I ran a simple test on A57 rev. 0, looping a million times around sqrt{,f} and the respective series iterations with the values in the sequence 1..1000000 and got these results:
sqrt(x): 36593844/s 1/sqrt(x): 18283875/s 3 Steps: 47922557/s 3 Steps: 49005194/s sqrtf(x): 143988480/s 1/sqrtf(x): 69516857/s 2 Steps: 78740157/s 2 Steps: 80385852/s I'm a bit surprised that the 3-iteration series for DP is faster than sqrt(), but not that it's much faster for the reciprocal of sqrt(). As for SP, the 2-iteration series is faster only for the reciprocal for sqrtf(). There might still be some leg for this patch in real-world cases which I'd like to investigate. -- Evandro Menezes Austin, TX > -----Original Message----- > From: gcc-patches-ow...@gcc.gnu.org [mailto:gcc-patches-ow...@gcc.gnu.org] On > Behalf Of Kumar, Venkataramanan > Sent: Monday, June 29, 2015 13:50 > To: pins...@gmail.com; Dr. Philipp Tomsich > Cc: James Greenhalgh; Benedikt Huber; gcc-patches@gcc.gnu.org; Marcus > Shawcroft; Ramana Radhakrishnan; Richard Earnshaw > Subject: RE: [PATCH] [aarch64] Implemented reciprocal square root (rsqrt) > estimation in -ffast-math > > Hi, > > > -----Original Message----- > > From: pins...@gmail.com [mailto:pins...@gmail.com] > > Sent: Monday, June 29, 2015 10:23 PM > > To: Dr. Philipp Tomsich > > Cc: James Greenhalgh; Kumar, Venkataramanan; Benedikt Huber; gcc- > > patc...@gcc.gnu.org; Marcus Shawcroft; Ramana Radhakrishnan; Richard > > Earnshaw > > Subject: Re: [PATCH] [aarch64] Implemented reciprocal square root > > (rsqrt) estimation in -ffast-math > > > > > > > > > > > > > On Jun 29, 2015, at 4:44 AM, Dr. Philipp Tomsich > > <philipp.toms...@theobroma-systems.com> wrote: > > > > > > James, > > > > > >> On 29 Jun 2015, at 13:36, James Greenhalgh > > <james.greenha...@arm.com> wrote: > > >> > > >>> On Mon, Jun 29, 2015 at 10:18:23AM +0100, Kumar, Venkataramanan > > wrote: > > >>> > > >>>> -----Original Message----- > > >>>> From: Dr. Philipp Tomsich > > >>>> [mailto:philipp.toms...@theobroma-systems.com] > > >>>> Sent: Monday, June 29, 2015 2:17 PM > > >>>> To: Kumar, Venkataramanan > > >>>> Cc: pins...@gmail.com; Benedikt Huber; gcc-patches@gcc.gnu.org > > >>>> Subject: Re: [PATCH] [aarch64] Implemented reciprocal square root > > >>>> (rsqrt) estimation in -ffast-math > > >>>> > > >>>> Kumar, > > >>>> > > >>>> This does not come unexpected, as the initial estimation and each > > >>>> iteration will add an architecturally-defined number of bits of > > >>>> precision (ARMv8 guarantuees only a minimum number of bits > > provided > > >>>> per operation… the exact number is specific to each micro-arch, > > though). > > >>>> Depending on your architecture and on the required number of > > >>>> precise bits by any given benchmark, one may see miscompares. > > >>> > > >>> True. > > >> > > >> I would be very uncomfortable with this approach. > > > > > > Same here. The default must be safe. Always. > > > Unlike other architectures, we don’t have a problem with making the > > > proper defaults for “safety”, as the ARMv8 ISA guarantees a minimum > > > number of precise bits per iteration. > > > > > >> From Richard Biener's post in the thread Michael Matz linked > > >> earlier in the thread: > > >> > > >> It would follow existing practice of things we allow in > > >> -funsafe-math-optimizations. Existing practice in that we > > >> want to allow -ffast-math use with common benchmarks we care > > >> about. > > >> > > >> https://gcc.gnu.org/ml/gcc-patches/2009-11/msg00100.html > > >> > > >> With the solution you seem to be converging on (2-steps for some > > >> microarchitectures, 3 for others), a binary generated for one > > >> micro-arch may drop below a minimum guarantee of precision when run > > >> on another. This seems to go against the spirit of the practice > > >> above. I would only support adding this optimization to -Ofast if > > >> we could keep to architectural guarantees of precision in the > > >> generated code > > (i.e. 3-steps everywhere). > > >> > > >> I don't object to adding a "-mlow-precision-recip-sqrt" style > > >> option, which would be off by default, would enable the 2-step > > >> mode, and would need to be explicitly enabled (i.e. not implied by > > >> -mcpu=foo) but I don't see what this buys you beyond the Gromacs > > >> boost (and even there you would be creating an Invalid Run as > > >> optimization flags must be applied across all workloads). > > > > > > Any flag that reduces precision (and thus breaks IEEE floating-point > > > semantics) needs to be gated with an “unsafe” flag (i.e. one that is > > > never > > on by default). > > > As a consequence, the “peak”-tuning for SPEC will turn this on… but > > > barely anyone else would. > > > > > >> For the 3-step optimization, it is clear to me that for "generic" > > >> tuning we don't want this to be enabled by default experimental > > >> results and advice in this thread argues against it for thunderx > > >> and cortex- > > a57 targets. > > >> However, enabling it based on the CPU tuning selected seems fine to me. > > > > > > I do not agree on this one, as I would like to see the safe form (i.e. > > > 3 and 5 iterations respectively) to become the default. Most > > > “server-type” chips should not see a performance regression, while > > > it will be easier to optimise for this in hardware than for a > > > (potentially microcoded) sqrt-instruction (and subsequent, dependent > > divide). > > > > > > I have not heard anyone claim a performance regression (either on > > > thunderx or on cortex-a57), but merely heard a “no speed-up”. > > > > Actually it does regress performance on thunderX, I just assumed that > > when I said not going to be a win it was taken as a slow down. It > > regress gromacs by more than 10% on thunderX but I can't remember how > > much as i had someone else run it. The latency difference is also over > > 40%; for example single precision: 29 cycles with div (12) sqrt(17) > > directly vs 42 cycles with the rsqrte and 2 iterations of 2mul/rsqrts > > (double is 53 vs 60). That is huge difference right there. ThunderX has a > fast div and a fast sqrt for 32bit and a > > reasonable one for double. So again this is not just not a win but rather > a > > regression for thunderX. I suspect cortex-a57 is also true. > > > > Thanks, > > Andrew > > > > Yes theoretically should be true for cortex-57 case as well. But I > believe hardware pipelining with instruction scheduling in compiler helps a > little for gromacs case ~3% to 4% with the original patch. > > I have not tested other FP benchmarks. As James said a flag -mlow- > precision-recip-sqrt if allowed can be used as a peak flag. > > > > > > > So I am strongly in favor of defaulting to the ‘safe’ number of > > > iterations, even when compiling for a generic target. > > > > > > Best, > > > Philipp. > > > > > Regards, > Venkat.