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Ingy döt Net 2023-07-01 11:58:00 -04:00
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74
Task/Miller-Rabin-primality-test/Clojure/miller-rabin-primality-test-1.clj Normal file
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(ns test-p.core
(:require [clojure.math.numeric-tower :as math])
(:require [clojure.set :as set]))
(def WITNESSLOOP "witness")
(def COMPOSITE "composite")
(defn m* [p q m]
" Computes (p*q) mod m "
(mod (*' p q) m))
(defn power
"modular exponentiation (i.e. b^e mod m"
[b e m]
(loop [b b, e e, x 1]
(if (zero? e)
x
(if (even? e) (recur (m* b b m) (quot e 2) x)
(recur (m* b b m) (quot e 2) (m* b x m))))))
; Sequence of random numbers to use in the test
(defn rand-num [n]
" random number between 2 and n-2 "
(bigint (math/floor (+' 2 (*' (- n 4) (rand))))))
; Unique set of random numbers
(defn unique-random-numbers [n k]
" k unique random numbers between 2 and n-2 "
(loop [a-set #{}]
(cond
(>= (count a-set) k) a-set
:else (recur (conj a-set (rand-num n))))))
(defn find-d-s [n]
" write n − 1 as 2s·d with d odd "
(loop [d (dec n), s 0]
(if (odd? d)
[d s]
(recur (quot d 2) (inc s)))))
(defn random-test
([n] (random-test n (min 1000 (bigint (/ n 2)))))
([n k]
" Random version of primality test"
(let [[d s] (find-d-s n)
; Individual Primality Test
single-test (fn [a s]
(let [z (power a d n)]
(if (some #{z} [1 (dec n)])
WITNESSLOOP
(loop [x (power z 2 n), r s]
(cond
(= x 1) COMPOSITE
(= x (dec n)) WITNESSLOOP
(= r 0) COMPOSITE
:else (recur (power x 2 n) (dec r)))))))]
; Apply Test
;(not-any? #(= COMPOSITE (local-test % s))
; (unique-random-numbers n k))))
(not-any? #(= COMPOSITE (single-test % s)) (unique-random-numbers n k)))))
;; Testing
(println "Primes beteen 900-1000:")
(doseq [q (range 900 1000)
:when (random-test q)]
(print " " q))
(println)
(println "Is Prime?" 4547337172376300111955330758342147474062293202868155909489 (random-test 4547337172376300111955330758342147474062293202868155909489))
(println "Is Prime?" 4547337172376300111955330758342147474062293202868155909393 (random-test 4547337172376300111955330758342147474062293202868155909393))
(println "Is Prime?" 643808006803554439230129854961492699151386107534013432918073439524138264842370630061369715394739134090922937332590384720397133335969549256322620979036686633213903952966175107096769180017646161851573147596390153
(random-test 643808006803554439230129854961492699151386107534013432918073439524138264842370630061369715394739134090922937332590384720397133335969549256322620979036686633213903952966175107096769180017646161851573147596390153))
(println "Is Prime?" 743808006803554439230129854961492699151386107534013432918073439524138264842370630061369715394739134090922937332590384720397133335969549256322620979036686633213903952966175107096769180017646161851573147596390153
(random-test 743808006803554439230129854961492699151386107534013432918073439524138264842370630061369715394739134090922937332590384720397133335969549256322620979036686633213903952966175107096769180017646161851573147596390153))

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Task/Miller-Rabin-primality-test/Clojure/miller-rabin-primality-test-2.clj Normal file
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(ns test-p.core
(:require [clojure.math.numeric-tower :as math]))
(def WITNESSLOOP "witness")
(def COMPOSITE "composite")
(defn m* [p q m]
" Computes (p*q) mod m "
(mod (*' p q) m))
(defn power
"modular exponentiation (i.e. b^e mod m"
[b e m]
(loop [b b, e e, x 1]
(if (zero? e)
x
(if (even? e) (recur (m* b b m) (quot e 2) x)
(recur (m* b b m) (quot e 2) (m* b x m))))))
(defn find-d-s [n]
" write n − 1 as 2s·d with d odd "
(loop [d (dec n), s 0]
(if (odd? d)
[d s]
(recur (quot d 2) (inc s)))))
;; Deterministic Test
(defn individual-deterministic-test [a d n s]
" Deterministic Primality Test "
(let [z (power a d n)]
(if (= z 1)
WITNESSLOOP
(loop [x z, r s]
(cond
(= x (dec n)) WITNESSLOOP
(zero? r) COMPOSITE
:else (recur (power x 2 n) (dec r)))))))
(defn deterministic-test [n]
