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BigIntegerTest.php
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BigIntegerTest.php
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<?php
declare(strict_types=1);
namespace Brick\Math\Tests;
use Brick\Math\BigInteger;
use Brick\Math\Exception\IntegerOverflowException;
use Brick\Math\Exception\MathException;
use Brick\Math\Exception\NegativeNumberException;
use Brick\Math\Exception\NumberFormatException;
use Brick\Math\Exception\DivisionByZeroException;
use Brick\Math\Exception\RoundingNecessaryException;
use Brick\Math\Internal\Calculator;
use Brick\Math\RoundingMode;
use Generator;
/**
* Unit tests for class BigInteger.
*/
class BigIntegerTest extends AbstractTestCase
{
/**
* @dataProvider providerOf
*
* @param string|number $value The value to convert to a BigInteger.
* @param string $expected The expected string value of the result.
*/
public function testOf($value, string $expected) : void
{
self::assertBigIntegerEquals($expected, BigInteger::of($value));
}
public function providerOf() : array
{
return [
[0, '0'],
[1, '1'],
[-1, '-1'],
[123456789, '123456789'],
[-123456789, '-123456789'],
[PHP_INT_MAX, (string) PHP_INT_MAX],
[PHP_INT_MIN, (string) PHP_INT_MIN],
[0.0, '0'],
[1.0, '1'],
[-0.0, '0'],
[-1.0, '-1'],
['0.0', '0'],
['1.0', '1'],
['-1.00', '-1'],
['.0', '0'],
['.00', '0'],
[1.2e5, '120000'],
[-1.2e5, '-120000'],
['1e20', '100000000000000000000'],
['-3e+50', '-300000000000000000000000000000000000000000000000000'],
['0', '0'],
['+0', '0'],
['-0', '0'],
['1.', '1'],
['+2.', '2'],
['-3.', '-3'],
['1.e0', '1'],
['1.e2', '100'],
['-1.e2', '-100'],
['+1.e3', '1000'],
['.1e1', '1'],
['.1e2', '10'],
['-.1e2', '-10'],
['+.1e3', '100'],
['1', '1'],
['+1', '1'],
['-1', '-1'],
['00', '0'],
['+00', '0'],
['-00', '0'],
['01', '1'],
['+01', '1'],
['-01', '-1'],
['123456789012345678901234567890', '123456789012345678901234567890'],
['+123456789012345678901234567890', '123456789012345678901234567890'],
['-123456789012345678901234567890', '-123456789012345678901234567890'],
['0123456789012345678901234567890', '123456789012345678901234567890'],
['+0123456789012345678901234567890', '123456789012345678901234567890'],
['-0123456789012345678901234567890', '-123456789012345678901234567890'],
['00123456789012345678901234567890', '123456789012345678901234567890'],
['+00123456789012345678901234567890', '123456789012345678901234567890'],
['-00123456789012345678901234567890', '-123456789012345678901234567890'],
];
}
public function testOfBigIntegerReturnsThis() : void
{
$decimal = BigInteger::of(123);
self::assertSame($decimal, BigInteger::of($decimal));
}
/**
* @dataProvider providerOfInvalidFormatThrowsException
*
* @param string|number $value
*/
public function testOfInvalidFormatThrowsException($value) : void
{
$this->expectException(NumberFormatException::class);
BigInteger::of($value);
}
public function providerOfInvalidFormatThrowsException() : array
{
return [
[''],
['a'],
[' 1'],
['1 '],
['+'],
['-'],
['+a'],
['-a'],
['a0'],
['0a'],
['1.a'],
['a.1'],
];
}
/**
* @dataProvider providerOfNonConvertibleValueThrowsException
*
* @param float|string $value
*/
public function testOfNonConvertibleValueThrowsException($value) : void
{
$this->expectException(RoundingNecessaryException::class);
BigInteger::of($value);
}
public function providerOfNonConvertibleValueThrowsException() : array
{
return [
[1.1],
['1e-1'],
['7/9'],
];
}
/**
* @dataProvider providerFromBase
*
* @param string $number The number to create.
* @param int $base The base of the number.
* @param string $expected The expected result in base 10.
