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.

This implementation is based off the Solidity trigonometry library written by Lefteris Karapetsas which can be found here: https://github.com/Sikorkaio/sikorka/blob/e75c91925c914beaedf4841c0336a806f2b5f66d/contracts/trigonometry.sol

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

Lefertis' implementation is based off Dave Dribin's trigint C library http://www.dribin.org/dave/trigint/

Which in turn is based from a now deleted article which can be found in the Wayback Machine: http://web.archive.org/web/20120301144605/http://www.dattalo.com/technical/software/pic/picsine.html

INDEX_WIDTH

uint256 INDEX_WIDTH

INTERP_WIDTH

uint256 INTERP_WIDTH

INDEX_OFFSET

uint256 INDEX_OFFSET

INTERP_OFFSET

uint256 INTERP_OFFSET

ANGLES_IN_CYCLE

uint32 ANGLES_IN_CYCLE

QUADRANT_HIGH_MASK

uint32 QUADRANT_HIGH_MASK

QUADRANT_LOW_MASK

uint32 QUADRANT_LOW_MASK

SINE_TABLE_SIZE

uint256 SINE_TABLE_SIZE

PI

uint256 PI

TWO_PI

uint256 TWO_PI

PI_OVER_TWO

uint256 PI_OVER_TWO

entry_bytes

uint8 entry_bytes

entry_mask

uint256 entry_mask

sin_table

bytes sin_table

sin

function sin(uint256 _angle) internal pure returns (int256)

Return the sine of a value, specified in radians scaled by 1e18

This algorithm for converting sine only uses integer values, and it works by dividing the circle into 30 bit angles, i.e. there are 1,073,741,824 (2^30) angle units, instead of the standard 360 degrees (2pi radians). From there, we get an output in range -2,147,483,647 to 2,147,483,647, (which is the max value of an int32) which is then converted back to the standard range of -1 to 1, again scaled by 1e18

Name	Type	Description
_angle	uint256	Angle to convert

Name	Type	Description
[0]	int256	Result scaled by 1e18

cos

function cos(uint256 _angle) internal pure returns (int256)

Return the cosine of a value, specified in radians scaled by 1e18

This is identical to the sin() method, and just computes the value by delegating to the sin() method using the identity cos(x) = sin(x + pi/2) Overflow when angle + PI_OVER_TWO > type(uint256).max is ok, results are still accurate

Name	Type	Description
_angle	uint256	Angle to convert

Name	Type	Description
[0]	int256	Result scaled by 1e18