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72 lines
2.7 KiB
Fortran
72 lines
2.7 KiB
Fortran
*DECK ATANH
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FUNCTION ATANH (X)
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C***BEGIN PROLOGUE ATANH
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C***PURPOSE Compute the arc hyperbolic tangent.
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C***LIBRARY SLATEC (FNLIB)
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C***CATEGORY C4C
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C***TYPE SINGLE PRECISION (ATANH-S, DATANH-D, CATANH-C)
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C***KEYWORDS ARC HYPERBOLIC TANGENT, ATANH, ELEMENTARY FUNCTIONS,
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C FNLIB, INVERSE HYPERBOLIC TANGENT
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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 ATANH(X) computes the arc hyperbolic tangent of X.
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C
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C Series for ATNH on the interval 0. to 2.50000D-01
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C with weighted error 6.70E-18
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C log weighted error 17.17
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C significant figures required 16.01
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C decimal places required 17.76
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C
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C***REFERENCES (NONE)
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C***ROUTINES CALLED 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 ATANH
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DIMENSION ATNHCS(15)
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LOGICAL FIRST
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SAVE ATNHCS, NTERMS, DXREL, SQEPS, FIRST
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DATA ATNHCS( 1) / .0943951023 93195492E0 /
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DATA ATNHCS( 2) / .0491984370 55786159E0 /
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DATA ATNHCS( 3) / .0021025935 22455432E0 /
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DATA ATNHCS( 4) / .0001073554 44977611E0 /
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DATA ATNHCS( 5) / .0000059782 67249293E0 /
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DATA ATNHCS( 6) / .0000003505 06203088E0 /
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DATA ATNHCS( 7) / .0000000212 63743437E0 /
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DATA ATNHCS( 8) / .0000000013 21694535E0 /
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DATA ATNHCS( 9) / .0000000000 83658755E0 /
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DATA ATNHCS(10) / .0000000000 05370503E0 /
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DATA ATNHCS(11) / .0000000000 00348665E0 /
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DATA ATNHCS(12) / .0000000000 00022845E0 /
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DATA ATNHCS(13) / .0000000000 00001508E0 /
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DATA ATNHCS(14) / .0000000000 00000100E0 /
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DATA ATNHCS(15) / .0000000000 00000006E0 /
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DATA FIRST /.TRUE./
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C***FIRST EXECUTABLE STATEMENT ATANH
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IF (FIRST) THEN
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NTERMS = INITS (ATNHCS, 15, 0.1*R1MACH(3))
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DXREL = SQRT (R1MACH(4))
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SQEPS = SQRT (3.0*R1MACH(3))
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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 .GE. 1.0) CALL XERMSG ('SLATEC', 'ATANH', 'ABS(X) GE 1', 2,
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+ 2)
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C
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IF (1.0-Y .LT. DXREL) CALL XERMSG ('SLATEC', 'ATANH',
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+ 'ANSWER LT HALF PRECISION BECAUSE ABS(X) TOO NEAR 1', 1, 1)
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C
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ATANH = X
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IF (Y.GT.SQEPS .AND. Y.LE.0.5) ATANH = X*(1.0 + CSEVL (8.*X*X-1.,
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1 ATNHCS, NTERMS))
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IF (Y.GT.0.5) ATANH = 0.5*LOG((1.0+X)/(1.0-X))
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C
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RETURN
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END
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