     1.4e-16
 *    IEEE      -30,0       40000       1.5e-15     2.2e-16
 *
 * ERROR MESSAGES:
 *     message         condition      value returned
 * psi singularity    x integer <=0      MAXNUM
 */

/*
Cephes Math Library Release 2.8:  June, 2000
Copyright 1984, 1987, 1992, 2000 by Stephen L. Moshier
*/

#include "mconf.h"

#ifdef UNK
static double A[] = {
 8.33333333333333333333E-2,
-2.10927960927960927961E-2,
 7.57575757575757575758E-3,
-4.16666666666666666667E-3,
 3.96825396825396825397E-3,
-8.33333333333333333333E-3,
 8.33333333333333333333E-2
};
#endif

#ifdef DEC
static unsigned short A[] = {
0037252,0125252,0125252,0125253,
0136654,0145314,0126312,0146255,
0036370,0037017,0101740,0174076,
0136210,0104210,0104210,0104211,
0036202,0004040,0101010,0020202,
0136410,0104210,0104210,0104211,
0037252,0125252,0125252,0125253
};
#endif

#ifdef IBMPC
static unsigned short A[] = {
0x5555,0x5555,0x5555,0x3fb5,
0x5996,0x9599,0x9959,0xbf95,
0x1f08,0xf07c,0x07c1,0x3f7f,