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#!/usr/bin/env perl
use strict;
use warnings;
use Test::More;
use Math::Prime::Util qw/
prime_count
ExponentialIntegral LogarithmicIntegral RiemannR RiemannZeta LambertW
/;
my $infinity = 20**20**20;
my %eivals = (
-10 => -0.00000415696892968532438,
-0.5 => -0.55977359477616,
-0.1 => -1.8229239584193906660809,
-0.001 => -6.33153936413615,
-0.00001 => -10.9357198000436956,
-0.00000001 => -17.843465089050832587,
0.693147180559945 => 1.0451637801174927848446, # log2
1 => 1.8951178163559367554665,
1.5 => 3.3012854491297978379574,
2 => 4.9542343560018901633795,
5 => 40.185275355803177455091,
10 => 2492.2289762418777591384,
12 => 14959.532666397528852292,
20 => 25615652.664056588820481,
40 => 6039718263611241.5783592,
41 => 16006649143245041.110700,
79 => 2.61362206325045575e+32,
);
my %livals = ( # In pari these are: -eint1(-log($n))
0 => 0,
1.01 => -4.0229586739299358695031,
2 => 1.0451637801174927848446,
10 => 6.1655995047872979375230,
24 => 11.200315795232698830550,
1000 => 177.60965799015222668764,
100000 => 9629.8090010507982050343,
100000000 => 5762209.3754480314675691,
4294967295 => 203284081.95454158906409,
10000000000 => 455055614.58662307560953,
100000000000 => 4118066400.6216115150394,
);
# Values from T. R. Nicely for comparison
my %rvals = (
1.01 => 1.0060697180622924796117,
2 => 1.5410090161871318832885,
10 => 4.5645831410050902398658,
1000 => 168.35944628116734806491,
1000000 => 78527.399429127704858870,
10000000 => 664667.44756474776798535,
4294967295 => 203280697.51326064541983,
10000000000 => 455050683.30684692446315,
18446744073709551615 => 4.25656284014012122706963685602e17,
);
my %rzvals = (
2 => 0.6449340668482264364724151666,
2.5 => 0.3414872572509171797567696934,
4.5 => 0.0547075107614542640229672890,
7 => 0.0083492773819228268397975498,
8.5 => 0.0028592508824156277133439825,
20.6 => 0.0000006293391573578212882457,
);
my %lamvals = (
-0.3678794411714423215955237701614608674458 => -0.99999995824889, # Ideally this would be -1
-.1 => -0.11183255915896296483356945682026584227264536229126586332968,
0 => 0,
0.3678794411714423215955237701614608674458 => 0.278464542761073795109358739022980155439470898229676526861772,
1 => 0.567143290409783872999968662210355549753815787186512508135131,
10 => 1.7455280027406993830743012648753899115,
10000 => 7.2318460380933727064756185001412538839,
100000000000 => 22.227122734961075624690200512898589272,
18446744073709551615 => 40.656266572498926634921823566267328254,
);
plan tests => 3 + 6 + 1
+ scalar(keys(%eivals))
+ scalar(keys(%livals))
+ scalar(keys(%rvals))
+ scalar(keys(%rzvals))
+ scalar(keys(%lamvals))
;
eval { LogarithmicIntegral(-1); };
like($@, qr/invalid/i, "li(-1) is invalid");
eval { RiemannR(0); };
like($@, qr/invalid/i, "R(0) is invalid");
eval { RiemannR(-1); };
like($@, qr/invalid/i, "R(-1) is invalid");
cmp_ok( ExponentialIntegral(0), '<=',-$infinity, "Ei(0) is -infinity");
cmp_ok( ExponentialIntegral(-$infinity),'==', 0, "Ei(-inf) is 0" );
cmp_ok( ExponentialIntegral($infinity), '>=', $infinity, "Ei(inf) is infinity");
cmp_ok( LogarithmicIntegral(0), '==', 0, "li(0) is 0");
cmp_ok( LogarithmicIntegral(1), '<=',-$infinity, "li(1) is -infinity");
cmp_ok( LogarithmicIntegral($infinity), '>=', $infinity, "li(inf) is infinity");
# Example used in Math::Cephes
cmp_closeto( ExponentialIntegral(2.2), 5.732614700, 1e-06, "Ei(2.2)");
while (my($n, $ein) = each (%eivals)) {
cmp_closeto( ExponentialIntegral($n), $ein, 0.00000001 * abs($ein), "Ei($n) ~= $ein");
}
while (my($n, $lin) = each (%livals)) {
cmp_closeto( LogarithmicIntegral($n), $lin, 0.00000001 * abs($lin), "li($n) ~= $lin");
}
while (my($n, $rin) = each (%rvals)) {
cmp_closeto( RiemannR($n), $rin, 0.00000001 * abs($rin), "R($n) ~= $rin");
}
while (my($n, $zin) = each (%rzvals)) {
cmp_closeto( RiemannZeta($n), $zin, 0.00000001 * abs($zin), "Zeta($n) ~= $zin");
}
while (my($n, $lin) = each (%lamvals)) {
# Machines with long double will be a little different near -1/e
cmp_closeto( LambertW($n), $lin, 0.0000001 * abs($lin), "LambertW($n) ~= $lin");
}
sub cmp_closeto {
my $got = shift;
my $expect = shift;
my $tolerance = shift;
my $message = shift;
cmp_ok( abs($got - $expect), '<=', $tolerance, $message );
}
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