121. rem_euclid — The Modulo That Doesn't Go Negative

-1 % 7 in Rust is -1, not 6. That’s a math gotcha lurking in every wraparound index, every clock arithmetic, every “what day of the week” calculation. rem_euclid is the modulo you actually wanted.

Rust’s % operator follows the same rule as C: the sign of the result matches the sign of the dividend. Useful sometimes, surprising the rest of the time:

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assert_eq!(-1_i32 % 7, -1);
assert_eq!(-8_i32 % 7, -1);
assert_eq!( 8_i32 % 7,  1);

Try indexing a circular buffer with that and you get a panic the first time you step backwards across zero. The fix is rem_euclid, which always returns a value in [0, |divisor|):

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assert_eq!((-1_i32).rem_euclid(7), 6);
assert_eq!((-8_i32).rem_euclid(7), 6);
assert_eq!(( 8_i32).rem_euclid(7), 1);

A real-world shape — wrap an index around a slice in either direction, no if ladder, no manual + len trick:

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let days = ["Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun"];

fn day_after(today: i32, delta: i32) -> i32 {
    (today + delta).rem_euclid(7)
}

assert_eq!(days[day_after(0, -1) as usize], "Sun"); // Mon - 1 = Sun
assert_eq!(days[day_after(2,  4) as usize], "Sun"); // Wed + 4 = Sun
assert_eq!(days[day_after(0, -8) as usize], "Sun"); // wraps past week boundary

div_euclid is the partner that pairs with it: a.div_euclid(b) * b + a.rem_euclid(b) == a always holds, even for negative a. Plain / and % only satisfy that identity for non-negative inputs.

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let a = -7_i32;
let b =  3_i32;
assert_eq!(a.div_euclid(b) * b + a.rem_euclid(b), a);

Both are available on every signed integer type (and floats), and they’re const. The rule of thumb: if your code can ever see a negative operand and you want the mathematician’s modulo — not the hardware’s — reach for rem_euclid.