وظيفة Math.Sin (مزدوجة) لوحدة معالجة الرسومات

using System; class Math_d { const double PI025 = Math.PI / 4; /// <summary> 2^17 = 131072 (1 ),   10000 ( ),  2^21 = 22097152 (16 )   +-1 ( ) (  ) </summary> const int length_mem = 22097152; const int length_mem_M1 = length_mem - 1; /// <summary>    sin,    . </summary> static double[] mem_sin; /// <summary>    cos,    . </summary> static double[] mem_cos; /// <summary>  ,   sin,    . </summary> public static void Initialise() { Ini_Mem_Sin(); Ini_Mem_Cos(); } /// <summary>       Cos,   . </summary> /// <param name="rad"></param> public static double Sin_3(double rad) { double rad_025; int i; //    //if (rad < 0) { rad = -rad + Math.PI; } i = (int)(rad / PI025); //   rad_025 = rad - PI025 * i; //     ( ) i = i & 7; //      8 //    switch (i) { case 0: return Sin_Lerp(rad_025); case 1: return Cos_Lerp(PI025 - rad_025); case 2: return Cos_Lerp(rad_025); case 3: return Sin_Lerp(PI025 - rad_025); case 4: return -Sin_Lerp(rad_025); case 5: return -Cos_Lerp(PI025 - rad_025); case 6: return -Cos_Lerp(rad_025); case 7: return -Sin_Lerp(PI025 - rad_025); } return 0; } /// <summary>   sin    </summary> static void Ini_Mem_Sin() { double rad; mem_sin = new double[length_mem]; for (int i = 0; i < length_mem; i++) { rad = (i * PI025) / length_mem_M1; mem_sin[i] = Math.Sin(rad); } } /// <summary>   cos    </summary> static void Ini_Mem_Cos() { double rad; mem_cos = new double[length_mem]; for (int i = 0; i < length_mem; i++) { rad = (i * PI025) / length_mem_M1; mem_cos[i] = Math.Cos(rad); } } /// <summary>      sin  0  pi/4. </summary> /// <param name="rad">     0  pi/4. </param> static double Sin_Lerp(double rad) { int i_0; int i_1; double i_0d; double percent; double a; double b; double s; percent = rad / PI025; i_0d = percent * length_mem_M1; i_0 = (int)i_0d; i_1 = i_0 + 1; a = mem_sin[i_0]; b = mem_sin[i_1]; s = i_0d - i_0; return Lerp(a, b, s); } /// <summary>      cos  0  pi/4. </summary> /// <param name="rad">     0  pi/4. </param> static double Cos_Lerp(double rad) { int i_0; int i_1; double i_0d; double percent; double a; double b; double s; percent = rad / PI025; i_0d = percent * length_mem_M1; i_0 = (int)i_0d; i_1 = i_0 + 1; a = mem_cos[i_0]; b = mem_cos[i_1]; s = i_0d - i_0; return Lerp(a, b, s); } /// <summary>      . (return a + s * (b - a)) </summary> /// <param name="a">  . </param> /// <param name="b">  . </param> /// <param name="s">  . 0 = a, 1 = b, 0.5 =   a  b. </param> public static double Lerp(double a, double b, double s) { return a + s * (b - a); } } 

  // <summary>  ,    Fact </summary> static double[] fact; /// <summary>            . ///   rad,   . ///  ( Math): 4% (fps)  steps = 17 </summary> /// <param name="rad">   .      pi/4. </param> /// <param name="steps">  :  ,   .  pi/4   E-15  8. </param> public static double Sin(double rad, int steps) { double ret; double a; //,     double aa; // *  int i_f; //  int sign; // (  -  +,     = +) ret = 0; sign = -1; aa = rad * rad; a = rad; i_f = 1; //      for (int n = 0; n < steps; n++) { sign *= -1; ret += sign * a / Fact(i_f); a *= aa; i_f += 2; } return ret; } /// <summary>   (n!).  n > fact.Length,  -1. </summary> /// <param name="n"> ,     . </param> public static double Fact(int n) { if (n >= 0 && n < fact.Length) { return fact[n]; } else { Debug.Log("    . n = " + n + ",   = " + fact.Length); return -1; } } /// <summary>  . </summary> static void Init_Fact() { int steps; steps = 46; fact = new double[steps]; fact[0] = 1; for (int n = 1; n < steps; n++) { fact[n] = fact[n - 1] * n; } } 

  // <summary>  ,    Fact </summary> static double[] fact; /// <summary>   Sin </summary> /// <param name="rad"></param> public static double Sin_2(double rad) { double rad_025; int i; //rad = rad % PI2; //% -   .  , fps   90  150 (  100 000   ) //rad_025 = rad % PI025; i = (int)(rad / PI025); rad_025 = rad - PI025 * i; i = i & 7; //     8  //    switch (i) { case 0: return Sin(rad_025, 8); case 1: return Cos(PI025 - rad_025, 8); case 2: return Cos(rad_025, 8); case 3: return Sin(PI025 - rad_025, 8); case 4: return -Sin(rad_025, 8); case 5: return -Cos(PI025 - rad_025, 8); case 6: return -Cos(rad_025, 8); case 7: return -Sin(PI025 - rad_025, 8); } return 0; } /// <summary>            . ///   rad,   . ///  ( Math): 10% (fps)  steps = 17 </summary> /// <param name="rad">   .      pi/4. </param> /// <param name="steps">  :  ,   .  pi/4   E-15  8. </param> public static double Sin(double rad, int steps) { double ret; double a; //,     double aa; // *  int i_f; //  int sign; // (  -  +,     = +) ret = 0; sign = -1; aa = rad * rad; a = rad; i_f = 1; //      for (int n = 0; n < steps; n++) { sign *= -1; ret += sign * a / Fact(i_f); a *= aa; i_f += 2; } return ret; } /// <summary>            . ///   rad,   . ///  ( Math): 10% (fps), 26% (test)  steps = 17 </summary> /// <param name="rad">   .      pi/4. </param> /// <param name="steps">  :  ,   .  pi/4   E-15  8. </param> public static double Cos(double rad, int steps) { double ret; double a; double aa; // *  int i_f; //  int sign; // (  -  +,     = +) ret = 0; sign = -1; aa = rad * rad; a = 1; i_f = 0; //      for (int n = 0; n < steps; n++) { sign *= -1; ret += sign * a / Fact(i_f); a *= aa; i_f += 2; } return ret; } /// <summary>   (n!).  n > fact.Length,  -1. </summary> /// <param name="n"> ,     . </param> public static double Fact(int n) { if (n >= 0 && n < fact.Length) { return fact[n]; } else { Debug.Log("    . n = " + n + ",   = " + fact.Length); return -1; } } /// <summary>  . </summary> static void Init_Fact() { int steps; steps = 46; fact = new double[steps]; fact[0] = 1; for (int n = 1; n < steps; n++) { fact[n] = fact[n - 1] * n; } } 

