[patch, libstdc++] std::shuffle: Generate two swap positions at a time if possible

[Jonathan Wakely]

On 31/08/16 13:45 +0100, Jonathan Wakely wrote:
>On 03/05/16 16:42 +0200, Eelis van der Weegen wrote:
>>Ah, thanks, I forgot to re-attach when I sent to include the libstdc++ list.
>>
>>On 2016-05-03 14:38, Jonathan Wakely wrote:
>>>ENOPATCH
>>>
>>>On 1 May 2016 at 15:21, Eelis <eelis@eelis.net> wrote:
>>>>Sorry, forgot to include the libstdc++ list.
>>>>
>>>>On 2016-05-01 16:18, Eelis wrote:
>>>>>
>>>>>Hi,
>>>>>
>>>>>The attached patch optimizes std::shuffle for the very common case
>>>>>where the generator range is large enough that a single invocation
>>>>>can produce two swap positions.
>>>>>
>>>>>This reduces the runtime of the following testcase by 37% on my machine:
>>>>>
>>>>>     int main()
>>>>>     {
>>>>>         std::mt19937 gen;
>>>>>
>>>>>         std::vector<int> v;
>>>>>         v.reserve(10000);
>>>>>         for (int i = 0; i != 10000; ++i)
>>>>>         {
>>>>>             v.push_back(i);
>>>>>             std::shuffle(v.begin(), v.end(), gen);
>>>>>         }
>>>>>
>>>>>         std::cout << v.front() << '\n';
>>>>>     }
>>>>>
>>>>>Thoughts?
>>>>>
>>>>>Thanks,
>>>>>
>>>>>Eelis
>>>>>
>>>>
>>>>
>>
>
>>Index: libstdc++-v3/include/bits/stl_algo.h
>>===================================================================
>>--- libstdc++-v3/include/bits/stl_algo.h	(revision 235680)
>>+++ libstdc++-v3/include/bits/stl_algo.h	(working copy)
>>@@ -3708,6 +3708,22 @@
>>#endif
>>
>>#ifdef _GLIBCXX_USE_C99_STDINT_TR1
>>+
>>+  template<typename _IntType, typename _UniformRandomNumberGenerator>
>
>We should avoid introducing new names based on "uniform random number
>generator" and use _UniformRandomBitGenerator as per
>https://wg21.link/p0346r1
>
>>+    inline _IntType
>>+    __generate_random_index_below(_IntType __bound, _UniformRandomNumberGenerator& __g)
>>+    {
>>+      const _IntType __urngrange = __g.max() - __g.min() + 1;
>
>Similarly, let's use __urbgrange here.
>
>>+      const _IntType __scaling = __urngrange / __bound;
>
>I think I'd like either a comment on the function documenting the
>assumption about __bound and __g, or an explicit check:
>
>       __glibcxx_assert( __scaling >= __bound );
>
>>+      const _IntType __past = __bound * __scaling;
>>+
>>+      for (;;)
>>+      {
>>+	const _IntType __r = _IntType(__g()) - __g.min();
>>+	if (__r < __past) return __r / __scaling;
>
>This is basically the same algorithm as uniform_int_distribution so
>doesn't introduce any bias, right?
>
>Is this significantly faster than just using
>uniform_int_distribution<_IntType>{0, __bound - 1}(__g) so we don't
>need to duplicate the logic? (And people maintaining the code won't
>reconvince themselves it's correct every time they look at it :-)
>
>
>>+      }
>>+    }
>>+
>>  /**
>>   *  @brief Shuffle the elements of a sequence using a uniform random
>>   *         number generator.
>>@@ -3740,6 +3756,40 @@
>>      typedef typename std::make_unsigned<_DistanceType>::type __ud_type;
>>      typedef typename std::uniform_int_distribution<__ud_type> __distr_type;
>>      typedef typename __distr_type::param_type __p_type;
>>+
>>+      typedef typename std::remove_reference<_UniformRandomNumberGenerator>::type _Gen;
>>+      typedef typename std::common_type<typename _Gen::result_type, __ud_type>::type __uc_type;
>>+
>>+      const __uc_type __urngrange = _Gen::max() - _Gen::min() + 1;
>>+      const __uc_type __urange = __uc_type(__last - __first);
>>+
>>+      if (__urngrange / __urange >= __urange)
>>+        // I.e. (__urngrange >= __urange * __urange) but without wrap issues.
>>+      {
>>+	for (_RandomAccessIterator __i = __first + 1; __i != __last; )
>>+	{
>>+	  const __uc_type __swap_range = __uc_type(__i - __first) + 1;
>>+
>>+	  if (__i + 1 == __last)
>
>Could we hoist this test out of the loop somehow?
>
>If we change the loop condition to be __i+1 < __last we don't need to
>test it on every iteration, and then after the loop we can just do
>the final swap if (__urange % 2).
>
>>+	  {
>>+	    const __uc_type __pos = __generate_random_index_below(__swap_range, __g);
>>+	    std::iter_swap(__i, __first + __pos);
>>+	    return;
>>+	  }
>>+
>>+	  // Use a single generator invocation to produce swap positions for
>>+	  // both of the next two elements:
>>+
>>+	  const __uc_type __comp_range = __swap_range * (__swap_range + 1);
>>+	  const __uc_type __pospos = __generate_random_index_below(__comp_range, __g);
>>+
>>+	  std::iter_swap(__i++, __first + (__pospos % __swap_range));
>>+	  std::iter_swap(__i++, __first + (__pospos / __swap_range));
>
>I think I've convinced myself this is correct :-)
>
>Values of __pospos will be uniformly distributed in [0, __comp_range)

iThis is true, but ...

>and so the / and % results will be too.

This isn't.

If __swap_range is 3, then __comp_range is 10 and
__pospos is uniformly distributed in [0, 9].

(__pospos % __swap_range) is not uniformly distributed, we get
P(0) = 0.4, P(1) = 0.3, P(2) = 0.3.

Similarly, (__pospos / __swap_range) is not uniform, we get
P(0) = 0.3, P(1) = 0.3, P(2) = 0.3, P(3) = 0.1

This means that certain permuations of the input are more likely than
others, which fails to meet the requirements of the function.

Or is there a flaw in my reasoning?