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If I were trying to make a synthetic unsigned integer_512, but the largest supported integer in Ethereum is u256, how would I combine 2 u256 to make a single u512 in solidity?

If I were also looking to overload operators like gt, lt, eq, read/show/tostring, being mappable keys, on this joint data type---all of the functions that exist on a base data type, where is a good template for how to do this correctly or get started?

Thank you

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If you're only interested in those three comparison operators, then it's pretty easy:

struct uint512 {
    uint256 hi;
    uint256 lo;
}

function eq(uint512 x, uint512 y) internal pure returns (bool) {
    return x.hi == y.hi && x.lo == y.lo;
}

function lt(uint512 x, uint512 y) internal pure returns (bool) {
    return x.hi < y.hi || (x.hi == y.hi && x.lo < y.lo);
}

function gt(uint512 x, uint512 y) internal pure returns (bool) {
    return x.hi > y.hi || (x.hi == y.hi && x.lo > y.lo);
}

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