Import Upstream version 3a1upstream/3a1

1 files changed, 41 insertions, 2 deletions

diff --git a/ratize.scm b/ratize.scm
index 9737934..35a9ded 100644
--- a/ratize.scm
+++ b/ratize.scm
@@ -1,5 +1,46 @@
 ;;;; "ratize.scm" Find simplest number ratios
 
+;;@code{(require 'rationalize)}
+;;@ftindex rationalize
+
+;;The procedure @dfn{rationalize} is interesting because most programming
+;;languages do not provide anything analogous to it.  Thanks to Alan
+;;Bawden for contributing this algorithm.
+
+;;@body
+;;Computes the correct result for exact arguments (provided the
+;;implementation supports exact rational numbers of unlimited precision);
+;;and produces a reasonable answer for inexact arguments when inexact
+;;arithmetic is implemented using floating-point.
+;;
+(define (rationalize x e) (apply / (find-ratio x e)))
+
+;;@code{Rationalize} has limited use in implementations lacking exact
+;;(non-integer) rational numbers.  The following procedures return a list
+;;of the numerator and denominator.
+
+;;@body
+;;@0 returns the list of the @emph{simplest}
+;;numerator and denominator whose quotient differs from @1 by no more
+;;than @2.
+;;
+;;@format
+;;@t{(find-ratio 3/97 .0001)             @result{} (3 97)
+;;(find-ratio 3/97 .001)              @result{} (1 32)
+;;}
+;;@end format
+(define (find-ratio x e) (find-ratio-between (- x e) (+ x e)))
+
+
+;;@body
+;;@0 returns the list of the @emph{simplest}
+;;numerator and denominator between @1 and @2.
+;;
+;;@format
+;;@t{(find-ratio-between 2/7 3/5)        @result{} (1 2)
+;;(find-ratio-between -3/5 -2/7)      @result{} (-1 2)
+;;}
+;;@end format
 (define (find-ratio-between x y)
   (define (sr x y)
     (let ((fx (inexact->exact (floor x))) (fy (inexact->exact (floor y))))
@@ -13,5 +54,3 @@
 	((negative? y) (let ((rat (sr (- y) (- x))))
 			 (list (- (car rat)) (cadr rat))))
 	(else '(0 1))))
-(define (find-ratio x e) (find-ratio-between (- x e) (+ x e)))
-(define (rationalize x e) (apply / (find-ratio x e)))