libcruft-util/maths.hpp

358 lines
8.4 KiB
C++

/*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
* Copyright 2010-2014 Danny Robson <danny@nerdcruft.net>
*/
#ifndef __MATHS_HPP
#define __MATHS_HPP
#include "debug.hpp"
#include "types/traits.hpp"
#include <cmath>
#include <cstdint>
#include <limits>
#include <type_traits>
#include <utility>
template <typename T>
T
abs (T value)
{ return value > 0 ? value : -value; }
//-----------------------------------------------------------------------------
// Exponentials
template <typename T>
constexpr T
pow2 [[gnu::pure]] (T value)
{ return value * value; }
template <typename T>
constexpr T
pow [[gnu::pure]] (T x, unsigned y);
template <typename T>
bool
is_pow2 [[gnu::pure]] (T value);
//-----------------------------------------------------------------------------
// Logarithms
template <typename T>
T
log2 [[gnu::pure]] (T val);
template <typename T>
T
log2up [[gnu::pure]] (T val);
//-----------------------------------------------------------------------------
// Roots
template <typename T>
double
rootsquare [[gnu::pure]] (T a, T b);
//-----------------------------------------------------------------------------
// Rounding
template <typename T, typename U>
typename std::common_type<T, U>::type
align [[gnu::pure]] (T value, U size);
template <typename T>
T
round_pow2 [[gnu::pure]] (T value);
template <typename T, typename U>
constexpr T
divup [[gnu::pure]] (const T a, const U b)
{ return (a + b - 1) / b; }
//-----------------------------------------------------------------------------
// Classification
template <typename T>
bool
is_integer [[gnu::pure]] (const T& value);
//-----------------------------------------------------------------------------
// Properties
template <typename T>
unsigned
digits [[gnu::pure]] (const T& value);
//-----------------------------------------------------------------------------
// factorisation
template <typename T>
constexpr T
gcd (T a, T b)
{
if (a == b) return a;
if (a > b) return gcd (a - b, b);
if (b > a) return gcd (a, b - a);
unreachable ();
}
//-----------------------------------------------------------------------------
constexpr int sign (int);
constexpr float sign (float);
constexpr double sign (double);
//-----------------------------------------------------------------------------
// Comparisons
template <typename T>
bool
almost_equal [[gnu::pure]] (const T &a, const T &b)
{ return a == b; }
template <>
bool
almost_equal [[gnu::pure]] (const float &a, const float &b);
template <>
bool
almost_equal [[gnu::pure]] (const double &a, const double &b);
template <typename Ta, typename Tb>
typename std::enable_if<
std::is_arithmetic<Ta>::value && std::is_arithmetic<Tb>::value,
bool
>::type
almost_equal [[gnu::pure]] (Ta a, Tb b) {
return almost_equal <decltype(a + b)> (static_cast<decltype(a + b)>(a),
static_cast<decltype(a + b)>(b));
}
template <typename Ta, typename Tb>
typename std::enable_if<
!std::is_arithmetic<Ta>::value || !std::is_arithmetic<Tb>::value,
bool
>::type
almost_equal [[gnu::pure]] (const Ta &a, const Tb &b)
{ return a == b; }
// Useful for explictly ignore equality warnings
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wfloat-equal"
template <typename T, typename U>
bool
exactly_equal [[gnu::pure]] (const T &a, const U &b)
{ return a == b; }
#pragma GCC diagnostic pop
template <typename T>
bool
almost_zero [[gnu::pure]] (T a)
{ return almost_equal (a, 0); }
template <typename T>
bool
exactly_zero [[gnu::pure]] (T a)
{ return exactly_equal (a, static_cast<T> (0)); }
//-----------------------------------------------------------------------------
// angles, trig
template <typename T>
constexpr T PI = T(3.141592653589793238462643);
template <typename T>
constexpr T E = T(2.71828182845904523536028747135266250);
