mirror of
https://gitee.com/jisol/jisol-game/
synced 2025-06-26 03:14:47 +00:00
835 lines
23 KiB
C#
835 lines
23 KiB
C#
/*
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* @FileName: LMath.cs
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* @Date: 2024-04-20 20:06:15
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* @LastEditTime: 2024-04-23 00:27:23
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* @Description: 定点数数学工具函数
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*/
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namespace JNGame.Math
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{
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/// <summary>
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/// 定点数数学工具库
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/// </summary>
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public static partial class LMath
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{
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public static LFloat Floor(LFloat value)
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{
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return FloorToInt(value);
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}
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public static LFloat Ceiling(LFloat value)
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{
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return CeilToInt(value);
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}
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#region 三角函数相关
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/// <summary>
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/// 定点数反余弦函数Acos
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/// </summary>
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/// <param name="val">余弦值</param>
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/// <returns>弧度</returns>
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public static LFloat Acos(LFloat val)
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{
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int idx = (int)(val.rawValue * LUTAcos.HALF_COUNT / LFloat.Precision) +
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LUTAcos.HALF_COUNT;
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idx = Clamp(idx, 0, LUTAcos.COUNT);
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return new LFloat(true, LUTAcos.table[idx]);
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}
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/// <summary>
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/// 定点数反正弦函数Asin
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/// </summary>
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/// <param name="val">正弦值</param>
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/// <returns>弧度</returns>
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public static LFloat Asin(LFloat val)
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{
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int idx = (int)(val.rawValue * LUTAsin.HALF_COUNT / LFloat.Precision) + LUTAsin.HALF_COUNT;
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idx = Clamp(idx, 0, LUTAsin.COUNT);
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return new LFloat(true, LUTAsin.table[idx]);
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}
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/// <summary>
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/// 定点数正弦函数Sin
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/// </summary>
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/// <param name="radians">弧度</param>
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/// <returns>正弦值</returns>
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public static LFloat Sin(LFloat radians)
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{
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return new LFloat(true, LUTSin.table[InternalGetIdx(radians)]);
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}
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/// <summary>
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/// 定点数版本余弦函数
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/// </summary>
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/// <param name="radians">弧度</param>
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/// <returns>余弦值</returns>
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public static LFloat Cos(LFloat radians)
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{
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return new LFloat(true, LUTCos.table[InternalGetIdx(radians)]);
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}
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/// <summary>
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/// 定点数版本正弦余弦函数，同时获取正弦值和余弦值
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/// </summary>
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/// <param name="sinValue">输出:正弦值</param>
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/// <param name="cosValue">输出:余弦值</param>
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/// <param name="radians">弧度</param>
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public static void SinCos(out LFloat sinValue, out LFloat cosValue, LFloat radians)
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{
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int idx = InternalGetIdx(radians);
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sinValue = new LFloat(true, LUTSin.table[idx]);
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cosValue = new LFloat(true, LUTCos.table[idx]);
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}
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/// <summary>
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/// 通过弧度获取查表索引
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/// </summary>
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/// <param name="radians">弧度</param>
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/// <returns></returns>
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private static int InternalGetIdx(LFloat radians)
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{
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var rawVal = radians.rawValue % LMath.kRawL2PI;
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if (rawVal < 0) rawVal += LMath.kRawL2PI;
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var val = new LFloat(true, rawVal) / LMath.PI2;
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var idx = (int)(val * LUTCos.COUNT);
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idx = Clamp(idx, 0, LUTCos.COUNT);
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return idx;
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}
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#region Atan2 & Atan
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/// <summary>
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/// 定点数版本反正切函数Atan2
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/// <para>值域[-PI, PI]，返回点(x,y)与X轴正向的夹角</para>
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/// <para>一二象限为正，三四象限为负</para>
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/// </summary>
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/// <param name="y"></param>
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/// <param name="x"></param>
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/// <returns>定点数，单位弧度</returns>
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public static LFloat Atan2(LFloat y, LFloat x)
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{
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return Atan2(y.rawValue, x.rawValue);
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}
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/// <summary>
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/// long版本反正切函数Atan2
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/// <para>值域[-PI, PI]，返回点(x,y)与X轴正向的夹角</para>
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/// <para>一二象限为正，三四象限为负</para>
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/// </summary>
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/// <param name="y"></param>
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/// <param name="x"></param>
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/// <returns>定点数，单位弧度</returns>
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public static LFloat Atan2(long y, long x)
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{
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return new LFloat(true, InternalAtan2(y, x));
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}
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/// <summary>
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/// int版本反正切函数Atan2
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/// <para>值域[-PI, PI]，返回点(x,y)与X轴正向的夹角</para>
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/// <para>一二象限为正，三四象限为负</para>
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/// </summary>
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/// <param name="y"></param>
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/// <param name="x"></param>
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/// <returns>定点数，单位弧度</returns>
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public static LFloat Atan2(int y, int x)
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{
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return new LFloat(true, InternalAtan2(y, x));
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}
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/// <summary>
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/// 定点数版本反正切函数Atan
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/// <para>值域[-PI/2, PI/2]，返回点(x,y)与X轴正向的夹角</para>
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/// </summary>
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/// <param name="val"></param>
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/// <returns></returns>
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public static LFloat Atan(LFloat val)
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{
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return new LFloat(true, InternalLutATan(val));
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}
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private struct LutAtan2Helper
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{
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public long sign;
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public long offset;
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public LutAtan2Helper(long sign, long offset)
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{
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this.sign = sign;
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this.offset = offset;
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}
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}
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private readonly static LutAtan2Helper[] s_Idx2LutInfo = new LutAtan2Helper[]
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{
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new LutAtan2Helper(-1, LMath.kRawLQuadPI),
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new LutAtan2Helper(1, LMath.kRawLQuadPI),
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new LutAtan2Helper(1, -LMath.kRawLQuadPI),
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new LutAtan2Helper(-1, -LMath.kRawLQuadPI),
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new LutAtan2Helper(1, LMath.kRawLQuadPI * 3),
