[base] Reduce trigonometric algorithms.
After we get within 45 degrees by means of true 90-degree rotations, we can remove initial 45-degree CORDIC iteration and start from atan(1/2) pseudorotation, reducing expansion factor thereby. * src/base/fttrigon.c (FT_TRIG_SCALE, FT_TRIG_COSCALE): Update macros. (ft_trig_pseudo_rotate, ft_trig_pseudo_polarize): Update. * src/tools/cordic.py: Bring up to date with trigonometric core. * docs/CHANGES: Old typo.
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Alexei Podtelezhnikov
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ChangeLog
17
ChangeLog
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@ -1,4 +1,19 @@
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2012-12-21 Alexei Podtelezhnikov <apodtele@gmail.com>
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2013-01-02 Alexei Podtelezhnikov <apodtele@gmail.com>
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[base] Reduce trigonometric algorithms.
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After we get within 45 degrees by means of true 90-degree rotations,
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we can remove initial 45-degree CORDIC iteration and start from
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atan(1/2) pseudorotation, reducing expansion factor thereby.
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* src/base/fttrigon.c (FT_TRIG_SCALE, FT_TRIG_COSCALE): Update macros.
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(ft_trig_pseudo_rotate, ft_trig_pseudo_polarize): Update.
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* src/tools/cordic.py: Bring up to date with trigonometric core.
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* docs/CHANGES: Old typo.
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2013-01-02 Alexei Podtelezhnikov <apodtele@gmail.com>
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* src/pshinter/pshalgo.h: Remove unused code.
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@ -2486,7 +2486,7 @@ CHANGES BETWEEN 2.0.3 and 2.0.2
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number. see <freetype/fterrors.h> for details.
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- A new public header file has been introduced, named
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FT_TRIGONOMETRY_H (include/freetype/fttrig.h), providing
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FT_TRIGONOMETRY_H (include/freetype/fttrigon.h), providing
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trigonometric functions to compute sines, cosines, arctangents,
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etc. with 16.16 fixed precision. The implementation is based on
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the CORDIC algorithm and is very fast while being sufficiently
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@ -4,7 +4,7 @@
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/* */
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/* FreeType trigonometric functions (body). */
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/* */
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/* Copyright 2001-2005, 2012 by */
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/* Copyright 2001-2005, 2012, 2013 by */
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/* David Turner, Robert Wilhelm, and Werner Lemberg. */
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/* */
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/* This file is part of the FreeType project, and may only be used, */
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@ -26,20 +26,20 @@
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#endif
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/* the Cordic shrink factor 0.607252935008887 * 2^32 */
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#define FT_TRIG_SCALE 0x9B74EDA8UL
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/* the Cordic shrink factor 0.858785336480436 * 2^32 */
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#define FT_TRIG_SCALE 0xDBD95B16UL
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/* the following is 0.607252935008887 * 2^30 */
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#define FT_TRIG_COSCALE 0x26DD3B6AUL
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/* the following is 0.858785336480436 * 2^30 */
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#define FT_TRIG_COSCALE 0x36F656C6UL
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/* this table was generated for FT_PI = 180L << 16, i.e. degrees */
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#define FT_TRIG_MAX_ITERS 23
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static const FT_Fixed
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ft_trig_arctan_table[23] =
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ft_trig_arctan_table[] =
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{
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2949120L, 1740967L, 919879L, 466945L, 234379L, 117304L, 58666L,
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29335L, 14668L, 7334L, 3667L, 1833L, 917L, 458L, 229L, 115L,
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1740967L, 919879L, 466945L, 234379L, 117304L, 58666L, 29335L,
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14668L, 7334L, 3667L, 1833L, 917L, 458L, 229L, 115L,
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57L, 29L, 14L, 7L, 4L, 2L, 1L
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};
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@ -199,25 +199,27 @@
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x = vec->x;
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y = vec->y;
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/* Get angle between -90 and 90 degrees */
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while ( theta <= -FT_ANGLE_PI2 )
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/* Rotate inside [-PI/4,PI/4] sector */
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while ( theta < -FT_ANGLE_PI4 )
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{
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x = -x;
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y = -y;
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theta += FT_ANGLE_PI;
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xtemp = y;
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y = -x;
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x = xtemp;
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theta += FT_ANGLE_PI2;
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}
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while ( theta > FT_ANGLE_PI2 )
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while ( theta > FT_ANGLE_PI4 )
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{
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x = -x;
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y = -y;
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theta -= FT_ANGLE_PI;
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xtemp = -y;
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y = x;
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x = xtemp;
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theta -= FT_ANGLE_PI2;
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}
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arctanptr = ft_trig_arctan_table;
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/* Pseudorotations, with right shifts */
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i = 0;
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i = 1;
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do
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{
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if ( theta < 0 )
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@ -253,22 +255,42 @@
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x = vec->x;
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y = vec->y;
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/* Get the vector into the right half plane */
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theta = 0;
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if ( x < 0 )
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/* Get the vector into [-PI/4,PI/4] sector */
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if ( y > x )
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{
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x = -x;
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y = -y;
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theta = 2 * FT_ANGLE_PI2;
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if ( y > -x )
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{
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theta = FT_ANGLE_PI2;
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xtemp = y;
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y = -x;
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x = xtemp;
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}
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else
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{
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theta = y > 0 ? FT_ANGLE_PI : -FT_ANGLE_PI;
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x = -x;
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y = -y;
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}
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}
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else
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{
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if ( y < -x )
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{
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theta = -FT_ANGLE_PI2;
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xtemp = -y;
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y = x;
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x = xtemp;
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}
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else
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{
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theta = 0;
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}
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}
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if ( y > 0 )
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theta = - theta;
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arctanptr = ft_trig_arctan_table;
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/* Pseudorotations, with right shifts */
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i = 0;
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i = 1;
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do
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{
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if ( y > 0 )
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@ -10,7 +10,7 @@ comma = ""
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print ""
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print "table of arctan( 1/2^n ) for PI = " + repr(units/65536.0) + " units"
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for n in range(0,32):
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for n in range(1,32):
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x = 0.5**n # tangent value
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