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The top value of the stack is deconstructed into a bit array. Each element in this array is complimented. That is, if it was a one, it's turned to a zero, and vice versa.

The effect is really quite interesting. The sign of the number changes, and its value becomes significantly different.

0 ~

would be -1 I believe.

64 ~

is -4294967231 I believe.

All values are me working from memory, but you get the idea.