const { BN, constants, expectRevert } = require('@openzeppelin/test-helpers');
const { expect } = require('chai');
const { MAX_UINT256 } = constants;
const { Rounding } = require('../../helpers/enums.js');
const Math = artifacts.require('$Math');
contract('Math', function () {
const min = new BN('1234');
const max = new BN('5678');
const MAX_UINT256_SUB1 = MAX_UINT256.sub(new BN('1'));
const MAX_UINT256_SUB2 = MAX_UINT256.sub(new BN('2'));
beforeEach(async function () {
this.math = await Math.new();
});
describe('max', function () {
it('is correctly detected in first argument position', async function () {
expect(await this.math.$max(max, min)).to.be.bignumber.equal(max);
});
it('is correctly detected in second argument position', async function () {
expect(await this.math.$max(min, max)).to.be.bignumber.equal(max);
});
});
describe('min', function () {
it('is correctly detected in first argument position', async function () {
expect(await this.math.$min(min, max)).to.be.bignumber.equal(min);
});
it('is correctly detected in second argument position', async function () {
expect(await this.math.$min(max, min)).to.be.bignumber.equal(min);
});
});
describe('average', function () {
function bnAverage(a, b) {
return a.add(b).divn(2);
}
it('is correctly calculated with two odd numbers', async function () {
const a = new BN('57417');
const b = new BN('95431');
expect(await this.math.$average(a, b)).to.be.bignumber.equal(bnAverage(a, b));
});
it('is correctly calculated with two even numbers', async function () {
const a = new BN('42304');
const b = new BN('84346');
expect(await this.math.$average(a, b)).to.be.bignumber.equal(bnAverage(a, b));
});
it('is correctly calculated with one even and one odd number', async function () {
const a = new BN('57417');
const b = new BN('84346');
expect(await this.math.$average(a, b)).to.be.bignumber.equal(bnAverage(a, b));
});
it('is correctly calculated with two max uint256 numbers', async function () {
const a = MAX_UINT256;
expect(await this.math.$average(a, a)).to.be.bignumber.equal(bnAverage(a, a));
});
});
describe('ceilDiv', function () {
it('does not round up on exact division', async function () {
const a = new BN('10');
const b = new BN('5');
expect(await this.math.$ceilDiv(a, b)).to.be.bignumber.equal('2');
});
it('rounds up on division with remainders', async function () {
const a = new BN('42');
const b = new BN('13');
expect(await this.math.$ceilDiv(a, b)).to.be.bignumber.equal('4');
});
it('does not overflow', async function () {
const b = new BN('2');
const result = new BN('1').shln(255);
expect(await this.math.$ceilDiv(MAX_UINT256, b)).to.be.bignumber.equal(result);
});
it('correctly computes max uint256 divided by 1', async function () {
const b = new BN('1');
expect(await this.math.$ceilDiv(MAX_UINT256, b)).to.be.bignumber.equal(MAX_UINT256);
});
});
describe('muldiv', function () {
it('divide by 0', async function () {
await expectRevert.unspecified(this.math.$mulDiv(1, 1, 0, Rounding.Down));
});
describe('does round down', async function () {
it('small values', async function () {
expect(await this.math.$mulDiv('3', '4', '5', Rounding.Down)).to.be.bignumber.equal('2');
expect(await this.math.$mulDiv('3', '5', '5', Rounding.Down)).to.be.bignumber.equal('3');
});
it('large values', async function () {
expect(
await this.math.$mulDiv(new BN('42'), MAX_UINT256_SUB1, MAX_UINT256, Rounding.Down),
