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### 794. `piecewise_constant_distribution` missing constructor

Section: 26.6.9.6.2 [rand.dist.samp.pconst] Status: Resolved Submitter: P.J. Plauger Opened: 2008-02-09 Last modified: 2016-01-28

Priority: Not Prioritized

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Discussion:

`piecewise_constant_distribution` should have a constructor like:

>     template<class _Fn>
>        piecewise_constant_distribution(size_t _Count,
>                 _Ty _Low, _Ty _High, _Fn& _Func);

(Makes it easier to fill a histogram with function values over a range. The two (reference 793) make a sensible replacement for `general_pdf_distribution`.)

[ Sophia Antipolis: ]

> Marc: uses variable width of bins and weight for each bin. This is not giving enough flexibility to control both variables.

> Add a library issue to provide an constructor taking an `initializer_list<double>` and `_Fn` for `piecewise_constant_distribution`.

> Daniel to draft wording.

[ Pre San Francisco, Daniel provided wording. ]

> The here proposed changes of the WP refer to the current state of N2691. For reasons explained in 793, the author decided to propose a function argument that is provided by value. The issue proposes a c'tor signature, that does not take advantage of the full flexibility of `piecewise_constant_distribution`, because it restricts on a constant bin width, but the use-case seems to be popular enough to justify it's introduction.

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(size_t nf, RealType xmin, RealType xmax, Func fw);

2. Between p.4 and p.5 insert a new sequence of paragraphs nominated below as [p5_1], [p5_2], [p5_3], and [p5_4] as part of the new member description:

   >     template<typename Func>
   >     piecewise_constant_distribution(size_t nf, RealType xmin, RealType xmax, Func fw);

   > > [p5_1] Complexity: Exactly `nf` 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. For all sample values `xk` defined below, fw(`xk`) shall return a weight value `wk` that is non-negative, non-NaN, and non-infinity;
   > > 3. The following relations shall hold: `xmin` < `xmax`, and 0 < S = `w0`+. . .+`wn-1`.

   > > [p5_3] Effects:

   > > 1. If nf == 0,

   > >    1. sets deltax = `xmax` - `xmin`, and
   > >    2. lets the sequence `w` have length `n = 1` and consist of the single value `w0` = 1, and
   > >    3. lets the sequence `b` have length `n+1` with `b0` = `xmin` and `b1` = `xmax`

   > > 2. Otherwise,

   > >    1. sets `n = nf`, `deltax =` (`xmax` - `xmin`)/n, `xcent` = `xmin` + 0.5 * deltax, and

   > >    2. lets the sequences `w` and `b` have length `n` and `n+1`, resp. and

   > >       for each k = 0, . . . ,n-1, calculates:

   > >       `dxk` = k * deltax `bk` = `xmin` + `dxk` `xk` = `xcent` + `dxk` `wk` = fw(`xk`),

   > >       and

   > >    3. sets `bn` = `xmax`

   > > 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 * deltax) for k = 0, . . . , n-1.

   > > [p5_4] [Note: In this context, the subintervals [`bk`, `bk+1`) are commonly known as the bins of a histogram. -- end note]

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(size_t nf, RealType xmin, RealType xmax, Func fw);

2. Between p.4 and p.5 insert a new sequence of paragraphs nominated below as [p5_1], [p5_2], [p5_3], and [p5_4] as part of the new member description:

   >     template<Callable<auto, RealType> Func>
   >      requires Convertible<Func::result_type, double>
   >     piecewise_constant_distribution(size_t nf, RealType xmin, RealType xmax, Func fw);

   > > [p5_1] Complexity: Exactly `nf` invocations of `fw`.

   > > [p5_2] Requires:

   > > 1. For all sample values `xk` defined below, fw(`xk`) shall return a weight value `wk` that is non-negative, non-NaN, and non-infinity;
   > > 2. The following relations shall hold: `xmin` < `xmax`, and 0 < S = `w0`+. . .+`wn-1`.

   > > [p5_3] Effects:

   > > 1. If nf == 0,

   > >    1. sets deltax = `xmax` - `xmin`, and
   > >    2. lets the sequence `w` have length `n = 1` and consist of the single value `w0` = 1, and
   > >    3. lets the sequence `b` have length `n+1` with `b0` = `xmin` and `b1` = `xmax`

   > > 2. Otherwise,

   > >    1. sets `n = nf`, `deltax =` (`xmax` - `xmin`)/n, `xcent` = `xmin` + 0.5 * deltax, and

   > >    2. lets the sequences `w` and `b` have length `n` and `n+1`, resp. and

   > >       for each k = 0, . . . ,n-1, calculates: `dxk` = k * deltax `bk` = `xmin` + `dxk` `xk` = `xcent` + `dxk` `wk` = fw(`xk`),

   > >       and

   > >    3. sets `bn` = `xmax`

   > > 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 * deltax) for k = 0, . . . , n-1.

   > > [p5_4] [Note: In this context, the subintervals [`bk`, `bk+1`) are commonly known as the bins of a histogram. -- end note]

Rationale:

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