358 lines
8.4 KiB
C++
358 lines
8.4 KiB
C++
/*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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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 "types/traits.hpp"
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#include <cmath>
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#include <cstdint>
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#include <limits>
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#include <type_traits>
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#include <utility>
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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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// factorisation
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template <typename T>
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constexpr T
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gcd (T a, T b)
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{
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if (a == b) return a;
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if (a > b) return gcd (a - b, b);
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if (b > a) return gcd (a, b - a);
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unreachable ();
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}
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//-----------------------------------------------------------------------------
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constexpr int sign (int);
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constexpr float sign (float);
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constexpr double sign (double);
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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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constexpr T PI = T(3.141592653589793238462643);
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template <typename T>
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constexpr T E = T(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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static_assert (std::is_floating_point<T>::value, "undefined for integral types");
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return radians * 180 / PI<T>;
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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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static_assert (std::is_floating_point<T>::value, "undefined for integral types");
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return degrees / 180 * PI<T>;
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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 (PI<T> * x) / (PI<T> * 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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/// stirlings approximation of factorials
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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> (
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std::sqrt (2 * PI<float> * n) * std::pow (n / E<float>, n)
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);
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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 "types/string.hpp"
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//-----------------------------------------------------------------------------
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template <typename T, typename U>
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U
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renormalise [[gnu::pure]] (T t)
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{
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static const T T_max = std::numeric_limits<T>::max ();
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static const U U_max = std::numeric_limits<U>::max ();
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static const bool shrinking = sizeof (U) < sizeof (T);
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static const bool T_float = std::is_floating_point<T>::value;
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static const bool U_float = std::is_floating_point<U>::value;
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if (T_float && U_float)
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return U (t);
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if (T_float) {
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return U (limit (t, 0, 1) * U_max);
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}
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if (U_float)
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return U(U (t) / T_max);
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if (shrinking)
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return U (t / (sizeof (T) / sizeof (U)));
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else
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return U (t) * (sizeof (U) / sizeof (T));
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}
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#include "maths.ipp"
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#endif // __MATHS_HPP
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