[libmath-prime-util-perl] 08/23: Split AKS out of isprime tests. Extend AKS from halfword to fullword.
Partha P. Mukherjee
ppm-guest at moszumanska.debian.org
Thu May 21 18:45:55 UTC 2015
This is an automated email from the git hooks/post-receive script.
ppm-guest pushed a commit to annotated tag v0.14
in repository libmath-prime-util-perl.
commit 29d4faa2c7e0bbca134ea4ce39090d3c883463b8
Author: Dana Jacobsen <dana at acm.org>
Date: Thu Nov 22 19:19:46 2012 -0800
Split AKS out of isprime tests. Extend AKS from halfword to fullword.
---
Changes | 6 ++
MANIFEST | 1 +
TODO | 3 +
aks.c | 19 ++++--
t/10-isprime.t | 193 ++++++++++++++++++++++++++-----------------------------
t/22-aks-prime.t | 69 ++++++++++++++++++++
6 files changed, 182 insertions(+), 109 deletions(-)
diff --git a/Changes b/Changes
index dde7860..e3eae4b 100644
--- a/Changes
+++ b/Changes
@@ -1,5 +1,11 @@
Revision history for Perl extension Math::Prime::Util.
+0.14 ?? November 2012
+
+ - Clean up some tests.
+
+ - XS AKS extended from half-word to full-word.
+
0.13 19 November 2012
- Fix an issue with prime count, and make prime count available as a
diff --git a/MANIFEST b/MANIFEST
index 4cf35c5..ef85997 100644
--- a/MANIFEST
+++ b/MANIFEST
@@ -69,6 +69,7 @@ t/16-randomprime.t
t/17-pseudoprime.t
t/18-functions.t
t/19-moebius.t
+t/22-aks-prime.t
t/30-relations.t
t/31-threading.t
t/50-factoring.t
diff --git a/TODO b/TODO
index e60e8c2..c35bdee 100644
--- a/TODO
+++ b/TODO
@@ -39,3 +39,6 @@
precision. We should be able to do better. One problem is the accuracy
bug in Math::BigFloat. Perhaps check for Math::MPFR installed and use it?
Alternately write real-number pow function using GMP.
+
+- An assembler version of mulmod for i386 would be _really_ helpful for
+ all the non-x86-64 Intel machines.
diff --git a/aks.c b/aks.c
index 43a116f..26cfd4a 100644
--- a/aks.c
+++ b/aks.c
@@ -4,12 +4,19 @@
#include <math.h>
/*
- * The AKS v6 algorithm, for native integers, where n < 2^(wordbits/2)-1.
- * Hence on 64-bit machines this works for n < 4294967295, because we do
- * r = (r + a * b) % n
- * where r, a, and b are mod n. This could be extended to a full word by
- * using a mulmod function (like factor.c has), but it's easier to go to
- * GMP at that point, which also lets one do r or 2r modulos instead of r*r.
+ * The AKS v6 algorithm, for native integers. Based on the AKS v6 paper.
+ * As with most AKS implementations, it's really slow.
+ *
+ * When n < 2^(wordbits/2)-1, we can do a straightforward intermediate:
+ * r = (r + a * b) % n
+ * If n is larger, then these are replaced with:
+ * r = addmod( r, mulmod(a, b, n), n)
+ * which is a lot more work, but keeps us correct.
+ *
+ * Software that does polynomial convolutions followed by a modulo can be
+ * very fast, but will fail when n >= (2^wordbits)/r.
+ *
+ * This is all much easier in GMP.
*
* Copyright 2012, Dana Jacobsen.
