machine¶
Returns information describing the computer’s floating-point arithmetic.
Synopsis¶
machine(n)
Required Arguments¶
- int
n(Input) - Index indicating which value is to be returned.The index must be between 1 and 8.
Return Value¶
The requested value is returned. If n is out of range, then NaN is
returned.
Description¶
The function machine returns information describing the computer’s
floating-point arithmetic. This can be used to make programs machine
independent. In addition, some of the functions are also important in
setting missing values (see below).
Assume that float numbers are represented in \(N_f\)-digit, base B form as
where σ is the sign, \(0\leq x_k<B\) for \(k=1,2,\ldots,N_f\), and
Note that B = iMachine(6), \(N_f\) = iMachine(7),
and
The ANSI/IEEE Std 754-1985 standard for binary arithmetic uses NaN (not a
number) as the result of various otherwise illegal operations, such as
computing 0/0. On computers that do not support NaN, a value larger than
machine(2) is returned for machine(6). On computers that do not have
a special representation for infinity, machine(2) returns the same value
as machine(7).
The function machine is defined by the following table:
| n | Definition |
|---|---|
| 1 | \(B^{E \min_f^{-1}}\), the smallest positive number |
| 2 | \(B^{E \max_f}\left( 1-B^{-Nf} \right)\), the largest number |
| 3 | \(B^{-N}_f\), the smallest relative spacing |
| 4 | \(B^{1-N_f}\), the largest relative spacing |
| 5 | \(log_{10}(B)\) |
| 6 | NaN (not a number) |
| 7 | positive machine infinity |
| 8 | negative machine infinity |
The function machine retrieves machine constants which define the
computer’s double arithmetic. Note that for double B = iMachine(6),
\(N_d\) = iMachine(10),
and
Missing values in PyIMSL functions are always indicated by NaN (Not a
Number). This is machine(6). There is no missing-value indicator for
integers. Users will almost always have to convert from their missing value
indicators to NaN.
Example¶
This example prints all eight values returned by machine and by
machine on a machine with IEEE arithmetic.
from __future__ import print_function
from pyimsl.math.machine import machine
for n in range(1, 9):
dans = machine(n)
print("machine[", n, "] = ", dans)
Output¶
machine[ 1 ] = 2.2250738585072014e-308
machine[ 2 ] = 1.7976931348623157e+308
machine[ 3 ] = 1.1102230246251565e-16
machine[ 4 ] = 2.220446049250313e-16
machine[ 5 ] = 0.30102998001990605
machine[ 6 ] = nan
machine[ 7 ] = inf
machine[ 8 ] = -inf