/*
 * @FileName: LMath.cs
 * @Date: 2024-04-20 20:06:15
 * @LastEditTime: 2024-04-23 00:27:23
 * @Description: 定点数数学工具函数
 */

namespace JNGame.Math
{
    /// <summary>
    /// 定点数数学工具库
    /// </summary>
    public static partial class LMath
    {
        public static LFloat Floor(LFloat value)
        {
            return FloorToInt(value);
        }
        public static LFloat Ceiling(LFloat value)
        {
            return CeilToInt(value);
        }
        
        #region 三角函数相关

        /// <summary>
        /// 定点数反余弦函数Acos
        /// </summary>
        /// <param name="val">余弦值</param>
        /// <returns>弧度</returns>
        public static LFloat Acos(LFloat val)
        {
            int idx = (int)(val.rawValue * LUTAcos.HALF_COUNT / LFloat.Precision) +
                      LUTAcos.HALF_COUNT;
            idx = Clamp(idx, 0, LUTAcos.COUNT);
            return new LFloat(true, LUTAcos.table[idx]);
        }

        /// <summary>
        /// 定点数反正弦函数Asin
        /// </summary>
        /// <param name="val">正弦值</param>
        /// <returns>弧度</returns>
        public static LFloat Asin(LFloat val)
        {
            int idx = (int)(val.rawValue * LUTAsin.HALF_COUNT / LFloat.Precision) + LUTAsin.HALF_COUNT;
            idx = Clamp(idx, 0, LUTAsin.COUNT);
            return new LFloat(true, LUTAsin.table[idx]);
        }

        /// <summary>
        /// 定点数正弦函数Sin
        /// </summary>
        /// <param name="radians">弧度</param>
        /// <returns>正弦值</returns>
        public static LFloat Sin(LFloat radians)
        {
            return new LFloat(true, LUTSin.table[InternalGetIdx(radians)]);
        }

        /// <summary>
        /// 定点数版本余弦函数
        /// </summary>
        /// <param name="radians">弧度</param>
        /// <returns>余弦值</returns>
        public static LFloat Cos(LFloat radians)
        {
            return new LFloat(true, LUTCos.table[InternalGetIdx(radians)]);
        }

        /// <summary>
        /// 定点数版本正弦余弦函数，同时获取正弦值和余弦值
        /// </summary>
        /// <param name="sinValue">输出:正弦值</param>
        /// <param name="cosValue">输出:余弦值</param>
        /// <param name="radians">弧度</param>
        public static void SinCos(out LFloat sinValue, out LFloat cosValue, LFloat radians)
        {
            int idx = InternalGetIdx(radians);
            sinValue = new LFloat(true, LUTSin.table[idx]);
            cosValue = new LFloat(true, LUTCos.table[idx]);
        }

        /// <summary>
        /// 通过弧度获取查表索引
        /// </summary>
        /// <param name="radians">弧度</param>
        /// <returns></returns>
        private static int InternalGetIdx(LFloat radians)
        {
            var rawVal = radians.rawValue % LMath.kRawL2PI;
            if (rawVal < 0) rawVal += LMath.kRawL2PI;
            var val = new LFloat(true, rawVal) / LMath.PI2;
            var idx = (int)(val * LUTCos.COUNT);
            idx = Clamp(idx, 0, LUTCos.COUNT);
            return idx;
        }

        #region Atan2 & Atan

        /// <summary>
        /// 定点数版本反正切函数Atan2
        /// <para>值域[-PI, PI]，返回点(x,y)与X轴正向的夹角</para>
        /// <para>一二象限为正，三四象限为负</para>
        /// </summary>
        /// <param name="y"></param>
        /// <param name="x"></param>
        /// <returns>定点数，单位弧度</returns>
        public static LFloat Atan2(LFloat y, LFloat x)
        {
            return Atan2(y.rawValue, x.rawValue);
        }

        /// <summary>
        /// long版本反正切函数Atan2
        /// <para>值域[-PI, PI]，返回点(x,y)与X轴正向的夹角</para>
        /// <para>一二象限为正，三四象限为负</para>
        /// </summary>
        /// <param name="y"></param>
        /// <param name="x"></param>
        /// <returns>定点数，单位弧度</returns>
        public static LFloat Atan2(long y, long x)
        {
            return new LFloat(true, InternalAtan2(y, x));
        }

