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libstdc++: Optimize uniform_int_distribution using Lemire's algorithm

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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.
This commit is contained in:
Daniel Lemire 2020-10-09 14:09:36 +01:00 committed by Jonathan Wakely
parent 6ce2cb116a
commit 98c37d3bac
1 changed files with 54 additions and 7 deletions
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49
libstdc++-v3/include/bits/uniform_int_dist.h
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@ -234,6 +234,34 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
const param_type& __p);
param_type _M_param;
// Lemire's nearly divisionless algorithm.
// Returns an unbiased random number from __g downscaled to [0,__range)
// using an unsigned type _Wp twice as wide as unsigned type _Up.
template<typename _Wp, typename _Urbg, typename _Up>
static _Up
_S_nd(_Urbg& __g, _Up __range)
{
using __gnu_cxx::__int_traits;
static_assert(!__int_traits<_Up>::__is_signed, "U must be unsigned");
static_assert(!__int_traits<_Wp>::__is_signed, "W must be unsigned");
// 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 __low = _Up(__product);
if (__low < __range)
{
_Up __threshold = -__range % __range;
while (__low < __threshold)
{
__product = _Wp(__g()) * _Wp(__range);
__low = _Up(__product);
}
}
return __product >> __gnu_cxx::__int_traits<_Up>::__digits;
}
};
template<typename _IntType>
@ -256,11 +284,29 @@ _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
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
@ -268,6 +314,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
while (__ret >= __past);
__ret /= __scaling;
}
}
else if (__urngrange < __urange)
{
// upscaling