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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.
;;> Returns a pair whose car is the power of 2 in the factorization of
;;> n, and whose cdr is the product of all remaining primes.
(define (factor-twos n)
(do ((p 0 (+ p 1))
(r n (arithmetic-shift r -1)))
((odd? r) (cons p r))))
;; Given \var{n} and a continuation \var{return},
;; returns (\var{return} \var{k2} \var{n2}) where
;; \var{k2} is the power of 2 in the factorization of \var{n}, and
;; \var{n2} is product of all other prime powers dividing \var{n}
(define (factor-twos n return)
(let ((b (first-set-bit n)))
(return b (arithmetic-shift n (- b)))))
;;> Returns the multiplicative inverse of \var{a} modulo \var{b}.
(define (modular-inverse a b)
@ -85,23 +86,22 @@
;;> Returns true if we can show \var{n} to be composite by finding an
;;> exception to the Miller Rabin lemma.
(define (miller-rabin-composite? n)
(let* ((neg1 (- n 1))
(factors (factor-twos neg1))
(twos (car factors))
(odd (cdr factors))
;; Each iteration of Miller Rabin reduces the odds by 1/4, so
;; this is a 1 in 2^40 probability of false positive,
;; assuming good randomness from SRFI 27 and no bugs, further
;; reduced by preliminary sieving.
(fixed-limit 16)
(rand-limit (if (< n 341550071728321) fixed-limit 20)))
(let try ((i 0))
(and (< i rand-limit)
(let ((a (if (< i fixed-limit)
(vector-ref prime-table i)
(+ (random-integer (- n 3)) 2))))
(or (not (modular-root-of-one? twos odd a n neg1))
(try (+ i 1))))))))
(let ((neg1 (- n 1)))
(factor-twos neg1
(lambda (twos odd)
;; Each iteration of Miller Rabin reduces the odds by 1/4, so
;; this is a 1 in 2^40 probability of false positive,
;; assuming good randomness from SRFI 27 and no bugs, further
;; reduced by preliminary sieving.
(let* ((fixed-limit 16)
(rand-limit (if (< n 341550071728321) fixed-limit 20)))
(let try ((i 0))
(and (< i rand-limit)
(let ((a (if (< i fixed-limit)
(vector-ref prime-table i)
(+ (random-integer (- n 3)) 2))))
(or (not (modular-root-of-one? twos odd a n neg1))
(try (+ i 1)))))))))))
;;> Returns true if \var{n} has a very high probability (enough that
;;> you can assume a false positive will never occur in your lifetime)