feat: Implement RLP Encoding and Decoding (#213)

Implementation of RLP encoding and decoding based on
https://ethereum.org/en/developers/docs/data-structures-and-encoding/rlp/
doc.

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above -->

## Pull Request type

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Please check the type of change your PR introduces:

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

## What is the current behavior?

<!-- Please describe the current behavior that you are modifying, or
link to a relevant issue. -->

Issue Number: #212 

## What is the new behavior?

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this PR. -->

-
-
-

## Does this introduce a breaking change?

- [ ] Yes
- [x] No

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impact and migration path for existing applications below. -->

## Other information

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Scarb.lock

@@ -28,6 +28,7 @@ name = "alexandria_encoding"
 version = "0.1.0"
 dependencies = [
  "alexandria_math",
+ "alexandria_numeric",
 ]
 
 [[package]]
@@ -48,6 +49,9 @@ version = "0.1.0"
 [[package]]
 name = "alexandria_numeric"
 version = "0.1.0"
+dependencies = [
+ "alexandria_math",
+]
 
 [[package]]
 name = "alexandria_searching"

src/data_structures/src/array_ext.cairo

@@ -4,6 +4,7 @@ trait ArrayTraitExt<T> {
     fn reverse(self: @Array<T>) -> Array<T>;
     fn contains<+PartialEq<T>>(self: @Array<T>, item: T) -> bool;
     fn concat(self: @Array<T>, a: @Array<T>) -> Array<T>;
+    fn concat_span<+Drop<T>>(ref self: Array<T>, arr2: Span<T>);
     fn index_of<+PartialEq<T>>(self: @Array<T>, item: T) -> Option<usize>;
     fn occurrences_of<+PartialEq<T>>(self: @Array<T>, item: T) -> usize;
     fn min<+PartialEq<T>, +PartialOrd<T>>(self: @Array<T>) -> Option<T>;
@@ -85,6 +86,15 @@ impl ArrayImpl<T, +Copy<T>, +Drop<T>> of ArrayTraitExt<T> {
         ret
     }
 
+    fn concat_span<+Destruct<T>>(ref self: Array<T>, mut arr2: Span<T>) {
+        loop {
+            match arr2.pop_front() {
+                Option::Some(elem) => self.append(*elem),
+                Option::None => { break; }
+            };
+        }
+    }
+
     fn index_of<+PartialEq<T>>(self: @Array<T>, item: T) -> Option<usize> {
         self.span().index_of(item)
     }

src/encoding/Scarb.toml

@@ -9,3 +9,4 @@ fmt.workspace = true
 
 [dependencies]
 alexandria_math = { path = "../math" }
+alexandria_numeric = { path = "../numeric" }

src/encoding/src/lib.cairo

@@ -1,5 +1,6 @@
 mod base64;
 mod reversible;
+mod rlp;
 
 #[cfg(test)]
 mod tests;

