ref: d7383b7b86bf9d8e37d73d2ac1a7fec54d8f746e
parent: 768590a99d36e87dd00df30435f274a4567f6ce3
author: Alexei Podtelezhnikov <[email protected]>
date: Wed Dec 19 20:03:22 EST 2012
[base] Improve trigonometric core. FreeType used to rely on a 24-step iteration CORDIC algorithm to calculate trigonometric functions and rotate vectors. It turns out that once the vector is in the right half-plane, the initial rotation by 63 degrees is not necessary. The algorithm is perfectly capable to converge to any angle starting from the second 45 degree rotation. This patch removes the first rotation and makes it a 23-step CORDIC algorithm. * src/base/fttrigon.c (FT_TRIG_SCALE, FT_TRIG_COSCALE): Update macro values. (ft_trig_pseudo_rotate, ft_trig_pseudo_polarize): Remove initial rotation.
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,20 @@
+2012-12-20 Alexei Podtelezhnikov <[email protected]>
+
+ [base] Improve trigonometric core.
+
+ FreeType used to rely on a 24-step iteration CORDIC algorithm to
+ calculate trigonometric functions and rotate vectors. It turns out
+ that once the vector is in the right half-plane, the initial rotation
+ by 63 degrees is not necessary. The algorithm is perfectly capable
+ to converge to any angle starting from the second 45 degree rotation.
+ This patch removes the first rotation and makes it a 23-step CORDIC
+ algorithm.
+
+ * src/base/fttrigon.c (FT_TRIG_SCALE, FT_TRIG_COSCALE): Update macro
+ values.
+ (ft_trig_pseudo_rotate, ft_trig_pseudo_polarize): Remove initial
+ rotation.
+
2012-12-19 Werner Lemberg <[email protected]>
* src/base/ftobjs.c (ft_property_do): Fix compiler warning.
--- a/src/base/fttrigon.c
+++ b/src/base/fttrigon.c
@@ -26,24 +26,24 @@
#endif
- /* the following is 0.2715717684432231 * 2^30 */
-#define FT_TRIG_COSCALE 0x11616E8EUL
+ /* the Cordic shrink factor 0.607252935008887 * 2^32 */
+#define FT_TRIG_SCALE 0x9B74EDA8UL
+ /* the following is 0.607252935008887 * 2^30 */
+#define FT_TRIG_COSCALE 0x26DD3B6AUL
+
/* this table was generated for FT_PI = 180L << 16, i.e. degrees */
#define FT_TRIG_MAX_ITERS 23
static const FT_Fixed
- ft_trig_arctan_table[24] =
+ ft_trig_arctan_table[23] =
{- 4157273L, 2949120L, 1740967L, 919879L, 466945L, 234379L, 117304L,
- 58666L, 29335L, 14668L, 7334L, 3667L, 1833L, 917L, 458L, 229L, 115L,
+ 2949120L, 1740967L, 919879L, 466945L, 234379L, 117304L, 58666L,
+ 29335L, 14668L, 7334L, 3667L, 1833L, 917L, 458L, 229L, 115L,
57L, 29L, 14L, 7L, 4L, 2L, 1L
};
- /* the Cordic shrink factor, multiplied by 2^32 */
-#define FT_TRIG_SCALE 1166391864UL /* 0x4585BA38UL */
-
#ifdef FT_LONG64
/* multiply a given value by the CORDIC shrink factor */
@@ -214,25 +214,9 @@
theta -= FT_ANGLE_PI;
}
- /* Initial pseudorotation, with left shift */
arctanptr = ft_trig_arctan_table;
- if ( theta < 0 )
- {- xtemp = x + ( y << 1 );
- y = y - ( x << 1 );
- x = xtemp;
- theta += *arctanptr++;
- }
- else
- {- xtemp = x - ( y << 1 );
- y = y + ( x << 1 );
- x = xtemp;
- theta -= *arctanptr++;
- }
-
- /* Subsequent pseudorotations, with right shifts */
+ /* Pseudorotations, with right shifts */
i = 0;
do
{@@ -283,22 +267,7 @@
arctanptr = ft_trig_arctan_table;
- if ( y > 0 )
- {- xtemp = x + ( y << 1 );
- y = y - ( x << 1 );
- x = xtemp;
- theta += *arctanptr++;
- }
- else
- {- xtemp = x - ( y << 1 );
- y = y + ( x << 1 );
- x = xtemp;
- theta -= *arctanptr++;
- }
-
- /* Subsequent pseudorotations, with right shifts */
+ /* Pseudorotations, with right shifts */
i = 0;
do
{