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[base] Use unsigned calculation in `FT_MulDiv'.

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* src/base/ftcalc.c (FT_MulDiv): Updated to expand 32-bit range.
This commit is contained in:
Alexei Podtelezhnikov 2014-08-20 00:08:38 -04:00
parent 382f3155f6
commit f09326a1a6
2 changed files with 26 additions and 15 deletions
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6
ChangeLog
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@ -1,3 +1,9 @@
2014-08-19 Alexei Podtelezhnikov <apodtele@gmail.com>
[base] Use unsigned calculation in `FT_MulDiv'.
* src/base/ftcalc.c (FT_MulDiv): Updated to expand 32-bit range.
2014-08-18 Alexei Podtelezhnikov <apodtele@gmail.com>
[base] Remove truncation in `FT_DivFix'.

35
src/base/ftcalc.c
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@ -358,11 +358,9 @@
}
/* documentation is in freetype.h */
/* The FT_MulDiv function has been optimized thanks to ideas from */
/* Graham Asher and Alexei Podtelezhnikov. The trick is to optimize */
/* a rather common case when everything fits within 32-bits. */
/* The FT_MulDiv function has been optimized thanks to ideas from */
/* Graham Asher and Alexei Podtelezhnikov. The trick is to optimize */
/* a rather common case when everything fits within 32-bits. */
/* */
/* We compute 'a*b+c/2', then divide it by 'c'. (positive values) */
/* */
@ -371,17 +369,24 @@
/* */
/* ( a + b ) / 2 <= sqrt( X - c/2 ) */
/* */
/* where X = 2^31 - 1. Now we replace sqrt with a linear function */
/* that is smaller or equal in the entire range of c from 0 to X; */
/* it should be equal to sqrt(X) and sqrt(X/2) at the range termini. */
/* where X = 2^32 - 1, the maximun unsigned 32-bit value, and using */
/* unsigned arithmetic. Now we replace sqrt with a linear function */
/* that is smaller or equal in the entire range of c from 0 to X/2; */
/* it should be equal to sqrt(X) and sqrt(3X/4) at the termini. */
/* Substituting the linear solution and explicit numbers we get */
/* */
/* a + b <= 92681.9 - c / 79108.95 */
/* a + b <= 131071.99 - c / 122291.84 */
/* */
/* In practice we use a faster and even stronger inequality */
/* In practice we should use a faster and even stronger inequality */
/* */
/* a + b <= 92681 - (c >> 16) */
/* a + b <= 131071 - (c >> 16) */
/* */
/* or, alternatively, */
/* */
/* a + b <= 129895 - (c >> 17) */
/* */
/* documentation is in freetype.h */
FT_EXPORT_DEF( FT_Long )
FT_MulDiv( FT_Long a,
@ -402,8 +407,8 @@
if ( c == 0 )
a = 0x7FFFFFFFL;
else if ( (FT_ULong)a + (FT_ULong)b <= 92681UL - ( c >> 16 ) )
a = ( a * b + ( c >> 1 ) ) / c;
else if ( (FT_ULong)a + b <= 129895UL - ( c >> 17 ) )
a = ( (FT_ULong)a * b + ( c >> 1 ) ) / c;
else
{
@ -440,8 +445,8 @@
if ( c == 0 )
a = 0x7FFFFFFFL;
else if ( (FT_ULong)a + (FT_ULong)b <= 92681UL )
a = a * b / c;
else if ( (FT_ULong)a + b <= 131071UL )
a = (FT_ULong)a * b / c;
else
{