 /// <summary>  ( Math): 9% (fps)</summary> /// <param name="x">     -2*Pi  2*Pi </param> public static double Sin_1(double x) { return 0.9999997192673006 * x - 0.1666657564532464 * Math.Pow(x, 3) + 0.008332803647181511 * Math.Pow(x, 5) - 0.00019830197237204295 * Math.Pow(x, 7) + 2.7444305061093514e-6 * Math.Pow(x, 9) - 2.442176561869478e-8 * Math.Pow(x, 11) + 1.407555708887347e-10 * Math.Pow(x, 13) - 4.240664814288337e-13 * Math.Pow(x, 15); } 

 /// <summary>  ( Math): 83% (fps)</summary> /// <param name="rad">     -2*Pi  2*Pi </param> public static double Sin_0(double rad) { double x; double xx; double ret; xx = rad * rad; x = rad; //1 ret = 0.9999997192673006 * x; x *= xx; //3 ret -= 0.1666657564532464 * x; x *= xx; //5 ret += 0.008332803647181511 * x; x *= xx; //7 ret -= 0.00019830197237204295 * x; x *= xx; //9 ret += 2.7444305061093514e-6 * x; x *= xx; //11 ret -= 2.442176561869478e-8 * x; x *= xx; //13 ret += 1.407555708887347e-10 * x; x *= xx; //15 ret -= 4.240664814288337e-13 * x; return ret; } 

 class Math_d { const double PI025 = Math.PI / 4; /// <summary> 2^17 = 131072 (1 ),   10000 ( ),  2^21 = 22097152 (16 )   +-1 ( ) (  ) </summary> const int length_mem = 22097152; const int length_mem_M1 = length_mem - 1; /// <summary>    sin,    . </summary> static double[] mem_sin; /// <summary>    cos,    . </summary> static double[] mem_cos; /// <summary>  ,   sin,    . </summary> public static void Initialise() { Ini_Mem_Sin(); Ini_Mem_Cos(); } /// <summary>       Cos,   . </summary> /// <param name="rad"></param> public static double Sin_3(double rad) { double rad_025; int i; //    //if (rad < 0) { rad = -rad + Math.PI; } i = (int)(rad / PI025); //   rad_025 = rad - PI025 * i; //     ( ) i = i & 7; //      8 //    switch (i) { case 0: return Sin_Lerp(rad_025); case 1: return Cos_Lerp(PI025 - rad_025); case 2: return Cos_Lerp(rad_025); case 3: return Sin_Lerp(PI025 - rad_025); case 4: return -Sin_Lerp(rad_025); case 5: return -Cos_Lerp(PI025 - rad_025); case 6: return -Cos_Lerp(rad_025); case 7: return -Sin_Lerp(PI025 - rad_025); } return 0; } /// <summary>   sin    </summary> static void Ini_Mem_Sin() { double rad; mem_sin = new double[length_mem]; for (int i = 0; i < length_mem; i++) { rad = (i * PI025) / length_mem_M1; mem_sin[i] = Math.Sin(rad); } } /// <summary>   cos    </summary> static void Ini_Mem_Cos() { double rad; mem_cos = new double[length_mem]; for (int i = 0; i < length_mem; i++) { rad = (i * PI025) / length_mem_M1; mem_cos[i] = Math.Cos(rad); } } /// <summary>      sin  0  pi/4. </summary> /// <param name="rad">     0  pi/4. </param> static double Sin_Lerp(double rad) { int i_0; int i_1; double i_0d; double percent; double a; double b; double s; percent = rad / PI025; i_0d = percent * length_mem_M1; i_0 = (int)i_0d; i_1 = i_0 + 1; a = mem_sin[i_0]; b = mem_sin[i_1]; s = i_0d - i_0; return Lerp(a, b, s); } /// <summary>      cos  0  pi/4. </summary> /// <param name="rad">     0  pi/4. </param> static double Cos_Lerp(double rad) { int i_0; int i_1; double i_0d; double percent; double a; double b; double s; percent = rad / PI025; i_0d = percent * length_mem_M1; i_0 = (int)i_0d; i_1 = i_0 + 1; a = mem_cos[i_0]; b = mem_cos[i_1]; s = i_0d - i_0; return Lerp(a, b, s); } /// <summary>      . (return a + s * (b - a)) </summary> /// <param name="a">  . </param> /// <param name="b">  . </param> /// <param name="s">  . 0 = a, 1 = b, 0.5 =   a  b. </param> public static double Lerp(double a, double b, double s) { return a + s * (b - a); } }