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Function RATIONAL, RATIONALIZE

Syntax:

rational number => rational

rationalize number => rational

Arguments and Values:

number---a real.

rational---a rational.

Description:

rational and rationalize convert reals to rationals.

If number is already rational, it is returned.

If number is a float, rational returns a rational that is mathematically equal in value to the float. rationalize returns a rational that approximates the float to the accuracy of the underlying floating-point representation.

rational assumes that the float is completely accurate.

rationalize assumes that the float is accurate only to the precision of the floating-point representation.

Examples:

     (rational 0) =>  0
     (rationalize -11/100) =>  -11/100
     (rational .1) =>  13421773/134217728 ;implementation-dependent
     (rationalize .1) =>  1/10

Side Effects: None.

Affected By:

The implementation.

Exceptional Situations:

Should signal an error of type type-error if number is not a real. Might signal arithmetic-error.

See Also: None.

Notes:

It is always the case that

     (float (rational x) x) ==  x

and

     (float (rationalize x) x) ==  x

That is, rationalizing a float by either method and then converting it back to a float of the same format produces the original number.

The following X3J13 cleanup issue, not part of the specification, applies to this section:

- REAL-NUMBER-TYPE:X3J13-MAR-89

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