*/
diff --git a/t/10-isprime.t b/t/10-isprime.t
index 768bf58..a3366a4 100644
--- a/t/10-isprime.t
+++ b/t/10-isprime.t
@@ -3,114 +3,111 @@ use strict;
use warnings;
use Test::More;
-use Math::Prime::Util qw/is_prime is_aks_prime/;
+use Math::Prime::Util qw/is_prime/;
my $use64 = Math::Prime::Util::prime_get_config->{'maxbits'} > 32;
my $extra = defined $ENV{RELEASE_TESTING} && $ENV{RELEASE_TESTING};
my $broken64 = (18446744073709550592 == ~0);
-plan tests => 6 + 19 + 3573 + (5 + 29 + 22 + 23 + 16) + 15 + 27 + 1 + 3
- + ($use64 ? 5+1 : 0)
- + ($extra ? 6 : 0)
- + (($extra && $use64) ? 19 : 0);
-
-# Some of these tests were inspired by Math::Primality's tests
-
+my @small_primes = qw/
+2 3 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 /;
+
+my @composites = (qw/
+ 9 121 341 561 645 703 781 1105 1387 1541 1729 1891 1905 2047 2465 2701 2821
+ 3277 3281 4033 4369 4371 4681 5461 5611 6601 7813 7957 8321 8401 8911 10585
+ 12403 13021 14981 15751 15841 16531 18721 19345 23521 24211 25351 29341
+ 29539 31621 38081 40501 41041 44287 44801 46657 47197 52633 53971 55969
+ 62745 63139 63973 74593 75361 79003 79381 82513 87913 88357 88573 97567
+ 101101 340561 488881 852841 1373653 1857241 6733693 9439201 17236801
+ 23382529 25326001 34657141 56052361 146843929 216821881 3215031751 /);
+
+push @composites, (qw/
+ 2152302898747 3474749660383 341550071728321 341550071728321
+ 3825123056546413051/) if $use64;
+
+my @primes = (qw/
+ 2 3 7 23 89 113 523 887 1129 1327 9551 15683 19609 31397 155921
+ 5 11 29 97 127 541 907 1151 1361 9587 15727 19661 31469 156007 360749
+ 370373 492227 1349651 1357333 2010881 4652507 17051887 20831533 47326913
+ 122164969 189695893 191913031 387096383 436273291 1294268779 1453168433
+ 2300942869 3842611109/);
+
+push @primes, (qw/
+ 4302407713 10726905041 20678048681 22367085353 25056082543 42652618807
+ 127976334671 182226896239 241160624143 297501075799 303371455241
+ 304599508537 416608695821 461690510011 614487453523 738832927927
+ 1346294310749 1408695493609 1968188556461 2614941710599/) if $use64;
+#@large_primes = grep { $extra || $_ <= 4_000_000_000 } @large_primes;
+
+# We're checking every integer from 0 to small_primes[-1], so don't bother
+# checking them twice.
+ at composites = grep { $_ > $small_primes[-1] } @composites;
+ at primes = grep { $_ > $small_primes[-1] } @primes;
+
+
+plan tests => 6 # range
+ + 1 # powers of 2
+ + 1 # small numbers
+ + scalar @composites
+ + scalar @primes
+ + 1 # 32-bit or 64-bit edge
+ + 0;
+
+ok(!eval { is_prime(undef); }, "is_prime(undef)");
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
-foreach my $k (2 .. 20) {
- my $k2 = 2**$k;
- ok(!is_prime($k2), "2**$k=$k2 is not prime");
+{
+ my @isprime = map { 0+!!is_prime( int(2**$_) ) } (2..20);
+ my @exprime = (0) x (20-2+1);
+ is_deeply( \@isprime, \@exprime, "is_prime powers of 2" );
}
-my @small_primes = qw/
-2 3 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
-/;
-my %small_primes;
-map { $small_primes{$_} = 1; } @small_primes;
-
-foreach my $n (0 .. 3572) {
- if (defined $small_primes{$n}) {
- ok(is_prime($n), "$n is prime");
- } else {
- ok(!is_prime($n), "$n is not prime");
- }
+{
+ my %small_primes = map { $_ => 1; } @small_primes;
+ my @isprime = map { is_prime($_) } (0..3572);
+ my @exprime = map { $small_primes{$_} ? 2 : 0 } (0..3572);
+ is_deeply( \@isprime, \@exprime, "is_prime 0..3572" );
}
-map { ok(!is_prime($_), "A006945 number $_ is not prime") }
- qw/9 2047 1373653 25326001 3215031751/;
-
-map { ok(!is_prime($_), "A006945 number $_ is not prime") }
- qw/2152302898747 3474749660383 341550071728321 341550071728321 3825123056546413051/ if $use64;
-
-map { ok(!is_prime($_), "Carmichael Number $_ is not prime") }
- qw/561 1105 1729 2465 2821 6601 8911 10585 15841 29341 41041 46657 52633
- 62745 63973 75361 101101 340561 488881 852841 1857241 6733693
