#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

}