In IEEE 754, why does adding negative zero result in a no-op but adding positive zero does not?

Question

I'm toying with some algorithm in Rust (though the language doesn't really matter for my question). Consider the code:

#[no_mangle]
pub fn test(x: f32) -> f32 {
    let m = 0.;
    x + m
}

fn main() {
    test(2.);
}

It produces the following LLVM IR and corresponding x86_64 asm (optimizations enabled):

;; LLVM IR
define float @test(float %x) unnamed_addr #0 {
start:
    %0 = fadd float %x, 0.000000e+00
    ret float %0
}

;; x86_64
; test:
    xorps xmm1, xmm1
    addss xmm0, xmm1
    ret

If I change let m = 0.; to let m = -0.; the floating point addition is optimized away:

;; LLVM IR
define float @test(float returned %x) unnamed_addr #0 {
start:
    ret float %x
}

;; x86_64
; fn disappears entirely

Parasympathetic

Consider fn(-0.0). – Gera

so far as I can tell so far gcc allows two different compile time options, and for a simple C example of the question, with default settings similar results, change the setting and both positive and negative zero generate code other than a return. so it sounds like the rouding answer is the key, but the compiler does matter and the settings. Does rust provide compile time options for different rounding mode choices? – Downthrow

didnt find a compile setting for clang that is supported, yet... – Downthrow

@old_timer, from what I've read, LLVM have no means to change the rounding mode (and assume any other than default during its optimization pass), so have Rust. – Parasympathetic

Does this answer your question? Why does Clang optimize away x * 1.0 but NOT x + 0.0? – Kenwood

Answer 1

In the default round-to-nearest mode, that most high-level languages support exclusively, because they do not provide options to disable floating-point optimizations that become inapplicable in other modes—I assume that Rust falls in this category—, adding -0.0 happens to have no effect on any floating-point value (omitting small details about NaNs), whereas adding +0.0 has an effect on -0.0 (the result of -0.0 + (+0.0) is +0.0).

Roquefort