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Code Issues 9 Releases Wiki Activity

[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.
This commit is contained in:
Alexei Podtelezhnikov 2013-01-02 22:21:37 -05:00
parent 50e634abe1
commit b4ac30b0ed
4 changed files with 68 additions and 31 deletions
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17
ChangeLog
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@ -1,4 +1,19 @@
2012-12-21 Alexei Podtelezhnikov <apodtele@gmail.com>
2013-01-02 Alexei Podtelezhnikov <apodtele@gmail.com>
[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.
2013-01-02 Alexei Podtelezhnikov <apodtele@gmail.com>
* src/pshinter/pshalgo.h: Remove unused code.

2
docs/CHANGES
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@ -2486,7 +2486,7 @@ CHANGES BETWEEN 2.0.3 and 2.0.2
number. see <freetype/fterrors.h> for details.
- A new public header file has been introduced, named
FT_TRIGONOMETRY_H (include/freetype/fttrig.h), providing
FT_TRIGONOMETRY_H (include/freetype/fttrigon.h), providing
trigonometric functions to compute sines, cosines, arctangents,
etc. with 16.16 fixed precision. The implementation is based on
the CORDIC algorithm and is very fast while being sufficiently

78
src/base/fttrigon.c
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@ -4,7 +4,7 @@
/* */
/* FreeType trigonometric functions (body). */
/* */
/* Copyright 2001-2005, 2012 by */
/* Copyright 2001-2005, 2012, 2013 by */
/* David Turner, Robert Wilhelm, and Werner Lemberg. */
/* */
/* This file is part of the FreeType project, and may only be used, */
@ -26,20 +26,20 @@
#endif
/* the Cordic shrink factor 0.607252935008887 * 2^32 */
#define FT_TRIG_SCALE 0x9B74EDA8UL
/* the Cordic shrink factor 0.858785336480436 * 2^32 */
#define FT_TRIG_SCALE 0xDBD95B16UL
/* the following is 0.607252935008887 * 2^30 */
#define FT_TRIG_COSCALE 0x26DD3B6AUL
/* the following is 0.858785336480436 * 2^30 */
#define FT_TRIG_COSCALE 0x36F656C6UL
/* 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[23] =
ft_trig_arctan_table[] =
{
2949120L, 1740967L, 919879L, 466945L, 234379L, 117304L, 58666L,
29335L, 14668L, 7334L, 3667L, 1833L, 917L, 458L, 229L, 115L,
1740967L, 919879L, 466945L, 234379L, 117304L, 58666L, 29335L,
14668L, 7334L, 3667L, 1833L, 917L, 458L, 229L, 115L,
57L, 29L, 14L, 7L, 4L, 2L, 1L
};
@ -199,25 +199,27 @@
x = vec->x;
y = vec->y;
/* Get angle between -90 and 90 degrees */
while ( theta <= -FT_ANGLE_PI2 )
/* Rotate inside [-PI/4,PI/4] sector */
while ( theta < -FT_ANGLE_PI4 )
{
x = -x;
y = -y;
theta += FT_ANGLE_PI;
xtemp = y;
y = -x;
x = xtemp;
theta += FT_ANGLE_PI2;
}
while ( theta > FT_ANGLE_PI2 )
while ( theta > FT_ANGLE_PI4 )
{
x = -x;
y = -y;
theta -= FT_ANGLE_PI;
xtemp = -y;
y = x;
x = xtemp;
theta -= FT_ANGLE_PI2;
}
arctanptr = ft_trig_arctan_table;
/* Pseudorotations, with right shifts */
i = 0;
i = 1;
do
{
if ( theta < 0 )
@ -253,22 +255,42 @@
x = vec->x;
y = vec->y;
/* Get the vector into the right half plane */
theta = 0;
if ( x < 0 )
/* Get the vector into [-PI/4,PI/4] sector */
if ( y > x )
{
x = -x;
y = -y;
theta = 2 * FT_ANGLE_PI2;
if ( y > -x )
{
theta = FT_ANGLE_PI2;
xtemp = y;
y = -x;
x = xtemp;
}
else
{
theta = y > 0 ? FT_ANGLE_PI : -FT_ANGLE_PI;
x = -x;
y = -y;
}
}
else
{
if ( y < -x )
{
theta = -FT_ANGLE_PI2;
xtemp = -y;
y = x;
x = xtemp;
}
else
{
theta = 0;
}
}
if ( y > 0 )
theta = - theta;
arctanptr = ft_trig_arctan_table;
/* Pseudorotations, with right shifts */
i = 0;
i = 1;
do
{
if ( y > 0 )

2
src/tools/cordic.py
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@ -10,7 +10,7 @@ comma = ""
print ""
print "table of arctan( 1/2^n ) for PI = " + repr(units/65536.0) + " units"
for n in range(0,32):
for n in range(1,32):
x = 0.5**n # tangent value