MACHAR
Dynamic Computation of Machine Constants

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

The constants include 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 default variable type in MATLAB is similar to a double precision complex variable. When doing real arithmetic, this means that calculations are done in double precision. MATLAB also offers a function called single that can be used to convert a value to a single precision real value. When used to initialize a variable, single effectively "declares" that variable to be a single precision real variable.

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.

Note that "Numerical Recipes" includes a listing and discussion of MACHAR.

Licensing:

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

Languages:

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

Related Data and Programs:

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

Author:

Original FORTRAN77 version by William Cody. MATLAB version by John Burkardt.

Reference:

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.
5. William Press, Brian Flannery, Saul Teukolsky, William Vetterling,
   Numerical Recipes in FORTRAN: The Art of Scientific Computing,
   Second Edition,
   Cambridge University Press, 1992,
   ISBN: 0-521-43064-X,
   LC: QA297.N866.

Source Code:

• r4_machar.m, determines single precision machine constants.
• r8_machar.m, determines double precision machine constants.
• timestamp.m, prints the current YMDHMS date as a time stamp.

Examples and Tests:

• machar_test.m, calls all the tests.
• machar_test01.m, tests R4_MACHAR.
• machar_test02.m, tests R8_MACHAR.
• machar_test_output.txt, the output file.

You can go up one level to the MATLAB source codes.