src/util/fast_idiv_by_const.c

   1 /*
   2  * Copyright © 2018 Advanced Micro Devices, Inc.
   3  *
   4  * Permission is hereby granted, free of charge, to any person obtaining a
   5  * copy of this software and associated documentation files (the "Software"),
   6  * to deal in the Software without restriction, including without limitation
   7  * the rights to use, copy, modify, merge, publish, distribute, sublicense,
   8  * and/or sell copies of the Software, and to permit persons to whom the
   9  * Software is furnished to do so, subject to the following conditions:
  10  *
  11  * The above copyright notice and this permission notice (including the next
  12  * paragraph) shall be included in all copies or substantial portions of the
  13  * Software.
  14  *
  15  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  16  * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  17  * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
  18  * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  19  * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
  20  * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
  21  * IN THE SOFTWARE.
  22  */
  23
  24 /* Imported from:
  25  *   https://raw.githubusercontent.com/ridiculousfish/libdivide/master/divide_by_constants_codegen_reference.c
  26  * Paper:
  27  *   http://ridiculousfish.com/files/faster_unsigned_division_by_constants.pdf
  28  *
  29  * The author, ridiculous_fish, wrote:
  30  *
  31  *  ''Reference implementations of computing and using the "magic number"
  32  *    approach to dividing by constants, including codegen instructions.
  33  *    The unsigned division incorporates the "round down" optimization per
  34  *    ridiculous_fish.
  35  *
  36  *    This is free and unencumbered software. Any copyright is dedicated
  37  *    to the Public Domain.''
  38  */
  39
  40 #include "fast_idiv_by_const.h"
  41 #include "u_math.h"
  42 #include <limits.h>
  43 #include <assert.h>
  44
  45 /* uint_t and sint_t can be replaced by different integer types and the code
  46  * will work as-is. The only requirement is that sizeof(uintN) == sizeof(intN).
  47  */
  48
  49 struct util_fast_udiv_info
  50 util_compute_fast_udiv_info(uint_t D, unsigned num_bits)
  51 {
  52    /* The numerator must fit in a uint_t */
  53    assert(num_bits > 0 && num_bits <= sizeof(uint_t) * CHAR_BIT);
  54    assert(D != 0);
  55
  56    /* The eventual result */
  57    struct util_fast_udiv_info result;
  58
  59    /* Bits in a uint_t */
  60    const unsigned UINT_BITS = sizeof(uint_t) * CHAR_BIT;
  61
  62    /* The extra shift implicit in the difference between UINT_BITS and num_bits
  63     */
  64    const unsigned extra_shift = UINT_BITS - num_bits;
  65
  66    /* The initial power of 2 is one less than the first one that can possibly
  67     * work.
  68     */
  69    const uint_t initial_power_of_2 = (uint_t)1 << (UINT_BITS-1);
  70
  71    /* The remainder and quotient of our power of 2 divided by d */
  72    uint_t quotient = initial_power_of_2 / D;
  73    uint_t remainder = initial_power_of_2 % D;
  74
  75    /* ceil(log_2 D) */
  76    unsigned ceil_log_2_D;
  77
  78    /* The magic info for the variant "round down" algorithm */
  79    uint_t down_multiplier = 0;
  80    unsigned down_exponent = 0;
  81    int has_magic_down = 0;
  82
  83    /* Compute ceil(log_2 D) */
  84    ceil_log_2_D = 0;
  85    uint_t tmp;
  86    for (tmp = D; tmp > 0; tmp >>= 1)
  87       ceil_log_2_D += 1;
  88
  89
  90    /* Begin a loop that increments the exponent, until we find a power of 2
  91     * that works.
  92     */
  93    unsigned exponent;
  94    for (exponent = 0; ; exponent++) {
  95       /* Quotient and remainder is from previous exponent; compute it for this
  96        * exponent.
  97        */
  98       if (remainder >= D - remainder) {
  99          /* Doubling remainder will wrap around D */
 100          quotient = quotient * 2 + 1;
 101          remainder = remainder * 2 - D;
 102       } else {
 103          /* Remainder will not wrap */
 104          quotient = quotient * 2;
 105          remainder = remainder * 2;
 106       }
 107
 108       /* We're done if this exponent works for the round_up algorithm.
