836 lines
22 KiB
C++
836 lines
22 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
|
|
|
|
// DO NOT INCLUDE debug.hpp
|
|
// it triggers a circular dependency; debug -> format -> maths -> debug
|
|
// instead, just use cassert
|
|
|
|
#include "./types/traits.hpp"
|
|
#include "./float.hpp"
|
|
|
|
#include <algorithm>
|
|
#include <cassert>
|
|
#include <cmath>
|
|
#include <cstdint>
|
|
#include <limits>
|
|
#include <numeric>
|
|
#include <type_traits>
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
// NOTE: You may be tempted to add all sorts of performance enhancing
|
|
// attributes (like gnu::const or gnu::pure). DO NOT DO THIS WITHOUT EXTENSIVE
|
|
// TESTING. Just about everything will break in some way with these attributes.
|
|
//
|
|
// In particular: it is safest to apply these only to leaf functions
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
namespace util {
|
|
///////////////////////////////////////////////////////////////////////////
|
|
// Comparisons
|
|
inline bool
|
|
almost_equal (const float &a, const float &b)
|
|
{
|
|
return ieee_single::almost_equal (a, b);
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
inline bool
|
|
almost_equal (const double &a, const double &b)
|
|
{
|
|
return ieee_double::almost_equal (a, b);
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
template <typename A, typename B>
|
|
inline
|
|
typename std::enable_if_t<
|
|
std::is_floating_point<A>::value &&
|
|
std::is_floating_point<B>::value &&
|
|
!std::is_same<A,B>::value ,
|
|
bool
|
|
>
|
|
almost_equal (const A &a, const B &b)
|
|
{
|
|
using common_t = std::common_type_t<A,B>;
|
|
return almost_equal<common_t> (static_cast<common_t> (a),
|
|
static_cast<common_t> (b));
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
template <typename A, typename B>
|
|
inline
|
|
typename std::enable_if_t<
|
|
std::is_integral<A>::value &&
|
|
std::is_integral<B>::value &&
|
|
std::is_signed<A>::value == std::is_signed<B>::value,
|
|
bool
|
|
>
|
|
almost_equal (const A &a, const B &b) {
|
|
using common_t = std::common_type_t<A,B>;
|
|
return static_cast<common_t> (a) == static_cast<common_t> (b);
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
template <typename Ta, typename Tb>
|
|
constexpr inline
|
|
typename std::enable_if<
|
|
!std::is_arithmetic<Ta>::value ||
|
|
!std::is_arithmetic<Tb>::value,
|
|
bool
|
|
>::type
|
|
almost_equal (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 Ta, typename Tb>
|
|
constexpr
|
|
typename std::enable_if_t<
|
|
std::is_arithmetic<Ta>::value &&
|
|
std::is_arithmetic<Tb>::value,
|
|
bool
|
|
>
|
|
exactly_equal (const Ta &a, const Tb &b)
|
|
{
|
|
return a == b;
|
|
}
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <typename Ta, typename Tb>
|
|
inline
|
|
typename std::enable_if_t<
|
|
!std::is_arithmetic<Ta>::value ||
|
|
!std::is_arithmetic<Tb>::value,
|
|
bool
|
|
>
|
|
exactly_equal (const Ta &a, const Tb &b)
|
|
{
|
|
return a == b;
|
|
}
|
|
#pragma GCC diagnostic pop
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
template <typename T>
|
|
constexpr
|
|
std::enable_if_t<
|
|
std::is_integral<T>::value, bool
|
|
>
|
|
almost_zero (T t)
|
|
{
|
|
return t == 0;
|
|
}
|
|
|
|
template <typename T>
|
|
std::enable_if_t<
|
|
!std::is_integral<T>::value, bool
|
|
>
|
|
almost_zero (T a)
|
|
{ return almost_equal (a, T{0}); }
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <typename T>
|
|
constexpr
|
|
typename std::enable_if_t<
|
|
std::is_integral<T>::value, bool
|
|
>
|
|
exactly_zero (T t)
|
|
{
|
|
return exactly_equal (t, T{0});
|
|
}
|
|
|
|
|
|
template <typename T>
|
|
constexpr
|
|
typename std::enable_if_t<
|
|
!std::is_integral<T>::value, bool
|
|
>
|
|
exactly_zero (T t)
|
|
{
