Integers in Cairo Cairo doesn’t offer the full range of integer sizes found in Solidity. While Solidity provides integer types for every multiple of 8 bits up to 256, Cairo supports only the...

Cairo Storage Variable Types In Starknet, Contract Storage is the persistent memory where your smart contract's state lives. Unlike variables declared inside a function which disappear after...

Cheatcodes in Starknet Foundry A "cheatcode" in Foundry is a mechanism that allows contract tests to control environment variables such as caller address, the current timestamp, and so on. In this...

Access Control in Cairo Access control defines who can call specific functions or modify contract behavior. This article explains how Cairo implements access control using the macro. A Review of...

Events in Starknet Events emit data from contract execution into the transaction receipt. The receipt holds metadata about what happened during the execution, which can be queried or indexed by...

Positions in Uniswap v3 Adding liquidity to an AMM means depositing tokens into the AMM pool. Liquidity providers do this in the hope of earning fees from users who swap with that pool. In Uniswap...

NTT Algorithm By Hand The NTT (Number Theoretic Transform) algorithm converts a polynomial in a finite field from coefficient form to point form. If a polynomial has degree $d$ then we evaluate it on...

The Image Preservation Theorem for Multivalued Functions We’ll start this chapter on an unusual note — the NTT algorithm is quite simple and can be implemented in less than 20 lines of code. However,...

Square Roots of Roots of Unity The square root of a number $x$ is $y$ such that $y^2=x$. When $x$ is of the form $x^m$ and $m$ is even, then the square root is easy to compute: it’s simply $x^{m/2}$....

Evaluating multivalued functions by square root expansion In the previous chapter on Image Preservation of Multivalued Functions we saw that instead of evaluating $f(x)$ on the $k$-th roots of unity,...