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[base] Small optimization of BBox calculation.

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* src/base/ftbbox.c (BBox_Cubic_Check): Use FT_MSB function in
scaling algorithm.
This commit is contained in:
Alexei Podtelezhnikov 2013-01-28 06:35:19 -05:00
parent c574d72ca8
commit ab02d9e8e7
2 changed files with 38 additions and 81 deletions
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7
ChangeLog
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@ -1,3 +1,10 @@
2013-01-28 Alexei Podtelezhnikov <apodtele@gmail.com>
[base] Small optimization of BBox calculation.
* src/base/ftbbox.c (BBox_Cubic_Check): Use FT_MSB function in
scaling algorithm.
2013-01-26 Infinality <infinality@infinality.net>
[truetype] Minor formatting fix.

112
src/base/ftbbox.c
View File

@ -358,13 +358,15 @@
return;
}
/* There are some split points. Find them. */
/* There are some split points. Find them. */
/* We already made sure that a, b, and c below cannot be all zero. */
{
FT_Pos a = y4 - 3*y3 + 3*y2 - y1;
FT_Pos b = y3 - 2*y2 + y1;
FT_Pos c = y2 - y1;
FT_Pos d;
FT_Fixed t;
FT_Int shift;
/* We need to solve `ax^2+2bx+c' here, without floating points! */
@ -375,90 +377,38 @@
/* These values must fit into a single 16.16 value. */
/* */
/* We normalize a, b, and c to `8.16' fixed-point values to ensure */
/* that its product is held in a `16.16' value. */
/* that its product is held in a `16.16' value. Necessarily, */
/* we need to shift `a', `b', and `c' so that the most significant */
/* bit of their absolute values is at _most_ at position 23. */
/* */
/* This also means that we are using 24 bits of precision to compute */
/* the zeros, independently of the range of the original polynomial */
/* coefficients. */
/* */
/* This algorithm should ensure reasonably accurate values for the */
/* zeros. Note that they are only expressed with 16 bits when */
/* computing the extrema (the zeros need to be in 0..1 exclusive */
/* to be considered part of the arc). */
shift = FT_MSB( FT_ABS( a ) | FT_ABS( b ) | FT_ABS( c ) );
if ( shift > 23 )
{
FT_ULong t1, t2;
int shift = 0;
shift -= 23;
/* this loses some bits of precision, but we use 24 of them */
/* for the computation anyway */
a >>= shift;
b >>= shift;
c >>= shift;
}
else
{
shift = 23 - shift;
/* The following computation is based on the fact that for */
/* any value `y', if `n' is the position of the most */
/* significant bit of `abs(y)' (starting from 0 for the */
/* least significant bit), then `y' is in the range */
/* */
/* -2^n..2^n-1 */
/* */
/* We want to shift `a', `b', and `c' concurrently in order */
/* to ensure that they all fit in 8.16 values, which maps */
/* to the integer range `-2^23..2^23-1'. */
/* */
/* Necessarily, we need to shift `a', `b', and `c' so that */
/* the most significant bit of its absolute values is at */
/* _most_ at position 23. */
/* */
/* We begin by computing `t1' as the bitwise `OR' of the */
/* absolute values of `a', `b', `c'. */
t1 = (FT_ULong)FT_ABS( a );
t2 = (FT_ULong)FT_ABS( b );
t1 |= t2;
t2 = (FT_ULong)FT_ABS( c );
t1 |= t2;
/* Now we can be sure that the most significant bit of `t1' */
/* is the most significant bit of either `a', `b', or `c', */
/* depending on the greatest integer range of the particular */
/* variable. */
/* */
/* Next, we compute the `shift', by shifting `t1' as many */
/* times as necessary to move its MSB to position 23. This */
/* corresponds to a value of `t1' that is in the range */
/* 0x40_0000..0x7F_FFFF. */
/* */
/* Finally, we shift `a', `b', and `c' by the same amount. */
/* This ensures that all values are now in the range */
/* -2^23..2^23, i.e., they are now expressed as 8.16 */
/* fixed-float numbers. This also means that we are using */
/* 24 bits of precision to compute the zeros, independently */
/* of the range of the original polynomial coefficients. */
/* */
/* This algorithm should ensure reasonably accurate values */
/* for the zeros. Note that they are only expressed with */
/* 16 bits when computing the extrema (the zeros need to */
/* be in 0..1 exclusive to be considered part of the arc). */
if ( t1 == 0 ) /* all coefficients are 0! */
return;
if ( t1 > 0x7FFFFFUL )
{
do
{
shift++;
t1 >>= 1;
} while ( t1 > 0x7FFFFFUL );
/* this loses some bits of precision, but we use 24 of them */
/* for the computation anyway */
a >>= shift;
b >>= shift;
c >>= shift;
}
else if ( t1 < 0x400000UL )
{
do
{
shift++;
t1 <<= 1;
} while ( t1 < 0x400000UL );
a <<= shift;
b <<= shift;
c <<= shift;
}
a <<= shift;
b <<= shift;
c <<= shift;
}
/* handle a == 0 */