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90 lines
3.4 KiB
Fortran
90 lines
3.4 KiB
Fortran
*DECK AI
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FUNCTION AI (X)
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C***BEGIN PROLOGUE AI
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C***PURPOSE Evaluate the Airy function.
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C***LIBRARY SLATEC (FNLIB)
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C***CATEGORY C10D
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C***TYPE SINGLE PRECISION (AI-S, DAI-D)
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C***KEYWORDS AIRY FUNCTION, FNLIB, SPECIAL FUNCTIONS
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C***AUTHOR Fullerton, W., (LANL)
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C***DESCRIPTION
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C
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C AI(X) computes the Airy function Ai(X)
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C Series for AIF on the interval -1.00000D+00 to 1.00000D+00
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C with weighted error 1.09E-19
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C log weighted error 18.96
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C significant figures required 17.76
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C decimal places required 19.44
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C
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C Series for AIG on the interval -1.00000D+00 to 1.00000D+00
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C with weighted error 1.51E-17
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C log weighted error 16.82
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C significant figures required 15.19
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C decimal places required 17.27
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C
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C***REFERENCES (NONE)
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C***ROUTINES CALLED AIE, CSEVL, INITS, R1MACH, R9AIMP, XERMSG
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C***REVISION HISTORY (YYMMDD)
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C 770701 DATE WRITTEN
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C 890531 Changed all specific intrinsics to generic. (WRB)
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C 890531 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
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C 900326 Removed duplicate information from DESCRIPTION section.
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C (WRB)
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C 920618 Removed space from variable names. (RWC, WRB)
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C***END PROLOGUE AI
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DIMENSION AIFCS(9), AIGCS(8)
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LOGICAL FIRST
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SAVE AIFCS, AIGCS, NAIF, NAIG, X3SML, XMAX, FIRST
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DATA AIFCS( 1) / -.0379713584 9666999750E0 /
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DATA AIFCS( 2) / .0591918885 3726363857E0 /
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DATA AIFCS( 3) / .0009862928 0577279975E0 /
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DATA AIFCS( 4) / .0000068488 4381907656E0 /
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DATA AIFCS( 5) / .0000000259 4202596219E0 /
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DATA AIFCS( 6) / .0000000000 6176612774E0 /
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DATA AIFCS( 7) / .0000000000 0010092454E0 /
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DATA AIFCS( 8) / .0000000000 0000012014E0 /
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DATA AIFCS( 9) / .0000000000 0000000010E0 /
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DATA AIGCS( 1) / .0181523655 8116127E0 /
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DATA AIGCS( 2) / .0215725631 6601076E0 /
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DATA AIGCS( 3) / .0002567835 6987483E0 /
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DATA AIGCS( 4) / .0000014265 2141197E0 /
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DATA AIGCS( 5) / .0000000045 7211492E0 /
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DATA AIGCS( 6) / .0000000000 0952517E0 /
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DATA AIGCS( 7) / .0000000000 0001392E0 /
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DATA AIGCS( 8) / .0000000000 0000001E0 /
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DATA FIRST /.TRUE./
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C***FIRST EXECUTABLE STATEMENT AI
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IF (FIRST) THEN
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NAIF = INITS (AIFCS, 9, 0.1*R1MACH(3))
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NAIG = INITS (AIGCS, 8, 0.1*R1MACH(3))
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C
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X3SML = R1MACH(3)**0.3334
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XMAXT = (-1.5*LOG(R1MACH(1)))**0.6667
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XMAX = XMAXT - XMAXT*LOG(XMAXT)/
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* (4.0*SQRT(XMAXT)+1.0) - 0.01
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ENDIF
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FIRST = .FALSE.
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C
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IF (X.GE.(-1.0)) GO TO 20
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CALL R9AIMP (X, XM, THETA)
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AI = XM * COS(THETA)
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RETURN
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C
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20 IF (X.GT.1.0) GO TO 30
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Z = 0.0
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IF (ABS(X).GT.X3SML) Z = X**3
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AI = 0.375 + (CSEVL (Z, AIFCS, NAIF) - X*(0.25 +
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1 CSEVL (Z, AIGCS, NAIG)) )
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RETURN
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C
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30 IF (X.GT.XMAX) GO TO 40
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AI = AIE(X) * EXP(-2.0*X*SQRT(X)/3.0)
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RETURN
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C
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40 AI = 0.0
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CALL XERMSG ('SLATEC', 'AI', 'X SO BIG AI UNDERFLOWS', 1, 1)
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RETURN
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C
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END
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