CONSTANT Function

Computes some machine and mathematical constants

Category: Mathematical

Syntax

CONSTANT ( constant <, parameter >)

Arguments

constant

• is a character string that identifies the constant. Valid constants are as follows :

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

• 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

• CONSTANT ('E')

The natural base is described by the following equation:

Euler constant

• CONSTANT ('EULER')

Euler's constant is described by the following equation:

Pi

• 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:

Exact integer

• 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

• CONSTANT ('BIG')

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

The log with respect to base of BIG

• 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.

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 log with respect to base of SMALL

• 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.

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 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

• CONSTANT ('MACEPS')

This case returns the smallest double-precision floating-point number (8-bytes) ˆˆ __2 ˆ’ ^j for some integer j , such that 1 + ˆˆ > 1.

This constant is important in finite precision computations . A number n ₁ is considered larger than another number n ₂ if the (8-byte) representation of n ₁ + n ₂ is identical to n ₁ . This constant can be used in summing series to implement a machine dependent stopping criterion.

The log with respect to base of MACEPS

• 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').

The square root of MACEPS

• CONSTANT ('SQRTMACEPS')

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