Add other sin method

small3dlib.h

@@ -10,7 +10,7 @@
   license: CC0 1.0 (public domain)
            found at https://creativecommons.org/publicdomain/zero/1.0/
            + additional waiver of all IP
-  version: 0.901d
+  version: 0.902d
 
   Before including the library, define S3L_PIXEL_FUNCTION to the name of the
   function you'll be using to draw single pixels (this function will be called
@@ -83,16 +83,6 @@
   vertical size (y) depends on the aspect ratio (S3L_RESOLUTION_X and
   S3L_RESOLUTION_Y). Camera FOV is defined by focal length in S3L_Units.
 
-           y ^
-             |  _
-             |  /| z
-         ____|_/__
-        |    |/   |
-     -----[0,0,0]-|-----> x
-        |____|____|
-             |    
-             |
-
   Rotations use Euler angles and are generally in the extrinsic Euler angles in
   ZXY order (by Z, then by X, then by Y). Positive rotation about an axis
   rotates CW (clock-wise) when looking in the direction of the axis.
@@ -180,6 +170,14 @@
   #define S3L_USE_WIDER_TYPES 0
 #endif
 
+#ifndef S3L_SIN_METHOD
+  /** Says which method should be used for computing sin/cos functions, possible
+  values: 0 (lookup table, takes more program memory), 1 (Bhaskara's
+  approximation, slower). This may cause the trigonometric functions give
+  slightly different results. */
+  #define S3L_SIN_METHOD 0
+#endif
+
 /** Units of measurement in 3D space. There is S3L_FRACTIONS_PER_UNIT in one
 spatial unit. By dividing the unit into fractions we effectively achieve a
 fixed point arithmetic. The number of fractions is a constant that serves as
@@ -907,6 +905,7 @@ static inline int8_t S3L_stencilTest(
 
 #define S3L_SIN_TABLE_LENGTH 128
 
+#if S3L_SIN_METHOD == 0
 static const S3L_Unit S3L_sinTable[S3L_SIN_TABLE_LENGTH] =
 {
   /* 511 was chosen here as a highest number that doesn't overflow during
@@ -977,6 +976,7 @@ static const S3L_Unit S3L_sinTable[S3L_SIN_TABLE_LENGTH] =
   (510*S3L_FRACTIONS_PER_UNIT)/511, (510*S3L_FRACTIONS_PER_UNIT)/511, 
   (510*S3L_FRACTIONS_PER_UNIT)/511, (510*S3L_FRACTIONS_PER_UNIT)/511
 };
+#endif
 
 #define S3L_SIN_TABLE_UNIT_STEP\
   (S3L_FRACTIONS_PER_UNIT / (S3L_SIN_TABLE_LENGTH * 4))
@@ -1349,6 +1349,7 @@ void S3L_mat4Xmat4(S3L_Mat4 m1, S3L_Mat4 m2)
 
 S3L_Unit S3L_sin(S3L_Unit x)
 {
+#if S3L_SIN_METHOD == 0
   x = S3L_wrap(x / S3L_SIN_TABLE_UNIT_STEP,S3L_SIN_TABLE_LENGTH * 4);
   int8_t positive = 1;
 
@@ -1371,10 +1372,37 @@ S3L_Unit S3L_sin(S3L_Unit x)
   }
 
   return positive ? S3L_sinTable[x] : -1 * S3L_sinTable[x];
+#else
+  int8_t sign = 1;
+    
+  if (x < 0) // odd function
+  {
+    x *= -1;
+    sign = -1;
+  }
+    
+  x %= S3L_FRACTIONS_PER_UNIT;
+  
+  if (x > S3L_FRACTIONS_PER_UNIT / 2)
+  {
+    x -= S3L_FRACTIONS_PER_UNIT / 2;
+    sign *= -1;
+  }
+
+  S3L_Unit tmp = S3L_FRACTIONS_PER_UNIT - 2 * x;
+ 
+  #define _PI2 ((S3L_Unit) (9.8696044 * S3L_FRACTIONS_PER_UNIT))
+  return sign * // Bhaskara's approximation
+    (((32 * x * _PI2) / S3L_FRACTIONS_PER_UNIT) * tmp) / 
+    ((_PI2 * (5 * S3L_FRACTIONS_PER_UNIT - (8 * x * tmp) / 
+      S3L_FRACTIONS_PER_UNIT)) / S3L_FRACTIONS_PER_UNIT);
+  #undef _PI2
+#endif
 }
 
 S3L_Unit S3L_asin(S3L_Unit x)
 {
+#if S3L_SIN_METHOD == 0
   x = S3L_clamp(x,-S3L_FRACTIONS_PER_UNIT,S3L_FRACTIONS_PER_UNIT);
 
   int8_t sign = 1;
@@ -1385,9 +1413,7 @@ S3L_Unit S3L_asin(S3L_Unit x)
     x *= -1;
   }
 
-  int16_t low = 0;
+  int16_t low = 0, high = S3L_SIN_TABLE_LENGTH -1, middle;
-  int16_t high = S3L_SIN_TABLE_LENGTH -1;
-  int16_t middle;
 
   while (low <= high) // binary search
   {
@@ -1406,6 +1432,27 @@ S3L_Unit S3L_asin(S3L_Unit x)
   middle *= S3L_SIN_TABLE_UNIT_STEP;
 
   return sign * middle;
+#else
+  S3L_Unit low = -1 * S3L_FRACTIONS_PER_UNIT / 4,
+           high = S3L_FRACTIONS_PER_UNIT / 4,
+           middle;
+    
+  while (low <= high) // binary search
+  {
+    middle = (low + high) / 2;
+
+    S3L_Unit v = S3L_sin(middle);
+
+    if (v > x)
+      high = middle - 1;
+    else if (v < x)
+      low = middle + 1;
+    else
+      break;
+  }
+
+  return middle;
+#endif
 }
 
 S3L_Unit S3L_cos(S3L_Unit x)
@@ -2244,7 +2291,6 @@ void S3L_drawTriangle(
 #endif
 
       // draw the row -- inner loop:
-
       for (S3L_ScreenCoord x = lXClipped; x < rXClipped; ++x)
       {
         int8_t testsPassed = 1;
@@ -2404,7 +2450,6 @@ if (_S3L_projectedTriangleState != 0)
   p.barycentric[2] = newBarycentric[2];
 }
 #endif
-
           S3L_PIXEL_FUNCTION(&p);
         } // tests passed