libcruft-util/maths.hpp
Danny Robson 585a0b464c maths: make sign query inline
code which needs this function tends to require a fairly simple
implementation inline for the optimiser to reach more successfully. we
tended to generate function calls to this which slowed this inner loops.
2015-03-20 01:36:15 +11:00

314 lines
7.4 KiB
C++

/*
* This file is part of libgim.
*
* libgim is free software: you can redistribute it and/or modify it under the
* terms of the GNU General Public License as published by the Free Software
* Foundation, either version 3 of the License, or (at your option) any later
* version.
*
* libgim is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
* details.
*
* You should have received a copy of the GNU General Public License
* along with libgim. If not, see <http://www.gnu.org/licenses/>.
*
* Copyright 2010-2014 Danny Robson <danny@nerdcruft.net>
*/
#ifndef __MATHS_HPP
#define __MATHS_HPP
#include "debug.hpp"
#include "types/traits.hpp"
#include <cstdint>
#include <type_traits>
#include <utility>
#include <cmath>
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);
//-----------------------------------------------------------------------------
template <typename T>
typename try_signed<T>::type
sign [[gnu::pure]] (T val);
//-----------------------------------------------------------------------------
// 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>
struct constants { };
constexpr double PI_d = 3.141592653589793238462643;
constexpr float PI_f = 3.141592653589793238462643f;
constexpr float E_f = 2.71828182845904523536028747135266250f;
constexpr double E_d = 2.71828182845904523536028747135266250;
template <typename T>
constexpr T
to_degrees [[gnu::pure]] (T radians)
{
return radians * 180 / constants<T>::PI;
}
template <typename T>
constexpr T
to_radians [[gnu::pure]] (T degrees)
{
return degrees / 180 * constants<T>::PI;
}
//! Normalised sinc function
template <typename T>
constexpr T
sincn [[gnu::pure]] (T x)
{
return almost_zero (x) ? 1 : std::sin (constants<T>::PI * x) / (constants<T>::PI * 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);
}
constexpr uintmax_t
stirling [[gnu::pure]] (unsigned n)
{
return static_cast<uintmax_t> (std::sqrt (2 * PI_f * n) * std::pow (n / E_f, 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 "maths.ipp"
#endif // __MATHS_HPP