# MACHINE Table of Machine Constants

MACHINE is a FORTRAN77 library which returns machine constants for integer and single and double precision quantities.

We assume that integer are represented using S digits in base A:

Sign * ( X(S-1)*A^(S-1) + ... + X(1)*A + X(0))
and that real numbers are represented using a mantissa T, base B and exponent E as:
Sign * T * BE

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.

R1MACH returns quantities associated with single 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)

### Languages:

MACHINE 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:

MACHAR, a FORTRAN77 library which can compute machine arithmetic quantities dynamically.

SLATEC, a FORTRAN90 library which includes MACHINE.

### Reference:

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.
2. http://www.netlib.org/toms/528
the NETLIB web site for ACM TOMS algorithms.

### List of Routines:

• D1MACH returns double precision machine constants.
• I1MACH returns integer machine constants.
• R1MACH returns single precision machine constants.

You can go up one level to the FORTRAN77 source codes.

Last revised on 08 December 2007.