C++ implementation of linspace.

example-linspace.cpp

// -*- coding:utf-8; mode:c++; mode:auto-fill; fill-column:80; -*-

/// @file      example-linspace.cpp
/// @brief     Sample use of Nabla Zero Labs' linspace utilities.
/// @author    J. Arrieta <Juan.Arrieta@nablazerolabs.com>
/// @date      November 01, 2017
/// @copyright (c) 2017 Nabla Zero Labs
/// @license   MIT License

// C++ Standard Library
#include <iomanip>
#include <iostream>
#include <list>
#include <vector>

// Nabla Zero Labs Library
#include "linspace.hpp"

template <typename T>
void run_example() {
  auto p = std::numeric_limits<T>::max_digits10;
  auto w = p + 7;
  std::cout << std::setprecision(p) << std::scientific;

  // low-level iterator interface
  auto it = nzl::linspace_iterator<T>(-10, 10, 5);
  auto it_end = nzl::linspace_iterator<T>{};  // sentinel

  std::cout << "linspace_iterator\n";
  for (auto count = 0; it != it_end; ++it) {
    std::cout << "    linspace[" << count++ << "] = " << std::setw(w) << *it
              << "\n";
  }

  // range-based for (also ilustrating decreasing values)
  std::cout << "range-based\n";
  for (auto&& value : nzl::linspace<T>(10, -5, 6)) {
    std::cout << "    " << std::setw(w) << value << "\n";
  }

  // fill exising containers
  std::vector<T> v;
  v.resize(7);
  nzl::fill_linspace(v, -8, 3);
  std::cout << "fill vector\n";
  for (auto&& vi : v) std::cout << "    " << std::setw(w) << vi << "\n";

  // only the first five elements
  std::list<T> l;
  l.resize(10);
  nzl::fill_linspace_n(l.begin(), -1, 3, 5);
  std::cout << "fill elements [0, 5) in list\n";
  for (auto&& li : l) std::cout << "    " << std::setw(w) << li << "\n";

  // put a linspace in a new container
  auto x = nzl::as_linspace<std::vector<T>>(-3, 8, 10);
  std::cout << "create container\n";
  for (auto&& xi : x) std::cout << "    " << std::setw(w) << xi << "\n";
}

int main() {
  std::cout << "float\n";
  run_example<float>();

  std::cout << "double\n";
  run_example<double>();

  std::cout << "long double\n";
  run_example<long double>();
}

linspace.hpp

// -*- coding:utf-8; mode:c++; mode:auto-fill; fill-column:80; -*-

/// @file      nzl/linspace.hpp
/// @brief     Generate an linear space of floating point numbers.
/// @author    J. Arrieta <Juan.Arrieta@nablazerolabs.com>
/// @date      November 01, 2017
/// @copyright (c) 2017 Nabla Zero Labs
/// @license   MIT License

#pragma once
#ifndef NZL_LINSPACE_HPP_HEADER_GUARD
#define NZL_LINSPACE_HPP_HEADER_GUARD

// C++ Standard Library
#include <cstddef>
#include <iterator>
#include <limits>

namespace nzl {

/// @brief Iterator producing elements of a linear space.
template <typename T>  // T is any floating point type
class linspace_iterator {
 public:
  using iterator_category = std::input_iterator_tag;
  using value_type = T;
  using reference = T&;
  using pointer = T*;
  using difference_type = std::size_t;

  static_assert(
      std::is_floating_point<T>::value,
      "nzl::linspace_iterator is only defined for floating point types");

  explicit linspace_iterator() noexcept(true)
      : m_remaining{std::numeric_limits<std::size_t>::max()} {}

  linspace_iterator(T first, T last, std::size_t n) noexcept(true)
      : m_remaining{n - 1},
        m_current{std::move(first)},
        m_step{(last - m_current) / m_remaining},
        m_final{std::move(last)} {}

  linspace_iterator<T>& operator++() {
    this->next();
    return *this;
  }

  linspace_iterator<T> operator++(int) {
    auto tmp = *this;
    this->next();
    return tmp;
  }

  const value_type& operator*() const { return m_current; }

  const value_type* operator->() const { return std::addressof(*this); }

  bool operator!=(const linspace_iterator<T>& other) {
    return not(*this == other);
  }

  bool operator==(const linspace_iterator<T>& other) {
    return ((this->is_invalid() and other.is_invalid()) or
            std::memcmp(this, &other, sizeof(other)) == 0);
  }

  std::size_t size() const noexcept(true) { return m_remaining + 1; }

 private:
  bool is_invalid() const {
    return m_remaining == std::numeric_limits<std::size_t>::max();
  }

  void next() {
    switch (m_remaining) {
      case 1:
        m_current = m_final;
        --m_remaining;
        break;
      case 0:
        m_remaining = std::numeric_limits<std::size_t>::max();
        break;
      case std::numeric_limits<std::size_t>::max():
        break;
      default:
        m_current += m_step;
        --m_remaining;
        break;
    }
  }

  std::size_t m_remaining;
  T m_current;
  T m_step;
  T m_final;
};

/// @brief Range containing a linear space of floating point numbers.
template <typename T>
class linspace {
 public:
  linspace(T first, T last, std::size_t n = 100) noexcept(true)
      : m_it{first, last, n}, m_it_end{} {}
  linspace_iterator<T> begin() const noexcept(true) { return m_it; }
  linspace_iterator<T> end() const noexcept(true) { return m_it_end; }
  std::size_t size() const noexcept(true) { return m_it.size(); }

 private:
  linspace_iterator<T> m_it;
  linspace_iterator<T> m_it_end;
};

