rationalize -- r7rs Definition

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Kind

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procedure;

Implemented by

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• rationalize (from vonuvoli);

Procedure signature

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Procedure variants:

• ((real-not-inf-not-nan real-positive-or-zero-not-inf) -> (rational))
  • inputs:
    • a value of type real-not-inf-not-nan;
    • a value of type real-positive-or-zero-not-inf;
  • output: a value of type rational;

Exports

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• scheme:base -- (scheme base);

Exports recursive

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• scheme -- (scheme);

Description

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(rationalize x y)

The rationalize procedure returns the simplest rational number differing from x by no more than y. A rational number r_1 is simpler (simplest rational) than another rational number r_2 if r_1 = p_1/q_1 and r_2 = p_2/q_2 (in lowest terms) and |p_1| <= |p_2| and |q_1| <= |q_2|. Thus 3/5 is simpler than 4/7. Although not all rationals are comparable in this ordering (consider 2/7 and 3/5), any interval contains a rational number that is simpler than every other rational number in that interval (the simpler 2/5 lies between 2/7 and 3/5). Note that 0 = 0/1 is the simplest rational of all.

(rationalize
  (exact .3) 1/10)           ===>  1/3    ; exact
(rationalize .3 1/10)        ===>  #i1/3  ; inexact

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The text herein was sourced and adapted as described in the "R7RS attribution of various text snippets" appendix.

Referenced-types

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• real-not-inf-not-nan;
• real-positive-or-zero-not-inf;
• rational;