src/numerical/slatec/fortran/dbi.f

   1 *DECK DBI
   2       DOUBLE PRECISION FUNCTION DBI (X)
   3 C***BEGIN PROLOGUE  DBI
   4 C***PURPOSE  Evaluate the Bairy function (the Airy function of the
   5 C            second kind).
   6 C***LIBRARY   SLATEC (FNLIB)
   7 C***CATEGORY  C10D
   8 C***TYPE      DOUBLE PRECISION (BI-S, DBI-D)
   9 C***KEYWORDS  BAIRY FUNCTION, FNLIB, SPECIAL FUNCTIONS
  10 C***AUTHOR  Fullerton, W., (LANL)
  11 C***DESCRIPTION
  12 C
  13 C DBI(X) calculates the double precision Airy function of the
  14 C second kind for double precision argument X.
  15 C
  16 C Series for BIF        on the interval -1.00000E+00 to  1.00000E+00
  17 C                                        with weighted error   1.45E-32
  18 C                                         log weighted error  31.84
  19 C                               significant figures required  30.85
  20 C                                    decimal places required  32.40
  21 C
  22 C Series for BIG        on the interval -1.00000E+00 to  1.00000E+00
  23 C                                        with weighted error   1.29E-33
  24 C                                         log weighted error  32.89
  25 C                               significant figures required  31.48
  26 C                                    decimal places required  33.45
  27 C
  28 C Series for BIF2       on the interval  1.00000E+00 to  8.00000E+00
  29 C                                        with weighted error   6.08E-32
  30 C                                         log weighted error  31.22
  31 C                        approx significant figures required  30.8
  32 C                                    decimal places required  31.80
  33 C
  34 C Series for BIG2       on the interval  1.00000E+00 to  8.00000E+00
  35 C                                        with weighted error   4.91E-33
  36 C                                         log weighted error  32.31
  37 C                        approx significant figures required  31.6
  38 C                                    decimal places required  32.90
  39 C
  40 C***REFERENCES  (NONE)
  41 C***ROUTINES CALLED  D1MACH, D9AIMP, DBIE, DCSEVL, INITDS, XERMSG
  42 C***REVISION HISTORY  (YYMMDD)
  43 C   770701  DATE WRITTEN
  44 C   890531  Changed all specific intrinsics to generic.  (WRB)
  45 C   890531  REVISION DATE from Version 3.2
  46 C   891214  Prologue converted to Version 4.0 format.  (BAB)
  47 C   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)
  48 C***END PROLOGUE  DBI
  49       DOUBLE PRECISION X, BIFCS(13), BIGCS(13), BIF2CS(15), BIG2CS(15),
  50      1  THETA, XM, XMAX, X3SML, Z,  D1MACH, DCSEVL, DBIE
  51       LOGICAL FIRST
  52       SAVE BIFCS, BIGCS, BIF2CS, BIG2CS, NBIF, NBIG,
  53      1 NBIF2, NBIG2, X3SML, XMAX, FIRST
  54       DATA BIFCS(  1) / -.1673021647 1986649483 5374239281 76 D-1     /
  55       DATA BIFCS(  2) / +.1025233583 4249445611 4263627777 57 D+0     /
  56       DATA BIFCS(  3) / +.1708309250 7381516539 4296502420 13 D-2     /
  57       DATA BIFCS(  4) / +.1186254546 7744681179 2164592100 40 D-4     /
  58       DATA BIFCS(  5) / +.4493290701 7792133694 5318879272 42 D-7     /
  59       DATA BIFCS(  6) / +.1069820714 3387889067 5677676636 28 D-9     /
  60       DATA BIFCS(  7) / +.1748064339 9771824706 0105176285 73 D-12    /
  61       DATA BIFCS(  8) / +.2081023107 1761711025 8818918343 99 D-15    /
  62       DATA BIFCS(  9) / +.1884981469 5665416509 9279717333 33 D-18    /
  63       DATA BIFCS( 10) / +.1342577917 3097804625 8826666666 66 D-21    /
  64       DATA BIFCS( 11) / +.7715959342 9658887893 3333333333 33 D-25    /
  65       DATA BIFCS( 12) / +.3653387961 7478566399 9999999999 99 D-28    /
  66       DATA BIFCS( 13) / +.1449756592 7953066666 6666666666 66 D-31    /
  67       DATA BIGCS(  1) / +.2246622324 8574522283 4682201390 24 D-1     /
  68       DATA BIGCS(  2) / +.3736477545 3019545441 7275616667 52 D-1     /
  69       DATA BIGCS(  3) / +.4447621895 7212285696 2152943266 39 D-3     /
  70       DATA BIGCS(  4) / +.2470807563 6329384245 4945919488 82 D-5     /
  71       DATA BIGCS(  5) / +.7919135339 5149635134 8624262855 96 D-8     /
