Cairo Math 64x61

A fixed point 64.61 math library for Cairo & Starknet

Usage

Install with pip install cairo_math_64x61 and import and use with from cairo_math_64x61.math64x61 import Math64x61. Previous installation as an npm module has been deprecated, the last available npm module is v1.2.0.

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://docs.openzeppelin.com/contracts-cairo/0.2.1/extensibility#libraries