Hi everyone, I have a technical question:

We know that L2s are taking transaction load off of the Ethereum, but how is that process taking place? Is there a threshold of optimum transaction speed/cost? Are L2s only intervening when the L1 is congested or that threshold is passed?

_This question was originally posted on [StarkNet Discord](https://www.newton.so/view?tags=discord)_

 Is there a threshold of optimum transaction speed/cost in L2s?

Hello! This is day 7 of the 17 days of the Cairo Challenge. And I have no idea how to solve the [playground](https://www.cairo-lang.org/playground/) exercise “Recursion”.  Perhaps you can help me?

```
// The following code prints the sum of the numbers from 1 to 10.
// Modify the function `compute_sum` to print all the intermediate sums:
// 1, 1 + 2, 1 + 2 + 3, ..., 1 + 2 + ... + 10.
// Note: you'll have to add the implicit argument output_ptr to the
// declaration of compute_sum (in order to use the serialize_word function):
//   func compute_sum{output_ptr: felt*}(n: felt) -> (sum: felt)

// Use the output builtin.
%builtins output

from starkware.cairo.common.serialize import serialize_word

func compute_sum(n: felt) -> (sum: felt) {
    if (n == 0) {
        // When 0 is reached, return 0.
        return (sum=0);
    }

    // Otherwise, call `compute_sum` recursively to compute 1 + 2 + ... + (n-1).
    let (sum) = compute_sum(n=n - 1);
    // Add the new value `n` to the sum.
    let new_sum = sum + n;
    return (sum=new_sum);
}

func main{output_ptr: felt*}() {
    let (res) = compute_sum(n=10);

    // Output the result.
    serialize_word(res);
    return ();
}
```

---

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> 
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How to make recursive function in Cairo Lang?

does anyone know of newsletters that focus on StarkNet or the zk ecosystem in general?

_This question was originally posted on [StarkNet Discord](https://www.newton.so/view?tags=discord)_

Does anyone know of newsletters that focus on StarkNet or the zk ecosystem in general?

Hello guys, does one know how to modify keccak.cairo and/or packed_keccak.cairo to compute a 512bits keccak hash instead of 256 bits?

I'm following a paper that needs 256 bits collision resistance so i need 512 bit keccak. 

There should only a few parameters to change but its quite hard to find them in the Cairo code 

_This question was originally posted on [StarkNet Discord](https://www.newton.so/view?tags=discord)_

---

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How to modify keccak.cairo and/or packed_keccak.cairo to compute a 512bits keccak hash instead of 256 bits?


Trying to install warp with command `yarn global add @nethermindeth/warp`

after successful install I try:
`warp install --verbose`
get this error:

```
zsh: command not found: warp
```


How to install Nethermind's Solidity to Cairo transpiler without an error "command not found: warp"?

Can someone explain the difference `between unsigned_div_rem` and `uint256_unsigned_div_rem`?

Why unit version process so many extra steps, but overall number of steps for computing are different for these methods?



Can someone explain the difference between unsigned_div_rem and uint256_unsigned_div_rem?

hi all. If I want to use starkex do I have to deploy my custom starkex contracts ?
however in my understanding startex is a protocol where I have to intergrate my dapp specific tx, isn't it ?
in the playground I saw there're some preimplemented tx like ERC20 interface 
is starknet a starkex with an integrated VirtualMachine ?

_This question was originally posted on [StarkNet Discord](https://www.newton.so/view?tags=discord)_

If I want to use starkex do I have to deploy my custom starkex contracts?

Handwritten code will always be more efficient than compiled code, this is true for any compiled program. With Warp 2.x; we greatly improved the performance of the transpiled code, and it sits around 8-20x overhead compared depending on the contract. We are working on more optimisations all the time so as the compiler matures we should be able to reduce the overhead ever more


What kind of efficiency gains can one expect from writing the contracts directly in Cairo as opposed to transpiling with warp?

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What are the efficiency gains of direct Cairo vs. transpiling with warp?

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