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  ANSI Common Lisp   12 Numbers   12.2 Dictionary of Numbers

12.2.54 rational, rationalize Function

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

Affected By:
The implementation.

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

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.

Allegro CL Implementation Details:
None.

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