MACHINE Function (PV-WAVE Advantage)

IMSL Statistics Reference Guide > Utilities > MACHINE Function (PV-WAVE Advantage)

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:

where σ is the sign and 0 ≤ xk < A for k = 0, ..., M. Integer Tags describes the tags.

Table 15-1: Integer Tags
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. Float Tags describes the tags.

Table 15-2: Float 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 IMACHINE Structure:

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

Version 2017.0