1      DOUBLE PRECISION FUNCTION DBI(X)
2C***BEGIN PROLOGUE  DBI
3C***DATE WRITTEN   770701   (YYMMDD)
4C***REVISION DATE  820801   (YYMMDD)
5C***CATEGORY NO.  C10D
6C***KEYWORDS  BAIRY FUNCTION,DOUBLE PRECISION,SPECIAL FUNCTION
7C***AUTHOR  FULLERTON, W., (LANL)
8C***PURPOSE  Calculates the d.p. Bairy function (Airy of second kind).
9C***DESCRIPTION
10C
11C DBI(X) calculates the double precision Airy function of the
12C second kind for double precision argument X.
13C
14C Series for BIF        on the interval -1.00000E+00 to  1.00000E+00
15C                                        with weighted error   1.45E-32
16C                                         log weighted error  31.84
17C                               significant figures required  30.85
18C                                    decimal places required  32.40
19C
20C Series for BIG        on the interval -1.00000E+00 to  1.00000E+00
21C                                        with weighted error   1.29E-33
22C                                         log weighted error  32.89
23C                               significant figures required  31.48
24C                                    decimal places required  33.45
25C
26C Series for BIF2       on the interval  1.00000E+00 to  8.00000E+00
27C                                        with weighted error   6.08E-32
28C                                         log weighted error  31.22
29C                        approx significant figures required  30.8
30C                                    decimal places required  31.80
31C
32C Series for BIG2       on the interval  1.00000E+00 to  8.00000E+00
33C                                        with weighted error   4.91E-33
34C                                         log weighted error  32.31
35C                        approx significant figures required  31.6
36C                                    decimal places required  32.90
37C***REFERENCES  (NONE)
38C***ROUTINES CALLED  D1MACH,D9AIMP,DBIE,DCSEVL,INITDS,XERROR
39C***END PROLOGUE  DBI
40      DOUBLE PRECISION X, BIFCS(13), BIGCS(13), BIF2CS(15), BIG2CS(15),
41     1  THETA, XM, XMAX, X3SML, Z,  D1MACH, DCSEVL, DBIE
42      DATA BIF CS(  1) / -.1673021647 1986649483 5374239281 76 D-1     /
43      DATA BIF CS(  2) / +.1025233583 4249445611 4263627777 57 D+0     /
44      DATA BIF CS(  3) / +.1708309250 7381516539 4296502420 13 D-2     /
45      DATA BIF CS(  4) / +.1186254546 7744681179 2164592100 40 D-4     /
46      DATA BIF CS(  5) / +.4493290701 7792133694 5318879272 42 D-7     /
47      DATA BIF CS(  6) / +.1069820714 3387889067 5677676636 28 D-9     /
48      DATA BIF CS(  7) / +.1748064339 9771824706 0105176285 73 D-12    /
49      DATA BIF CS(  8) / +.2081023107 1761711025 8818918343 99 D-15    /
50      DATA BIF CS(  9) / +.1884981469 5665416509 9279717333 33 D-18    /
51      DATA BIF CS( 10) / +.1342577917 3097804625 8826666666 66 D-21    /
52      DATA BIF CS( 11) / +.7715959342 9658887893 3333333333 33 D-25    /
53      DATA BIF CS( 12) / +.3653387961 7478566399 9999999999 99 D-28    /
54      DATA BIF CS( 13) / +.1449756592 7953066666 6666666666 66 D-31    /
55      DATA BIG CS(  1) / +.2246622324 8574522283 4682201390 24 D-1     /
56      DATA BIG CS(  2) / +.3736477545 3019545441 7275616667 52 D-1     /
57      DATA BIG CS(  3) / +.4447621895 7212285696 2152943266 39 D-3     /
58      DATA BIG CS(  4) / +.2470807563 6329384245 4945919488 82 D-5     /
59      DATA BIG CS(  5) / +.7919135339 5149635134 8624262855 96 D-8     /
60      DATA BIG CS(  6) / +.1649807985 1827779880 8878724027 06 D-10    /
61      DATA BIG CS(  7) / +.2411990666 4835455909 2475011228 41 D-13    /
62      DATA BIG CS(  8) / +.2610373623 6091436985 1847812693 33 D-16    /