        /// <summary>
        /// int版本反正切函数Atan2
        /// <para>值域[-PI, PI]，返回点(x,y)与X轴正向的夹角</para>
        /// <para>一二象限为正，三四象限为负</para>
        /// </summary>
        /// <param name="y"></param>
        /// <param name="x"></param>
        /// <returns>定点数，单位弧度</returns>
        public static LFloat Atan2(int y, int x)
        {
            return new LFloat(true, InternalAtan2(y, x));
        }

        /// <summary>
        /// 定点数版本反正切函数Atan
        /// <para>值域[-PI/2, PI/2]，返回点(x,y)与X轴正向的夹角</para>
        /// </summary>
        /// <param name="val"></param>
        /// <returns></returns>
        public static LFloat Atan(LFloat val)
        {
            return new LFloat(true, InternalLutATan(val));
        }

        private struct LutAtan2Helper
        {
            public long sign;
            public long offset;

            public LutAtan2Helper(long sign, long offset)
            {
                this.sign = sign;
                this.offset = offset;
            }
        }

        private readonly static LutAtan2Helper[] s_Idx2LutInfo = new LutAtan2Helper[]
        {
            new LutAtan2Helper(-1, LMath.kRawLQuadPI),
            new LutAtan2Helper(1, LMath.kRawLQuadPI),
            new LutAtan2Helper(1, -LMath.kRawLQuadPI),
            new LutAtan2Helper(-1, -LMath.kRawLQuadPI),

            new LutAtan2Helper(1, LMath.kRawLQuadPI * 3),
            new LutAtan2Helper(-1, LMath.kRawLQuadPI * 3),
            new LutAtan2Helper(-1, -LMath.kRawLQuadPI * 3),
            new LutAtan2Helper(1, -LMath.kRawLQuadPI * 3),
        };

        /// <summary>
        /// Atan2的内部实现
        /// <para>值域[-PI, PI]，返回点(x,y)与X轴正向的夹角</para>
        /// <para>一二象限为正，三四象限为负</para>
        /// </summary>
        /// <param name="y"></param>
        /// <param name="x"></param>
        /// <returns></returns>
        private static long InternalAtan2(long y, long x)
        {
            //特殊情况处理
            if (y == 0)
            {
                if (x == 0)
                {
                    return 0;
                }

                return x < 0 ? LMath.kRawLPI : 0;
            }

            if (x == 0)
            {
                return y > 0 ? LMath.kRawLHalfPI : -LMath.kRawLHalfPI;
            }

            //决定象限
            int idxV = 0;
            if (x < 0)
            {
                x = -x;
                idxV += 4;
            }

            if (y < 0)
            {
                y = -y;
                idxV += 2;
            }

            LFloat factor = 0;
            if (y > x)
            {
                idxV += 1;
                factor = new LFloat(y) / x;
            }
            else
            {
                factor = new LFloat(x) / y;
            }

            //逆时针 idx 为 0 1 5 4 6 7 3 2
            var info = s_Idx2LutInfo[idxV];
            if (x == y)
            {
                return info.offset;
            }

            var deg = InternalLutATan(factor) - LMath.kRawLQuadPI;
            return info.sign * deg + info.offset;
        }

        /// <summary>
        /// ATan内部实现(查表)
        /// </summary>
        /// <param name="ydx">y/x的值</param>
        /// <returns></returns>
        private static long InternalLutATan(LFloat ydx)
        {
            //Debug.Assert(ydx >= 1);
            if (ydx >= LUTAtan2.MaxQueryIdx) { return LMath.kRawLHalfPI; }
            var iydx = (int)ydx;
            var startIdx = LUTAtan2._startIdx[iydx - 1];
            var size = LUTAtan2._arySize[iydx - 1];
            var remaind = ydx - iydx;
            var idx = startIdx + (int)(remaind * size);
            return LUTAtan2._tblTbl[idx];
        }

