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/* dgamma.f -- translated by f2c (version 20041007).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
/** This routine has been editted to be thread safe **/
#define V3P_NETLIB_SRC
#include "v3p_netlib.h"
/* Table of constant values */
static integer c__3 = 3;
static integer c__42 = 42;
static integer c__4 = 4;
static integer c__2 = 2;
static integer c__1 = 1;
/* DECK DGAMMA */
doublereal dgamma_(doublereal *x)
{
/* Initialized data */
static doublereal gamcs[42] = { .008571195590989331421920062399942,
.004415381324841006757191315771652,
.05685043681599363378632664588789,
-.004219835396418560501012500186624,
.001326808181212460220584006796352,
-1.893024529798880432523947023886e-4,
3.606925327441245256578082217225e-5,
-6.056761904460864218485548290365e-6,
1.055829546302283344731823509093e-6,
-1.811967365542384048291855891166e-7,
3.117724964715322277790254593169e-8,
-5.354219639019687140874081024347e-9,
9.19327551985958894688778682594e-10,
-1.577941280288339761767423273953e-10,
2.707980622934954543266540433089e-11,
-4.646818653825730144081661058933e-12,
7.973350192007419656460767175359e-13,
-1.368078209830916025799499172309e-13,
2.347319486563800657233471771688e-14,
-4.027432614949066932766570534699e-15,
6.910051747372100912138336975257e-16,
-1.185584500221992907052387126192e-16,
2.034148542496373955201026051932e-17,
-3.490054341717405849274012949108e-18,
5.987993856485305567135051066026e-19,
-1.027378057872228074490069778431e-19,
1.762702816060529824942759660748e-20,
-3.024320653735306260958772112042e-21,
5.188914660218397839717833550506e-22,
-8.902770842456576692449251601066e-23,
1.527474068493342602274596891306e-23,
-2.620731256187362900257328332799e-24,
4.496464047830538670331046570666e-25,
-7.714712731336877911703901525333e-26,
1.323635453126044036486572714666e-26,
-2.270999412942928816702313813333e-27,
3.896418998003991449320816639999e-28,
-6.685198115125953327792127999999e-29,
1.146998663140024384347613866666e-29,
-1.967938586345134677295103999999e-30,
3.376448816585338090334890666666e-31,
-5.793070335782135784625493333333e-32 };
static doublereal pi = 3.1415926535897932384626433832795;
static doublereal sq2pil = .91893853320467274178032973640562;
// static logical first = TRUE_;
/* System generated locals */
integer i__1;
real r__1;
doublereal ret_val, d__1, d__2;
/* Builtin functions */
double sqrt(doublereal), d_int(doublereal *), log(doublereal), exp(
doublereal), sin(doublereal);
/* Local variables */
integer i__, n;
doublereal y;
/* static */ integer ngam;
/* static */ doublereal xmin, xmax, dxrel;
extern doublereal d1mach_(integer *), d9lgmc_(doublereal *);
extern /* Subroutine */ int dgamlm_(doublereal *, doublereal *);
extern doublereal dcsevl_(doublereal *, doublereal *, integer *);
extern integer initds_(doublereal *, integer *, real *);
extern /* Subroutine */ int xermsg_(char *, char *, char *, integer *,
integer *, ftnlen, ftnlen, ftnlen);
doublereal sinpiy;
/* ***BEGIN PROLOGUE DGAMMA */
/* ***PURPOSE Compute the complete Gamma function. */
/* ***LIBRARY SLATEC (FNLIB) */
/* ***CATEGORY C7A */
/* ***TYPE DOUBLE PRECISION (GAMMA-S, DGAMMA-D, CGAMMA-C) */
/* ***KEYWORDS COMPLETE GAMMA FUNCTION, FNLIB, SPECIAL FUNCTIONS */
/* ***AUTHOR Fullerton, W., (LANL) */
/* ***DESCRIPTION */
/* DGAMMA(X) calculates the double precision complete Gamma function */
