toms743, a Python code which evaluates Lambert's W function. This is a version of ACM TOMS algorithm 743, by Barry, Barry and Culligan-Hensley.

Lambert's W function W(X) satisfies the equation

        W(x) * exp ( W(x) ) = x

The text of many ACM TOMS algorithms is available online through ACM: or NETLIB:


The computer code and data files made available on this web page are distributed under the MIT license


toms743 is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

test_values, a Python code which contains routines which return sample values of various functions, including the modified beta function, and the logarithm of the gamma function.


  1. Fred Fritsch, RE Shafer, WP Crowley,
    Algorithm 443: Solution of the Transcendental Equation W*exp(W)=X,
    Communications of the ACM,
    Volume 16, Number 1, February 1973, pages 123-124.
  2. Andrew Barry, S. J. Barry, Patricia Culligan-Hensley,
    Algorithm 743: WAPR - A Fortran routine for calculating real values of the W-function,
    ACM Transactions on Mathematical Software,
    Volume 21, Number 2, June 1995, pages 172-181.

Source Code:

Last revised on 07 February 2020.