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### 875. Missing `initializer_list` constructor for `piecewise_constant_distribution`

Section: 26.6.9.6.2 [rand.dist.samp.pconst] Status: Resolved Submitter: Daniel Krügler Opened: 2008-08-22 Last modified: 2016-01-28

Priority: Not Prioritized

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Discussion:

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.

Proposed resolution:

Non-concept version of the proposed resolution

1. In 26.6.9.6.2 [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+. . .+wn-1` shall hold. For all sampled values `xk` defined below, `fw(xk)` shall return a weight value `wk` that is non-negative, non-NaN, and non-infinity;
   > > 3. If `nf > 0` let `bk = *(bl.begin() + k), k = 0, . . . , bl.size()-1` and the following relations shall hold for `k = 0, . . . , nf-1: bk < bk+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:

   > >       > xk = 0.5*(bk+1 + bk) wk = fw(xk)

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

   > >    > ρk = wk/(S * (bk+1 - bk)) for k = 0, . . . , n-1.

Concept version of the proposed resolution

1. In 26.6.9.6.2 [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+. . .+wn-1` shall hold. For all sampled values `xk` defined below, `fw(xk)` shall return a weight value `wk` that is non-negative, non-NaN, and non-infinity;
   > > 2. If `nf > 0` let `bk = *(bl.begin() + k), k = 0, . . . , bl.size()-1` and the following relations shall hold for `k = 0, . . . , nf-1: bk < bk+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:

   > >       > xk = 0.5*(bk+1 + bk) wk = fw(xk)

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

   > >    > ρk = wk/(S * (bk+1 - bk)) for k = 0, . . . , n-1.

Rationale:

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