*/
public function testFromBase(string $number, int $base, string $expected) : void
{
self::assertBigIntegerEquals($expected, BigInteger::fromBase($number, $base));
}
/**
* @return array
*/
public function providerFromBase() : array
{
return [
['0', 10, '0'],
['-0', 10, '0'],
['+0', 10, '0'],
['00', 16, '0'],
['-00', 16, '0'],
['+00', 16, '0'],
['1', 10, '1'],
['-1', 10, '-1'],
['+1', 10, '1'],
['01', 8, '1'],
['-01', 8, '-1'],
['+01', 8, '1'],
['123', 10, '123'],
['+456', 10, '456'],
['-789', 10, '-789'],
['0123', 10, '123'],
['+0456', 10, '456'],
['-0789', 10, '-789'],
['123', 11, '146'],
['+456', 11, '545'],
['-789', 11, '-944'],
['0123', 11, '146'],
['+0456', 11, '545'],
['-0789', 11, '-944'],
['110011001100110011001111', 36, '640998479760579495168036691627608949'],
['110011001100110011001111', 35, '335582856048758779730579523833856636'],
['110011001100110011001111', 34, '172426711023004493064981145981549295'],
['110011001100110011001111', 33, '86853227285668653965326574185738990'],
['110011001100110011001111', 32, '42836489934972583913564073319498785'],
['110011001100110011001111', 31, '20658924711984480538771889603666144'],
['110011001100110011001111', 30, '9728140488839986222205212599027931'],
['110011001100110011001111', 29, '4465579470019956787945275674107410'],
['110011001100110011001111', 28, '1994689924537781753408144504465645'],
['110011001100110011001111', 27, '865289950909412968716094193925700'],
['110011001100110011001111', 26, '363729369583879309352831568000039'],
['110011001100110011001111', 25, '147793267388865354156500488297526'],
['110011001100110011001111', 24, '57888012016107577099138793486425'],
['110011001100110011001111', 23, '21788392294523974761749372677800'],
['110011001100110011001111', 22, '7852874701996329566765721637715'],
['110011001100110011001111', 21, '2699289081943123258094476428634'],
['110011001100110011001111', 20, '880809345058406615041344008421'],
['110011001100110011001111', 19, '271401690926468032718781859340'],
['110011001100110011001111', 18, '78478889737009209699633503455'],
['110011001100110011001111', 17, '21142384915931646646976872830'],
['110011001100110011001111', 16, '5261325448418072742917574929'],
['110011001100110011001111', 15, '1197116069565850925807253616'],
['110011001100110011001111', 14, '245991074299834917455374155'],
['110011001100110011001111', 13, '44967318722190498361960610'],
['110011001100110011001111', 12, '7177144825886069940574045'],
['110011001100110011001111', 11, '976899716207148313491924'],
['110011001100110011001111', 10, '110011001100110011001111'],
['110011001100110011001111', 9, '9849210196991880028870'],
['110011001100110011001111', 8, '664244955832213832265'],
['110011001100110011001111', 7, '31291601125492514360'],
['110011001100110011001111', 6, '922063395565287619'],
['110011001100110011001111', 5, '14328039609468906'],
['110011001100110011001111', 4, '88305875046485'],
['110011001100110011001111', 3, '127093291420'],
['110011001100110011001111', 2, '13421775'],
['ZyXwVuTsRqPoNmLkJiHgFeDcBa9876543210', 36, '106300512100105327644605138221229898724869759421181854980'],
['YxWvUtSrQpOnMlKjIhGfEdCbA9876543210', 35, '1101553773143634726491620528194292510495517905608180485'],
['XwVuTsRqPoNmLkJiHgFeDcBa9876543210', 34, '11745843093701610854378775891116314824081102660800418'],
['WvUtSrQpOnMlKjIhGfEdCbA9876543210', 33, '128983956064237823710866404905431464703849549412368'],
['VuTsRqPoNmLkJiHgFeDcBa9876543210', 32, '1459980823972598128486511383358617792788444579872'],
['UtSrQpOnMlKjIhGfEdCbA9876543210', 31, '17050208381689099029767742314582582184093573615'],
['TsRqPoNmLkJiHgFeDcBa9876543210', 30, '205646315052919334126040428061831153388822830'],
['SrQpOnMlKjIhGfEdCbA9876543210', 29, '2564411043271974895869785066497940850811934'],
['RqPoNmLkJiHgFeDcBa9876543210', 28, '33100056003358651440264672384704297711484'],
['QpOnMlKjIhGfEdCbA9876543210', 27, '442770531899482980347734468443677777577'],
['PoNmLkJiHgFeDcBa9876543210', 26, '6146269788878825859099399609538763450'],
['OnMlKjIhGfEdCbA9876543210', 25, '88663644327703473714387251271141900'],
['NmLkJiHgFeDcBa9876543210', 24, '1331214537196502869015340298036888'],
['MlKjIhGfEdCbA9876543210', 23, '20837326537038308910317109288851'],
['LkJiHgFeDcBa9876543210', 22, '340653664490377789692799452102'],