|
|
return exactly_equal (t, T{0});
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <typename T>
|
|
constexpr
|
|
typename std::enable_if_t<
|
|
std::is_floating_point<T>::value, bool
|
|
>
|
|
is_nan (T t)
|
|
{
|
|
return std::isnan (t);
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <typename T>
|
|
constexpr
|
|
typename std::enable_if_t<
|
|
!std::is_floating_point<T>::value, bool
|
|
>
|
|
is_nan (const T&)
|
|
{
|
|
return false;
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
template <typename T>
|
|
T
|
|
abs [[gnu::const]] (T t)
|
|
{
|
|
return t > 0 ? t : -t;
|
|
}
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
// exponentials
|
|
|
|
template <typename T>
|
|
constexpr T
|
|
pow2 [[gnu::const]] (T value)
|
|
{
|
|
return value * value;
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
template <typename T>
|
|
constexpr T
|
|
pow [[gnu::const]] (T x, unsigned y)
|
|
{
|
|
return y == 0 ? T{1} : x * pow (x, y - 1);
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <typename T>
|
|
constexpr
|
|
std::enable_if_t<std::is_integral<T>::value, bool>
|
|
is_pow2 [[gnu::const]] (T value)
|
|
{
|
|
return value && !(value & (value - 1));
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Logarithms
|
|
template <typename T>
|
|
T
|
|
log2 (T val);
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <typename T>
|
|
T
|
|
log2up (T val);
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
// Rounding
|
|
template <typename T, typename U>
|
|
inline
|
|
typename std::common_type<
|
|
std::enable_if_t<std::is_integral<T>::value,T>,
|
|
std::enable_if_t<std::is_integral<U>::value,U>
|
|
>::type
|
|
round_to (T value, U size)
|
|
{
|
|
if (value % size == 0)
|
|
return value;
|
|
|
|
return value + (size - value % size);
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
template <typename T>
|
|
constexpr
|
|
std::enable_if_t<
|
|
std::is_integral<T>::value, T
|
|
>
|
|
round_pow2 (T value)
|
|
{
|
|
using return_type = std::enable_if_t<std::is_integral<T>::value, T>;
|
|
|
|
--value;
|
|
|
|
for (unsigned i = 1; i < sizeof (T) * 8; i <<= 1) {
|
|
value |= value >> i;
|
|
}
|
|
|
|
++value;
|
|
return (return_type)value;
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
template <typename T, typename U>
|
|
constexpr std::enable_if_t<
|
|
std::is_integral<T>::value &&
|
|
std::is_integral<U>::value,
|
|
T
|
|
>
|
|
divup (const T a, const U b)
|
|
{
|
|
return (a + b - 1) / b;
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
// Properties
|
|
template <typename T>
|
|
constexpr
|
|
std::enable_if_t<std::is_integral<T>::value, bool>
|
|
is_integer (T)
|
|
{
|
|
return true;
|
|
}
|
|
|
|
template <typename T>
|
|
constexpr
|
|
std::enable_if_t<std::is_floating_point<T>::value, bool>
|
|
is_integer (T t)
|
|
{
|
|
T i = 0;
|
|
return exactly_equal (std::modf (t, &i), T{0});
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
constexpr
|
|
unsigned
|
|
digits10 (uint32_t v) noexcept
|
|
{
|
|
return (v >= 1000000000) ? 10 :
|
|
(v >= 100000000) ? 9 :
|
|
(v >= 10000000) ? 8 :
|
|
(v >= 1000000) ? 7 :
|
|
(v >= 100000) ? 6 :
|
|
(v >= 10000) ? 5 :
|
|
(v >= 1000) ? 4 :
|
|
(v >= 100) ? 3 :
|
|
(v >= 10) ? 2 :
|
|
1;
|
|
}
|
|
|
|
|
|
template <typename ValueT, typename BaseT>
|
|
constexpr
|
|
std::enable_if_t<
|
|
std::is_integral<ValueT>::value && std::is_unsigned<BaseT>::value,
|
|
unsigned
|
|
>
|
|
digits (ValueT value, BaseT base) noexcept
|
|
{
|
|
if (value < 0)
|
|
value *= -1;
|
|
|
|
unsigned tally = 1;
|
|
while (value /= base)
|
|
++tally;
|
|
|
|
return tally;
|
|
}
|
|
|
|
|
|
///----------------------------------------------------------------------------
|
|
/// return positive or negative unit value corresponding to the input.
