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  1. /*****************************************************************
  2. Name : 
  3. Date : 2018/02/07
  4. By   : CharlotteHonG
  5. Final: 2018/02/07
  6. *****************************************************************/
  7. #include <iostream>
  8. #include <cmath>
  9. #include <iomanip>
  10. using namespace std;
  11. #define M_PI 3.14159265358979323846
  12.  
  13. // 快速 atan2 算法
  14. float fastAtan2f(float dy, float dx){
  15.     static const float atan2_p1 = 0.9997878412794807f*(float)(180/M_PI);
  16.     static const float atan2_p3 = -0.3258083974640975f*(float)(180/M_PI);
  17.     static const float atan2_p5 = 0.1555786518463281f*(float)(180/M_PI);
  18.     static const float atan2_p7 = -0.04432655554792128f*(float)(180/M_PI);
  19.     static const float atan2_DBL_EPSILON = 2.2204460492503131e-016;
  20.  
  21.     float ax = std::abs(dx), ay = std::abs(dy);
  22.     float a, c, c2;
  23.     if (ax >= ay) {
  24.         c = ay/(ax + static_cast<float>(atan2_DBL_EPSILON));
  25.         c2 = c*c;
  26.         a = (((atan2_p7*c2 + atan2_p5)*c2 + atan2_p3)*c2 + atan2_p1)*c;
  27.     } else {
  28.         c = ax/(ay + static_cast<float>(atan2_DBL_EPSILON));
  29.         c2 = c*c;
  30.         a = 90.f - (((atan2_p7*c2 + atan2_p5)*c2 + atan2_p3)*c2 + atan2_p1)*c;
  31.     }
  32.     if (dx < 0)
  33.         a = 180.f - a;
  34.     if (dy < 0)
  35.         a = 360.f - a;
  36.     return a;
  37. }
  38. float fastAtan2f_rad(float dy, float dx){
  39.     static const float atan2_p1 =  0.9997878412794807f;
  40.     static const float atan2_p3 = -0.3258083974640975f;
  41.     static const float atan2_p5 =  0.1555786518463281f;
  42.     static const float atan2_p7 = -0.04432655554792128f;
  43.     static const float atan2_DBL_EPSILON = 2.2204460492503131e-016;
  44.  
  45.     float ax = std::abs(dx), ay = std::abs(dy);
  46.     float a, c, c2;
  47.     if (ax >= ay) {
  48.         c = ay/(ax + static_cast<float>(atan2_DBL_EPSILON));
  49.         c2 = c*c;
  50.         a = (((atan2_p7*c2 + atan2_p5)*c2 + atan2_p3)*c2 + atan2_p1)*c;
  51.     } else {
  52.         c = ax/(ay + static_cast<float>(atan2_DBL_EPSILON));
  53.         c2 = c*c;
  54.         a = M_PI/0.5 - (((atan2_p7*c2 + atan2_p5)*c2 + atan2_p3)*c2 + atan2_p1)*c;
  55.     }
  56.     if (dx < 0)
  57.         a = M_PI - a;
  58.     if (dy < 0)
  59.         a = M_PI*2.0 - a;
  60.     return a;
  61. }
  62. // 快速 atan 算法
  63. float fastAtanf(float dy){
  64.     static const float atan2_p1 = 0.9997878412794807f*(float)(180/M_PI);
  65.     static const float atan2_p3 = -0.3258083974640975f*(float)(180/M_PI);
  66.     static const float atan2_p5 = 0.1555786518463281f*(float)(180/M_PI);
  67.     static const float atan2_p7 = -0.04432655554792128f*(float)(180/M_PI);
  68.     static const float atan2_DBL_EPSILON = 2.2204460492503131e-016;
  69.  
