Commit 70961e57729350aad01ace23c2529265045af85b
2014-08-20T16:19:32
Minor.
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diff --git a/src/base/ftcalc.c b/src/base/ftcalc.c
index 5b17232..8eed4ce 100644
--- a/src/base/ftcalc.c
+++ b/src/base/ftcalc.c
@@ -362,35 +362,37 @@
/* 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' (all positive values). */
/* */
/* The product of two positive numbers never exceeds the square of */
- /* their mean. Therefore, we always avoid the overflow by imposing */
+ /* its mean values. Therefore, we always avoid the overflow by */
+ /* imposing */
/* */
- /* ( a + b ) / 2 <= sqrt( X - c/2 ) */
+ /* (a + b) / 2 <= sqrt(X - c/2) , */
/* */
- /* where X = 2^32 - 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 */
+ /* where X = 2^32 - 1, the maximum unsigned 32-bit value, and using */
+ /* unsigned arithmetic. Now we replace `sqrt' with a linear function */
+ /* that is smaller or equal for all values of c in the interval */
+ /* [0;X/2]; it should be equal to sqrt(X) and sqrt(3X/4) at the */
+ /* endpoints. Substituting the linear solution and explicit numbers */
+ /* we get */
/* */
- /* a + b <= 131071.99 - c / 122291.84 */
+ /* a + b <= 131071.99 - c / 122291.84 . */
/* */
- /* In practice we should use a faster and even stronger inequality */
+ /* In practice, we should use a faster and even stronger inequality */
/* */
- /* a + b <= 131071 - (c >> 16) */
+ /* a + b <= 131071 - (c >> 16) */
/* */
/* or, alternatively, */
/* */
- /* a + b <= 129895 - (c >> 17) */
+ /* a + b <= 129895 - (c >> 17) . */
/* */
/* FT_MulFix, on the other hand, is optimized for a small value of */
/* the first argument, when the second argument can be much larger. */
/* This can be achieved by scaling the second argument and the limit */
- /* in the above inequalities. For example, */
+ /* in the above inequalities. For example, */
/* */
- /* a + (b >> 8) <= (131071 >> 4) */
+ /* a + (b >> 8) <= (131071 >> 4) */
/* */
/* should work well to avoid the overflow. */
/* */