*DECK DAI DOUBLE PRECISION FUNCTION DAI (X) C***BEGIN PROLOGUE DAI C***PURPOSE Evaluate the Airy function. C***LIBRARY SLATEC (FNLIB) C***CATEGORY C10D C***TYPE DOUBLE PRECISION (AI-S, DAI-D) C***KEYWORDS AIRY FUNCTION, FNLIB, SPECIAL FUNCTIONS C***AUTHOR Fullerton, W., (LANL) C***DESCRIPTION C C DAI(X) calculates the double precision Airy function for double C precision argument X. C C Series for AIF on the interval -1.00000E+00 to 1.00000E+00 C with weighted error 8.37E-33 C log weighted error 32.08 C significant figures required 30.87 C decimal places required 32.63 C C Series for AIG on the interval -1.00000E+00 to 1.00000E+00 C with weighted error 7.47E-34 C log weighted error 33.13 C significant figures required 31.50 C decimal places required 33.68 C C***REFERENCES (NONE) C***ROUTINES CALLED D1MACH, D9AIMP, DAIE, DCSEVL, INITDS, 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 920618 Removed space from variable names. (RWC, WRB) C***END PROLOGUE DAI DOUBLE PRECISION X, AIFCS(13), AIGCS(13), THETA, XM, XMAX, X3SML, 1 Z, D1MACH, DCSEVL, DAIE, XMAXT LOGICAL FIRST SAVE AIFCS, AIGCS, NAIF, NAIG, X3SML, XMAX, FIRST DATA AIFCS( 1) / -.3797135849 6669997496 1970894694 14 D-1 / DATA AIFCS( 2) / +.5919188853 7263638574 3197280137 77 D-1 / DATA AIFCS( 3) / +.9862928057 7279975365 6038910440 60 D-3 / DATA AIFCS( 4) / +.6848843819 0765667554 8548301824 12 D-5 / DATA AIFCS( 5) / +.2594202596 2194713019 4892790814 03 D-7 / DATA AIFCS( 6) / +.6176612774 0813750329 4457496972 36 D-10 / DATA AIFCS( 7) / +.1009245417 2466117901 4295562246 01 D-12 / DATA AIFCS( 8) / +.1201479251 1179938141 2880332253 33 D-15 / DATA AIFCS( 9) / +.1088294558 8716991878 5252954666 66 D-18 / DATA AIFCS( 10) / +.7751377219 6684887039 2384000000 00 D-22 / DATA AIFCS( 11) / +.4454811203 7175638391 4666666666 66 D-25 / DATA AIFCS( 12) / +.2109284523 1692343466 6666666666 66 D-28 / DATA AIFCS( 13) / +.8370173591 0741333333 3333333333 33 D-32 / DATA AIGCS( 1) / +.1815236558 1161273011 5562099578 64 D-1 / DATA AIGCS( 2) / +.2157256316 6010755534 0306388199 68 D-1 / DATA AIGCS( 3) / +.2567835698 7483249659 0524280901 33 D-3 / DATA AIGCS( 4) / +.1426521411 9792403898 8294969217 21 D-5 / DATA AIGCS( 5) / +.4572114920 0180426070 4340975581 91 D-8 / DATA AIGCS( 6) / +.9525170843 5647098607 3922788405 92 D-11 / DATA AIGCS( 7) / +.1392563460 5771399051 1504206861 90 D-13 / DATA AIGCS( 8) / +.1507099914 2762379592 3069911386 66 D-16 / DATA AIGCS( 9) / +.1255914831 2567778822 7032053333 33 D-19 / DATA AIGCS( 10) / +.8306307377 0821340343 8293333333 33 D-23 / DATA AIGCS( 11) / +.4465753849 3718567445 3333333333 33 D-26 / DATA AIGCS( 12) / +.1990085503 4518869333 3333333333 33 D-29 / DATA AIGCS( 13) / +.7470288525 6533333333 3333333333 33 D-33 / DATA FIRST /.TRUE./ C***FIRST EXECUTABLE STATEMENT DAI IF (FIRST) THEN NAIF = INITDS (AIFCS, 13, 0.1*REAL(D1MACH(3))) NAIG = INITDS (AIGCS, 13, 0.1*REAL(D1MACH(3))) C X3SML = D1MACH(3)**0.3334D0 XMAXT = (-1.5D0*LOG(D1MACH(1)))**0.6667D0 XMAX = XMAXT - XMAXT*LOG(XMAXT)/(4.0D0*SQRT(XMAXT)+1.0D0) * - 0.01D0 ENDIF FIRST = .FALSE. C IF (X.GE.(-1.D0)) GO TO 20 CALL D9AIMP (X, XM, THETA) DAI = XM * COS(THETA) RETURN C 20 IF (X.GT.1.0D0) GO TO 30 Z = 0.0D0 IF (ABS(X).GT.X3SML) Z = X**3 DAI = 0.375D0 + (DCSEVL (Z, AIFCS, NAIF) - X*(0.25D0 + 1 DCSEVL (Z, AIGCS, NAIG)) ) RETURN C 30 IF (X.GT.XMAX) GO TO 40 DAI = DAIE(X) * EXP(-2.0D0*X*SQRT(X)/3.0D0) RETURN C 40 DAI = 0.0D0 CALL XERMSG ('SLATEC', 'DAI', 'X SO BIG AI UNDERFLOWS', 1, 1) RETURN C END