1#**include** "jemalloc/internal/jemalloc_preamble.h"
2
3#**include** "jemalloc/internal/div.h"
4
5#**include** "jemalloc/internal/assert.h"
6
7/*
8 * Suppose we have n = q * d, all integers. We know n and d, and want q = n / d.
9 *
10 * For any k, we have (here, all division is exact; not C-style rounding):
11 * floor(ceil(2^k / d) * n / 2^k) = floor((2^k + r) / d * n / 2^k), where
12 * r = (-2^k) mod d.
13 *
14 * Expanding this out:
15 * ... = floor(2^k / d * n / 2^k + r / d * n / 2^k)
16 * = floor(n / d + (r / d) * (n / 2^k)).
17 *
18 * The fractional part of n / d is 0 (because of the assumption that d divides n
19 * exactly), so we have:
20 * ... = n / d + floor((r / d) * (n / 2^k))
21 *
22 * So that our initial expression is equal to the quantity we seek, so long as
23 * (r / d) * (n / 2^k) < 1.
24 *
25 * r is a remainder mod d, so r < d and r / d < 1 always. We can make
26 * n / 2 ^ k < 1 by setting k = 32. This gets us a value of magic that works.
27 */
28
29**void**
30div_init(div_info_t *div_info, size_t d) {
31 /* Nonsensical. */
32 assert(d != 0);
33 /*
34 * This would make the value of magic too high to fit into a uint32_t
35 * (we would want magic = 2^32 exactly). This would mess with code gen
36 * on 32-bit machines.
37 */
38 assert(d != 1);
39
40 uint64_t two_to_k = ((uint64_t)1 << 32);
41 uint32_t magic = (uint32_t)(two_to_k / d);
42
43 /*
44 * We want magic = ceil(2^k / d), but C gives us floor. We have to
45 * increment it unless the result was exact (i.e. unless d is a power of
46 * two).
47 */
48 **if** (two_to_k % d != 0) {
49 magic++;
50 }
51 div_info->magic = magic;
52#**ifdef** JEMALLOC_DEBUG
53 div_info->d = d;
54#**endif**
55}
56