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#!perl
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# Test blog function (and bpow, since it uses blog), as well as bexp().
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# It is too slow to be simple included in bigfltpm.inc, where it would get
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# executed 3 times. One time would be under Math::BigInt::BareCalc, which
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# shouldn't make any difference since there is no CALC->_log() function, and
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# one time under a subclass, which *should* work.
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# But it is better to test the numerical functionality, instead of not testing
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# it at all (which did lead to wrong answers for 0 < $x < 1 in blog() in
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# versions up to v1.63, and for bsqrt($x) when $x << 1 for instance).
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use strict;
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use warnings;
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use Test::More tests => 73;
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use Math::BigFloat only => 'FastCalc';
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use Math::BigInt;
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my $class = "Math::BigInt";
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###############################################################################
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# test $n->blog() in Math::BigInt (broken until 1.80)
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is($class->new(2)->blog(), '0', "$class->new(2)->blog()");
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is($class->new(288)->blog(), '5', "$class->new(288)->blog()");
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is($class->new(2000)->blog(), '7', "$class->new(2000)->blog()");
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###############################################################################
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# test $n->bexp() in Math::BigInt
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is($class->new(1)->bexp(), '2', "$class->new(1)->bexp()");
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is($class->new(2)->bexp(), '7', "$class->new(2)->bexp()");
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is($class->new(3)->bexp(), '20', "$class->new(3)->bexp()");
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###############################################################################
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###############################################################################
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# Math::BigFloat tests
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###############################################################################
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# test $n->blog(undef, N) where N > 67 (broken until 1.82)
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$class = "Math::BigFloat";
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# These tests can take quite a while, but are necessary. Maybe protect them
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# with some alarm()?
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# this triggers the calculation and caching of ln(2):
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is($class->new(5)->blog(undef, 71),
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'1.6094379124341003746007593332261876395256013542685177219126478914741790',
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"$class->new(5)->blog(undef, 71)");
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# if the cache was correct, we should get this result, fast:
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is($class->new(2)->blog(undef, 71),
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'0.69314718055994530941723212145817656807550013436025525412068000949339362',
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"$class->new(2)->blog(undef, 71)");
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is($class->new(11)->blog(undef, 71),
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'2.3978952727983705440619435779651292998217068539374171752185677091305736',
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"$class->new(11)->blog(undef, 71)");
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is($class->new(21)->blog(undef, 71),
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'3.0445224377234229965005979803657054342845752874046106401940844835750742',
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"$class->new(21)->blog(undef, 71)");
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###############################################################################
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# These tests are now really fast, since they collapse to blog(10), basically
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# Don't attempt to run them with older versions. You are warned.
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# $x < 0 => NaN
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is($class->new(-2)->blog(), 'NaN', "$class->new(-2)->blog()");
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is($class->new(-1)->blog(), 'NaN', "$class->new(-1)->blog()");
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is($class->new(-10)->blog(), 'NaN', "$class->new(-10)->blog()");
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is($class->new(-2, 2)->blog(), 'NaN', "$class->new(-2, 2)->blog()");
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my $ten = $class->new(10)->blog();
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# 10 is cached (up to 75 digits)
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is($class->new(10)->blog(),
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'2.302585092994045684017991454684364207601',
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qq|$class->new(10)->blog()|);
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# 0.1 is using the cached value for log(10), too
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is($class->new("0.1")->blog(), -$ten,
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qq|$class->new("0.1")->blog()|);
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is($class->new("0.01")->blog(), -$ten * 2,
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qq|$class->new("0.01")->blog()|);
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is($class->new("0.001")->blog(), -$ten * 3,
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qq|$class->new("0.001")->blog()|);
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is($class->new("0.0001")->blog(), -$ten * 4,
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qq|$class->new("0.0001")->blog()|);
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# also cached
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is($class->new(2)->blog(),
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'0.6931471805599453094172321214581765680755',
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qq|$class->new(2)->blog()|);
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is($class->new(4)->blog(), $class->new(2)->blog * 2,
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qq|$class->new(4)->blog()|);
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# These are still slow, so do them only to 10 digits
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is($class->new("0.2")->blog(undef, 10), "-1.609437912",
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qq|$class->new("0.2")->blog(undef, 10)|);
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is($class->new("0.3")->blog(undef, 10), "-1.203972804",
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qq|$class->new("0.3")->blog(undef, 10)|);
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is($class->new("0.4")->blog(undef, 10), "-0.9162907319",
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qq|$class->new("0.4")->blog(undef, 10)|);
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is($class->new("0.5")->blog(undef, 10), "-0.6931471806",
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qq|$class->new("0.5")->blog(undef, 10)|);
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is($class->new("0.6")->blog(undef, 10), "-0.5108256238",
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qq|$class->new("0.6")->blog(undef, 10)|);
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is($class->new("0.7")->blog(undef, 10), "-0.3566749439",
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qq|$class->new("0.7")->blog(undef, 10)|);
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is($class->new("0.8")->blog(undef, 10), "-0.2231435513",
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qq|$class->new("0.8")->blog(undef, 10)|);
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is($class->new("0.9")->blog(undef, 10), "-0.1053605157",
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qq|$class->new("0.9")->blog(undef, 10)|);
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is($class->new("9")->blog(undef, 10), "2.197224577",
