split Math/Physics/Time const to new files.

inc/hgl/math/FastTriangle.h

@@ -1,16 +1,42 @@
 #ifndef HGL_ALGORITHM_MATH_FAST_TRIANGLE_FUNCTION_INCLUDE
 #define HGL_ALGORITHM_MATH_FAST_TRIANGLE_FUNCTION_INCLUDE
 
+#include<hgl/math/MathConst.h>
+#include<math.h>
 namespace hgl
 {
     double Lsin(int angle);                                     ///<低精度sin计算,注意传入的参数为角度而非弧度
     double Lcos(int angle);                                     ///<低精度cos计算,注意传入的参数为角度而非弧度
     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
 
+    /**
+     * Approximates acos(x) with a max absolute error of 9.0x10^-3.
+     * Valid in the range -1..1.
+     */
+    inline float Lacos(float x)
+    {
+        // Lagarde 2014, "Inverse trigonometric functions GPU optimization for AMD GCN architecture"
+        // This is the approximation of degree 1, with a max absolute error of 9.0x10^-3
+        float y = fabs(x);
+        float p = -0.1565827 * y + 1.570796;
+        p *= sqrt(1.0 - y);
+        return x >= 0.0 ? p : HGL_PI - p;
+    }
+
+    /**
+     * Approximates acos(x) with a max absolute error of 9.0x10^-3.
+     * Valid only in the range 0..1.
+     */
+    inline float LacosPositive(float x)
+    {
+        float p = -0.1565827 * x + 1.570796;
+        return p * sqrt(1.0 - x);
+    }
+
     /**
      * 低精度atan函数
      */
-    double inline Latan(double z)
+    inline double Latan(double z)
     {
         constexpr double n1 = 0.97239411f;
         constexpr double n2 = -0.19194795f;
@@ -23,7 +49,7 @@ namespace hgl
     /**
      * 近似Pow2.2，使用此函数等于pow(x,2.2)
      */
-    double inline LPow22(double x)
+    inline double LPow22(double x)
     {
         return x*(1.12*x - 0.12);
     }