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# -*- mode: perl; -*-
# Test blog function (and bpow, since it uses blog), as well as bexp().
# It is too slow to be simple included in bigfltpm.inc, where it would get
# executed 3 times. One time would be under Math::BigInt::BareCalc, which
# shouldn't make any difference since there is no $LIB->_log() function, and
# one time under a subclass, which *should* work.
# But it is better to test the numerical functionality, instead of not testing
# it at all (which did lead to wrong answers for 0 < $x < 1 in blog() in
# versions up to v1.63, and for bsqrt($x) when $x << 1 for instance).
use strict;
use warnings;
use Test::More tests => 73;
use Math::BigFloat only => 'Calc';
use Math::BigInt;
my $class = "Math::BigInt";
###############################################################################
# test $n->blog() in Math::BigInt (broken until 1.80)
is($class->new(2)->blog(), '0', "$class->new(2)->blog()");
is($class->new(288)->blog(), '5', "$class->new(288)->blog()");
is($class->new(2000)->blog(), '7', "$class->new(2000)->blog()");
###############################################################################
# test $n->bexp() in Math::BigInt
is($class->new(1)->bexp(), '2', "$class->new(1)->bexp()");
is($class->new(2)->bexp(), '7', "$class->new(2)->bexp()");
is($class->new(3)->bexp(), '20', "$class->new(3)->bexp()");
###############################################################################
# Math::BigFloat tests
###############################################################################
# test $n->blog(undef, N) where N > 67 (broken until 1.82)
$class = "Math::BigFloat";
# These tests can take quite a while, but are necessary. Maybe protect them
# with some alarm()?
# this triggers the calculation and caching of ln(2):
is($class->new(5)->blog(undef, 71),
'1.6094379124341003746007593332261876395256013542685177219126478914741790',
"$class->new(5)->blog(undef, 71)");
# if the cache was correct, we should get this result, fast:
is($class->new(2)->blog(undef, 71),
'0.69314718055994530941723212145817656807550013436025525412068000949339362',
"$class->new(2)->blog(undef, 71)");
is($class->new(11)->blog(undef, 71),
'2.3978952727983705440619435779651292998217068539374171752185677091305736',
"$class->new(11)->blog(undef, 71)");
is($class->new(21)->blog(undef, 71),
'3.0445224377234229965005979803657054342845752874046106401940844835750742',
"$class->new(21)->blog(undef, 71)");
###############################################################################
# These tests are now really fast, since they collapse to blog(10), basically
# Don't attempt to run them with older versions. You are warned.
# $x < 0 => NaN
is($class->new(-2)->blog(), 'NaN', "$class->new(-2)->blog()");
is($class->new(-1)->blog(), 'NaN', "$class->new(-1)->blog()");
is($class->new(-10)->blog(), 'NaN', "$class->new(-10)->blog()");
is($class->new(-2, 2)->blog(), 'NaN', "$class->new(-2, 2)->blog()");
my $ten = $class->new(10)->blog();
# 10 is cached (up to 75 digits)
is($class->new(10)->blog(),
'2.302585092994045684017991454684364207601',
qq|$class->new(10)->blog()|);
# 0.1 is using the cached value for log(10), too
is($class->new("0.1")->blog(), -$ten,
qq|$class->new("0.1")->blog()|);
is($class->new("0.01")->blog(), -$ten * 2,
qq|$class->new("0.01")->blog()|);
is($class->new("0.001")->blog(), -$ten * 3,
qq|$class->new("0.001")->blog()|);
is($class->new("0.0001")->blog(), -$ten * 4,
qq|$class->new("0.0001")->blog()|);
# also cached
is($class->new(2)->blog(),
'0.6931471805599453094172321214581765680755',
qq|$class->new(2)->blog()|);
is($class->new(4)->blog(), $class->new(2)->blog * 2,
qq|$class->new(4)->blog()|);
# These are still slow, so do them only to 10 digits
is($class->new("0.2")->blog(undef, 10), "-1.609437912",
qq|$class->new("0.2")->blog(undef, 10)|);
is($class->new("0.3")->blog(undef, 10), "-1.203972804",
qq|$class->new("0.3")->blog(undef, 10)|);
is($class->new("0.4")->blog(undef, 10), "-0.9162907319",
qq|$class->new("0.4")->blog(undef, 10)|);
is($class->new("0.5")->blog(undef, 10), "-0.6931471806",
qq|$class->new("0.5")->blog(undef, 10)|);
is($class->new("0.6")->blog(undef, 10), "-0.5108256238",
qq|$class->new("0.6")->blog(undef, 10)|);
is($class->new("0.7")->blog(undef, 10), "-0.3566749439",
qq|$class->new("0.7")->blog(undef, 10)|);
is($class->new("0.8")->blog(undef, 10), "-0.2231435513",
qq|$class->new("0.8")->blog(undef, 10)|);
is($class->new("0.9")->blog(undef, 10), "-0.1053605157",
