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;; Ported to Common Lisp by Daniel Spangberg
;; Converted to be used in Programming Language and compiler Benchmarks by Bela Pecsek
;; Changed CLOS sieve-state class to struct
(declaim (optimize (speed 3) (safety 0) (debug 0)))
(defun binarize (expr)
(if (and (nthcdr 3 expr) (member (car expr) '(+ - * / ash abs sin cos tan cot
ceiling isqrt signum log exp expt)))
(destructuring-bind (op a1 a2 . rest) expr
(binarize `(,op (,op ,a1 ,a2) ,@rest))) expr))
(defun expand-call (type expr)
`(,(car expr) ,@(mapcar #'(lambda (a) `(with-type ,type ,a)) (cdr expr))))
(defmacro with-type (type expr)
`(#+sbcl sb-ext:truly-the #-sbcl the ,type
,(if (and (consp expr) (member (car expr) '(1+ 1- + - * / ash abs sin cos
tan cot ceiling isqrt signum log exp expt)
:test #'eq)) (expand-call type (binarize expr)) expr)))
(declaim (type '(simple-array fixnum 1) +steps+))
(defconstant +steps+ (coerce
#(8 1 2 3 1 3 2 1 2 3 3 1 3 2 1 3 2 3 4 2 1 2 1 2 7
2 3 1 5 1 3 3 2 3 3 1 5 1 2 1 6 6 2 1 2 3 1 5 3 3
3 1 3 2 1 3 2 7 2 1 2 3 4 3 5 1 2 3 1 3 3 3 2 3 1
3 2 4 5 1 5 1 2 1 2 3 4 2 1 2 6 4 2 1 3 2 3 6 1 2
1 6 3 2 3 3 3 1 3 5 1 2 3 1 3 3 2 1 5 1 5 1 2 3 3
1 3 3 2 3 4 3 2 1 3 2 3 4 2 1 3 2 4 3 2 4 2 3 4 5
1 5 1 3 2 1 2 1 5 1 5 1 2 1 2 7 2 1 2 3 3 1 3 2 4
5 4 2 1 2 3 4 3 2 3 3 3 1 3 3 2 1 2 3 1 5 1 2 1 5
1 5 1 3 2 4 3 2 1 2 3 3 4 2 1 3 5 4 2 1 3 2 4 5 3
1 2 4 3 3 2 1 2 3 1 3 2 3 1 5 6 1 2 1 2 3 1 3 2 1
2 6 1 3 3 5 3 4 2 1 2 1 2 4 3 6 2 3 1 6 2 1 2 3 4
2 1 2 1 6 5 1 2 1 2 3 1 5 1 2 3 4 3 2 1 3 2 3 4 2
3 1 2 4 3 2 3 1 2 3 1 3 3 2 3 3 4 3 2 1 5 1 5 1 2
1 5 1 3 2 1 5 3 1 3 2 1 3 2 3 4 3 2 1 6 5 3 1 2 3
1 6 2 1 2 4 3 2 1 2 1 5 1 5 3 1 2 3 1 3 2 1 5 3 1
3 2 6 3 4 3 2 1 2 4 3 2 3 1 2 3 4 3 3 2 3 1 3 2 1
2 1 5 6 1 2 6 1 3 2 1 2 3 3 1 6 3 2 9 1 2 1 2 4 3
2 3 1 2 4 3 3 2 1 2 3 1 3 2 1 2 6 1 6 3 2 3 1 3 2
