iMachine¶

Returns integer information describing the computer’s arithmetic.

Synopsis¶

iMachine(n)

Required Arguments¶

int n (Input): Index indicating which value is to be returned. It must be between 0 and 12.

Return Value¶

The requested value is returned. If n is out of range, then NaN is returned.

Description¶

The function iMachine returns information describing the computer’s arithmetic. This can be used to make programs machine independent.

\[\texttt{iMachine(0)} = \text{ Number of bits per byte}\]

Assume that integers are represented in M-digit, base-A form as

\[\sigma \textstyle\sum_{k=0}^{M} x_k A^k\]

where σ is the sign and $0\leq x_k<A$ for $k=0,\ldots,M$. Then,

n	Definition
0	C, bits per character
1	A, the base
2	$M_s$, the number of base-A digits in a short int
3	$A^{M_s}-1$, the largest short int
4	$M_l$, the number of base-A digits in a long int
5	$A^{M_1}-1$, the largest long int

Assume that floating-point numbers are represented in N-digit, base B form as

\[\sigma B^E \textstyle\sum_{k=1}^{N} x_k B^{-k}\]

where σ is the sign and $0\leq x_k<B$ for $k=1,\ldots,N$ for and $E_$\leq E\leq E_"$.

Then,

n	Definition
6	B, the base
7	$N_f$, the number of base-B digits in float
8	$E_{\min_f},\text{the smallest } \mathit{float} \text{ exponent}$
9	$E_{\max_f},\text{the largest } \mathit{float} \text{ exponent}$
10	$N_d$, the number of base-B digits in double
11	$E_{\min_d},\text{the smallest } \mathit{double} \text{ exponent}$
12	$E_{\max_d},\text{the largest } \mathit{double} \text{ exponent}$

Example¶

This example prints all the values returned by iMachine on a 32-bit machine with IEEE (Institute for Electrical and Electronics Engineer) arithmetic.

from __future__ import print_function
from pyimsl.math.iMachine import iMachine

for n in range(0, 13):
    ans = iMachine(n)
    print("iMachine[", n, "] = ", ans)

Output¶

iMachine[ 0 ] =  8
iMachine[ 1 ] =  2
iMachine[ 2 ] =  15
iMachine[ 3 ] =  32767
iMachine[ 4 ] =  63
iMachine[ 5 ] =  9223372036854775807
iMachine[ 6 ] =  2
iMachine[ 7 ] =  24
iMachine[ 8 ] =  -125
iMachine[ 9 ] =  128
iMachine[ 10 ] =  53
iMachine[ 11 ] =  -1021
iMachine[ 12 ] =  1024

n	Definition
0	C, bits per character
1	A, the base
2	\(M_s\), the number of base-A digits in a short int
3	\(A^{M_s}-1\), the largest short int
4	\(M_l\), the number of base-A digits in a long int
5	\(A^{M_1}-1\), the largest long int

n	Definition
6	B, the base
7	\(N_f\), the number of base-B digits in float
8	\(E_{\min_f},\text{the smallest } \mathit{float} \text{ exponent}\)
9	\(E_{\max_f},\text{the largest } \mathit{float} \text{ exponent}\)
10	\(N_d\), the number of base-B digits in double
11	\(E_{\min_d},\text{the smallest } \mathit{double} \text{ exponent}\)
12	\(E_{\max_d},\text{the largest } \mathit{double} \text{ exponent}\)