├── .dapprc ├── .gas-snapshot ├── .gitattributes ├── .github └── workflows │ └── tests.yml ├── .gitignore ├── .gitmodules ├── .prettierrc ├── .vscode └── settings.json ├── LICENSE ├── Makefile ├── README.md ├── package-lock.json ├── package.json ├── scripts └── contract-size.sh ├── shell.nix └── src ├── MulDivs.sol └── test └── MulDivs.t.sol /.dapprc: -------------------------------------------------------------------------------- 1 | # Basic build/test configuration. 2 | export DAPP_SOLC_VERSION=0.7.6 3 | export DAPP_BUILD_OPTIMIZE=1 4 | export DAPP_BUILD_OPTIMIZE_RUNS=1000000 5 | export DAPP_LINK_TEST_LIBRARIES=0 6 | export DAPP_TEST_VERBOSITY=1 7 | export DAPP_TEST_SMTTIMEOUT=500000 8 | 9 | # These normally default to 0 which breaks some tests. 10 | export DAPP_TEST_TIMESTAMP=1000000000 11 | export DAPP_TEST_NUMBER=10000000 12 | 13 | if [ "$DEEP_FUZZ" = "true" ] 14 | then 15 | export DAPP_TEST_FUZZ_RUNS=10000 # Fuzz for a long time if DEEP_FUZZ is set to true. 16 | else 17 | export DAPP_TEST_FUZZ_RUNS=100 # Only fuzz briefly if DEEP_FUZZ is not set to true. 18 | fi 19 | -------------------------------------------------------------------------------- /.gas-snapshot: -------------------------------------------------------------------------------- 1 | testMikhailBig() (gas: 1666) 2 | testMikhailInlinedFullMul() (gas: 1591) 3 | testMikhail() (gas: 1666) 4 | testRemcoBig() (gas: 1512) 5 | testRemco() (gas: 1164) 6 | testMikhailInlinedFullMulBig() (gas: 1612) 7 | -------------------------------------------------------------------------------- /.gitattributes: -------------------------------------------------------------------------------- 1 | *.sol linguist-language=Solidity 2 | .dapprc linguist-language=Shell 3 | .gas-snapshot linguist-language=Julia -------------------------------------------------------------------------------- /.github/workflows/tests.yml: -------------------------------------------------------------------------------- 1 | name: Tests 2 | 3 | on: [push, pull_request] 4 | 5 | jobs: 6 | tests: 7 | runs-on: ubuntu-latest 8 | 9 | steps: 10 | - uses: actions/checkout@v2 11 | - uses: actions/setup-node@v2 12 | - uses: cachix/install-nix-action@v13 13 | - uses: cachix/cachix-action@v10 14 | with: 15 | name: dapp 16 | 17 | - name: Install dependencies 18 | run: nix-shell --run 'make' 19 | 20 | - name: Check gas snapshots 21 | run: nix-shell --run 'dapp check-snapshot' 22 | 23 | - name: Run tests 24 | run: nix-shell --run 'dapp test' 25 | env: 26 | # Only fuzz deeply if we're pushing to main or this is a PR to main: 27 | DEEP_FUZZ: ${{ github.ref == 'refs/heads/main' || github.base_ref == 'main' }} 28 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | /out 2 | /node_modules -------------------------------------------------------------------------------- /.gitmodules: -------------------------------------------------------------------------------- 1 | [submodule "lib/ds-test"] 2 | path = lib/ds-test 3 | url = https://github.com/dapphub/ds-test 4 | [submodule "lib/solmate"] 5 | path = lib/solmate 6 | url = https://github.com/rari-capital/solmate 7 | -------------------------------------------------------------------------------- /.prettierrc: -------------------------------------------------------------------------------- 