  70.     float ax = 1.0, ay = std::abs(dy);
  71.     float a, c, c2;
  72.     if (ax >= ay) {
  73.         c = ay/(ax + static_cast<float>(atan2_DBL_EPSILON));
  74.         c2 = c*c;
  75.         a = (((atan2_p7*c2 + atan2_p5)*c2 + atan2_p3)*c2 + atan2_p1)*c;
  76.     } else {
  77.         c = ax/(ay + static_cast<float>(atan2_DBL_EPSILON));
  78.         c2 = c*c;
  79.         a = 90.f - (((atan2_p7*c2 + atan2_p5)*c2 + atan2_p3)*c2 + atan2_p1)*c;
  80.     }
  81.  
  82.     if (dy < 0)
  83.         a = - a;
  84.  
  85.     return a;
  86. }
  87. float fastAtanf_rad(float dy){
  88.     static const float atan2_p1 =  0.9997878412794807f;
  89.     static const float atan2_p3 = -0.3258083974640975f;
  90.     static const float atan2_p5 =  0.1555786518463281f;
  91.     static const float atan2_p7 = -0.04432655554792128f;
  92.     static const float atan2_DBL_EPSILON = 2.2204460492503131e-016;
  93.  
  94.     float ax = 1.0, ay = std::abs(dy);
  95.     float a, c, c2;
  96.     if (ax >= ay) {
  97.         c = ay/(ax + static_cast<float>(atan2_DBL_EPSILON));
  98.         c2 = c*c;
  99.         a = (((atan2_p7*c2 + atan2_p5)*c2 + atan2_p3)*c2 + atan2_p1)*c;
  100.     } else {
  101.         c = ax/(ay + static_cast<float>(atan2_DBL_EPSILON));
  102.         c2 = c*c;
  103.         a = M_PI*0.5 - (((atan2_p7*c2 + atan2_p5)*c2 + atan2_p3)*c2 + atan2_p1)*c;
  104.     }
  105.  
  106.     if (dy < 0)
  107.         a = - a;
  108.  
  109.     return a;
  110. }
  111.  
  112. double rounding(double num, int index)
  113. {
  114.     bool isNegative = false; // whether is negative number or not
  115.  
  116.     if(num < 0) // if this number is negative, then convert to positive number
  117.     {
  118.         isNegative = true;  
  119.         num = -num;
  120.     }
  121.  
  122.     if(index >= 0)
  123.     {
  124.         int multiplier;
  125.         multiplier = pow(10, index);
  126.         num = (int)(num * multiplier + 0.5) / (multiplier * 1.0);
  127.     }
  128.  
  129.     if(isNegative) // if this number is negative, then convert to negative number
  130.     {
  131.         num = -num;
  132.     }
  133.  
  134.     return num;
  135. }
  136.  
  137. void test_fast(int i) {
  138.  
  139.     int corn = i;
  140.     float val = corn *M_PI/180.0;
  141.     float test = tan(val);
  142.  
  143.     float theta2 = atan(test) *180.0/M_PI;
  144.     float theta3 = fastAtanf_rad(test) *180.0/M_PI;
  145.  
  146.     int idx = 2;
  147.     if( rounding(theta2, idx) != rounding(theta3, idx)) {
  148.         cout << fixed << setprecision(2) << "atan- cmath/fast = (" << theta2 << ", " << theta3 << ")" << endl;
  149.     }
  150.     //cout << fixed << setprecision(2) << "atan- cmath/fast = (" << theta2 << ", " << theta3 << ")" << endl;
  151. }
  152. //================================================================
  153. int main(int argc, char const *argv[]){
  154.  
  155.     for(int i = -720; i < 720; ++i) {
  156.         test_fast(i);
  157.     }
  158.     return 0;
  159. }
  160. //====================================================================================
  161.  
