; digits of e
(define (make-list n x)
(let loop ((n n) (xs '()))
(if (zero? n) xs
(loop (- n 1) (cons x xs)))))
(define-syntax define-generator
(lambda (x)
(syntax-case x (lambda)
((stx name (lambda formals e0 e1 ...))
(with-syntax ((yield (datum->syntax-object (syntax stx) 'yield)))
(syntax (define name
(lambda formals
(let ((resume #f) (return #f))
(define yield
(lambda args
(call-with-current-continuation
(lambda (cont)
(set! resume cont)
(apply return args)))))
(lambda ()
(call-with-current-continuation
(lambda (cont)
(set! return cont)
(cond (resume (resume))
(else (let () e0 e1 ...)
(error 'name "unexpected return"))))))))))))
((stx (name . formals) e0 e1 ...)
(syntax (stx name (lambda formals e0 e1 ...)))))))
(define (take-gen n gen)
(let loop ((n n) (xs (list)))
(if (zero? n) (reverse xs)
(loop (- n 1) (cons (gen) xs)))))
(define-generator (e-spigot n)
(define (times10 x) (* 10 x))
(yield 2)
(let loop1 ((ts (make-list n 10)) (k n))
(if (< 1 k)
(let loop2 ((ts ts) (rs (list)) (i (+ n 1)) (carry 0))
(if (= i 1)
(begin (yield carry) (loop1 (map times10 (reverse rs)) (- k 1)))
(let* ((x (+ (car ts) carry)) (q (quotient x i)) (r (remainder x i)))
(loop2 (cdr ts) (cons r rs) (- i 1) q))))))
(let loop3 () (yield #f) (loop3)))
(display (take-gen 30 (e-spigot 25))) (newline)
(define-generator (make-spigot f lo hi)
(define (split v)
(values (vector-ref v 0) (vector-ref v 1) (vector-ref v 2)))
(define (approx abc n)
(let-values (((a b c) (split abc)))
(quotient (+ (* a n) b) c)))
(define (mul abc def)
(let-values (((a b c) (split abc)) ((d e f) (split def)))
(vector (* a d) (+ (* a e) (* b f)) (* c f))))
(define (g k) (let-values (((n d a) (f k))) (vector n (* a d) d)))
(let loop ((z (vector 1 0 1)) (k 1))
(let ((lbound (approx z lo)))
(cond ((= lbound (approx z hi))
(yield lbound)
(loop (mul (vector 10 (* -10 lbound) 1) z) k))
(else (loop (mul z (g k)) (+ k 1)))))))
(define pi-spigot (make-spigot (lambda (k) (values k (+ k k 1) 2)) 3 4))
(define e-spigot (make-spigot (lambda (k) (values 1 k 1)) 1 2))
(define sqrt2-spigot
(make-spigot
(lambda (k)
(if (= k 1)
(values 7 5 0)
(values (+ k k -3) (* (- k 1) 100) 1)))
1 2))
(display (take-gen 30 pi-spigot)) (newline)
(display (take-gen 30 e-spigot)) (newline)
(display (take-gen 30 sqrt2-spigot)) (newline)