['KjIhGfEdCbA9876543210', 21, '5827980550840017565077671610'],
['JiHgFeDcBa9876543210', 20, '104567135734072022160664820'],
['IhGfEdCbA9876543210', 19, '1972313422155189164466189'],
['HgFeDcBa9876543210', 18, '39210261334551566857170'],
['GfEdCbA9876543210', 17, '824008854613343261192'],
['FeDcBa9876543210', 16, '18364758544493064720'],
['EdCbA9876543210', 15, '435659737878916215'],
['DcBa9876543210', 14, '11046255305880158'],
['CbA9876543210', 13, '300771807240918'],
['Ba9876543210', 12, '8842413667692'],
['A9876543210', 11, '282458553905'],
['9876543210', 10, '9876543210'],
['876543210', 9, '381367044'],
['76543210', 8, '16434824'],
['6543210', 7, '800667'],
['543210', 6, '44790'],
['43210', 5, '2930'],
['3210', 4, '228'],
['210', 3, '21'],
['10', 2, '2'],
];
}
/**
* @dataProvider providerFromBaseWithInvalidValue
*/
public function testFromBaseWithInvalidValue(string $value, int $base) : void
{
$this->expectException(NumberFormatException::class);
BigInteger::fromBase($value, $base);
}
public function providerFromBaseWithInvalidValue() : array
{
return [
['', 10],
[' ', 10],
['+', 10],
['-', 10],
['1 ', 10],
[' 1', 10],
['Z', 35],
['y', 34],
['X', 33],
['w', 32],
['V', 31],
['u', 30],
['T', 29],
['s', 28],
['R', 27],
['q', 26],
['P', 25],
['o', 24],
['N', 23],
['m', 22],
['L', 21],
['k', 20],
['J', 19],
['i', 18],
['H', 17],
['g', 16],
['F', 15],
['e', 14],
['D', 13],
['c', 12],
['B', 11],
['a', 10],
['9', 9],
['8', 8],
['7', 7],
['6', 6],
['5', 5],
['4', 4],
['3', 3],
['2', 2]
];
}
/**
* @dataProvider providerFromBaseWithInvalidBase
*/
public function testFromBaseWithInvalidBase(int $base) : void
{
$this->expectException(\InvalidArgumentException::class);
BigInteger::fromBase('0', $base);
}
public function providerFromBaseWithInvalidBase() : array
{
return [
[-2],
[-1],
[0],
[1],
[37]
];
}
public function testZero() : void
{
self::assertBigIntegerEquals('0', BigInteger::zero());
self::assertSame(BigInteger::zero(), BigInteger::zero());
}
public function testOne() : void
{
self::assertBigIntegerEquals('1', BigInteger::one());
self::assertSame(BigInteger::one(), BigInteger::one());
}
public function testTen() : void
{
self::assertBigIntegerEquals('10', BigInteger::ten());
self::assertSame(BigInteger::ten(), BigInteger::ten());
}
/**
* @param string[] $values
*
* @dataProvider providerGcdMultiple
*/
public function testGcdMultiple(array $values, string $expectedGCD): void
{
$values = array_map(fn (string $value) => BigInteger::of($value), $values);
$actualGCD = BigInteger::gcdMultiple(...$values);
self::assertSame($expectedGCD, (string) $actualGCD);
}
public function providerGcdMultiple(): Generator
{
// 1 value
foreach (['-2', '-1', '0', '1', '2'] as $value) {
yield [[$value], $value];
}
// 2 values
foreach ($this->providerGcd() as [$a, $b, $gcd]) {
yield [[$a, $b], $gcd];
}
// n values
yield [['2', '4', '7'], '1'];
yield [['2', '4', '8'], '2'];
yield [['2', '4', '-7'], '1'];
yield [['2', '4', '-8'], '2'];
yield [['28', '56', '77777'], '7'];
yield [['28', '56', '77778'], '2'];
yield [['28', '56', '77782'], '2'];
yield [['28', '56', '77783'], '1'];
yield [['28', '56', '77784'], '28'];
yield [['28', '56', '77784', '4'], '4'];
yield [['28', '56', '77784', '14'], '14'];
yield [['28', '56', '77784', '14', '4'], '2'];
}
/**
* @dataProvider providerMin
*
* @param array $values The values to compare.
* @param string $min The expected minimum value.
*/
public function testMin(array $values, string $min) : void
{
self::assertBigIntegerEquals($min, BigInteger::min(... $values));
}
public function providerMin() : array
{
return [
[[0, 1, -1], '-1'],
[[0, '10', '5989'], '0'],
[[0, '10', '5989', '-1.00'], '-1'],
[['-2/2', '1'], '-1'],
[['-1.0', '1', '2', '-300/4', '-100'], '-100'],
[['999999999999999999999999999', '1000000000000000000000000000'], '999999999999999999999999999'],
[['-999999999999999999999999999', '-1000000000000000000000000000'], '-1000000000000000000000000000']
];
}
public function testMinOfZeroValuesThrowsException() : void
{
$this->expectException(\InvalidArgumentException::class);
BigInteger::min();
}
public function testMinOfNonIntegerValuesThrowsException() : void
{
$this->expectException(RoundingNecessaryException::class);
BigInteger::min(1, 1.2);
}
/**
* @dataProvider providerMax
*
* @param array $values The values to compare.
