Storage limit of 2-level mapping

Question

I know that you can have up to 2^256 entries in a single mapping.

However, if I am creating a mapping(address => mapping(uint => uint)), then does it mean that the inner mapping can also contain 2^256 entries?

Answer 1

Consider a 2-dimensional mapping mapping(uint256 => mapping(uint256 => uint256)) m;

You could insert 2²⁵⁶ values into m[0][0], m[0][1], ..., m[0][2 ** 256 - 1]. But there are “only” 2²⁵⁶ storage slots in the EVM, so if you proceeded to insert a further 2²⁵⁶ values into m[1][0], m[1][1], ..., m[1][2 ** 256 - 1], they would overwrite all the others.

Multi-dimensional mappings are just an illusion. When you access m[k1][k2], Solidity translates it into slot[f(k1, k2)]^†. So all 2²⁵⁶ × 2²⁵⁶ = 2⁵¹² possible combinations of k1 X k2 will have to map onto 2²⁵⁶ storage slots, so there are going to be many dogs for the same bone, so to speak. The good news is that 2²⁵⁶ is such an inconcievably large number that the probability of accessing two mapping values whose storage slots collide is inconcievably small, so in practice the illusion will never be broken and you don’t need to worry about it.

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† f(k1, k2) = keccak256(k2 . keccak256(k1 . p)), where p is 0 if the mapping is declared as the first storage variable, 1 if second, etc. More info in the docs.