MACHINE Function
Returns information describing the computer’s arithmetic.
Usage
result = MACHINE( )
Returned Value
result—The information describing the computer’s arithmetic is returned in a structure.
Output Keywords
Float—If present and nonzero, a structure containing the information describing the single-precision, floating-point arithmetic is returned.
Double—If present and nonzero, a structure containing the information describing the single-precision, floating-point arithmetic is returned.
Discussion
Function MACHINE returns information describing the computer’s arithmetic. This can be used to make programs machine independent. The information returned by MACHINE is in the form of a structure. A different structure is used for each type: integer, float, and double. Depending on how MACHINE is called, a different structure is returned.
The default action of MACHINE is to return the structure IMACHINE which contains integer information on the computer’s arithmetic. By using either the keywords Float or Double, information about the floating- or double-precision arithmetic is returned in structures FMACHINE or DMACHINE.
The contents of the these structures are described in the following sections.
Integer Information: IMACHINE
Assume that integers are represented in M-digit, base A form as:
Tag | Definition |
|---|---|
BITS_PER_CHAR | C, bits per character |
INTEGER_BASE | A, the base |
INTEGER_DIGITS | Ms, the number of base-A digits in a short int |
MAX_INTEGER |  , the largest short int |
LONG_DIGITS | Ml, the number of base-A digits in a long int |
MAX_LONG |  , the largest long int |
Assume that floating-point numbers are represented in N-digit, base B form as:
where σ is the sign and 0 ≤ xk < B for k = 1, ..., N for and Emin ≤ E ≤ Emax. Table 15-2: Float Tags describes the tags.
Tag | Definition |
|---|---|
FLOAT_BASE | B, the base |
FLOAT_DIGITS | Nf, the number of base-B digits in float |
FLOAT_MIN_EXP |  , the smallest float exponent |
FLOAT_MAX_EXP |  , the largest float exponent |
DOUBLE_DIGETS | Nd, the number of base-B digits in double |
DOUBLE_MIN_EXP |  , the largest long int |
DOUBLE_MAX_EXP |  , the number of base-B digits in double |
Floating- and Double-precision Information: FMACHINE and DMACHINE
Information concerning the floating- or double-precision arithmetic of the computer is contained in the structures FMACHINE and DMACHINE. These structures are returned into named variables by calling MACHINE with the keywords Float for FMACHINE and Double for DMACHINE.
Assume that float numbers are represented in Nf- digit, base B form as:
where σ is the sign, 0 ≤ xk < B for k = 1, 2, ..., Nf and:
Note that if we make the assignment imach = MACHINE( ), then B = imach.FLOAT_BASE, Nf = imach.FLOAT_DIGITS:
and:
The ANSI/IEEE 754-1985 standard for binary arithmetic uses NaN (Not a Number) as the result of various otherwise illegal operations, such as computing 0/0. If the assignment amach = MACHINE(/Float) is made, then on computers that do not support NaN, a value larger than amach. MAX_POS is returned in amach.NAN. On computers that do not have a special representation for infinity, amach.POS_INF contains the same value as amach.MAX_POS.
The structure IMACHINE is defined by Table 15-3: IMACHINE Structure:
Tag | Definition |
|---|---|
MIN_POS | BEminf –1, the smallest positive number |
MAX_POS | BEmaxf(1 – B–Nf ), the largest number |
MIN_REL_SPACE | B – Nf, the smallest relative spacing |
MAX_REL_SPACE | B1– Nf, the largest relative spacing |
LOG10_BASE | log10(B) |
NAN | NaN |
POS_INF | positive machine infinity |
NEG_INF | negative machine infinity |
The structure DMACHINE contains machine constants that define the computer’s double arithmetic. Note that for double, if the assignment imach = MACHINE( ) is made, then it:
B = imach.FLOAT_BASE, Nf = imach.DOUBLE_DIGITS
and:
Missing values in PV-WAVE IMSL Statistics procedures and functions are often indicated by NaN. There is no missing-value indicator for integers. Users ususally have to convert from their missing value indicators to NaN.
Example
In this example, all values returned by MACHINE are printed on a machine with IEEE (Institute for Electrical and Electronics Engineering) arithmetic.
i = MACHINE()
f = MACHINE(/Float)
d = MACHINE(/Double)
; Call INFO with keyword Structure set to view the contents of the
; structures.
INFO, i, f, d, /Structure
This results in the following output:
** Structure IMACHINE, 13 tags, length=52:
BITS_PER_CHAR LONG 8
INTEGER_BASE LONG 2
INTEGER_DIGITS LONG 15
MAX_INTEGER LONG 32767
LONG_DIGITS LONG 31
MAX_LONG LONG 2147483647
FLOAT_BASE LONG 2
FLOAT_DIGITS LONG 24
FLOAT_MIN_EXP LONG -125
FLOAT_MAX_EXP LONG 128
DOUBLE_DIGITS LONG 53
DOUBLE_MIN_EXP LONG -1021
DOUBLE_MAX_EXP LONG 1024
** Structure FMACHINE, 8 tags, length=32:
MIN_POS FLOAT 1.17549e-38
MAX_POS FLOAT 3.40282e+38
MIN_REL_SPACE FLOAT 5.96046e-08
MAX_REL_SPACE FLOAT 1.19209e-07
LOG_10 FLOAT 0.301030
NAN FLOAT NaN
POS_INF FLOAT Inf
NEG_INF FLOAT -Inf
** Structure DMACHINE, 8 tags, length=64:
MIN_POS DOUBLE 2.2250739e-308
MAX_POS DOUBLE 1.7976931e+308
MIN_REL_SPACE DOUBLE 1.1102230e-16
MAX_REL_SPACE DOUBLE 2.2204460e-16
LOG_10 DOUBLE 0.30102998
NAN DOUBLE NaN
POS_INF DOUBLE Infinity
NEG_INF DOUBLE -Infinity
