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- *DECK BI
- FUNCTION BI (X)
- C***BEGIN PROLOGUE BI
- C***PURPOSE Evaluate the Bairy function (the Airy function of the
- C second kind).
- C***LIBRARY SLATEC (FNLIB)
- C***CATEGORY C10D
- C***TYPE SINGLE PRECISION (BI-S, DBI-D)
- C***KEYWORDS BAIRY FUNCTION, FNLIB, SPECIAL FUNCTIONS
- C***AUTHOR Fullerton, W., (LANL)
- C***DESCRIPTION
- C
- C BI(X) calculates the Airy function of the second kind for real
- C argument X.
- C
- C Series for BIF on the interval -1.00000D+00 to 1.00000D+00
- C with weighted error 1.88E-19
- C log weighted error 18.72
- C significant figures required 17.74
- C decimal places required 19.20
- C
- C Series for BIG on the interval -1.00000D+00 to 1.00000D+00
- C with weighted error 2.61E-17
- C log weighted error 16.58
- C significant figures required 15.17
- C decimal places required 17.03
- C
- C Series for BIF2 on the interval 1.00000D+00 to 8.00000D+00
- C with weighted error 1.11E-17
- C log weighted error 16.95
- C approx significant figures required 16.5
- C decimal places required 17.45
- C
- C Series for BIG2 on the interval 1.00000D+00 to 8.00000D+00
- C with weighted error 1.19E-18
- C log weighted error 17.92
- C approx significant figures required 17.2
- C decimal places required 18.42
- C
- C***REFERENCES (NONE)
- C***ROUTINES CALLED BIE, 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***END PROLOGUE BI
- DIMENSION BIFCS(9), BIGCS(8), BIF2CS(10), BIG2CS(10)
- LOGICAL FIRST
- SAVE BIFCS, BIGCS, BIF2CS, BIG2CS, NBIF, NBIG, NBIF2,
- 1 NBIG2, X3SML, XMAX, FIRST
- DATA BIFCS( 1) / -.0167302164 7198664948E0 /
- DATA BIFCS( 2) / .1025233583 424944561E0 /
- DATA BIFCS( 3) / .0017083092 5073815165E0 /
- DATA BIFCS( 4) / .0000118625 4546774468E0 /
- DATA BIFCS( 5) / .0000000449 3290701779E0 /
- DATA BIFCS( 6) / .0000000001 0698207143E0 /
- DATA BIFCS( 7) / .0000000000 0017480643E0 /
- DATA BIFCS( 8) / .0000000000 0000020810E0 /
- DATA BIFCS( 9) / .0000000000 0000000018E0 /
- DATA BIGCS( 1) / .0224662232 4857452E0 /
- DATA BIGCS( 2) / .0373647754 5301955E0 /
- DATA BIGCS( 3) / .0004447621 8957212E0 /
- DATA BIGCS( 4) / .0000024708 0756363E0 /
- DATA BIGCS( 5) / .0000000079 1913533E0 /
- DATA BIGCS( 6) / .0000000000 1649807E0 /
- DATA BIGCS( 7) / .0000000000 0002411E0 /
- DATA BIGCS( 8) / .0000000000 0000002E0 /
- DATA BIF2CS( 1) / 0.0998457269 3816041E0 /
- DATA BIF2CS( 2) / .4786249778 63005538E0 /
- DATA BIF2CS( 3) / .0251552119 604330118E0 /
- DATA BIF2CS( 4) / .0005820693 885232645E0 /
- DATA BIF2CS( 5) / .0000074997 659644377E0 /
- DATA BIF2CS( 6) / .0000000613 460287034E0 /
- DATA BIF2CS( 7) / .0000000003 462753885E0 /
- DATA BIF2CS( 8) / .0000000000 014288910E0 /
- DATA BIF2CS( 9) / .0000000000 000044962E0 /
- DATA BIF2CS(10) / .0000000000 000000111E0 /
- DATA BIG2CS( 1) / .0333056621 45514340E0 /
- DATA BIG2CS( 2) / .1613092151 23197068E0 /
- DATA BIG2CS( 3) / .0063190073 096134286E0 /
- DATA BIG2CS( 4) / .0001187904 568162517E0 /
- DATA BIG2CS( 5) / .0000013045 345886200E0 /
- DATA BIG2CS( 6) / .0000000093 741259955E0 /
- DATA BIG2CS( 7) / .0000000000 474580188E0 /
- DATA BIG2CS( 8) / .0000000000 001783107E0 /
- DATA BIG2CS( 9) / .0000000000 000005167E0 /
- DATA BIG2CS(10) / .0000000000 000000011E0 /
- DATA FIRST /.TRUE./
- C***FIRST EXECUTABLE STATEMENT BI
- IF (FIRST) THEN
- ETA = 0.1*R1MACH(3)
- NBIF = INITS (BIFCS , 9, ETA)
- NBIG = INITS (BIGCS , 8, ETA)
- NBIF2 = INITS (BIF2CS, 10, ETA)
- NBIG2 = INITS (BIG2CS, 10, ETA)
- C
- X3SML = ETA**0.3333
- XMAX = (1.5*LOG(R1MACH(2)))**0.6666
- ENDIF
- FIRST = .FALSE.
- C
- IF (X.GE.(-1.0)) GO TO 20
- CALL R9AIMP (X, XM, THETA)
- BI = XM * SIN(THETA)
- RETURN
- C
- 20 IF (X.GT.1.0) GO TO 30
- Z = 0.0
- IF (ABS(X).GT.X3SML) Z = X**3
- BI = 0.625 + CSEVL (Z, BIFCS, NBIF) + X*(0.4375 +
- 1 CSEVL (Z, BIGCS, NBIG))
- RETURN
- C
- 30 IF (X.GT.2.0) GO TO 40
- Z = (2.0*X**3 - 9.0) / 7.0
- BI = 1.125 + CSEVL (Z, BIF2CS, NBIF2) + X*(0.625 +
- 1 CSEVL (Z, BIG2CS, NBIG2))
- RETURN
- C
- 40 IF (X .GT. XMAX) CALL XERMSG ('SLATEC', 'BI',
- + 'X SO BIG THAT BI OVERFLOWS', 1, 2)
- C
- BI = BIE(X) * EXP(2.0*X*SQRT(X)/3.0)
- RETURN
- C
- END
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