        #endregion

        #endregion

        #region 平方、开方相关

        /// <summary>
        /// 开方-int版本
        /// </summary>
        /// <param name="value"></param>
        /// <returns></returns>
        public static int Sqrt(int value)
        {
            if (value <= 0)
            {
                return 0;
            }

            return (int)LMath.InternalSqrt32((uint)value);
        }

        /// <summary>
        /// 开方 - long版本
        /// </summary>
        /// <param name="value"></param>
        /// <returns></returns>
        public static long Sqrt(long value)
        {
            if (value <= 0L)
            {
                return 0;
            }

            if (value <= (long)(0xffffffffu))
            {
                return (long)LMath.InternalSqrt32((uint)value);
            }

            return (long)LMath.InternalSqrt64((ulong)value);
        }

        /// <summary>
        /// 开方 - ulong版本
        /// </summary>
        /// <param name="value"></param>
        /// <returns></returns>
        public static long Sqrt(ulong value)
        {
            return (long)LMath.InternalSqrt64(value);
        }

        /// <summary>
        /// 开方 - LFloat版本
        /// </summary>
        /// <param name="value"></param>
        /// <returns></returns>
        public static LFloat Sqrt(LFloat value)
        {
            if (value.rawValue <= 0)
            {
                return LFloat.Zero;
            }

            return new LFloat(true, Sqrt(value.rawValue) * LFloat.RateOfOldPrecision);
        }

        /// <summary>
        /// 32位开平方计算内部实现
        /// </summary>
        /// <param name="val"></param>
        /// <returns></returns>
        private static uint InternalSqrt32(uint val)
        {
            ulong rem = 0;
            ulong root = 0;
            ulong divisor = 0;
            for (int i = 0; i < 16; i++)
            {
                root <<= 1;
                rem = ((rem << 2) + (val >> 30));
                val <<= 2;
                divisor = (root << 1) + 1;
                if (divisor <= rem)
                {
                    rem -= divisor;
                    root++;
                }
            }

            return (uint)root;
        }

        /// <summary>
        /// 64位开平方计算内部实现
        /// x = 2*p + q  
        /// x^2 = 4*p^2 + 4pq + q^2
        /// q = (x^2 - 4*p^2)/(4*p+q)  
        /// https://www.cnblogs.com/10cm/p/3922398.html
        /// </summary>
        /// <param name="value"></param>
        /// <returns></returns>
        private static uint InternalSqrt64(ulong value)
        {
            ulong rem = 0;
            ulong root = 0;
            ulong divisor = 0;
            for (int i = 0; i < 32; i++)
            {
                root <<= 1;
                rem = ((rem << 2) + (value >> 62)); //(x^2 - 4*p^2)  
                value <<= 2;
                divisor = (root << 1) + 1; //(4*p+q) 
                if (divisor <= rem)
                {
                    rem -= divisor;
                    root++;
                }
            }

            return (uint)root;
        }

        /// <summary>
        /// 定点数版本 - 平方计算
        /// </summary>
        /// <param name="value"></param>
        /// <returns></returns>
        public static LFloat Sqr(LFloat value)
        {
            return value * value;
        }
        
        /// <summary>
        /// 获取参数value向上取整到2的整数倍
        /// </summary>
        /// <param name="value"></param>
        /// <returns></returns>
        public static int CeilPowerOfTwo(int value)
        {
            value--;
            value |= value >> 1;
            value |= value >> 2;
            value |= value >> 4;
            value |= value >> 8;
            value |= value >> 16;
            value++;
            return value;
        }

        /// <summary>
        /// 是否是2的指数倍
        /// </summary>
        /// <param name="value"></param>
        /// <returns></returns>
        public static bool IsPowerOfTwo(int value)
        {
            return (value & (value - 1)) == 0;
        }

        #endregion

        #region 绝对值、符号位、取整相关

        /// <summary>
        /// 判断两个定点数是否同符号
        /// </summary>
        /// <param name="a"></param>
        /// <param name="b"></param>
        /// <returns></returns>
        public static bool SameSign(LFloat a, LFloat b)
        {
            return a.rawValue * b.rawValue > 0L;
        }

        public static int Abs(int val)
        {
            if (val < 0)
            {
                return -val;
            }

            return val;
        }

        public static long Abs(long val)
        {
            if (val < 0L)
            {
                return -val;
            }

            return val;
        }

        public static LFloat Abs(LFloat val)
        {
            if (val.rawValue < 0)
            {
                return new LFloat(true, -val.rawValue);
            }