src/encoding/src/rlp.cairo

@@ -0,0 +1,198 @@
+use alexandria_data_structures::array_ext::ArrayTraitExt;
+use alexandria_numeric::integers::UIntBytes;
+
+// Possible RLP errors
+#[derive(Drop, Copy, PartialEq)]
+enum RLPError {
+    EmptyInput,
+    InputTooShort,
+    PayloadTooLong
+}
+
+// Possible RLP types
+#[derive(Drop, PartialEq)]
+enum RLPType {
+    String,
+    List
+}
+
+#[derive(Drop, Copy, PartialEq)]
+enum RLPItem {
+    String: Span<u8>,
+    List: Span<RLPItem>
+}
+
+#[generate_trait]
+impl RLPImpl of RLPTrait {
+    /// Returns RLPType from the leading byte with
+    /// its offset in the array as well as its size.
+    ///
+    /// # Arguments
+    /// * `input` - Array of byte to decode
+    /// # Returns
+    /// * `(RLPType, offset, size)` - A tuple containing the RLPType
+    /// the offset and the size of the RLPItem to decode
+    /// # Errors
+    /// * empty input - if the input is empty
+    /// * input too short - if the input is too short for a given
+    fn decode_type(input: Span<u8>) -> Result<(RLPType, u32, u32), RLPError> {
+        let input_len = input.len();
+        if input_len == 0 {
+            return Result::Err(RLPError::EmptyInput);
+        }
+
+        let prefix_byte = *input[0];
+
+        if prefix_byte < 0x80 { // Char
+            return Result::Ok((RLPType::String, 0, 1));
+        } else if prefix_byte < 0xb8 { // Short String
+            return Result::Ok((RLPType::String, 1, prefix_byte.into() - 0x80));
+        } else if prefix_byte < 0xc0 { // Long String
+            let len_bytes_count: u32 = (prefix_byte - 0xb7).into();
+            if input_len <= len_bytes_count {
+                return Result::Err(RLPError::InputTooShort);
+            }
+            let string_len_bytes = input.slice(1, len_bytes_count);
+            let string_len: u32 = UIntBytes::from_bytes(string_len_bytes)
+                .ok_or(RLPError::PayloadTooLong)?;
+
+            return Result::Ok((RLPType::String, 1 + len_bytes_count, string_len));
+        } else if prefix_byte < 0xf8 { // Short List
+            return Result::Ok((RLPType::List, 1, prefix_byte.into() - 0xc0));
+        } else { // Long List
+            let len_bytes_count = prefix_byte.into() - 0xf7;
+            if input.len() <= len_bytes_count {
+                return Result::Err(RLPError::InputTooShort);
+            }
+            let list_len_bytes = input.slice(1, len_bytes_count);
+            let list_len: u32 = UIntBytes::from_bytes(list_len_bytes)
+                .ok_or(RLPError::PayloadTooLong)?;
+            return Result::Ok((RLPType::List, 1 + len_bytes_count, list_len));
+        }
+    }
+
+    /// Recursively encodes multiple a list of RLPItems
+    /// # Arguments
+    /// * `input` - Span of RLPItem to encode
+    /// # Returns
+    /// * `Span<u8> - RLP encoded items as a span of bytes
+    /// # Errors
+    /// * empty input - if the input is empty
+    fn encode(mut input: Span<RLPItem>) -> Result<Span<u8>, RLPError> {
+        if input.len() == 0 {
+            return Result::Err(RLPError::EmptyInput);
+        }
+
+        let mut output: Array<u8> = Default::default();
+        // Safe to unwrap because input length is not 0
+        let item = input.pop_front().unwrap();
+
+        match item {
+            RLPItem::String(string) => { output.concat_span(RLPTrait::encode_string(*string)?); },
+            RLPItem::List(list) => {
+                if (*list).len() == 0 {
+                    output.append(0xc0);
+                } else {
+                    let payload = RLPTrait::encode(*list)?;
+                    let payload_len = payload.len();
+                    if payload_len > 55 {
+                        let len_in_bytes = payload_len.to_bytes();
+                        // The payload length being a u32, the length in bytes
+                        // will maximum be equal to 4, making the unwrap safe
+                        output.append(0xf7 + len_in_bytes.len().try_into().unwrap());
+                        output.concat_span(len_in_bytes);
+                    } else {
+                        // Safe to unwrap because payload_len<55
+                        output.append(0xc0 + payload_len.try_into().unwrap());
+                    }
+                    output.concat_span(payload);
+                }
+            }
+        }
+
+        if input.len() > 0 {
+            output.concat_span(RLPTrait::encode(input)?);
+        }
+
+        Result::Ok(output.span())
+    }
+
+    /// RLP encodes a Array of bytes representing a RLP String.
+    /// # Arguments
+    /// * `input` - Array of bytes representing a RLP String to encode
+    /// # Returns
+    /// * `Span<u8> - RLP encoded items as a span of bytes
+    fn encode_string(input: Span<u8>) -> Result<Span<u8>, RLPError> {
+        let len = input.len();
+        if len == 0 {
+            return Result::Ok(array![0x80].span());
+        } else if len == 1 && *input[0] < 0x80 {
+            return Result::Ok(input);
+        } else if len < 56 {
+            let mut encoding: Array<u8> = Default::default();
+            // Safe to unwrap because len<56
+            encoding.append(0x80 + len.try_into().unwrap());
+            encoding.concat_span(input);
+            return Result::Ok(encoding.span());
+        } else {
+            let mut encoding: Array<u8> = Default::default();
+            let len_as_bytes = len.to_bytes();
+            let len_bytes_count = len_as_bytes.len();
+            // The payload length being a u32, the length in bytes
+            // will maximum be equal to 4, making the unwrap safe
+            let prefix = 0xb7 + len_bytes_count.try_into().unwrap();
+            encoding.append(prefix);
+            encoding.concat_span(len_as_bytes);
+            encoding.concat_span(input);
+            return Result::Ok(encoding.span());
+        }
+    }
+
+    /// Recursively decodes a rlp encoded byte array
+    /// as described in https://ethereum.org/en/developers/docs/data-structures-and-encoding/rlp/
+    ///
+    /// # Arguments
+    /// * `input` - Array of bytes to decode
+    /// # Returns
+    /// * `Span<RLPItem>` - Span of RLPItem
+    /// # Errors
+    /// * input too short - if the input is too short for a given
+    fn decode(input: Span<u8>) -> Result<Span<RLPItem>, RLPError> {
+        let mut output: Array<RLPItem> = Default::default();
+        let input_len = input.len();
+
+        let (rlp_type, offset, len) = RLPTrait::decode_type(input)?;
+
+        if input_len < offset + len {
+            return Result::Err(RLPError::InputTooShort);
+        }
+
+        match rlp_type {
+            RLPType::String => {
+                if (len == 0) {
+                    output.append(RLPItem::String(array![].span()));
+                } else {
+                    output.append(RLPItem::String(input.slice(offset, len)));
+                }
+            },
+            RLPType::List => {
+                if len > 0 {
+                    let res = RLPTrait::decode(input.slice(offset, len))?;
+                    output.append(RLPItem::List(res));
+                } else {
+                    output.append(RLPItem::List(array![].span()));
+                }
+            }
+        };
+
+        let total_item_len = len + offset;
+        if total_item_len < input_len {
+            output
+                .concat_span(
+                    RLPTrait::decode(input.slice(total_item_len, input_len - total_item_len))?
+                );
+        }
+
+        Result::Ok(output.span())
+    }
+}

src/encoding/src/tests.cairo

@@ -1,2 +1,3 @@
 mod base64_test;
 mod reversible_test;
+mod rlp_test;