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#!/usr/bin/env perl
use strict;
use warnings;
use Test::More;
use Math::Prime::Util qw/prime_count prime_count_lower prime_count_upper/;
use Digest::SHA qw/sha256_hex/;
my $use64 = ~0 > 4294967295;
my %pivals = (
1000 => 168,
10000 => 1229,
100000 => 9592,
1000000 => 78498,
10000000 => 664579,
100000000 => 5761455,
1000000000 => 50847534,
10000000000 => 455052511,
100000000000 => 4118054813,
1000000000000 => 37607912018,
2000000000000 => 73301896139,
3000000000000 => 108340298703,
4000000000000 => 142966208126,
5000000000000 => 177291661649,
6000000000000 => 211381427039,
7000000000000 => 245277688804,
8000000000000 => 279010070811,
9000000000000 => 312600354108,
10000000000000 => 346065536839,
20000000000000 => 675895909271,
30000000000000 => 1000121668853,
40000000000000 => 1320811971702,
50000000000000 => 1638923764567,
60000000000000 => 1955010428258,
70000000000000 => 2269432871304,
80000000000000 => 2582444113487,
90000000000000 => 2894232250783,
100000000000000 => 3204941750802,
200000000000000 => 6270424651315,
300000000000000 => 9287441600280,
400000000000000 => 12273824155491,
500000000000000 => 15237833654620,
600000000000000 => 18184255291570,
700000000000000 => 21116208911023,
800000000000000 => 24035890368161,
900000000000000 => 26944926466221,
1000000000000000 => 29844570422669,
10000000000000000 => 279238341033925,
20000000000000000 => 547863431950008,
40000000000000000 => 1075292778753150,
100000000000000000 => 2623557157654233,
1000000000000000000 => 24739954287740860,
2000000000000000000 => 48645161281738535,
3000000000000000000 => 72254704797687083,
4000000000000000000 => 95676260903887607,
4185296581467695669 => 100000000000000000,
5000000000000000000 => 118959989688273472,
6000000000000000000 => 142135049412622144,
7000000000000000000 => 165220513980969424,
8000000000000000000 => 188229829247429504,
9000000000000000000 => 211172979243258278,
10000000000000000000 => 234057667276344607,
524288 => 43390,
1048576 => 82025,
2097152 => 155611,
4194304 => 295947,
8388608 => 564163,
16777216 => 1077871,
33554432 => 2063689,
67108864 => 3957809,
134217728 => 7603553,
268435456 => 14630843,
536870912 => 28192750,
1073741824 => 54400028,
2147483648 => 105097565,
4294967296 => 203280221,
8589934592 => 393615806,
17179869184 => 762939111,
34359738368 => 1480206279,
68719476736 => 2874398515,
137438953472 => 5586502348,
274877906944 => 10866266172,
549755813888 => 21151907950,
1099511627776 => 41203088796,
2199023255552 => 80316571436,
4398046511104 => 156661034233,
8796093022208 => 305761713237,
17592186044416 => 597116381732,
35184372088832 => 1166746786182,
70368744177664 => 2280998753949,
140737488355328 => 4461632979717,
281474976710656 => 8731188863470,
562949953421312 => 17094432576778,
1125899906842624 => 33483379603407,
2251799813685248 => 65612899915304,
4503599627370496 => 128625503610475,
9007199254740992 => 252252704148404,
18014398509481984 => 494890204904784,
36028797018963968 => 971269945245201,
72057594037927936 => 1906879381028850,
144115188075855872 => 3745011184713964,
288230376151711744 => 7357400267843990,
576460752303423488 => 14458792895301660,
1152921504606846976 => 28423094496953330,
2305843009213693952 => 55890484045084135,
4611686018427387904 => 109932807585469973,
9223372036854775808 => 216289611853439384,
# Leading up to 2**32-1
4294000000 => 203236859,
4294900000 => 203277205,
4294960000 => 203279882,
4294967000 => 203280211,
4294967200 => 203280218,
4294967290 => 203280220,
4294967295 => 203280221,
# From http://trac.sagemath.org/ticket/7539 plus sieving.
# All these results were verified on with MPU's LMO (28 July 2014).
# 11000000000000000000 => 256890014776557326,
# 12000000000000000000 => 279675001309887227,
# 13000000000000000000 => 302416755645383081,
# 14000000000000000000 => 325118755759814408,
# 15000000000000000000 => 347783970566657581,
# 16000000000000000000 => 370414963651223281,
# 17000000000000000000 => 393013970558176111,
# 18000000000000000000 => 415582957615112220,
# 18400000000000000000 => 424602543873663577,
18440000000000000000 => 425504257754137607,
18446700000000000000 => 425655290520421050,
# 18446740000000000000 => 425656192205366999,
# 18446744000000000000 => 425656282373661946,
# 18446744030000000000 => 425656283049924141,
# 18446744040000000000 => 425656283275356419,
# 18446744050000000000 => 425656283500787632,
# 18446744070000000000 => 425656283951611098,
# 18446744073000000000 => 425656284019227775,
# 18446744073700000000 => 425656284035002496,
# 18446744073709000000 => 425656284035205391,
# 18446744073709550000 => 425656284035217706,
# 18446744073709551000 => 425656284035217730,
18446744073709551615 => 425656284035217743,
#
);
if (!$use64) {
delete @pivals{ grep { $_ > ~0 } keys %pivals };
}
plan tests => 5 + scalar(keys %pivals);
# Test prime counts using sampling
diag "Sampling small prime counts, should take < 1 minute";
{
my $countstr;
$countstr = join(" ", map { prime_count($_) } 1 .. 100000);
is(sha256_hex($countstr), "cdbc5c94a927d0d9481cb26b3d3e60c0617a4be65ce9db3075c0363c7a81ef52", "prime counts 1..10^5");
$countstr = join(" ", map { prime_count(100*$_ + ($_%101)) } 1000 .. 100000);
is(sha256_hex($countstr), "73a0b71dedff9611e06fd57e52b88c8afd7f86b5351e4950b2dd5c1d68845b6e", "prime counts 10^5..10^7 (sample 100)");
$countstr = join(" ", map { prime_count(10000*$_ + ($_%9973)) } 1000 .. 10000);
is(sha256_hex($countstr), "d73736c54362136aa0a48bab44b55004b2e63e0d1d03a6cbe1aab42c6a579d0c", "prime counts 10^7..10^8 (sample 10k)");
$countstr = join(" ", map { prime_count(500000*$_ + 250837 + $_) } 200 .. 2000);
is(sha256_hex($countstr), "00a580b2f52b661f065f5ce49bd2aeacb3b169d8903cf824b65731441e40f0b9", "prime counts 10^8..10^9 (sample 500k)");
SKIP: {
skip "Skipping 10^9 to 10^10 if 32-bit", 1 unless $use64;
$countstr = join(" ", map { prime_count(10000000*$_ + 250837 + $_) } 100 .. 1000);
is(sha256_hex($countstr), "9fd78debf4b510ee6d230cabf314ebef5eb253ee63d5df658e45414613f7b8c2", "prime counts 10^9..10^10 (sample 10M)");
}
}
diag "Selected prime counts, will take hours to complete"
if $use64;
foreach my $n (sort {$a <=> $b} keys %pivals) {
my $pin = $pivals{$n};
is( prime_count($n), $pin, "Pi($n) = $pin" );
}
|