3 3 3 1 3 2 1 3 2 3 4 2 1 2 1 2 7 2 3 1 5 1 3 3 2
1 5 1 5 1 2 7 5 1 2 1 2 3 1 3 5 3 3 1 5 1 3 2 3 4
2 1 2 3 4 3 5 1 2 3 1 3 3 2 1 2 3 1 3 2 1 3 5 1 5
3 1 2 3 4 2 1 2 6 1 3 2 1 3 2 3 6 1 2 1 2 4 3 2 3
1 5 1 3 5 3 3 1 3 2 1 2 1 5 1 6 2 3 3 1 6 2 3 3 1
3 2 1 3 2 7 2 1 3 2 4 3 2 3 1 2 3 4 3 3 5 1 3 2 3
1 5 1 5 1 2 1 2 4 3 2 1 2 3 3 4 2 4 2 3 4 2 1 2 1
6 3 2 3 3 3 1 3 3 2 1 2 3 1 3 3 2 1 5 1 5 1 3 2 3
1 3 2 1 2 3 7 2 1 3 5 4 2 1 2 1 2 4 5 4 2 4 3 5 1
2 3 1 3 2 3 1 5 1 5 1 2 1 2 3 4 2 1 2 3 3 1 3 3 3
5 4 2 1 2 3 4 3 2 4 2 3 1 3 3 2 1 2 3 6 1 2 1 5 1
5 1 2 1 2 4 5 1 2 3 4 3 2 1 3 2 3 4 2 4 2 4 3 2 3
1 2 3 1 3 3 2 3 3 1 3 3 2 1 5 6 1 2 1 2 3 1 3 2 1
8 1 3 2 1 5 3 4 2 1 2 1 6 3 5 1 2 3 1 6 2 1 2 4 3
2 1 2 1 6 5 3 1 2 3 1 3 2 1 2 3 3 1 3 2 1 5 3 4 5
1 2 4 3 2 3 1 2 3 1 3 3 3 2 3 4 2 1 2 1 5 6 1 2 1
5 1 3 2 1 2 3 3 1 5 1 3 2 7 3 2 1 2 4 5 3 1 2 3 1
3 3 2 1 2 4 3 2 1 2 6 1 6 2 1 2 3 1 3 2 1 5 3 1 3
2 4 2 3 4 2 1 2 1 2 7 2 3 1 5 4 3 2 1 2 3 1 5 1 2
1 6 5 1 2 3 3 1 3 2 3 3 3 1 3 3 3 2 3 6 1 2 3 4 3
5 1 2 4 3 3 2 1 2 3 1 3 2 1 3 5 1 5 1 3 2 3 4 2 3
6 1 3 2 1 3 2 3 6 1 2 1 2 7 2 3 1 2 3 1 3 5 1 5 1
3 2 1 2 6 1 5 1 2 3 3 1 3 3 2 3 3 1 5 1 3 2 3 4 2
1 3 2 4 3 2 3 1 2 3 4 3 2 1 5 1 3 2 1 3 5 1 5 3 1
2 4 3 2 1 2 3 3 1 3 2 4 2 3 4 2 1 2 1 2 4 3 2 3 6
1 3 3 2 3 3 1 3 2 1 2 1 5 1 6 3 2 3 1 5 1 2 3 3 4
2 1 3 9 2 1 2 1 2 4 5 3 1 2 4 3 3 3 2 3 1 3 2 3 1
5 1 5 1 2 1 2 3 1 3 2 1 2 3 3 4 3 3 2 3 4 2 1 2 1
6 3 2 6 3 1 3 3 2 1 2 3 4 3 2 1 5 1 5 1 2 1 2 3 1
5 1 2 3 4 3 2 1 3 2 3 4 2 3 1 2 4 3 2 4 2 3 1 3 5
3 3 1 3 3 2 1 5 1 5 1 2 1 2 3 4 2 1 5 3 1 3 2 1 3
5 4 2 1 2 7 3 2 3 1 2 3 1 6 2 1 2 4 5 1 2 1 5 1 5
3 1 2 4 3 2 1 2 3 3 1 3 2 1 5 3 4 3 3 2 4 3 2 3 1
2 3 1 3 3 3 2 3 1 3 2 1 2 1 5 6 1 2 1 5 1 3 2 1 2
6 1 5 1 5 7 2 1 2 1 2 4 3 5 1 2 3 1 6 2 1 2 3 1 3
2 1 2 7 6 2 1 2 3 1 3 2 1 2 3 3 1 3 2 1 3 2 3 4 2
3 1 2 7 2 3 1 5 1 3 3 2 1 2 3 6 1 2 1 6 5 1 2 1 5
