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Add 512bits add and mult operations (#5035)

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This commit is contained in:
Hadrien Croubois
2025-02-26 11:04:14 +01:00
committed by GitHub
parent 2ed8956992
commit f999ba42a1
5 changed files with 372 additions and 195 deletions
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5
.changeset/blue-nails-give.md Normal file
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@ -0,0 +1,5 @@
---
'openzeppelin-solidity': minor
---
`Math`: Add `add512`, `mul512` and `mulShr`.

82
contracts/utils/math/Math.sol
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@ -17,6 +17,34 @@ library Math {
Expand // Away from zero Expand // Away from zero
} }
/**
* @dev Return the 512-bit addition of two uint256.
*
* The result is stored in two 256 variables such that sum = high * 2²⁵⁶ + low.
*/
function add512(uint256 a, uint256 b) internal pure returns (uint256 high, uint256 low) {
assembly ("memory-safe") {
low := add(a, b)
high := lt(low, a)
}
}
/**
* @dev Return the 512-bit multiplication of two uint256.
*
* The result is stored in two 256 variables such that product = high * 2²⁵⁶ + low.
*/
function mul512(uint256 a, uint256 b) internal pure returns (uint256 high, uint256 low) {
// 512-bit multiply [high low] = x * y. Compute the product mod 2²⁵⁶ and mod 2²⁵⁶ - 1, then use
// the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
// variables such that product = high * 2²⁵⁶ + low.
assembly ("memory-safe") {
let mm := mulmod(a, b, not(0))
low := mul(a, b)
high := sub(sub(mm, low), lt(mm, low))
}
}
/** /**
* @dev Returns the addition of two unsigned integers, with an success flag (no overflow). * @dev Returns the addition of two unsigned integers, with an success flag (no overflow).
*/ */
@ -143,26 +171,18 @@ library Math {
*/ */
function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) { function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {
unchecked { unchecked {
// 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2²⁵⁶ and mod 2²⁵⁶ - 1, then use (uint256 high, uint256 low) = mul512(x, y);
// the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
// variables such that product = prod1 * 2²⁵⁶ + prod0.
uint256 prod0 = x * y; // Least significant 256 bits of the product
uint256 prod1; // Most significant 256 bits of the product
assembly {
let mm := mulmod(x, y, not(0))
prod1 := sub(sub(mm, prod0), lt(mm, prod0))
}
// Handle non-overflow cases, 256 by 256 division. // Handle non-overflow cases, 256 by 256 division.
if (prod1 == 0) { if (high == 0) {
// Solidity will revert if denominator == 0, unlike the div opcode on its own. // Solidity will revert if denominator == 0, unlike the div opcode on its own.
// The surrounding unchecked block does not change this fact. // The surrounding unchecked block does not change this fact.
// See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic. // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.
return prod0 / denominator; return low / denominator;
} }
// Make sure the result is less than 2²⁵⁶. Also prevents denominator == 0. // Make sure the result is less than 2²⁵⁶. Also prevents denominator == 0.
if (denominator <= prod1) { if (denominator <= high) {
Panic.panic(ternary(denominator == 0, Panic.DIVISION_BY_ZERO, Panic.UNDER_OVERFLOW)); Panic.panic(ternary(denominator == 0, Panic.DIVISION_BY_ZERO, Panic.UNDER_OVERFLOW));
} }
@ -170,15 +190,15 @@ library Math {
// 512 by 256 division. // 512 by 256 division.
/////////////////////////////////////////////// ///////////////////////////////////////////////
// Make division exact by subtracting the remainder from [prod1 prod0]. // Make division exact by subtracting the remainder from [high low].
uint256 remainder; uint256 remainder;
assembly { assembly {
// Compute remainder using mulmod. // Compute remainder using mulmod.
remainder := mulmod(x, y, denominator) remainder := mulmod(x, y, denominator)
// Subtract 256 bit number from 512 bit number. // Subtract 256 bit number from 512 bit number.
prod1 := sub(prod1, gt(remainder, prod0)) high := sub(high, gt(remainder, low))
prod0 := sub(prod0, remainder) low := sub(low, remainder)
} }
// Factor powers of two out of denominator and compute largest power of two divisor of denominator. // Factor powers of two out of denominator and compute largest power of two divisor of denominator.
@ -189,15 +209,15 @@ library Math {
// Divide denominator by twos. // Divide denominator by twos.
denominator := div(denominator, twos) denominator := div(denominator, twos)
// Divide [prod1 prod0] by twos. // Divide [high low] by twos.
prod0 := div(prod0, twos) low := div(low, twos)
// Flip twos such that it is 2²⁵⁶ / twos. If twos is zero, then it becomes one. // Flip twos such that it is 2²⁵⁶ / twos. If twos is zero, then it becomes one.
twos := add(div(sub(0, twos), twos), 1) twos := add(div(sub(0, twos), twos), 1)
} }
// Shift in bits from prod1 into prod0. // Shift in bits from high into low.
prod0 |= prod1 * twos; low |= high * twos;
// Invert denominator mod 2²⁵⁶. Now that denominator is an odd number, it has an inverse modulo 2²⁵⁶ such // Invert denominator mod 2²⁵⁶. Now that denominator is an odd number, it has an inverse modulo 2²⁵⁶ such
// that denominator * inv ≡ 1 mod 2²⁵⁶. Compute the inverse by starting with a seed that is correct for // that denominator * inv ≡ 1 mod 2²⁵⁶. Compute the inverse by starting with a seed that is correct for
@ -215,9 +235,9 @@ library Math {
// Because the division is now exact we can divide by multiplying with the modular inverse of denominator. // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
// This will give us the correct result modulo 2²⁵⁶. Since the preconditions guarantee that the outcome is // This will give us the correct result modulo 2²⁵⁶. Since the preconditions guarantee that the outcome is
// less than 2²⁵⁶, this is the final result. We don't need to compute the high bits of the result and prod1 // less than 2²⁵⁶, this is the final result. We don't need to compute the high bits of the result and high
// is no longer required. // is no longer required.
result = prod0 * inverse; result = low * inverse;
return result; return result;
} }
} }
@ -229,6 +249,26 @@ library Math {
return mulDiv(x, y, denominator) + SafeCast.toUint(unsignedRoundsUp(rounding) && mulmod(x, y, denominator) > 0); return mulDiv(x, y, denominator) + SafeCast.toUint(unsignedRoundsUp(rounding) && mulmod(x, y, denominator) > 0);
} }
/**
* @dev Calculates floor(x * y >> n) with full precision. Throws if result overflows a uint256.
