312 lines
7.3 KiB
C++
312 lines
7.3 KiB
C++
/*
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* This file is part of libgim.
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*
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* libgim is free software: you can redistribute it and/or modify it under the
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* terms of the GNU General Public License as published by the Free Software
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* Foundation, either version 3 of the License, or (at your option) any later
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* version.
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*
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* libgim is distributed in the hope that it will be useful, but WITHOUT ANY
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* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
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* details.
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*
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* You should have received a copy of the GNU General Public License
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* along with libgim. If not, see <http://www.gnu.org/licenses/>.
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*
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* Copyright 2010-2014 Danny Robson <danny@nerdcruft.net>
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*/
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#ifndef __MATHS_HPP
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#define __MATHS_HPP
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#include "debug.hpp"
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#include <cstdint>
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#include <type_traits>
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#include <utility>
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#include <cmath>
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template <typename T>
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T
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abs (T value)
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{ return value > 0 ? value : -value; }
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//-----------------------------------------------------------------------------
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// Exponentials
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template <typename T>
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constexpr T
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pow2 [[gnu::pure]] (T value)
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{ return value * value; }
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template <typename T>
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constexpr T
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pow [[gnu::pure]] (T x, unsigned y);
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template <typename T>
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bool
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is_pow2 [[gnu::pure]] (T value);
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//-----------------------------------------------------------------------------
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// Logarithms
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template <typename T>
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T
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log2 [[gnu::pure]] (T val);
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template <typename T>
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T
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log2up [[gnu::pure]] (T val);
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//-----------------------------------------------------------------------------
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// Roots
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template <typename T>
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double
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rootsquare [[gnu::pure]] (T a, T b);
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//-----------------------------------------------------------------------------
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// Rounding
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template <typename T, typename U>
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typename std::common_type<T, U>::type
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align [[gnu::pure]] (T value, U size);
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template <typename T>
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T
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round_pow2 [[gnu::pure]] (T value);
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template <typename T, typename U>
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constexpr T
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divup [[gnu::pure]] (const T a, const U b)
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{ return (a + b - 1) / b; }
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//-----------------------------------------------------------------------------
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// Classification
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template <typename T>
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bool
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is_integer [[gnu::pure]] (const T& value);
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//-----------------------------------------------------------------------------
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// Properties
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template <typename T>
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unsigned
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digits [[gnu::pure]] (const T& value);
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//-----------------------------------------------------------------------------
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template <typename T>
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int sign [[gnu::pure]] (T val);
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//-----------------------------------------------------------------------------
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// Comparisons
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template <typename T>
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bool
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almost_equal [[gnu::pure]] (const T &a, const T &b)
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{ return a == b; }
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template <>
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bool
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almost_equal [[gnu::pure]] (const float &a, const float &b);
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template <>
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bool
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almost_equal [[gnu::pure]] (const double &a, const double &b);
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template <typename Ta, typename Tb>
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typename std::enable_if<
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std::is_arithmetic<Ta>::value && std::is_arithmetic<Tb>::value,
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bool
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>::type
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almost_equal [[gnu::pure]] (Ta a, Tb b) {
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return almost_equal <decltype(a + b)> (static_cast<decltype(a + b)>(a),
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static_cast<decltype(a + b)>(b));
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}
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template <typename Ta, typename Tb>
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typename std::enable_if<
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!std::is_arithmetic<Ta>::value || !std::is_arithmetic<Tb>::value,
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bool
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>::type
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almost_equal [[gnu::pure]] (const Ta &a, const Tb &b)
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{ return a == b; }
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// Useful for explictly ignore equality warnings
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#pragma GCC diagnostic push
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#pragma GCC diagnostic ignored "-Wfloat-equal"
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template <typename T, typename U>
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bool
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exactly_equal [[gnu::pure]] (const T &a, const U &b)
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{ return a == b; }
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#pragma GCC diagnostic pop
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template <typename T>
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bool
