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Implement Montgomery's batch inversion optimization #559

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Implement Montgomery's batch inversion optimization #559

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29 changes: 28 additions & 1 deletion jolt-evm-verifier/src/subprotocols/Fr.sol
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Original file line number Diff line number Diff line change
Expand Up @@ -81,7 +81,34 @@ library FrLib {
return Fr.wrap(result);
}

// TODO: Montgomery's batch inversion trick
// Montgomery's batch inversion trick implementation
function batchInvert(Fr[] memory values) internal view returns (Fr[] memory) {
uint256 n = values.length;
if (n == 0) return new Fr[](0);
if (n == 1) return [invert(values[0])];

Fr[] memory products = new Fr[](n);
products[0] = values[0];

// Compute partial products
for (uint256 i = 1; i < n; i++) {
products[i] = products[i-1] * values[i];
}

// Invert the final product
Fr running = invert(products[n-1]);
Fr[] memory results = new Fr[](n);

// Unwind the products
for (uint256 i = n-1; i > 0; i--) {
results[i] = running * products[i-1];
running = running * values[i];
}
results[0] = running;

return results;
}

function div(Fr numerator, Fr denominator) internal view returns (Fr) {
return numerator * invert(denominator);
}
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