*/
function mulShr(uint256 x, uint256 y, uint8 n) internal pure returns (uint256 result) {
unchecked {
(uint256 high, uint256 low) = mul512(x, y);
if (high >= 1 << n) {
Panic.panic(Panic.UNDER_OVERFLOW);
}
return (high << (256 - n)) | (low >> n);
}
}
/**
* @dev Calculates x * y >> n with full precision, following the selected rounding direction.
*/
function mulShr(uint256 x, uint256 y, uint8 n, Rounding rounding) internal pure returns (uint256) {
return mulShr(x, y, n) + SafeCast.toUint(unsignedRoundsUp(rounding) && mulmod(x, y, 1 << n) > 0);
}
/** /**
* @dev Calculate the modular multiplicative inverse of a number in Z/nZ. * @dev Calculate the modular multiplicative inverse of a number in Z/nZ.
* *

12
test/helpers/enums.js
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@ -1,12 +1,14 @@
function Enum(...options) { const { ethers } = require('ethers');
return Object.fromEntries(options.map((key, i) => [key, BigInt(i)]));
} const Enum = (...options) => Object.fromEntries(options.map((key, i) => [key, BigInt(i)]));
const EnumTyped = (...options) => Object.fromEntries(options.map((key, i) => [key, ethers.Typed.uint8(i)]));
module.exports = { module.exports = {
Enum, Enum,
EnumTyped,
ProposalState: Enum('Pending', 'Active', 'Canceled', 'Defeated', 'Succeeded', 'Queued', 'Expired', 'Executed'), ProposalState: Enum('Pending', 'Active', 'Canceled', 'Defeated', 'Succeeded', 'Queued', 'Expired', 'Executed'),
VoteType: Object.assign(Enum('Against', 'For', 'Abstain'), { Parameters: 255n }), VoteType: Object.assign(Enum('Against', 'For', 'Abstain'), { Parameters: 255n }),
Rounding: Enum('Floor', 'Ceil', 'Trunc', 'Expand'), Rounding: EnumTyped('Floor', 'Ceil', 'Trunc', 'Expand'),
OperationState: Enum('Unset', 'Waiting', 'Ready', 'Done'), OperationState: Enum('Unset', 'Waiting', 'Ready', 'Done'),
RevertType: Enum('None', 'RevertWithoutMessage', 'RevertWithMessage', 'RevertWithCustomError', 'Panic'), RevertType: EnumTyped('None', 'RevertWithoutMessage', 'RevertWithMessage', 'RevertWithCustomError', 'Panic'),
}; };

79
test/utils/math/Math.t.sol
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@ -11,6 +11,48 @@ contract MathTest is Test {
assertEq(Math.ternary(f, a, b), f ? a : b); assertEq(Math.ternary(f, a, b), f ? a : b);
} }
// ADD512 & MUL512
function testAdd512(uint256 a, uint256 b) public pure {
(uint256 high, uint256 low) = Math.add512(a, b);
// test against tryAdd
(bool success, uint256 result) = Math.tryAdd(a, b);
if (success) {
assertEq(high, 0);
assertEq(low, result);
} else {
assertEq(high, 1);
}
// test against unchecked
unchecked {
assertEq(low, a + b); // unchecked allow overflow
}
}
function testMul512(uint256 a, uint256 b) public pure {
(uint256 high, uint256 low) = Math.mul512(a, b);
// test against tryMul
(bool success, uint256 result) = Math.tryMul(a, b);
if (success) {
assertEq(high, 0);
assertEq(low, result);
} else {
assertGt(high, 0);
}
// test against unchecked
unchecked {
assertEq(low, a * b); // unchecked allow overflow
}
// test against alternative method
(uint256 _high, uint256 _low) = _mulKaratsuba(a, b);
assertEq(high, _high);
assertEq(low, _low);
}
// MIN & MAX // MIN & MAX
function testSymbolicMinMax(uint256 a, uint256 b) public pure { function testSymbolicMinMax(uint256 a, uint256 b) public pure {
assertEq(Math.min(a, b), a < b ? a : b); assertEq(Math.min(a, b), a < b ? a : b);
@ -184,7 +226,7 @@ contract MathTest is Test {
// MULDIV // MULDIV
function testMulDiv(uint256 x, uint256 y, uint256 d) public pure { function testMulDiv(uint256 x, uint256 y, uint256 d) public pure {
// Full precision for x * y // Full precision for x * y
(uint256 xyHi, uint256 xyLo) = _mulHighLow(x, y); (uint256 xyHi, uint256 xyLo) = Math.mul512(x, y);
// Assume result won't overflow (see {testMulDivDomain}) // Assume result won't overflow (see {testMulDivDomain})
// This also checks that `d` is positive // This also checks that `d` is positive
@ -194,9 +236,9 @@ contract MathTest is Test {
uint256 q = Math.mulDiv(x, y, d); uint256 q = Math.mulDiv(x, y, d);
// Full precision for q * d // Full precision for q * d
(uint256 qdHi, uint256 qdLo) = _mulHighLow(q, d); (uint256 qdHi, uint256 qdLo) = Math.mul512(q, d);
// Add remainder of x * y / d (computed as rem = (x * y % d)) // Add remainder of x * y / d (computed as rem = (x * y % d))
(uint256 qdRemLo, uint256 c) = _addCarry(qdLo, mulmod(x, y, d)); (uint256 c, uint256 qdRemLo) = Math.add512(qdLo, mulmod(x, y, d));
uint256 qdRemHi = qdHi + c; uint256 qdRemHi = qdHi + c;
// Full precision check that x * y = q * d + rem // Full precision check that x * y = q * d + rem
@ -206,7 +248,7 @@ contract MathTest is Test {
/// forge-config: default.allow_internal_expect_revert = true /// forge-config: default.allow_internal_expect_revert = true
function testMulDivDomain(uint256 x, uint256 y, uint256 d) public { function testMulDivDomain(uint256 x, uint256 y, uint256 d) public {
(uint256 xyHi, ) = _mulHighLow(x, y); (uint256 xyHi, ) = Math.mul512(x, y);
// Violate {testMulDiv} assumption (covers d is 0 and result overflow) // Violate {testMulDiv} assumption (covers d is 0 and result overflow)
vm.assume(xyHi >= d); vm.assume(xyHi >= d);
@ -266,26 +308,13 @@ contract MathTest is Test {
} }
} }
function _nativeModExp(uint256 b, uint256 e, uint256 m) private pure returns (uint256) {
if (m == 1) return 0;
uint256 r = 1;
while (e > 0) {
if (e % 2 > 0) {
r = mulmod(r, b, m);
}
b = mulmod(b, b, m);
e >>= 1;
}
return r;
}
// Helpers // Helpers
function _asRounding(uint8 r) private pure returns (Math.Rounding) { function _asRounding(uint8 r) private pure returns (Math.Rounding) {
