Serialization of Cairo types

When you interact with contracts, especially if you are a library or SDK developer that wants to construct transactions, you need to understand how Cairo handles types that are larger than 252 bits so you can correctly formulate the calldata in a transaction.

The field element (felt252), which contains 252 bits, is the only actual type in the Cairo VM. So all high-level Cairo types that are larger than 252 bits, such as u256 or arrays, are ultimately represented by a list of felts. In order to interact with a contract, you need to know how to encode its arguments as a list of felts so you can correctly formulate the calldata in the transaction. SDKs, such as starknet.js, encode the calldata for you, so you can simply specify any type and the SDK properly formulates the calldata. For example, you don’t need to know that a u256 value is represented by two felt252 values. You can simply specify a single integer in your code, and the SDK takes care of the serialization and encoding.

Data types of 252 bits or less

The following types are smaller than 252 bits. For these types, each value is serialized as a single-member list that contains one felt252 value.

ContractAddress
EthAddress
StorageAddress
ClassHash
Unsigned integers smaller than 252 bits: u8, u16, u32, u64, u128, and usize
bytes31
felt252
Signed integers smaller than 252 bits: i8, i16, i32, i64, and i128.

A negative value, \(-x\), is serialized as \(P-x\), where:

\[P = 2^{251} + 17*2^{192} + 1\]

For example, -5 is serialized as \(P-5\). For more information on the value of \(P\), see The STARK field.

Data types greater than 252 bits

The following Cairo data types have non-trivial serialization:

u256 and u512
arrays
enums
structs
ByteArray, which represents strings

Serialization of unsigned integers

Among unsigned integers, only u256 and u512 have non-trivial serialization.

Serialization of `u256` values

A u256 value in Cairo is represented by two felt252 values, as follows:

The first felt252 value contains the 128 least significant bits, usually referred to as the low part of the original u256 value.
The second felt252 value contains the 128 most significant bits, usually referred to as the high part of the original u256 value.

For example:

A u256 variable whose decimal value is 2 is serialized as [2,0]. To understand why, examine the binary representation of 2 and split it into two 128-bit parts, as follows:

\[\underbrace{0\cdots0}_{\text{128 high bits}} | \underbrace{0\cdots10}_{\text{128 low bits}}\]
A u256 variable whose decimal value is 2¹²⁸ is serialized as [0,1]. To understand why, examine the binary representation of 2¹²⁸ and split it into two 128-bit parts, as follows:

\[\underbrace{0\cdots01}_{\text{128 high bits}} | \underbrace{0\cdots0}_{\text{128 low bits}}\]
A u256 variable whose decimal value is 2¹²⁹+2¹²⁸+20, is serialized as [20,3]. To understand why, examine the binary representation of the 2¹²⁹+2¹²⁸+20 and split it into two 128-bit parts, as follows:

\[\underbrace{0\cdots011}_{\text{128 high bits}} | \underbrace{0\cdots10100}_{\text{128 low bits}}\]

Serialization of `u512` values

The u512 type in Cairo is a struct containing four felt252 members, each representing a 128-bit limb of the original integer, similar to the u256 type.

Serialization of arrays

Arrays are serialized as follows:

<array_length>, <serialized_member_0>,…, <serialized_member_n>

For example, consider the following array of u256 values:

let POW_2_128: u256 = 0x100000000000000000000000000000000
let array: Array<u256> = array![10, 20, POW_2_128]

Each u256 value in the array is represented by two felt252 values. So the array above is serialized as follows:

\[\underbrace{3}_{\textit{number_of_array_members}} , \underbrace{10,0}_{\textit{serialized_member_0}} , \underbrace{20,0}_{\textit{serialized_member_1}} , \underbrace{0,1}_{\textit{serialized_member_2}}\]

Combining the above, the array is serialized as follows: [3,10,0,20,0,0,1]

Serialization of enums

An enum is serialized as follows:

<index_of_enum_variant>,<serialized_variant>

Enum serialization example 1

Consider the following definition of an enum named Week:

enum Week {
    Sunday: (), // Index=1. The variant type is the unit type.
    Monday: u256, // Index=2. The variant type is u256.
}

Now consider instantiations of the Week enum’s variants as shown in the table Serialization of Week variants:

Table 1. Serialization of `Week` variants
Instance	Description	Serialization
`Week::Sunday`	Index=`1`. The variant’s type is the unit type.	`[1]`
`Week::Monday(5)`	Index=`2`. The variant’s type is `u256`.	`[2,5,0]`

Enum serialization example 2

Consider the following definition of an enum named MessageType:

enum MessageType {
    A,
    #[default]
    B: u128,
    C
}

Now consider instantiations of the MessageType enum’s variants as shown in the table Serialization of MessageType variants:

Table 2. Serialization of `MessageType` variants
Instance	Description	Serialization
`MessageType::A`	Index=`1`. The variant’s type is the unit type.	`[1]`
`MessageType::B(6)`	Index=`0`. The variant’s type is `u128`.	`[0,6]`
`MessageType::C`	Index=`2`. The variant’s type is the unit type.	`[2]`

Serialization of structs

You serialize a struct by serializing its members one at a time.

Its members are serialized in the order in which they appear in the definition of the struct.

For example, consider the following definition of the struct MyStruct:

struct MyStruct {
    a: u256,
    b: felt252,
    c: Array<felt252>
}

The serialization is the same for both of the following instantiations of the struct’s members:

let my_struct = MyStruct {
    a: 2, b: 5, c: [1,2,3]
};

let my_struct = MyStruct {
    b: 5, c: [1,2,3], a: 2
};

The serialization of MyStruct is determined as shown in the table Serialization for a struct in Cairo.

Table 3. Serialization for a struct in Cairo
Member	Description	Serialization
`a: 2`	For information on serializing `u256` values, see Serialization of `u256` values	[`2,0`]
`b: 5`	One `felt252` value	`5`
`c: [1,2,3]`	An array of three `felt252` values	[`3,1,2,3`]

Combining the above, the struct is serialized as follows: [0,2,5,3,1,2,3]

Serialization of byte arrays

A string is represented in Cairo as a ByteArray type. A byte array is actually a struct with the following members:

data: Array<felt252>
Contains 31-byte chunks of the byte array. Each felt252 value has exactly 31 bytes. If the number of bytes in the byte array is less than 31, then this array is empty.
pending_word: felt252
The bytes that remain after filling the data array with full 31-byte chunks. The pending word consists of at most 30 bytes.
pending_word_len: usize
The number of bytes in pending_word.

Example 1: A string shorter than 31 characters

Consider the string hello, whose ASCII encoding is the 5-byte hex value 0x68656c6c6f. The resulting byte array is serialized as follows:

    0, // Number of 31-byte words in the data array.
    0x68656c6c6f, // Pending word
    5 // Length of the pending word, in bytes

Example 2: A string longer than 31 bytes

Consider the string Long string, more than 31 characters., which is represented by the following hex values:

0x4c6f6e6720737472696e672c206d6f7265207468616e203331206368617261 (31-byte word)
0x63746572732e (6-byte pending word)

The resulting byte array is serialized as follows:

    1, // Number of 31-byte words in the array construct.
    0x4c6f6e6720737472696e672c206d6f7265207468616e203331206368617261, // 31-byte word.
    0x63746572732e, // Pending word
    6 // Length of the pending word, in bytes

Additional resources

Integer types in The Cairo Programming Language.