An algorithm to compute the gamma function and the loggamma function of a complex variable is presented. The standard algorithm is modified in several respects to insure the continuity of the function value and to reduce accumulation of round-off errors. In addition to computation of function values, this algorithm includes an object-time estimation of round-off errors. Experimental data with regard to the effectiveness of this error control are presented. A Fortran program for the algorithm appears in the algorithms section of this issue.