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factor-twos cps version using first-bit-set

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first-bit-set is way faster than looping
This commit is contained in:
Roger Crew 2021-06-27 02:42:03 -07:00
parent 73da0a88d4
commit 7d39108e72
1 changed files with 23 additions and 23 deletions
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46
lib/chibi/math/prime.scm
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@ -4,12 +4,13 @@
;;> Prime and number theoretic utilities. ;;> Prime and number theoretic utilities.
;;> Returns a pair whose car is the power of 2 in the factorization of ;; Given \var{n} and a continuation \var{return},
;;> n, and whose cdr is the product of all remaining primes. ;; returns (\var{return} \var{k2} \var{n2}) where
(define (factor-twos n) ;; \var{k2} is the power of 2 in the factorization of \var{n}, and
(do ((p 0 (+ p 1)) ;; \var{n2} is product of all other prime powers dividing \var{n}
(r n (arithmetic-shift r -1))) (define (factor-twos n return)
((odd? r) (cons p r)))) (let ((b (first-set-bit n)))
(return b (arithmetic-shift n (- b)))))
;;> Returns the multiplicative inverse of \var{a} modulo \var{b}. ;;> Returns the multiplicative inverse of \var{a} modulo \var{b}.
(define (modular-inverse a b) (define (modular-inverse a b)
@ -85,23 +86,22 @@
;;> Returns true if we can show \var{n} to be composite by finding an ;;> Returns true if we can show \var{n} to be composite by finding an
;;> exception to the Miller Rabin lemma. ;;> exception to the Miller Rabin lemma.
(define (miller-rabin-composite? n) (define (miller-rabin-composite? n)
(let* ((neg1 (- n 1)) (let ((neg1 (- n 1)))
(factors (factor-twos neg1)) (factor-twos neg1
(twos (car factors)) (lambda (twos odd)
(odd (cdr factors)) ;; Each iteration of Miller Rabin reduces the odds by 1/4, so
;; Each iteration of Miller Rabin reduces the odds by 1/4, so ;; this is a 1 in 2^40 probability of false positive,
;; this is a 1 in 2^40 probability of false positive, ;; assuming good randomness from SRFI 27 and no bugs, further
;; assuming good randomness from SRFI 27 and no bugs, further ;; reduced by preliminary sieving.
;; reduced by preliminary sieving. (let* ((fixed-limit 16)
(fixed-limit 16) (rand-limit (if (< n 341550071728321) fixed-limit 20)))
(rand-limit (if (< n 341550071728321) fixed-limit 20))) (let try ((i 0))
(let try ((i 0)) (and (< i rand-limit)
(and (< i rand-limit) (let ((a (if (< i fixed-limit)
(let ((a (if (< i fixed-limit) (vector-ref prime-table i)
(vector-ref prime-table i) (+ (random-integer (- n 3)) 2))))
(+ (random-integer (- n 3)) 2)))) (or (not (modular-root-of-one? twos odd a n neg1))
(or (not (modular-root-of-one? twos odd a n neg1)) (try (+ i 1)))))))))))
(try (+ i 1))))))))
;;> Returns true if \var{n} has a very high probability (enough that ;;> Returns true if \var{n} has a very high probability (enough that
;;> you can assume a false positive will never occur in your lifetime) ;;> you can assume a false positive will never occur in your lifetime)