clnrel.f
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