[PATCH, libstdc++] Improve the performance of std::uniform_int_distribution (fewer divisions)
Jonathan Wakely
jwakely@redhat.com
Mon Oct 5 23:38:32 GMT 2020
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.
>
>i.e.
>
> unsigned __int128 __product = (unsigned __int128)__urng() * (unsigned __int128)__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;
>>+ }
>>+ else
>>+#endif // _GLIBCXX_USE_INT128 == 1
>>+ if(sizeof(__uctype) == sizeof(uint32_t)
>>+ and (__urngrange == numeric_limits<uint32_t>::max()) )
>>+ {
>>+ // 32-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
>>+ uint64_t __product = uint64_t(__uctype(__urng()) - __urngmin) * uint64_t(__uerange);
>>+ uint32_t __lsb = uint32_t(__product);
>>+ if(__lsb < __uerange) {
>>+ uint64_t __threshold = -uint32_t(__uerange) % uint32_t(__uerange);
>
>This __threshold should be uint32_t, right?
>
>>+ while (__lsb < __threshold) {
>>+ __product = uint64_t(__uctype(__urng()) - __urngmin) * uint64_t(__uerange);
>>+ __lsb = uint32_t(__product);
>>+ }
>>+ }
>>+ __ret = __product >> 32;
>>+ }
>>+ else
>>+ {
>>+ // fallback case (2 divisions)
>>+ const __uctype __scaling = __urngrange / __uerange;
>>+ const __uctype __past = __uerange * __scaling;
>>+ do
>>+ __ret = __uctype(__urng()) - __urngmin;
>>+ while (__ret >= __past);
>>+ __ret /= __scaling;
>>+ }
>>+ }
>> else if (__urngrange < __urange)
>> {
>> // upscaling
>
>I've attached a revised patch which hoists the clever bit into a
>separate function template so we don't need to repeat the code. I
>think it's still right and I haven't broken your logic.
>
>Does it look OK to you?
>
>
>commit b6e2027df22d9f3837b906c5b3de5cfe1fc5f0d7
>Author: Daniel Lemire <lemire@gmail.com>
>Date: Tue Oct 6 00:05:52 2020
>
> libstdc++: Optimize uniform_int_distribution using Lemire's algorithm
>
> Co-authored-by: Jonathan Wakely <jwakely@redhat.com>
>
> libstdc++-v3/ChangeLog:
>
> * include/bits/uniform_int_dist.h (uniform_int_distribution::_S_nd):
> New member function implementing Lemire's "nearly divisionless"
> algorithm.
> (uniform_int_distribution::operator()): Use _S_nd when the range
> of the URBG is the full width of the result type.
>
>diff --git a/libstdc++-v3/include/bits/uniform_int_dist.h b/libstdc++-v3/include/bits/uniform_int_dist.h
>index 6e1e3d5fc5f..9c6927e6923 100644
>--- a/libstdc++-v3/include/bits/uniform_int_dist.h
>+++ b/libstdc++-v3/include/bits/uniform_int_dist.h
>@@ -234,6 +234,33 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
> const param_type& __p);
>
> param_type _M_param;
>+
>+ // Lemire's nearly divisionless algorithm
>+ template<typename _Wp, typename _Urbg, typename _Up>
>+ static _Up
>+ _S_nd(_Urbg& __g, _Up __range)
>+ {
>+ using __gnu_cxx::__int_traits;
>+ constexpr __digits = __int_traits<_Up>::__digits;
>+ static_assert(__int_traits<_Wp>::__digits == (2 * __digits),
>+ "_Wp must be twice as wide as _Up");
Gah, this static_assert needs to be removed (the function is
instantiated for arguments that cause it to fail, even though that
instantiation isn't called). I hadn't committed that fix to git
before generating the patch though.
Correct patch attached.
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