vm.assume(r < uint8(type(Math.Rounding).max)); vm.assume(r < uint8(type(Math.Rounding).max));
return Math.Rounding(r); return Math.Rounding(r);
} }
function _mulHighLow(uint256 x, uint256 y) private pure returns (uint256 high, uint256 low) { function _mulKaratsuba(uint256 x, uint256 y) private pure returns (uint256 high, uint256 low) {
(uint256 x0, uint256 x1) = (x & type(uint128).max, x >> 128); (uint256 x0, uint256 x1) = (x & type(uint128).max, x >> 128);
(uint256 y0, uint256 y1) = (y & type(uint128).max, y >> 128); (uint256 y0, uint256 y1) = (y & type(uint128).max, y >> 128);
@ -305,10 +334,16 @@ contract MathTest is Test {
} }
} }
function _addCarry(uint256 x, uint256 y) private pure returns (uint256 res, uint256 carry) { function _nativeModExp(uint256 b, uint256 e, uint256 m) private pure returns (uint256) {
unchecked { if (m == 1) return 0;
res = x + y; uint256 r = 1;
while (e > 0) {
if (e % 2 > 0) {
r = mulmod(r, b, m);
} }
carry = res < x ? 1 : 0; b = mulmod(b, b, m);
e >>= 1;
}
return r;
} }
} }

389
test/utils/math/Math.test.js
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@ -16,10 +16,13 @@ const uint256 = value => ethers.Typed.uint256(value);
bytes.zero = '0x'; bytes.zero = '0x';
uint256.zero = 0n; uint256.zero = 0n;
async function testCommutative(fn, lhs, rhs, expected, ...extra) { const testCommutative = (fn, lhs, rhs, expected, ...extra) =>
expect(await fn(lhs, rhs, ...extra)).to.deep.equal(expected); Promise.all([
expect(await fn(rhs, lhs, ...extra)).to.deep.equal(expected); expect(fn(lhs, rhs, ...extra)).to.eventually.deep.equal(expected),
} expect(fn(rhs, lhs, ...extra)).to.eventually.deep.equal(expected),
]);
const splitHighLow = n => [n / (1n << 256n), n % (1n << 256n)];
async function fixture() { async function fixture() {
const mock = await ethers.deployContract('$Math'); const mock = await ethers.deployContract('$Math');
@ -39,6 +42,24 @@ describe('Math', function () {
Object.assign(this, await loadFixture(fixture)); Object.assign(this, await loadFixture(fixture));
}); });
describe('add512', function () {
it('adds correctly without reverting', async function () {
const values = [0n, 1n, 17n, 42n, ethers.MaxUint256 - 1n, ethers.MaxUint256];
for (const [a, b] of product(values, values)) {
await expect(this.mock.$add512(a, b)).to.eventually.deep.equal(splitHighLow(a + b));
}
});
});
describe('mul512', function () {
it('multiplies correctly without reverting', async function () {
const values = [0n, 1n, 17n, 42n, ethers.MaxUint256 - 1n, ethers.MaxUint256];
for (const [a, b] of product(values, values)) {
await expect(this.mock.$mul512(a, b)).to.eventually.deep.equal(splitHighLow(a * b));
}
});
});
describe('tryAdd', function () { describe('tryAdd', function () {
it('adds correctly', async function () { it('adds correctly', async function () {
const a = 5678n; const a = 5678n;
@ -57,13 +78,13 @@ describe('Math', function () {
it('subtracts correctly', async function () { it('subtracts correctly', async function () {
const a = 5678n; const a = 5678n;
const b = 1234n; const b = 1234n;
expect(await this.mock.$trySub(a, b)).to.deep.equal([true, a - b]); await expect(this.mock.$trySub(a, b)).to.eventually.deep.equal([true, a - b]);
}); });
it('reverts if subtraction result would be negative', async function () { it('reverts if subtraction result would be negative', async function () {
const a = 1234n; const a = 1234n;
const b = 5678n; const b = 5678n;
expect(await this.mock.$trySub(a, b)).to.deep.equal([false, 0n]); await expect(this.mock.$trySub(a, b)).to.eventually.deep.equal([false, 0n]);
}); });
}); });
@ -91,25 +112,25 @@ describe('Math', function () {
it('divides correctly', async function () { it('divides correctly', async function () {
const a = 5678n; const a = 5678n;
const b = 5678n; const b = 5678n;
expect(await this.mock.$tryDiv(a, b)).to.deep.equal([true, a / b]); await expect(this.mock.$tryDiv(a, b)).to.eventually.deep.equal([true, a / b]);
}); });
it('divides zero correctly', async function () { it('divides zero correctly', async function () {
const a = 0n; const a = 0n;
const b = 5678n; const b = 5678n;
expect(await this.mock.$tryDiv(a, b)).to.deep.equal([true, a / b]); await expect(this.mock.$tryDiv(a, b)).to.eventually.deep.equal([true, a / b]);
}); });
it('returns complete number result on non-even division', async function () { it('returns complete number result on non-even division', async function () {
const a = 7000n; const a = 7000n;
const b = 5678n; const b = 5678n;
expect(await this.mock.$tryDiv(a, b)).to.deep.equal([true, a / b]); await expect(this.mock.$tryDiv(a, b)).to.eventually.deep.equal([true, a / b]);
}); });
it('reverts on division by zero', async function () { it('reverts on division by zero', async function () {
const a = 5678n; const a = 5678n;
const b = 0n; const b = 0n;
expect(await this.mock.$tryDiv(a, b)).to.deep.equal([false, 0n]); await expect(this.mock.$tryDiv(a, b)).to.eventually.deep.equal([false, 0n]);
}); });
}); });
@ -118,32 +139,32 @@ describe('Math', function () {
it('when the dividend is smaller than the divisor', async function () { it('when the dividend is smaller than the divisor', async function () {
const a = 284n; const a = 284n;
const b = 5678n; const b = 5678n;
expect(await this.mock.$tryMod(a, b)).to.deep.equal([true, a % b]); await expect(this.mock.$tryMod(a, b)).to.eventually.deep.equal([true, a % b]);
}); });
it('when the dividend is equal to the divisor', async function () { it('when the dividend is equal to the divisor', async function () {
const a = 5678n; const a = 5678n;