* @param string $max The expected maximum value.
*/
public function testMax(array $values, string $max) : void
{
self::assertBigIntegerEquals($max, BigInteger::max(... $values));
}
public function providerMax() : array
{
return [
[[0, 1, -1], '1'],
[[0, '10', '5989.0'], '5989'],
[[0, '10', '5989', '-1'], '5989'],
[[0, '10', '5989', '-1', 6000.0], '6000'],
[['-1', '0'], '0'],
[['-1', '1', '2', '27/9', '-100'], '3'],
[['999999999999999999999999999', '1000000000000000000000000000'], '1000000000000000000000000000'],
[['-999999999999999999999999999', '-1000000000000000000000000000'], '-999999999999999999999999999']
];
}
public function testMaxOfZeroValuesThrowsException() : void
{
$this->expectException(\InvalidArgumentException::class);
BigInteger::max();
}
public function testMaxOfNonIntegerValuesThrowsException() : void
{
$this->expectException(RoundingNecessaryException::class);
BigInteger::max(1, '3/2');
}
/**
* @dataProvider providerSum
*
* @param array $values The values to add.
* @param string $sum The expected sum.
*/
public function testSum(array $values, string $sum) : void
{
self::assertBigIntegerEquals($sum, BigInteger::sum(... $values));
}
public function providerSum() : array
{
return [
[[-1], '-1'],
[[0, 1, -1], '0'],
[[0, '10', '5989.0'], '5999'],
[[0, '10', '5989', '-1'], '5998'],
[[0, '10', '5989', '-1', 6000.0], '11998'],
[['-1', '0'], '-1'],
[['-1', '1', '2', '27/9', '-100'], '-95'],
[['1234567', '-1233.00', 137, '406847567975012457258945126', ], '406847567975012457260178597'],
[['-165504564654654879742303821254754', '-4455454', 455879563], '-165504564654654879742303369830645']
];
}
public function testSumOfZeroValuesThrowsException() : void
{
$this->expectException(\InvalidArgumentException::class);
BigInteger::sum();
}
public function testSumOfNonIntegerValuesThrowsException() : void
{
$this->expectException(RoundingNecessaryException::class);
BigInteger::sum(1, '3/2');
}
/**
* @dataProvider providerPlus
*
* @param string $a The base number.
* @param string $b The number to add.
* @param string $r The expected result.
*/
public function testPlus(string $a, string $b, string $r) : void
{
self::assertBigIntegerEquals($r, BigInteger::of($a)->plus($b));
}
public function providerPlus() : array
{
return [
['5165450198704521651351654564564089798441', '0', '5165450198704521651351654564564089798441'],
['-5165450198704521651351654564564089798441', '0', '-5165450198704521651351654564564089798441'],
['0', '5165450198704521651351654564564089798441', '5165450198704521651351654564564089798441'],
['0', '-5165450198704521651351654564564089798441', '-5165450198704521651351654564564089798441'],
['5165450198704521651351654564564089798441', '-5165450198704521651351654564564089798441', '0'],
['-5165450198704521651351654564564089798441', '5165450198704521651351654564564089798441', '0'],
['3493049309220392055810', '9918493493849898938928310121', '9918496986899208159320365931'],
['546254089287665464650654', '-4654654565726542654005465', '-4108400476438877189354811'],
['-54654654625426504062224', '406546504670332465465435004', '406491850015707038961372780'],
['-78706406576549688403246', '-3064672987984605465406546', '-3143379394561155153809792']
];
}
/**
* @dataProvider providerMinus
*
* @param string $a The base number.
* @param string $b The number to subtract.
* @param string $r The expected result.
*/
public function testMinus(string $a, string $b, string $r) : void
{
self::assertBigIntegerEquals($r, BigInteger::of($a)->minus($b));
}
public function providerMinus() : array
{
return [
['5165450198704521651351654564564089798441', '0', '5165450198704521651351654564564089798441'],
['-5165450198704521651351654564564089798441', '0', '-5165450198704521651351654564564089798441'],
['0', '5165450198704521651351654564564089798441', '-5165450198704521651351654564564089798441'],
['0', '-5165450198704521651351654564564089798441', '5165450198704521651351654564564089798441'],
['879798276565798787646', '2345178709879804654605406456', '-2345177830081528088806618810'],
['99465465545004066406868767', '-79870987954654608076067608768', '79970453420199612142474477535'],
['-46465465478979879230745664', '21316504468760001807687078994', '-21362969934238981686917824658'],
['-2154799048440940949896046', '-9000454956465465424345404846624', '9000452801666416983404454950578']
];
}
/**
* @dataProvider providerMultipliedBy
*
* @param string $a The base number.