63      DATA BIG CS(  9) / +.2175308297 7160323853 1237920000 00 D-19    /
64      DATA BIG CS( 10) / +.1438694640 0390433219 4837333333 33 D-22    /
65      DATA BIG CS( 11) / +.7734912561 2083468629 3333333333 33 D-26    /
66      DATA BIG CS( 12) / +.3446929203 3849002666 6666666666 66 D-29    /
67      DATA BIG CS( 13) / +.1293891927 3216000000 0000000000 00 D-32    /
68      DATA BIF2CS(  1) / +.0998457269 3816041044 6828425799 3 D+0      /
69      DATA BIF2CS(  2) / +.4786249778 6300553772 2114673182 31 D+0     /
70      DATA BIF2CS(  3) / +.2515521196 0433011771 3244154366 75 D-1     /
71      DATA BIF2CS(  4) / +.5820693885 2326456396 5156978722 16 D-3     /
72      DATA BIF2CS(  5) / +.7499765964 4377865943 8614573782 17 D-5     /
73      DATA BIF2CS(  6) / +.6134602870 3493836681 4030103564 74 D-7     /
74      DATA BIF2CS(  7) / +.3462753885 1480632900 4342687333 59 D-9     /
75      DATA BIF2CS(  8) / +.1428891008 0270254287 7708467489 31 D-11    /
76      DATA BIF2CS(  9) / +.4496270429 8334641895 0564721792 00 D-14    /
77      DATA BIF2CS( 10) / +.1114232306 5833011708 4283001066 66 D-16    /
78      DATA BIF2CS( 11) / +.2230479106 6175002081 5178666666 66 D-19    /
79      DATA BIF2CS( 12) / +.3681577873 6393142842 9226666666 66 D-22    /
80      DATA BIF2CS( 13) / +.5096086844 9338261333 3333333333 33 D-25    /
81      DATA BIF2CS( 14) / +.6000338692 6288554666 6666666666 66 D-28    /
82      DATA BIF2CS( 15) / +.6082749744 6570666666 6666666666 66 D-31    /
83      DATA BIG2CS(  1) / +.0333056621 4551434046 5176188111 647 D+0    /
84      DATA BIG2CS(  2) / +.1613092151 2319706761 3287532084 943 D+0    /
85      DATA BIG2CS(  3) / +.6319007309 6134286912 1615634921 173 D-2    /
86      DATA BIG2CS(  4) / +.1187904568 1625173638 9780192304 567 D-3    /
87      DATA BIG2CS(  5) / +.1304534588 6200265614 7116485012 843 D-5    /
88      DATA BIG2CS(  6) / +.9374125995 5352172954 6809615508 936 D-8    /
89      DATA BIG2CS(  7) / +.4745801886 7472515378 8510169834 595 D-10   /
90      DATA BIG2CS(  8) / +.1783107265 0948139980 0065667560 946 D-12   /
91      DATA BIG2CS(  9) / +.5167591927 8495818037 4276356640 000 D-15   /
92      DATA BIG2CS( 10) / +.1190045083 8682712512 9496251733 333 D-17   /
93      DATA BIG2CS( 11) / +.2229828806 6640351727 7063466666 666 D-20   /
94      DATA BIG2CS( 12) / +.3465519230 2768941972 2666666666 666 D-23   /
95      DATA BIG2CS( 13) / +.4539263363 2050451413 3333333333 333 D-26   /
96      DATA BIG2CS( 14) / +.5078849965 1352234666 6666666666 666 D-29   /
97      DATA BIG2CS( 15) / +.4910206746 9653333333 3333333333 333 D-32   /
98      DATA NBIF, NBIG, NBIF2, NBIG2, X3SML, XMAX / 4*0, 2*0.D0 /
99C***FIRST EXECUTABLE STATEMENT  DBI
100      IF (NBIF.NE.0) GO TO 10
101      ETA = 0.1*SNGL(D1MACH(3))
102      NBIF = INITDS (BIFCS, 13, ETA)
103      NBIG = INITDS (BIGCS, 13, ETA)
104      NBIF2 = INITDS (BIF2CS, 15, ETA)
105      NBIG2 = INITDS (BIG2CS, 15, ETA)
106C
107      X3SML = ETA**0.3333
108      XMAX = (1.5*DLOG(D1MACH(2)))**0.6666D0
109C
110 10   IF (X.GE.(-1.0D0)) GO TO 20
111      CALL D9AIMP (X, XM, THETA)
112      DBI = XM * DSIN(THETA)
113      RETURN
114C
115 20   IF (X.GT.1.0D0) GO TO 30
116      Z = 0.D0
117      IF (DABS(X).GT.X3SML) Z = X**3
118      DBI = 0.625 + DCSEVL (Z, BIFCS, NBIF) + X*(0.4375D0 +
119     1  DCSEVL (Z, BIGCS, NBIG))
120      RETURN
121C
122 30   IF (X.GT.2.0D0) GO TO 40
123      Z = (2.0D0*X**3 - 9.0D0)/7.D0
124      DBI = 1.125D0 + DCSEVL (Z, BIF2CS, NBIF2) + X*(0.625D0 +
125     1  DCSEVL (Z, BIG2CS, NBIG2))
126      RETURN
127C
128 40   IF (X.GT.XMAX) CALL XERROR ( 'DBI     X SO BIG THAT BI OVERFLOWS',
129     1 34, 1, 2)
130C
131      DBI = DBIE(X) * DEXP(2.0D0*X*DSQRT(X)/3.0D0)
132      RETURN
133C
134      END
135