# 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