1 | { 2 | "tabWidth": 2, 3 | "printWidth": 100, 4 | 5 | "overrides": [ 6 | { 7 | "files": "*.sol", 8 | "options": { 9 | "tabWidth": 4, 10 | "printWidth": 120 11 | } 12 | } 13 | ] 14 | } 15 | -------------------------------------------------------------------------------- /.vscode/settings.json: -------------------------------------------------------------------------------- 1 | { 2 | "solidity.packageDefaultDependenciesContractsDirectory": "src", 3 | "solidity.packageDefaultDependenciesDirectory": "lib", 4 | "solidity.compileUsingRemoteVersion": "v0.7.6", 5 | "search.exclude": { "lib": true }, 6 | "files.associations": { 7 | ".dapprc": "shellscript", 8 | ".gas-snapshot": "julia" 9 | } 10 | } 11 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU AFFERO GENERAL PUBLIC LICENSE 2 | Version 3, 19 November 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU Affero General Public License is a free, copyleft license for 11 | software and other kinds of works, specifically designed to ensure 12 | cooperation with the community in the case of network server software. 13 | 14 | The licenses for most software and other practical works are designed 15 | to take away your freedom to share and change the works. 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-------------------------------------------------------------------------------- 1 | # muldiv-battle 2 | 3 | Gas comparison between [Remco Bloemen's](https://xn--2-umb.com/21/muldiv/) and [Mikhail Vladimirov's](https://medium.com/coinmonks/math-in-solidity-part-3-percents-and-proportions-4db014e080b1) `mulDiv` implementations. 4 | 5 | ## Results 6 | 7 | Results can be found in the auto-generated [`.gas-snapshot`](.gas-snapshot) file. 8 | 9 | ## Getting Started 10 | 11 | ```sh 12 | git clone https://github.com/transmissions11/muldiv-battle.git 13 | cd muldiv-battle 14 | make 15 | ``` 16 | -------------------------------------------------------------------------------- /package-lock.json: -------------------------------------------------------------------------------- 1 | { 2 | "name": "muldiv-battle", 3 | "version": "1.0.0", 4 | "lockfileVersion": 2, 5 | "requires": true, 6 | "packages": { 7 | "": { 8 | "name": "muldiv-battle", 9 | "version": "1.0.0", 10 | "license": "AGPL-3.0-only", 11 | "devDependencies": { 12 | "prettier": "^2.3.1", 13 | "prettier-plugin-solidity": "^1.0.0-beta.13" 14 | } 15 | }, 16 | "node_modules/@solidity-parser/parser": { 17 | "version": "0.14.0", 18 | "resolved": "https://registry.npmjs.org/@solidity-parser/parser/-/parser-0.14.0.tgz", 19 | "integrity": "sha512-cX0JJRcmPtNUJpzD2K7FdA7qQsTOk1UZnFx2k7qAg9ZRvuaH5NBe5IEdBMXGlmf2+FmjhqbygJ26H8l2SV7aKQ==", 20 | "dev": true, 21 | "dependencies": { 22 | "antlr4ts": "^0.5.0-alpha.4" 23 | } 24 | }, 25 | "node_modules/ansi-regex": { 26 | "version": "5.0.1", 27 | "resolved": "https://registry.npmjs.org/ansi-regex/-/ansi-regex-5.0.1.tgz", 28 | "integrity": "sha512-quJQXlTSUGL2LH9SUXo8VwsY4soanhgo6LNSm84E1LBcE8s3O0wpdiRzyR9z/ZZJMlMWv37qOOb9pdJlMUEKFQ==", 29 | "dev": true, 30 | "engines": { 31 | "node": ">=8" 32 | } 33 | }, 34 | "node_modules/antlr4ts": { 35 | "version": "0.5.0-alpha.4", 36 | "resolved": "https://registry.npmjs.org/antlr4ts/-/antlr4ts-0.5.0-alpha.4.tgz", 37 | "integrity": 