            return val;
        }

        /// <summary>
        /// 定点数向下取整
        /// </summary>
        /// <param name="value"></param>
        /// <returns></returns>
        public static int FloorToInt(LFloat value)
        {
            var x = value.rawValue;
            if (x > 0)
            {
                x /= LFloat.Precision;
            }
            else
            {
                if (x % LFloat.Precision == 0)
                {
                    x /= LFloat.Precision;
                }
                else
                {
                    x = x / LFloat.Precision - 1;
                }
            }

            return (int)x;
        }

        /// <summary>
        /// 定点数向上取整
        /// </summary>
        /// <returns></returns>
        public static int CeilToInt(LFloat value)
        {
            var x = value.rawValue;
            if (x < 0)
            {
                x /= LFloat.Precision;
            }
            else
            {
                if (x % LFloat.Precision == 0)
                {
                    x /= LFloat.Precision;
                }
                else
                {
                    x = x / LFloat.Precision + 1;
                }
            }

            return (int)x;
        }

        /// <summary>
        /// 定点数四舍五入取整
        /// </summary>
        /// <param name="val"></param>
        /// <returns></returns>
        public static int RoundToInt(LFloat value)
        {
            var val = value.rawValue;
            if (val >= 0L)
            {
                var rd = val % LFloat.Precision;
                var retVal = (int)(val / LFloat.Precision);
                if (rd > LFloat.HalfPrecision)
                {
                    return retVal + 1;
                }
                return retVal;
            }
            else
            {
                val = -val;
                var rd = val % LFloat.Precision;
                var retVal = -(int)(val / LFloat.Precision);
                if (rd > LFloat.HalfPrecision)
                {
                    return (retVal - 1);
                }
                return retVal;
            }
        }

        /// <summary>
        /// 定点数四舍五入取整
        /// </summary>
        /// <param name="val"></param>
        /// <returns></returns>
        public static LFloat Round(LFloat val)
        {
            if (val <= 0)
            {
                var remainder = (-val.rawValue) % LFloat.Precision;
                if (remainder > LFloat.HalfPrecision)
                {
                    return new LFloat(true, val.rawValue + remainder - LFloat.Precision);
                }
                else
                {
                    return new LFloat(true, val.rawValue + remainder);
                }
            }
            else
            {
                var remainder = (val.rawValue) % LFloat.Precision;
                if (remainder > LFloat.HalfPrecision)
                {
                    return new LFloat(true, val.rawValue - remainder + LFloat.Precision);
                }
                else
                {
                    return new LFloat(true, val.rawValue - remainder);
                }
            }
        }

        #endregion

        #region Min、Max、Clamp相关

        public static bool Approximately(LFloat a, LFloat b)
        {
            // 计算两个浮点数之间的差的绝对值  
            float difference = Abs(a - b);  
            // 检查差的绝对值是否小于阈值  
            return difference < LFloat.EPSILON;  
        }

        public static int Clamp(int value, int min, int max)
        {
            if (value < min)
                value = min;
            else if (value > max)
                value = max;
            return value;
        }

        public static long Clamp(long value, long min, long max)
        {
            if (value < min)
            {
                return min;
            }

            if (value > max)
            {
                return max;
            }

            return value;
        }

        public static LFloat Clamp(LFloat value, LFloat min, LFloat max)
        {
            if (value < min)
            {
                return min;
            }

            if (value > max)
            {
                return max;
            }

            return value;
        }

        public static LFloat Clamp01(LFloat value)
        {
            if (value < LFloat.Zero)
            {
                return LFloat.Zero;
            }

            if (value > LFloat.One)
            {
                return LFloat.One;
            }

            return value;
        }
        
        public static long Max(long a, long b)
        {
            return (a <= b) ? b : a;
        }

        public static int Max(int a, int b)
        {
            return (a <= b) ? b : a;
        }

        public static long Min(long a, long b)
        {
            return (a > b) ? b : a;
        }

        public static int Min(int a, int b)
        {
            return (a > b) ? b : a;
        }

        public static LFloat Min(LFloat a, LFloat b)
        {
            return new LFloat(true, Min(a.rawValue, b.rawValue));
        }

        public static LFloat Min(LFloat a, int b)
        {
            return new LFloat(true, Min(a.rawValue, b * LFloat.Precision));
        }

        public static LFloat Min(int a, LFloat b)
        {
            return new LFloat(true, Min(a * LFloat.Precision, b.rawValue));
        }

        public static LFloat Max(LFloat a, LFloat b)
        {
            return new LFloat(true, Max(a.rawValue, b.rawValue));
        }

