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Function RATIONAL, RATIONALIZE

Syntax

  • rational numberrational rationalize numberrational

Arguments and Values

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

Exceptional Situations

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

See Also

None.

Notes

Rationalizing a float by either method and then converting it back to a float of the same format produces the original number.

(float (rational x) x) ≡ (float (rationalize x) x) ≡ x

\issue{REAL-NUMBER-TYPE:X3J13-MAR-89}