Add the div module, which allows fast division by dynamic values.

1 files changed, 55 insertions, 0 deletions

diff --git a/src/div.c b/src/div.c
new file mode 100644
index 0000000..808892a
--- /dev/null
+++ b/src/div.c
@@ -0,0 +1,55 @@
+#include "jemalloc/internal/jemalloc_preamble.h"
+
+#include "jemalloc/internal/div.h"
+
+#include "jemalloc/internal/assert.h"
+
+/*
+ * Suppose we have n = q * d, all integers. We know n and d, and want q = n / d.
+ *
+ * For any k, we have (here, all division is exact; not C-style rounding):
+ * floor(ceil(2^k / d) * n / 2^k) = floor((2^k + r) / d * n / 2^k), where
+ * r = (-2^k) mod d.
+ *
+ * Expanding this out:
+ * ... = floor(2^k / d * n / 2^k + r / d * n / 2^k)
+ *     = floor(n / d + (r / d) * (n / 2^k)).
+ *
+ * The fractional part of n / d is 0 (because of the assumption that d divides n
+ * exactly), so we have:
+ * ... = n / d + floor((r / d) * (n / 2^k))
+ *
+ * So that our initial expression is equal to the quantity we seek, so long as
+ * (r / d) * (n / 2^k) < 1.
+ *
+ * r is a remainder mod d, so r < d and r / d < 1 always. We can make
+ * n / 2 ^ k < 1 by setting k = 32. This gets us a value of magic that works.
+ */
+
+void
+div_init(div_info_t *div_info, size_t d) {
+	/* Nonsensical. */
+	assert(d != 0);
+	/*
+	 * This would make the value of magic too high to fit into a uint32_t
+	 * (we would want magic = 2^32 exactly). This would mess with code gen
+	 * on 32-bit machines.
+	 */
+	assert(d != 1);
+
+	uint64_t two_to_k = ((uint64_t)1 << 32);
+	uint32_t magic = (uint32_t)(two_to_k / d);
+
+	/*
+	 * We want magic = ceil(2^k / d), but C gives us floor. We have to
+	 * increment it unless the result was exact (i.e. unless d is a power of
+	 * two).
+	 */
+	if (two_to_k % d != 0) {
+		magic++;
+	}
+	div_info->magic = magic;
+#ifdef JEMALLOC_DEBUG
+	div_info->d = d;
+#endif
+}