- 9439201 17236801 23382529 34657141 56052361 146843929 216821881/;
-
-map { ok(!is_prime($_), "Pseudoprime (base 2) $_ is not prime" ) }
- qw/341 561 645 1105 1387 1729 1905 2047 2465 2701 2821 3277 4033 4369 4371
- 4681 5461 6601 7957 8321 52633 88357/;
-
-map { ok(!is_prime($_), "Pseudoprime (base 3) $_ is not prime" ) }
- qw/121 703 1891 3281 8401 8911 10585 12403 16531 18721 19345 23521 31621
- 44287 47197 55969 63139 74593 79003 82513 87913 88573 97567/;
-
-map { ok(!is_prime($_), "Pseudoprime (base 5) $_ is not prime" ) }
- qw/781 1541 5461 5611 7813 13021 14981 15751 24211 25351 29539 38081
- 40501 44801 53971 79381/;
-
-map { ok(is_prime($_), "Primegap start $_ is prime" ) }
- qw/2 3 7 23 89 113 523 887 1129 1327 9551 15683 19609 31397 155921/;
-
-map { ok(is_prime($_), "Primegap end $_ is prime" ) }
- qw/5 11 29 97 127 541 907 1151 1361 9587 15727 19661 31469 156007 360749
- 370373 492227 1349651 1357333 2010881 4652507 17051887 20831533 47326913
- 122164969 189695893 191913031/;
-
-map { ok(is_prime($_), "Primegap end $_ is prime" ) }
- qw/10726905041/ if $use64;
-
-map { ok(is_prime($_), "Primegap end $_ is prime" ) }
- qw/387096383 436273291 1294268779 1453168433 2300942869 3842611109/ if $extra;
-
-map { ok(is_prime($_), "Primegap end $_ is prime" ) }
- qw/4302407713 20678048681 22367085353
- 25056082543 42652618807 127976334671 182226896239 241160624143
- 297501075799 303371455241 304599508537 416608695821 461690510011
- 614487453523 738832927927 1346294310749 1408695493609 1968188556461
- 2614941710599/
- if $use64 && $extra;
+foreach my $n (@composites) {
+ is( is_prime($n), 0, "$n is composite" );
+}
+foreach my $n (@primes) {
+ is( is_prime($n), 2, "$n is definitely prime" );
+}
# Check that we do the right thing near the word-size edge
SKIP: {
@@ -118,13 +115,3 @@ SKIP: {
eval { is_prime( $use64 ? "18446744073709551629" : "4294967306" ); };
like($@, qr/range/i, "is_prime on ~0 + delta without bigint should croak");
}
-
-# Simple AKS
-is( is_aks_prime(877), 1, "is_aks_prime(877) is true" );
-SKIP: {
- skip "Skipping is_aks_prime tests on 32-bit Perl", 2 if !$use64;
- # The first number that makes it past the sqrt test to actually run.
- is( is_aks_prime(69197), 1, "is_aks_prime(69197) is true" );
- # A composite (product of two 5-digit primes)
- is( is_aks_prime(1262952907), 0, "is_aks_prime(1262952907) is false" );
-}
diff --git a/t/22-aks-prime.t b/t/22-aks-prime.t
new file mode 100644
index 0000000..2d68eb0
--- /dev/null
+++ b/t/22-aks-prime.t
@@ -0,0 +1,69 @@
+#!/usr/bin/env perl
+use strict;
+use warnings;
+
+use Test::More;
+use Math::Prime::Util qw/is_aks_prime/;
+
+my $use64 = Math::Prime::Util::prime_get_config->{'maxbits'} > 32;
+my $extra = defined $ENV{RELEASE_TESTING} && $ENV{RELEASE_TESTING};
+my $broken64 = (18446744073709550592 == ~0);
+
+my @small_primes = qw/
+2 3 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 /;
+
+plan tests => 6 # range
+ + 1 # small number
+ + 2 # medium numbers
+ + 1*$extra
+ + 0;
+
+ok(!eval { is_aks_prime(undef); }, "is_prime(undef)");
+ok( is_aks_prime(2), '2 is prime');
+ok(!is_aks_prime(1), '1 is not prime');
+ok(!is_aks_prime(0), '0 is not prime');
+ok(!is_aks_prime(-1), '-1 is not prime');
+ok(!is_aks_prime(-2), '-2 is not prime');
+
+# Simple number (cought by sqrt test
+is( is_aks_prime(877), 1, "is_aks_prime(877) is true" );
+
+# The first number that makes it past the sqrt test to actually run.
+is( is_aks_prime(69197), 1, "is_aks_prime(69197) is true" );
+
+# A small composite that runs the real primality test.
+is( is_aks_prime(69199), 0, "is_aks_prime(69199) is false" );
+
+if ($extra) {
+ # A composite (product of two 5-digit primes)
+ is( is_aks_prime(1262952907), 0, "is_aks_prime(1262952907) is false" );
+}
--
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