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| -rw-r--r-- | net/ricketyspace/sicp/one/twentyeight.scm | 34 |
1 files changed, 34 insertions, 0 deletions
diff --git a/net/ricketyspace/sicp/one/twentyeight.scm b/net/ricketyspace/sicp/one/twentyeight.scm new file mode 100644 index 0000000..bad63a0 --- /dev/null +++ b/net/ricketyspace/sicp/one/twentyeight.scm @@ -0,0 +1,34 @@ +;;;; Under Creative Commons Attribution-ShareAlike 4.0 +;;;; International. See +;;;; <https://creativecommons.org/licenses/by-sa/4.0/>. + +(define-module (net ricketyspace sicp one twentyeight) + #:use-module (srfi srfi-1) + #:export (miller-rabin-test prime?)) + +(define (sqmod x m) + "Return x^2 if `x^2 mod m` is not equal to `1 mod m` +and x != m - 1 and x != 1; 0 otherwise." + (let ((square (* x x))) + (cond ((and (= (remainder square m) 1) ; 1 mod m = 1 + (not (= x (1- m))) + (not (= x 1))) + 0) + (else square)))) + +(define (expmod base exp m) + (cond ((= exp 0) 1) + ((even? exp) + (remainder (sqmod (expmod base (/ exp 2) m) m) + m)) + (else + (remainder (* base (expmod base (- exp 1) m)) + m)))) + +(define (miller-rabin-test n) + (define (pass? a) + (= (expmod a (1- n) n) 1)) + (fold (lambda (a p) (and (pass? a) p)) #t (iota (1- n) 1))) + +(define (prime? n) + (if (miller-rabin-test n) #t #f)) |