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 <lem...@gmail.com>
Date: Tue Oct 6 00:05:52 2020
libstdc++: Optimize uniform_int_distribution using Lemire's algorithm
Co-authored-by: Jonathan Wakely <jwak...@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.
commit 5905c99cabca1433ff56befde5003fede50a5dc3
Author: Daniel Lemire <lem...@gmail.com>
Date: Tue Oct 6 00:34:39 2020
libstdc++: Optimize uniform_int_distribution using Lemire's algorithm
Co-authored-by: Jonathan Wakely <jwak...@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..18c88ca506d 100644
--- a/libstdc++-v3/include/bits/uniform_int_dist.h
+++ b/libstdc++-v3/include/bits/uniform_int_dist.h
@@ -234,6 +234,28 @@ _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)
+ {
+ // reference: Fast Random Integer Generation in an Interval
+ // ACM Transactions on Modeling and Computer Simulation 29 (1), 2019
+ // https://arxiv.org/abs/1805.10941
+ _Wp __product = _Wp(__g()) * _Wp(__range);
+ _Up __lsb = _Up(__product);
+ if (__lsb < __range)
+ {
+ _Up __threshold = -__range % __range;
+ while (__lsb < __threshold)
+ {
+ __product = _Wp(__g()) * _Wp(__range);
+ __lsb = _Up(__product);
+ }
+ }
+ return __product >> __gnu_cxx::__int_traits<_Up>::__digits;
+ }
};
template<typename _IntType>
@@ -256,17 +278,30 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
= __uctype(__param.b()) - __uctype(__param.a());
__uctype __ret;
-
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;
+
+ using __gnu_cxx::__int_traits;
+#if __SIZEOF_INT128__
+ if (__int_traits<__uctype>::__digits == 64
+ && __urngrange == __int_traits<__uctype>::__max)
+ __ret = _S_nd<unsigned __int128>(__urng, __uerange);
+ else
+#endif
+ if (__int_traits<__uctype>::__digits == 32
+ && __urngrange == __int_traits<__uctype>::__max)
+ __ret = _S_nd<__UINT64_TYPE__>(__urng, __uerange);
+ 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)
{
