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Implemented rounding division. (#349)
* Implemented rounding towards zero division. * Implemented rounding away from zero division.
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‎contracts/math/DecimalMath.sol

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Original file line numberDiff line numberDiff line change
@@ -82,4 +82,70 @@ library DecimalMath {
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{
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return x.mul(int(unit(decimals))).div(y);
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}
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/// @dev Divides x between y, rounding to the closes representable number.
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/// Assumes x and y are both fixed point with 18 digits.
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function divdr(uint256 x, uint256 y) internal pure returns (uint256) {
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return divdr(x, y, 18);
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}
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/// @dev Divides x between y, rounding to the closes representable number.
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/// Assumes x and y are both fixed point with 18 digits.
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function divdr(int256 x, int256 y) internal pure returns (int256) {
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return divdr(x, y, 18);
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}
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/// @dev Divides x between y, rounding to the closest representable number.
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/// Assumes x and y are both fixed point with `decimals` digits.
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function divdr(uint256 x, uint256 y, uint8 decimals)
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internal pure returns (uint256)
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{
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uint256 z = x.mul(unit(decimals + 1)).div(y);
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if (z % 10 > 5) return z / 10 + 1;
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else return z / 10;
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}
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/// @dev Divides x between y, rounding to the closest representable number.
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/// Assumes x and y are both fixed point with `decimals` digits.
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function divdr(int256 x, int256 y, uint8 decimals)
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internal pure returns (int256)
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{
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int256 z = x.mul(int256(unit(decimals + 1))).div(y);
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if (z % 10 > 5) return z / 10 + 1;
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else if (z % 10 < -5) return z / 10 - 1;
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else return z / 10;
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}
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/// @dev Divides x between y, rounding to the closes representable number.
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/// Assumes x and y are both fixed point with 18 digits.
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function divdrup(uint256 x, uint256 y) internal pure returns (uint256) {
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return divdrup(x, y, 18);
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}
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/// @dev Divides x between y, rounding to the closes representable number.
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/// Assumes x and y are both fixed point with 18 digits.
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function divdrup(int256 x, int256 y) internal pure returns (int256) {
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return divdrup(x, y, 18);
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}
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/// @dev Divides x between y, rounding to the closest representable number.
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/// Assumes x and y are both fixed point with `decimals` digits.
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function divdrup(uint256 x, uint256 y, uint8 decimals)
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internal pure returns (uint256)
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{
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uint256 z = x.mul(unit(decimals + 1)).div(y);
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if (z % 10 > 0) return z / 10 + 1;
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else return z / 10;
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}
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/// @dev Divides x between y, rounding to the closest representable number.
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/// Assumes x and y are both fixed point with `decimals` digits.
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function divdrup(int256 x, int256 y, uint8 decimals)
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internal pure returns (int256)
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{
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int256 z = x.mul(int256(unit(decimals + 1))).div(y);
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if (z % 10 > 0) return z / 10 + 1;
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else if (z % 10 < 0) return z / 10 - 1;
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else return z / 10;
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}
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}

‎contracts/test/math/DecimalMathMock.sol

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Original file line numberDiff line numberDiff line change
@@ -66,4 +66,52 @@ contract DecimalMathMock {
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{
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return x.divd(y, decimals);
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}
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function divdr(uint256 x, uint256 y)
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public virtual pure returns (uint256)
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{
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return x.divdr(y);
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}
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function divdrInt(int256 x, int256 y)
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public virtual pure returns (int256)
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{
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return x.divdr(y);
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}
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function divdr2(uint256 x, uint256 y, uint8 decimals)
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public virtual pure returns (uint256)
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{
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return x.divdr(y, decimals);
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}
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function divdr2Int(int256 x, int256 y, uint8 decimals)
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public virtual pure returns (int256)
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{
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return x.divdr(y, decimals);
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}
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function divdrup(uint256 x, uint256 y)
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public virtual pure returns (uint256)
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{
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return x.divdrup(y);
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}
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function divdrupInt(int256 x, int256 y)
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public virtual pure returns (int256)
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{
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return x.divdrup(y);
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}
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function divdrup2(uint256 x, uint256 y, uint8 decimals)
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public virtual pure returns (uint256)
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{
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return x.divdrup(y, decimals);
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}
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function divdrup2Int(int256 x, int256 y, uint8 decimals)
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public virtual pure returns (int256)
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{
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return x.divdrup(y, decimals);
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}
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}