  72       DATA BIGCS(  6) / +.1649807985 1827779880 8878724027 06 D-10    /
  73       DATA BIGCS(  7) / +.2411990666 4835455909 2475011228 41 D-13    /
  74       DATA BIGCS(  8) / +.2610373623 6091436985 1847812693 33 D-16    /
  75       DATA BIGCS(  9) / +.2175308297 7160323853 1237920000 00 D-19    /
  76       DATA BIGCS( 10) / +.1438694640 0390433219 4837333333 33 D-22    /
  77       DATA BIGCS( 11) / +.7734912561 2083468629 3333333333 33 D-26    /
  78       DATA BIGCS( 12) / +.3446929203 3849002666 6666666666 66 D-29    /
  79       DATA BIGCS( 13) / +.1293891927 3216000000 0000000000 00 D-32    /
  80       DATA BIF2CS(  1) / +.0998457269 3816041044 6828425799 3 D+0      /
  81       DATA BIF2CS(  2) / +.4786249778 6300553772 2114673182 31 D+0     /
  82       DATA BIF2CS(  3) / +.2515521196 0433011771 3244154366 75 D-1     /
  83       DATA BIF2CS(  4) / +.5820693885 2326456396 5156978722 16 D-3     /
  84       DATA BIF2CS(  5) / +.7499765964 4377865943 8614573782 17 D-5     /
  85       DATA BIF2CS(  6) / +.6134602870 3493836681 4030103564 74 D-7     /
  86       DATA BIF2CS(  7) / +.3462753885 1480632900 4342687333 59 D-9     /
  87       DATA BIF2CS(  8) / +.1428891008 0270254287 7708467489 31 D-11    /
  88       DATA BIF2CS(  9) / +.4496270429 8334641895 0564721792 00 D-14    /
  89       DATA BIF2CS( 10) / +.1114232306 5833011708 4283001066 66 D-16    /
  90       DATA BIF2CS( 11) / +.2230479106 6175002081 5178666666 66 D-19    /
  91       DATA BIF2CS( 12) / +.3681577873 6393142842 9226666666 66 D-22    /
  92       DATA BIF2CS( 13) / +.5096086844 9338261333 3333333333 33 D-25    /
  93       DATA BIF2CS( 14) / +.6000338692 6288554666 6666666666 66 D-28    /
  94       DATA BIF2CS( 15) / +.6082749744 6570666666 6666666666 66 D-31    /
  95       DATA BIG2CS(  1) / +.0333056621 4551434046 5176188111 647 D+0    /
  96       DATA BIG2CS(  2) / +.1613092151 2319706761 3287532084 943 D+0    /
  97       DATA BIG2CS(  3) / +.6319007309 6134286912 1615634921 173 D-2    /
  98       DATA BIG2CS(  4) / +.1187904568 1625173638 9780192304 567 D-3    /
  99       DATA BIG2CS(  5) / +.1304534588 6200265614 7116485012 843 D-5    /
 100       DATA BIG2CS(  6) / +.9374125995 5352172954 6809615508 936 D-8    /
 101       DATA BIG2CS(  7) / +.4745801886 7472515378 8510169834 595 D-10   /
 102       DATA BIG2CS(  8) / +.1783107265 0948139980 0065667560 946 D-12   /
 103       DATA BIG2CS(  9) / +.5167591927 8495818037 4276356640 000 D-15   /
 104       DATA BIG2CS( 10) / +.1190045083 8682712512 9496251733 333 D-17   /
 105       DATA BIG2CS( 11) / +.2229828806 6640351727 7063466666 666 D-20   /
 106       DATA BIG2CS( 12) / +.3465519230 2768941972 2666666666 666 D-23   /
 107       DATA BIG2CS( 13) / +.4539263363 2050451413 3333333333 333 D-26   /
 108       DATA BIG2CS( 14) / +.5078849965 1352234666 6666666666 666 D-29   /
 109       DATA BIG2CS( 15) / +.4910206746 9653333333 3333333333 333 D-32   /
 110       DATA FIRST /.TRUE./
 111 C***FIRST EXECUTABLE STATEMENT  DBI
 112       IF (FIRST) THEN
 113          ETA = 0.1*REAL(D1MACH(3))
 114          NBIF = INITDS (BIFCS, 13, ETA)
 115          NBIG = INITDS (BIGCS, 13, ETA)
 116          NBIF2 = INITDS (BIF2CS, 15, ETA)
 117          NBIG2 = INITDS (BIG2CS, 15, ETA)
 118 C
 119          X3SML = ETA**0.3333
 120          XMAX = (1.5*LOG(D1MACH(2)))**0.6666D0
 121       ENDIF
 122       FIRST = .FALSE.
 123 C
 124       IF (X.GE.(-1.0D0)) GO TO 20
 125       CALL D9AIMP (X, XM, THETA)
 126       DBI = XM * SIN(THETA)
 127       RETURN
 128 C
 129  20   IF (X.GT.1.0D0) GO TO 30
 130       Z = 0.D0
 131       IF (ABS(X).GT.X3SML) Z = X**3
 132       DBI = 0.625D0 + DCSEVL (Z, BIFCS, NBIF) + X*(0.4375D0 +
 133      1  DCSEVL (Z, BIGCS, NBIG))
 134       RETURN
 135 C
 136  30   IF (X.GT.2.0D0) GO TO 40
 137       Z = (2.0D0*X**3 - 9.0D0)/7.D0
 138       DBI = 1.125D0 + DCSEVL (Z, BIF2CS, NBIF2) + X*(0.625D0 +
 139      1  DCSEVL (Z, BIG2CS, NBIG2))
 140       RETURN
 141 C
 142  40   IF (X .GT. XMAX) CALL XERMSG ('SLATEC', 'DBI',
 143      +   'X SO BIG THAT BI OVERFLOWS', 1, 2)
 144 C
 145       DBI = DBIE(X) * EXP(2.0D0*X*SQRT(X)/3.0D0)
 146       RETURN
 147 C
 148       END