CONSTANT Function

Computes machine and mathematical constants.

Category:

Mathematical

Syntax

CONSTANT(constant<, parameter> )

Required Argument

constant

is a character constant, variable, or expression that identifies the constant to be returned. Valid constants are as follows:

Description	Constant
The natural base	'E'
Euler constant	'EULER'
Pi	'PI'
Exact integer	'EXACTINT' <,nbytes>
The largest double-precision number	'BIG'
The log with respect to base of BIG	'LOGBIG' <,base>
The square root of BIG	'SQRTBIG'
The smallest double-precision number	'SMALL'
The log with respect to base of SMALL	'LOGSMALL' <,base>
The square root of SMALL	'SQRTSMALL'
Machine precision constant	'MACEPS'
The log with respect to base of MACEPS	'LOGMACEPS' <,base>
The square root of MACEPS	'SQRTMACEPS'

Optional Argument

parameter

is an optional numeric parameter. Some of the constants specified in constant have an optional argument that alters the functionality of the CONSTANT function.

Details

Overview

CAUTION:

In some operating environments, the run-time library might have limitations that prevent the use of the full range of floating-point numbers that the hardware provides.

In such cases, the CONSTANT function attempts to return values that are compatible with the limitations of the run-time library. For example, if the run-time library cannot compute EXP(LOG(CONSTANT('BIG'))), then CONSTANT('LOGBIG') will not return the same value as LOG(CONSTANT('BIG')), but will return a value such that EXP(CONSTANT('LOGBIG')) can be computed.

The natural base

CONSTANT('E')

The natural base is described by the following equation:

\begin{matrix} \lim_{x \to 0} {(1 + x)}^{\frac{1}{x}} \approx 2.718281828459045 \end{matrix}

Euler constant

CONSTANT('EULER')

Euler's constant is described by the following equation:

\begin{matrix} \lim_{n \to \infty} {Σ_{j = 1}^{j = n} \frac{1}{j} - l o g (n)} \approx 0.577215664901532860 \end{matrix}

Pi

CONSTANT('PI')

Pi is the ratio between the circumference and the diameter of a circle. Many expressions exist for computing this constant. One such expression for the series is described by the following equation:

\begin{matrix} 4 Σ_{j = 0}^{j = \infty} \frac{{(- 1)}^{j}}{2 j + 1} \approx 3.14159265358979323846 \end{matrix}

Exact integer

CONSTANT('EXACTINT' <, nbytes> )

Arguments

nbytes

is a numeric value that is the number of bytes.

Range	2 ≤ nbytes ≤ 8
Default	8

The exact integer is the largest integer k such that all integers less than or equal to k in absolute value have an exact representation in a SAS numeric variable of length nbytes. This information can be useful to know before you trim a SAS numeric variable from the default 8 bytes of storage to a lower number of bytes to save storage.

The largest double-precision number

CONSTANT('BIG')

This case returns the largest double-precision floating-point number (8-bytes) that is representable on your computer.

The logarithm of BIG

CONSTANT('LOGBIG' <, base> )

Arguments

base

is a numeric value that is the base of the logarithm.

Restriction	The base that you specify must be greater than the value of 1+SQRTMACEPS.
Default	the natural base, E.

This case returns the logarithm with respect to base of the largest double-precision floating-point number (8-bytes) that is representable on your computer.

It is safe to exponentiate the given base raised to a power less than or equal to CONSTANT('LOGBIG', base) by using the power operation (**) without causing any overflows.

It is safe to exponentiate any floating-point number less than or equal to CONSTANT('LOGBIG') by using the exponential function, EXP, without causing any overflows.

The square root of BIG

CONSTANT('SQRTBIG')

This case returns the square root of the largest double-precision floating-point number (8-bytes) that is representable on your computer.

It is safe to square any floating-point number less than or equal to CONSTANT('SQRTBIG') without causing any overflows.

The smallest double-precision number

CONSTANT('SMALL')

This case returns the smallest double-precision floating-point number (8-bytes) that is representable on your computer.

The logarithm of SMALL

CONSTANT('LOGSMALL' <, base> )

Arguments

base

is a numeric value that is the base of the logarithm.

Restriction	The base that you specify must be greater than the value of 1+SQRTMACEPS.
Default	the natural base, E.

This case returns the logarithm with respect to base of the smallest double-precision floating-point number (8-bytes) that is representable on your computer.

It is safe to exponentiate the given base raised to a power greater than or equal to CONSTANT('LOGSMALL', base) by using the power operation (**) without causing any underflows or 0.

It is safe to exponentiate any floating-point number greater than or equal to CONSTANT('LOGSMALL') by using the exponential function, EXP, without causing any underflows or 0.

The square root of SMALL

CONSTANT('SQRTSMALL')

This case returns the square root of the smallest double-precision floating-point number (8-bytes) that is representable on the computer.

It is safe to square any floating-point number greater than or equal to CONSTANT('SQRTBIG') without causing any underflows or 0.

Machine precision

CONSTANT('MACEPS')

This case returns the smallest double-precision floating-point number (8-bytes)

ε = 2^{- j}

for some integer j, such that

1 + ε > 1

This constant is important in finite precision computations.

The logarithm of MACEPS

CONSTANT('LOGMACEPS' <, base> )

Arguments

base

is a numeric value that is the base of the logarithm.

Restriction	The base that you specify must be greater than the value of 1+SQRTMACEPS.
Default	the natural base, E.

This case returns the logarithm with respect to base of CONSTANT('MACEPS').

The square root of MACEPS

CONSTANT('SQRTMACEPS')

This case returns the square root of CONSTANT('MACEPS').