|
|
template <typename T>
|
|
constexpr std::enable_if_t<
|
|
std::is_signed<T>::value && std::is_integral<T>::value, T
|
|
>
|
|
sign (T t)
|
|
{
|
|
return t < 0 ? -1 : 1;
|
|
}
|
|
|
|
///------------------------------------------------------------------------
|
|
/// return positive or negative unit value corresponding to the input.
|
|
/// guaranteed to give correct results for signed zeroes, use another
|
|
/// method if extreme speed is important.
|
|
template <typename T>
|
|
constexpr std::enable_if_t<
|
|
std::is_floating_point<T>::value, T
|
|
>
|
|
sign (T t)
|
|
{
|
|
return std::signbit (t) ? -1 : 1;
|
|
}
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <typename T>
|
|
constexpr
|
|
bool
|
|
samesign (T a, T b)
|
|
{
|
|
return a < 0 && b < 0 || a > 0 && b > 0;
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
// factorisation
|
|
template <typename T>
|
|
constexpr T
|
|
gcd (T a, T b)
|
|
{
|
|
assert (a);
|
|
assert (b);
|
|
|
|
while (a != b) {
|
|
if (a > b)
|
|
a -= b;
|
|
else if (b > a)
|
|
b -= a;
|
|
}
|
|
|
|
return a;
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
template <typename T>
|
|
const T&
|
|
identity (const T& t)
|
|
{
|
|
return t;
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
// Modulus/etc
|
|
|
|
// namespaced wrapper for `man 3 fmod`
|
|
template <typename T>
|
|
constexpr
|
|
std::enable_if_t<
|
|
std::is_floating_point<T>::value, T
|
|
>
|
|
mod (T x, T y)
|
|
{
|
|
return std::fmod (x, y);
|
|
}
|
|
|
|
|
|
template <typename T>
|
|
constexpr
|
|
std::enable_if_t<
|
|
std::is_integral<T>::value, T
|
|
>
|
|
mod (T x, T y)
|
|
{
|
|
return x % y;
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
// 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 (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 (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 (T x)
|
|
{
|
|
return almost_zero (x) ? 1 : std::sin (PI<T> * x) / (PI<T> * x);
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
//! Unnormalised sinc function
|
|
template <typename T>
|
|
constexpr T
|
|
sincu (T x)
|
|
{
|
|
return almost_zero (x) ? 1 : std::sin (x) / x;
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
// combinatorics
|
|
|
|
constexpr uintmax_t
|
|
factorial (unsigned i)
|
|
{
|
|
return i <= 1 ? 0 : i * factorial (i - 1);
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
/// stirlings approximation of factorials
|
|
inline uintmax_t
|
|
stirling (unsigned n)
|
|
{
|
|
using real_t = double;
|
|
|
|
return static_cast<uintmax_t> (
|
|
std::sqrt (2 * PI<real_t> * n) * std::pow (n / E<real_t>, n)
|
|
);
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
constexpr uintmax_t
|
|
combination (unsigned n, unsigned k)
|
|
{
|
|
return factorial (n) / (factorial (k) / (factorial (n - k)));
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
// kahan summation for long floating point sequences
|
|
|
|
template <class InputT>
|
|
std::enable_if_t<
|
|
std::is_floating_point<
|
|
typename std::iterator_traits<InputT>::value_type
|
|
>::value,
|
|
typename std::iterator_traits<InputT>::value_type
|
|
>
|
|
sum (InputT first, InputT last)
|
|
{
|
|
using T = typename std::iterator_traits<InputT>::value_type;
|
|
|
|
T sum = 0;
|
|
T c = 0;
|
|
|
|
for (auto cursor = first; cursor != last; ++cursor) {
|
|
T y = *cursor - c;
|
|
T t = sum + y;
|
|
c = (t - sum) - y;
|
|
sum = t;
|
|
}
|
|
|
|
return sum;
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <class InputT>
|
|
std::enable_if_t<
|
