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