2329
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1 *DECK D9LGMC |
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2 DOUBLE PRECISION FUNCTION D9LGMC (X) |
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3 C***BEGIN PROLOGUE D9LGMC |
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4 C***SUBSIDIARY |
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5 C***PURPOSE Compute the log Gamma correction factor so that |
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6 C LOG(DGAMMA(X)) = LOG(SQRT(2*PI)) + (X-5.)*LOG(X) - X |
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7 C + D9LGMC(X). |
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8 C***LIBRARY SLATEC (FNLIB) |
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9 C***CATEGORY C7E |
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10 C***TYPE DOUBLE PRECISION (R9LGMC-S, D9LGMC-D, C9LGMC-C) |
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11 C***KEYWORDS COMPLETE GAMMA FUNCTION, CORRECTION TERM, FNLIB, |
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12 C LOG GAMMA, LOGARITHM, SPECIAL FUNCTIONS |
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13 C***AUTHOR Fullerton, W., (LANL) |
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14 C***DESCRIPTION |
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15 C |
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16 C Compute the log gamma correction factor for X .GE. 10. so that |
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17 C LOG (DGAMMA(X)) = LOG(SQRT(2*PI)) + (X-.5)*LOG(X) - X + D9lGMC(X) |
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18 C |
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19 C Series for ALGM on the interval 0. to 1.00000E-02 |
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20 C with weighted error 1.28E-31 |
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21 C log weighted error 30.89 |
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22 C significant figures required 29.81 |
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23 C decimal places required 31.48 |
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24 C |
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25 C***REFERENCES (NONE) |
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26 C***ROUTINES CALLED D1MACH, DCSEVL, INITDS, XERMSG |
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27 C***REVISION HISTORY (YYMMDD) |
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28 C 770601 DATE WRITTEN |
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29 C 890531 Changed all specific intrinsics to generic. (WRB) |
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30 C 890531 REVISION DATE from Version 3.2 |
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31 C 891214 Prologue converted to Version 4.0 format. (BAB) |
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32 C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ) |
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33 C 900720 Routine changed from user-callable to subsidiary. (WRB) |
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34 C***END PROLOGUE D9LGMC |
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35 DOUBLE PRECISION X, ALGMCS(15), XBIG, XMAX, DCSEVL, D1MACH |
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36 LOGICAL FIRST |
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37 SAVE ALGMCS, NALGM, XBIG, XMAX, FIRST |
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38 DATA ALGMCS( 1) / +.1666389480 4518632472 0572965082 2 D+0 / |
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39 DATA ALGMCS( 2) / -.1384948176 0675638407 3298605913 5 D-4 / |
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40 DATA ALGMCS( 3) / +.9810825646 9247294261 5717154748 7 D-8 / |
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41 DATA ALGMCS( 4) / -.1809129475 5724941942 6330626671 9 D-10 / |
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42 DATA ALGMCS( 5) / +.6221098041 8926052271 2601554341 6 D-13 / |
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43 DATA ALGMCS( 6) / -.3399615005 4177219443 0333059966 6 D-15 / |
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44 DATA ALGMCS( 7) / +.2683181998 4826987489 5753884666 6 D-17 / |
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45 DATA ALGMCS( 8) / -.2868042435 3346432841 4462239999 9 D-19 / |
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46 DATA ALGMCS( 9) / +.3962837061 0464348036 7930666666 6 D-21 / |
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47 DATA ALGMCS( 10) / -.6831888753 9857668701 1199999999 9 D-23 / |
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48 DATA ALGMCS( 11) / +.1429227355 9424981475 7333333333 3 D-24 / |
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49 DATA ALGMCS( 12) / -.3547598158 1010705471 9999999999 9 D-26 / |
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50 DATA ALGMCS( 13) / +.1025680058 0104709120 0000000000 0 D-27 / |
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51 DATA ALGMCS( 14) / -.3401102254 3167487999 9999999999 9 D-29 / |
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52 DATA ALGMCS( 15) / +.1276642195 6300629333 3333333333 3 D-30 / |
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53 DATA FIRST /.TRUE./ |
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54 C***FIRST EXECUTABLE STATEMENT D9LGMC |
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55 IF (FIRST) THEN |
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56 NALGM = INITDS (ALGMCS, 15, REAL(D1MACH(3)) ) |
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57 XBIG = 1.0D0/SQRT(D1MACH(3)) |
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58 XMAX = EXP (MIN(LOG(D1MACH(2)/12.D0), -LOG(12.D0*D1MACH(1)))) |
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59 ENDIF |
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60 FIRST = .FALSE. |
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61 C |
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62 IF (X .LT. 10.D0) CALL XERMSG ('SLATEC', 'D9LGMC', |
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63 + 'X MUST BE GE 10', 1, 2) |
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64 IF (X.GE.XMAX) GO TO 20 |
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65 C |
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66 D9LGMC = 1.D0/(12.D0*X) |
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67 IF (X.LT.XBIG) D9LGMC = DCSEVL (2.0D0*(10.D0/X)**2-1.D0, ALGMCS, |
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68 1 NALGM) / X |
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69 RETURN |
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70 C |
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71 20 D9LGMC = 0.D0 |
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72 CALL XERMSG ('SLATEC', 'D9LGMC', 'X SO BIG D9LGMC UNDERFLOWS', 2, |
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73 + 1) |
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74 RETURN |
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75 C |
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76 END |