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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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