在IEEE 754中，为什么添加负零会导致无操作，而添加正零却不会呢? [英] In IEEE 754, why does adding negative zero result in a no-op but adding positive zero does not?

问题描述

我正在研究Rust中的一些算法(尽管语言对我的问题并不重要).考虑代码:

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.);
}

它会产生以下LLVM IR和相应的x86_64 asm(启用优化):

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

如果将let m = 0.;更改为let m = -0.;，浮点加法将被优化:

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

推荐答案

在默认的最近舍入模式下，大多数高级语言都专门支持，因为它们不提供禁用浮点优化的选项在其他模式下不适用(我认为Rust属于此类)，添加-0.0不会对任何浮点值产生影响(忽略有关NaN的小细节)，而添加+0.0会对-0.0产生影响(-0.0 + (+0.0)的结果是+0.0).

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).

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