const b = 5678n; const b = 5678n;
expect(await this.mock.$tryMod(a, b)).to.deep.equal([true, a % b]); await expect(this.mock.$tryMod(a, b)).to.eventually.deep.equal([true, a % b]);
}); });
it('when the dividend is larger than the divisor', async function () { it('when the dividend is larger than the divisor', async function () {
const a = 7000n; const a = 7000n;
const b = 5678n; const b = 5678n;
expect(await this.mock.$tryMod(a, b)).to.deep.equal([true, a % b]); await expect(this.mock.$tryMod(a, b)).to.eventually.deep.equal([true, a % b]);
}); });
it('when the dividend is a multiple of the divisor', async function () { it('when the dividend is a multiple of the divisor', async function () {
const a = 17034n; // 17034 == 5678 * 3 const a = 17034n; // 17034 == 5678 * 3
const b = 5678n; const b = 5678n;
expect(await this.mock.$tryMod(a, b)).to.deep.equal([true, a % b]); await expect(this.mock.$tryMod(a, b)).to.eventually.deep.equal([true, a % b]);
}); });
}); });
it('reverts with a 0 divisor', async function () { it('reverts with a 0 divisor', async function () {
const a = 5678n; const a = 5678n;
const b = 0n; const b = 0n;
expect(await this.mock.$tryMod(a, b)).to.deep.equal([false, 0n]); await expect(this.mock.$tryMod(a, b)).to.eventually.deep.equal([false, 0n]);
}); });
}); });
@ -163,24 +184,24 @@ describe('Math', function () {
it('is correctly calculated with two odd numbers', async function () { it('is correctly calculated with two odd numbers', async function () {
const a = 57417n; const a = 57417n;
const b = 95431n; const b = 95431n;
expect(await this.mock.$average(a, b)).to.equal((a + b) / 2n); await expect(this.mock.$average(a, b)).to.eventually.equal((a + b) / 2n);
}); });
it('is correctly calculated with two even numbers', async function () { it('is correctly calculated with two even numbers', async function () {
const a = 42304n; const a = 42304n;
const b = 84346n; const b = 84346n;
expect(await this.mock.$average(a, b)).to.equal((a + b) / 2n); await expect(this.mock.$average(a, b)).to.eventually.equal((a + b) / 2n);
}); });
it('is correctly calculated with one even and one odd number', async function () { it('is correctly calculated with one even and one odd number', async function () {
const a = 57417n; const a = 57417n;
const b = 84346n; const b = 84346n;
expect(await this.mock.$average(a, b)).to.equal((a + b) / 2n); await expect(this.mock.$average(a, b)).to.eventually.equal((a + b) / 2n);
}); });
it('is correctly calculated with two max uint256 numbers', async function () { it('is correctly calculated with two max uint256 numbers', async function () {
const a = ethers.MaxUint256; const a = ethers.MaxUint256;
expect(await this.mock.$average(a, a)).to.equal(a); await expect(this.mock.$average(a, a)).to.eventually.equal(a);
}); });
}); });
@ -196,35 +217,35 @@ describe('Math', function () {
const a = 0n; const a = 0n;
const b = 2n; const b = 2n;
const r = 0n; const r = 0n;
expect(await this.mock.$ceilDiv(a, b)).to.equal(r); await expect(this.mock.$ceilDiv(a, b)).to.eventually.equal(r);
}); });
it('does not round up on exact division', async function () { it('does not round up on exact division', async function () {
const a = 10n; const a = 10n;
const b = 5n; const b = 5n;
const r = 2n; const r = 2n;
expect(await this.mock.$ceilDiv(a, b)).to.equal(r); await expect(this.mock.$ceilDiv(a, b)).to.eventually.equal(r);
}); });
it('rounds up on division with remainders', async function () { it('rounds up on division with remainders', async function () {
const a = 42n; const a = 42n;
const b = 13n; const b = 13n;
const r = 4n; const r = 4n;
expect(await this.mock.$ceilDiv(a, b)).to.equal(r); await expect(this.mock.$ceilDiv(a, b)).to.eventually.equal(r);
}); });
it('does not overflow', async function () { it('does not overflow', async function () {
const a = ethers.MaxUint256; const a = ethers.MaxUint256;
const b = 2n; const b = 2n;
const r = 1n << 255n; const r = 1n << 255n;
expect(await this.mock.$ceilDiv(a, b)).to.equal(r); await expect(this.mock.$ceilDiv(a, b)).to.eventually.equal(r);
}); });
it('correctly computes max uint256 divided by 1', async function () { it('correctly computes max uint256 divided by 1', async function () {
const a = ethers.MaxUint256; const a = ethers.MaxUint256;
const b = 1n; const b = 1n;
const r = ethers.MaxUint256; const r = ethers.MaxUint256;
expect(await this.mock.$ceilDiv(a, b)).to.equal(r); await expect(this.mock.$ceilDiv(a, b)).to.eventually.equal(r);
}); });
}); });
@ -248,28 +269,97 @@ describe('Math', function () {
describe('does round down', function () { describe('does round down', function () {
it('small values', async function () { it('small values', async function () {
for (const rounding of RoundingDown) { for (const rounding of RoundingDown) {
expect(await this.mock.$mulDiv(3n, 4n, 5n, rounding)).to.equal(2n); await expect(this.mock.$mulDiv(3n, 4n, 5n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$mulDiv(3n, 5n, 5n, rounding)).to.equal(3n); await expect(this.mock.$mulDiv(3n, 5n, 5n, rounding)).to.eventually.equal(3n);
} }
}); });
it('large values', async function () { it('large values', async function () {
for (const rounding of RoundingDown) { for (const rounding of RoundingDown) {
expect(await this.mock.$mulDiv(42n, ethers.MaxUint256 - 1n, ethers.MaxUint256, rounding)).to.equal(41n); await expect(this.mock.$mulDiv(42n, ethers.MaxUint256 - 1n, ethers.MaxUint256, rounding)).to.eventually.equal(
41n,
);
expect(await this.mock.$mulDiv(17n, ethers.MaxUint256, ethers.MaxUint256, rounding)).to.equal(17n); await expect(this.mock.$mulDiv(17n, ethers.MaxUint256, ethers.MaxUint256, rounding)).to.eventually.equal(17n);
