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53 lines
1.6 KiB
Fortran
53 lines
1.6 KiB
Fortran
*DECK EXPREL
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FUNCTION EXPREL (X)
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C***BEGIN PROLOGUE EXPREL
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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 SINGLE 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. EXPREL and X are single precision.
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C
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C***REFERENCES (NONE)
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C***ROUTINES CALLED R1MACH
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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 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***END PROLOGUE EXPREL
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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 EXPREL
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IF (FIRST) THEN
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ALNEPS = LOG(R1MACH(3))
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XN = 3.72 - 0.3*ALNEPS
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XLN = LOG((XN+1.0)/1.36)
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NTERMS = XN - (XN*XLN+ALNEPS)/(XLN+1.36) + 1.5
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XBND = R1MACH(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.0.5) EXPREL = (EXP(X) - 1.0) / X
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IF (ABSX.GT.0.5) RETURN
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C
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EXPREL = 1.0
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IF (ABSX.LT.XBND) RETURN
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C
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EXPREL = 0.0
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DO 20 I=1,NTERMS
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EXPREL = 1.0 + EXPREL*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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