FixedVector2D.h

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/* Copyright (C) 2017 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);
    }

    /// Scalar division by an integer. Must not have n == 0.
    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) const
    {
        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() const
    {
        return CFixedVector2D(Y, -X);
    }

    /**
     * Rotate the vector by the given angle (anticlockwise).
     */
    CFixedVector2D Rotate(fixed angle) const
    {
        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