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Optimization Coach Demo - RacketCon 2012
#lang racket
(require slideshow unstable/gui/slideshow)
(define points
(for/list ([i 10])
(disk 10)))
(define named-points
(for/list ([p points] [i (in-naturals)])
(vc-append p (blank 5) (text (number->string i)))))
(define padded-points
(for/list ([p named-points])
(inset p 20)))
(define placed-points
(tabular (list (list-ref padded-points 9)
(blank)
(blank)
(blank))
(list (list-ref padded-points 5)
(list-ref padded-points 8)
(blank)
(blank))
(list (list-ref padded-points 2)
(list-ref padded-points 4)
(list-ref padded-points 7)
(blank))
(list (list-ref padded-points 0)
(list-ref padded-points 1)
(list-ref padded-points 3)
(list-ref padded-points 6))))
(define chained-points
(for/fold ([res placed-points])
([from points]
[to (rest points)])
(pin-arrow-line 15 res from cc-find to cc-find)))
chained-points
#lang typed/racket
(: pair : Integer Integer -> Integer)
(define (pair x y)
(+ (quotient (* (+ x y) (+ y x 1)) 2) y))
(: unpair : Integer -> (values Integer Integer))
(define (unpair z)
(define w (inexact->exact (floor (assert (/ (- (sqrt (+ (* 8 z) 1)) 1) 2)
real?))))
(define t (/ (+ (* w w) w) 2))
(define y (assert (- z t) exact-integer?))
(define x (assert (- w y) exact-integer?))
(values x y))
(: check : Integer -> Void)
(define (check z)
(define-values (x y) (unpair z))
(unless (= (pair x y) z)
(eprintf "~s => ~s ~s => ~s\n"
z x y (pair x y))))
(time
(for ([i (in-range 3000000)])
(check i)))
#lang typed/racket
(require racket/flonum)
(: pair : Integer Integer -> Integer)
(define (pair x y)
(+ (quotient (* (+ x y) (+ y x 1)) 2) y))
(: unpair : Integer -> (values Integer Integer))
(define (unpair z)
(define w (inexact->exact (floor (/ (- (flsqrt (+ (* 8 (->fl z)) 1)) 1) 2))))
(define t (/ (+ (* w w) w) 2))
(define y (assert (- z t) exact-integer?))
(define x (assert (- w y) exact-integer?))
(values x y))
(: check : Integer -> Void)
(define (check z)
(define-values (x y) (unpair z))
(unless (= (pair x y) z)
(eprintf "~s => ~s ~s => ~s\n"
z x y (pair x y))))
(time
(for ([i (in-range 3000000)])
(check i)))
#lang typed/racket
(require racket/flonum)
(: pair : Float Float -> Float)
(define (pair x y)
(+ (/ (* (+ x y) (+ y x 1)) 2) y))
(: unpair : Float -> (values Float Float))
(define (unpair z)
(define w (floor (/ (- (flsqrt (+ (* 8 z) 1)) 1) 2)))
(define t (/ (+ (* w w) w) 2))
(define y (- z t))
(define x (- w y))
(values x y))
(: check : Float -> Void)
(define (check z)
(define-values (x y) (unpair z))
(unless (= (pair x y) z)
(eprintf "~s => ~s ~s => ~s\n"
z x y (pair x y))))
(time
(for ([i (in-range 3000000)])
(check (->fl i))))
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