cstd.hh

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#ifndef CSTD_HH
#define CSTD_HH

#include "string_view.hh"
#include <cmath>
#include <cstddef>
#include <functional>
#include <utility>

namespace cstd {

// Inspired by this post:
//    http://tristanbrindle.com/posts/a-more-useful-compile-time-quicksort

// Constexpr reimplementations of standard algorithms or data-structures.
//
// Everything implemented in 'cstd' will very likely become part of standard
// C++ in the future. Or it already is part of C++17. So in the future we can
// remove our (re)implementation and change the callers from 'cstd::xxx()' to
// 'std::xxx()'.

//
// Various constexpr reimplementation of STL algorithms.
//
// Many of these are already constexpr in C++17, or are proposed to be made
// constexpr for the next C++ standard.
//

// begin/end are already constexpr in c++17
template<typename Container>
constexpr auto begin(Container&& c)
{
        return c.begin();
}

template<typename Container>
constexpr auto end(Container&& c)
{
        return c.end();
}


template<typename Iter1, typename Iter2>
constexpr void iter_swap(Iter1 a, Iter2 b)
{
        auto temp = std::move(*a);
        *a = std::move(*b);
        *b = std::move(temp);
}

template<typename InputIt, typename UnaryPredicate>
constexpr InputIt find_if_not(InputIt first, InputIt last, UnaryPredicate p)
{
        for (; first != last; ++first) {
                if (!p(*first)) {
                        return first;
                }
        }
        return last;
}

template<typename ForwardIt, typename UnaryPredicate>
constexpr ForwardIt partition(ForwardIt first, ForwardIt last, UnaryPredicate p)
{
        first = cstd::find_if_not(first, last, p);
        if (first == last) return first;

        for (ForwardIt i = first + 1; i != last; ++i) {
                if (p(*i)) {
                        cstd::iter_swap(i, first);
                        ++first;
                }
        }
        return first;
}

// Workaround for lack of C++17 constexpr-lambda-functions.
template<typename T, typename Compare>
struct CmpLeft
{
        T pivot;
        Compare cmp;

        constexpr bool operator()(const T& elem) const {
                return cmp(elem, pivot);
        }
};

// Workaround for lack of C++17 constexpr-lambda-functions.
template<typename T, typename Compare>
struct CmpRight
{
        T pivot;
        Compare cmp;

        constexpr bool operator()(const T& elem) const {
                return !cmp(pivot, elem);
        }
};

// Textbook implementation of quick sort. Not optimized, but the intention is
// that it only gets executed during compile-time.
template<typename RAIt, typename Compare = std::less<>>
constexpr void sort(RAIt first, RAIt last, Compare cmp = Compare{})
{
        auto const N = last - first;
        if (N <= 1) return;
        auto const pivot = *(first + N / 2);
        auto const middle1 = cstd::partition(
                first, last, CmpLeft<decltype(pivot), Compare>{pivot, cmp});
        auto const middle2 = cstd::partition(
                middle1, last, CmpRight<decltype(pivot), Compare>{pivot, cmp});
        cstd::sort(first, middle1, cmp);
        cstd::sort(middle2, last, cmp);
}

template<typename RandomAccessRange, typename Compare = std::less<>>
constexpr void sort(RandomAccessRange&& range, Compare cmp = Compare{})
{
        cstd::sort(cstd::begin(range), cstd::end(range), cmp);
}

template<typename InputIt1, typename InputIt2>
constexpr bool lexicographical_compare(InputIt1 first1, InputIt1 last1,
                                       InputIt2 first2, InputIt2 last2)
{
        for (; (first1 != last1) && (first2 != last2); ++first1, ++first2) {
                if (*first1 < *first2) return true;
                if (*first2 < *first1) return false;
        }
        return (first1 == last1) && (first2 != last2);
}

// In C++17 this is (constexpr) available as std::char_traits::length().
constexpr size_t strlen(const char* s) noexcept
{
        auto* p = s;
        while (*p) ++p;
        return p - s;
}


