FixedVector3D.h

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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_VECTOR3D
#define INCLUDED_FIXED_VECTOR3D

#include "maths/Fixed.h"
#include "maths/Sqrt.h"

class CFixedVector3D
{
public:
    fixed X, Y, Z;

    CFixedVector3D() { }

    CFixedVector3D(fixed X, fixed Y, fixed Z) : X(X), Y(Y), Z(Z) { }

    /// Vector equality
    bool operator==(const CFixedVector3D& v) const
    {
        return (X == v.X && Y == v.Y && Z == v.Z);
    }

    /// Vector inequality
    bool operator!=(const CFixedVector3D& v) const
    {
        return (X != v.X || Y != v.Y || Z != v.Z);
    }

    /// Vector addition
    CFixedVector3D operator+(const CFixedVector3D& v) const
    {
        return CFixedVector3D(X + v.X, Y + v.Y, Z + v.Z);
    }

    /// Vector subtraction
    CFixedVector3D operator-(const CFixedVector3D& v) const
    {
        return CFixedVector3D(X - v.X, Y - v.Y, Z - v.Z);
    }

    /// Negation
    CFixedVector3D operator-() const
    {
        return CFixedVector3D(-X, -Y, -Z);
    }

    /// Vector addition
    CFixedVector3D& operator+=(const CFixedVector3D& v)
    {
        *this = *this + v;
        return *this;
    }

    /// Vector subtraction
    CFixedVector3D& operator-=(const CFixedVector3D& v)
    {
        *this = *this - v;
        return *this;
    }


    /**
     * 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();
        i32 z = Z.GetInternalValue();
        u64 xx = (u64)FIXED_MUL_I64_I32_I32(x, x);
        u64 yy = (u64)FIXED_MUL_I64_I32_I32(y, y);
        u64 zz = (u64)FIXED_MUL_I64_I32_I32(z, z);
        u64 t = xx + yy;
        CheckUnsignedAdditionOverflow(t, xx, L"Overflow in CFixedVector3D::Length() part 1")

        u64 d2 = t + zz;
        CheckUnsignedAdditionOverflow(d2, t, L"Overflow in CFixedVector3D::Length() part 2")

        u32 d = isqrt64(d2);

        CheckU32CastOverflow(d, i32, L"Overflow in CFixedVector3D::Length() part 3")
        fixed r;
        r.SetInternalValue((i32)d);
        return r;
    }

    /**
     * Normalize the vector so that length is close to 1.
     * If length is 0, does nothing.
     */
    void Normalize()
    {
        fixed l = Length();
        if (!l.IsZero())
        {
            X = X / l;
            Y = Y / l;
            Z = Z / 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);
            Z = Z.MulDiv(n, l);
        }
    }

    /**
     * Compute the cross product of this vector with another.
     */
    CFixedVector3D Cross(const CFixedVector3D& v)
    {
        i64 y_vz = FIXED_MUL_I64_I32_I32(Y.GetInternalValue(), v.Z.GetInternalValue());
        i64 z_vy = FIXED_MUL_I64_I32_I32(Z.GetInternalValue(), v.Y.GetInternalValue());
        CheckSignedSubtractionOverflow(i64, y_vz, z_vy, L"Overflow in CFixedVector3D::Cross() part 1", L"Underflow in CFixedVector3D::Cross() part 1")
        i64 x = y_vz - z_vy;
        x >>= fixed::fract_bits;

        i64 z_vx = FIXED_MUL_I64_I32_I32(Z.GetInternalValue(), v.X.GetInternalValue());
        i64 x_vz = FIXED_MUL_I64_I32_I32(X.GetInternalValue(), v.Z.GetInternalValue());
        CheckSignedSubtractionOverflow(i64, z_vx, x_vz, L"Overflow in CFixedVector3D::Cross() part 2", L"Underflow in CFixedVector3D::Cross() part 2")
        i64 y = z_vx - x_vz;
        y >>= fixed::fract_bits;

        i64 x_vy = FIXED_MUL_I64_I32_I32(X.GetInternalValue(), v.Y.GetInternalValue());
        i64 y_vx = FIXED_MUL_I64_I32_I32(Y.GetInternalValue(), v.X.GetInternalValue());
        CheckSignedSubtractionOverflow(i64, x_vy, y_vx, L"Overflow in CFixedVector3D::Cross() part 3", L"Underflow in CFixedVector3D::Cross() part 3")
        i64 z = x_vy - y_vx;
        z >>= fixed::fract_bits;

        CheckCastOverflow(x, i32, L"Overflow in CFixedVector3D::Cross() part 4", L"Underflow in CFixedVector3D::Cross() part 4")
        CheckCastOverflow(y, i32, L"Overflow in CFixedVector3D::Cross() part 5", L"Underflow in CFixedVector3D::Cross() part 5")
        CheckCastOverflow(z, i32, L"Overflow in CFixedVector3D::Cross() part 6", L"Underflow in CFixedVector3D::Cross() part 6")
        CFixedVector3D ret;
        ret.X.SetInternalValue((i32)x);
        ret.Y.SetInternalValue((i32)y);
        ret.Z.SetInternalValue((i32)z);
        return ret;
    }

    /**
     * Compute the dot product of this vector with another.
     */
    fixed Dot(const CFixedVector3D& 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());
        i64 z = FIXED_MUL_I64_I32_I32(Z.GetInternalValue(), v.Z.GetInternalValue());
        CheckSignedAdditionOverflow(i64, x, y, L"Overflow in CFixedVector3D::Dot() part 1", L"Underflow in CFixedVector3D::Dot() part 1")
        i64 t = x + y;

        CheckSignedAdditionOverflow(i64, t, z, L"Overflow in CFixedVector3D::Dot() part 2", L"Underflow in CFixedVector3D::Dot() part 2")
        i64 sum = t + z;
        sum >>= fixed::fract_bits;
        CheckCastOverflow(sum, i32, L"Overflow in CFixedVector3D::Dot() part 3", L"Underflow in CFixedVector3D::Dot() part 3")

        fixed ret;
        ret.SetInternalValue((i32)sum);
        return ret;
    }
};

#endif // INCLUDED_FIXED_VECTOR3D