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new LutAtan2Helper(-1, LMath.kRawLQuadPI * 3),
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new LutAtan2Helper(-1, -LMath.kRawLQuadPI * 3),
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new LutAtan2Helper(1, -LMath.kRawLQuadPI * 3),
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};
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/// <summary>
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/// Atan2的内部实现
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/// <para>值域[-PI, PI]，返回点(x,y)与X轴正向的夹角</para>
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/// <para>一二象限为正，三四象限为负</para>
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/// </summary>
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/// <param name="y"></param>
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/// <param name="x"></param>
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/// <returns></returns>
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private static long InternalAtan2(long y, long x)
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{
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//特殊情况处理
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if (y == 0)
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{
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if (x == 0)
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{
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return 0;
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}
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return x < 0 ? LMath.kRawLPI : 0;
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}
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if (x == 0)
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{
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return y > 0 ? LMath.kRawLHalfPI : -LMath.kRawLHalfPI;
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}
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//决定象限
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int idxV = 0;
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if (x < 0)
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{
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x = -x;
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idxV += 4;
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}
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if (y < 0)
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{
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y = -y;
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idxV += 2;
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}
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LFloat factor = 0;
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if (y > x)
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{
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idxV += 1;
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factor = new LFloat(y) / x;
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}
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else
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{
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factor = new LFloat(x) / y;
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}
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//逆时针 idx 为 0 1 5 4 6 7 3 2
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var info = s_Idx2LutInfo[idxV];
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if (x == y)
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{
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return info.offset;
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}
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var deg = InternalLutATan(factor) - LMath.kRawLQuadPI;
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return info.sign * deg + info.offset;
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}
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/// <summary>
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/// ATan内部实现(查表)
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/// </summary>
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/// <param name="ydx">y/x的值</param>
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/// <returns></returns>
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private static long InternalLutATan(LFloat ydx)
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{
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//Debug.Assert(ydx >= 1);
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if (ydx >= LUTAtan2.MaxQueryIdx) { return LMath.kRawLHalfPI; }
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var iydx = (int)ydx;
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var startIdx = LUTAtan2._startIdx[iydx - 1];
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var size = LUTAtan2._arySize[iydx - 1];
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var remaind = ydx - iydx;
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var idx = startIdx + (int)(remaind * size);
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return LUTAtan2._tblTbl[idx];
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}
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#endregion
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#endregion
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#region 平方、开方相关
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/// <summary>
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/// 开方-int版本
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/// </summary>
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/// <param name="value"></param>
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/// <returns></returns>
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public static int Sqrt(int value)
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{
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if (value <= 0)
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{
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return 0;
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}
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return (int)LMath.InternalSqrt32((uint)value);
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}
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/// <summary>
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/// 开方 - long版本
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/// </summary>
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/// <param name="value"></param>
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/// <returns></returns>
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public static long Sqrt(long value)
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{
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if (value <= 0L)
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{
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return 0;
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}
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if (value <= (long)(0xffffffffu))
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{
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return (long)LMath.InternalSqrt32((uint)value);
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}
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return (long)LMath.InternalSqrt64((ulong)value);
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}
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/// <summary>
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/// 开方 - ulong版本
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/// </summary>
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/// <param name="value"></param>
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/// <returns></returns>
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public static long Sqrt(ulong value)
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{
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return (long)LMath.InternalSqrt64(value);
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}
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/// <summary>
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/// 开方 - LFloat版本
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/// </summary>
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/// <param name="value"></param>
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/// <returns></returns>
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public static LFloat Sqrt(LFloat value)
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{
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if (value.rawValue <= 0)
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{
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return LFloat.Zero;
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}
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return new LFloat(true, Sqrt(value.rawValue) * LFloat.RateOfOldPrecision);
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}
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/// <summary>
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/// 32位开平方计算内部实现
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/// </summary>
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/// <param name="val"></param>
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/// <returns></returns>
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private static uint InternalSqrt32(uint val)
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{
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ulong rem = 0;
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ulong root = 0;
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ulong divisor = 0;
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for (int i = 0; i < 16; i++)
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{
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root <<= 1;
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rem = ((rem << 2) + (val >> 30));
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val <<= 2;
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divisor = (root << 1) + 1;
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if (divisor <= rem)
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{
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rem -= divisor;
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root++;
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}
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}
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return (uint)root;
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}
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/// <summary>
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/// 64位开平方计算内部实现
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/// x = 2*p + q
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/// x^2 = 4*p^2 + 4pq + q^2
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/// q = (x^2 - 4*p^2)/(4*p+q)
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/// https://www.cnblogs.com/10cm/p/3922398.html
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/// </summary>
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/// <param name="value"></param>
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/// <returns></returns>
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private static uint InternalSqrt64(ulong value)
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{
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ulong rem = 0;
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ulong root = 0;
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ulong divisor = 0;