//
// Constrexpr reimplementation of (a subset of) std::array.
// Can be removed once we switch to C++17.
//

template<typename T, size_t N> struct array
{
        T storage[N];

        using value_type             = T;
        using pointer                = T*;
        using const_pointer          = const T*;
        using reference              = T&;
        using const_reference        = const T&;
        using iterator               = T*;
        using const_iterator         = const T*;
        using size_type              = size_t;
        using difference_type        = ptrdiff_t;

        constexpr T* begin() noexcept
        {
                return storage;
        }

        constexpr const T* begin() const noexcept
        {
                return storage;
        }

        constexpr T* end() noexcept
        {
                return storage + N;
        }

        constexpr const T* end() const noexcept
        {
                return storage + N;
        }

        constexpr size_type size() const noexcept
        {
                return N;
        }

        constexpr bool empty() const noexcept
        {
                return N == 0;
        }

        constexpr T& operator[](size_type n) noexcept
        {
                return storage[n];
        }

        constexpr const T& operator[](size_type n) const noexcept
        {
                return storage[n];
        }

        constexpr T& front() noexcept
        {
                return storage[0];
        }

        constexpr const T& front() const noexcept
        {
                return storage[0];
        }

        constexpr T& back() noexcept
        {
                return storage[N - 1];
        }

        constexpr const T& back() const noexcept
        {
                return storage[N - 1];
        }

        constexpr T* data() noexcept
        {
                return storage;
        }

        constexpr const T* data() const noexcept
        {
                return storage;
        }
};

template<typename V, typename ...Ts>
constexpr cstd::array<V, sizeof...(Ts)> array_of(Ts&& ...ts)
{
    return {{ std::forward<Ts>(ts)... }};
}


//
// Reimplementation of (a very small subset of) C++17 std::string_view.
//
// The main difference with our string_view class is that cstd::string offers
// a constexpr constructor.
//

class string
{
public:
        constexpr string(const char* s)
                : dat(s), sz(cstd::strlen(s))
        {
        }

        constexpr const char* begin() const
        {
                return dat;
        }

        constexpr const char* end() const
        {
                return dat + sz;
        }

        friend constexpr bool operator<(string x, string y)
        {
                return cstd::lexicographical_compare(x.begin(), x.end(),
                                                     y.begin(), y.end());
        }

        operator string_view() const
        {
                return string_view(dat, sz);
        }

private:
        const char* dat;
        size_t sz;
};

// Reimplementation of various mathematical functions. You must specify an
// iteration count, this controls how accurate the result will be.
#if (defined(__GNUC__) && !defined(__clang__))

// Gcc has constexpr versions of most mathematical functions (this is a
// non-standard extension). Prefer those over our implementations.
template<int>      constexpr double sin  (double x) { return std::sin  (x); }
template<int>      constexpr double cos  (double x) { return std::cos  (x); }
template<int, int> constexpr double log  (double x) { return std::log  (x); }
template<int, int> constexpr double log2 (double x) { return    ::log  (x) / ::log(2); } // should be std::log2(x) but this doesn't seem to compile in g++-4.8/g++-4.9 (bug?)
template<int, int> constexpr double log10(double x) { return std::log10(x); }
template<int>      constexpr double exp  (double x) { return std::exp  (x); }
template<int>      constexpr double exp2 (double x) { return    ::exp2 (x); } // see log2, but apparently no need to use exp(log(2) * x) here?!
template<int, int> constexpr double pow(double x, double y) { return std::pow(x, y); }
inline constexpr double round(double x) { return ::round(x); } // should be std::round(), see above

#else

constexpr double upow(double x, unsigned u)
{
    double y = 1.0;
    while (u) {
        if (u & 1) y *= x;
        x *= x;
        u >>= 1;
    }
    return y;
}

constexpr double ipow(double x, int i)
{
        return (i >= 0) ? upow(x, i) : upow(x, -i);
}

template<int ITERATIONS>
constexpr double exp(double x)
{
    // Split x into integral and fractional part:
    //   exp(x) = exp(i + f) = exp(i) * exp(f)
    //   with: i an int     (undefined if out of range)
    //         -1 < f < 1
    int i = int(x);
    double f = x - i;

    // Approximate exp(f) with Taylor series.
    double y = 1.0;
    double t = f;
    double n = 1.0;
    for (int k = 2; k < (2 + ITERATIONS); ++k) {
        y += t / n;
        t *= f;
        n *= k;
    }