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qq|$class->new("9")->blog(undef, 10)|);
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is($class->new("10")->blog(10, 10), "1.000000000",
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qq|$class->new("10")->blog(10, 10)|);
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is($class->new("20")->blog(20, 10), "1.000000000",
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qq|$class->new("20")->blog(20, 10)|);
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is($class->new("100")->blog(100, 10), "1.000000000",
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qq|$class->new("100")->blog(100, 10)|);
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is($class->new("100")->blog(10, 10), "2.000000000", # 10 ** 2 == 100
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qq|$class->new("100")->blog(10, 10)|);
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is($class->new("400")->blog(20, 10), "2.000000000", # 20 ** 2 == 400
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qq|$class->new("400")->blog(20, 10)|);
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is($class->new("4")->blog(2, 10), "2.000000000", # 2 ** 2 == 4
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qq|$class->new("4")->blog(2, 10)|);
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is($class->new("16")->blog(2, 10), "4.000000000", # 2 ** 4 == 16
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qq|$class->new("16")->blog(2, 10)|);
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is($class->new("1.2")->bpow("0.3", 10), "1.056219968",
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qq|$class->new("1.2")->bpow("0.3", 10)|);
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is($class->new("10")->bpow("0.6", 10), "3.981071706",
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qq|$class->new("10")->bpow("0.6", 10)|);
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# blog should handle bigint input
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is(Math::BigFloat::blog(Math::BigInt->new(100), 10), 2, "blog(100)");
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###############################################################################
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# some integer results
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is($class->new(2)->bpow(32)->blog(2), "32", "2 ** 32");
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is($class->new(3)->bpow(32)->blog(3), "32", "3 ** 32");
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is($class->new(2)->bpow(65)->blog(2), "65", "2 ** 65");
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my $x = Math::BigInt->new('777') ** 256;
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my $base = Math::BigInt->new('12345678901234');
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is($x->copy()->blog($base), 56, 'blog(777**256, 12345678901234)');
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$x = Math::BigInt->new('777') ** 777;
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$base = Math::BigInt->new('777');
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is($x->copy()->blog($base), 777, 'blog(777**777, 777)');
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###############################################################################
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# test for bug in bsqrt() not taking negative _e into account
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test_bpow('200', '0.5', 10, '14.14213562');
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test_bpow('20', '0.5', 10, '4.472135955');
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test_bpow('2', '0.5', 10, '1.414213562');
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test_bpow('0.2', '0.5', 10, '0.4472135955');
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test_bpow('0.02', '0.5', 10, '0.1414213562');
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test_bpow('0.49', '0.5', undef, '0.7');
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test_bpow('0.49', '0.5', 10, '0.7000000000');
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test_bpow('0.002', '0.5', 10, '0.04472135955');
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test_bpow('0.0002', '0.5', 10, '0.01414213562');
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test_bpow('0.0049', '0.5', undef, '0.07');
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test_bpow('0.0049', '0.5', 10, '0.07000000000');
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test_bpow('0.000002', '0.5', 10, '0.001414213562');
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test_bpow('0.021', '0.5', 10, '0.1449137675');
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test_bpow('1.2', '0.5', 10, '1.095445115');
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test_bpow('1.23', '0.5', 10, '1.109053651');
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test_bpow('12.3', '0.5', 10, '3.507135583');
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test_bpow('9.9', '0.5', 10, '3.146426545');
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test_bpow('9.86902225', '0.5', 10, '3.141500000');
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test_bpow('9.86902225', '0.5', undef, '3.1415');
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###############################################################################
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# other tests for bpow()
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test_bpow('0.2', '0.41', 10, '0.5169187652');
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is($class->new("0.01")->bpow("28.4", 40)->bsstr(),
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'1584893192461113485202101373391507013269e-96',
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qq|$class->new("0.01")->bpow("28.4", 40)->bsstr()|);
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# The following test takes too long.
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#is($class->new("2")->bpow("-1034.5", 40)->bsstr(),
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# '3841222690408590466868250378242558090957e-351',
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# qq|$class->new("2")->bpow("-1034.5", 40)|);
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###############################################################################
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# test bexp() with cached results
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is($class->new(1)->bexp(), '2.718281828459045235360287471352662497757',
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'bexp(1)');
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is($class->new(2)->bexp(40), $class->new(1)->bexp(45)->bpow(2, 40),
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'bexp(2)');
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is($class->new("12.5")->bexp(61), $class->new(1)->bexp(65)->bpow(12.5, 61),
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'bexp(12.5)');
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###############################################################################
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# test bexp() with big values (non-cached)
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is($class->new(1)->bexp(100),
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'2.7182818284590452353602874713526624977572470936999'
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. '59574966967627724076630353547594571382178525166427',
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qq|$class->new(1)->bexp(100)|);
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is($class->new("12.5")->bexp(91), $class->new(1)->bexp(95)->bpow(12.5, 91),
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qq|$class->new("12.5")->bexp(91)|);
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is($class->new("-118.5")->bexp(20)->bsstr(),
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'34364014567198602057e-71',
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qq|$class->new("-118.5")->bexp(20)->bsstr()|);
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is($class->new("-394.84010945715266885")->bexp(20)->bsstr(),
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'33351796227864913873e-191',
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qq|$class->new("-118.5")->bexp(20)->bsstr()|);
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# all done
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1;
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###############################################################################
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sub test_bpow {
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my ($x, $y, $scale, $result) = @_;
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is($class->new($x)->bpow($y, $scale), $result,
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qq|$class->new($x)->bpow($y, |
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. (defined($scale) ? $scale : 'undef')
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. qq|)|);
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}
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