The following code runs in reasonable time (about 5s) on 64-bit 5.3.4, but
takes about 20x as long on 32-bit. I adapted this code from some scheme
code on the PE forum. Thoughts?
Thanks,
-Joe
(define (euler210)
(define limit (expt 10 8))
(define ldiv4 (quotient limit 4))
(define ldiv8 (quotient limit 8))
(define ldiv8xrad2 (inexact->exact (floor (* ldiv8 (sqrt 2)))))
(define sqrldiv8x2 (* ldiv8 ldiv8 2))
(+
(* 3 (* limit (/ limit 2))) ; rectangular regions
(- (* ldiv4 (add1 ldiv4)) 2)
(* 8
(let loop ([x (add1 ldiv8)] [sum 0]) ; 1/8 of circle points (outside
of inner square)
(if (< ldiv8xrad2 x) sum
(let* ([y (sqrt (- sqrldiv8x2 (* x x)))] [ymax (inexact->exact
(floor (if (integer? y) (- y 1) y)))])
(loop (add1 x) (+ sum ymax))))))
(* 4 (- ldiv8xrad2 ldiv8))))
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