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======= At 2005-06-20, 10:06:21 Aubrey Jaffer wrote: ======= > | procedure: = z1 z2 z3 ... > | procedure: < x1 x2 x3 ... > | procedure: > x1 x2 x3 ... > | procedure: <= x1 x2 x3 ... > | procedure: >= x1 x2 x3 ... > | These procedures return #t if their arguments are (respectively): > | equal, monotonically increasing, monotonically decreasing, > | monotonically nondecreasing, or monotonically nonincreasing. > | > | ... > | (= 0 -0) ==> #t > | > | For any finite positive number x: > | > | (< #e-1/0 -x -0 0 x 1/0)) ==> #t > | > | These predicates are required to be transitive. > >A sequence cannot be both equal and monotonically increasing. >(= -0 0) conflicts with (< -0 0). > My fault. (= -0 0) should be #f. > | library procedure: infinite? z > >"Infinite" means not finite. R5RS has `ZERO?' but not `NONZERO?'; >`POSITIVE?', but not `NONPOSITIVE?'; `NEGATIVE?' but not `NONNEGATIVE?' >`FINITE?' is more in keeping with R5RS procedure names. The reason I define "infinite?" instead of "finite?" is that: (cond ((infinite? x) ...) ((zero? x) ...) ...) As I understand the problem, we always use a predicator to select a minority (with some single character) (instead of a big part that can be further divided) form the whole. > > | library procedure: zero? z > | library procedure: positive? x > | library procedure: negative? x > | library procedure: odd? n > | library procedure: even? n > | These numerical predicates test a number for a particular > | property, returning #t or #f. See note above. > | > | (positive? #e1/0) ==> #t > | (negative? #e-1/0) ==> #t > | (infinite? #e-1/0) ==> #t > | (infinite? #e0/0) ==> #t > | (positive? 0) ==> #f > | (negative? -0) ==> #f > >What does (zero? -0) return? > >If (negative? -0) returns #f, and (= -0 0) returns #t, how does one >test for `-0'? (zero? -0) ==> #t > > | procedure: numerator q > | procedure: denominator q > | These procedures return the numerator or denominator of their > | argument; the result is computed as if the argument was > | represented as a fraction in lowest terms. The denominator is > | always positive or zero. The denominator of 0 is defined to be > | 1. > | > | (numerator (/ 6 4)) ==> 3 > | (denominator (/ 6 4)) ==> 2 > | (denominator > | (exact->inexact (/ 6 4))) ==> 2.0 > | >*| (denominator #e1/0) ==> 1 >*| (denominator #e-1/0) ==> -1 >*| (numerator #e1/0) ==> 0 >*| (numerator #e-1/0) ==> 0 > >*Should numerator and denominator be swapped in the last 4 lines? Yes. My fault. > >What does (exact? -0) return? >What does (integer? -0) return? >What does (rational? -0) return? >What does (numerator -0) return? >What does (denominator -0) return? > >What does (floor -0) return? >What does (ceiling -0) return? > >What does (* -0 -0) return? >What does (sqrt 0) return? Please see the implementation. > > | procedure: - z1 z2 > | procedure: - z > | optional procedure: - z1 z2 ... > | procedure: / z1 z2 > | procedure: / z > | optional procedure: / z1 z2 ... > | With one argument, these procedures return the additive or > | multiplicative inverse of their argument. > | > | With two or more arguments: > | > | (- z1 . z2) => (apply + z1 (map - z2)) > | (/ z1 . z2) => (apply * z1 (map / z2)) > | > | (- 0) ==> -0 > | (- -0) ==> 0 > | (- #e1/0) ==> #e-1/0 > | (- #-e1/0) ==> #e1/0 > | (- 3) ==> -3 > | > | (/ 0) ==> #e1/0 > | (/ -0) ==> #e-1/0 >*| (/ #e1/0) ==> #0 >*| (/ #e-1/0) ==> #-0 > | (/ 3) ==> 1/3 > >*Should `==> #' be replaced with `==> #e'? Typo. (/ #e1/0) ==> 0 (/ #e-1/0) ==> -0 > > | Implementation > | > | Here is my implementation, which is based on a Scheme implementation > | that supports arbitrary-big integer arithmetic as well as exact > | rational number computation. To avoid confusion with identifies in > | base-Scheme, all procedures defined in this SRFI (except infinite?) > | and prefixed with "my" or "my-". This reference implementation also > | requires SRFI-9, SRFI-13, SRFI-16, and SRFI-23. > | > | (separate file attached) > >There is no link to the implementation file. > It is at http://srfi.schemers.org/srfi-73/exact.scm Sorry that I have made so many typos. A revised verions has been send to Mike Sperber. - Chongkai Zhu