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53 lines
1.6 KiB
Fortran
53 lines
1.6 KiB
Fortran
*DECK CEXPRL
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COMPLEX FUNCTION CEXPRL (Z)
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C***BEGIN PROLOGUE CEXPRL
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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 COMPLEX (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 (EXP(Z)-1)/Z . For small ABS(Z), we use the Taylor
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C series. We could instead use the expression
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C CEXPRL(Z) = (EXP(X)*EXP(I*Y)-1)/Z
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C = (X*EXPREL(X) * (1 - 2*SIN(Y/2)**2) - 2*SIN(Y/2)**2
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C + I*SIN(Y)*(1+X*EXPREL(X))) / Z
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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 CEXPRL
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COMPLEX Z
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LOGICAL FIRST
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SAVE NTERMS, RBND, FIRST
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DATA FIRST / .TRUE. /
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C***FIRST EXECUTABLE STATEMENT CEXPRL
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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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RBND = R1MACH(3)
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ENDIF
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FIRST = .FALSE.
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C
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R = ABS(Z)
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IF (R.GT.0.5) CEXPRL = (EXP(Z) - 1.0) / Z
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IF (R.GT.0.5) RETURN
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C
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CEXPRL = (1.0, 0.0)
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IF (R.LT.RBND) RETURN
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C
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CEXPRL = (0.0, 0.0)
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DO 20 I=1,NTERMS
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CEXPRL = 1.0 + CEXPRL*Z/(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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