Solidity Trigonometry

Solidity library offering basic trigonometry functions where inputs and outputs are integers. Inputs are specified in radians scaled by 1e18, and similarly outputs are scaled by 1e18. Each invocation of the sin() and cos() functions cost around 1600–1700 gas (see the testNoReverts costs in .gas-snapshot for more info).

This implementation is based off the Solidity trigonometry library written by Lefteris Karapetsas which can be found here. Compared to Lefteris' implementation, this version makes the following changes:

• Uses a 32 bits instead of 16 bits for improved accuracy
• Updated for Solidity 0.8.x
• Various gas optimizations
• Change inputs/outputs to standard trig format (scaled by 1e18) instead of requiring the integer format used by the algorithm

The original implementation by Lefteris is based off Dave Dribin's trigint C library, which in turn is based on an article by Scott Dattalo.

Usage

When using this library, it's recommended to wrap input values (which are in radians) between 2 * PI * 1e18 and 4 * PI * 1e18 to avoid precision errors. This is equivalent to wrapping standard values between 0 and 2π. There is some flexibility on that range, but it should stay within reasonable bounds.

To use this in a Foundry project, install it with:

forge install https://github.com/mds1/solidity-trigonometry

To use this in a dapptools project, install it with:

dapp install https://github.com/mds1/solidity-trigonometry

There is currently no npm package, so for projects using npm for package management, such as Hardhat projects, use:

yarn add https://github.com/mds1/solidity-trigonometry.git

Development

Setup

This library is developed with Foundry. If you don't have Foundry installed, run the command below to get foundryup, the Foundry toolchain installer:

curl -L https://foundry.paradigm.xyz | bash

Then in a new terminal session or after reloading your PATH, run foundryup to get the latest forge and cast binaries.

Testing

Run tests with forge test, and update gas snapshots with FOUNDRY_FUZZ_RUNS=50000 forge snapshot (this will take a while to run since that many FFI runs can be slow).

NOTE: Tests are configured to run with the --ffi flag enabled for fuzz testing, so review the test commands before executing them to ensure you aren't running any malicious code on your machine.