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/* Double precision version of the routine in ALGAMA from the netlib */
/* SPECFUN library. Translated by f2c and modified. */
#include "xlisp.h"
#include "xlstat.h"
double gamma P1C(double, x)
{
/* Local variables */
double xden, corr, xnum;
int i;
double y, xm1, xm2, xm4, res, ysq;
/* ---------------------------------------------------------------------- */
/* This routine calculates the LOG(GAMMA) function for a positive real */
/* argument X. Computation is based on an algorithm outlined in */
/* references 1 and 2. The program uses rational functions that */
/* theoretically approximate LOG(GAMMA) to at least 18 significant */
/* decimal digits. The approximation for X > 12 is from reference */
/* 3, while approximations for X < 12.0 are similar to those in */
/* reference 1, but are unpublished. The accuracy achieved depends */
/* on the arithmetic system, the compiler, the intrinsic functions, */
/* and proper selection of the machine-dependent constants. */
/* ********************************************************************* */
/* ********************************************************************* */
/* Explanation of machine-dependent constants */
/* beta - radix for the floating-point representation */
/* maxexp - the smallest positive power of beta that overflows */
/* XBIG - largest argument for which LN(GAMMA(X)) is representable */
/* in the machine, i.e., the solution to the equation */
/* LN(GAMMA(XBIG)) = beta**maxexp */
/* XINF - largest machine representable floating-point number; */
/* approximately beta**maxexp. */
/* EPS - The smallest positive floating-point number such that */
/* 1.0+EPS .GT. 1.0 */
/* FRTBIG - Rough estimate of the fourth root of XBIG */
/* Approximate values for some important machines are: */
/* beta maxexp XBIG */
/* CRAY-1 (S.P.) 2 8191 9.62E+2461 */
/* Cyber 180/855 */
/* under NOS (S.P.) 2 1070 1.72E+319 */
/* IEEE (IBM/XT, */
/* SUN, etc.) (S.P.) 2 128 4.08E+36 */
/* IEEE (IBM/XT, */
/* SUN, etc.) (D.P.) 2 1024 2.55D+305 */
/* IBM 3033 (D.P.) 16 63 4.29D+73 */
/* VAX D-Format (D.P.) 2 127 2.05D+36 */
/* VAX G-Format (D.P.) 2 1023 1.28D+305 */
/* XINF EPS FRTBIG */
/* CRAY-1 (S.P.) 5.45E+2465 7.11E-15 3.13E+615 */
/* Cyber 180/855 */
/* under NOS (S.P.) 1.26E+322 3.55E-15 6.44E+79 */
/* IEEE (IBM/XT, */
/* SUN, etc.) (S.P.) 3.40E+38 1.19E-7 1.42E+9 */
/* IEEE (IBM/XT, */
/* SUN, etc.) (D.P.) 1.79D+308 2.22D-16 2.25D+76 */
/* IBM 3033 (D.P.) 7.23D+75 2.22D-16 2.56D+18 */
/* VAX D-Format (D.P.) 1.70D+38 1.39D-17 1.20D+9 */
/* VAX G-Format (D.P.) 8.98D+307 1.11D-16 1.89D+76 */
/* ************************************************************** */
/* ************************************************************** */
/* Error returns */
/* The program returns the value XINF for X .LE. 0.0 or when */
/* overflow would occur. The computation is believed to */
/* be free of underflow and overflow. */
/* Intrinsic functions required are: */
/* LOG */
/* References: */
/* 1) W. J. Cody and K. E. Hillstrom, 'Chebyshev Approximations for */
/* the Natural Logarithm of the Gamma Function,' Math. Comp. 21, */
/* 1967, pp. 198-203. */
/* 2) K. E. Hillstrom, ANL/AMD Program ANLC366S, DGAMMA/DLGAMA, May, */
/* 1969. */
/* 3) Hart, Et. Al., Computer Approximations, Wiley and sons, New */
/* York, 1968. */
/* Authors: W. J. Cody and L. Stoltz */
/* Argonne National Laboratory */
/* Latest modification: June 16, 1988 */
/* ---------------------------------------------------------------------- */
/* ---------------------------------------------------------------------- */
/* Mathematical constants */
/* ---------------------------------------------------------------------- */
static double one = 1.;
static double half = .5;
static double twelve = 12.;
static double zero = 0.;
static double four = 4.;
static double thrhal = 1.5;
static double two = 2.;
static double pnt68 = .6796875;
static double sqrtpi = .9189385332046727417803297;
/* ---------------------------------------------------------------------- */
/* Machine dependent parameters */
/* ---------------------------------------------------------------------- */
#ifdef IEEEFP
static double xbig = 2.55e305;
static double xinf = 1.79e308;
static double eps = 2.22e-16;
static double frtbig = 2.25e76;
#else
#ifdef CRAYCC
static double xbig = 9.62e+2461;
static double xinf = 5.45e+2465;
static double eps = 7.11e-15;
static double frtbig = 3.13e+615;
#else /* use IBM 3033 values */
static double xbig = 4.29e+73;
static double xinf = 7.23e+75;
static double eps = 2.22e-16;
static double frtbig = 2.56e+18;
#endif /* CRAYCC */
#endif /* IEEEFP */
/* ---------------------------------------------------------------------- */
/* Numerator and denominator coefficients for rational minimax */
/* approximation over (0.5,1.5). */
/* ---------------------------------------------------------------------- */
static double d1 = -.5772156649015328605195174;
