[bjourne]

Everything is relative. :) Compared to the add instruction itself, the overflow check is very expensive. But the big problem is that your types widen. E.g:

    // x and y are hardware integers >= 0
    var z = x + y
    for (var i = 0; i < z; i++) {
        ...
    }

If your language used modular arithmetic, 'z' would also be a hardware integer and the induction variable 'i' could be kept in a cpu register. But with real arithmetic using bignums you can't assume that anymore and each iteration of the loop must do a relatively expensive comparison of 'i' against 'z'. In pseudo code:

    var z = x + y
    var i = 0
    if (!hw_int(z)) i = new_bignum(0)
    while (true) {
      // i < z
      if (hw_ints?(i, z)) {
        if (i >= z) break
      } else {        
        if (bignum_gte(i, z)) break
      }        
      ... body ...
      // i++
      if (hw_int?(i)) {
        i++;
      } else {
        i = bignum_add(i, 1)
      }
    }

[rurban]

No, it's super cheap. overflows happen <1%, so you mark it as UNLIKELY, and the branch prediction units just don't care about all those bignum branches.

If you know to use bigints or bignums, just type it and use their variants from the beginning.

Most better dynamic languages already use tagged ints, so they have only say ~30bits for an int and do a lot of those overflow checks and still beat the hell out of the poorly designed dynamic languages with full boxed ints or nums.