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math: clean up the polynomial.h header.

wip/core-clipp
Sam Hocevar 4 years ago
parent
a38dc4a104
commit
8d5891b88a
1 changed files with 45 additions and 44 deletions
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  1. +45
    -44
      include/lol/math/polynomial.h

legacy/lol/math/polynomial.h → include/lol/math/polynomial.h View File

@@ -1,25 +1,27 @@
//
// Lol Engine
// Lol Engine
//
// Copyright: (c) 2010-2014 Sam Hocevar <sam@hocevar.net>
// This program is free software; you can redistribute it and/or
// modify it under the terms of the Do What The Fuck You Want To
// Public License, Version 2, as published by Sam Hocevar. See
// http://www.wtfpl.net/ for more details.
// Copyright © 2010—2020 Sam Hocevar <sam@hocevar.net>
//
// Lol Engine is free software. It comes without any warranty, to
// the extent permitted by applicable law. You can redistribute it
// and/or modify it under the terms of the Do What the Fuck You Want
// to Public License, Version 2, as published by the WTFPL Task Force.
// See http://www.wtfpl.net/ for more details.
//

#pragma once

//
// The polynomial class
// --------------------
//
// ————————————————————
// The data structure is a simple dynamic array of scalars, with the
// added guarantee that the leading coefficient is always non-zero.
//

#include <functional>

#include <lol/base/features.h>
#include <tuple> // std::tuple
#include <cassert> // assert()

namespace lol
{
@@ -33,7 +35,7 @@ struct LOL_ATTR_NODISCARD polynomial
/* A constant polynomial */
explicit inline polynomial(T const &a)
{
m_coefficients.push(a);
m_coefficients.push_back(a);
reduce_degree();
}

@@ -41,7 +43,7 @@ struct LOL_ATTR_NODISCARD polynomial
explicit polynomial(std::initializer_list<T> const &init)
{
for (auto a : init)
m_coefficients.push(a);
m_coefficients.push_back(a);

reduce_degree();
}
@@ -50,7 +52,7 @@ struct LOL_ATTR_NODISCARD polynomial
static polynomial<T> chebyshev(int n)
{
/* Use T0(x) = 1, T1(x) = x, Tn(x) = 2 x Tn-1(x) - Tn-2(x) */
std::function<int64_t (int, int)> coeff = [&](int i, int j)
auto coeff = [&](int i, int j) -> int64_t
{
if (i > j || i < 0 || ((j ^ i) & 1))
return (int64_t)0;
@@ -61,7 +63,7 @@ struct LOL_ATTR_NODISCARD polynomial

polynomial<T> ret;
for (int k = 0; k <= n; ++k)
ret.m_coefficients.push(T(coeff(k, n)));
ret.m_coefficients.push_back(T(coeff(k, n)));
return ret;
}

@@ -69,19 +71,19 @@ struct LOL_ATTR_NODISCARD polynomial
* degree -1 on purpose. */
inline int degree() const
{
return (int)m_coefficients.count() - 1;
return (int)m_coefficients.size() - 1;
}

/* Set one of the polynomial’s coefficients */
void set(int n, T const &a)
{
ASSERT(n >= 0);
assert(n >= 0);

if (n > degree() && !a)
return;

while (n > degree())
m_coefficients.push(T(0));
m_coefficients.push_back(T(0));

m_coefficients[n] = a;
reduce_degree();
@@ -103,27 +105,26 @@ struct LOL_ATTR_NODISCARD polynomial
/* No need to reduce the degree after deriving. */
polynomial<T> ret;
for (int i = 1; i <= degree(); ++i)
ret.m_coefficients.push(m_coefficients[i] * T(i));
ret.m_coefficients.push_back(m_coefficients[i] * T(i));
return ret;
}

array<T> roots() const
std::vector<T> roots() const
{
/* For now we can only solve polynomials of degrees 0, 1, 2 or 3. */
ASSERT(degree() >= 0 && degree() <= 3,
"roots() called on polynomial of degree %d", degree());
assert(degree() >= 0 && degree() <= 3);

