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71 lines
2.6 KiB
Fortran
71 lines
2.6 KiB
Fortran
*DECK BESI0
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FUNCTION BESI0 (X)
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C***BEGIN PROLOGUE BESI0
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C***PURPOSE Compute the hyperbolic Bessel function of the first kind
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C of order zero.
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C***LIBRARY SLATEC (FNLIB)
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C***CATEGORY C10B1
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C***TYPE SINGLE PRECISION (BESI0-S, DBESI0-D)
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C***KEYWORDS FIRST KIND, FNLIB, HYPERBOLIC BESSEL FUNCTION,
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C MODIFIED BESSEL FUNCTION, ORDER ZERO, SPECIAL FUNCTIONS
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C***AUTHOR Fullerton, W., (LANL)
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C***DESCRIPTION
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C
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C BESI0(X) computes the modified (hyperbolic) Bessel function
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C of the first kind of order zero and real argument X.
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C
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C Series for BI0 on the interval 0. to 9.00000D+00
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C with weighted error 2.46E-18
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C log weighted error 17.61
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C significant figures required 17.90
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C decimal places required 18.15
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C
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C***REFERENCES (NONE)
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C***ROUTINES CALLED BESI0E, CSEVL, INITS, R1MACH, XERMSG
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C***REVISION HISTORY (YYMMDD)
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C 770401 DATE WRITTEN
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C 890531 Changed all specific intrinsics to generic. (WRB)
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C 890531 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
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C 900326 Removed duplicate information from DESCRIPTION section.
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C (WRB)
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C***END PROLOGUE BESI0
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DIMENSION BI0CS(12)
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LOGICAL FIRST
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SAVE BI0CS, NTI0, XSML, XMAX, FIRST
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DATA BI0CS( 1) / -.0766054725 2839144951E0 /
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DATA BI0CS( 2) / 1.9273379539 93808270E0 /
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DATA BI0CS( 3) / .2282644586 920301339E0 /
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DATA BI0CS( 4) / .0130489146 6707290428E0 /
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DATA BI0CS( 5) / .0004344270 9008164874E0 /
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DATA BI0CS( 6) / .0000094226 5768600193E0 /
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DATA BI0CS( 7) / .0000001434 0062895106E0 /
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DATA BI0CS( 8) / .0000000016 1384906966E0 /
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DATA BI0CS( 9) / .0000000000 1396650044E0 /
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DATA BI0CS(10) / .0000000000 0009579451E0 /
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DATA BI0CS(11) / .0000000000 0000053339E0 /
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DATA BI0CS(12) / .0000000000 0000000245E0 /
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DATA FIRST /.TRUE./
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C***FIRST EXECUTABLE STATEMENT BESI0
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IF (FIRST) THEN
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NTI0 = INITS (BI0CS, 12, 0.1*R1MACH(3))
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XSML = SQRT (4.5*R1MACH(3))
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XMAX = LOG (R1MACH(2))
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ENDIF
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FIRST = .FALSE.
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C
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Y = ABS(X)
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IF (Y.GT.3.0) GO TO 20
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C
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BESI0 = 1.0
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IF (Y.GT.XSML) BESI0 = 2.75 + CSEVL (Y*Y/4.5-1.0, BI0CS, NTI0)
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RETURN
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C
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20 IF (Y .GT. XMAX) CALL XERMSG ('SLATEC', 'BESI0',
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+ 'ABS(X) SO BIG I0 OVERFLOWS', 1, 2)
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C
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BESI0 = EXP(Y) * BESI0E(X)
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C
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RETURN
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END
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