* @param string|int $b The number to multiply.
* @param string $r The expected result.
*/
public function testMultipliedBy(string $a, $b, string $r) : void
{
self::assertBigIntegerEquals($r, BigInteger::of($a)->multipliedBy($b));
}
public function providerMultipliedBy() : array
{
return [
['123456789098765432101234567890987654321', '1', '123456789098765432101234567890987654321'],
['123456789098765432101234567890987654321', '-1', '-123456789098765432101234567890987654321'],
['1', '123456789098765432101234567890987654321', '123456789098765432101234567890987654321'],
['15892588375910581333', '2485910409339228962451', '39507550875019745254366764864945838527183'],
['341581435989834012309', '-91050393818389238433', '-31101124267925302088072082300643257871797'],
['-1204902920503999920003', '1984389583950290232332', '-2390996805119422027350037939263960284136996'],
['-991230349304902390122', '-3483910549230593053437', '3453357870660875087266990729629471366949314'],
['0', '-3483910549230593053437', '0'],
['-991230349304902390122', '0', '0'],
['1274837942798479387498237897498734984', 30, '38245138283954381624947136924962049520'],
['1274837942798479387498237897498734984', 30.0, '38245138283954381624947136924962049520'],
['1274837942798479387498237897498734984', '30', '38245138283954381624947136924962049520'],
['1274837942798479387498237897498734984', '30.0', '38245138283954381624947136924962049520'],
['1274837942798479387498237897498734984', '90/3', '38245138283954381624947136924962049520'],
];
}
/**
* @dataProvider providerDividedBy
*
* @param string $number The base number.
* @param string|int|float $divisor The divisor.
* @param string $expected The expected result, or a class name if an exception is expected.
*/
public function testDividedBy(string $number, $divisor, string $expected) : void
{
$number = BigInteger::of($number);
if (self::isException($expected)) {
$this->expectException($expected);
}
$actual = $number->dividedBy($divisor);
if (! self::isException($expected)) {
self::assertBigIntegerEquals($expected, $actual);
}
}
public function providerDividedBy() : array
{
return [
['123456789098765432101234567890987654321', 1, '123456789098765432101234567890987654321'],
['123456789098765432101234567890987654321', 2, RoundingNecessaryException::class],
['123456789098765432101234567890987654321', 0, DivisionByZeroException::class],
['123456789098765432101234567890987654321', 0.0, DivisionByZeroException::class],
['123456789098765432101234567890987654321', 0.1, RoundingNecessaryException::class],
['123456789098765432101234567890987654322', 2, '61728394549382716050617283945493827161'],
['123456789098765432101234567890987654322', 2.0, '61728394549382716050617283945493827161'],
['123456789098765432101234567890987654322', '2', '61728394549382716050617283945493827161'],
['123456789098765432101234567890987654322', '2.0', '61728394549382716050617283945493827161'],
['123456789098765432101234567890987654322', '14/7', '61728394549382716050617283945493827161'],
['61728394549382716050617283945493827161', '0.5', RoundingNecessaryException::class],
['61728394549382716050617283945493827161', '1/2', RoundingNecessaryException::class],
['0', '61728394549382716050617283945493827161', '0'],
// overflowing native integer division
['-2147483648', '-1', '2147483648'], // 32-bit
['-9223372036854775808', '-1', '9223372036854775808'], // 64-bit
];
}
public function testDividedByWithInvalidRoundingModeThrowsException() : void
{
$this->expectException(\InvalidArgumentException::class);
BigInteger::of(1)->dividedBy(2, -1);
}
/**
* @dataProvider providerDividedByWithRoundingMode
*
* @param int $roundingMode The rounding mode.
* @param string $number The number to round.
* @param string|null $ten The expected rounding divided by 10, or null if an exception is expected.
* @param string|null $hundred The expected rounding divided by 100 or null if an exception is expected.
* @param string|null $thousand The expected rounding divided by 1000, or null if an exception is expected.
*/
public function testDividedByWithRoundingMode(int $roundingMode, string $number, ?string $ten, ?string $hundred, ?string $thousand) : void
{
$number = BigInteger::of($number);
$this->doTestDividedByWithRoundingMode($roundingMode, $number, '1', $ten, $hundred, $thousand);
$this->doTestDividedByWithRoundingMode($roundingMode, $number->negated(), '-1', $ten, $hundred, $thousand);
}
/**
* @param int $roundingMode The rounding mode.
* @param BigInteger $number The number to round.
* @param string $divisor The divisor.
* @param string|null $ten The expected rounding to a scale of two, or null if an exception is expected.
* @param string|null $hundred The expected rounding to a scale of one, or null if an exception is expected.
* @param string|null $thousand The expected rounding to a scale of zero, or null if an exception is expected.
