Table of Machine Constants

MACHINE, an R library which returns machine constants, particularly those related to arithmetic with double precision real and integer quantities.

MACHINE must be reset for your computer

MACHINE is not an "intelligent" program; it's simply a way to store and retrieve the information necessary to describe the arithmetic performed on a given computer. Therefore, if you plan to use MACHINE on a particular kind of computer, you must verify that the values being returned are appropriate.

One way to do this is to run the program MACHAR which is an "intelligent" program that actually tries to determine machine arithmetic properties dynamically.

MACHINE's arithmetic assumptions

MACHINE uses some simple conventions to describe how integers and real numbers are stored on an arbitrary computer.

MACHINE assumes that integers are represented using S digits in base A:

Sign * ( X(S-1)*A^(S-1) + ... + X(1)*A + X(0))

MACHINE assumes that real numbers are represented using a mantissa T, base B and exponent E as:

Sign * T * BE

What MACHINE can return

D1MACH returns quantities associated with double precision arithmetic, including:

  1. B^(EMIN-1), the smallest positive magnitude.
  2. B^EMAX*(1-B^(-T)), the largest magnitude.
  3. B^(-T), the smallest relative spacing.
  4. B^(1-T), the largest relative spacing.
  5. log10(B)

I1MACH returns quantities associated with integer arithmetic, as well as some integer quantities associated with real and double precision arithmetic, and other machine-specific information.

  1. the standard input unit.
  2. the standard output unit.
  3. the standard punch unit.
  4. the standard error message unit.
  5. the number of bits per integer storage unit.
  6. the number of characters per integer storage unit.
  7. A, the base for integers.
  8. S, the number of base A digits in an integer.
  9. A^S-1, the largest integer.
  10. B, the base for single and double precision numbers.
  11. T, the number of base B digits for single precision.
  12. EMIN, the smallest exponent E for single precision.
  13. EMAX, the largest exponent E for single precision.
  14. T, the number of base B digits for double precision.
  15. EMIN, the smallest exponent E for double precision.
  16. EMAX, the largest exponent E for double precision.


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


machine is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version and an R version.

Related Data and Programs:



  1. Phyllis Fox, Andrew Hall, Norman Schryer,
    Algorithm 528: Framework for a Portable Library,
    ACM Transactions on Mathematical Software,
    Volume 4, Number 2, June 1978, page 176-188.
    the NETLIB web site for ACM TOMS algorithms.

Source Code:

Last revised on 06 February 2020.