).to.be.bignumber.equal(new BN('41'));
expect(await this.math.$mulDiv(new BN('17'), MAX_UINT256, MAX_UINT256, Rounding.Down)).to.be.bignumber.equal(
new BN('17'),
);
expect(
await this.math.$mulDiv(MAX_UINT256_SUB1, MAX_UINT256_SUB1, MAX_UINT256, Rounding.Down),
).to.be.bignumber.equal(MAX_UINT256_SUB2);
expect(
await this.math.$mulDiv(MAX_UINT256, MAX_UINT256_SUB1, MAX_UINT256, Rounding.Down),
).to.be.bignumber.equal(MAX_UINT256_SUB1);
expect(await this.math.$mulDiv(MAX_UINT256, MAX_UINT256, MAX_UINT256, Rounding.Down)).to.be.bignumber.equal(
MAX_UINT256,
);
});
});
describe('does round up', async function () {
it('small values', async function () {
expect(await this.math.$mulDiv('3', '4', '5', Rounding.Up)).to.be.bignumber.equal('3');
expect(await this.math.$mulDiv('3', '5', '5', Rounding.Up)).to.be.bignumber.equal('3');
});
it('large values', async function () {
expect(await this.math.$mulDiv(new BN('42'), MAX_UINT256_SUB1, MAX_UINT256, Rounding.Up)).to.be.bignumber.equal(
new BN('42'),
);
expect(await this.math.$mulDiv(new BN('17'), MAX_UINT256, MAX_UINT256, Rounding.Up)).to.be.bignumber.equal(
new BN('17'),
);
expect(
await this.math.$mulDiv(MAX_UINT256_SUB1, MAX_UINT256_SUB1, MAX_UINT256, Rounding.Up),
).to.be.bignumber.equal(MAX_UINT256_SUB1);
expect(await this.math.$mulDiv(MAX_UINT256, MAX_UINT256_SUB1, MAX_UINT256, Rounding.Up)).to.be.bignumber.equal(
MAX_UINT256_SUB1,
);
expect(await this.math.$mulDiv(MAX_UINT256, MAX_UINT256, MAX_UINT256, Rounding.Up)).to.be.bignumber.equal(
MAX_UINT256,
);
});
});
});
describe('sqrt', function () {
it('rounds down', async function () {
expect(await this.math.$sqrt('0', Rounding.Down)).to.be.bignumber.equal('0');
expect(await this.math.$sqrt('1', Rounding.Down)).to.be.bignumber.equal('1');
expect(await this.math.$sqrt('2', Rounding.Down)).to.be.bignumber.equal('1');
expect(await this.math.$sqrt('3', Rounding.Down)).to.be.bignumber.equal('1');
expect(await this.math.$sqrt('4', Rounding.Down)).to.be.bignumber.equal('2');
expect(await this.math.$sqrt('144', Rounding.Down)).to.be.bignumber.equal('12');
expect(await this.math.$sqrt('999999', Rounding.Down)).to.be.bignumber.equal('999');
expect(await this.math.$sqrt('1000000', Rounding.Down)).to.be.bignumber.equal('1000');
expect(await this.math.$sqrt('1000001', Rounding.Down)).to.be.bignumber.equal('1000');
expect(await this.math.$sqrt('1002000', Rounding.Down)).to.be.bignumber.equal('1000');
expect(await this.math.$sqrt('1002001', Rounding.Down)).to.be.bignumber.equal('1001');
expect(await this.math.$sqrt(MAX_UINT256, Rounding.Down)).to.be.bignumber.equal(
'340282366920938463463374607431768211455',
);
});
it('rounds up', async function () {
expect(await this.math.$sqrt('0', Rounding.Up)).to.be.bignumber.equal('0');
expect(await this.math.$sqrt('1', Rounding.Up)).to.be.bignumber.equal('1');
expect(await this.math.$sqrt('2', Rounding.Up)).to.be.bignumber.equal('2');
expect(await this.math.$sqrt('3', Rounding.Up)).to.be.bignumber.equal('2');
expect(await this.math.$sqrt('4', Rounding.Up)).to.be.bignumber.equal('2');
expect(await this.math.$sqrt('144', Rounding.Up)).to.be.bignumber.equal('12');
expect(await this.math.$sqrt('999999', Rounding.Up)).to.be.bignumber.equal('1000');
expect(await this.math.$sqrt('1000000', Rounding.Up)).to.be.bignumber.equal('1000');