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for (int i = 0; i < 32; i++)
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{
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root <<= 1;
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rem = ((rem << 2) + (value >> 62)); //(x^2 - 4*p^2)
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value <<= 2;
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divisor = (root << 1) + 1; //(4*p+q)
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if (divisor <= rem)
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{
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rem -= divisor;
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root++;
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}
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}
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return (uint)root;
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}
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/// <summary>
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/// 定点数版本 - 平方计算
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/// </summary>
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/// <param name="value"></param>
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/// <returns></returns>
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public static LFloat Sqr(LFloat value)
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{
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return value * value;
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}
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/// <summary>
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/// 获取参数value向上取整到2的整数倍
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/// </summary>
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/// <param name="value"></param>
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/// <returns></returns>
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public static int CeilPowerOfTwo(int value)
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{
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value--;
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value |= value >> 1;
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value |= value >> 2;
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value |= value >> 4;
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value |= value >> 8;
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value |= value >> 16;
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value++;
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return value;
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}
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/// <summary>
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/// 是否是2的指数倍
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/// </summary>
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/// <param name="value"></param>
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/// <returns></returns>
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public static bool IsPowerOfTwo(int value)
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{
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return (value & (value - 1)) == 0;
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}
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#endregion
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#region 绝对值、符号位、取整相关
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/// <summary>
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/// 判断两个定点数是否同符号
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/// </summary>
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/// <param name="a"></param>
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/// <param name="b"></param>
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/// <returns></returns>
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public static bool SameSign(LFloat a, LFloat b)
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{
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return a.rawValue * b.rawValue > 0L;
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}
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public static int Abs(int val)
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{
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if (val < 0)
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{
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return -val;
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}
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return val;
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}
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public static long Abs(long val)
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{
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if (val < 0L)
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{
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return -val;
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}
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return val;
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}
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public static LFloat Abs(LFloat val)
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{
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if (val.rawValue < 0)
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{
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return new LFloat(true, -val.rawValue);
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}
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return val;
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}
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/// <summary>
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/// 定点数向下取整
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/// </summary>
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/// <param name="value"></param>
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/// <returns></returns>
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public static int FloorToInt(LFloat value)
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{
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var x = value.rawValue;
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if (x > 0)
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{
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x /= LFloat.Precision;
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}
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else
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{
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if (x % LFloat.Precision == 0)
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{
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x /= LFloat.Precision;
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}
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else
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{
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x = x / LFloat.Precision - 1;
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}
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}
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return (int)x;
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}
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/// <summary>
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/// 定点数向上取整
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/// </summary>
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/// <returns></returns>
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public static int CeilToInt(LFloat value)
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{
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var x = value.rawValue;
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if (x < 0)
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{
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x /= LFloat.Precision;
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}
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else
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{
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if (x % LFloat.Precision == 0)
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{
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x /= LFloat.Precision;
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}
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else
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{
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x = x / LFloat.Precision + 1;
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}
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}
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return (int)x;
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}
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/// <summary>
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/// 定点数四舍五入取整
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/// </summary>
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/// <param name="val"></param>
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/// <returns></returns>
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public static int RoundToInt(LFloat value)
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{
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var val = value.rawValue;
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if (val >= 0L)
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{
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var rd = val % LFloat.Precision;
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var retVal = (int)(val / LFloat.Precision);
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if (rd > LFloat.HalfPrecision)
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{
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return retVal + 1;
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}
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return retVal;
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}
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else
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{
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val = -val;
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var rd = val % LFloat.Precision;
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var retVal = -(int)(val / LFloat.Precision);
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if (rd > LFloat.HalfPrecision)
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{
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return (retVal - 1);
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}
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return retVal;
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}
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}
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/// <summary>
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/// 定点数四舍五入取整
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/// </summary>
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/// <param name="val"></param>
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/// <returns></returns>
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public static LFloat Round(LFloat val)
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{
|
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if (val <= 0)
|
|
{
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var remainder = (-val.rawValue) % LFloat.Precision;
|
|
if (remainder > LFloat.HalfPrecision)
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|
{
|
|
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
|
|
}
|
|
} |