75 lines
2.3 KiB
C++
75 lines
2.3 KiB
C++
#pragma once
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#include<hgl/math/MathConst.h>
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#include<math.h>
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namespace hgl
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{
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double Lsin(int angle); ///<低精度sin计算,注意传入的参数为角度而非弧度
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double Lcos(int angle); ///<低精度cos计算,注意传入的参数为角度而非弧度
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void Lsincos(int angle, double &s, double &c); ///<低精度sin+cos计算,注意传入的参数为角度而非弧度
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/**
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* Approximates acos(x) with a max absolute error of 9.0x10^-3.
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* Valid in the range -1..1.
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*/
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inline const float Lacos(float x)
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{
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// Lagarde 2014, "Inverse trigonometric functions GPU optimization for AMD GCN architecture"
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// This is the approximation of degree 1, with a max absolute error of 9.0x10^-3
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float y = fabs(x);
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float p = -0.1565827 * y + 1.570796;
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p *= sqrt(1.0 - y);
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return x >= 0.0 ? p : HGL_PI - p;
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}
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/**
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* Approximates acos(x) with a max absolute error of 9.0x10^-3.
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* Valid only in the range 0..1.
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*/
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inline const float LacosPositive(float x)
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{
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return (-0.1565827 * x + 1.570796) * sqrt(1.0 - x);
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}
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inline constexpr double ApproxSin(double angle)
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{
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return angle*(1.27323954f-angle*angle*(0.405284735f-angle*angle*(0.075133f-angle*angle*0.0078f)));
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}
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inline constexpr double ApproxCos(double angle)
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{
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return 1.27323954f-angle*angle*(0.405284735f-angle*angle*(0.075133f-angle*angle*0.0078f));
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}
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inline constexpr double ApproxAtan2(double x,double y)
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{
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return x/(1.27323954f+y*y*(0.405284735f+y*y*(0.075133f+y*y*0.0078f)));
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}
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inline constexpr double ApproxAtan(double z)
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{
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return z*(1.27323954f-z*z*(0.405284735f-z*z*(0.075133f-z*z*0.0078f)));
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}
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/**
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* 低精度atan函数
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*/
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inline constexpr double Latan(double z)
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{
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constexpr double n1 = 0.97239411f;
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constexpr double n2 = -0.19194795f;
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return (n1 + n2 * z * z) * z;
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}
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double Latan2(double y, double x); ///<低精度atan2函数
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/**
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* 近似Pow2.2，使用此函数等于pow(x,2.2)
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*/
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inline constexpr double LPow22(double x)
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{
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return x*(1.12*x - 0.12);
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}
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}//namespace hgl
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