111 lines
3.9 KiB
C#
111 lines
3.9 KiB
C#
//-----------------------------------------------------------------------
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//-----------------------------------------------------------------------
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// file="Sqrt.cs"
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// Project: StgSharp
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// AuthorGroup: Nitload Space
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// Copyright (c) Nitload Space. All rights reserved.
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the “Software”), to deal in the Software without restriction,
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// including without limitation the rights to use, copy, modify, merge,
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// publish, distribute, sublicense, and/or sell copies of the Software,
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// and to permit persons to whom the Software is furnished to do so,
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// subject to the following conditions:
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//
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// The above copyright notice and
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// this permission notice shall be included in all copies
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// or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED “AS IS”,
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// WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
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// INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
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// IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
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// DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
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// ARISING FROM, OUT OF OR IN CONNECTION WITH
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// THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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//
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//-----------------------------------------------------------------------
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//-----------------------------------------------------------------------
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using System;
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using System.Runtime.CompilerServices;
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namespace StgSharp.Math
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{
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public static partial class Scaler
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{
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public static unsafe float SeedSqrt( float x )
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{
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/*
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* 本方法采用分别对指数和小数处理的方法计算平方根
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* 将指数除以2即可获得结果的指数
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* （补充：指数最低位被加到小数位中以抵消一个多余的2 ^ 1的影响）
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* 小数部分则统一乘以2 ^ 16后由y = Sqrt(x)在1.5 * 2 ^ 16处的切线近似
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* 为简化操作，提高计算速度，切线左界被移动到远点
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* 在进一步简化操作后，计算精度达到0.5%，速度约为.Net库函数的3倍
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*/
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if( x < 0 )
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{
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throw new ArgumentOutOfRangeException( "Input is smaller than zero!" );
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}
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if( x == 0 ) {
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return 0;
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}
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/*
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* 提取指数位并减半
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* 由于平方根仅对正数有效
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* 故不考虑正负号
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*/
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if( x < 0 )
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{
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throw new ArgumentOutOfRangeException();
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}
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if( x <= 1e-12 ) {
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return 0;
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}
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//提取指数位并减去指数位中的127
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//由于平方根仅对正数有效
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//故不考虑正负号
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uint a = *( uint* )&x;
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uint f = a;
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f >>= 23;
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f /= 2;
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f += 64;
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//提取小数位
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//由于平方根仅对正数有效
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//故不考虑正负号
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a -= 0b_0011_1111_0000_0000_0000_0000_0000_0000;
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uint e = a << 8;
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e >>= 8;
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//线性近似
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e *= 0b_1101_0001;
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e >>= 24;
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e += 0b_0000_0000_0001_0000_1010_1000_1110_0010;
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//还原指数
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f <<= 23;
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e += f;
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float result = *( float* )&e;
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result = ( result + ( x / result ) ) / 2;
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return ( result + ( x / result ) ) / 2;
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}
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public static float Sqrt( float x )
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{
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return MathF.Sqrt( x );
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/**/
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}
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}
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}
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