if (degree() == 0)
{
/* p(x) = a > 0 */
return array<T> {};
return {};
}
else if (degree() == 1)
{
/* p(x) = ax + b */
T const &a = m_coefficients[1];
T const &b = m_coefficients[0];
return array<T> { -b / a };
return { -b / a };
}
else if (degree() == 2)
{
@@ -137,16 +138,16 @@ struct LOL_ATTR_NODISCARD polynomial

if (delta < T(0))
{
return array<T> {};
return {};
}
else if (delta > T(0))
{
T const sqrt_delta = sqrt(delta);
return array<T> { -k - sqrt_delta, -k + sqrt_delta };
return { -k - sqrt_delta, -k + sqrt_delta };
}
else
{
return array<T> { -k };
return { -k };
}
}
else if (degree() == 3)
@@ -227,33 +228,33 @@ struct LOL_ATTR_NODISCARD polynomial

if (a == d && b == c && b == T(3)*a) // triple solution
{
return array<T> { solutions[0] - k };
return { solutions[0] - k };
}

// if root of the derivative is also root of the current polynomial, we have a double root.
for (auto root : (polynomial<T>{ c, T(2) * b, T(3) * a }).roots())
{
if (eval(root) == T(0))
return array<T> { (solutions[0] + solutions[2]) / T(2) - k,
solutions[1] - k };
return { (solutions[0] + solutions[2]) / T(2) - k,
solutions[1] - k };
}

// we have 3 or 1 root depending on delta sign
if (delta > 0)
{
return array<T> { solutions[0] - k };
return { solutions[0] - k };
}
else // if (delta < 0) 3 real solutions
{
return array<T> { solutions[0] - k,
solutions[1] - k,
solutions[2] - k };
return { solutions[0] - k,
solutions[1] - k,
solutions[2] - k };
}
}

/* It is an error to reach this point. */
ASSERT(false);
return array<T> {};
assert(false);
return {};
}

/* Access individual coefficients. This is read-only and returns a
@@ -296,7 +297,7 @@ struct LOL_ATTR_NODISCARD polynomial
{
polynomial<T> ret;
for (auto a : m_coefficients)
ret.m_coefficients.push(-a);
ret.m_coefficients.push_back(-a);
return ret;
}

@@ -309,7 +310,7 @@ struct LOL_ATTR_NODISCARD polynomial
m_coefficients[i] += p[i];

for (int i = min_degree + 1; i <= p.degree(); ++i)
m_coefficients.push(p[i]);
m_coefficients.push_back(p[i]);

reduce_degree();
return *this;
@@ -371,7 +372,7 @@ struct LOL_ATTR_NODISCARD polynomial
{
int n = p.degree() + q.degree();
for (int i = 0; i <= n; ++i)
ret.m_coefficients.push(T(0));
ret.m_coefficients.push_back(T(0));

for (int i = 0; i <= p.degree(); ++i)
for (int j = 0; j <= q.degree(); ++j)
@@ -385,13 +386,13 @@ struct LOL_ATTR_NODISCARD polynomial

/* Divide a polynomial by another one. There is no /= variant because
* the return value contains both the quotient and the remainder. */
tuple<polynomial<T>, polynomial<T>> operator /(polynomial<T> p) const
std::tuple<polynomial<T>, polynomial<T>> operator /(polynomial<T> p) const
{
ASSERT(p.degree() >= 0);
assert(p.degree() >= 0);

tuple<polynomial<T>, polynomial<T>> ret;
polynomial<T> &quotient = ret.m1;
polynomial<T> &remainder = ret.m2;
std::tuple<polynomial<T>, polynomial<T>> ret;
polynomial<T> &quotient = std::get<0>(ret);
polynomial<T> &remainder = std::get<1>(ret);

remainder = *this / p.leading();
p /= p.leading();
@@ -416,7 +417,7 @@ private:
}

/* The polynomial coefficients */
array<T> m_coefficients;
std::vector<T> m_coefficients;
};

template<typename T>

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