RFR 8209171 : Simplify Java implementation of Integer/Long.numberOfTrailingZeros()
Ivan Gerasimov
ivan.gerasimov at oracle.com
Mon Aug 13 06:30:25 UTC 2018
On 8/12/18 10:57 AM, Martin Buchholz wrote:
> If delegating to nlz is the winner so far, we should be able to do at
> least as well by inlining nlz into ntz and then looking for more
> optimizations. Following this strategy leads naturally to
>
> static int ntz_inlineNlz2(int i) {
> i &= -i;
> if (i <= 0) return 32 - (i >>> 31);
> int n = 0;
> if (i >= 1 << 16) { n += 16; i >>>= 16; }
> if (i >= 1 << 8) { n += 8; i >>>= 8; }
> if (i >= 1 << 4) { n += 4; i >>>= 4; }
> if (i >= 1 << 2) { n += 2; i >>>= 2; }
> return n + (i >>> 1);
> }
>
Right. The variant numberOfLeadingZeros_01() from the benchmark is very
close to this, though you've got better handling of (i <= 0) case, so I
added it as numberOfLeadingZeros_01a() with a minor modification.
> which should save a branch and so should be a benchmark winner.
>
> A reason why delegating to nlz may have beat my previous attempt is
> because direct comparison with a constant is an operation the hardware
> tries hard to optimize, e.g. branch predict.
>
> Most of the comparisons should be false in practice because "most ints
> are small".
>
> I also see that our nlz implementation favors small integers, which
> helps with ntz.
>
> It's possible that benchmarking may cause branches to be very highly
> predictable. It should be more real-world for each benchmark method
> to see a variety of inputs, perhaps in an array.
>
Okay. Now I tried to combine calculating of several results in one
iteration of benchmark to make it harder to predict branches :)
Surprisingly, this made the variant 05 (reducing to nlz) the leader, for
which I don't have a good explanation, as it does strictly more
calculations than 01 or 01a even after inlining.
Anyways, please find the updated benchmark here:
http://cr.openjdk.java.net/~igerasim/8209171/03/bench/int/MyBenchmark.java
The graphs for -client and -server are here:
http://cr.openjdk.java.net/~igerasim/8209171/03/bench/int/bench-int-03-client.png
http://cr.openjdk.java.net/~igerasim/8209171/03/bench/int/bench-int-03-server.png
It took almost an hour to generate the results, so they seem to be quite
accurate.
So, I'm still inclined to prefer the variant 05 (which is to reduce ntz
to nlz) :)
With kind regards,
Ivan
>
> On Sun, Aug 12, 2018 at 7:22 AM, Ivan Gerasimov
> <ivan.gerasimov at oracle.com <mailto:ivan.gerasimov at oracle.com>> wrote:
>
> Hi Martin!
>
>
> On 8/11/18 5:54 PM, Martin Buchholz wrote:
>> Hi Ivan,
>>
>> Oh the allure of bit-twiddling!
>>
> Yes :)
>
>> I'm skeptical that ntz should ever delegate to nlz, and not only
>> because of the overhead of a wrapper, but because small numbers
>> are more common, and we can take that into account when
>> implementing ntz.
> I was under impression that the more frequently a function is
> called the faster it gets compiled, so all the callers of this
> function will benefit.
> For example, if numberOfTrailingZeros is reduced to
> numberOfLeadingZeros then when the later is compiled while the
> former is still not, it will still be running faster than the
> variant with independent implementations.
>
>> At least add "1" to the set of numbers to benchmark.
> In the last proposed patch, all odd numbers will be processed via
> a fast path (because for any odd i, ~i & (i - 1) == 0).
> So, I added 1, 16 and 42 -- small numbers with different number of
> trailing zeros.
>
> Here's the updated benchmark:
> http://cr.openjdk.java.net/~igerasim/8209171/02/bench/int/MyBenchmark.java
> <http://cr.openjdk.java.net/%7Eigerasim/8209171/02/bench/int/MyBenchmark.java>
> (I only executed four implementations to keep the picture clear.)
