Anchor: How to know instruction number without having to run "cargo expand"?

Question

I have a Tic Tac Toe game contract which looks like this:

#[program]
pub mod tic_tac_toe {
    use super::*;

    pub fn start_game(ctx: Context<StartGame>) -> Result<()> {
        start::start_game(ctx)
    }

    // two other instructions here
}

If I run cargo expand I se that instruction numbers are expanded to this:

match sighash {
    [249, 47, 252, 172, 184, 162, 245, 14] => {
        __private::__global::start_game(program_id, accounts, ix_data)
    }
    // two other instructions here
    _ => Err(anchor_lang::error::ErrorCode::InstructionFallbackNotFound.into()),
}

Questions:

1. I have only three instructions. Why does Anchor generates 8 bytes per instruction? Why not one byte which would be enough to encode my three instruction numbers?
2. How can I derive this byte array without having to run cargo expand? I want to use this instruction id in Java and I cannot use the Anchors JavaScript APIs.
3. Can I give instructions predefined numbers? Let's say I want my instructions to be 1, 2 and 3.

Answer 1

Anchor uses the first 8 bytes of the sha256 of "namespace":"function_name" as the instruction identifiers. One byte would increase the risk of collision. At eight bytes, it's still possible for two different function names to generate the same 8 byte identifier, but very very unlikely.

You could rename your functions until the sha256 result is in the order you want, but you probably don't want to do that.

Here's a Rust function to compute the sighash:

pub fn get_function_hash(namespace: &str, name: &str) -> [u8; 8] {
    let preimage = format!("{}:{}", namespace, name);
    let mut sighash = [0u8; 8];
    sighash.copy_from_slice(
        &anchor_lang::solana_program::hash::hash(preimage.as_bytes()).to_bytes()
            [..8],
    );
    sighash
}