refactor: rm math package dependencies (#325)

<!--- Please provide a general summary of your changes in the title
above -->

## Pull Request type

<!-- Please try to limit your pull request to one type; submit multiple
pull requests if needed. -->

Please check the type of change your PR introduces:

- [ ] Bugfix
- [ ] Feature
- [ ] Code style update (formatting, renaming)
- [x] Refactoring (no functional changes, no API changes)
- [ ] Build-related changes
- [ ] Documentation content changes
- [ ] Other (please describe):

## What is the current behavior?

The `math` package has a dependency on `data_structures` package only
because the `ed25519.cairo` module uses 3 trivial functions from the
`SpanTraitExt` trait. However, `data_structures` has a rather wild
dependency tree by itself, so it pulls in `encoding`, `numeric`, `bytes`
and `searching` 💀

## What is the new behavior?

This PR removes the dependency of the `math` package on
`data_structures` (and hence all its downstream deps) by adding (or
rather, copy-pasting) two private functions (`dedup` and `reverse`) to
the `ed25519.cairo` and replacing the third one (`concat`) by the use of
`append_span` from Cairo core.

## Does this introduce a breaking change?

- [ ] Yes
- [x] No

## Other information

There's no regression in performance of the ed25519.

Before this change:

```shell
$ scarb test -f ed255
running 7 tests
test alexandria_math::tests::ed25519_test::affine_point_op ... ok (gas usage est.: 411440)
test alexandria_math::tests::ed25519_test::verify_signature_invalid_length ... ok (gas usage est.: 5284792)
test alexandria_math::tests::ed25519_test::verify_signature_test_2 ... ok (gas usage est.: 390532238)
test alexandria_math::tests::ed25519_test::verify_signature_test_1 ... ok (gas usage est.: 382719878)
test alexandria_math::tests::ed25519_test::verify_signature_test_0 ... ok (gas usage est.: 389881208)
test alexandria_math::tests::ed25519_test::verify_signature_invalid ... ok (gas usage est.: 389229898)
test alexandria_math::tests::ed25519_test::verify_signature_test_3 ... ok (gas usage est.: 413750688)
test result: ok. 7 passed; 0 failed; 0 ignored; 143 filtered out;
```

After:

```shell
scarb test -f ed255
testing alexandria_math ...
running 7 tests
test alexandria_math::tests::ed25519_test::affine_point_op ... ok (gas usage est.: 411440)
test alexandria_math::tests::ed25519_test::verify_signature_invalid_length ... ok (gas usage est.: 5272652)
test alexandria_math::tests::ed25519_test::verify_signature_test_2 ... ok (gas usage est.: 390378618)
test alexandria_math::tests::ed25519_test::verify_signature_test_1 ... ok (gas usage est.: 382566258)
test alexandria_math::tests::ed25519_test::verify_signature_test_0 ... ok (gas usage est.: 389727588)
test alexandria_math::tests::ed25519_test::verify_signature_invalid ... ok (gas usage est.: 389076278)
test alexandria_math::tests::ed25519_test::verify_signature_test_3 ... ok (gas usage est.: 413597068)
test result: ok. 7 passed; 0 failed; 0 ignored; 143 filtered out;
```

Scarb.lock

@@ -41,10 +41,7 @@ dependencies = [
 
 [[package]]
 name = "alexandria_math"
-version = "0.2.0"
-dependencies = [
- "alexandria_data_structures",
-]
+version = "0.2.1"
 
 [[package]]
 name = "alexandria_merkle_tree"

packages/math/Scarb.toml

@@ -1,16 +1,12 @@
 [package]
 name = "alexandria_math"
-version = "0.2.0"
+version = "0.2.1"
 description = "A set of math libraries and algorithms"
 homepage = "https://github.com/keep-starknet-strange/alexandria/tree/main/packages/math"
 edition = "2023_11"
 
