Potential solution to the overflow problem; 64-bit considered harmful, 32- or 21-bit better

General Usage
3

On X86, overflow checks should be cheap already because the carry and overflow flags will be set.
See MUL — Unsigned Multiply or IMUL — Signed Multiply for example.
Promoting to a larger integer size and then checking will not be faster.

You can confirm that Base.checked_add’s generated code is just an add followed by jo (jump if overflow flag is set):

# julia> @code_native debuginfo=:none syntax=:intel Base.checked_add(typemax(Int), 2)
        .text
        .file   "checked_add"
        .globl  julia_checked_add_5462          # -- Begin function julia_checked_add_5462
        .p2align        4, 0x90
        .type   julia_checked_add_5462,@function
julia_checked_add_5462:                 # @julia_checked_add_5462
        .cfi_startproc
# %bb.0:                                # %top
        mov     rdx, rsi
        mov     rax, rdi
        add     rax, rsi
        jo      .LBB0_1
# %bb.2:                                # %L7
        ret
.LBB0_1:                                # %L5
        sub     rsp, 8
        .cfi_def_cfa_offset 16
        mov     rsi, rdi
        movabs  rax, offset j_throw_overflowerr_binaryop_5464
        movabs  rdi, 140041153683800
        call    rax
        ud2
.Lfunc_end0:
        .size   julia_checked_add_5462, .Lfunc_end0-julia_checked_add_5462
        .cfi_endproc
                                        # -- End function
        .section        ".note.GNU-stack","",@progbits

Base.checked_add, Base.checked_mul, etc all already exist and are going to be about as efficient as it gets.

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