expect(await this.math.$sqrt('1000001', Rounding.Up)).to.be.bignumber.equal('1001');
expect(await this.math.$sqrt('1002000', Rounding.Up)).to.be.bignumber.equal('1001');
expect(await this.math.$sqrt('1002001', Rounding.Up)).to.be.bignumber.equal('1001');
expect(await this.math.$sqrt(MAX_UINT256, Rounding.Up)).to.be.bignumber.equal(
'340282366920938463463374607431768211456',
);
});
});
describe('log', function () {
describe('log2', function () {
it('rounds down', async function () {
expect(await this.math.methods['$log2(uint256,uint8)']('0', Rounding.Down)).to.be.bignumber.equal('0');
expect(await this.math.methods['$log2(uint256,uint8)']('1', Rounding.Down)).to.be.bignumber.equal('0');
expect(await this.math.methods['$log2(uint256,uint8)']('2', Rounding.Down)).to.be.bignumber.equal('1');
expect(await this.math.methods['$log2(uint256,uint8)']('3', Rounding.Down)).to.be.bignumber.equal('1');
expect(await this.math.methods['$log2(uint256,uint8)']('4', Rounding.Down)).to.be.bignumber.equal('2');
expect(await this.math.methods['$log2(uint256,uint8)']('5', Rounding.Down)).to.be.bignumber.equal('2');
expect(await this.math.methods['$log2(uint256,uint8)']('6', Rounding.Down)).to.be.bignumber.equal('2');
expect(await this.math.methods['$log2(uint256,uint8)']('7', Rounding.Down)).to.be.bignumber.equal('2');
expect(await this.math.methods['$log2(uint256,uint8)']('8', Rounding.Down)).to.be.bignumber.equal('3');
expect(await this.math.methods['$log2(uint256,uint8)']('9', Rounding.Down)).to.be.bignumber.equal('3');
expect(await this.math.methods['$log2(uint256,uint8)'](MAX_UINT256, Rounding.Down)).to.be.bignumber.equal(
'255',
);
});
it('rounds up', async function () {
expect(await this.math.methods['$log2(uint256,uint8)']('0', Rounding.Up)).to.be.bignumber.equal('0');
expect(await this.math.methods['$log2(uint256,uint8)']('1', Rounding.Up)).to.be.bignumber.equal('0');
expect(await this.math.methods['$log2(uint256,uint8)']('2', Rounding.Up)).to.be.bignumber.equal('1');
expect(await this.math.methods['$log2(uint256,uint8)']('3', Rounding.Up)).to.be.bignumber.equal('2');
expect(await this.math.methods['$log2(uint256,uint8)']('4', Rounding.Up)).to.be.bignumber.equal('2');
expect(await this.math.methods['$log2(uint256,uint8)']('5', Rounding.Up)).to.be.bignumber.equal('3');
expect(await this.math.methods['$log2(uint256,uint8)']('6', Rounding.Up)).to.be.bignumber.equal('3');
expect(await this.math.methods['$log2(uint256,uint8)']('7', Rounding.Up)).to.be.bignumber.equal('3');
expect(await this.math.methods['$log2(uint256,uint8)']('8', Rounding.Up)).to.be.bignumber.equal('3');
expect(await this.math.methods['$log2(uint256,uint8)']('9', Rounding.Up)).to.be.bignumber.equal('4');
expect(await this.math.methods['$log2(uint256,uint8)'](MAX_UINT256, Rounding.Up)).to.be.bignumber.equal('256');
});
});
describe('log10', function () {
it('rounds down', async function () {
expect(await this.math.$log10('0', Rounding.Down)).to.be.bignumber.equal('0');
expect(await this.math.$log10('1', Rounding.Down)).to.be.bignumber.equal('0');
expect(await this.math.$log10('2', Rounding.Down)).to.be.bignumber.equal('0');
expect(await this.math.$log10('9', Rounding.Down)).to.be.bignumber.equal('0');
expect(await this.math.$log10('10', Rounding.Down)).to.be.bignumber.equal('1');
expect(await this.math.$log10('11', Rounding.Down)).to.be.bignumber.equal('1');