>
>> Here's my own entry in this race:
>>
>> static int ntz(int i) {
>> if (i == 0) return 32;
>> int n = 0;
>> if ((i << 16) == 0) { n += 16; i >>>= 16; }
>> if ((i & 0xFF) == 0) { n += 8; i >>>= 8; }
>> if ((i & 0xF) == 0) { n += 4; i >>>= 4; }
>> if ((i & 0x3) == 0) { n += 2; i >>>= 2; }
>> return n + (~i & 1);
>> }
>>
> Interesting!
> You might also avoid inversion at the end, if n is initialized
> with 1, and then the last line may be written as return n - (i & 1).
>
> Still this variant appears to be slower in most tried cases.
> Here's the graph of the latest benchmark:
> http://cr.openjdk.java.net/~igerasim/8209171/02/bench/int/bench-int-02-client.png
> <http://cr.openjdk.java.net/%7Eigerasim/8209171/02/bench/int/bench-int-02-client.png>
> http://cr.openjdk.java.net/~igerasim/8209171/02/bench/int/bench-int-02-server.png
> <http://cr.openjdk.java.net/%7Eigerasim/8209171/02/bench/int/bench-int-02-server.png>
>
> The variant from the test01 is the fastest in most cases, but I
> would prefer to proceed with the variant from test05:
> It's only slightly slower than 01, but contains less bytecode and
> helps to warm up numberOfLeadingZeros().
>
>> Whatever happens, we ought to check in the microbenchmarks
>> somewhere. It looks like the new jmh-jdk-microbenchmarks is the
>> place.
>> I also suspect that tests for these methods could be improved
>> (but there are existing hotspot tests).
>>
> To make sure the new code is correct I ran an exhaustive loop from
> Integer.MIN_VALUE to MAX_VALUE inclusive and checked all the
> tested variants of implementation.
>
>> nlz seems harder than ntz in the sense that for nlz "small ints"
>> and random bits may have different optimal implementations.
>>
>>
>> On Fri, Aug 10, 2018 at 7:03 PM, Ivan Gerasimov
>> <ivan.gerasimov at oracle.com <mailto:ivan.gerasimov at oracle.com>> wrote:
>>
>> Thanks Martin!
>>
>>
>> On 8/9/18 5:42 PM, Martin Buchholz wrote:
>>>
>>>
>>> On Thu, Aug 9, 2018 at 5:27 PM, Ivan Gerasimov
>>> <ivan.gerasimov at oracle.com
>>> <mailto:ivan.gerasimov at oracle.com>> wrote:
>>>
>>> I did not use the intrinsified variants of
>>> numberOfLeadingZeros in the benchmark.
>>>
>>>
>>> Oops! Should have looked more closely!
>>> Did you know about
>>> http://www.hackersdelight.org/hdcodetxt/ntz.c.txt
>>> <http://www.hackersdelight.org/hdcodetxt/ntz.c.txt>
>>
>> Ah, right, ntz1() is even better because it has less
>> branches. How could I miss that?
>>
>> Here's the updated webrev and benchmarks:
>>
>> http://cr.openjdk.java.net/~igerasim/8209171/01/webrev/
>> <http://cr.openjdk.java.net/%7Eigerasim/8209171/01/webrev/>
>> http://cr.openjdk.java.net/~igerasim/8209171/01/bench/int/MyBenchmark.java
>> <http://cr.openjdk.java.net/%7Eigerasim/8209171/01/bench/int/MyBenchmark.java>
>> http://cr.openjdk.java.net/~igerasim/8209171/01/bench/long/MyBenchmark.java
>> <http://cr.openjdk.java.net/%7Eigerasim/8209171/01/bench/long/MyBenchmark.java>
>>
>> --
>> With kind regards,
>> Ivan Gerasimov
>>
>>
>
> --
> With kind regards,
> Ivan Gerasimov
>
>
--
With kind regards,
Ivan Gerasimov
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