1 3 2 3 3 3 1 3 2 1 3 2 3 4 3 2 3 4 8 1 2 3 1 3 3
2 1 2 4 3 2 1 3 5 1 5 1 2 1 2 3 4 2 1 8 1 3 2 4 2
3 6 1 2 1 2 4 3 2 3 1 2 3 4 5 1 2 3 1 3 2 1 2 1 5
1 5 1 2 3 3 1 3 3 2 3 3 1 3 3 3 2 3 6 1 3 2 4 3 2
3 1 2 7 3 2 1 5 1 3 2 1 2 1 5 1 5 1 3 2 4 3 2 3 3
3 1 3 2 4 2 3 4 2 1 2 1 2 7 2 3 3 3 1 3 3 2 1 5 1
3 2 1 2 6 1 5 1 3 2 3 1 3 3 2 3 3 6 1 3 5 4 2 1 2
1 2 4 5 3 1 2 4 3 3 2 1 2 3 1 3 2 4 5 1 5 3 1 2 3
1 3 2 1 2 3 3 1 3 3 3 2 3 4 2 1 2 1 2 4 3 2 4 5 1
3 3 2 3 3 4 2 1 2 1 5 1 6 2 1 2 3 1 5 1 2 3 4 3 2
1 3 2 7 2 3 1 2 4 3 2 3 1 2 3 1 3 3 5 3 1 3 5 1 5
1 5 1 2 1 2 3 1 3 2 1 5 3 4 2 1 3 2 3 4 2 1 2 1 6
3 2 3 3 3 1 6 2 1 2 4 3 3 2 1 5 1 5 3 1 2 3 1 3 2
1 2 3 4 3 2 1 5 3 4 3 2 1 2 4 3 2 4 2 3 1 3 6 2 3
1 3 2 1 2 1 5 6 1 2 1 5 4 2 1 2 3 3 1 5 1 3 9 2 1
2 3 4 3 2 3 1 2 3 1 3 3 2 1 2 3 1 5 1 2 6 1 6 2 1
2 4 3 2 1 2 3 3 1 3 2 1 3 2 3 4 2 1 3 2 7 2 3 1 5
1 3 3 2 1 2 3 1 5 1 2 1 11 1 2 1 2 3 1 3 2 3 6 1 3
2 1 5 3 4 2 1 2 3 4 3 5 1 2 3 1 6 2 1 2 3 1 3 2 1
3 6 5 1 2 1 2 3 4 2 1 2 6 1 3 2 1 3 2 3 6 3 1 2 4
3 2 3 1 2 3 1 3 5 1 2 3 4 2 1 2 1 5 1 5 1 2 6 1 3
3 2 3 3 1 3 2 1 3 2 3 4 3 3 2 4 5 3 1 2 3 4 3 2 1
6 3 2 1 2 1 5 1 5 1 2 1 2 4 3 2 1 5 3 1 3 2 4 2 3
4 2 1 2 1 2 4 3 2 3 3 3 4 3 2 1 2 3 1 3 2 1 2 1 5
1 5 1 5 3 1 3 2 1 2 3 3 4 3 3 5 6 1 2 1 2 4 5 3 1
2 4 3 3 2 1 2 3 1 3 2 3 1 5 1 5 1 3 2 3 1 3 2 3 3
3 1 3 3 3 2 3 4 2 1 2 1 2 7 2 4 2 3 1 3 3 2 1 5 4
2 1 2 6 1 5 1 2 1 2 3 1 6 2 3 4 5 1 3 2 3 4 2 3 1
2 4 3 2 3 1 2 3 1 3 3 2 3 3 1 3 3 3 5 1 5 3 1 2 3
1 3 2 1 5 3 1 3 2 1 3 2 3 4 2 1 2 1 6 3 2 3 1 5 1
6 2 3 4 3 2 1 2 1 5 1 8 1 2 3 1 5 1 2 3 3 1 3 2 1
5 7 3 2 1 2 4 3 2 3 1 2 3 1 3 3 3 2 3 1 3 2 3 1 5
6 1 2 1 5 1 3 2 1 2 3 3 6 1 3 2 7 2 1 2 1 6 3 2 3
3 3 1 3 3 2 1 2 3 1 3 3 2 6 1 6 2 1 2 3 1 3 2 1 2
3 4 3 2 1 3 2 3 4 2 1 2 1 2 7 2 4 5 1 3 5 1 2 3 1
5 1 2 1 6 5 1 2 1 2 3 4 2 3 3 3 1 3 2 1 3 5 4 2 1
2 3 4 3 5 1 2 3 1 3 3 2 1 2 3 1 5 1 3 5 1 5 1 2 1
