Why does long long n = 2000*2000*2000*2000; overflow?

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Because 2000 is an int which is usually 32-bit. Just use 2000LL.

Using LL suffix instead of ll was suggested by @AdrianMole in, now deleted, comment. Please check his answer.

By default, integer literals are of the smallest type that can hold their value but not smaller than int. 2000 can easily be stored in an int since the Standard guarantees it is effectively at least a 16-bit type.

Arithmetic operators are always called with the larger of the types present but not smaller than int:

  • char*char will be promoted to operator*(int,int)->int
  • char*int calls operator*(int,int)->int
  • long*int calls operator*(long,long)->long
  • int*int still calls operator*(int,int)->int.

Crucially, the type is not dependent on whether the result can be stored in the inferred type. Which is exactly the problem happening in your case – multiplication is done with ints but the result overflows as it is still stored as int.

C++ does not support inferring types based on their destination like Haskell does so the assignment is irrelevant.

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