/// @brief Fill a range with a linear space.
template <typename I>  // I models InputIterator
inline void fill_linspace_n(I begin, typename I::value_type first,
                            typename I::value_type last, std::size_t n) {
  std::copy(linspace_iterator<typename I::value_type>(first, last, n),
            linspace_iterator<typename I::value_type>(), begin);
}

/// @brief Fill a range with a linear space.
template <typename I>  // I models InputIterator
inline void fill_linspace(I begin, I end, typename I::value_type first,
                          typename I::value_type last) {
  return fill_linspace_n(begin, first, last, std::distance(begin, end));
}

/// @brief Fill an existing sequence with a linear space.
template <typename S>  // S models SequenceContainer
inline S& fill_linspace(S& sequence_container, typename S::value_type first,
                        typename S::value_type last) {
  fill_linspace_n(sequence_container.begin(), first, last,
                  sequence_container.size());
  return sequence_container;
}

/// @brief Create a sequence filled with a linear space.
template <typename S>  // S models SequenceContainer
inline S as_linspace(typename S::value_type first, typename S::value_type last,
                     std::size_t n) {
  return S(linspace_iterator<typename S::value_type>(first, last, n),
           linspace_iterator<typename S::value_type>());
}

}  // namespace nzl

#endif  // NZL_LINSPACE_HPP_HEADER_GUARD

results.txt

$ clang++ example-linspace.cpp -std=c++17 -Wall -Wextra -Ofast -march=native
$ ./a.out
float
linspace_iterator
    linspace[0] = -1.000000000e+01
    linspace[1] = -5.000000000e+00
    linspace[2] =  0.000000000e+00
    linspace[3] =  5.000000000e+00
    linspace[4] =  1.000000000e+01
range-based
     1.000000000e+01
     7.000000000e+00
     4.000000000e+00
     1.000000000e+00
    -2.000000000e+00
    -5.000000000e+00
fill vector
    -8.000000000e+00
    -6.166666508e+00
    -4.333333015e+00
    -2.499999523e+00
    -6.666661501e-01
     1.166667223e+00
     3.000000000e+00
fill elements [0, 5) in list
    -1.000000000e+00
     0.000000000e+00
     1.000000000e+00
     2.000000000e+00
     3.000000000e+00
     0.000000000e+00
     0.000000000e+00
     0.000000000e+00
     0.000000000e+00
     0.000000000e+00
create container
    -3.000000000e+00
    -1.777777791e+00
    -5.555555820e-01
     6.666666269e-01
     1.888888836e+00
     3.111111164e+00
     4.333333492e+00
     5.555555820e+00
     6.777778149e+00
     8.000000000e+00
double
linspace_iterator
    linspace[0] = -1.00000000000000000e+01
    linspace[1] = -5.00000000000000000e+00
    linspace[2] =  0.00000000000000000e+00
    linspace[3] =  5.00000000000000000e+00
    linspace[4] =  1.00000000000000000e+01
range-based
     1.00000000000000000e+01
     7.00000000000000000e+00
     4.00000000000000000e+00
     1.00000000000000000e+00
    -2.00000000000000000e+00
    -5.00000000000000000e+00
fill vector
    -8.00000000000000000e+00
    -6.16666666666666696e+00
    -4.33333333333333393e+00
    -2.50000000000000089e+00
    -6.66666666666667629e-01
     1.16666666666666563e+00
     3.00000000000000000e+00
fill elements [0, 5) in list
    -1.00000000000000000e+00
     0.00000000000000000e+00
     1.00000000000000000e+00
     2.00000000000000000e+00
     3.00000000000000000e+00
     0.00000000000000000e+00
     0.00000000000000000e+00
     0.00000000000000000e+00
     0.00000000000000000e+00
     0.00000000000000000e+00
create container
    -3.00000000000000000e+00
    -1.77777777777777768e+00
    -5.55555555555555358e-01
     6.66666666666666963e-01
     1.88888888888888928e+00
     3.11111111111111160e+00
     4.33333333333333393e+00
     5.55555555555555625e+00
     6.77777777777777857e+00
     8.00000000000000000e+00
long double
linspace_iterator
    linspace[0] = -1.000000000000000000000e+01
    linspace[1] = -5.000000000000000000000e+00
    linspace[2] =  0.000000000000000000000e+00
    linspace[3] =  5.000000000000000000000e+00
    linspace[4] =  1.000000000000000000000e+01
range-based
     1.000000000000000000000e+01
     7.000000000000000000000e+00
     4.000000000000000000000e+00
     1.000000000000000000000e+00
    -2.000000000000000000000e+00
    -5.000000000000000000000e+00
fill vector
    -8.000000000000000000000e+00
    -6.166666666666666666522e+00
    -4.333333333333333333044e+00
    -2.499999999999999999566e+00
    -6.666666666666666661968e-01
     1.166666666666666667173e+00
     3.000000000000000000000e+00
fill elements [0, 5) in list
    -1.000000000000000000000e+00
     0.000000000000000000000e+00
     1.000000000000000000000e+00
     2.000000000000000000000e+00
     3.000000000000000000000e+00
     0.000000000000000000000e+00
     0.000000000000000000000e+00
     0.000000000000000000000e+00
     0.000000000000000000000e+00
     0.000000000000000000000e+00
create container
    -3.000000000000000000000e+00
    -1.777777777777777777754e+00
    -5.555555555555555555074e-01
     6.666666666666666667389e-01
     1.888888888888888888985e+00
     3.111111111111111111232e+00
     4.333333333333333333478e+00
     5.555555555555555555941e+00
     6.777777777777777777971e+00
     8.000000000000000000000e+00