From: Jonathan Wakely <jwakely@redhat.com>
To: Daniel Lemire <lemire@gmail.com>
Cc: libstdc++@gcc.gnu.org, gcc-patches@gcc.gnu.org
Subject: Re: [PATCH, libstdc++] Improve the performance of std::uniform_int_distribution (fewer divisions)
Date: Tue, 6 Oct 2020 00:40:31 +0100 [thread overview]
Message-ID: <20201005234031.GF7004@redhat.com> (raw)
In-Reply-To: <20201005232515.GD7004@redhat.com>
On 06/10/20 00:25 +0100, Jonathan Wakely wrote:
>I'm sorry it's taken a year to review this properly. Comments below ...
>
>On 27/09/19 14:18 -0400, Daniel Lemire wrote:
>>(This is a revised patch proposal. I am revising both the description
>>and the code itself.)
>>
>>Even on recent processors, integer division is relatively expensive.
>>The current implementation of std::uniform_int_distribution typically
>>requires two divisions by invocation:
>>
>> // downscaling
>> const __uctype __uerange = __urange + 1; // __urange can be zero
>> const __uctype __scaling = __urngrange / __uerange;
>> const __uctype __past = __uerange * __scaling;
>> do
>> __ret = __uctype(__urng()) - __urngmin;
>> while (__ret >= __past);
>> __ret /= __scaling;
>>
>>We can achieve the same algorithmic result with at most one division,
>>and typically no division at all without requiring more calls to the
>>random number generator.
>>This was recently added to Swift (https://github.com/apple/swift/pull/25286)
>>
>>The main challenge is that we need to be able to compute the "full"
>>product. E.g., given two 64-bit integers, we want the 128-bit result;
>>given two 32-bit integers we want the 64-bit result. This is fast on
>>common processors.
>>The 128-bit product is not natively supported in C/C++ but can be
>>achieved with the
>>__int128 extension when it is available. The patch checks for
>>__int128 support; when
>>support is lacking, we fallback on the existing approach which uses
>>two divisions per
>>call.
>>
>>For example, if we replace the above code by the following, we get a substantial
>>performance boost on skylake microarchitectures. E.g., it can
>>be twice as fast to shuffle arrays of 1 million elements (e.g., using
>>the followingbenchmark: https://github.com/lemire/simple_cpp_shuffle_benchmark )
>>
>>
>> unsigned __int128 __product = (unsigned
>>__int128)(__uctype(__urng()) - __urngmin) * uint64_t(__uerange);
>> uint64_t __lsb = uint64_t(__product);
>> if(__lsb < __uerange)
>> {
>> uint64_t __threshold = -uint64_t(__uerange) % uint64_t(__uerange);
>> while (__lsb < __threshold)
>> {
>> __product = (unsigned __int128)(__uctype(__urng()) -
>>__urngmin) * (unsigned __int128)(__uerange);
>> __lsb = uint64_t(__product);
>> }
>> }
>> __ret = __product >> 64;
>>
>>Included is a patch that would bring better performance (e.g., 2x gain) to
>>std::uniform_int_distribution in some cases. Here are some actual numbers...
>>
>>With this patch:
>>
>>std::shuffle(testvalues, testvalues + size, g) : 7952091
>>ns total, 7.95 ns per input key
>>
>>Before this patch:
>>
>>std::shuffle(testvalues, testvalues + size, g) :
>>14954058 ns total, 14.95 ns per input key
>>
>>
>>Compiler: GNU GCC 8.3 with -O3, hardware: Skylake (i7-6700).
>>
>>Furthermore, the new algorithm is unbiased, so the randomness of the
>>result is not affected.
>>
>>I ran both performance and biases tests with the proposed patch.
