Binary parity

The fn odd_ones(x: u32) -> bool function should return true when x binary representation contains a odd number of 1s.
Assumption:

1. x is 32 bit unsigned.

Restriction:

1. The code should contain a total of at most 12 arithmetic, bitwise and logical operations.

Forbidden:

1. Conditionals ,loops, function calls and macros.
2. Division, modulus and multiplication.
3. Relative comparison operators (<, >, <= and >=).

Allowed operations:

1. All bit level and logic operations.
2. Left and right shifts, but only with shift amounts between 0 and w - 1
3. Addition and subtraction.
4. Equality (==) and inequality (!=) tests.
5. Casting between u32 and i32.

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My code: (Rust playground)

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fn odd_ones(x: u32) -> bool { let mid = (x >> 16) ^ x; let mid2 = (mid >> 8) ^ mid; let mid3 = (mid2 >> 4) ^ mid2; let mid4 = (mid3 >> 2) ^ mid3; (((mid4 >> 1) ^ mid4) & 1) == 1 } fn alternative_odd_ones(x: u32) -> bool { const NUM_BITS_EXPONENT: u32 = 5; let bit = (0..NUM_BITS_EXPONENT).rev() .map(|y| 1 << y ) .fold(x, |sum, y| (sum >> y) ^ sum ); (bit & 1) == 1 } fn odd_ones_test(x: u32) -> bool { let sum = (0..32).map(|y| x >> y & 1) .fold(0, |sum, y| sum + y); sum % 2 != 0 } fn test (from: u32, to: u32) -> bool { (from..to).all(|x| odd_ones_test(x) == odd_ones(x)) } fn main() { for x in (0..5).rev() { println!("{}", x);} println!("{}", test(!0 - 45345, !0)); }