macro: add DIV_ROUND_UP()

This macro calculates A / B but rounds up instead of down. We explicitly
do *NOT* use:
        (A + B - 1) / A
as it suffers from an integer overflow, even though the passed values are
properly tested against overflow. Our test-cases show this behavior.

Instead, we use:
        A / B + !!(A % B)

Note that on "Real CPUs" this does *NOT* result in two divisions. Instead,
instructions like idivl@x86 provide both, the quotient and the remainder.
Therefore, both algorithms should perform equally well (I didn't verify
this, though).

1 files changed, 11 insertions, 0 deletions

diff --git a/src/shared/macro.h b/src/shared/macro.h
index 548294e47b..6a57428244 100644
--- a/src/shared/macro.h
+++ b/src/shared/macro.h
@@ -197,6 +197,17 @@ static inline unsigned long ALIGN_POWER2(unsigned long u) {
                                         UNIQ_T(X,xq);                   \
         })
 
+/* [(x + y - 1) / y] suffers from an integer overflow, even though the
+ * computation should be possible in the given type. Therefore, we use
+ * [x / y + !!(x % y)]. Note that on "Real CPUs" a division returns both the
+ * quotient and the remainder, so both should be equally fast. */
+#define DIV_ROUND_UP(_x, _y)                                            \
+        __extension__ ({                                                \
+                const typeof(_x) __x = (_x);                            \
+                const typeof(_y) __y = (_y);                            \
+                (__x / __y + !!(__x % __y));                            \
+        })
+
 #define assert_se(expr)                                                 \
         do {                                                            \
                 if (_unlikely_(!(expr)))                                \