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almost_zero [[gnu::pure]] (T a)
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{ return almost_equal (a, 0); }
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template <typename T>
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bool
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exactly_zero [[gnu::pure]] (T a)
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{ return exactly_equal (a, static_cast<T> (0)); }
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//-----------------------------------------------------------------------------
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// angles, trig
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template <typename T>
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struct constants { };
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constexpr double PI_d = 3.141592653589793238462643;
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constexpr float PI_f = 3.141592653589793238462643f;
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constexpr float E_f = 2.71828182845904523536028747135266250f;
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constexpr double E_d = 2.71828182845904523536028747135266250;
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template <typename T>
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constexpr T
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to_degrees [[gnu::pure]] (T radians)
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{
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return radians * 180 / constants<T>::PI;
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}
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template <typename T>
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constexpr T
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to_radians [[gnu::pure]] (T degrees)
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{
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return degrees / 180 * constants<T>::PI;
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}
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//! Normalised sinc function
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template <typename T>
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constexpr T
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sincn [[gnu::pure]] (T x)
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{
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return almost_zero (x) ? 1 : std::sin (constants<T>::PI * x) / (constants<T>::PI * x);
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}
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//! Unnormalised sinc function
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template <typename T>
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constexpr T
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sincu [[gnu::pure]] (T x)
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{
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return almost_zero (x) ? 1 : std::sin (x) / x;
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}
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//-----------------------------------------------------------------------------
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constexpr uintmax_t
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factorial [[gnu::pure]] (unsigned i)
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{
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return i <= 1 ? 0 : i * factorial (i - 1);
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}
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constexpr uintmax_t
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stirling [[gnu::pure]] (unsigned n)
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{
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return static_cast<uintmax_t> (std::sqrt (2 * PI_f * n) * std::pow (n / E_f, n));
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}
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constexpr uintmax_t
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combination [[gnu::pure]] (unsigned n, unsigned k)
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{
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return factorial (n) / (factorial (k) / (factorial (n - k)));
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}
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//-----------------------------------------------------------------------------
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/// Variadic minimum
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namespace util {
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template <typename T>
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constexpr T
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min [[gnu::pure]] (const T a)
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{ return a; }
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template <typename T, typename U, typename ...Args>
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constexpr typename std::enable_if<
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std::is_unsigned<typename std::decay<T>::type>::value == std::is_unsigned<typename std::decay<U>::type>::value &&
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std::is_integral<typename std::decay<T>::type>::value == std::is_integral<typename std::decay<U>::type>::value,
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typename std::common_type<T,U>::type
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>::type
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min [[gnu::pure]] (const T a, const U b, Args ...args)
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{
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return min (a < b ? a : b, std::forward<Args> (args)...);
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}
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//-----------------------------------------------------------------------------
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/// Variadic maximum
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template <typename T>
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constexpr T
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max [[gnu::pure]] (const T a)
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{ return a; }
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template <typename T, typename U, typename ...Args>
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constexpr typename std::enable_if<
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std::is_unsigned<typename std::decay<T>::type>::value == std::is_unsigned<typename std::decay<U>::type>::value &&
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std::is_integral<typename std::decay<T>::type>::value == std::is_integral<typename std::decay<U>::type>::value,
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typename std::common_type<T,U>::type
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>::type
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max [[gnu::pure]] (const T a, const U b, Args ...args)
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{
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return max (a > b ? a : b, std::forward<Args> (args)...);
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}
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}
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//-----------------------------------------------------------------------------
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// Limiting functions
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// min/max clamping
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template <typename T, typename U, typename V>
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T
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limit [[gnu::pure]] (const T val, const U lo, const V hi)
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{
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CHECK_LE(
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decltype (lo+hi) (lo),
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decltype (hi+lo) (hi)
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);
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return val > hi ? hi:
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val < lo ? lo:
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val;
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}
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// clamped cubic hermite interpolation
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template <typename T>
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T
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smoothstep [[gnu::pure]] (T a, T b, T x)
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{
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CHECK_LE(a, b);
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x = limit ((x - a) / (b - a), T{0}, T{1});
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return x * x * (3 - 2 * x);
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}
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#include "maths.ipp"
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#endif // __MATHS_HPP
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