/* for double precision argument X. */
/* Series for GAM on the interval 0. to 1.00000E+00 */
/* with weighted error 5.79E-32 */
/* log weighted error 31.24 */
/* significant figures required 30.00 */
/* decimal places required 32.05 */
/* ***REFERENCES (NONE) */
/* ***ROUTINES CALLED D1MACH, D9LGMC, DCSEVL, DGAMLM, INITDS, XERMSG */
/* ***REVISION HISTORY (YYMMDD) */
/* 770601 DATE WRITTEN */
/* 890531 Changed all specific intrinsics to generic. (WRB) */
/* 890911 Removed unnecessary intrinsics. (WRB) */
/* 890911 REVISION DATE from Version 3.2 */
/* 891214 Prologue converted to Version 4.0 format. (BAB) */
/* 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ) */
/* 920618 Removed space from variable name. (RWC, WRB) */
/* ***END PROLOGUE DGAMMA */
/* ***FIRST EXECUTABLE STATEMENT DGAMMA */
// d1mach has been made thread safe, so there is no need for the
// statics in determining these values
// if (first) {
// r__1 = (real) d1mach_(&c__3) * .1f;
// ngam = initds_(gamcs, &c__42, &r__1);
// dgamlm_(&xmin, &xmax);
// dxrel = sqrt(d1mach_(&c__4));
// }
// first = FALSE_;
r__1 = (real) d1mach_(&c__3) * .1f;
ngam = initds_(gamcs, &c__42, &r__1);
dgamlm_(&xmin, &xmax);
dxrel = sqrt(d1mach_(&c__4));
y = abs(*x);
if (y > 10.) {
goto L50;
}
/* COMPUTE GAMMA(X) FOR -XBND .LE. X .LE. XBND. REDUCE INTERVAL AND FIND */
/* GAMMA(1+Y) FOR 0.0 .LE. Y .LT. 1.0 FIRST OF ALL. */
n = (integer) (*x);
if (*x < 0.) {
--n;
}
y = *x - n;
--n;
d__1 = y * 2. - 1.;
ret_val = dcsevl_(&d__1, gamcs, &ngam) + .9375;
if (n == 0) {
return ret_val;
}
if (n > 0) {
goto L30;
}
/* COMPUTE GAMMA(X) FOR X .LT. 1.0 */
n = -n;
if (*x == 0.) {
xermsg_("SLATEC", "DGAMMA", "X IS 0", &c__4, &c__2, (ftnlen)6, (
ftnlen)6, (ftnlen)6);
}
if (*x < 0.f && *x + n - 2 == 0.) {
xermsg_("SLATEC", "DGAMMA", "X IS A NEGATIVE INTEGER", &c__4, &c__2, (
ftnlen)6, (ftnlen)6, (ftnlen)23);
}
d__2 = *x - .5;
if (*x < -.5 && (d__1 = (*x - d_int(&d__2)) / *x, abs(d__1)) < dxrel) {
xermsg_("SLATEC", "DGAMMA", "ANSWER LT HALF PRECISION BECAUSE X TOO "
"NEAR NEGATIVE INTEGER", &c__1, &c__1, (ftnlen)6, (ftnlen)6, (
ftnlen)60);
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
ret_val /= *x + i__ - 1;
/* L20: */
}
return ret_val;
/* GAMMA(X) FOR X .GE. 2.0 AND X .LE. 10.0 */
L30:
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
ret_val = (y + i__) * ret_val;
/* L40: */
}
return ret_val;
/* GAMMA(X) FOR ABS(X) .GT. 10.0. RECALL Y = ABS(X). */
L50:
if (*x > xmax) {
xermsg_("SLATEC", "DGAMMA", "X SO BIG GAMMA OVERFLOWS", &c__3, &c__2,
(ftnlen)6, (ftnlen)6, (ftnlen)24);
}
ret_val = 0.;
if (*x < xmin) {
xermsg_("SLATEC", "DGAMMA", "X SO SMALL GAMMA UNDERFLOWS", &c__2, &
c__1, (ftnlen)6, (ftnlen)6, (ftnlen)27);
}
if (*x < xmin) {
return ret_val;
}
ret_val = exp((y - .5) * log(y) - y + sq2pil + d9lgmc_(&y));
if (*x > 0.) {
return ret_val;
}
d__2 = *x - .5;
if ((d__1 = (*x - d_int(&d__2)) / *x, abs(d__1)) < dxrel) {
xermsg_("SLATEC", "DGAMMA", "ANSWER LT HALF PRECISION, X TOO NEAR NE"
"GATIVE INTEGER", &c__1, &c__1, (ftnlen)6, (ftnlen)6, (ftnlen)
53);
}
sinpiy = sin(pi * y);
if (sinpiy == 0.) {
xermsg_("SLATEC", "DGAMMA", "X IS A NEGATIVE INTEGER", &c__4, &c__2, (
ftnlen)6, (ftnlen)6, (ftnlen)23);
}
ret_val = -pi / (y * sinpiy * ret_val);
return ret_val;
} /* dgamma_ */
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