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[base] CORDIC improvements.

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The scaling between the hypotenuse and its CORDIC approximation is
based on regression analysis. The smaller padding for `theta' is
justifed by its maximum error of less than 6.

* src/base/fttrigon.c (ft_trig_downscale): Borrow code from
./ftcalc.c (ft_multo64), change linear intercept.
(ft_trig_pseudo_polarize): Decrease `theta' padding.
This commit is contained in:
Alexei Podtelezhnikov 2014-11-09 23:22:43 -05:00
parent c3e9f02605
commit 2e73a1b4fd
2 changed files with 56 additions and 26 deletions
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12
ChangeLog
View File

@ -1,3 +1,15 @@
2014-11-10 Alexei Podtelezhnikov <apodtele@gmail.com>
[base] CORDIC improvements.
The scaling between the hypotenuse and its CORDIC approximation is
based on regression analysis. The smaller padding for `theta' is
justifed by its maximum error of less than 6.
* src/base/fttrigon.c (ft_trig_downscale): Borrow code from
./ftcalc.c (ft_multo64), change linear intercept.
(ft_trig_pseudo_polarize): Decrease `theta' padding.
2014-11-09 Werner Lemberg <wl@gnu.org>
* src/base/ftstroke.c (ft_stroker_inside): Fix border intersections.

70
src/base/fttrigon.c
View File

@ -60,15 +60,18 @@
static FT_Fixed
ft_trig_downscale( FT_Fixed val )
{
FT_Fixed s;
FT_Int64 v;
FT_Int s = 1;
s = val;
val = FT_ABS( val );
if ( val < 0 )
{
val = -val;
s = -1;
}
v = ( val * (FT_Int64)FT_TRIG_SCALE ) + 0x100000000UL;
val = (FT_Fixed)( v >> 32 );
/* 0x40000000 comes from regression analysis between true */
/* and CORDIC hypotenuse, so it minimizes the error */
val = (FT_Fixed)( ( (FT_Int64)val * FT_TRIG_SCALE + 0x40000000UL ) >> 32 );
return ( s >= 0 ) ? val : -val;
}
@ -79,29 +82,43 @@
static FT_Fixed
ft_trig_downscale( FT_Fixed val )
{
FT_Fixed s;
FT_UInt32 v1, v2, k1, k2, hi, lo1, lo2, lo3;
FT_Int s = 1;
FT_UInt32 lo1, hi1, lo2, hi2, lo, hi, i1, i2;
s = val;
val = FT_ABS( val );
if ( val < 0 )
{
val = -val;
s = -1;
}
v1 = (FT_UInt32)val >> 16;
v2 = (FT_UInt32)( val & 0xFFFFL );
lo1 = val & 0x0000FFFFU;
hi1 = val >> 16;
lo2 = FT_TRIG_SCALE & 0x0000FFFFU;
hi2 = FT_TRIG_SCALE >> 16;
k1 = (FT_UInt32)FT_TRIG_SCALE >> 16; /* constant */
k2 = (FT_UInt32)( FT_TRIG_SCALE & 0xFFFFL ); /* constant */
lo = lo1 * lo2;
i1 = lo1 * hi2;
i2 = lo2 * hi1;
hi = hi1 * hi2;
hi = k1 * v1;
lo1 = k1 * v2 + k2 * v1; /* can't overflow */
/* Check carry overflow of i1 + i2 */
i1 += i2;
hi += (FT_UInt32)( i1 < i2 ) << 16;
lo2 = ( k2 * v2 ) >> 16;
lo3 = FT_MAX( lo1, lo2 );
lo1 += lo2;
hi += i1 >> 16;
i1 = i1 << 16;
hi += lo1 >> 16;
if ( lo1 < lo3 )
hi += (FT_UInt32)0x10000UL;
/* Check carry overflow of i1 + lo */
lo += i1;
hi += ( lo < i1 );
/* 0x40000000 comes from regression analysis between true */
/* and CORDIC hypotenuse, so it minimizes the error */
/* Check carry overflow of lo + 0x40000000 */
lo += 0x40000000U;
hi += ( lo < 0x40000000U );
val = (FT_Fixed)hi;
@ -111,7 +128,7 @@
#endif /* !FT_LONG64 */
/* undefined and never called for zero vector */
/* undefined and never called for zero vector */
static FT_Int
ft_trig_prenorm( FT_Vector* vec )
{
@ -262,11 +279,12 @@
}
}
/* round theta */
/* round theta to acknowledge its error that mostly comes */
/* from accumulated rounding errors in the arctan table */
if ( theta >= 0 )
theta = FT_PAD_ROUND( theta, 32 );
theta = FT_PAD_ROUND( theta, 16 );
else
theta = -FT_PAD_ROUND( -theta, 32 );
theta = -FT_PAD_ROUND( -theta, 16 );
vec->x = x;
vec->y = theta;