template <typename T>
constexpr T
to_degrees [[gnu::pure]] (T radians)
{
static_assert (std::is_floating_point<T>::value, "undefined for integral types");
return radians * 180 / PI<T>;
}
template <typename T>
constexpr T
to_radians [[gnu::pure]] (T degrees)
{
static_assert (std::is_floating_point<T>::value, "undefined for integral types");
return degrees / 180 * PI<T>;
}
//! Normalised sinc function
template <typename T>
constexpr T
sincn [[gnu::pure]] (T x)
{
return almost_zero (x) ? 1 : std::sin (PI<T> * x) / (PI<T> * x);
}
//! Unnormalised sinc function
template <typename T>
constexpr T
sincu [[gnu::pure]] (T x)
{
return almost_zero (x) ? 1 : std::sin (x) / x;
}
//-----------------------------------------------------------------------------
constexpr uintmax_t
factorial [[gnu::pure]] (unsigned i)
{
return i <= 1 ? 0 : i * factorial (i - 1);
}
/// stirlings approximation of factorials
constexpr uintmax_t
stirling [[gnu::pure]] (unsigned n)
{
return static_cast<uintmax_t> (
std::sqrt (2 * PI<float> * n) * std::pow (n / E<float>, n)
);
}
constexpr uintmax_t
combination [[gnu::pure]] (unsigned n, unsigned k)
{
return factorial (n) / (factorial (k) / (factorial (n - k)));
}
//-----------------------------------------------------------------------------
/// Variadic minimum
namespace util {
template <typename T>
constexpr T
min [[gnu::pure]] (const T a)
{ return a; }
template <typename T, typename U, typename ...Args>
constexpr typename std::enable_if<
std::is_unsigned<typename std::decay<T>::type>::value == std::is_unsigned<typename std::decay<U>::type>::value &&
std::is_integral<typename std::decay<T>::type>::value == std::is_integral<typename std::decay<U>::type>::value,
typename std::common_type<T,U>::type
>::type
min [[gnu::pure]] (const T a, const U b, Args ...args)
{
return min (a < b ? a : b, std::forward<Args> (args)...);
}
//-----------------------------------------------------------------------------
/// Variadic maximum
template <typename T>
constexpr T
max [[gnu::pure]] (const T a)
{ return a; }
template <typename T, typename U, typename ...Args>
constexpr typename std::enable_if<
std::is_unsigned<typename std::decay<T>::type>::value == std::is_unsigned<typename std::decay<U>::type>::value &&
std::is_integral<typename std::decay<T>::type>::value == std::is_integral<typename std::decay<U>::type>::value,
typename std::common_type<T,U>::type
>::type
max [[gnu::pure]] (const T a, const U b, Args ...args)
{
return max (a > b ? a : b, std::forward<Args> (args)...);
}
}
//-----------------------------------------------------------------------------
// Limiting functions
// min/max clamping
template <typename T, typename U, typename V>
T
limit [[gnu::pure]] (const T val, const U lo, const V hi)
{
CHECK_LE(
decltype (lo+hi) (lo),
decltype (hi+lo) (hi)
);
return val > hi ? hi:
val < lo ? lo:
val;
}
// clamped cubic hermite interpolation
template <typename T>
T
smoothstep [[gnu::pure]] (T a, T b, T x)
{
CHECK_LE(a, b);
x = limit ((x - a) / (b - a), T{0}, T{1});
return x * x * (3 - 2 * x);
}
#include "types/string.hpp"
//-----------------------------------------------------------------------------
template <typename T, typename U>
U
renormalise [[gnu::pure]] (T t)
{
static const T T_max = std::numeric_limits<T>::max ();
static const U U_max = std::numeric_limits<U>::max ();
static const bool shrinking = sizeof (U) < sizeof (T);
static const bool T_float = std::is_floating_point<T>::value;
static const bool U_float = std::is_floating_point<U>::value;
if (T_float && U_float)
return U (t);
if (T_float) {
return U (limit (t, 0, 1) * U_max);
}
if (U_float)
return U(U (t) / T_max);
if (shrinking)
return U (t / (sizeof (T) / sizeof (U)));
else
return U (t) * (sizeof (U) / sizeof (T));
}
#include "maths.ipp"
#endif // __MATHS_HPP