From 97a5f4aae43221ca29bad3f006a8aa74bf24aeaf Mon Sep 17 00:00:00 2001
From: 0xalizk <42751398+0xalizk@users.noreply.github.com>
Date: Thu, 5 Dec 2024 14:22:42 +0300
Subject: [PATCH] Update README.md

---
 README.md | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

diff --git a/README.md b/README.md
index 7583385..cf5ec7c 100644
--- a/README.md
+++ b/README.md
@@ -1,35 +1,35 @@
 # mopro msm gpu-acceleration
 
-We are researching the methods and implement the methods that can accelerate multi-scalar multiplication (MSM) on IOS mobile device.
+We are researching and implementing methods to accelerate multi-scalar multiplication (MSM) on IOS mobile device.
 
 ## mopro-msm
 
-This is the crate that possess various of implementation of MSM functions, which are integrated in `mopro-core`.
+This is a of various implementations of MSM functions, which are then integrated in `mopro-core`.
 
 ### Run benchmark on the laptop
-Currently we support these MSM algorithms on BN254
+Currently we support these MSM algorithms on BN254:
 - arkworks_pippenger
 - bucket_wise_msm
 - precompute_msm
 - metal::msm (GPU)
 
-Replace `MSM_ALGO` with the algorithm name below to get the benchmarks
+Replace `MSM_ALGO` with one of the algorithms above to get the corresponding benchmarks.
 
-Benchmarking for <u>single instance size</u>
+Benchmarking for <u>single instance size</u>:
 ```sh
 cargo test --release --package mopro-msm --lib -- msm::MSM_ALGO::tests::test_run_benchmark --exact --nocapture
 ```
 
-Benchmarking for <u>multiple instance size</u>
+Benchmarking for <u>multiple instance size</u>:
 ```sh
 cargo test --release --package mopro-msm --lib -- msm::MSM_ALGO::tests::test_run_multi_benchmarks --exact --nocapture
 ```
 
 ## gpu-exploration-app
 
-This is a benchmark app to compare the performance of different algorithm on IOS device.
+This is a benchmark app to compare the performance of different algorithms on iOS device.
 
-Run this command on the project root directory to compile metal library for OS
+You can run the following commands in the root directory of the project to compile the metal library for a given OS:
 ```sh
 # for macOS
 bash mopro-msm/src/msm/metal/compile_metal.sh