 [tool]
 fmt.workspace = true
 
-[dependencies]
-# dependency due to ArrayTraitExt::concat in ed25519.cairo
-alexandria_data_structures = { path = "../data_structures" }
-
 [dev-dependencies]
-cairo_test.workspace = true
+cairo_test.workspace = true

packages/math/src/ed25519.cairo

@@ -1,14 +1,11 @@
-use alexandria_data_structures::span_ext::SpanTraitExt;
 use alexandria_math::mod_arithmetics::{mult_mod, sqr_mod, div_mod, pow_mod, equality_mod};
 use alexandria_math::sha512::{sha512, SHA512_LEN};
 use alexandria_math::u512_arithmetics::{u512_add, u512_sub};
-use core::array::ArrayTrait;
 use core::integer::{u512, u512_safe_div_rem_by_u256};
 use core::math::u256_inv_mod;
 use core::num::traits::{OverflowingMul, WideMul};
 use core::option::OptionTrait;
-use core::traits::Div;
-use core::traits::TryInto;
+use core::traits::{Div, TryInto};
 
 // Subtraction without modulo operation
 // assumes a, b < modulo
@@ -239,12 +236,12 @@ impl U256TryIntoPoint of TryInto<u256, Point> {
     fn try_into(self: u256) -> Option<Point> {
         let mut x = 0;
         let mut y_span: Span<u8> = self.into();
-        let mut y_le_span: Span<u8> = y_span.reversed().span();
+        let mut y_le_span: Span<u8> = reverse(y_span);
 
         let last_byte = *y_le_span[31];
 
         let _ = y_le_span.pop_back();
-        let mut normed_array: Array<u8> = y_le_span.dedup();
+        let mut normed_array: Array<u8> = dedup(y_le_span);
         normed_array.append(last_byte & ~0x80);
 
         let x_0: u256 = (last_byte.into() / 128) & 1; // bitshift of 255
@@ -361,8 +358,8 @@ pub fn verify_signature(msg: Span<u8>, signature: Span<u256>, pub_key: u256) ->
 
     let s: u256 = *signature[1];
     let s_span: Span<u8> = s.into();
-    let reversed_s_span = s_span.reversed();
-    let s: u256 = reversed_s_span.span().into();
+    let reversed_s_span = reverse(s_span);
+    let s: u256 = reversed_s_span.into();
     if (s >= l) {
         return false;
     }
@@ -376,11 +373,15 @@ pub fn verify_signature(msg: Span<u8>, signature: Span<u256>, pub_key: u256) ->
     let A_prime: Point = A_prime_opt.unwrap();
 
     let r_bytes: Span<u8> = r.into();
-    let r_bytes = r_bytes.reversed().span();
+    let r_bytes = reverse(r_bytes);
     let pub_key_bytes: Span<u8> = pub_key.into();
-    let pub_key_bytes = pub_key_bytes.reversed().span();
+    let pub_key_bytes = reverse(pub_key_bytes);
+
+    let mut hashable = array![];
+    hashable.append_span(r_bytes);
+    hashable.append_span(pub_key_bytes);
+    hashable.append_span(msg);
 
-    let hashable = r_bytes.concat(pub_key_bytes).span().concat(msg);
     // k = SHA512(dom2(F, C) -> empty string || R -> half of sig || A -> pub_key || PH(M) ->
     // identity function for msg)
     let k: Array<u8> = sha512(hashable);
@@ -391,3 +392,30 @@ pub fn verify_signature(msg: Span<u8>, signature: Span<u256>, pub_key: u256) ->
 
     check_group_equation(s, R, k_reduced, A_prime)
 }
+
+// reverse and dedup are helper functions copy-pasted here from
+// the data_structures SpanTraitExt implementation to prevent
+// dependency of the math package on the data_structures package
+// and all its heavy dependencies
+
+fn reverse(mut span: Span<u8>) -> Span<u8> {
+    let mut res = array![];
+    while let Option::Some(v) = span.pop_back() {
+        res.append(v.clone());
+    };
+    res.span()
+}
+
+fn dedup(mut span: Span<u8>) -> Array<u8> {
+    let mut last_value = span.pop_front().unwrap();
+    let mut ret = array![last_value.clone()];
+
+    for v in span {
+        if (last_value != v) {
+            last_value = v;
+            ret.append(v.clone());
+        }
+    };
+
+    ret
+}