*/
private function doTestDividedByWithRoundingMode(int $roundingMode, BigInteger $number, string $divisor, ?string $ten, ?string $hundred, ?string $thousand) : void
{
foreach ([$ten, $hundred, $thousand] as $expected) {
$divisor .= '0';
if ($expected === null) {
$this->expectException(RoundingNecessaryException::class);
}
$actual = $number->dividedBy($divisor, $roundingMode);
if ($expected !== null) {
self::assertBigIntegerEquals($expected, $actual);
}
}
}
public function providerDividedByWithRoundingMode() : array
{
return [
[RoundingMode::UP, '3501', '351', '36', '4'],
[RoundingMode::UP, '3500', '350', '35', '4'],
[RoundingMode::UP, '3499', '350', '35', '4'],
[RoundingMode::UP, '3001', '301', '31', '4'],
[RoundingMode::UP, '3000', '300', '30', '3'],
[RoundingMode::UP, '2999', '300', '30', '3'],
[RoundingMode::UP, '2501', '251', '26', '3'],
[RoundingMode::UP, '2500', '250', '25', '3'],
[RoundingMode::UP, '2499', '250', '25', '3'],
[RoundingMode::UP, '2001', '201', '21', '3'],
[RoundingMode::UP, '2000', '200', '20', '2'],
[RoundingMode::UP, '1999', '200', '20', '2'],
[RoundingMode::UP, '1501', '151', '16', '2'],
[RoundingMode::UP, '1500', '150', '15', '2'],
[RoundingMode::UP, '1499', '150', '15', '2'],
[RoundingMode::UP, '1001', '101', '11', '2'],
[RoundingMode::UP, '1000', '100', '10', '1'],
[RoundingMode::UP, '999', '100', '10', '1'],
[RoundingMode::UP, '501', '51', '6', '1'],
[RoundingMode::UP, '500', '50', '5', '1'],
[RoundingMode::UP, '499', '50', '5', '1'],
[RoundingMode::UP, '1', '1', '1', '1'],
[RoundingMode::UP, '0', '0', '0', '0'],
[RoundingMode::UP, '-1', '-1', '-1', '-1'],
[RoundingMode::UP, '-499', '-50', '-5', '-1'],
[RoundingMode::UP, '-500', '-50', '-5', '-1'],
[RoundingMode::UP, '-501', '-51', '-6', '-1'],
[RoundingMode::UP, '-999', '-100', '-10', '-1'],
[RoundingMode::UP, '-1000', '-100', '-10', '-1'],
[RoundingMode::UP, '-1001', '-101', '-11', '-2'],
[RoundingMode::UP, '-1499', '-150', '-15', '-2'],
[RoundingMode::UP, '-1500', '-150', '-15', '-2'],
[RoundingMode::UP, '-1501', '-151', '-16', '-2'],
[RoundingMode::UP, '-1999', '-200', '-20', '-2'],
[RoundingMode::UP, '-2000', '-200', '-20', '-2'],
[RoundingMode::UP, '-2001', '-201', '-21', '-3'],
[RoundingMode::UP, '-2499', '-250', '-25', '-3'],
[RoundingMode::UP, '-2500', '-250', '-25', '-3'],
[RoundingMode::UP, '-2501', '-251', '-26', '-3'],
[RoundingMode::UP, '-2999', '-300', '-30', '-3'],
[RoundingMode::UP, '-3000', '-300', '-30', '-3'],
[RoundingMode::UP, '-3001', '-301', '-31', '-4'],
[RoundingMode::UP, '-3499', '-350', '-35', '-4'],
[RoundingMode::UP, '-3500', '-350', '-35', '-4'],
[RoundingMode::UP, '-3501', '-351', '-36', '-4'],
[RoundingMode::DOWN, '3501', '350', '35', '3'],
[RoundingMode::DOWN, '3500', '350', '35', '3'],
[RoundingMode::DOWN, '3499', '349', '34', '3'],
[RoundingMode::DOWN, '3001', '300', '30', '3'],
[RoundingMode::DOWN, '3000', '300', '30', '3'],
[RoundingMode::DOWN, '2999', '299', '29', '2'],
[RoundingMode::DOWN, '2501', '250', '25', '2'],
[RoundingMode::DOWN, '2500', '250', '25', '2'],
[RoundingMode::DOWN, '2499', '249', '24', '2'],
[RoundingMode::DOWN, '2001', '200', '20', '2'],
[RoundingMode::DOWN, '2000', '200', '20', '2'],
[RoundingMode::DOWN, '1999', '199', '19', '1'],
[RoundingMode::DOWN, '1501', '150', '15', '1'],