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| "dev": true 288 | } 289 | } 290 | } 291 | -------------------------------------------------------------------------------- /package.json: -------------------------------------------------------------------------------- 1 | { 2 | "name": "muldiv-battle", 3 | "license": "AGPL-3.0-only", 4 | "version": "1.0.0", 5 | "description": "Gas comparison between Remco Bloemen's and Mikhail Vladimirov's mulDiv implementations.", 6 | "files": [ 7 | "src/**/*.sol" 8 | ], 9 | "repository": { 10 | "type": "git", 11 | "url": "git+https://github.com/transmissions11/muldiv-battle.git" 12 | }, 13 | "devDependencies": { 14 | "prettier": "^2.3.1", 15 | "prettier-plugin-solidity": "^1.0.0-beta.13" 16 | }, 17 | "scripts": { 18 | "lint": "prettier --write src/**/*.sol" 19 | } 20 | } 21 | -------------------------------------------------------------------------------- /scripts/contract-size.sh: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env bash 2 | 3 | set -eo pipefail 4 | 5 | contract_size() { 6 | NAME=$1 7 | ARGS=${@:2} 8 | # select the filename and the contract in it 9 | PATTERN=".contracts[\"src/$NAME.sol\"].$NAME" 10 | 11 | dapp build # first, build the contract 12 | 13 | # get the bytecode from the compiled file 14 | BYTECODE=0x$(jq -r "$PATTERN.evm.bytecode.object" out/dapp.sol.json) 15 | length=$(echo "$BYTECODE" | wc -m) 16 | echo $(($length / 2)) 17 | } 18 | 19 | if [[ -z $contract ]]; then 20 | if [[ -z ${1} ]];then 21 | echo '"$contract" env variable is not set. Set it to the name of the contract you want to estimate size for.' 22 | exit 1 23 | else 24 | contract=${1} 25 | fi 26 | fi 27 | 28 | contract_size=$(contract_size ${contract}) 29 | echo "Contract Name: ${contract}" 30 | echo "Contract Size: ${contract_size} bytes" 31 | echo 32 | echo "$(( 24576 - ${contract_size} )) bytes left to reach the smart contract size limit of 24576 bytes." 33 | -------------------------------------------------------------------------------- /shell.nix: -------------------------------------------------------------------------------- 1 | let 2 | pkgs = import (builtins.fetchGit rec { 3 | name = "dapptools-${rev}"; 4 | url = https://github.com/dapphub/dapptools; 5 | rev = "fb9476ded759da44c449eb391cc67bfb0df61112"; 6 | }) {}; 7 | 8 | in 9 | pkgs.mkShell { 10 | src = null; 11 | name = "muldiv-battle"; 12 | buildInputs = with pkgs; [ 13 | pkgs.dapp 14 | ]; 15 | } 16 | -------------------------------------------------------------------------------- /src/MulDivs.sol: -------------------------------------------------------------------------------- 1 | // SPDX-License-Identifier: AGPL-3.0-only 2 | pragma solidity 0.7.6; 3 | 4 | contract MulDivs { 5 | // from https://xn--2-umb.com/21/muldiv/ 6 | function remcoMulDiv( 7 | uint256 a, 8 | uint256 b, 9 | uint256 denominator 10 | ) external pure returns (uint256 result) { 11 | // Handle division by zero 12 | require(denominator > 0); 13 | 14 | // 512-bit multiply [prod1 prod0] = a * b 15 | // Compute the product mod 2**256 and mod 2**256 - 1 16 | // then use the Chinese Remiander Theorem to reconstruct 17 | // the 512 bit result. The result is stored in two 256 18 | // variables such that product = prod1 * 2**256 + prod0 19 | uint256 prod0; // Least significant 256 bits of the product 20 | uint256 prod1; // Most significant 256 bits of the product 21 | assembly { 22 | let mm := mulmod(a, b, not(0)) 23 | prod0 := mul(a, b) 24 | prod1 := sub(sub(mm, prod0), lt(mm, prod0)) 25 | } 26 | 27 | // Short circuit 256 by 256 division 28 | // This saves gas when a * b is small, at the cost of making the 29 | // large case a bit more expensive. Depending on your use case you 30 | // may want to remove this short circuit and always go through the 31 | // 512 bit path. 32 | if (prod1 == 0) { 33 | assembly { 34 | result := div(prod0, denominator) 35 | } 36 | return result; 37 | } 38 | 39 | /////////////////////////////////////////////// 40 | // 512 by 256 division. 41 | /////////////////////////////////////////////// 42 | 43 | // Handle overflow, the result must be < 2**256 44 | require(prod1 < denominator); 45 | 46 | // Make division exact by subtracting the remainder from [prod1 prod0] 47 | // Compute remainder using mulmod 48 | // Note mulmod(_, _, 0) == 0 49 | uint256 remainder; 50 | assembly { 51 | remainder := mulmod(a, b, denominator) 52 | } 53 | // Subtract 256 bit number from 512 bit number 54 | assembly { 55 | prod1 := sub(prod1, gt(remainder, prod0)) 56 | prod0 := sub(prod0, remainder) 57 | } 58 | 59 | // Factor powers of two out of denominator 60 | // Compute largest power of two divisor of denominator. 61 | // Always >= 1 unless denominator is zero, then twos is zero. 62 | uint256 twos = -denominator & denominator; 63 | // Divide denominator by power of two 64 | assembly { 65 | denominator := div(denominator, twos) 66 | } 67 | 68 | // Divide [prod1 prod0] by the factors of two 69 | assembly { 70 | prod0 := div(prod0, twos) 71 | } 72 | // Shift in bits from prod1 into prod0. For this we need 73 | // to flip `twos` such that it is 2**256 / twos. 74 | // If twos is zero, then it becomes one 75 | assembly { 76 | twos := add(div(sub(0, twos), twos), 1) 77 | } 78 | prod0 |= prod1 * twos; 79 | 80 | // Invert denominator mod 2**256 81 | // Now that denominator is an odd number, it has an inverse 82 | // modulo 2**256 such that denominator * inv = 1 mod 2**256. 83 | // Compute the inverse by starting with a seed that is correct 84 | // correct for four bits. That is, denominator * inv = 1 mod 2**4 85 | // If denominator is zero the inverse starts with 2 86 | uint256 inv = (3 * denominator) ^ 2; 87 | // Now use Newton-Raphson itteration to improve the precision. 88 | // Thanks to Hensel's lifting lemma, this also works in modular 89 | // arithmetic, doubling the correct bits in each step. 90 | inv *= 2 - denominator * inv; // inverse mod 2**8 91 | inv *= 2 - denominator * inv; // inverse mod 2**16 92 | inv *= 2 - denominator * inv; // inverse mod 2**32 93 | inv *= 2 - denominator * inv; // inverse mod 2**64 94 | inv *= 2 - denominator * inv; // inverse mod 2**128 95 | inv *= 2 - denominator * inv; // inverse mod 2**256 96 | // If denominator is zero, inv is now 128 97 | 98 | // Because the division is now exact we can divide by multiplying 99 | // with the modular inverse of denominator. This will give us the 100 | // correct result modulo 2**256. Since the precoditions guarantee 101 | // that the outcome is less than 2**256, this is the final result. 102 | // We don't need to compute the high bits of the result and prod1 103 | // is no longer required. 