    // Approximate exp(i) by squaring.
    int p = (i >= 0) ? i : -i; // abs(i);
    double s = upow(M_E, p);

    // Combine the results.
    if (i >= 0) {
        return y * s;
    } else {
        return y / s;
    }
}

constexpr double simple_fmod(double x, double y)
{
    assert(y > 0.0);
    return x - int(x / y) * y;
}

template<int ITERATIONS>
constexpr double sin_iter(double x)
{
    double x2 = x * x;
    double y = 0.0;
    double t = x;
    double n = 1.0;
    for (int k = 1; k < (1 + 4 * ITERATIONS); ) {
        y += t / n;
        t *= x2;
        n *= ++k;
        n *= ++k;

        y -= t / n;
        t *= x2;
        n *= ++k;
        n *= ++k;
    }
    return y;
}

template<int ITERATIONS>
constexpr double cos_iter(double x)
{
    double x2 = x * x;
    double y = 1.0;
    double t = x2;
    double n = 2.0;
    for (int k = 2; k < (2 + 4 * ITERATIONS); ) {
        y -= t / n;
        t *= x2;
        n *= ++k;
        n *= ++k;

        y += t / n;
        t *= x2;
        n *= ++k;
        n *= ++k;
    }
    return y;
}

template<int ITERATIONS>
constexpr double sin(double x)
{
    double sign = 1.0;

    // reduce to [0, +inf)
    if (x < 0.0) {
        sign = -1.0;
        x = -x;
    }

    // reduce to [0, 2pi)
    x = simple_fmod(x, 2 * M_PI);

    // reduce to [0, pi]
    if (x > M_PI) {
        sign = -sign;
        x -= M_PI;
    }

    // reduce to [0, pi/2]
    if (x > M_PI/2) {
        x = M_PI - x;
    }

    // reduce to [0, pi/4]
    if (x > M_PI/4) {
        x = M_PI/2 - x;
        return sign * cos_iter<ITERATIONS>(x);
    } else {
        return sign * sin_iter<ITERATIONS>(x);
    }
}

template<int ITERATIONS>
constexpr double cos(double x)
{
    double sign = 1.0;

    // reduce to [0, +inf)
    if (x < 0.0) {
        x = -x;
    }

    // reduce to [0, 2pi)
    x = simple_fmod(x, 2 * M_PI);

    // reduce to [0, pi]
    if (x > M_PI) {
        x = 2.0 * M_PI - x;
    }

    // reduce to [0, pi/2]
    if (x > M_PI/2) {
        sign = -sign;
        x = M_PI - x;
    }

    // reduce to [0, pi/4]
    if (x > M_PI/4) {
        x = M_PI/2 - x;
        return sign * sin_iter<ITERATIONS>(x);
    } else {
        return sign * cos_iter<ITERATIONS>(x);
    }
}


// https://en.wikipedia.org/wiki/Natural_logarithm#High_precision
template<int E_ITERATIONS, int L_ITERATIONS>
constexpr double log(double x)
{
        int a = 0;
        while (x <= 0.25) {
                x *= M_E;
                ++a;
        }
        double y = 0.0;
        for (int i = 0; i < L_ITERATIONS; ++i) {
                auto ey = cstd::exp<E_ITERATIONS>(y);
                y = y + 2.0 * (x - ey) / (x + ey);
        }
        return y - a;
}

template<int E_ITERATIONS, int L_ITERATIONS>
constexpr double log2(double x)
{
        return cstd::log<E_ITERATIONS, L_ITERATIONS>(x) / M_LN2;
}

template<int E_ITERATIONS, int L_ITERATIONS>
constexpr double log10(double x)
{
        return cstd::log<E_ITERATIONS, L_ITERATIONS>(x) / M_LN10;
}

template<int E_ITERATIONS, int L_ITERATIONS>
constexpr double pow(double x, double y)
{
        return cstd::exp<E_ITERATIONS>(cstd::log<E_ITERATIONS, L_ITERATIONS>(x) * y);
}

template<int ITERATIONS>
constexpr double exp2(double x)
{
        return cstd::exp<ITERATIONS>(M_LN2 * x);
}

constexpr double round(double x)
{
        return (x >= 0) ?  int( x + 0.5)
                        : -int(-x + 0.5);
}

#endif

} // namespace cstd

#endif