[RoundingMode::DOWN, '1500', '150', '15', '1'],
[RoundingMode::DOWN, '1499', '149', '14', '1'],
[RoundingMode::DOWN, '1001', '100', '10', '1'],
[RoundingMode::DOWN, '1000', '100', '10', '1'],
[RoundingMode::DOWN, '999', '99', '9', '0'],
[RoundingMode::DOWN, '501', '50', '5', '0'],
[RoundingMode::DOWN, '500', '50', '5', '0'],
[RoundingMode::DOWN, '499', '49', '4', '0'],
[RoundingMode::DOWN, '1', '0', '0', '0'],
[RoundingMode::DOWN, '0', '0', '0', '0'],
[RoundingMode::DOWN, '-1', '0', '0', '0'],
[RoundingMode::DOWN, '-499', '-49', '-4', '0'],
[RoundingMode::DOWN, '-500', '-50', '-5', '0'],
[RoundingMode::DOWN, '-501', '-50', '-5', '0'],
[RoundingMode::DOWN, '-999', '-99', '-9', '0'],
[RoundingMode::DOWN, '-1000', '-100', '-10', '-1'],
[RoundingMode::DOWN, '-1001', '-100', '-10', '-1'],
[RoundingMode::DOWN, '-1499', '-149', '-14', '-1'],
[RoundingMode::DOWN, '-1500', '-150', '-15', '-1'],
[RoundingMode::DOWN, '-1501', '-150', '-15', '-1'],
[RoundingMode::DOWN, '-1999', '-199', '-19', '-1'],
[RoundingMode::DOWN, '-2000', '-200', '-20', '-2'],
[RoundingMode::DOWN, '-2001', '-200', '-20', '-2'],
[RoundingMode::DOWN, '-2499', '-249', '-24', '-2'],
[RoundingMode::DOWN, '-2500', '-250', '-25', '-2'],
[RoundingMode::DOWN, '-2501', '-250', '-25', '-2'],
[RoundingMode::DOWN, '-2999', '-299', '-29', '-2'],
[RoundingMode::DOWN, '-3000', '-300', '-30', '-3'],
[RoundingMode::DOWN, '-3001', '-300', '-30', '-3'],
[RoundingMode::DOWN, '-3499', '-349', '-34', '-3'],
[RoundingMode::DOWN, '-3500', '-350', '-35', '-3'],
[RoundingMode::DOWN, '-3501', '-350', '-35', '-3'],
[RoundingMode::CEILING, '3501', '351', '36', '4'],
[RoundingMode::CEILING, '3500', '350', '35', '4'],
[RoundingMode::CEILING, '3499', '350', '35', '4'],
[RoundingMode::CEILING, '3001', '301', '31', '4'],
[RoundingMode::CEILING, '3000', '300', '30', '3'],
[RoundingMode::CEILING, '2999', '300', '30', '3'],
[RoundingMode::CEILING, '2501', '251', '26', '3'],
[RoundingMode::CEILING, '2500', '250', '25', '3'],
[RoundingMode::CEILING, '2499', '250', '25', '3'],
[RoundingMode::CEILING, '2001', '201', '21', '3'],
[RoundingMode::CEILING, '2000', '200', '20', '2'],
[RoundingMode::CEILING, '1999', '200', '20', '2'],
[RoundingMode::CEILING, '1501', '151', '16', '2'],
[RoundingMode::CEILING, '1500', '150', '15', '2'],
[RoundingMode::CEILING, '1499', '150', '15', '2'],
[RoundingMode::CEILING, '1001', '101', '11', '2'],
[RoundingMode::CEILING, '1000', '100', '10', '1'],
[RoundingMode::CEILING, '999', '100', '10', '1'],
[RoundingMode::CEILING, '501', '51', '6', '1'],
[RoundingMode::CEILING, '500', '50', '5', '1'],
[RoundingMode::CEILING, '499', '50', '5', '1'],
[RoundingMode::CEILING, '1', '1', '1', '1'],
[RoundingMode::CEILING, '0', '0', '0', '0'],
[RoundingMode::CEILING, '-1', '0', '0', '0'],
[RoundingMode::CEILING, '-499', '-49' , '-4', '0'],
[RoundingMode::CEILING, '-500', '-50' , '-5', '0'],
[RoundingMode::CEILING, '-501', '-50', '-5', '0'],
[RoundingMode::CEILING, '-999', '-99', '-9', '0'],
[RoundingMode::CEILING, '-1000', '-100', '-10', '-1'],
[RoundingMode::CEILING, '-1001', '-100', '-10', '-1'],
[RoundingMode::CEILING, '-1499', '-149', '-14', '-1'],
[RoundingMode::CEILING, '-1500', '-150', '-15', '-1'],
[RoundingMode::CEILING, '-1501', '-150', '-15', '-1'],
[RoundingMode::CEILING, '-1999', '-199', '-19', '-1'],
