Develop a highly-optimized integer square root algorithm for constant-function automated market makers (AMM)

[Damola-Sodiq]

Description

Implement a native, gas-efficient integer square root (isqrt) function in Rust to handle complex liquidity pool calculations for fractional token pricing.

Architecture & Context

When swapping fractional tokens natively on-chain, calculating the exact xy=k AMM curve requires square roots. Floating point math is non-deterministic and unsupported in WASM. A highly optimized, bitwise-shifting integer square root algorithm is critical for cheap execution.

Technical Requirements

• Write an isqrt function utilizing Newton's method or fast bitwise shifts in #![no_std] Rust.
• Eliminate any potential integer overflow panics up to u128 constraints.
• Write extensive proptest cases validating accuracy against known mathematical bounds.

Acceptance Criteria

• The algorithm calculates accurate roots without precision loss.
• CPU instructions consumed are orders of magnitude lower than unoptimized iteration.
• The execution is deterministic and safe across all architectures.

[Brainoncrack]

Hi maintainer, i will love to work on this

[grantfox-oss]

🦊 GrantFox — @Brainoncrack has been assigned to this issue as part of the Official Campaign | FWC26 campaign!

Next steps:

1. Open a Pull Request referencing this issue (e.g., Closes #475)
2. Your PR will be reviewed by the Sahara-Pay maintainers

Good luck! Track your progress on GrantFox.

[grantfox-oss]

🎉 This issue has been marked as completed on GrantFox as part of the Official Campaign | FWC26 campaign!

@Brainoncrack's PR #502 was approved and merged by @Damola-Sodiq.

🏆 @Brainoncrack: You earned 35 FoxPoints for this contribution! Your current tier: Explorer (296 total points). Track your full progress on GrantFox.

👏 Great work, @Brainoncrack! Keep contributing to Sahara-Pay.