Success #stdin #stdout 0s 4224KB
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atan- cmath/fast = (32.00, 31.99)
atan- cmath/fast = (33.00, 32.99)
atan- cmath/fast = (34.00, 33.99)
atan- cmath/fast = (35.00, 34.99)
atan- cmath/fast = (36.00, 35.99)
atan- cmath/fast = (37.00, 36.99)
atan- cmath/fast = (41.00, 41.01)
atan- cmath/fast = (42.00, 42.01)
atan- cmath/fast = (43.00, 43.01)
atan- cmath/fast = (45.00, 44.99)
atan- cmath/fast = (47.00, 46.99)
atan- cmath/fast = (48.00, 47.99)
atan- cmath/fast = (49.00, 48.99)
atan- cmath/fast = (53.00, 53.01)
atan- cmath/fast = (54.00, 54.01)
atan- cmath/fast = (55.00, 55.01)
atan- cmath/fast = (56.00, 56.01)
atan- cmath/fast = (57.00, 57.01)
atan- cmath/fast = (58.00, 58.01)
atan- cmath/fast = (-58.00, -58.01)
atan- cmath/fast = (-57.00, -57.01)
atan- cmath/fast = (-56.00, -56.01)
atan- cmath/fast = (-55.00, -55.01)
atan- cmath/fast = (-54.00, -54.01)
atan- cmath/fast = (-53.00, -53.01)
atan- cmath/fast = (-49.00, -48.99)
atan- cmath/fast = (-48.00, -47.99)
atan- cmath/fast = (-47.00, -46.99)
atan- cmath/fast = (-45.00, -45.01)
atan- cmath/fast = (-43.00, -43.01)
atan- cmath/fast = (-42.00, -42.01)
atan- cmath/fast = (-41.00, -41.01)
atan- cmath/fast = (-37.00, -36.99)
atan- cmath/fast = (-36.00, -35.99)
atan- cmath/fast = (-35.00, -34.99)
atan- cmath/fast = (-34.00, -33.99)
atan- cmath/fast = (-33.00, -32.99)
atan- cmath/fast = (-32.00, -31.99)
atan- cmath/fast = (32.00, 31.99)
atan- cmath/fast = (33.00, 32.99)
atan- cmath/fast = (34.00, 33.99)
atan- cmath/fast = (35.00, 34.99)
atan- cmath/fast = (36.00, 35.99)
atan- cmath/fast = (37.00, 36.99)
atan- cmath/fast = (41.00, 41.01)
atan- cmath/fast = (42.00, 42.01)
atan- cmath/fast = (43.00, 43.01)
atan- cmath/fast = (45.00, 45.01)
atan- cmath/fast = (47.00, 46.99)
atan- cmath/fast = (48.00, 47.99)
atan- cmath/fast = (49.00, 48.99)
atan- cmath/fast = (53.00, 53.01)
atan- cmath/fast = (54.00, 54.01)
atan- cmath/fast = (55.00, 55.01)
atan- cmath/fast = (56.00, 56.01)
atan- cmath/fast = (57.00, 57.01)
atan- cmath/fast = (58.00, 58.01)
atan- cmath/fast = (-58.00, -58.01)
atan- cmath/fast = (-57.00, -57.01)
atan- cmath/fast = (-56.00, -56.01)
atan- cmath/fast = (-55.00, -55.01)
atan- cmath/fast = (-54.00, -54.01)
atan- cmath/fast = (-53.00, -53.01)
atan- cmath/fast = (-49.00, -48.99)
atan- cmath/fast = (-48.00, -47.99)
atan- cmath/fast = (-47.00, -46.99)
atan- cmath/fast = (-45.00, -44.99)
atan- cmath/fast = (-43.00, -43.01)
atan- cmath/fast = (-42.00, -42.01)
atan- cmath/fast = (-41.00, -41.01)
atan- cmath/fast = (-37.00, -36.99)
atan- cmath/fast = (-36.00, -35.99)
atan- cmath/fast = (-35.00, -34.99)
atan- cmath/fast = (-34.00, -33.99)
atan- cmath/fast = (-33.00, -32.99)
