# leto/math--primality

first working is_prime() with lots of tests

1 parent 20f51cf commit 3c40e129611b868f4818ced7fe3f669a4257ef77 committed Jun 3, 2009
Showing with 94 additions and 24 deletions.
1. +1 −0 Build.PL
2. +15 −9 lib/Math/Primality.pm
3. +78 −15 t/is_prime.t
 @@ -11,6 +11,7 @@ my \$builder = Module::Build->new( include_dirs => '', build_requires => { 'Test::More' => 0, + 'Test::Exception' => 0, }, requires => { 'Math::GMPz' => 0.26,
 @@ -162,6 +162,10 @@ sub _find_s_d(\$) return (\$s,\$d); } +=head2 is_strong_lucas_pseudoprime(\$n) + +=cut + sub is_strong_lucas_pseudoprime(\$) { my (\$n) = @_; @@ -319,21 +323,23 @@ sub _check_two_and_even(\$) { my \$cmp = Rmpz_cmp_ui(\$n, 2 ); return 1 if \$cmp == 0; return 0 if \$cmp < 0; - return 0 if Rmpz_even_p(\$n); + return 0 if Rmpz_even_p(\$n); return 2; } -# should do exactly what it says - returns true if number is prime, false if number is composite +=head2 is_prime(\$n) + +Returns true if number is prime, false if number is composite. + +=cut + sub is_prime(\$) { my \$n = GMP->new(\$_[0]); - # first eliminate all n < 2 and even n > 3 - my \$cmp = _check_two_and_even(\$n); - return \$cmp if \$cmp != 2; + # TODO: # trial division of n up to some small number (perhaps a thousand) - # try Miller-Rabin strong psuedoprime test with base 2 - # try Lucas-Selfridge strong psuedoprime test - # is a BPSW probable prime - return 1; + + # the lucas test is stronger so do it first + return is_strong_lucas_pseudoprime(\$n) && is_strong_pseudoprime(\$n,2); } # given a number, produces the next prime number
 @@ -2,22 +2,85 @@ use strict; use warnings; -use Test::More tests => 3; - +use Data::Dumper; +use Test::More tests => 573; +use Test::Exception; use Math::Primality qw/is_prime/; -use Math::GMPz; +use Math::GMPz qw/:mpz/; +### test small numbers (<1000) ### +### test Lucas psuedoprimes ### ### basic method handling ### + my \$z = Math::GMPz->new(3); -ok( is_prime(3), "is_prime should handle Math::GMPz objects, three is prime" ); -ok( is_prime(2), "is_prime should handle 2 as a prime"); -ok( !is_prime(20), "is_prime should even numbers"); - -TODO: { - local \$TODO = "is_prime is being worked on"; - - ### test small numbers (<1000) ### - ### test known Miller-Rabin psuedoprimes base 2 ### - ### test Carmichael numbers ### - ### test Lucas psuedoprimes ### -}; +ok( is_prime(\$z), "is_prime should handle Math::GMPz objects, three is prime" ); +ok( is_prime(2), '2 is prime'); +ok(!is_prime(1), '1 is not prime'); +ok(!is_prime(0), '0 is not prime'); +ok(!is_prime(-1), '-1 is not prime'); +ok(!is_prime(-2), '-2 is not prime'); +ok( !is_prime(20), "20 is not prime"); + +# powers of 2 are never prime +for my \$k (1..20) { + Rmpz_ui_pow_ui(\$z, 2, ++\$k ); + ok(!is_prime(\$z), "2**\$k=\$z is not prime"); +} + +my @small_primes = qw/ +5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 +73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 +179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 +283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 +419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 +547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 +661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 +811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 +947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 +1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 +1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 +1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 1471 1481 1483 1487 1489 1493 1499 1511 +1523 1531 1543 1549 1553 1559 1567 1571 1579 1583 1597 1601 1607 1609 1613 1619 1621 1627 1637 1657 +1663 1667 1669 1693 1697 1699 1709 1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 1811 +1823 1831 1847 1861 1867 1871 1873 1877 1879 1889 1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 +1993 1997 1999 2003 2011 2017 2027 2029 2039 2053 2063 2069 2081 2083 2087 2089 2099 2111 2113 2129 +2131 2137 2141 2143 2153 2161 2179 2203 2207 2213 2221 2237 2239 2243 2251 2267 2269 2273 2281 2287 +2293 2297 2309 2311 2333 2339 2341 2347 2351 2357 2371 2377 2381 2383 2389 2393 2399 2411 2417 2423 +2437 2441 2447 2459 2467 2473 2477 2503 2521 2531 2539 2543 2549 2551 2557 2579 2591 2593 2609 2617 +2621 2633 2647 2657 2659 2663 2671 2677 2683 2687 2689 2693 2699 2707 2711 2713 2719 2729 2731 2741 +2749 2753 2767 2777 2789 2791 2797 2801 2803 2819 2833 2837 2843 2851 2857 2861 2879 2887 2897 2903 +2909 2917 2927 2939 2953 2957 2963 2969 2971 2999 3001 3011 3019 3023 3037 3041 3049 3061 3067 3079 +3083 3089 3109 3119 3121 3137 3163 3167 3169 3181 3187 3191 3203 3209 3217 3221 3229 3251 3253 3257 +3259 3271 3299 3301 3307 3313 3319 3323 3329 3331 3343 3347 3359 3361 3371 3373 3389 3391 3407 3413 +3433 3449 3457 3461 3463 3467 3469 3491 3499 3511 3517 3527 3529 3533 3539 3541 3547 3557 3559 3571 +/; + +map { ok(is_prime(\$_), "\$_ is prime") } @small_primes; + +my @carmichael = qw/561 1105 1729 2465 2821 6601 8911 + 10585 15841 29341 41041 46657 52633 + 62745 63973 75361 101101 + 999838193331601 + 999840927672001 + 999851057445241 + 999878556600001 + 999885684921481 + 999895175363161 + 999902676805201 + 999907821232321 + 999919121100481 + 999922265173441 +/; +map { ok(!is_prime(\$_), "Carmichael Number \$_ is not prime") } @carmichael; + +# First 20 psp(2)'s +map { ok(!is_prime(\$_), "Pseudoprime (base 2) \$_ is not prime" ) } qw/ + 341 561 645 1105 1387 1729 1905 2047 + 2465 2701 2821 3277 4033 4369 4371 + 4681 5461 6601 7957 8321 +/; + +throws_ok( sub { is_prime('foo') }, qr/First argument supplied to Rmpz_init_set_str/, + 'is_prime warns about string not being valid'); + +

#### 2 comments on commit `3c40e12`

Collaborator
commented on `t/is_prime.t` in `3c40e12` Jun 3, 2009
 You've still got use Data::Dumper on line 5
Owner
commented on `3c40e12` Jun 4, 2009
 Yeah, I leave Data::Dumper in test code so that you don't have to type it and delete it constantly when writing tests.