# cexprl.f

          COMPLEX FUNCTION CEXPRL (Z)
    C***BEGIN PROLOGUE  CEXPRL
    C***PURPOSE  Calculate the relative error exponential (EXP(X)-1)/X.
    C***LIBRARY   SLATEC (FNLIB)
    C***CATEGORY  C4B
    C***TYPE      COMPLEX (EXPREL-S, DEXPRL-D, CEXPRL-C)
    C***KEYWORDS  ELEMENTARY FUNCTIONS, EXPONENTIAL, FIRST ORDER, FNLIB
    C***AUTHOR  Fullerton, W., (LANL)
    C***DESCRIPTION
    C
    C Evaluate  (EXP(Z)-1)/Z .  For small ABS(Z), we use the Taylor
    C series.  We could instead use the expression
    C        CEXPRL(Z) = (EXP(X)*EXP(I*Y)-1)/Z
    C                  = (X*EXPREL(X) * (1 - 2*SIN(Y/2)**2) - 2*SIN(Y/2)**2
    C                                    + I*SIN(Y)*(1+X*EXPREL(X))) / Z
    C
    C***REFERENCES  (NONE)
    C***ROUTINES CALLED  R1MACH
    C***REVISION HISTORY  (YYMMDD)
    C   770801  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***END PROLOGUE  CEXPRL