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First attempt at single precision tyeps * * * corrections to qrupdate single precision routines * * * prefer demotion to single over promotion to double * * * Add single precision support to log2 function * * * Trivial PROJECT file update * * * Cache optimized hermitian/transpose methods * * * Add tests for tranpose/hermitian and ChangeLog entry for new transpose code
author David Bateman <dbateman@free.fr>
date Sun, 27 Apr 2008 22:34:17 +0200
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1 *DECK R9GMIT
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2 FUNCTION R9GMIT (A, X, ALGAP1, SGNGAM, ALX)
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3 C***BEGIN PROLOGUE R9GMIT
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4 C***SUBSIDIARY
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5 C***PURPOSE Compute Tricomi's incomplete Gamma function for small
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6 C arguments.
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7 C***LIBRARY SLATEC (FNLIB)
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8 C***CATEGORY C7E
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9 C***TYPE SINGLE PRECISION (R9GMIT-S, D9GMIT-D)
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10 C***KEYWORDS COMPLEMENTARY INCOMPLETE GAMMA FUNCTION, FNLIB, SMALL X,
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11 C SPECIAL FUNCTIONS, TRICOMI
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12 C***AUTHOR Fullerton, W., (LANL)
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13 C***DESCRIPTION
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14 C
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15 C Compute Tricomi's incomplete gamma function for small X.
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16 C
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17 C***REFERENCES (NONE)
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18 C***ROUTINES CALLED ALNGAM, R1MACH, XERMSG
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19 C***REVISION HISTORY (YYMMDD)
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20 C 770701 DATE WRITTEN
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21 C 890531 Changed all specific intrinsics to generic. (WRB)
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22 C 890531 REVISION DATE from Version 3.2
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23 C 891214 Prologue converted to Version 4.0 format. (BAB)
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24 C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
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25 C 900720 Routine changed from user-callable to subsidiary. (WRB)
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26 C***END PROLOGUE R9GMIT
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27 SAVE EPS, BOT
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28 DATA EPS, BOT / 2*0.0 /
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29 C***FIRST EXECUTABLE STATEMENT R9GMIT
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30 IF (EPS.EQ.0.0) EPS = 0.5*R1MACH(3)
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31 IF (BOT.EQ.0.0) BOT = LOG(R1MACH(1))
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32 C
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33 IF (X .LE. 0.0) CALL XERMSG ('SLATEC', 'R9GMIT',
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34 + 'X SHOULD BE GT 0', 1, 2)
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35 C
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36 MA = A + 0.5
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37 IF (A.LT.0.0) MA = A - 0.5
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38 AEPS = A - MA
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39 C
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40 AE = A
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41 IF (A.LT.(-0.5)) AE = AEPS
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42 C
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43 T = 1.0
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44 TE = AE
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45 S = T
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46 DO 20 K=1,200
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47 FK = K
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48 TE = -X*TE/FK
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49 T = TE/(AE+FK)
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50 S = S + T
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51 IF (ABS(T).LT.EPS*ABS(S)) GO TO 30
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52 20 CONTINUE
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53 CALL XERMSG ('SLATEC', 'R9GMIT',
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54 + 'NO CONVERGENCE IN 200 TERMS OF TAYLOR-S SERIES', 2, 2)
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55 C
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56 30 IF (A.GE.(-0.5)) ALGS = -ALGAP1 + LOG(S)
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57 IF (A.GE.(-0.5)) GO TO 60
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58 C
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59 ALGS = -ALNGAM(1.0+AEPS) + LOG(S)
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60 S = 1.0
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61 M = -MA - 1
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62 IF (M.EQ.0) GO TO 50
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63 T = 1.0
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64 DO 40 K=1,M
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65 T = X*T/(AEPS-M-1+K)
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66 S = S + T
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67 IF (ABS(T).LT.EPS*ABS(S)) GO TO 50
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68 40 CONTINUE
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69 C
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70 50 R9GMIT = 0.0
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71 ALGS = -MA*LOG(X) + ALGS
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72 IF (S.EQ.0.0 .OR. AEPS.EQ.0.0) GO TO 60
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73 C
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74 SGNG2 = SGNGAM*SIGN(1.0,S)
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75 ALG2 = -X - ALGAP1 + LOG(ABS(S))
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76 C
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77 IF (ALG2.GT.BOT) R9GMIT = SGNG2*EXP(ALG2)
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78 IF (ALGS.GT.BOT) R9GMIT = R9GMIT + EXP(ALGS)
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79 RETURN
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80 C
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81 60 R9GMIT = EXP(ALGS)
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82 RETURN
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83 C
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84 END