2 7 2 1 2 6 1 3 2 1 3 2 3 6 1 3 2 4 3 2 3 1 2 3 1
3 5 1 2 3 1 3 2 1 2 1 5 6 1 2 3 3 1 3 3 2 6 1 3 2
1 5 3 4 2 1 3 2 4 3 5 1 2 3 7 2 1 5 1 3 2 1 2 1 6
5 1 2 1 2 4 3 2 1 2 3 3 1 3 2 4 2 3 4 2 3 1 2 4 3
2 3 3 3 1 3 3 2 1 2 3 4 2 1 2 1 5 1 5 1 3 5 1 3 2
1 2 3 3 4 2 1 3 5 4 3 2 1 2 4 5 3 1 2 4 3 3 2 1 2
4 3 2 3 1 5 1 5 1 2 1 2 3 1 3 2 1 5 3 1 3 6 2 3 4
2 1 2 1 2 4 3 2 4 2 3 4 3 2 1 2 3 4 2 1 2 1 5 1 5
1 2 3 3 1 5 1 2 3 4 3 3 3 2 3 6 3 1 2 4 3 2 3 1 2
4 3 3 2 3 3 1 3 3 2 1 5 1 5 1 3 2 3 1 3 2 6 3 1 3
2 1 3 2 3 4 2 1 2 1 9 2 3 1 2 3 1 6 2 1 6 3 2 1 2
6 1 5 3 1 2 3 1 3 3 2 3 3 1 5 1 5 3 4 3 2 1 2 4 3
2 3 1 2 3 1 3 3 3 2 3 1 3 2 1 3 5 6 3 1 5 1 3 2 1
2 3 3 1 5 1 3 2 7 2 1 2 1 2 4 3 2 3 1 5 1 3 3 2 3
3 1 3 2 1 2 6 1 6 2 1 2 3 1 5 1 2 3 3 1 3 2 1 3 2
7 2 1 2 1 2 7 2 3 1 5 1 3 3 3 2 3 1 5 3 1 6 5 1 2
1 2 3 1 3 2 3 3 3 4 2 1 3 2 3 4 2 1 2 7 3 5 3 3 1
3 3 2 1 2 3 1 3 3 3 5 1 5 1 2 1 2 3 4 2 1 2 7 3 2
1 3 2 3 6 1 2 1 2 4 3 2 4 2 3 1 3 5 1 2 3 1 3 2 1
2 1 5 1 5 1 2 3 3 4 3 2 3 3 1 3 2 1 3 5 4 2 1 5 4
3 2 3 1 2 3 4 3 2 1 5 1 5 1 2 1 5 1 5 1 2 1 2 4 3
2 1 2 3 3 1 3 2 4 2 3 4 2 1 3 2 4 3 2 3 3 3 1 3 3
2 1 2 3 1 3 2 1 2 1 5 6 1 3 2 3 1 3 2 1 2 6 4 2 1
8 4 2 1 2 1 2 4 8 1 2 4 6 2 1 2 3 1 3 2 3 1 6 5 1
2 1 2 3 1 3 2 1 2 3 3 1 3 3 3 2 3 4 2 3 1 2 4 3 2
4 2 3 1 3 3 2 1 2 3 4 2 1 2 1 5 1 5 1 2 1 5 1 5 1
2 3 4 3 2 1 3 2 3 4 5 1 2 4 5 3 1 2 3 1 3 3 2 3 4
3 3 2 1 5 1 5 1 2 1 2 3 1 3 2 1 5 3 1 3 2 4 2 3 4
2 1 2 1 6 3 2 3 1 2 3 7 2 1 2 4 3 2 1 2 1 5 1 5 3
3 3 1 3 2 1 2 3 3 1 3 3 5 3 7 2 1 2 4 3 2 3 1 2 4
3 3 3 2 3 1 3 2 1 2 1 5 6 1 3 5 1 3 2 3 3 3 1 5 1
3 2 7 2 1 2 1 2 7 2 3 1 2 3 1 3 3 2 1 5 1 3 2 1 2
6 1 6 2 1 2 3 1 3 3 2 3 3 1 5 1 3 2 3 4 2 1 2 1 2
7 2 3 1 5 1 3 3 2 1 2 3 1 5 1 3 6 5 3 1 2 3 1 3 2
3 3 3 1 3 2 1 3 2 3 4 2 1 2 3 4 3 5 1 5 1 3 3 2 3
3 1 3 2 1 3 5 1 6 2 1 2 3 6 1 2 6 1 3 2 1 3 2 9 1
2 1 2 4 3 2 3 1 2 3 1 3 6 2 3 1 3 2 3 1 5 1 5 1 2