expect( await expect(
await this.mock.$mulDiv(ethers.MaxUint256 - 1n, ethers.MaxUint256 - 1n, ethers.MaxUint256, rounding), this.mock.$mulDiv(ethers.MaxUint256 - 1n, ethers.MaxUint256 - 1n, ethers.MaxUint256, rounding),
).to.equal(ethers.MaxUint256 - 2n); ).to.eventually.equal(ethers.MaxUint256 - 2n);
expect( await expect(
await this.mock.$mulDiv(ethers.MaxUint256, ethers.MaxUint256 - 1n, ethers.MaxUint256, rounding), this.mock.$mulDiv(ethers.MaxUint256, ethers.MaxUint256 - 1n, ethers.MaxUint256, rounding),
).to.equal(ethers.MaxUint256 - 1n); ).to.eventually.equal(ethers.MaxUint256 - 1n);
expect(await this.mock.$mulDiv(ethers.MaxUint256, ethers.MaxUint256, ethers.MaxUint256, rounding)).to.equal( await expect(
this.mock.$mulDiv(ethers.MaxUint256, ethers.MaxUint256, ethers.MaxUint256, rounding),
).to.eventually.equal(ethers.MaxUint256);
}
});
});
describe('does round up', function () {
it('small values', async function () {
for (const rounding of RoundingUp) {
await expect(this.mock.$mulDiv(3n, 4n, 5n, rounding)).to.eventually.equal(3n);
await expect(this.mock.$mulDiv(3n, 5n, 5n, rounding)).to.eventually.equal(3n);
}
});
it('large values', async function () {
for (const rounding of RoundingUp) {
await expect(this.mock.$mulDiv(42n, ethers.MaxUint256 - 1n, ethers.MaxUint256, rounding)).to.eventually.equal(
42n,
);
await expect(this.mock.$mulDiv(17n, ethers.MaxUint256, ethers.MaxUint256, rounding)).to.eventually.equal(17n);
await expect(
this.mock.$mulDiv(ethers.MaxUint256 - 1n, ethers.MaxUint256 - 1n, ethers.MaxUint256, rounding),
).to.eventually.equal(ethers.MaxUint256 - 1n);
await expect(
this.mock.$mulDiv(ethers.MaxUint256, ethers.MaxUint256 - 1n, ethers.MaxUint256, rounding),
).to.eventually.equal(ethers.MaxUint256 - 1n);
await expect(
this.mock.$mulDiv(ethers.MaxUint256, ethers.MaxUint256, ethers.MaxUint256, rounding),
).to.eventually.equal(ethers.MaxUint256);
}
});
});
});
describe('mulShr', function () {
it('reverts with result higher than 2 ^ 256', async function () {
const a = 5n;
const b = ethers.MaxUint256;
const c = 1n;
await expect(this.mock.$mulShr(a, b, c, Rounding.Floor)).to.be.revertedWithPanic(
PANIC_CODES.ARITHMETIC_UNDER_OR_OVERFLOW,
);
});
describe('does round down', function () {
it('small values', async function () {
for (const rounding of RoundingDown) {
await expect(this.mock.$mulShr(3n, 5n, 1n, rounding)).to.eventually.equal(7n);
await expect(this.mock.$mulShr(3n, 5n, 2n, rounding)).to.eventually.equal(3n);
}
});
it('large values', async function () {
for (const rounding of RoundingDown) {
await expect(this.mock.$mulShr(42n, ethers.MaxUint256, 255n, rounding)).to.eventually.equal(83n);
await expect(this.mock.$mulShr(17n, ethers.MaxUint256, 255n, rounding)).to.eventually.equal(33n);
await expect(this.mock.$mulShr(ethers.MaxUint256, ethers.MaxInt256 + 1n, 255n, rounding)).to.eventually.equal(
ethers.MaxUint256, ethers.MaxUint256,
); );
await expect(this.mock.$mulShr(ethers.MaxUint256, ethers.MaxInt256, 255n, rounding)).to.eventually.equal(
ethers.MaxUint256 - 2n,
);
} }
}); });
}); });
@ -277,28 +367,24 @@ describe('Math', function () {
describe('does round up', function () { describe('does round up', function () {
it('small values', async function () { it('small values', async function () {
for (const rounding of RoundingUp) { for (const rounding of RoundingUp) {
expect(await this.mock.$mulDiv(3n, 4n, 5n, rounding)).to.equal(3n); await expect(this.mock.$mulShr(3n, 5n, 1n, rounding)).to.eventually.equal(8n);
expect(await this.mock.$mulDiv(3n, 5n, 5n, rounding)).to.equal(3n); await expect(this.mock.$mulShr(3n, 5n, 2n, rounding)).to.eventually.equal(4n);
} }
}); });
it('large values', async function () { it('large values', async function () {
for (const rounding of RoundingUp) { for (const rounding of RoundingUp) {
expect(await this.mock.$mulDiv(42n, ethers.MaxUint256 - 1n, ethers.MaxUint256, rounding)).to.equal(42n); await expect(this.mock.$mulShr(42n, ethers.MaxUint256, 255n, rounding)).to.eventually.equal(84n);
expect(await this.mock.$mulDiv(17n, ethers.MaxUint256, ethers.MaxUint256, rounding)).to.equal(17n); await expect(this.mock.$mulShr(17n, ethers.MaxUint256, 255n, rounding)).to.eventually.equal(34n);
expect( await expect(this.mock.$mulShr(ethers.MaxUint256, ethers.MaxInt256 + 1n, 255n, rounding)).to.eventually.equal(
await this.mock.$mulDiv(ethers.MaxUint256 - 1n, ethers.MaxUint256 - 1n, ethers.MaxUint256, rounding),
).to.equal(ethers.MaxUint256 - 1n);
expect(
await this.mock.$mulDiv(ethers.MaxUint256, ethers.MaxUint256 - 1n, ethers.MaxUint256, rounding),
).to.equal(ethers.MaxUint256 - 1n);
expect(await this.mock.$mulDiv(ethers.MaxUint256, ethers.MaxUint256, ethers.MaxUint256, rounding)).to.equal(
ethers.MaxUint256, ethers.MaxUint256,
); );
await expect(this.mock.$mulShr(ethers.MaxUint256, ethers.MaxInt256, 255n, rounding)).to.eventually.equal(
ethers.MaxUint256 - 1n,
);
} }
}); });
}); });
@ -320,8 +406,8 @@ describe('Math', function () {
describe(`using p=${p} which is ${p > 1 && factors.length > 1 ? 'not ' : ''}a prime`, function () { describe(`using p=${p} which is ${p > 1 && factors.length > 1 ? 'not ' : ''}a prime`, function () {
it('trying to inverse 0 returns 0', async function () { it('trying to inverse 0 returns 0', async function () {
expect(await this.mock.$invMod(0, p)).to.equal(0n); await expect(this.mock.$invMod(0, p)).to.eventually.equal(0n);
expect(await this.mock.$invMod(p, p)).to.equal(0n); // p is 0 mod p await expect(this.mock.$invMod(p, p)).to.eventually.equal(0n); // p is 0 mod p
