⚡️ Optimise the Zero Point Threshold in wad_exp

[engn33r]

✅ PR Checklist

• Because this PR includes a bug fix, relevant tests have been included.
• Because this PR includes a new feature, the change was previously discussed in an issue or in the discussions section.
• I didn't do anything of this.

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This PR is for a very small optimization that is possible by increasing the range of values that will take the short logic path of wad_exp() and return zero. I am not sure how the previously chosen value of -42_139_678_854_452_767_551 was selected, but these tests demonstrate the actual turning point when the result of the current wad_exp() implementation transitions from 1 to zero.

    function testWadExpZeroPoint() public {
        assertEq(math.wad_exp(-41_446_531_673_892_822_312), 1);
        assertEq(math.wad_exp(-41_446_531_673_892_822_313), 0);
    }

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🐶 Cute Animal Picture

[pcaversaccio]

@engn33r great catch! The original number stems from Remco's article: https://xn--2-umb.com/22/exp-ln/index.html.

Can you please adjust the tests accordingly:

-  assertEq(math.wad_exp(-42_139_678_854_452_767_551), 0);
+ assertEq(math.wad_exp(-41_446_531_673_892_822_313), 0);
+ assertEq(math.wad_exp(-41_446_531_673_892_822_312), 1);

and also update the .gas-snapshot file (run forge snapshot). After that I will quickly make a CHANGELOG entry and merge.

[engn33r]

I made the requested changes.

Thanks for sharing the source, I didn't realize that's where the number originated from. I see solmate and solady are using the same value, I'll verify the same change can happen in their implementations and if so I'll link to this PR.

[pcaversaccio]

I made the requested changes.

Thanks for sharing the source, I didn't realize that's where the number originated from. I see solmate and solady are using the same value, I'll verify the same change can happen in their implementations and if so I'll link to this PR.

FWIW, I already shared it with @Vectorized!

[Vectorized]

@engn33r Beautiful optimization!

[engn33r]

Solmate PR and solady PR created

[pcaversaccio]

Solmate PR created and solady PR inbound (2 mins)

Sweet, will merge tomorrow (busy day due to Ledger...)

[pcaversaccio]

For anyone who wants to understand how to replicate this using Titanoboa, here a step-by-step guide:

~$ pip install git+https://github.com/vyperlang/titanoboa
~$ git clone https://github.com/pcaversaccio/snekmate.git
~$ cd snekmate/src/utils/
~$ python
>>> import boa
>>> c = boa.load("Math.vy")
>>> c.wad_exp(-41_446_531_673_892_822_312)
1
>>> c.wad_exp(-41_446_531_673_892_822_313)
0

[pcaversaccio]

Thx @engn33r!