3 3 1 3 3 2 3 3 4 2 1 3 2 3 4 2 1 3 6 3 2 3 3 3 4
3 2 1 5 1 3 3 2 1 5 1 5 1 2 1 2 4 3 2 1 2 3 4 3 2
4 2 3 4 2 1 2 1 2 4 3 2 6 3 1 3 5 1 2 3 1 3 2 1 2
1 5 1 5 1 3 2 3 4 2 1 2 3 3 4 2 1 3 5 4 2 1 2 3 4
5 3 1 2 4 3 3 2 1 2 3 1 5 3 1 5 1 5 1 2 1 2 4 3 2
1 2 3 3 1 3 3 3 2 3 4 2 1 3 2 4 3 2 4 2 3 1 3 3 2
1 2 3 4 2 1 2 1 5 6 1 2 1 2 3 1 5 1 2 7 3 2 1 5 3
4 2 3 1 2 4 3 5 1 2 3 1 6 2 3 3 1 3 3 2 1 6 5 1 2
1 2 3 1 3 2 1 5 3 1 3 2 1 3 2 3 4 2 3 1 6 3 2 3 1
2 3 1 6 2 1 2 7 2 1 2 1 5 1 5 3 1 5 1 3 2 1 2 3 3
1 3 2 1 5 3 4 3 2 1 2 4 5 3 1 2 3 1 3 3 3 2 4 3 2
1 2 1 5 6 1 2 1 5 1 3 2 1 5 3 1 5 4 2 7 2 1 2 1 2
4 3 2 3 1 2 3 4 3 2 1 2 3 1 3 2 1 2 6 1 6 2 3 3 1
3 2 1 2 3 3 1 3 3 3 2 3 6 1 2 1 2 7 2 3 1 6 3 3 2
1 2 3 1 5 1 2 1 6 5 1 3 2 3 1 3 2 3 3 3 1 3 2 1 3
2 3 4 2 1 2 3 7 5 1 2 3 1 3 3 2 1 5 1 3 2 1 8 1 5
1 2 1 2 3 4 3 2 6 1 5 1 3 2 3 6 1 2 1 2 4 3 2 3 1
2 3 1 3 5 1 2 3 1 3 2 1 3 5 1 5 3 3 3 1 3 3 2 3 3
1 3 2 1 3 2 3 4 2 1 3 2 4 3 2 3 1 5 4 3 2 6 1 3 2
1 2 1 5 1 6 2 1 2 4 5 1 2 3 3 1 3 2 4 2 7 2 1 2 1
2 4 3 2 3 3 3 1 3 3 3 2 3 1 3 2 3 1 5 1 5 1 3 2 3
1 3 2 1 2 3 3 4 2 1 3 5 4 2 1 2 1 6 5 3 3 4 3 3 2
1 2 3 1 3 5 1 5 1 5 1 2 1 2 3 1 3 2 1 2 3 4 3 3 3
2 3 4 2 1 2 1 2 4 3 2 4 2 3 1 3 5 1 2 3 4 2 1 2 1
5 1 5 1 2 1 2 3 6 1 2 3 4 3 2 1 3 5 4 2 3 3 4 3 2
3 1 2 3 1 3 3 2 3 3 1 6 2 1 5 1 5 1 2 1 2 4 3 2 1
5 3 1 3 2 1 3 2 3 4 2 1 3 6 3 2 3 1 2 3 1 6 2 1 2
4 3 2 1 2 1 5 6 3 1 2 3 1 3 2 1 2 6 1 3 2 1 5 3 4
3 2 1 2 4 3 5 1 2 3 1 6 3 2 3 1 3 2 1 2 1 11 1 2 1
5 1 3 2 1 2 3 3 1 5 1 3 2 7 2 3 1 2 4 3 2 3 1 2 3
1 3 3 2 1 2 3 4 2 1 2 6 1 6 2 1 5 1 3 2 1 2 3 3 1
3 2 1 3 2 3 4 3 2 1 2 9 3 1 5 1 3 3 2 1 2 4 5 1 2
1 6 5 1 2 1 2 3 1 3 2 6 3 1 3 2 4 2 3 4 2 1 2 3 4
3 5 1 2 3 4 3 2 1 2 3 1 3 2 1 3 5 1 5 1 2 3 3 4 2
1 2 6 1 3 3 3 2 3 6 1 2 1 2 4 3 2 3 1 2 4 3 5 1 2
3 1 3 2 1 2 1 5 1 5 1 5 3 1 3 5 3 3 1 3 2 1 3 2 3
4 2 1 3 2 7 2 3 1 2 3 4 3 2 1 5 1 3 2 1 2 6 1 5 1