expect(await this.math.$log10('99', Rounding.Down)).to.be.bignumber.equal('1');
expect(await this.math.$log10('100', Rounding.Down)).to.be.bignumber.equal('2');
expect(await this.math.$log10('101', Rounding.Down)).to.be.bignumber.equal('2');
expect(await this.math.$log10('999', Rounding.Down)).to.be.bignumber.equal('2');
expect(await this.math.$log10('1000', Rounding.Down)).to.be.bignumber.equal('3');
expect(await this.math.$log10('1001', Rounding.Down)).to.be.bignumber.equal('3');
expect(await this.math.$log10(MAX_UINT256, Rounding.Down)).to.be.bignumber.equal('77');
});
it('rounds up', async function () {
expect(await this.math.$log10('0', Rounding.Up)).to.be.bignumber.equal('0');
expect(await this.math.$log10('1', Rounding.Up)).to.be.bignumber.equal('0');
expect(await this.math.$log10('2', Rounding.Up)).to.be.bignumber.equal('1');
expect(await this.math.$log10('9', Rounding.Up)).to.be.bignumber.equal('1');
expect(await this.math.$log10('10', Rounding.Up)).to.be.bignumber.equal('1');
expect(await this.math.$log10('11', Rounding.Up)).to.be.bignumber.equal('2');
expect(await this.math.$log10('99', Rounding.Up)).to.be.bignumber.equal('2');
expect(await this.math.$log10('100', Rounding.Up)).to.be.bignumber.equal('2');
expect(await this.math.$log10('101', Rounding.Up)).to.be.bignumber.equal('3');
expect(await this.math.$log10('999', Rounding.Up)).to.be.bignumber.equal('3');
expect(await this.math.$log10('1000', Rounding.Up)).to.be.bignumber.equal('3');
expect(await this.math.$log10('1001', Rounding.Up)).to.be.bignumber.equal('4');
expect(await this.math.$log10(MAX_UINT256, Rounding.Up)).to.be.bignumber.equal('78');
});
});
describe('log256', function () {
it('rounds down', async function () {
expect(await this.math.$log256('0', Rounding.Down)).to.be.bignumber.equal('0');
expect(await this.math.$log256('1', Rounding.Down)).to.be.bignumber.equal('0');
expect(await this.math.$log256('2', Rounding.Down)).to.be.bignumber.equal('0');
expect(await this.math.$log256('255', Rounding.Down)).to.be.bignumber.equal('0');
expect(await this.math.$log256('256', Rounding.Down)).to.be.bignumber.equal('1');
expect(await this.math.$log256('257', Rounding.Down)).to.be.bignumber.equal('1');
expect(await this.math.$log256('65535', Rounding.Down)).to.be.bignumber.equal('1');
expect(await this.math.$log256('65536', Rounding.Down)).to.be.bignumber.equal('2');
expect(await this.math.$log256('65537', Rounding.Down)).to.be.bignumber.equal('2');
expect(await this.math.$log256(MAX_UINT256, Rounding.Down)).to.be.bignumber.equal('31');
});
it('rounds up', async function () {
expect(await this.math.$log256('0', Rounding.Up)).to.be.bignumber.equal('0');
expect(await this.math.$log256('1', Rounding.Up)).to.be.bignumber.equal('0');
expect(await this.math.$log256('2', Rounding.Up)).to.be.bignumber.equal('1');
expect(await this.math.$log256('255', Rounding.Up)).to.be.bignumber.equal('1');
expect(await this.math.$log256('256', Rounding.Up)).to.be.bignumber.equal('1');
expect(await this.math.$log256('257', Rounding.Up)).to.be.bignumber.equal('2');
expect(await this.math.$log256('65535', Rounding.Up)).to.be.bignumber.equal('2');
expect(await this.math.$log256('65536', Rounding.Up)).to.be.bignumber.equal('2');
expect(await this.math.$log256('65537', Rounding.Up)).to.be.bignumber.equal('3');
expect(await this.math.$log256(MAX_UINT256, Rounding.Up)).to.be.bignumber.equal('32');
});
});
});
});