CONSTANT

CONSTANT

Computes some machine and mathematical constants and returns a value

Category: Mathematical

Syntax
Arguments
Details
	The natural base
	Euler constant
	Pi
	Exact Integer
	The largest double-precision number
	The smallest double-precision number
	Machine precision

Syntax

CONSTANT(constant<, parameter>)

Arguments

constant

is a character string that identifies the constant. Valid constants are

Constant Argument

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'

parameter

Constant	Argument
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'

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

The natural base

Syntax

CONSTANT('E')

The natural base is described by the following equation:

[IMAGE]

Euler constant

Syntax

CONSTANT('EULER')

Euler's constant is described by the following equation:

[IMAGE]

Pi

Syntax

CONSTANT('PI')

Pi is the well-known constant in trigonometry that 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:

[IMAGE]

Exact Integer

Syntax

CONSTANT('EXACTINT' <, nbytes>)

where

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

Syntax

CONSTANT('BIG')

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

Syntax

CONSTANT('LOGBIG' <, base>)

where

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.

Syntax

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

Syntax

CONSTANT('SMALL')

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

Syntax

CONSTANT('LOGSMALL' <, base>)

where

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.

Syntax

CONSTANT('SQRTSMALL')

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

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

Machine precision

Syntax

CONSTANT('MACEPS')

This case returns the smallest double-precision floating point number (8-bytes) [IMAGE] for some integer j, such that [IMAGE] .

This constant is important in finite precision computations. A number n₁ is considered larger than another number n₂ if the (8-byte) representation of n₁ + n₂ is identical to n₁. This constant can be used in summing series to implement a machine dependent stopping criterion.

Syntax

CONSTANT('LOGMACEPS' <, base>)

where

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').

Syntax

CONSTANT('SQRTMACEPS')

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

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