        public static LFloat Max(int a, LFloat b)
        {
            return new LFloat(true, Max(a * LFloat.Precision, b.rawValue));
        }

        public static LFloat Max(LFloat a, int b)
        {
            return new LFloat(true, Max(a.rawValue, b * LFloat.Precision));
        }

        public static int Min(params int[] values)
        {
            int length = values.Length;
            if (length == 0) { return 0; }
            int num = values[0];
            for (int index = 1; index < length; ++index)
            {
                if (values[index] < num)
                    num = values[index];
            }

            return num;
        }

        public static LFloat Min(params LFloat[] values)
        {
            int length = values.Length;
            if (length == 0) { return LFloat.Zero; }
            LFloat num = values[0];
            for (int index = 1; index < length; ++index)
            {
                if (values[index] < num)
                    num = values[index];
            }

            return num;
        }

        public static int Max(params int[] values)
        {
            int length = values.Length;
            if (length == 0)
                return 0;
            int num = values[0];
            for (int index = 1; index < length; ++index)
            {
                if (values[index] > num)
                    num = values[index];
            }

            return num;
        }

        public static LFloat Max(params LFloat[] values)
        {
            int length = values.Length;
            if (length == 0)
                return LFloat.Zero;
            var num = values[0];
            for (int index = 1; index < length; ++index)
            {
                if (values[index] > num)
                    num = values[index];
            }

            return num;
        }

        #endregion

        #region Lerp相关

        /// <summary>
        /// 定点数线性插值
        /// </summary>
        /// <param name="from"></param>
        /// <param name="to"></param>
        /// <param name="f"></param>
        /// <returns></returns>
        public static LFloat Lerp(LFloat from, LFloat to, LFloat f)
        {
            return new LFloat(true, ((to.rawValue - from.rawValue) * f.rawValue / LFloat.Precision) + from.rawValue);
        }

        /// <summary>
        /// 获取线性插值比例
        /// </summary>
        /// <param name="from"></param>
        /// <param name="to"></param>
        /// <param name="value"></param>
        /// <returns></returns>
        public static LFloat InverseLerp(LFloat from, LFloat to, LFloat value)
        {
            if (from != to) { return Clamp01(((value - from) / (to - from))); }
            return LFloat.Zero;
        }

        #endregion

        #region constant value

        /// <summary>
        /// 数学常数 - 定点数四分PI
        /// </summary>
        public static readonly LFloat QuadPI = new LFloat(true, kRawLQuadPI);
        /// <summary>
        /// 数学常数 - 定点数二分PI
        /// </summary>
        public static readonly LFloat HalfPI = new LFloat(true, kRawLHalfPI);
        /// <summary>
        /// 数学常数 - 定点数PI
        /// </summary>
        public static readonly LFloat PI = new LFloat(true, kRawLPI);
        /// <summary>
        /// 数学常数 - 定点数2PI
        /// </summary>
        public static readonly LFloat PI2 = new LFloat(true, kRawL2PI);
        /// <summary>
        /// 数学常数 - 定点数弧度转角度的算术因子
        /// </summary>
        public static readonly LFloat Rad2Deg = new LFloat(true, kRawLRad2Deg);
        /// <summary>
        /// 数学常数 - 定点数角度转弧度的算术因子
        /// </summary>
        public static readonly LFloat Deg2Rad = new LFloat(true, kRawLDeg2Rad);

        /// <summary>
        /// 四分PI定点数真实值
        /// </summary>
        private const long kRawLQuadPI = 785398L; //0.7853981
        /// <summary>
        /// 二分PI定点数真实值
        /// </summary>
        private const long kRawLHalfPI = 1570796L; //1.5707963
        /// <summary>
        /// PI定点数真实值
        /// </summary>
        private const long kRawLPI = 3141593L; //3.1415926
        /// <summary>
        /// 2PI定点数真实值
        /// </summary>
        private const long kRawL2PI = 6283185L; //6.2831853
        /// <summary>
        /// 弧度转角度的算术因子定点数真实值
        /// </summary>
        private const long kRawLRad2Deg = 57295780L; //57.2957795
        /// <summary>
        /// 角度转弧度的算术因子定点数真实值
        /// </summary>
        private const long kRawLDeg2Rad = 17453L; //0.0174532

        #endregion
    }
}