Dynamically Compute Machine Constants

MACHAR is a C++ library which dynamically computes constants that characterize the floating point arithmetic system on a computer, by William Cody.

This includes the value of the "machine epsilon", the smallest number that can be added to 1 and make a difference. However, it includes many other quantities of interest, including the arithmetic base, the largest and smallest magnitudes, and so on.

The FORTRAN77 version of these routines was supplied as part of ACM TOMS algorithm 665.

A C version of these routines was supplied as part of ACM TOMS algorithm 722.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


MACHAR is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

MACHINE, a C++ library which stores the appropriate values of machine constants for a given machine.


Original FORTRAN77 version by William Cody. C++ version by John Burkardt.


  1. William Cody,
    Algorithm 665: MACHAR, a subroutine to dynamically determine machine parameters,
    ACM Transactions on Mathematical Software,
    Volume 14, Number 4, December 1988, pages 303-311.
  2. William Cody, William Waite,
    Software Manual for the Elementary Functions,
    Prentice Hall, 1980,
    ISBN: 0138220646,
    LC: QA331.C635.
  3. Morven Gentleman, Scott Marovich,
    More on Algorithms that Reveal Properties of Floating Point Arithmetic Units,
    Communications of the ACM,
    Volume 17, Number 5, May 1974, pages 276-277.
  4. Michael Malcolm,
    Algorithms to Reveal Properties of Floating Point Arithmetic,
    Communications of the ACM,
    Volume 15, Number 11, November 1972, pages 949-951.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the C++ source codes.

Last revised on 11 November 2006.