|
std::is_integral<
|
|
typename std::iterator_traits<InputT>::value_type
|
|
>::value,
|
|
typename std::iterator_traits<InputT>::value_type
|
|
>
|
|
sum (InputT first, InputT last)
|
|
{
|
|
using T = typename std::iterator_traits<InputT>::value_type;
|
|
return std::accumulate (first, last, T{0});
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
/// Variadic minimum
|
|
template <typename T>
|
|
constexpr T
|
|
min (const T a)
|
|
{ return a; }
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <typename T, typename U, typename ...Args>
|
|
constexpr std::enable_if_t<
|
|
std::is_unsigned<std::decay_t<T>>::value == std::is_unsigned<std::decay_t<U>>::value &&
|
|
std::is_integral<std::decay_t<T>>::value == std::is_integral<std::decay_t<U>>::value,
|
|
std::common_type_t<T,U>
|
|
>
|
|
min (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 (const T a)
|
|
{ return a; }
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <typename T, typename U, typename ...Args>
|
|
constexpr std::enable_if_t<
|
|
std::is_unsigned<std::decay_t<T>>::value == std::is_unsigned<std::decay_t<U>>::value &&
|
|
std::is_integral<std::decay_t<T>>::value == std::is_integral<std::decay_t<U>>::value,
|
|
std::common_type_t<T,U>
|
|
>
|
|
max (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>
|
|
constexpr
|
|
T
|
|
limit (const T val, const U lo, const V hi)
|
|
{
|
|
assert (lo <= hi);
|
|
|
|
return val > hi ? hi:
|
|
val < lo ? lo:
|
|
val;
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
// clamped cubic hermite interpolation
|
|
template <typename T>
|
|
constexpr
|
|
T
|
|
smoothstep (T a, T b, T x)
|
|
{
|
|
assert (a <= b);
|
|
x = limit ((x - a) / (b - a), T{0}, T{1});
|
|
return x * x * (3 - 2 * x);
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <typename U, typename T>
|
|
constexpr
|
|
std::enable_if_t<std::is_floating_point<T>::value, U>
|
|
mix (U a, U b, T t)
|
|
{
|
|
assert (t >= 0);
|
|
assert (t <= 1);
|
|
|
|
return a * (1 - t) + b * t;
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
/// convert between different representations of normalised quantities.
|
|
///
|
|
/// * floating point values must be within [0, 1] (otherwise undefined)
|
|
/// * signed values are handled by converting to unsigned representations
|
|
/// * may introduce small biases when expanding values so that low order
|
|
/// bits have some meaning (particularly when dealing with UINTMAX)
|
|
|
|
// uint -> float
|
|
template <typename T, typename U>
|
|
constexpr
|
|
typename std::enable_if<
|
|
std::is_unsigned<T>::value && std::is_floating_point<U>::value, U
|
|
>::type
|
|
renormalise (T t)
|
|
{
|
|
return t / static_cast<U> (std::numeric_limits<T>::max ());
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
// float -> uint
|
|
template <typename T, typename U>
|
|
constexpr
|
|
typename std::enable_if<
|
|
std::is_floating_point<T>::value && std::is_unsigned<U>::value, U
|
|
>::type
|
|
renormalise (T t)
|
|
{
|
|
// Ideally std::ldexp would be involved but it complicates handing
|
|
// integers with greater precision than our floating point type. Also it
|
|
// would prohibit constexpr and involve errno.
|
|
|
|
size_t usable = std::numeric_limits<T>::digits;
|
|
size_t available = sizeof (U) * 8;
|
|
size_t shift = std::max (available, usable) - usable;
|
|
|
|
t = limit (t, 0, 1);
|
|
|
|
// construct an integer of the float's mantissa size, multiply it by our
|
|
// parameter, then shift it back into the full range of the integer type.