" Sequence of Primality Tests "
(cond
(some #{n} [0 1 4]) false
(some #{n} [2 3]) true
(even? n) false
:else (let [[d s] (find-d-s n)]
(cond
(< n 2047) (not-any? #(= COMPOSITE (individual-deterministic-test % d n s)) [2 ])
(< n 1373653) (not-any? #(= COMPOSITE (individual-deterministic-test % d n s)) [2 3])
(< n 9090191) (not-any? #(= COMPOSITE (individual-deterministic-test % d n s)) [31 73])
(< n 25326001) (not-any? #(= COMPOSITE (individual-deterministic-test % d n s)) [2 3 5])
(< n 3215031751) (not-any? #(= COMPOSITE (individual-deterministic-test % d n s)) [2 3 5 7])
(< n 1122004669633) (not-any? #(= COMPOSITE (individual-deterministic-test % d n s)) [2 13 23 1662803])
(< n 2152302898747) (not-any? #(= COMPOSITE (individual-deterministic-test % d n s)) [2 3 5 7 11])
(< n 2152302898747) (not-any? #(= COMPOSITE (individual-deterministic-test % d n s)) [2 3 5 7 11])
(< n 3474749660383) (not-any? #(= COMPOSITE (individual-deterministic-test % d n s)) [2 3 5 7 11 13])
(< n 341550071728321) (not-any? #(= COMPOSITE (individual-deterministic-test % d n s)) [2 3 5 7 11 13 17])
(< n 3825123056546,413,051) (not-any? #(= COMPOSITE (individual-deterministic-test % d n s)) [2 3 5 7 11 13 17 19 23])
(< n (math/expt 2 64) ) (not-any? #(= COMPOSITE (individual-deterministic-test % d n s)) [2 3 5 7 11 13 17 19 23 29 31 37])
(< n 318665857834031151167461) (not-any? #(= COMPOSITE (individual-deterministic-test % d n s)) [2 3 5 7 11 13 17 19 23 29 31 37])
(< n 3317044064679887385961981) (not-any? #(= COMPOSITE (individual-deterministic-test % d n s)) [2 3 5 7 11 13 17 19 23 29 31 37 41])
:else (let [k (min (dec n) (int (math/expt (Math/log n) 2)))]
(not-any? #(= COMPOSITE (individual-deterministic-test % d n s)) (range 2 (inc k))))))))
;; Testing
(println "Primes beteen 900-1000:")
(doseq [q (range 900 1000)
:when (deterministic-test q)]
(print " " q))
(println)
(println "Is Prime?" 4547337172376300111955330758342147474062293202868155909489 (deterministic-test 4547337172376300111955330758342147474062293202868155909489))
(println "Is Prime?" 4547337172376300111955330758342147474062293202868155909393 (deterministic-test 4547337172376300111955330758342147474062293202868155909393))
println "Is Prime?" 643808006803554439230129854961492699151386107534013432918073439524138264842370630061369715394739134090922937332590384720397133335969549256322620979036686633213903952966175107096769180017646161851573147596390153
(deterministic-test 643808006803554439230129854961492699151386107534013432918073439524138264842370630061369715394739134090922937332590384720397133335969549256322620979036686633213903952966175107096769180017646161851573147596390153))
(println "Is Prime?" 743808006803554439230129854961492699151386107534013432918073439524138264842370630061369715394739134090922937332590384720397133335969549256322620979036686633213903952966175107096769180017646161851573147596390153
(deterministic-test 743808006803554439230129854961492699151386107534013432918073439524138264842370630061369715394739134090922937332590384720397133335969549256322620979036686633213903952966175107096769180017646161851573147596390153))
(println "Is Prime?" 643808006803554439230129854961492699151386107534013432918073439524138264842370630061369715394739134090922937332590384720397133335969549256322620979036686633213903952966175107096769180017646161851573147596390153
(deterministic-test 643808006803554439230129854961492699151386107534013432918073439524138264842370630061369715394739134090922937332590384720397133335969549256322620979036686633213903952966175107096769180017646161851573147596390153))
(println "Is Prime?" 743808006803554439230129854961492699151386107534013432918073439524138264842370630061369715394739134090922937332590384720397133335969549256322620979036686633213903952966175107096769180017646161851573147596390153
(deterministic-test 743808006803554439230129854961492699151386107534013432918073439524138264842370630061369715394739134090922937332590384720397133335969549256322620979036686633213903952966175107096769180017646161851573147596390153))