2 1 2 4 3 3 2 3 3 1 5 4 2 3 4 2 1 2 1 2 4 3 2 3 3
3 1 3 3 2 1 2 3 1 3 2 1 3 5 1 5 4 2 3 1 3 2 1 2 3
3 4 2 1 3 5 4 2 1 2 1 2 4 5 3 1 6 3 3 2 3 3 1 3 2
3 1 5 1 6 2 1 2 3 1 5 1 2 3 3 1 3 3 3 2 7 2 1 2 1
2 4 3 2 4 2 3 1 3 3 3 2 3 4 2 3 1 5 1 5 1 2 1 2 3
1 5 1 2 3 7 2 1 3 2 3 4 2 3 1 6 3 2 3 3 3 1 3 3 2
3 3 1 3 3 2 1 5 1 5 1 2 1 2 3 1 3 2 1 5 4 3 2 1 3
2 3 4 2 1 2 1 6 3 2 4 2 3 1 8 1 2 4 3 2 1 2 1 5 1
5 3 1 2 3 4 2 1 2 3 3 1 3 2 1 8 4 3 2 3 4 3 2 3 1
2 3 1 3 3 3 2 3 1 5 1 2 1 5 6 1 2 1 6 3 2 1 2 3 3
1 5 1 3 2 7 2 1 3 2 4 3 2 3 1 2 3 1 3 3 2 1 2 3 1
3 2 1 2 6 7 2 1 2 3 1 3 2 1 2 6 1 3 2 1 5 3 4 2 1
2 1 2 7 5 1 5 1 6 2 1 2 3 1 5 1 2 1 6 5 1 2 1 2 3
1 3 2 3 3 3 1 3 2 1 3 2 3 4 2 3 3 4 3 5 1 2 3 1 3
3 2 1 2 3 4 2 1 3 5 1 5 1 2 1 5 4 2 1 2 6 1 3 2 1
3 2 3 7 2 1 2 4 5 3 1 2 3 1 3 5 1 2 4 3 2 1 2 1 5
1 5 1 2 3 3 1 3 3 5 3 1 3 2 4 2 3 4 2 1 3 2 4 3 2
3 1 2 3 4 3 2 1 5 1 3 2 1 2 1 5 1 5 1 2 3 4 3 2 1
2 3 3 1 3 6 2 3 6 1 2 1 2 4 3 2 3 3 4 3 3 2 1 2 3
1 3 2 1 2 1 5 1 5 1 3 2 3 1 3 2 3 3 3 4 2 1 3 5 4
2 1 2 1 2 9 3 1 2 4 3 3 2 1 5 1 3 2 3 6 1 5 1 2 1
2 3 1 3 3 2 3 3 1 6 3 2 3 4 2 1 2 1 2 4 3 2 4 2 3
1 3 3 2 1 2 3 4 2 1 3 5 1 5 3 1 2 3 1 5 1 2 3 4 3
2 1 3 2 3 4 2 3 1 2 4 3 2 3 1 5 1 3 3 2 3 3 1 3 3
2 1 5 1 6 2 1 2 3 1 5 1 5 3 1 3 2 1 3 2 7 2 1 2 1
6 3 2 3 1 2 3 1 6 3 2 4 3 2 3 1 5 1 5 3 1 2 3 1 3
2 1 2 3 3 4 2 1 5 3 4 3 2 1 6 3 2 3 3 3 1 3 3 3 2
3 1 3 3 2 1 5 6 1 2 1 5 1 3 2 1 2 3 4 5 1 3 2 7 2
1 2 1 2 4 3 2 4 2 3 1 3 5 1 2 3 1 3 2 1 2 6 1 6 2
1 2 3 4 2 1 2 3 3 1 3 2 1 3 5 4 2 1 2 3 7 2 3 1 5
1 3 3 2 1 2 3 1 5 1 2 1 6 5 1 2 1 2 4 3 2 3 3 3 1
3 2 1 3 2 3 4 2 1 5 4 3 5 1 2 3 1 3 3 2 1 2 3 1 3
2 1 3 5 6 1 2 1 2 3 4 2 1 2 6 1 3 2 1 5 3 6 1 2 1
2 4 3 5 1 2 3 1 8 1 2 3 1 3 2 1 2 1 6 5 1 2 3 3 1
3 3 2 3 3 1 3 2 1 3 2 3 4 2 4 2 4 3 2 3 1 2 3 4 3
2 1 5 4 2 1 2 1 5 1 5 1 2 1 6 3 2 1 2 3 3 1 3 2 4
2 3 4 3 2 1 2 4 5 3 3 3 1 3 3 2 1 2 4 3 2 1 2 1 5
