Rationale:

Addressed by N2836 "Wording Tweaks for Concept-enabled Random Number Generation in C++0X".

Proposed resolution:

Non-concept version of the proposed resolution

1. In [rand.dist.samp.pconst]/1, class piecewise_constant_distribution, just before the member declaration

   explicit piecewise_constant_distribution(const param_type& parm);
   

   insert

   template<typename Func>
   piecewise_constant_distribution(initializer_list<RealType> bl, Func fw);
   

2. Between p.4 and p.5 of the same section insert a series of new paragraphs nominated below as [p5_1], [p5_2], and [p5_3] as part of the new member description:

   template<typename Func>
   piecewise_constant_distribution(initializer_list<RealType> bl, Func fw);
   

   [p5_1] Complexity: Exactly nf = max(bl.size(), 1) - 1 invocations of fw.

   [p5_2] Requires:

   1. fw shall be callable with one argument of type RealType, and shall return values of a type convertible to double;
   2. The relation 0 < S = w₀+. . .+w_n-1 shall hold. For all sampled values x_k defined below, fw(x_k) shall return a weight value w_k that is non-negative, non-NaN, and non-infinity;
   3. If nf > 0 let b_k = *(bl.begin() + k), k = 0, . . . , bl.size()-1 and the following relations shall hold for k = 0, . . . , nf-1: b_k < b_k+1.

   [p5_3] Effects:

   1. If nf == 0,

      1. lets the sequence w have length n = 1 and consist of the single value w₀ = 1, and
      2. lets the sequence b have length n+1 with b₀ = 0 and b₁ = 1.

   2. Otherwise,

      1. sets n = nf, and [bl.begin(), bl.end()) shall form the sequence b of length n+1, and

      2. lets the sequences w have length n and for each k = 0, . . . ,n-1, calculates:

         x_k = 0.5*(b_k+1 + b_k) w_k = fw(x_k)

   3. Constructs a piecewise_constant_distribution object with the above computed sequence b as the interval boundaries and with the probability densities:

      ρ_k = w_k/(S * (b_k+1 - b_k)) for k = 0, . . . , n-1.

Concept version of the proposed resolution

1. In [rand.dist.samp.pconst]/1, class piecewise_constant_distribution, just before the member declaration

   explicit piecewise_constant_distribution(const param_type& parm);
   

   insert

   template<Callable<auto, RealType> Func>
    requires Convertible<Func::result_type, double>
   piecewise_constant_distribution(initializer_list<RealType> bl, Func fw);
   

2. Between p.4 and p.5 of the same section insert a series of new paragraphs nominated below as [p5_1], [p5_2], and [p5_3] as part of the new member description:

   template<Callable<auto, RealType> Func>
    requires Convertible<Func::result_type, double>
   piecewise_constant_distribution(initializer_list<RealType> bl, Func fw);
   

   [p5_1] Complexity: Exactly nf = max(bl.size(), 1) - 1 invocations of fw.

   [p5_2] Requires:

   1. The relation 0 < S = w₀+. . .+w_n-1 shall hold. For all sampled values x_k defined below, fw(x_k) shall return a weight value w_k that is non-negative, non-NaN, and non-infinity;
   2. If nf > 0 let b_k = *(bl.begin() + k), k = 0, . . . , bl.size()-1 and the following relations shall hold for k = 0, . . . , nf-1: b_k < b_k+1.

   [p5_3] Effects:

   1. If nf == 0,

      1. lets the sequence w have length n = 1 and consist of the single value w₀ = 1, and
      2. lets the sequence b have length n+1 with b₀ = 0 and b₁ = 1.

   2. Otherwise,

      1. sets n = nf, and [bl.begin(), bl.end()) shall form the sequence b of length n+1, and

      2. lets the sequences w have length n and for each k = 0, . . . ,n-1, calculates:

         x_k = 0.5*(b_k+1 + b_k) w_k = fw(x_k)

   3. Constructs a piecewise_constant_distribution object with the above computed sequence b as the interval boundaries and with the probability densities:

      ρ_k = w_k/(S * (b_k+1 - b_k)) for k = 0, . . . , n-1.

During the Sophia Antipolis meeting it was decided to separate from 794 a subrequest that adds initializer list support to piecewise_constant_distribution, specifically, the issue proposed to add a c'tor taking a initializer_list<double> and a Callable to evaluate weight values. For consistency with the remainder of this class and the remainder of the initializer_list-aware library the author decided to change the list argument type to the template parameter RealType instead. For the reasoning to use Func instead of Func&& as c'tor function argument see issue 793.