qq|$class->new("0.9")->blog(undef, 10)|);
is($class->new("9")->blog(undef, 10), "2.197224577",
qq|$class->new("9")->blog(undef, 10)|);
is($class->new("10")->blog(10, 10), "1.000000000",
qq|$class->new("10")->blog(10, 10)|);
is($class->new("20")->blog(20, 10), "1.000000000",
qq|$class->new("20")->blog(20, 10)|);
is($class->new("100")->blog(100, 10), "1.000000000",
qq|$class->new("100")->blog(100, 10)|);
is($class->new("100")->blog(10, 10), "2.000000000", # 10 ** 2 == 100
qq|$class->new("100")->blog(10, 10)|);
is($class->new("400")->blog(20, 10), "2.000000000", # 20 ** 2 == 400
qq|$class->new("400")->blog(20, 10)|);
is($class->new("4")->blog(2, 10), "2.000000000", # 2 ** 2 == 4
qq|$class->new("4")->blog(2, 10)|);
is($class->new("16")->blog(2, 10), "4.000000000", # 2 ** 4 == 16
qq|$class->new("16")->blog(2, 10)|);
is($class->new("1.2")->bpow("0.3", 10), "1.056219968",
qq|$class->new("1.2")->bpow("0.3", 10)|);
is($class->new("10")->bpow("0.6", 10), "3.981071706",
qq|$class->new("10")->bpow("0.6", 10)|);
# blog should handle bigint input
is(Math::BigFloat->blog(Math::BigInt->new(100), 10), 2, "blog(100)");
###############################################################################
# some integer results
is($class->new(2)->bpow(32)->blog(2), "32", "2 ** 32");
is($class->new(3)->bpow(32)->blog(3), "32", "3 ** 32");
is($class->new(2)->bpow(65)->blog(2), "65", "2 ** 65");
my $x = Math::BigInt->new('777') ** 256;
my $base = Math::BigInt->new('12345678901234');
is($x->copy()->blog($base), 56, 'blog(777**256, 12345678901234)');
$x = Math::BigInt->new('777') ** 777;
$base = Math::BigInt->new('777');
is($x->copy()->blog($base), 777, 'blog(777**777, 777)');
###############################################################################
# test for bug in bsqrt() not taking negative _e into account
test_bpow('200', '0.5', 10, '14.14213562');
test_bpow('20', '0.5', 10, '4.472135955');
test_bpow('2', '0.5', 10, '1.414213562');
test_bpow('0.2', '0.5', 10, '0.4472135955');
test_bpow('0.02', '0.5', 10, '0.1414213562');
test_bpow('0.49', '0.5', undef, '0.7');
test_bpow('0.49', '0.5', 10, '0.7000000000');
test_bpow('0.002', '0.5', 10, '0.04472135955');
test_bpow('0.0002', '0.5', 10, '0.01414213562');
test_bpow('0.0049', '0.5', undef, '0.07');
test_bpow('0.0049', '0.5', 10, '0.07000000000');
test_bpow('0.000002', '0.5', 10, '0.001414213562');
test_bpow('0.021', '0.5', 10, '0.1449137675');
test_bpow('1.2', '0.5', 10, '1.095445115');
test_bpow('1.23', '0.5', 10, '1.109053651');
test_bpow('12.3', '0.5', 10, '3.507135583');
test_bpow('9.9', '0.5', 10, '3.146426545');
test_bpow('9.86902225', '0.5', 10, '3.141500000');
test_bpow('9.86902225', '0.5', undef, '3.1415');
###############################################################################
# other tests for bpow()
test_bpow('0.2', '0.41', 10, '0.5169187652');
is($class->new("0.1")->bpow("28.4", 40)->bsstr(),
'3981071705534972507702523050877520434877e-68',
qq|$class->new("0.1")->bpow("28.4", 40)->bsstr()|);
# The following test takes too long.
#is($class->new("2")->bpow("-1034.5", 40)->bsstr(),
# '3841222690408590466868250378242558090957e-351',
# qq|$class->new("2")->bpow("-1034.5", 40)|);
###############################################################################
# test bexp() with cached results
is($class->new(1)->bexp(), '2.718281828459045235360287471352662497757',
'bexp(1)');
is($class->new(2)->bexp(40), $class->new(1)->bexp(45)->bpow(2, 40),
'bexp(2)');
is($class->new("12.5")->bexp(61), $class->new(1)->bexp(65)->bpow(12.5, 61),
'bexp(12.5)');
###############################################################################
# test bexp() with big values (non-cached)
is($class->new(1)->bexp(100),
'2.7182818284590452353602874713526624977572470936999'
. '59574966967627724076630353547594571382178525166427',
qq|$class->new(1)->bexp(100)|);
is($class->new("12.5")->bexp(91), $class->new(1)->bexp(95)->bpow(12.5, 91),
qq|$class->new("12.5")->bexp(91)|);
is($class->new("-118.5")->bexp(20)->bsstr(),
'34364014567198602057e-71',
qq|$class->new("-118.5")->bexp(20)->bsstr()|);
is($class->new("-394.84010945715266885")->bexp(20)->bsstr(),
'33351796227864913873e-191',
qq|$class->new("-118.5")->bexp(20)->bsstr()|);
# all done
###############################################################################
sub test_bpow {
my ($x, $y, $scale, $result) = @_;
is($class->new($x)->bpow($y, $scale), $result,
qq|$class->new($x)->bpow($y, |
. (defined($scale) ? $scale : 'undef')
. qq|)|);
}
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