Ticket #2109: Atan2.patch

source/maths/Fixed.cpp

@@ +1 @@
+
 /* Copyright (C) 2010 Wildfire Games.
  * This file is part of 0 A.D.
  *
@@ -143 +144 @@
     return r.str();
 }
 
-// Based on http://www.dspguru.com/dsp/tricks/fixed-point-atan2-with-self-normalization
+//angles: 45, 26.565, 14.036, 7.125, 3.576, 1.790, 0.895, 0.448
+static const CFixed_15_16 tan_angle_table_rad[8] = {CFixed_15_16(51472), CFixed_15_16(30386), CFixed_15_16(16055), CFixed_15_16(8150), CFixed_15_16(4091), CFixed_15_16(2047), CFixed_15_16(1042), CFixed_15_16(512) };
+//angles 90 and 180
+static const CFixed_15_16 angle_0_5_pi = CFixed_15_16(102944);
+static const CFixed_15_16 angle_1_0_pi = CFixed_15_16(205887);
+static const CFixed_15_16 zero = CFixed_15_16();
+
 CFixed_15_16 atan2_approx(CFixed_15_16 y, CFixed_15_16 x)
 {
-    CFixed_15_16 zero;
+    CFixed_15_16 angle;
+    i32 loop_var;
+    i32 previous_x_val;
+    i32 new_x_val;
 
-    // Special case to avoid division-by-zero
-    if (x.IsZero() && y.IsZero())
-        return zero;
+    //quadrant 2
+    if(x < zero && y > zero)
+    {
+        angle += angle_0_5_pi;
+        x.SetInternalValue(x.GetInternalValue()* -1);
+    }
 
-    CFixed_15_16 c1;
-    c1.SetInternalValue(51472); // pi/4 << 16
+    //quadrant 4
+    else if(x > zero && y < zero)
+    {
+        angle -= angle_0_5_pi;
+        y.SetInternalValue(y.GetInternalValue()* -1);
+    }
 
-    CFixed_15_16 c2;
-    c2.SetInternalValue(154415); // 3*pi/4 << 16
+    //quadrant 3
+    else if(x < zero && y < zero)
+    {
+        angle -= angle_1_0_pi;
+        x.SetInternalValue(x.GetInternalValue()* -1);
+        y.SetInternalValue(y.GetInternalValue()* -1);
+    }
 
-    CFixed_15_16 abs_y = y.Absolute();
+    for(loop_var = 0; loop_var < 5; ++loop_var)
+    {
+        i32 factor;
+        //these divisions should be optimised by the compiler to shifts because the operations are always division by a power of two
+        //this makes the cost of each division 1 cycle.
+        if( y.GetInternalValue() < 0 )
+        {
+            factor = (1 << loop_var);
+            previous_x_val = x.GetInternalValue();
+            x -= (y/factor);
+            new_x_val = x.GetInternalValue();
+            x.SetInternalValue(previous_x_val);
+            y += (x/factor);
+            x.SetInternalValue(new_x_val);
 
-    CFixed_15_16 angle;
-    if (x >= zero)
-    {
-        CFixed_15_16 r = (x - abs_y) / (x + abs_y);
-        angle = c1 - c1.Multiply(r);
-    }
-    else
-    {
-        CFixed_15_16 r = (x + abs_y) / (abs_y - x);
-        angle = c2 - c1.Multiply(r);
-    }
+            angle -= tan_angle_table_rad[loop_var];
+        }
+        else
+        {
+            factor = (1 << loop_var);
+            previous_x_val = x.GetInternalValue();
+            x += (y/factor);
+            new_x_val = x.GetInternalValue();
+            x.SetInternalValue(previous_x_val);
+            y -= (x/factor);
+            x.SetInternalValue(new_x_val);
 
-    if (y < zero)
-        return -angle;
-    else
-        return angle;
+            angle += tan_angle_table_rad[loop_var];
+        }
+    }
+
+    return angle;
 }
 
 template<>

source/maths/Fixed.h

@@ +1 @@
+
 /* Copyright (C) 2010 Wildfire Games.
  * This file is part of 0 A.D.
  *
@@ -109 +110 @@
 private:
     T value;
 
-    explicit CFixed(T v) : value(v) { }
 
 public:
     enum { fract_bits = fract_bits_ };
 
     CFixed() : value(0) { }
+    explicit CFixed(T v) : value(v) { }
 
     static CFixed Zero() { return CFixed(0); }
     static CFixed Epsilon() { return CFixed(1); }
@@ -348 +349 @@
 
 /**
  * Inaccurate approximation of atan2 over fixed-point numbers.
- * Maximum error is almost 0.08 radians (4.5 degrees).
+ * Maximum error is dependent on the number of iterations for 5 iterations the maximum error is about 0.062rad (3.57deg).
  */
 CFixed_15_16 atan2_approx(CFixed_15_16 y, CFixed_15_16 x);