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first working is_prime() with lots of tests

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1 parent 20f51cf commit 3c40e129611b868f4818ced7fe3f669a4257ef77 @leto 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
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@@ -11,6 +11,7 @@ my $builder = Module::Build->new(
include_dirs => '',
build_requires => {
'Test::More' => 0,
+ 'Test::Exception' => 0,
},
requires => {
'Math::GMPz' => 0.26,
View
@@ -162,6 +162,10 @@ sub _find_s_d($)
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
View
@@ -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

@bubaflub
Collaborator

You've still got use Data::Dumper on line 5

@leto
Owner
leto 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.

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