atan- cmath/fast = (-32.00, -31.99)
atan- cmath/fast = (32.00, 31.99)
atan- cmath/fast = (33.00, 32.99)
atan- cmath/fast = (34.00, 33.99)
atan- cmath/fast = (35.00, 34.99)
atan- cmath/fast = (36.00, 35.99)
atan- cmath/fast = (37.00, 36.99)
atan- cmath/fast = (41.00, 41.01)
atan- cmath/fast = (42.00, 42.01)
atan- cmath/fast = (43.00, 43.01)
atan- cmath/fast = (45.00, 45.01)
atan- cmath/fast = (47.00, 46.99)
atan- cmath/fast = (48.00, 47.99)
atan- cmath/fast = (49.00, 48.99)
atan- cmath/fast = (53.00, 53.01)
atan- cmath/fast = (54.00, 54.01)
atan- cmath/fast = (55.00, 55.01)
atan- cmath/fast = (56.00, 56.01)
atan- cmath/fast = (57.00, 57.01)
atan- cmath/fast = (58.00, 58.01)
atan- cmath/fast = (-58.00, -58.01)
atan- cmath/fast = (-57.00, -57.01)
atan- cmath/fast = (-56.00, -56.01)
atan- cmath/fast = (-55.00, -55.01)
atan- cmath/fast = (-54.00, -54.01)
atan- cmath/fast = (-53.00, -53.01)
atan- cmath/fast = (-49.00, -48.99)
atan- cmath/fast = (-48.00, -47.99)
atan- cmath/fast = (-47.00, -46.99)
atan- cmath/fast = (-45.00, -44.99)
atan- cmath/fast = (-43.00, -43.01)
atan- cmath/fast = (-42.00, -42.01)
atan- cmath/fast = (-41.00, -41.01)
atan- cmath/fast = (-37.00, -36.99)
atan- cmath/fast = (-36.00, -35.99)
atan- cmath/fast = (-35.00, -34.99)
atan- cmath/fast = (-34.00, -33.99)
atan- cmath/fast = (-33.00, -32.99)
atan- cmath/fast = (-32.00, -31.99)
atan- cmath/fast = (32.00, 31.99)
atan- cmath/fast = (33.00, 32.99)
atan- cmath/fast = (34.00, 33.99)
atan- cmath/fast = (35.00, 34.99)
atan- cmath/fast = (36.00, 35.99)
atan- cmath/fast = (37.00, 36.99)
atan- cmath/fast = (41.00, 41.01)
atan- cmath/fast = (42.00, 42.01)
atan- cmath/fast = (43.00, 43.01)
atan- cmath/fast = (45.00, 44.99)
atan- cmath/fast = (47.00, 46.99)
atan- cmath/fast = (48.00, 47.99)
atan- cmath/fast = (49.00, 48.99)
atan- cmath/fast = (53.00, 53.01)
atan- cmath/fast = (54.00, 54.01)
atan- cmath/fast = (55.00, 55.01)
atan- cmath/fast = (56.00, 56.01)
atan- cmath/fast = (57.00, 57.01)
atan- cmath/fast = (58.00, 58.01)
atan- cmath/fast = (-58.00, -58.01)
atan- cmath/fast = (-57.00, -57.01)
atan- cmath/fast = (-56.00, -56.01)
atan- cmath/fast = (-55.00, -55.01)
atan- cmath/fast = (-54.00, -54.01)
atan- cmath/fast = (-53.00, -53.01)
atan- cmath/fast = (-49.00, -48.99)
atan- cmath/fast = (-48.00, -47.99)
atan- cmath/fast = (-47.00, -46.99)
atan- cmath/fast = (-45.00, -44.99)
atan- cmath/fast = (-43.00, -43.01)
atan- cmath/fast = (-42.00, -42.01)
atan- cmath/fast = (-41.00, -41.01)
atan- cmath/fast = (-37.00, -36.99)
atan- cmath/fast = (-36.00, -35.99)
atan- cmath/fast = (-35.00, -34.99)
atan- cmath/fast = (-34.00, -33.99)
atan- cmath/fast = (-33.00, -32.99)
atan- cmath/fast = (-32.00, -31.99)
atan- cmath/fast = (32.00, 31.99)
