jburkardt

MACHINE\ Table of Machine Constants {#machine-table-of-machine-constants align=”center”} ==========================

MACHINE is a C++ library which returns machine constants, particularly those related to arithmetic with single precision real and double precision real quantities.

MACHINE must be reset for your computer {#machine-must-be-reset-for-your-computer align=”center”}

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 {#machines-arithmetic-assumptions align=”center”}

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 * B^E^

What MACHINE can return {#what-machine-can-return align=”center”}

D1MACH returns quantities associated with double precision arithmetic, including:

B\^(EMIN-1), the smallest positive magnitude.
B\^EMAX*(1-B\^(-T)), the largest magnitude.
B\^(-T), the smallest relative spacing.
B\^(1-T), the largest relative spacing.
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.

the standard input unit.
the standard output unit.
the standard punch unit.
the standard error message unit.
the number of bits per integer storage unit.
the number of characters per integer storage unit.
A, the base for integers.
S, the number of base A digits in an integer.
A\^S-1, the largest integer.
B, the base for single and double precision numbers.
T, the number of base B digits for single precision.
EMIN, the smallest exponent E for single precision.
EMAX, the largest exponent E for single precision.
T, the number of base B digits for double precision.
EMIN, the smallest exponent E for double precision.
EMAX, the largest exponent E for double precision.

R1MACH returns quantities associated with single precision arithmetic, including:

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

Licensing: {#licensing align=”center”}

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

Languages: {#languages align=”center”}

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.

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

Reference: {#reference align=”center”}

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

Source Code: {#source-code align=”center”}

machine.cpp, the source code.
machine.hpp, the include file.

Examples and Tests: {#examples-and-tests align=”center”}

machine_prb.cpp, a sample calling program.
machine_prb_output.txt, the output from a run of the sample program.

List of Routines: {#list-of-routines align=”center”}

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 C++ source codes.

Last revised on 24 April 2007.