static double p1[8] = { 4.945235359296727046734888,
201.8112620856775083915565,
2290.838373831346393026739,
11319.67205903380828685045,
28557.24635671635335736389,
38484.96228443793359990269,
26377.48787624195437963534,
7225.813979700288197698961 };
static double q1[8] = { 67.48212550303777196073036,
1113.332393857199323513008,
7738.757056935398733233834,
27639.87074403340708898585,
54993.10206226157329794414,
61611.22180066002127833352,
36351.27591501940507276287,
8785.536302431013170870835 };
/* ---------------------------------------------------------------------- */
/* Numerator and denominator coefficients for rational minimax */
/* Approximation over (1.5,4.0). */
/* ---------------------------------------------------------------------- */
static double d2 = .4227843350984671393993777;
static double p2[8] = { 4.974607845568932035012064,
542.4138599891070494101986,
15506.93864978364947665077,
184793.2904445632425417223,
1088204.76946882876749847,
3338152.967987029735917223,
5106661.678927352456275255,
3074109.054850539556250927 };
static double q2[8] = { 183.0328399370592604055942,
7765.049321445005871323047,
133190.3827966074194402448,
1136705.821321969608938755,
5267964.117437946917577538,
13467014.54311101692290052,
17827365.30353274213975932,
9533095.591844353613395747 };
/* ---------------------------------------------------------------------- */
/* Numerator and denominator coefficients for rational minimax */
/* Approximation over (4.0,12.0). */
/* ---------------------------------------------------------------------- */
static double d4 = 1.791759469228055000094023;
static double p4[8] = { 14745.02166059939948905062,
2426813.369486704502836312,
121475557.4045093227939592,
2663432449.630976949898078,
29403789566.34553899906876,
170266573776.5398868392998,
492612579337.743088758812,
560625185622.3951465078242 };
static double q4[8] = { 2690.530175870899333379843,
639388.5654300092398984238,
41355999.30241388052042842,
1120872109.61614794137657,
14886137286.78813811542398,
101680358627.2438228077304,
341747634550.7377132798597,
446315818741.9713286462081 };
/* ---------------------------------------------------------------------- */
/* Coefficients for minimax approximation over (12, INF). */
/* ---------------------------------------------------------------------- */
static double c[7] = { -.001910444077728,
8.4171387781295e-4,
-5.952379913043012e-4,
7.93650793500350248e-4,
-.002777777777777681622553,
.08333333333333333331554247,
.0057083835261 };
/* ---------------------------------------------------------------------- */
y = x;
if (y > zero && y <= xbig) {
if (y <= eps) {
res = -log(y);
} else if (y <= thrhal) {
/* ------------------------------------------------------------------- */
/* EPS .LT. X .LE. 1.5 */
/* ------------------------------------------------------------------- */
if (y < pnt68) {
corr = -log(y);
xm1 = y;
} else {
corr = zero;
xm1 = y - half - half;
}
if (y <= half || y >= pnt68) {
xden = one;
xnum = zero;
for (i = 1; i <= 8; ++i) {
xnum = xnum * xm1 + p1[i - 1];
xden = xden * xm1 + q1[i - 1];
}
res = corr + xm1 * (d1 + xm1 * (xnum / xden));
} else {
xm2 = y - half - half;
xden = one;
xnum = zero;
for (i = 1; i <= 8; ++i) {
xnum = xnum * xm2 + p2[i - 1];
xden = xden * xm2 + q2[i - 1];
}
res = corr + xm2 * (d2 + xm2 * (xnum / xden));
}
} else if (y <= four) {
/* ------------------------------------------------------------------- */
/* 1.5 .LT. X .LE. 4.0 */
/* ------------------------------------------------------------------- */
xm2 = y - two;
xden = one;
xnum = zero;
for (i = 1; i <= 8; ++i) {
xnum = xnum * xm2 + p2[i - 1];
xden = xden * xm2 + q2[i - 1];
}
res = xm2 * (d2 + xm2 * (xnum / xden));
} else if (y <= twelve) {
/* ------------------------------------------------------------------- */
/* 4.0 .LT. X .LE. 12.0 */
/* ------------------------------------------------------------------- */
xm4 = y - four;
xden = -one;
xnum = zero;
for (i = 1; i <= 8; ++i) {
xnum = xnum * xm4 + p4[i - 1];
xden = xden * xm4 + q4[i - 1];
}
res = d4 + xm4 * (xnum / xden);
} else {
/* ------------------------------------------------------------------- */
/* Evaluate for argument .GE. 12.0, */
/* ------------------------------------------------------------------- */
res = zero;
if (y <= frtbig) {
res = c[6];
ysq = y * y;
for (i = 1; i <= 6; ++i) {
res = res / ysq + c[i - 1];
}
}
res /= y;
corr = log(y);
res = res + sqrtpi - half * corr;
res += y * (corr - one);
}
} else {
/* -------------------------------------------------------------------- */
/* Return for bad arguments */
/* -------------------------------------------------------------------- */
res = xinf;
}
/* ---------------------------------------------------------------------- */
/* Final adjustments and return */
/* ---------------------------------------------------------------------- */
return res;
/* ---------- Last line of DLGAMA ---------- */
}
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