}); });
if (p != 0) { if (p != 0) {
@ -349,7 +435,7 @@ describe('Math', function () {
const e = 200n; const e = 200n;
const m = 50n; const m = 50n;
expect(await this.mock.$modExp(type(b), type(e), type(m))).to.equal(type(b ** e % m).value); await expect(this.mock.$modExp(type(b), type(e), type(m))).to.eventually.equal(type(b ** e % m).value);
}); });
it('is correctly reverting when modulus is zero', async function () { it('is correctly reverting when modulus is zero', async function () {
@ -373,7 +459,9 @@ describe('Math', function () {
it(`calculates b ** e % m (b=2**${log2b}+1) (e=2**${log2e}+1) (m=2**${log2m}+1)`, async function () { it(`calculates b ** e % m (b=2**${log2b}+1) (e=2**${log2e}+1) (m=2**${log2m}+1)`, async function () {
const mLength = ethers.dataLength(ethers.toBeHex(m)); const mLength = ethers.dataLength(ethers.toBeHex(m));
expect(await this.mock.$modExp(bytes(b), bytes(e), bytes(m))).to.equal(bytes(modExp(b, e, m), mLength).value); await expect(this.mock.$modExp(bytes(b), bytes(e), bytes(m))).to.eventually.equal(
bytes(modExp(b, e, m), mLength).value,
);
}); });
} }
}); });
@ -387,7 +475,10 @@ describe('Math', function () {
const e = 200n; const e = 200n;
const m = 50n; const m = 50n;
expect(await this.mock.$tryModExp(type(b), type(e), type(m))).to.deep.equal([true, type(b ** e % m).value]); await expect(this.mock.$tryModExp(type(b), type(e), type(m))).to.eventually.deep.equal([
true,
type(b ** e % m).value,
]);
}); });
it('is correctly reverting when modulus is zero', async function () { it('is correctly reverting when modulus is zero', async function () {
@ -395,7 +486,7 @@ describe('Math', function () {
const e = 200n; const e = 200n;
const m = 0n; const m = 0n;
expect(await this.mock.$tryModExp(type(b), type(e), type(m))).to.deep.equal([false, type.zero]); await expect(this.mock.$tryModExp(type(b), type(e), type(m))).to.eventually.deep.equal([false, type.zero]);
}); });
}); });
} }
@ -409,7 +500,7 @@ describe('Math', function () {
it(`calculates b ** e % m (b=2**${log2b}+1) (e=2**${log2e}+1) (m=2**${log2m}+1)`, async function () { it(`calculates b ** e % m (b=2**${log2b}+1) (e=2**${log2e}+1) (m=2**${log2m}+1)`, async function () {
const mLength = ethers.dataLength(ethers.toBeHex(m)); const mLength = ethers.dataLength(ethers.toBeHex(m));
expect(await this.mock.$tryModExp(bytes(b), bytes(e), bytes(m))).to.deep.equal([ await expect(this.mock.$tryModExp(bytes(b), bytes(e), bytes(m))).to.eventually.deep.equal([
true, true,
bytes(modExp(b, e, m), mLength).value, bytes(modExp(b, e, m), mLength).value,
]); ]);
@ -421,35 +512,39 @@ describe('Math', function () {
describe('sqrt', function () { describe('sqrt', function () {
it('rounds down', async function () { it('rounds down', async function () {
for (const rounding of RoundingDown) { for (const rounding of RoundingDown) {
expect(await this.mock.$sqrt(0n, rounding)).to.equal(0n); await expect(this.mock.$sqrt(0n, rounding)).to.eventually.equal(0n);
expect(await this.mock.$sqrt(1n, rounding)).to.equal(1n); await expect(this.mock.$sqrt(1n, rounding)).to.eventually.equal(1n);
expect(await this.mock.$sqrt(2n, rounding)).to.equal(1n); await expect(this.mock.$sqrt(2n, rounding)).to.eventually.equal(1n);
expect(await this.mock.$sqrt(3n, rounding)).to.equal(1n); await expect(this.mock.$sqrt(3n, rounding)).to.eventually.equal(1n);
expect(await this.mock.$sqrt(4n, rounding)).to.equal(2n); await expect(this.mock.$sqrt(4n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$sqrt(144n, rounding)).to.equal(12n); await expect(this.mock.$sqrt(144n, rounding)).to.eventually.equal(12n);
expect(await this.mock.$sqrt(999999n, rounding)).to.equal(999n); await expect(this.mock.$sqrt(999999n, rounding)).to.eventually.equal(999n);
expect(await this.mock.$sqrt(1000000n, rounding)).to.equal(1000n); await expect(this.mock.$sqrt(1000000n, rounding)).to.eventually.equal(1000n);
expect(await this.mock.$sqrt(1000001n, rounding)).to.equal(1000n); await expect(this.mock.$sqrt(1000001n, rounding)).to.eventually.equal(1000n);
expect(await this.mock.$sqrt(1002000n, rounding)).to.equal(1000n); await expect(this.mock.$sqrt(1002000n, rounding)).to.eventually.equal(1000n);
expect(await this.mock.$sqrt(1002001n, rounding)).to.equal(1001n); await expect(this.mock.$sqrt(1002001n, rounding)).to.eventually.equal(1001n);
expect(await this.mock.$sqrt(ethers.MaxUint256, rounding)).to.equal(340282366920938463463374607431768211455n); await expect(this.mock.$sqrt(ethers.MaxUint256, rounding)).to.eventually.equal(
340282366920938463463374607431768211455n,
);
} }
}); });
it('rounds up', async function () { it('rounds up', async function () {
for (const rounding of RoundingUp) { for (const rounding of RoundingUp) {
expect(await this.mock.$sqrt(0n, rounding)).to.equal(0n); await expect(this.mock.$sqrt(0n, rounding)).to.eventually.equal(0n);
expect(await this.mock.$sqrt(1n, rounding)).to.equal(1n); await expect(this.mock.$sqrt(1n, rounding)).to.eventually.equal(1n);
expect(await this.mock.$sqrt(2n, rounding)).to.equal(2n); await expect(this.mock.$sqrt(2n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$sqrt(3n, rounding)).to.equal(2n); await expect(this.mock.$sqrt(3n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$sqrt(4n, rounding)).to.equal(2n); await expect(this.mock.$sqrt(4n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$sqrt(144n, rounding)).to.equal(12n); await expect(this.mock.$sqrt(144n, rounding)).to.eventually.equal(12n);
expect(await this.mock.$sqrt(999999n, rounding)).to.equal(1000n); await expect(this.mock.$sqrt(999999n, rounding)).to.eventually.equal(1000n);
