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/*
* Copyright © 2018 Advanced Micro Devices, Inc.
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and associated documentation files (the "Software"),
* to deal in the Software without restriction, including without limitation
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
* and/or sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice (including the next
* paragraph) shall be included in all copies or substantial portions of the
* Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
* IN THE SOFTWARE.
*/
/* Imported from:
* https://raw.githubusercontent.com/ridiculousfish/libdivide/master/divide_by_constants_codegen_reference.c
* Paper:
* http://ridiculousfish.com/files/faster_unsigned_division_by_constants.pdf
*
* The author, ridiculous_fish, wrote:
*
* ''Reference implementations of computing and using the "magic number"
* approach to dividing by constants, including codegen instructions.
* The unsigned division incorporates the "round down" optimization per
* ridiculous_fish.
*
* This is free and unencumbered software. Any copyright is dedicated
* to the Public Domain.''
*/
#include "fast_idiv_by_const.h"
#include "u_math.h"
#include <limits.h>
#include <assert.h>
/* uint_t and sint_t can be replaced by different integer types and the code
* will work as-is. The only requirement is that sizeof(uintN) == sizeof(intN).
*/
struct util_fast_udiv_info
util_compute_fast_udiv_info(uint_t D, unsigned num_bits)
{
/* The numerator must fit in a uint_t */
assert(num_bits > 0 && num_bits <= sizeof(uint_t) * CHAR_BIT);
assert(D != 0);
/* The eventual result */
struct util_fast_udiv_info result;
/* Bits in a uint_t */
const unsigned UINT_BITS = sizeof(uint_t) * CHAR_BIT;
/* The extra shift implicit in the difference between UINT_BITS and num_bits
*/
const unsigned extra_shift = UINT_BITS - num_bits;
/* The initial power of 2 is one less than the first one that can possibly
* work.
*/
const uint_t initial_power_of_2 = (uint_t)1 << (UINT_BITS-1);
/* The remainder and quotient of our power of 2 divided by d */
uint_t quotient = initial_power_of_2 / D;
uint_t remainder = initial_power_of_2 % D;
/* ceil(log_2 D) */
unsigned ceil_log_2_D;
/* The magic info for the variant "round down" algorithm */
uint_t down_multiplier = 0;
unsigned down_exponent = 0;
int has_magic_down = 0;
/* Compute ceil(log_2 D) */
ceil_log_2_D = 0;
uint_t tmp;
for (tmp = D; tmp > 0; tmp >>= 1)
ceil_log_2_D += 1;
/* Begin a loop that increments the exponent, until we find a power of 2
* that works.
*/
unsigned exponent;
for (exponent = 0; ; exponent++) {
/* Quotient and remainder is from previous exponent; compute it for this
* exponent.
*/
if (remainder >= D - remainder) {
/* Doubling remainder will wrap around D */
quotient = quotient * 2 + 1;
remainder = remainder * 2 - D;
} else {
/* Remainder will not wrap */
quotient = quotient * 2;
remainder = remainder * 2;
}
/* We're done if this exponent works for the round_up algorithm.
* Note that exponent may be larger than the maximum shift supported,
* so the check for >= ceil_log_2_D is critical.
*/
if ((exponent + extra_shift >= ceil_log_2_D) ||
(D - remainder) <= ((uint_t)1 << (exponent + extra_shift)))
break;
/* Set magic_down if we have not set it yet and this exponent works for
* the round_down algorithm
*/
if (!has_magic_down &&
remainder <= ((uint_t)1 << (exponent + extra_shift))) {
has_magic_down = 1;
down_multiplier = quotient;
down_exponent = exponent;
}
}
if (exponent < ceil_log_2_D) {
/* magic_up is efficient */
result.multiplier = quotient + 1;
result.pre_shift = 0;
result.post_shift = exponent;
result.increment = 0;
} else if (D & 1) {
/* Odd divisor, so use magic_down, which must have been set */
assert(has_magic_down);
result.multiplier = down_multiplier;
result.pre_shift = 0;
result.post_shift = down_exponent;
result.increment = 1;
} else {
/* Even divisor, so use a prefix-shifted dividend */
unsigned pre_shift = 0;
uint_t shifted_D = D;
while ((shifted_D & 1) == 0) {
shifted_D >>= 1;
pre_shift += 1;
}
result = util_compute_fast_udiv_info(shifted_D, num_bits - pre_shift);
/* expect no increment or pre_shift in this path */
assert(result.increment == 0 && result.pre_shift == 0);
result.pre_shift = pre_shift;
}
return result;
}
struct util_fast_sdiv_info
util_compute_fast_sdiv_info(sint_t D)
{
/* D must not be zero. */
assert(D != 0);
/* The result is not correct for these divisors. */
assert(D != 1 && D != -1);
/* Our result */
struct util_fast_sdiv_info result;
/* Bits in an sint_t */
const unsigned SINT_BITS = sizeof(sint_t) * CHAR_BIT;
/* Absolute value of D (we know D is not the most negative value since
* that's a power of 2)
*/
const uint_t abs_d = (D < 0 ? -D : D);
/* The initial power of 2 is one less than the first one that can possibly
* work */
/* "two31" in Warren */
unsigned exponent = SINT_BITS - 1;
const uint_t initial_power_of_2 = (uint_t)1 << exponent;
/* Compute the absolute value of our "test numerator,"
* which is the largest dividend whose remainder with d is d-1.
* This is called anc in Warren.
*/
const uint_t tmp = initial_power_of_2 + (D < 0);
const uint_t abs_test_numer = tmp - 1 - tmp % abs_d;
/* Initialize our quotients and remainders (q1, r1, q2, r2 in Warren) */
uint_t quotient1 = initial_power_of_2 / abs_test_numer;
uint_t remainder1 = initial_power_of_2 % abs_test_numer;
uint_t quotient2 = initial_power_of_2 / abs_d;
uint_t remainder2 = initial_power_of_2 % abs_d;
uint_t delta;
/* Begin our loop */
do {
/* Update the exponent */
exponent++;
/* Update quotient1 and remainder1 */
quotient1 *= 2;
remainder1 *= 2;
if (remainder1 >= abs_test_numer) {
quotient1 += 1;
remainder1 -= abs_test_numer;
}
/* Update quotient2 and remainder2 */
quotient2 *= 2;
remainder2 *= 2;
if (remainder2 >= abs_d) {
quotient2 += 1;
remainder2 -= abs_d;
}
/* Keep going as long as (2**exponent) / abs_d <= delta */
delta = abs_d - remainder2;
} while (quotient1 < delta || (quotient1 == delta && remainder1 == 0));
result.multiplier = quotient2 + 1;
if (D < 0) result.multiplier = -result.multiplier;
result.shift = exponent - SINT_BITS;
return result;
}
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