1 5 1 3 2 3 1 3 2 1 5 3 4 2 4 5 4 2 1 2 1 2 4 5 3
1 2 7 3 2 1 2 3 1 3 2 3 1 5 1 5 1 2 3 3 1 3 2 1 2
3 3 1 3 3 3 2 3 6 1 2 1 2 4 3 2 4 2 4 3 3 2 1 2 3
4 2 1 2 1 5 1 5 1 3 2 3 1 5 3 3 4 3 2 1 3 2 3 4 2
3 1 2 7 2 3 1 2 3 1 3 3 2 6 1 3 3 2 6 1 5 1 2 1 2
3 1 3 3 5 3 1 5 1 3 2 3 4 2 1 2 1 6 3 2 3 1 2 3 1
6 2 1 2 4 3 2 1 3 5 1 5 3 1 2 3 1 3 2 1 2 3 3 1 3
2 1 5 3 4 3 2 1 2 4 3 2 3 1 5 1 3 3 5 3 1 3 2 1 2
1 5 7 2 1 5 1 5 1 2 3 3 1 5 1 3 2 7 2 1 2 1 2 4 3
2 3 1 2 3 1 3 3 3 2 3 1 3 2 3 6 1 6 2 1 2 3 1 3 2
1 2 3 3 4 2 1 3 2 3 4 2 1 2 1 9 2 3 6 1 3 3 2 1 2
3 1 6 2 1 6 5 1 2 1 2 3 1 3 2 3 3 4 3 2 1 3 2 3 4
2 1 2 3 4 3 6 2 3 1 3 5 1 2 3 1 3 2 1 3 5 1 5 1 2
1 2 3 4 2 1 2 6 1 3 2 1 3 5 6 1 2 3 4 3 2 3 1 2 3
1 3 5 1 2 3 1 5 1 2 1 5 1 5 1 2 3 4 3 3 2 3 3 1 3
2 1 3 2 3 4 2 1 3 2 4 3 2 3 1 2 3 4 3 2 1 5 1 3 2
1 2 1 5 6 1 2 1 2 4 3 2 1 2 6 1 3 2 6 3 4 2 1 2 1
2 4 3 5 3 3 1 6 2 1 2 3 1 3 2 1 2 1 6 5 1 3 2 3 1
3 2 1 2 3 3 4 2 1 3 5 4 2 3 1 2 4 5 3 1 2 4 3 3 2
1 2 3 4 2 3 1 5 1 5 1 2 1 5 1 3 2 1 2 3 3 1 3 3 3
2 3 4 3 2 1 2 4 5 4 2 3 1 3 3 2 1 2 7 2 1 2 1 5 1
5 1 2 1 2 3 1 5 1 5 4 3 2 4 2 3 4 2 3 1 2 4 3 2 3
1 2 3 4 3 2 3 3 1 3 3 2 1 5 1 5 1 2 3 3 1 3 2 1 5
3 1 3 3 3 2 3 6 1 2 1 6 3 2 3 1 2 4 6 2 1 2 4 3 2
1 2 1 5 1 5 4 2 3 1 3 2 3 3 3 1 3 2 1 5 3 4 3 2 1
2 7 2 3 1 2 3 1 3 3 3 5 1 3 2 1 2 6 6 1 2 1 5 1 3
3 2 3 3 1 5 1 3 2 7 2 1 2 1 2 4 3 2 3 1 2 3 1 3 3
2 1 2 3 1 3 2 1 8 1) '(simple-array fixnum 1)))
(declaim (inline make-sieve-state maxints (setf maxints) sieve (setf sieve)))
(defstruct (sieve-state (:conc-name nil)
(:constructor make-sieve-state (maxints sieve)))
(maxints nil :type fixnum)
(sieve nil :type simple-bit-vector))
(declaim (ftype (function (fixnum) (values sieve-state &optional)) create-sieve))
(defun create-sieve (maxints)
(make-sieve-state maxints (make-array (/ maxints 2) :element-type 'bit :initial-element 0)))
(declaim (ftype (function (sieve-state (simple-array fixnum (*)))
