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- *DECK ASINH
- FUNCTION ASINH (X)
- C***BEGIN PROLOGUE ASINH
- C***PURPOSE Compute the arc hyperbolic sine.
- C***LIBRARY SLATEC (FNLIB)
- C***CATEGORY C4C
- C***TYPE SINGLE PRECISION (ASINH-S, DASINH-D, CASINH-C)
- C***KEYWORDS ARC HYPERBOLIC SINE, ASINH, ELEMENTARY FUNCTIONS, FNLIB,
- C INVERSE HYPERBOLIC SINE
- C***AUTHOR Fullerton, W., (LANL)
- C***DESCRIPTION
- C
- C ASINH(X) computes the arc hyperbolic sine of X.
- C
- C Series for ASNH on the interval 0. to 1.00000D+00
- C with weighted error 2.19E-17
- C log weighted error 16.66
- C significant figures required 15.60
- C decimal places required 17.31
- C
- C***REFERENCES (NONE)
- C***ROUTINES CALLED CSEVL, INITS, R1MACH
- C***REVISION HISTORY (YYMMDD)
- C 770401 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***END PROLOGUE ASINH
- DIMENSION ASNHCS(20)
- LOGICAL FIRST
- SAVE ALN2, ASNHCS, NTERMS, XMAX, SQEPS, FIRST
- DATA ALN2 /0.6931471805 5994530942E0/
- DATA ASNHCS( 1) / -.1282003991 1738186E0 /
- DATA ASNHCS( 2) / -.0588117611 89951768E0 /
- DATA ASNHCS( 3) / .0047274654 32212481E0 /
- DATA ASNHCS( 4) / -.0004938363 16265361E0 /
- DATA ASNHCS( 5) / .0000585062 07058557E0 /
- DATA ASNHCS( 6) / -.0000074669 98328931E0 /
- DATA ASNHCS( 7) / .0000010011 69358355E0 /
- DATA ASNHCS( 8) / -.0000001390 35438587E0 /
- DATA ASNHCS( 9) / .0000000198 23169483E0 /
- DATA ASNHCS(10) / -.0000000028 84746841E0 /
- DATA ASNHCS(11) / .0000000004 26729654E0 /
- DATA ASNHCS(12) / -.0000000000 63976084E0 /
- DATA ASNHCS(13) / .0000000000 09699168E0 /
- DATA ASNHCS(14) / -.0000000000 01484427E0 /
- DATA ASNHCS(15) / .0000000000 00229037E0 /
- DATA ASNHCS(16) / -.0000000000 00035588E0 /
- DATA ASNHCS(17) / .0000000000 00005563E0 /
- DATA ASNHCS(18) / -.0000000000 00000874E0 /
- DATA ASNHCS(19) / .0000000000 00000138E0 /
- DATA ASNHCS(20) / -.0000000000 00000021E0 /
- DATA FIRST /.TRUE./
- C***FIRST EXECUTABLE STATEMENT ASINH
- IF (FIRST) THEN
- NTERMS = INITS (ASNHCS, 20, 0.1*R1MACH(3))
- SQEPS = SQRT (R1MACH(3))
- XMAX = 1.0/SQEPS
- ENDIF
- FIRST = .FALSE.
- C
- Y = ABS(X)
- IF (Y.GT.1.0) GO TO 20
- C
- ASINH = X
- IF (Y.GT.SQEPS) ASINH = X*(1.0 + CSEVL (2.*X*X-1., ASNHCS,NTERMS))
- RETURN
- C
- 20 IF (Y.LT.XMAX) ASINH = LOG (Y + SQRT(Y**2+1.))
- IF (Y.GE.XMAX) ASINH = ALN2 + LOG(Y)
- ASINH = SIGN (ASINH, X)
- C
- RETURN
- END
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