|
|
U in = std::numeric_limits<U>::max () >> shift;
|
|
U mid = static_cast<U> (t * in);
|
|
U out = mid << shift;
|
|
|
|
// use the top bits of the output to fill the bottom bits which through
|
|
// shifting would otherwise be zero. this gives us the full extent of the
|
|
// integer range, while varying predictably through the entire output
|
|
// space.
|
|
return out | out >> (available - shift);
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
// float -> float, avoids identity conversion as we don't want to create
|
|
// ambiguous overloads
|
|
template <typename T, typename U>
|
|
constexpr
|
|
typename std::enable_if<
|
|
std::is_floating_point<T>::value &&
|
|
std::is_floating_point<U>::value &&
|
|
!std::is_same<T,U>::value, U
|
|
>::type
|
|
renormalise (T t)
|
|
{
|
|
return static_cast<U> (t);
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
// hi_uint -> lo_uint
|
|
template <typename T, typename U>
|
|
constexpr
|
|
typename std::enable_if<
|
|
std::is_unsigned<T>::value &&
|
|
std::is_unsigned<U>::value &&
|
|
(sizeof (T) > sizeof (U)), U
|
|
>::type
|
|
renormalise (T t)
|
|
{
|
|
static_assert (sizeof (T) > sizeof (U),
|
|
"assumes right shift is sufficient");
|
|
|
|
// we have excess bits ,just shift and return
|
|
constexpr auto shift = 8 * (sizeof (T) - sizeof (U));
|
|
return t >> shift;
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
// lo_uint -> hi_uint
|
|
template <typename T, typename U>
|
|
constexpr
|
|
typename std::enable_if<
|
|
std::is_unsigned<T>::value &&
|
|
std::is_unsigned<U>::value &&
|
|
sizeof (T) < sizeof (U), U
|
|
>::type
|
|
renormalise (T t)
|
|
{
|
|
static_assert (sizeof (T) < sizeof (U),
|
|
"assumes bit creation is required to fill space");
|
|
|
|
// we need to create bits. fill the output integer with copies of ourself.
|
|
// this is approximately correct in the general case (introducing a small
|
|
// linear positive bias), but allows us to fill the output space in the
|
|
// case of input maximum.
|
|
|
|
static_assert (sizeof (U) % sizeof (T) == 0,
|
|
"assumes integer multiple of sizes");
|
|
|
|
U out = 0;
|
|
|
|
for (size_t i = 0; i < sizeof (U) / sizeof (T); ++i)
|
|
out |= U (t) << sizeof (T) * 8 * i;
|
|
|
|
return out;
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
// identity transformation. must precede the signed cases, as they may rely
|
|
// on this as a side effect of casts.
|
|
template <typename T, typename U>
|
|
constexpr
|
|
typename std::enable_if<
|
|
std::is_same<T,U>::value, U
|
|
>::type
|
|
renormalise (T t)
|
|
{ return t; }
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
// anything-to-sint
|
|
template <typename T, typename U>
|
|
constexpr
|
|
typename std::enable_if<
|
|
std::is_signed<U>::value &&
|
|
std::is_integral<U>::value &&
|
|
!std::is_same<T,U>::value,
|
|
U
|
|
>::type
|
|
renormalise (T t)
|
|
{
|
|
using uint_t = typename std::make_unsigned<U>::type;
|
|
|
|
return static_cast<U> (
|
|
::util::renormalise<T,uint_t> (t) + std::numeric_limits<U>::min ()
|
|
);
|
|
};
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
// sint-to-anything
|
|
template <typename T, typename U>
|
|
constexpr
|
|
typename std::enable_if<
|
|
std::is_signed<T>::value &&
|
|
std::is_integral<T>::value &&
|
|
!std::is_same<T,U>::value,
|
|
U
|
|
>::type
|
|
renormalise (T sint)
|
|
{
|
|
using uint_t = typename std::make_unsigned<T>::type;
|
|
|
|
return ::util::renormalise<uint_t,U> (
|
|
static_cast<uint_t> (sint) - std::numeric_limits<T>::min ()
|
|
);
|
|
};
|
|
}
|
|
|
|
|
|
#endif // __MATHS_HPP
|