atan- cmath/fast = (33.00, 32.99)
atan- cmath/fast = (34.00, 33.99)
atan- cmath/fast = (35.00, 34.99)
atan- cmath/fast = (36.00, 35.99)
atan- cmath/fast = (37.00, 36.99)
atan- cmath/fast = (41.00, 41.01)
atan- cmath/fast = (42.00, 42.01)
atan- cmath/fast = (43.00, 43.01)
atan- cmath/fast = (45.00, 44.99)
atan- cmath/fast = (47.00, 46.99)
atan- cmath/fast = (48.00, 47.99)
atan- cmath/fast = (49.00, 48.99)
atan- cmath/fast = (53.00, 53.01)
atan- cmath/fast = (54.00, 54.01)
atan- cmath/fast = (55.00, 55.01)
atan- cmath/fast = (56.00, 56.01)
atan- cmath/fast = (57.00, 57.01)
atan- cmath/fast = (58.00, 58.01)
atan- cmath/fast = (-58.00, -58.01)
atan- cmath/fast = (-57.00, -57.01)
atan- cmath/fast = (-56.00, -56.01)
atan- cmath/fast = (-55.00, -55.01)
atan- cmath/fast = (-54.00, -54.01)
atan- cmath/fast = (-53.00, -53.01)
atan- cmath/fast = (-49.00, -48.99)
atan- cmath/fast = (-48.00, -47.99)
atan- cmath/fast = (-47.00, -46.99)
atan- cmath/fast = (-45.00, -44.99)
atan- cmath/fast = (-43.00, -43.01)
atan- cmath/fast = (-42.00, -42.01)
atan- cmath/fast = (-41.00, -41.01)
atan- cmath/fast = (-37.00, -36.99)
atan- cmath/fast = (-36.00, -35.99)
atan- cmath/fast = (-35.00, -34.99)
atan- cmath/fast = (-34.00, -33.99)
atan- cmath/fast = (-33.00, -32.99)
atan- cmath/fast = (-32.00, -31.99)
atan- cmath/fast = (32.00, 31.99)
atan- cmath/fast = (33.00, 32.99)
atan- cmath/fast = (34.00, 33.99)
atan- cmath/fast = (35.00, 34.99)
atan- cmath/fast = (36.00, 35.99)
atan- cmath/fast = (37.00, 36.99)
atan- cmath/fast = (41.00, 41.01)
atan- cmath/fast = (42.00, 42.01)
atan- cmath/fast = (43.00, 43.01)
atan- cmath/fast = (45.00, 44.99)
atan- cmath/fast = (47.00, 46.99)
atan- cmath/fast = (48.00, 47.99)
atan- cmath/fast = (49.00, 48.99)
atan- cmath/fast = (53.00, 53.01)
atan- cmath/fast = (54.00, 54.01)
atan- cmath/fast = (55.00, 55.01)
atan- cmath/fast = (56.00, 56.01)
atan- cmath/fast = (57.00, 57.01)
atan- cmath/fast = (58.00, 58.01)
atan- cmath/fast = (-58.00, -58.01)
atan- cmath/fast = (-57.00, -57.01)
atan- cmath/fast = (-56.00, -56.01)
atan- cmath/fast = (-55.00, -55.01)
atan- cmath/fast = (-54.00, -54.01)
atan- cmath/fast = (-53.00, -53.01)
atan- cmath/fast = (-49.00, -48.99)
atan- cmath/fast = (-48.00, -47.99)
atan- cmath/fast = (-47.00, -46.99)
atan- cmath/fast = (-45.00, -45.01)
atan- cmath/fast = (-43.00, -43.01)
atan- cmath/fast = (-42.00, -42.01)
atan- cmath/fast = (-41.00, -41.01)
atan- cmath/fast = (-37.00, -36.99)
atan- cmath/fast = (-36.00, -35.99)
atan- cmath/fast = (-35.00, -34.99)
atan- cmath/fast = (-34.00, -33.99)
atan- cmath/fast = (-33.00, -32.99)
atan- cmath/fast = (-32.00, -31.99)
atan- cmath/fast = (32.00, 31.99)
atan- cmath/fast = (33.00, 32.99)
atan- cmath/fast = (34.00, 33.99)
