在某些情况下，在x86-64 Intel / AMD CPU上，128bit / 64bit硬件无符号除法能否比64bit / 32bit除法更快？

Question

Can a scaled 64bit/32bit division performed by the hardware 128bit/64bit division instruction, such as:

; Entry arguments: Dividend in EAX, Divisor in EBX
shl rax, 32  ;Scale up the Dividend by 2^32
xor rdx,rdx
and rbx, 0xFFFFFFFF  ;Clear any garbage that might have been in the upper half of RBX
div rbx  ; RAX = RDX:RAX / RBX

...be faster in some special cases than the scaled 64bit/32bit division performed by the hardware 64bit/32bit division instruction, such as:

; Entry arguments: Dividend in EAX, Divisor in EBX
mov edx,eax  ;Scale up the Dividend by 2^32
xor eax,eax
div ebx  ; EAX = EDX:EAX / EBX

By "some special cases" I mean unusual dividends and divisors. I am interested in comparing the div instruction only.

Answer 1

You're asking about optimizing uint64_t / uint64_t C division to a 64b / 32b => 32b x86 asm division, when the divisor is known to be 32-bit. The compiler must of course avoid the possibility of a #DE exception on a perfectly valid (in C) 64-bit division, otherwise it wouldn't have followed the as-if rule. So it can only do this if it's provable that the quotient will fit in 32 bits.

Yes, that's a win or at least break-even. On some CPUs it's even worth checking for the possibility at runtime because 64-bit division is so much slower. But unfortunately current x86 compilers don't have an optimizer pass to look for this optimization even when you do manage to give them enough info that they could prove it's safe. eg if (edx >= ebx) __builtin_unreachable(); doesn't help last time I tried.

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For the same inputs, 32-bit operand-size will always be at least as fast

16 or 8-bit could maybe be slower than 32 because they may have a false dependency writing their output, but writing a 32-bit register zero-extends to 64 to avoid that. (That's why mov ecx, ebx is a good way to zero-extend ebx to 64-bit, better than and a value that's not encodeable as a 32-bit sign-extended immediate, like harold pointed out). But other than partial-register shenanigans, 16-bit and 8-bit division are generally also as fast as 32-bit, or not worse.

On AMD CPUs, division performance doesn't depend on operand-size, just the data . 0 / 1 with 128/64-bit should be faster than worst-case of any smaller operand-size. AMD's integer-division instruction is only a 2 uops (presumably because it has to write 2 registers), with all the logic done in the execution unit.

16-bit / 8-bit => 8-bit division on Ryzen is a single uop (because it only has to write AH:AL = AX).

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On Intel CPUs, div / idiv is microcoded as many uops . About the same number of uops for all operand-sizes up to 32-bit (Skylake = 10), but 64-bit is much much slower . (Skylake div r64 is 36 uops, Skylake idiv r64 is 57 uops). See Agner Fog's instruction tables: https://agner.org/optimize/

div/idiv throughput for operand-sizes up to 32-bit is fixed at 1 per 6 cycles on Skylake. But div/idiv r64 throughput is one per 24-90 cycles.

See also Trial-division code runs 2x faster as 32-bit on Windows than 64-bit on Linux for a specific performance experiment where modifying the REX.W prefix in an existing binary to change div r64 into div r32 made a factor of ~3 difference in throughput.

And Why does Clang do this optimization trick only from Sandy Bridge onward? shows clang opportunistically using 32-bit division when the dividend is small, when tuning for Intel CPUs. But you have a large dividend and a large-enough divisor, which is a more complex case. That clang optimization is still zeroing the upper half of the dividend in asm, never using a non-zero or non-sign-extended EDX.

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I have failed to make the popular C compilers generate the latter code when dividing an unsigned 32-bit integer (shifted left 32 bits) by another 32-bit integer.

I'm assuming you cast that 32-bit integer to uint64_t first , to avoid UB and get a normal uint64_t / uint64_t in the C abstract machine.

That makes sense: Your way wouldn't be safe, it will fault with #DE when edx >= ebx . x86 division faults when the quotient overflows AL / AX / EAX / RAX, instead of silently truncating. There's no way to disable that.

So compilers normally only use idiv after cdq or cqo , and div only after zeroing the high half, unless you use an intrinsic or inline asm to open yourself up to the possibility of your code faulting. In C, x / y only faults if y = 0 (or for signed, INT_MIN / -1 is also allowed to fault ¹ ).

GNU C doesn't have an intrinsic for wide division, but MSVC has _udiv64 . (With gcc/clang, division wider than 1 register uses a helper function which does try to optimize for small inputs. But this doesn't help for 64/32 division on a 64-bit machine, where GCC and clang just use the 128/64-bit division instruction.)

Even if there were some way to promise the compiler that your divisor would be big enough to make the quotient fit in 32 bits, current gcc and clang don't look for that optimization in my experience. It would be a useful optimization for your case (if it's always safe), but compilers won't look for it.

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Footnote 1: To be more specific, ISO C describes those cases as "undefined behaviour"; some ISAs like ARM have non-faulting division instructions. C UB means anything can happen, including just truncation to 0 or some other integer result. See Why does integer division by -1 (negative one) result in FPE? for an example of AArch64 vs. x86 code-gen and results. Allowed to fault doesn't mean required to fault.

Answer 2

Can 128bit/64bit hardware unsigned division be faster in some cases than 64bit/32bit division on x86-64 Intel/AMD CPUs?

In theory, anything is possible (eg maybe in 50 years time Nvidia creates an 80x86 CPU that ...).

However, I can't think of a single plausible reason why a 128bit/64bit division would ever be faster than (not merely equivalent to) a 64bit/32bit division on x86-64.

I suspect this because I assume that the C compiler authors are very smart and so far I have failed to make the popular C compilers generate the latter code when dividing an unsigned 32-bit integer (shifted left 32 bits) by another 32-bit integer. It always compiles to the128bit/64bit div instruction. PS The left shift compiles fine to shl .

Compiler developers are smart, but compilers are complex and the C language rules get in the way. For example, if you just do a a = b/c; (with b being 64 bit and c being 32-bit) the language's rules are that c gets promoted to 64-bit before the division happens, so it ends up being a 64-bit divisor in some kind of intermediate language, and that makes it hard for the back-end translation (from intermediate language to assembly language) to tell that the 64-bit divisor could be a 32-bit divisor.