104 | result = prod0 * inv; 105 | return result; 106 | } 107 | 108 | // from https://medium.com/coinmonks/math-in-solidity-part-3-percents-and-proportions-4db014e080b1 109 | function mikhailMulDiv( 110 | uint256 x, 111 | uint256 y, 112 | uint256 z 113 | ) external pure returns (uint256) { 114 | (uint256 l, uint256 h) = fullMul(x, y); 115 | require(h < z); 116 | uint256 mm = mulmod(x, y, z); 117 | if (mm > l) h -= 1; 118 | l -= mm; 119 | uint256 pow2 = z & -z; 120 | z /= pow2; 121 | l /= pow2; 122 | l += h * ((-pow2) / pow2 + 1); 123 | uint256 r = 1; 124 | r *= 2 - z * r; 125 | r *= 2 - z * r; 126 | r *= 2 - z * r; 127 | r *= 2 - z * r; 128 | r *= 2 - z * r; 129 | r *= 2 - z * r; 130 | r *= 2 - z * r; 131 | r *= 2 - z * r; 132 | return l * r; 133 | } 134 | 135 | // derived from https://medium.com/coinmonks/math-in-solidity-part-3-percents-and-proportions-4db014e080b1 136 | function mikhailMulDivInlinedFullMul( 137 | uint256 x, 138 | uint256 y, 139 | uint256 z 140 | ) external pure returns (uint256) { 141 | uint256 mm = mulmod(x, y, uint256(-1)); 142 | uint256 l = x * y; 143 | uint256 h = mm - l; 144 | if (mm < l) h -= 1; 145 | require(h < z); 146 | uint256 mm2 = mulmod(x, y, z); 147 | if (mm2 > l) h -= 1; 148 | l -= mm2; 149 | uint256 pow2 = z & -z; 150 | z /= pow2; 151 | l /= pow2; 152 | l += h * ((-pow2) / pow2 + 1); 153 | uint256 r = 1; 154 | r *= 2 - z * r; 155 | r *= 2 - z * r; 156 | r *= 2 - z * r; 157 | r *= 2 - z * r; 158 | r *= 2 - z * r; 159 | r *= 2 - z * r; 160 | r *= 2 - z * r; 161 | r *= 2 - z * r; 162 | return l * r; 163 | } 164 | 165 | // from https://medium.com/coinmonks/math-in-solidity-part-3-percents-and-proportions-4db014e080b1 166 | function fullMul(uint256 x, uint256 y) internal pure returns (uint256 l, uint256 h) { 167 | uint256 mm = mulmod(x, y, uint256(-1)); 168 | l = x * y; 169 | h = mm - l; 170 | if (mm < l) h -= 1; 171 | } 172 | } 173 | -------------------------------------------------------------------------------- /src/test/MulDivs.t.sol: -------------------------------------------------------------------------------- 1 | // SPDX-License-Identifier: AGPL-3.0-only 2 | pragma solidity 0.7.6; 3 | 4 | import {DSTestPlus} from "solmate/test/utils/DSTestPlus.sol"; 5 | 6 | import {MulDivs} from "../MulDivs.sol"; 7 | 8 | contract MulDivTests is DSTestPlus { 9 | MulDivs mulDivs; 10 | 11 | function setUp() public { 12 | mulDivs = new MulDivs(); 13 | } 14 | 15 | function testRemco() public { 16 | assertEq(mulDivs.remcoMulDiv(5e18, 0.1e18, 1e18), 0.5e18); 17 | } 18 | 19 | function testRemcoBig() public { 20 | assertEq(mulDivs.remcoMulDiv(5000e45, 0.1e45, 1e45), 500e45); 21 | } 22 | 23 | function testMikhail() public { 24 | assertEq(mulDivs.mikhailMulDiv(5e18, 0.1e18, 1e18), 0.5e18); 25 | } 26 | 27 | function testMikhailBig() public { 28 | assertEq(mulDivs.mikhailMulDiv(5000e45, 0.1e45, 1e45), 500e45); 29 | } 30 | 31 | function testMikhailInlinedFullMul() public { 32 | assertEq(mulDivs.mikhailMulDivInlinedFullMul(5e18, 0.1e18, 1e18), 0.5e18); 33 | } 34 | 35 | function testMikhailInlinedFullMulBig() public { 36 | assertEq(mulDivs.mikhailMulDivInlinedFullMul(5000e45, 0.1e45, 1e45), 500e45); 37 | } 38 | } 39 | --------------------------------------------------------------------------------