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REBOL [ Title: "Prime number checker" Date: 21-Jul-1999 Version: 0.0.2 File: %prime.r Home: Author: "Tom Conlin" Owner: "Intuitec" Rights: "yes" Tabs: 4 Purpose: { Address the question, could this integer be a prime number? results of false are not prime, results of true are very probably prime and with the /strong refinement, ( I still have to verify this ) true ( should ) guarantee prime. if the argument is outside the domain of the function, none is returned } Comment: { Able to handle integers up to one bit less than the machine (or rebol) is using for a ( signed? ) integer, this may vary -- but 30 bits probabaly. If you use the xxx-modulus functions elsewhere (they were kept general), be sure to keep "m" non-zero The /strong refinement is yet to be formaly proven (by me) to garantee primes. } History: [ 0.0.1 [19-Jul-1999 {typed (2 ** (n - 1 )) // n at the prompt, for n > 1024 }] 0.0.2 [21-Jul-1999 "dug out old homework"] ] Language: 'English Email: %tomc--cs--uoregon--edu Need: 0.2.1 Charset: 'ANSI Example: "is-prime? 1073741789" library: [ level: 'intermediate platform: none type: none domain: 'math tested-under: none support: none license: none see-also: none ] ] is-prime?: func ["return false if argument is composite, and none if can't tell" n [integer!] /strong /local b e p z ][ if n < 2 [return false] ; no negatives if any [error? try [z: n + n] z < n][return none] e: n - 1 p: power-modulus 2 e n if strong [ b: 3 z: to-integer (log-2 n + 1 ) while [ (p == 1) and (b < z) ][ p: power-modulus b e n b: b + 1 ] ] p == 1 ] comment { an efficent recursive power function, will recurse only the number of (significant) bits in the exponent, squareing the base at each level but only accumulating the base if the least significant bit of the exponent at that level is set. note: just forwards the modulus to the multiply function. } power-modulus: func [ "b to the e power, mod m" b [integer!] "base" e [integer!] "exponent" m [integer!] "modulus" /local t ][ if e == 0 [return 1] t: power-modulus (multiply-modulus b b m ) to-integer(e / 2) m if odd? e [ t: multiply-modulus t b m ] t ] comment { a multiply which if need be, guarantees the product is never more than one bit longer than the modulus } multiply-modulus: func[ "j times k, mod m" j [integer!] k [integer!] m [integer!] "modulus" /local product ][ if error? try [ product: j * k // m ] [ product: 0 while[ k > 0 ][ if(odd? k ) [ product: to-integer( product + j ) // m ] j: j + j // m k: to-integer k / 2 ] ] to-integer product ]
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