expect(await this.mock.$sqrt(1000000n, rounding)).to.equal(1000n); await expect(this.mock.$sqrt(1000000n, rounding)).to.eventually.equal(1000n);
expect(await this.mock.$sqrt(1000001n, rounding)).to.equal(1001n); await expect(this.mock.$sqrt(1000001n, rounding)).to.eventually.equal(1001n);
expect(await this.mock.$sqrt(1002000n, rounding)).to.equal(1001n); await expect(this.mock.$sqrt(1002000n, rounding)).to.eventually.equal(1001n);
expect(await this.mock.$sqrt(1002001n, rounding)).to.equal(1001n); await expect(this.mock.$sqrt(1002001n, rounding)).to.eventually.equal(1001n);
expect(await this.mock.$sqrt(ethers.MaxUint256, rounding)).to.equal(340282366920938463463374607431768211456n); await expect(this.mock.$sqrt(ethers.MaxUint256, rounding)).to.eventually.equal(
340282366920938463463374607431768211456n,
);
} }
}); });
}); });
@ -458,33 +553,33 @@ describe('Math', function () {
describe('log2', function () { describe('log2', function () {
it('rounds down', async function () { it('rounds down', async function () {
for (const rounding of RoundingDown) { for (const rounding of RoundingDown) {
expect(await this.mock.$log2(0n, rounding)).to.equal(0n); await expect(this.mock.$log2(0n, rounding)).to.eventually.equal(0n);
expect(await this.mock.$log2(1n, rounding)).to.equal(0n); await expect(this.mock.$log2(1n, rounding)).to.eventually.equal(0n);
expect(await this.mock.$log2(2n, rounding)).to.equal(1n); await expect(this.mock.$log2(2n, rounding)).to.eventually.equal(1n);
expect(await this.mock.$log2(3n, rounding)).to.equal(1n); await expect(this.mock.$log2(3n, rounding)).to.eventually.equal(1n);
expect(await this.mock.$log2(4n, rounding)).to.equal(2n); await expect(this.mock.$log2(4n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$log2(5n, rounding)).to.equal(2n); await expect(this.mock.$log2(5n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$log2(6n, rounding)).to.equal(2n); await expect(this.mock.$log2(6n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$log2(7n, rounding)).to.equal(2n); await expect(this.mock.$log2(7n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$log2(8n, rounding)).to.equal(3n); await expect(this.mock.$log2(8n, rounding)).to.eventually.equal(3n);
expect(await this.mock.$log2(9n, rounding)).to.equal(3n); await expect(this.mock.$log2(9n, rounding)).to.eventually.equal(3n);
expect(await this.mock.$log2(ethers.MaxUint256, rounding)).to.equal(255n); await expect(this.mock.$log2(ethers.MaxUint256, rounding)).to.eventually.equal(255n);
} }
}); });
it('rounds up', async function () { it('rounds up', async function () {
for (const rounding of RoundingUp) { for (const rounding of RoundingUp) {
expect(await this.mock.$log2(0n, rounding)).to.equal(0n); await expect(this.mock.$log2(0n, rounding)).to.eventually.equal(0n);
expect(await this.mock.$log2(1n, rounding)).to.equal(0n); await expect(this.mock.$log2(1n, rounding)).to.eventually.equal(0n);
expect(await this.mock.$log2(2n, rounding)).to.equal(1n); await expect(this.mock.$log2(2n, rounding)).to.eventually.equal(1n);
expect(await this.mock.$log2(3n, rounding)).to.equal(2n); await expect(this.mock.$log2(3n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$log2(4n, rounding)).to.equal(2n); await expect(this.mock.$log2(4n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$log2(5n, rounding)).to.equal(3n); await expect(this.mock.$log2(5n, rounding)).to.eventually.equal(3n);
expect(await this.mock.$log2(6n, rounding)).to.equal(3n); await expect(this.mock.$log2(6n, rounding)).to.eventually.equal(3n);
expect(await this.mock.$log2(7n, rounding)).to.equal(3n); await expect(this.mock.$log2(7n, rounding)).to.eventually.equal(3n);
expect(await this.mock.$log2(8n, rounding)).to.equal(3n); await expect(this.mock.$log2(8n, rounding)).to.eventually.equal(3n);
expect(await this.mock.$log2(9n, rounding)).to.equal(4n); await expect(this.mock.$log2(9n, rounding)).to.eventually.equal(4n);
expect(await this.mock.$log2(ethers.MaxUint256, rounding)).to.equal(256n); await expect(this.mock.$log2(ethers.MaxUint256, rounding)).to.eventually.equal(256n);
} }
}); });
}); });
@ -492,37 +587,37 @@ describe('Math', function () {
describe('log10', function () { describe('log10', function () {
it('rounds down', async function () { it('rounds down', async function () {
for (const rounding of RoundingDown) { for (const rounding of RoundingDown) {
expect(await this.mock.$log10(0n, rounding)).to.equal(0n); await expect(this.mock.$log10(0n, rounding)).to.eventually.equal(0n);
expect(await this.mock.$log10(1n, rounding)).to.equal(0n); await expect(this.mock.$log10(1n, rounding)).to.eventually.equal(0n);
expect(await this.mock.$log10(2n, rounding)).to.equal(0n); await expect(this.mock.$log10(2n, rounding)).to.eventually.equal(0n);
expect(await this.mock.$log10(9n, rounding)).to.equal(0n); await expect(this.mock.$log10(9n, rounding)).to.eventually.equal(0n);
expect(await this.mock.$log10(10n, rounding)).to.equal(1n); await expect(this.mock.$log10(10n, rounding)).to.eventually.equal(1n);
expect(await this.mock.$log10(11n, rounding)).to.equal(1n); await expect(this.mock.$log10(11n, rounding)).to.eventually.equal(1n);
expect(await this.mock.$log10(99n, rounding)).to.equal(1n); await expect(this.mock.$log10(99n, rounding)).to.eventually.equal(1n);
expect(await this.mock.$log10(100n, rounding)).to.equal(2n); await expect(this.mock.$log10(100n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$log10(101n, rounding)).to.equal(2n); await expect(this.mock.$log10(101n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$log10(999n, rounding)).to.equal(2n); await expect(this.mock.$log10(999n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$log10(1000n, rounding)).to.equal(3n); await expect(this.mock.$log10(1000n, rounding)).to.eventually.equal(3n);
