Java results differ for (int)Math.pow(2,x) and 1<<x
bit-shift, bitwise-operators, java
Solution
There are multiple issues at play:
- An `int` can only store values between `-2147483648` and `2147483647`.
- `1 << x` only uses the lowest five bits of `x`. Thus, `1 << 32` is by definition the same as `1 << 0`.
- Shift operations are performed on the two's-complement integer representation of the value of the left operand; this explains why `1 << 31` is negative.
- `Math.pow(2, 32)` returns a `double`.
- `(int)(d)`, where `d` is a `double` greater than `2147483647` returns `2147483647` ("the largest representable value of type `int`").
What this interview question does is show that `(int)Math.pow(2, x)` and `1 << x` are not equivalent for values of `x` outside the `0`...`30` range.
P.S. It is perhaps interesting to note that using `long` in place of `int` (and `1L` in place of `1`) would give yet another set of results different from the other two. This holds even if the final results are converted to `int`.
Problem
Why do the following two operations yield different results in Java for `x = 31` or `32` but the same results for `x=3`? ``` int x=3; int b = (int) Math.pow(2,x); int c = 1<<x; ``` Results: ``` x=32: b=2147483647; c=1; x=31: b=2147483647; c=-2147483648; x=3: b=8 ; c=8 ```