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- *DECK CLNREL
- COMPLEX FUNCTION CLNREL (Z)
- C***BEGIN PROLOGUE CLNREL
- C***PURPOSE Evaluate ln(1+X) accurate in the sense of relative error.
- C***LIBRARY SLATEC (FNLIB)
- C***CATEGORY C4B
- C***TYPE COMPLEX (ALNREL-S, DLNREL-D, CLNREL-C)
- C***KEYWORDS ELEMENTARY FUNCTIONS, FNLIB, LOGARITHM
- C***AUTHOR Fullerton, W., (LANL)
- C***DESCRIPTION
- C
- C CLNREL(Z) = LOG(1+Z) with relative error accuracy near Z = 0.
- C Let RHO = ABS(Z) and
- C R**2 = ABS(1+Z)**2 = (1+X)**2 + Y**2 = 1 + 2*X + RHO**2 .
- C Now if RHO is small we may evaluate CLNREL(Z) accurately by
- C LOG(1+Z) = CMPLX (LOG(R), CARG(1+Z))
- C = CMPLX (0.5*LOG(R**2), CARG(1+Z))
- C = CMPLX (0.5*ALNREL(2*X+RHO**2), CARG(1+Z))
- C
- C***REFERENCES (NONE)
- C***ROUTINES CALLED ALNREL, CARG, R1MACH, XERMSG
- 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 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
- C***END PROLOGUE CLNREL
- COMPLEX Z
- SAVE SQEPS
- DATA SQEPS /0.0/
- C***FIRST EXECUTABLE STATEMENT CLNREL
- IF (SQEPS.EQ.0.) SQEPS = SQRT (R1MACH(4))
- C
- IF (ABS(1.+Z) .LT. SQEPS) CALL XERMSG ('SLATEC', 'CLNREL',
- + 'ANSWER LT HALF PRECISION BECAUSE Z TOO NEAR -1', 1, 1)
- C
- RHO = ABS(Z)
- IF (RHO.GT.0.375) CLNREL = LOG (1.0+Z)
- IF (RHO.GT.0.375) RETURN
- C
- X = REAL(Z)
- CLNREL = CMPLX (0.5*ALNREL(2.*X+RHO**2), CARG(1.0+Z))
- C
- RETURN
- END
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