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#pragma once
#include "base/assert.hpp"
#include "std/cmath.hpp"
#include <algorithm>
#include <cmath>
#include <functional>
#include <limits>
#include <type_traits>
#include <boost/integer.hpp>
namespace math
{
double constexpr pi = 3.14159265358979323846;
double constexpr pi2 = pi / 2.;
double constexpr pi4 = pi / 4.;
double constexpr twicePi = 2. * pi;
template <class T> T sqr(T t) { return (t*t); }
}
namespace my
{
template <typename T> inline T Abs(T x)
{
return (x < 0 ? -x : x);
}
// Compare floats or doubles for almost equality.
// maxULPs - number of closest floating point values that are considered equal.
// Infinity is treated as almost equal to the largest possible floating point values.
// NaN produces undefined result.
// See https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
// for details.
template <typename TFloat>
bool AlmostEqualULPs(TFloat x, TFloat y, unsigned int maxULPs = 256)
{
static_assert(std::is_floating_point<TFloat>::value, "");
static_assert(std::numeric_limits<TFloat>::is_iec559, "");
// Make sure maxUlps is non-negative and small enough that the
// default NaN won't compare as equal to anything.
ASSERT_LESS(maxULPs, 4 * 1024 * 1024, ());
int const bits = CHAR_BIT * sizeof(TFloat);
typedef typename boost::int_t<bits>::exact IntType;
typedef typename boost::uint_t<bits>::exact UIntType;
IntType xInt = *reinterpret_cast<IntType const *>(&x);
IntType yInt = *reinterpret_cast<IntType const *>(&y);
// Make xInt and yInt lexicographically ordered as a twos-complement int
IntType const highestBit = IntType(1) << (bits - 1);
if (xInt < 0)
xInt = highestBit - xInt;
if (yInt < 0)
yInt = highestBit - yInt;
UIntType const diff = Abs(xInt - yInt);
return diff <= maxULPs;
}
// Returns true if x and y are equal up to the absolute difference eps.
// Does not produce a sensible result if any of the arguments is NaN or infinity.
// The default value for eps is deliberately not provided: the intended usage
// is for the client to choose the precision according to the problem domain,
// explicitly define the precision constant and call this function.
template <typename TFloat>
inline bool AlmostEqualAbs(TFloat x, TFloat y, TFloat eps)
{
return fabs(x - y) < eps;
}
// Returns true if x and y are equal up to the relative difference eps.
// Does not produce a sensible result if any of the arguments is NaN, infinity or zero.
// The same considerations as in AlmostEqualAbs apply.
template <typename TFloat>
inline bool AlmostEqualRel(TFloat x, TFloat y, TFloat eps)
{
return fabs(x - y) < eps * std::max(fabs(x), fabs(y));
}
// Returns true if x and y are equal up to the absolute or relative difference eps.
template <typename TFloat>
inline bool AlmostEqualAbsOrRel(TFloat x, TFloat y, TFloat eps)
{
return AlmostEqualAbs(x, y, eps) || AlmostEqualRel(x, y, eps);
}
template <typename TFloat> inline TFloat DegToRad(TFloat deg)
{
return deg * TFloat(math::pi) / TFloat(180);
}
template <typename TFloat> inline TFloat RadToDeg(TFloat rad)
{
return rad * TFloat(180) / TFloat(math::pi);
}
template <typename T> inline T id(T const & x)
{
return x;
}
template <typename T> inline T sq(T const & x)
{
return x * x;
}
template <typename T>
inline T clamp(T const x, T const xmin, T const xmax)
{
if (x > xmax)
return xmax;
if (x < xmin)
return xmin;
return x;
}
template <typename T>
inline T cyclicClamp(T const x, T const xmin, T const xmax)
{
if (x > xmax)
return xmin;
if (x < xmin)
return xmax;
return x;
}
template <typename T> inline bool between_s(T const a, T const b, T const x)
{
return (a <= x && x <= b);
}
template <typename T> inline bool between_i(T const a, T const b, T const x)
{
return (a < x && x < b);
}
inline int rounds(double x)
{
return (x > 0.0 ? int(x + 0.5) : int(x - 0.5));
}
inline size_t SizeAligned(size_t size, size_t align)
{
// static_cast .
return size + (static_cast<size_t>(-static_cast<ptrdiff_t>(size)) & (align - 1));
}
template <typename T>
bool IsIntersect(T const & x0, T const & x1, T const & x2, T const & x3)
{
return !((x1 < x2) || (x3 < x0));
}
// Computes x^n.
template <typename T> inline T PowUint(T x, uint64_t n)
{
T res = 1;
for (T t = x; n > 0; n >>= 1, t *= t)
if (n & 1)
res *= t;
return res;
}
template <typename T> inline T NextModN(T x, T n)
{
return x + 1 == n ? 0 : x + 1;
}
template <typename T> inline T PrevModN(T x, T n)
{
return x == 0 ? n - 1 : x - 1;
}
inline uint32_t NextPowOf2(uint32_t v)
{
v = v - 1;
v |= (v >> 1);
v |= (v >> 2);
v |= (v >> 4);
v |= (v >> 8);
v |= (v >> 16);
return v + 1;
}
template <typename Number,
typename EnableIf = typename std::enable_if<
std::is_integral<Number>::value, void>::type>
// Greatest Common Divisor
Number constexpr GCD(Number const a, Number const b) { return b == 0 ? a : GCD(b, a % b); }
template <typename Number,
typename EnableIf = typename std::enable_if<
std::is_integral<Number>::value, void>::type>
// Lowest Common Multiple.
Number constexpr LCM(Number const a, Number const b) { return a / GCD(a, b) * b; }
/// Calculate hash for the pair of values.
template <typename T1, typename T2>
size_t Hash(T1 const & t1, T2 const & t2)
{
/// @todo Probably, we need better hash for 2 integral types.
return (std::hash<T1>()(t1) ^ (std::hash<T2>()(t2) << 1));
}
template <typename Number,
typename EnableIf = typename std::enable_if<
std::is_integral<Number>::value || std::is_floating_point<Number>::value,
void>::type>
int constexpr Sign(Number const number) noexcept
{
return number == 0 ? 0 : number > 0 ? 1 : -1;
}
}
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