[RoundingMode::CEILING, '-2000', '-200', '-20', '-2'],
[RoundingMode::CEILING, '-2001', '-200', '-20', '-2'],
[RoundingMode::CEILING, '-2499', '-249', '-24', '-2'],
[RoundingMode::CEILING, '-2500', '-250', '-25', '-2'],
[RoundingMode::CEILING, '-2501', '-250', '-25', '-2'],
[RoundingMode::CEILING, '-2999', '-299', '-29', '-2'],
[RoundingMode::CEILING, '-3000', '-300', '-30', '-3'],
[RoundingMode::CEILING, '-3001', '-300', '-30', '-3'],
[RoundingMode::CEILING, '-3499', '-349', '-34', '-3'],
[RoundingMode::CEILING, '-3500', '-350', '-35', '-3'],
[RoundingMode::CEILING, '-3501', '-350', '-35', '-3'],
[RoundingMode::FLOOR, '3501', '350', '35', '3'],
[RoundingMode::FLOOR, '3500', '350', '35', '3'],
[RoundingMode::FLOOR, '3499', '349', '34', '3'],
[RoundingMode::FLOOR, '3001', '300', '30', '3'],
[RoundingMode::FLOOR, '3000', '300', '30', '3'],
[RoundingMode::FLOOR, '2999', '299', '29', '2'],
[RoundingMode::FLOOR, '2501', '250', '25', '2'],
[RoundingMode::FLOOR, '2500', '250', '25', '2'],
[RoundingMode::FLOOR, '2499', '249', '24', '2'],
[RoundingMode::FLOOR, '2001', '200', '20', '2'],
[RoundingMode::FLOOR, '2000', '200', '20', '2'],
[RoundingMode::FLOOR, '1999', '199', '19', '1'],
[RoundingMode::FLOOR, '1501', '150', '15', '1'],
[RoundingMode::FLOOR, '1500', '150', '15', '1'],
[RoundingMode::FLOOR, '1499', '149', '14', '1'],
[RoundingMode::FLOOR, '1001', '100', '10', '1'],
[RoundingMode::FLOOR, '1000', '100', '10', '1'],
[RoundingMode::FLOOR, '999', '99', '9', '0'],
[RoundingMode::FLOOR, '501', '50', '5', '0'],
[RoundingMode::FLOOR, '500', '50', '5', '0'],
[RoundingMode::FLOOR, '499', '49', '4', '0'],
[RoundingMode::FLOOR, '1', '0', '0', '0'],
[RoundingMode::FLOOR, '0', '0', '0', '0'],
[RoundingMode::FLOOR, '-1', '-1', '-1', '-1'],
[RoundingMode::FLOOR, '-499', '-50', '-5', '-1'],
[RoundingMode::FLOOR, '-500', '-50', '-5', '-1'],
[RoundingMode::FLOOR, '-501', '-51', '-6', '-1'],
[RoundingMode::FLOOR, '-999', '-100', '-10', '-1'],
[RoundingMode::FLOOR, '-1000', '-100', '-10', '-1'],
[RoundingMode::FLOOR, '-1001', '-101', '-11', '-2'],
[RoundingMode::FLOOR, '-1499', '-150', '-15', '-2'],
[RoundingMode::FLOOR, '-1500', '-150', '-15', '-2'],
[RoundingMode::FLOOR, '-1501', '-151', '-16', '-2'],
[RoundingMode::FLOOR, '-1999', '-200', '-20', '-2'],
[RoundingMode::FLOOR, '-2000', '-200', '-20', '-2'],
[RoundingMode::FLOOR, '-2001', '-201', '-21', '-3'],
[RoundingMode::FLOOR, '-2499', '-250', '-25', '-3'],
[RoundingMode::FLOOR, '-2500', '-250', '-25', '-3'],
[RoundingMode::FLOOR, '-2501', '-251', '-26', '-3'],
[RoundingMode::FLOOR, '-2999', '-300', '-30', '-3'],
[RoundingMode::FLOOR, '-3000', '-300', '-30', '-3'],
[RoundingMode::FLOOR, '-3001', '-301', '-31', '-4'],
[RoundingMode::FLOOR, '-3499', '-350', '-35', '-4'],
[RoundingMode::FLOOR, '-3500', '-350', '-35', '-4'],
[RoundingMode::FLOOR, '-3501', '-351', '-36', '-4'],
[RoundingMode::HALF_UP, '3501', '350', '35', '4'],
[RoundingMode::HALF_UP, '3500', '350', '35', '4'],
[RoundingMode::HALF_UP, '3499', '350', '35', '3'],
[RoundingMode::HALF_UP, '3001', '300', '30', '3'],
[RoundingMode::HALF_UP, '3000', '300', '30', '3'],
[RoundingMode::HALF_UP, '2999', '300', '30', '3'],
[RoundingMode::HALF_UP, '2501', '250', '25', '3'],
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