# Cairo Math 64×61

A fixed point 64.61 math library for Cairo & Starknet

## 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 `mul`

, `div`

, `sqrt`

, `exp`

, `ln`

, `log2`

, `log10`

, and `pow`

as well as conversion 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.

## Extensibility

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