Cairo Math 64x61

A fixed point 64.61 math library for Cairo & Starknet

Usage ##

For use with starknet-hardhat-plugin, install via npm with npm install --save-dev @influenceth/cairo-math-64x61 and add ./node_modules/@influenceth/cairo-math-64x61 to cairoPaths in your hardhat config (see https://github.com/Shard-Labs/starknet-hardhat-plugin#paths). Then you can import with, for example: from contracts.Math64x61 import Math64x61_mul

Signed 64.61 Fixed Point Numbers ##

A signed 64.61-bit fixed point number is a fraction in which the numerator is a signed 125-bit integer and the denominator is 2^61. Since the denominator stays the same there is no need to store it (as in a floating point value).

64.61 is utilized as the 125 bit representation allows for overflow up to 2^125 * 2^125 (250 bits) during calculation taking advantage of Cairo's 251 bit felts.

Can represent values in the range of -2^64 to 2^64 with precision to 4.34e-19.

Standard Library ##

Math64x61 includes implementation of add, sub, mul, div, sqrt, exp, ln, log2, log10, and pow as well as conversion to / from felts and Uint256 values, floor, ceil, min, max and assertion methods.

Trigonometry Library ##

Trig64x61 includes implementation of sin, cos, tan and their inverses.

Hyperbolic Library ##

Hyp64x61 includes implementation of sinh, cosh, tanh, and their inverses.

Vector Library ##

Vec64x61 includes implementation of vector arithmetic (add, sub, div), dot product (dot), cross product (cross) and norm.

Extensibility ##

This library strives to adhere to the OpenZeppelin extensibility pattern: https://github.com/OpenZeppelin/cairo-contracts/blob/main/docs/Extensibility.md