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/* Copyright (C) 2013 Wildfire Games.
* This file is part of 0 A.D.
*
* 0 A.D. 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 2 of the License, or
* (at your option) any later version.
*
* 0 A.D. 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 0 A.D. If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef INCLUDED_FIXED_VECTOR2D
#define INCLUDED_FIXED_VECTOR2D
#include "maths/Fixed.h"
#include "maths/Sqrt.h"
class CFixedVector2D
{
public:
fixed X, Y;
CFixedVector2D() { }
CFixedVector2D(fixed X, fixed Y) : X(X), Y(Y) { }
/// Vector equality
bool operator==(const CFixedVector2D& v) const
{
return (X == v.X && Y == v.Y);
}
/// Vector inequality
bool operator!=(const CFixedVector2D& v) const
{
return (X != v.X || Y != v.Y);
}
/// Vector addition
CFixedVector2D operator+(const CFixedVector2D& v) const
{
return CFixedVector2D(X + v.X, Y + v.Y);
}
/// Vector subtraction
CFixedVector2D operator-(const CFixedVector2D& v) const
{
return CFixedVector2D(X - v.X, Y - v.Y);
}
/// Negation
CFixedVector2D operator-() const
{
return CFixedVector2D(-X, -Y);
}
/// Vector addition
CFixedVector2D& operator+=(const CFixedVector2D& v)
{
*this = *this + v;
return *this;
}
/// Vector subtraction
CFixedVector2D& operator-=(const CFixedVector2D& v)
{
*this = *this - v;
return *this;
}
/// Scalar multiplication by an integer
CFixedVector2D operator*(int n) const
{
return CFixedVector2D(X*n, Y*n);
}
/**
* Multiply by a CFixed. Likely to overflow if both numbers are large,
* so we use an ugly name instead of operator* to make it obvious.
*/
CFixedVector2D Multiply(fixed n) const
{
return CFixedVector2D(X.Multiply(n), Y.Multiply(n));
}
/**
* Returns the length of the vector.
* Will not overflow if the result can be represented as type 'fixed'.
*/
fixed Length() const
{
// Do intermediate calculations with 64-bit ints to avoid overflows
i32 x = X.GetInternalValue();
i32 y = Y.GetInternalValue();
u64 xx = (u64)FIXED_MUL_I64_I32_I32(x, x);
u64 yy = (u64)FIXED_MUL_I64_I32_I32(y, y);
u64 d2 = xx + yy;
CheckUnsignedAdditionOverflow(d2, xx, L"Overflow in CFixedVector2D::Length() part 1")
u32 d = isqrt64(d2);
CheckU32CastOverflow(d, i32, L"Overflow in CFixedVector2D::Length() part 2")
fixed r;
r.SetInternalValue((i32)d);
return r;
}
/**
* Returns -1, 0, +1 depending on whether length is less/equal/greater
* than the argument.
* Avoids sqrting and overflowing.
*/
int CompareLength(fixed cmp) const
{
i32 x = X.GetInternalValue(); // abs(x) <= 2^31
i32 y = Y.GetInternalValue();
u64 xx = (u64)FIXED_MUL_I64_I32_I32(x, x); // xx <= 2^62
u64 yy = (u64)FIXED_MUL_I64_I32_I32(y, y);
u64 d2 = xx + yy; // d2 <= 2^63 (no overflow)
i32 c = cmp.GetInternalValue();
u64 c2 = (u64)FIXED_MUL_I64_I32_I32(c, c);
if (d2 < c2)
return -1;
else if (d2 > c2)
return +1;
else
return 0;
}
/**
* Returns -1, 0, +1 depending on whether length is less/equal/greater
* than the argument's length.
* Avoids sqrting and overflowing.
*/
int CompareLength(const CFixedVector2D& other) const
{
i32 x = X.GetInternalValue();
i32 y = Y.GetInternalValue();
u64 d2 = (u64)FIXED_MUL_I64_I32_I32(x, x) + (u64)FIXED_MUL_I64_I32_I32(y, y);
i32 ox = other.X.GetInternalValue();
i32 oy = other.Y.GetInternalValue();
u64 od2 = (u64)FIXED_MUL_I64_I32_I32(ox, ox) + (u64)FIXED_MUL_I64_I32_I32(oy, oy);
if (d2 < od2)
return -1;
else if (d2 > od2)
return +1;
else
return 0;
}
bool IsZero() const
{
return (X.IsZero() && Y.IsZero());
}
/**
* Normalize the vector so that length is close to 1.
* If length is 0, does nothing.
*/
void Normalize()
{
if (!IsZero())
{
fixed l = Length();
X = X / l;
Y = Y / l;
}
}
/**
* Normalize the vector so that length is close to n.
* If length is 0, does nothing.
*/
void Normalize(fixed n)
{
fixed l = Length();
if (!l.IsZero())
{
X = X.MulDiv(n, l);
Y = Y.MulDiv(n, l);
}
}
/**
* Compute the dot product of this vector with another.
*/
fixed Dot(const CFixedVector2D& v)
{
i64 x = FIXED_MUL_I64_I32_I32(X.GetInternalValue(), v.X.GetInternalValue());
i64 y = FIXED_MUL_I64_I32_I32(Y.GetInternalValue(), v.Y.GetInternalValue());
CheckSignedAdditionOverflow(i64, x, y, L"Overflow in CFixedVector2D::Dot() part 1", L"Underflow in CFixedVector2D::Dot() part 1")
i64 sum = x + y;
sum >>= fixed::fract_bits;
CheckCastOverflow(sum, i32, L"Overflow in CFixedVector2D::Dot() part 2", L"Underflow in CFixedVector2D::Dot() part 2")
fixed ret;
ret.SetInternalValue((i32)sum);
return ret;
}
CFixedVector2D Perpendicular()
{
return CFixedVector2D(Y, -X);
}
/**
* Rotate the vector by the given angle (anticlockwise).
*/
CFixedVector2D Rotate(fixed angle)
{
fixed s, c;
sincos_approx(angle, s, c);
return CFixedVector2D(X.Multiply(c) + Y.Multiply(s), Y.Multiply(c) - X.Multiply(s));
}
};
#endif // INCLUDED_FIXED_VECTOR2D
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