‎test/math/DecimalMath.test.ts

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Original file line numberDiff line numberDiff line change
@@ -18,6 +18,7 @@ contract('DecimalMath', () => {
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let decimal1_18: BN;
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let decimal2_18: BN;
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let decimal3_18: BN;
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let decimal4_18: BN;
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let decimal6_18: BN;
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let decimal1_16: BN;
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let decimal2_16: BN;
@@ -30,6 +31,7 @@ contract('DecimalMath', () => {
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decimal1_18 = new BN(await tokenMath.unit(decimals18.toString()));
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decimal2_18 = decimal1_18.mul(new BN('2'));
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decimal3_18 = decimal1_18.mul(new BN('3'));
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decimal4_18 = decimal1_18.mul(new BN('4'));
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decimal6_18 = decimal1_18.mul(new BN('6'));
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decimal1_16 = new BN(await tokenMath.unit(decimals16.toString()));
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decimal2_16 = decimal1_16.mul(new BN('2'));
@@ -128,4 +130,58 @@ contract('DecimalMath', () => {
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decimals16.toString(),
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)).should.be.bignumber.equal(decimal2_16.mul(minus1));
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});
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/**
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* @test {DecimalMath#divdr()}
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*/
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it('divides decimal values, rounding away from zero to the closest representable number.', async () => {
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BN(await tokenMath.divdr(
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decimal4_18.toString(),
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decimal6_18.toString(),
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)).should.be.bignumber.equal(new BN('666666666666666667'));
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BN(await tokenMath.divdrInt(
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decimal4_18.toString(),
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decimal6_18.toString(),
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)).should.be.bignumber.equal(new BN('666666666666666667'));
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BN(await tokenMath.divdrInt(
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decimal4_18.mul(minus1).toString(),
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decimal6_18.toString(),
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)).should.be.bignumber.equal((new BN('666666666666666667')).mul(minus1));
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});
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/**
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* @test {DecimalMath#divdr()}
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*/
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it('divides decimal values, rounding towards zero to the closest representable number.', async () => {
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BN(await tokenMath.divdr(
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decimal2_18.toString(),
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decimal6_18.toString(),
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)).should.be.bignumber.equal(new BN('333333333333333333'));
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BN(await tokenMath.divdrInt(
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decimal2_18.toString(),
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decimal6_18.toString(),
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)).should.be.bignumber.equal(new BN('333333333333333333'));
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BN(await tokenMath.divdrInt(
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decimal2_18.mul(minus1).toString(),
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decimal6_18.toString(),
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)).should.be.bignumber.equal((new BN('333333333333333333')).mul(minus1));
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});
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/**
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* @test {DecimalMath#divdr()}
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*/
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it('divides decimal values, rounding towards zero to the closest representable number.', async () => {
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BN(await tokenMath.divdrup(
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decimal2_18.toString(),
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decimal6_18.toString(),
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)).should.be.bignumber.equal(new BN('333333333333333334'));
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BN(await tokenMath.divdrupInt(
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decimal2_18.toString(),
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decimal6_18.toString(),
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)).should.be.bignumber.equal(new BN('333333333333333334'));
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BN(await tokenMath.divdrupInt(
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decimal2_18.mul(minus1).toString(),
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decimal6_18.toString(),
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)).should.be.bignumber.equal((new BN('333333333333333334')).mul(minus1));
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});
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});

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