Are local variables stored in memory or on the stack in Solidity?
If memory, is the memory freed after the function returns?
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For value types (booleans, integers, addresses ...) it's memory. For complex types (arrays, structs, maps) the default location depends on the context and can be overridden by
Whenever there is a need to perform some computation on the variable (adding, multiplying, negating ...) the variable will be moved from the memory/storage to the stack (along with other variables needed for the operation), the result will be put back to the memory/storage.
After returning from a function the free memory pointer will be updated so the unused memory can be reused. The return value of a function can also be located in the memory or storage.
The EVM has a stack-based architecture. It has a volatile memory where items are stored as byte arrays. The size of each stack item is 256-bit and the stack has a maximum size of 1024.
The memory is freed but your program will stop running if the new stack size is greater than 1024.
White paper - https://ethereum.org/whitepaper/
Yellow paper - https://ethereum.github.io/yellowpaper/paper.pdf