first working is_prime() with lots of tests

Build.PL

@@ -11,6 +11,7 @@ my $builder = Module::Build->new(
     include_dirs        => '',
     build_requires => {
         'Test::More' => 0,
+        'Test::Exception' => 0,
     },
     requires => {
         'Math::GMPz' => 0.26,

lib/Math/Primality.pm

@@ -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

t/is_prime.t

@@ -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');
+
+