atan- cmath/fast = (35.00, 34.99)
atan- cmath/fast = (36.00, 35.99)
atan- cmath/fast = (37.00, 36.99)
atan- cmath/fast = (41.00, 41.01)
atan- cmath/fast = (42.00, 42.01)
atan- cmath/fast = (43.00, 43.01)
atan- cmath/fast = (45.00, 44.99)
atan- cmath/fast = (47.00, 46.99)
atan- cmath/fast = (48.00, 47.99)
atan- cmath/fast = (49.00, 48.99)
atan- cmath/fast = (53.00, 53.01)
atan- cmath/fast = (54.00, 54.01)
atan- cmath/fast = (55.00, 55.01)
atan- cmath/fast = (56.00, 56.01)
atan- cmath/fast = (57.00, 57.01)
atan- cmath/fast = (58.00, 58.01)
atan- cmath/fast = (-58.00, -58.01)
atan- cmath/fast = (-57.00, -57.01)
atan- cmath/fast = (-56.00, -56.01)
atan- cmath/fast = (-55.00, -55.01)
atan- cmath/fast = (-54.00, -54.01)
atan- cmath/fast = (-53.00, -53.01)
atan- cmath/fast = (-49.00, -48.99)
atan- cmath/fast = (-48.00, -47.99)
atan- cmath/fast = (-47.00, -46.99)
atan- cmath/fast = (-45.00, -45.01)
atan- cmath/fast = (-43.00, -43.01)
atan- cmath/fast = (-42.00, -42.01)
atan- cmath/fast = (-41.00, -41.01)
atan- cmath/fast = (-37.00, -36.99)
atan- cmath/fast = (-36.00, -35.99)
atan- cmath/fast = (-35.00, -34.99)
atan- cmath/fast = (-34.00, -33.99)
atan- cmath/fast = (-33.00, -32.99)
atan- cmath/fast = (-32.00, -31.99)
atan- cmath/fast = (32.00, 31.99)
atan- cmath/fast = (33.00, 32.99)
atan- cmath/fast = (34.00, 33.99)
atan- cmath/fast = (35.00, 34.99)
atan- cmath/fast = (36.00, 35.99)
atan- cmath/fast = (37.00, 36.99)
atan- cmath/fast = (41.00, 41.01)
atan- cmath/fast = (42.00, 42.01)
atan- cmath/fast = (43.00, 43.01)
atan- cmath/fast = (45.00, 45.01)
atan- cmath/fast = (47.00, 46.99)
atan- cmath/fast = (48.00, 47.99)
atan- cmath/fast = (49.00, 48.99)
atan- cmath/fast = (53.00, 53.01)
atan- cmath/fast = (54.00, 54.01)
atan- cmath/fast = (55.00, 55.01)
atan- cmath/fast = (56.00, 56.01)
atan- cmath/fast = (57.00, 57.01)
atan- cmath/fast = (58.00, 58.01)
atan- cmath/fast = (-58.00, -58.01)
atan- cmath/fast = (-57.00, -57.01)
atan- cmath/fast = (-56.00, -56.01)
atan- cmath/fast = (-55.00, -55.01)
atan- cmath/fast = (-54.00, -54.01)
atan- cmath/fast = (-53.00, -53.01)
atan- cmath/fast = (-49.00, -48.99)
atan- cmath/fast = (-48.00, -47.99)
atan- cmath/fast = (-47.00, -46.99)
atan- cmath/fast = (-45.00, -44.99)
atan- cmath/fast = (-43.00, -43.01)
atan- cmath/fast = (-42.00, -42.01)
atan- cmath/fast = (-41.00, -41.01)
atan- cmath/fast = (-37.00, -36.99)
atan- cmath/fast = (-36.00, -35.99)
atan- cmath/fast = (-35.00, -34.99)
atan- cmath/fast = (-34.00, -33.99)
atan- cmath/fast = (-33.00, -32.99)
atan- cmath/fast = (-32.00, -31.99)
https://ideone.com/wYXmnA
快速 atan, atan2 算法
language:
C++14 (gcc 8.3)
created:
6 years ago
visibility:
public

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