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⚡️ Optimize SignedWadMath.wadLn integer part calculation #416

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@sodii sodii commented Jul 5, 2024

Description

I've changed the SignedWadMath.wadLn to use a precomputed table for calculating integer part.

assembly {
    r := shl(7, lt(0xffffffffffffffffffffffffffffffff, x))
    r := or(r, shl(6, lt(0xffffffffffffffff, shr(r, x))))
    r := or(r, shl(5, lt(0xffffffff, shr(r, x))))
    r := or(r, shl(4, lt(0xffff, shr(r, x))))
    r := or(r, shl(3, lt(0xff, shr(r, x))))
    r := or(r, shl(2, lt(0xf, shr(r, x))))
    
    // I've changed the two lines below:
    // r := or(r, shl(1, lt(0x3, shr(r, x))))
    // r := or(r, lt(0x1, shr(r, x)))

    // into:
    r := or(r, byte(shr(r, x), 0x0000010102020202030303030303030303000000000000000000000000000000))
}

This saves 45 gas.

To measure gas savings of the change, I've also implemented a crude test for wadLn and wadExp:

function testWadLnExp(uint256 x) public {
    x = bound(x, 0, 135305999368893231588 + 10e18);

    int256 xPrime = int256(x) - 10e18;
    int256 diff = wadLn(wadExp(xPrime)) - xPrime;

    assertLe(diff < 0 ? -diff : diff, 100000);
}

The tested range is -10e18 <= x <= 135305999368893231588.
135305999368893231588 is the largest integer where wadExp(x) doesn't overflow.
-10e18 is somewhat arbitariliy chosen because the test was failing for -20e18.

Checklist

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  • Ran forge snapshot?
  • Ran npm run lint?
  • Ran forge test?

Pull requests with an incomplete checklist will be thrown out.

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