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46 lines
1.6 KiB
Fortran
46 lines
1.6 KiB
Fortran
*DECK CLNREL
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COMPLEX FUNCTION CLNREL (Z)
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C***BEGIN PROLOGUE CLNREL
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C***PURPOSE Evaluate ln(1+X) accurate in the sense of relative error.
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C***LIBRARY SLATEC (FNLIB)
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C***CATEGORY C4B
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C***TYPE COMPLEX (ALNREL-S, DLNREL-D, CLNREL-C)
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C***KEYWORDS ELEMENTARY FUNCTIONS, FNLIB, LOGARITHM
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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 CLNREL(Z) = LOG(1+Z) with relative error accuracy near Z = 0.
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C Let RHO = ABS(Z) and
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C R**2 = ABS(1+Z)**2 = (1+X)**2 + Y**2 = 1 + 2*X + RHO**2 .
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C Now if RHO is small we may evaluate CLNREL(Z) accurately by
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C LOG(1+Z) = CMPLX (LOG(R), CARG(1+Z))
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C = CMPLX (0.5*LOG(R**2), CARG(1+Z))
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C = CMPLX (0.5*ALNREL(2*X+RHO**2), CARG(1+Z))
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C
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C***REFERENCES (NONE)
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C***ROUTINES CALLED ALNREL, CARG, 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***END PROLOGUE CLNREL
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COMPLEX Z
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SAVE SQEPS
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DATA SQEPS /0.0/
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C***FIRST EXECUTABLE STATEMENT CLNREL
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IF (SQEPS.EQ.0.) SQEPS = SQRT (R1MACH(4))
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C
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IF (ABS(1.+Z) .LT. SQEPS) CALL XERMSG ('SLATEC', 'CLNREL',
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+ 'ANSWER LT HALF PRECISION BECAUSE Z TOO NEAR -1', 1, 1)
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C
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RHO = ABS(Z)
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IF (RHO.GT.0.375) CLNREL = LOG (1.0+Z)
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IF (RHO.GT.0.375) RETURN
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C
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X = REAL(Z)
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CLNREL = CMPLX (0.5*ALNREL(2.*X+RHO**2), CARG(1.0+Z))
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C
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RETURN
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END
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