(values sieve-state &optional)) run-sieve))
(defun run-sieve (sieve-state steps)
(do* ((maxints (maxints sieve-state))
(qh (with-type fixnum (ash (ceiling (isqrt maxints)) -1)))
(maxintsh (ash maxints -1))
(sieve (sieve sieve-state))
(step 1 (if (>= step 5759) 0 (with-type fixnum (1+ step))))
(factorh (with-type fixnum (ash 17 -1))))
((> factorh qh) sieve-state)
(declare (type fixnum maxints maxintsh qh step factorh)
(type simple-bit-vector sieve))
(when (zerop (sbit sieve factorh))
(do* ((istep step (if (>= istep 5759) 0 (with-type fixnum (1+ istep))))
(ninc (aref steps istep) (aref steps istep))
(factor (with-type fixnum (1+ (* factorh 2))))
(i (with-type fixnum (ash (* factor factor) -1))))
((>= i maxintsh))
(declare (fixnum istep ninc factor i))
(setf (sbit sieve i) 1)
(incf i (with-type fixnum (* factor ninc)))))
(setq factorh (+ factorh (aref steps step)))))
(declaim (ftype (function (sieve-state) (values fixnum &optional)) count-primes))
(defun count-primes (sieve-state)
(let ((maxints (maxints sieve-state)))
(do* ((sieve (sieve sieve-state))
(ncount (if (<= maxints 10) 4 6))
(factor 17)
(step 1 (if (>= step 5759) 0 (with-type fixnum (1+ step))))
(inc (* (aref +steps+ step) 2) (* (aref +steps+ step) 2)))
((> factor maxints) ncount)
(declare (type fixnum maxints ncount factor inc)
(type simple-bit-vector sieve))
(when (zerop (sbit sieve (ash factor -1)))
(incf ncount))
(incf factor inc))))
(declaim (ftype (function (&optional (integer 0 16)) null) main))
(defun main (&optional n-supplied)
(let* ((n (or n-supplied (parse-integer (car (last sb-ext:*posix-argv*))))))
(declare ((integer 0 16) n))
(loop for k below 3
for m = (ash 10000 (- n k))
for sieve-state of-type sieve-state = (create-sieve m)
do (format t "Primes up to~T~8<~d~>~T~8<~d~>~%"
m (count-primes (run-sieve sieve-state +steps+))))))