>>
>>
>>This patch proposal was improved following feedback by Jonathan
>>Wakely. An earlier version used the __uint128_t type, which is widely
>>supported but not used in the C++ library, instead we now use unsigned
>>__int128. Furthermore, the previous patch was accidentally broken: it
>>was not computing the full product since a rhs cast was missing. These
>>issues are fixed and verified.
>
>After looking at GCC's internals, it looks like __uint128_t is
>actually fine to use, even though we never currently use it in the
>library. I didn't even know it was supported for C++ mode, sorry!
>
>>Reference: Fast Random Integer Generation in an Interval, ACM Transactions on
>>Modeling and Computer Simulation 29 (1), 2019 https://arxiv.org/abs/1805.10941
>
>>Index: libstdc++-v3/include/bits/uniform_int_dist.h
>>===================================================================
>>--- libstdc++-v3/include/bits/uniform_int_dist.h (revision 276183)
>>+++ libstdc++-v3/include/bits/uniform_int_dist.h (working copy)
>>@@ -33,7 +33,8 @@
>>
>>#include <type_traits>
>>#include <limits>
>>-
>>+#include <cstdint>
>>+#include <cstdio>
>>namespace std _GLIBCXX_VISIBILITY(default)
>>{
>>_GLIBCXX_BEGIN_NAMESPACE_VERSION
>>@@ -239,18 +240,61 @@
>> = __uctype(__param.b()) - __uctype(__param.a());
>>
>> __uctype __ret;
>>-
>>- if (__urngrange > __urange)
>>+ if (__urngrange > __urange)
>> {
>>- // downscaling
>>- const __uctype __uerange = __urange + 1; // __urange can be zero
>>- const __uctype __scaling = __urngrange / __uerange;
>>- const __uctype __past = __uerange * __scaling;
>>- do
>>- __ret = __uctype(__urng()) - __urngmin;
>>- while (__ret >= __past);
>>- __ret /= __scaling;
>>- }
>>+ const __uctype __uerange = __urange + 1; // __urange can be zero
>>+#if _GLIBCXX_USE_INT128 == 1
>>+ if(sizeof(__uctype) == sizeof(uint64_t) and
>>+ (__urngrange == numeric_limits<uint64_t>::max()))
>>+ {
>>+ // 64-bit case
>>+ // reference: Fast Random Integer Generation in an Interval
>>+ // ACM Transactions on Modeling and Computer Simulation 29 (1), 2019
>>+ // https://arxiv.org/abs/1805.10941
>>+ unsigned __int128 __product = (unsigned __int128)(__uctype(__urng()) - __urngmin) * uint64_t(__uerange);
>
>Is subtracting __urngmin necessary here?
>
>The condition above checks that __urngrange == 2**64-1 which means
>that U::max() - U::min() is the maximum 64-bit value, which means
>means U::max()==2**64-1 and U::min()==0. So if U::min() is 0 we don't
>need to subtract it.
>
>Also, I think the casts to uint64_t are unnecessary. We know that
>__uctype is an unsigned integral type, and we've checked that it has
>exactly 64-bits, so I think we can just use __uctype. It's got the
>same width and signedness as uint64_t anyway.
>
>That said, the uint64_t(__uerange) above isn't redundant, because it
>should be (unsigned __int128)__uerange, I think.
Ah yes, you pointed out that last bit in your Sept 28 2019 email.
next prev parent reply other threads:[~2020-10-05 23:40 UTC|newest]
Thread overview: 9+ messages / expand[flat|nested] mbox.gz Atom feed top
2019-09-08 16:10 Daniel Lemire
2019-09-27 18:19 ` Daniel Lemire
2020-10-05 23:25 ` Jonathan Wakely
2020-10-05 23:38 ` Jonathan Wakely
2020-10-05 23:40 ` Jonathan Wakely [this message]
2020-10-06 19:09 ` Daniel Lemire
2020-10-06 19:55 ` Daniel Lemire
2020-10-06 20:04 ` Jonathan Wakely
2020-10-09 13:17 ` Jonathan Wakely
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