expect(await this.mock.$log10(1001n, rounding)).to.equal(3n); await expect(this.mock.$log10(1001n, rounding)).to.eventually.equal(3n);
expect(await this.mock.$log10(ethers.MaxUint256, rounding)).to.equal(77n); await expect(this.mock.$log10(ethers.MaxUint256, rounding)).to.eventually.equal(77n);
} }
}); });
it('rounds up', async function () { it('rounds up', async function () {
for (const rounding of RoundingUp) { for (const rounding of RoundingUp) {
expect(await this.mock.$log10(0n, rounding)).to.equal(0n); await expect(this.mock.$log10(0n, rounding)).to.eventually.equal(0n);
expect(await this.mock.$log10(1n, rounding)).to.equal(0n); await expect(this.mock.$log10(1n, rounding)).to.eventually.equal(0n);
expect(await this.mock.$log10(2n, rounding)).to.equal(1n); await expect(this.mock.$log10(2n, rounding)).to.eventually.equal(1n);
expect(await this.mock.$log10(9n, rounding)).to.equal(1n); await expect(this.mock.$log10(9n, rounding)).to.eventually.equal(1n);
expect(await this.mock.$log10(10n, rounding)).to.equal(1n); await expect(this.mock.$log10(10n, rounding)).to.eventually.equal(1n);
expect(await this.mock.$log10(11n, rounding)).to.equal(2n); await expect(this.mock.$log10(11n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$log10(99n, rounding)).to.equal(2n); await expect(this.mock.$log10(99n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$log10(100n, rounding)).to.equal(2n); await expect(this.mock.$log10(100n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$log10(101n, rounding)).to.equal(3n); await expect(this.mock.$log10(101n, rounding)).to.eventually.equal(3n);
expect(await this.mock.$log10(999n, rounding)).to.equal(3n); await expect(this.mock.$log10(999n, rounding)).to.eventually.equal(3n);
expect(await this.mock.$log10(1000n, rounding)).to.equal(3n); await expect(this.mock.$log10(1000n, rounding)).to.eventually.equal(3n);
expect(await this.mock.$log10(1001n, rounding)).to.equal(4n); await expect(this.mock.$log10(1001n, rounding)).to.eventually.equal(4n);
expect(await this.mock.$log10(ethers.MaxUint256, rounding)).to.equal(78n); await expect(this.mock.$log10(ethers.MaxUint256, rounding)).to.eventually.equal(78n);
} }
}); });
}); });
@ -530,31 +625,31 @@ describe('Math', function () {
describe('log256', function () { describe('log256', function () {
it('rounds down', async function () { it('rounds down', async function () {
for (const rounding of RoundingDown) { for (const rounding of RoundingDown) {
expect(await this.mock.$log256(0n, rounding)).to.equal(0n); await expect(this.mock.$log256(0n, rounding)).to.eventually.equal(0n);
expect(await this.mock.$log256(1n, rounding)).to.equal(0n); await expect(this.mock.$log256(1n, rounding)).to.eventually.equal(0n);
expect(await this.mock.$log256(2n, rounding)).to.equal(0n); await expect(this.mock.$log256(2n, rounding)).to.eventually.equal(0n);
expect(await this.mock.$log256(255n, rounding)).to.equal(0n); await expect(this.mock.$log256(255n, rounding)).to.eventually.equal(0n);
expect(await this.mock.$log256(256n, rounding)).to.equal(1n); await expect(this.mock.$log256(256n, rounding)).to.eventually.equal(1n);
expect(await this.mock.$log256(257n, rounding)).to.equal(1n); await expect(this.mock.$log256(257n, rounding)).to.eventually.equal(1n);
expect(await this.mock.$log256(65535n, rounding)).to.equal(1n); await expect(this.mock.$log256(65535n, rounding)).to.eventually.equal(1n);
expect(await this.mock.$log256(65536n, rounding)).to.equal(2n); await expect(this.mock.$log256(65536n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$log256(65537n, rounding)).to.equal(2n); await expect(this.mock.$log256(65537n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$log256(ethers.MaxUint256, rounding)).to.equal(31n); await expect(this.mock.$log256(ethers.MaxUint256, rounding)).to.eventually.equal(31n);
} }
}); });
it('rounds up', async function () { it('rounds up', async function () {
for (const rounding of RoundingUp) { for (const rounding of RoundingUp) {
expect(await this.mock.$log256(0n, rounding)).to.equal(0n); await expect(this.mock.$log256(0n, rounding)).to.eventually.equal(0n);
expect(await this.mock.$log256(1n, rounding)).to.equal(0n); await expect(this.mock.$log256(1n, rounding)).to.eventually.equal(0n);
expect(await this.mock.$log256(2n, rounding)).to.equal(1n); await expect(this.mock.$log256(2n, rounding)).to.eventually.equal(1n);
expect(await this.mock.$log256(255n, rounding)).to.equal(1n); await expect(this.mock.$log256(255n, rounding)).to.eventually.equal(1n);
expect(await this.mock.$log256(256n, rounding)).to.equal(1n); await expect(this.mock.$log256(256n, rounding)).to.eventually.equal(1n);
expect(await this.mock.$log256(257n, rounding)).to.equal(2n); await expect(this.mock.$log256(257n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$log256(65535n, rounding)).to.equal(2n); await expect(this.mock.$log256(65535n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$log256(65536n, rounding)).to.equal(2n); await expect(this.mock.$log256(65536n, rounding)).to.eventually.equal(2n);
expect(await this.mock.$log256(65537n, rounding)).to.equal(3n); await expect(this.mock.$log256(65537n, rounding)).to.eventually.equal(3n);
expect(await this.mock.$log256(ethers.MaxUint256, rounding)).to.equal(32n); await expect(this.mock.$log256(ethers.MaxUint256, rounding)).to.eventually.equal(32n);
} }
}); });
}); });