"<i>Can compilers (specifically rustc) really simplify triangle-summation to avoid a loop?<\/i>编译器（特别是 rustc）真的可以简化三角求和以避免循环吗？<\/b> <i>How?<\/i>如何？<\/b>"

Question

On page 322 of Programming Rust by Blandy and Orendorff is this claim:

...Rust...recognizes that there's a simpler way to sum the numbers from one to n : the sum is always equal to n * (n+1) / 2 .

This is of course a fairly well-known equivalence, but how does the compiler recognize it? I'm guessing it's in an LLVM optimization pass, but is LLVM somehow deriving the equivalence from first principles, or does it just have some set of "common loop computations" that can be simplified to arithmetic operations?

Answer 1

First of all, let's demonstrate that this actually happens.

pub fn sum(start: i32, end: i32) -> i32 {
    let mut result = 0;
    for i in start..end {
        result += i;
    }
    return result;
}