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[base] Improve comment.

This commit is contained in:
Alexei Podtelezhnikov 2014-07-05 22:29:26 -04:00
parent ceab95a649
commit 2f52df4a0d
1 changed files with 12 additions and 8 deletions
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20
src/base/ftcalc.c
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@ -358,20 +358,24 @@
/* documentation is in freetype.h */
/* The FT_MulDiv function has been optimized thanks to ideas from */
/* Graham Asher. The trick is to optimize computation when everything */
/* fits within 32-bits (a rather common case). */
/* 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) */
/* We compute 'a*b+c/2', then divide it by 'c'. (positive values) */
/* */
/* A sufficient condition to avoid overflow is as follows. */
/* The product of two positive numbers never exceeds the square of */
/* their mean. Therefore, we always avoid the overflow by imposing */
/* */
/* a + b <= 2 * sqrt( X - c/2 ) */
/* ( a + b ) / 2 <= sqrt( X - c/2 ) */
/* */
/* where X = 2^31 - 1. After Taylor expansion, we make it stronger */
/* 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. */
/* Substituting the linear solution and explicit numbers we get */
/* */
/* a + b <= 92681.9 - c / 92681.9 */
/* a + b <= 92681.9 - c / 79108.95 */
/* */
/* with explicit 2*sqrt(X) = 92681.9. What we actually use is this */
/* In practice we use a faster and even stronger inequality */
/* */
/* a + b <= 92681 - (c >> 16) */
/* */