#include "cdflib.h" double Xgamm(double *a) /* ----------------------------------------------------------------------- EVALUATION OF THE GAMMA FUNCTION FOR REAL ARGUMENTS ----------- GAMMA(A) IS ASSIGNED THE VALUE 0 WHEN THE GAMMA FUNCTION CANNOT BE COMPUTED. ----------------------------------------------------------------------- WRITTEN BY ALFRED H. MORRIS, JR. NAVAL SURFACE WEAPONS CENTER DAHLGREN, VIRGINIA ----------------------------------------------------------------------- */ { static double d = .41893853320467274178e0; static double pi = 3.1415926535898e0; static double r1 = .820756370353826e-03; static double r2 = -.595156336428591e-03; static double r3 = .793650663183693e-03; static double r4 = -.277777777770481e-02; static double r5 = .833333333333333e-01; static double p[7] = { .539637273585445e-03,.261939260042690e-02,.204493667594920e-01, .730981088720487e-01,.279648642639792e+00,.553413866010467e+00,1.0e0 }; static double q[7] = { -.832979206704073e-03,.470059485860584e-02,.225211131035340e-01, -.170458969313360e+00,-.567902761974940e-01,.113062953091122e+01,1.0e0 }; static int K2 = 3; static int K3 = 0; static double Xgamm,bot,g,lnx,s,t,top,w,x,z; static int i,j,m,n,T1; /* .. .. Executable Statements .. */ Xgamm = 0.0e0; x = *a; if(fabs(*a) >= 15.0e0) goto S110; /* ----------------------------------------------------------------------- EVALUATION OF GAMMA(A) FOR ABS(A) .LT. 15 ----------------------------------------------------------------------- */ t = 1.0e0; m = fifidint(*a)-1; /* LET T BE THE PRODUCT OF A-J WHEN A .GE. 2 */ T1 = m; if(T1 < 0) goto S40; else if(T1 == 0) goto S30; else goto S10; S10: for(j=1; j<=m; j++) { x -= 1.0e0; t = x*t; } S30: x -= 1.0e0; goto S80; S40: /* LET T BE THE PRODUCT OF A+J WHEN A .LT. 1 */ t = *a; if(*a > 0.0e0) goto S70; m = -m-1; if(m == 0) goto S60; for(j=1; j<=m; j++) { x += 1.0e0; t = x*t; } S60: x += (0.5e0+0.5e0); t = x*t; if(t == 0.0e0) return Xgamm; S70: /* THE FOLLOWING CODE CHECKS IF 1/T CAN OVERFLOW. THIS CODE MAY BE OMITTED IF DESIRED. */ if(fabs(t) >= 1.e-30) goto S80; if(fabs(t)*spmpar(&K2) <= 1.0001e0) return Xgamm; Xgamm = 1.0e0/t; return Xgamm; S80: /* COMPUTE GAMMA(1 + X) FOR 0 .LE. X .LT. 1 */ top = p[0]; bot = q[0]; for(i=1; i<7; i++) { top = p[i]+x*top; bot = q[i]+x*bot; } Xgamm = top/bot; /* TERMINATION */ if(*a < 1.0e0) goto S100; Xgamm *= t; return Xgamm; S100: Xgamm /= t; return Xgamm; S110: /* ----------------------------------------------------------------------- EVALUATION OF GAMMA(A) FOR ABS(A) .GE. 15 ----------------------------------------------------------------------- */ if(fabs(*a) >= 1.e3) return Xgamm; if(*a > 0.0e0) goto S120; x = -*a; n = x; t = x-(double)n; if(t > 0.9e0) t = 1.0e0-t; s = sin(pi*t)/pi; if(fifmod(n,2) == 0) s = -s; if(s == 0.0e0) return Xgamm; S120: /* COMPUTE THE MODIFIED ASYMPTOTIC SUM */ t = 1.0e0/(x*x); g = ((((r1*t+r2)*t+r3)*t+r4)*t+r5)/x; /* ONE MAY REPLACE THE NEXT STATEMENT WITH LNX = ALOG(X) BUT LESS ACCURACY WILL NORMALLY BE OBTAINED. */ lnx = log(x); /* FINAL ASSEMBLY */ z = x; g = d+g+(z-0.5e0)*(lnx-1.e0); w = g; t = g-w; if(w > 0.99999e0*exparg(&K3)) return Xgamm; Xgamm = exp(w)*(1.0e0+t); if(*a < 0.0e0) Xgamm = 1.0e0/(Xgamm*s)/x; return Xgamm; } /* END */