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55 lines
1.7 KiB
Fortran
55 lines
1.7 KiB
Fortran
*DECK DEXPRL
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DOUBLE PRECISION FUNCTION DEXPRL (X)
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C***BEGIN PROLOGUE DEXPRL
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C***PURPOSE Calculate the relative error exponential (EXP(X)-1)/X.
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C***LIBRARY SLATEC (FNLIB)
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C***CATEGORY C4B
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C***TYPE DOUBLE PRECISION (EXPREL-S, DEXPRL-D, CEXPRL-C)
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C***KEYWORDS ELEMENTARY FUNCTIONS, EXPONENTIAL, FIRST ORDER, FNLIB
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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 Evaluate EXPREL(X) = (EXP(X) - 1.0) / X. For small ABS(X) the
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C Taylor series is used. If X is negative the reflection formula
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C EXPREL(X) = EXP(X) * EXPREL(ABS(X))
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C may be used. This reflection formula will be of use when the
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C evaluation for small ABS(X) is done by Chebyshev series rather than
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C Taylor series.
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C
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C***REFERENCES (NONE)
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C***ROUTINES CALLED D1MACH
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C***REVISION HISTORY (YYMMDD)
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C 770801 DATE WRITTEN
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C 890531 Changed all specific intrinsics to generic. (WRB)
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C 890911 Removed unnecessary intrinsics. (WRB)
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C 890911 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***END PROLOGUE DEXPRL
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DOUBLE PRECISION X, ABSX, ALNEPS, XBND, XLN, XN, D1MACH
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LOGICAL FIRST
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SAVE NTERMS, XBND, FIRST
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DATA FIRST /.TRUE./
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C***FIRST EXECUTABLE STATEMENT DEXPRL
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IF (FIRST) THEN
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ALNEPS = LOG(D1MACH(3))
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XN = 3.72D0 - 0.3D0*ALNEPS
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XLN = LOG((XN+1.0D0)/1.36D0)
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NTERMS = XN - (XN*XLN+ALNEPS)/(XLN+1.36D0) + 1.5D0
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XBND = D1MACH(3)
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ENDIF
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FIRST = .FALSE.
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C
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ABSX = ABS(X)
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IF (ABSX.GT.0.5D0) DEXPRL = (EXP(X)-1.0D0)/X
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IF (ABSX.GT.0.5D0) RETURN
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C
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DEXPRL = 1.0D0
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IF (ABSX.LT.XBND) RETURN
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C
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DEXPRL = 0.0D0
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DO 20 I=1,NTERMS
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DEXPRL = 1.0D0 + DEXPRL*X/(NTERMS+2-I)
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20 CONTINUE
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C
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RETURN
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END
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