 109        * Note that exponent may be larger than the maximum shift supported,
 110        * so the check for >= ceil_log_2_D is critical.
 111        */
 112       if ((exponent + extra_shift >= ceil_log_2_D) ||
 113           (D - remainder) <= ((uint_t)1 << (exponent + extra_shift)))
 114          break;
 115
 116       /* Set magic_down if we have not set it yet and this exponent works for
 117        * the round_down algorithm
 118        */
 119       if (!has_magic_down &&
 120           remainder <= ((uint_t)1 << (exponent + extra_shift))) {
 121          has_magic_down = 1;
 122          down_multiplier = quotient;
 123          down_exponent = exponent;
 124       }
 125    }
 126
 127    if (exponent < ceil_log_2_D) {
 128       /* magic_up is efficient */
 129       result.multiplier = quotient + 1;
 130       result.pre_shift = 0;
 131       result.post_shift = exponent;
 132       result.increment = 0;
 133    } else if (D & 1) {
 134       /* Odd divisor, so use magic_down, which must have been set */
 135       assert(has_magic_down);
 136       result.multiplier = down_multiplier;
 137       result.pre_shift = 0;
 138       result.post_shift = down_exponent;
 139       result.increment = 1;
 140    } else {
 141       /* Even divisor, so use a prefix-shifted dividend */
 142       unsigned pre_shift = 0;
 143       uint_t shifted_D = D;
 144       while ((shifted_D & 1) == 0) {
 145          shifted_D >>= 1;
 146          pre_shift += 1;
 147       }
 148       result = util_compute_fast_udiv_info(shifted_D, num_bits - pre_shift);
 149       /* expect no increment or pre_shift in this path */
 150       assert(result.increment == 0 && result.pre_shift == 0);
 151       result.pre_shift = pre_shift;
 152    }
 153    return result;
 154 }
 155
 156 struct util_fast_sdiv_info
 157 util_compute_fast_sdiv_info(sint_t D)
 158 {
 159    /* D must not be zero. */
 160    assert(D != 0);
 161    /* The result is not correct for these divisors. */
 162    assert(D != 1 && D != -1);
 163
 164    /* Our result */
 165    struct util_fast_sdiv_info result;
 166
 167    /* Bits in an sint_t */
 168    const unsigned SINT_BITS = sizeof(sint_t) * CHAR_BIT;
 169
 170    /* Absolute value of D (we know D is not the most negative value since
 171     * that's a power of 2)
 172     */
 173    const uint_t abs_d = (D < 0 ? -D : D);
 174
 175    /* The initial power of 2 is one less than the first one that can possibly
 176     * work */
 177    /* "two31" in Warren */
 178    unsigned exponent = SINT_BITS - 1;
 179    const uint_t initial_power_of_2 = (uint_t)1 << exponent;
 180
 181    /* Compute the absolute value of our "test numerator,"
 182     * which is the largest dividend whose remainder with d is d-1.
 183     * This is called anc in Warren.
 184     */
 185    const uint_t tmp = initial_power_of_2 + (D < 0);
 186    const uint_t abs_test_numer = tmp - 1 - tmp % abs_d;
 187
 188    /* Initialize our quotients and remainders (q1, r1, q2, r2 in Warren) */
 189    uint_t quotient1 = initial_power_of_2 / abs_test_numer;
 190    uint_t remainder1 = initial_power_of_2 % abs_test_numer;
 191    uint_t quotient2 = initial_power_of_2 / abs_d;
 192    uint_t remainder2 = initial_power_of_2 % abs_d;
 193    uint_t delta;
 194
 195    /* Begin our loop */
 196    do {
 197       /* Update the exponent */
 198       exponent++;
 199
 200       /* Update quotient1 and remainder1 */
 201       quotient1 *= 2;
 202       remainder1 *= 2;
 203       if (remainder1 >= abs_test_numer) {
 204          quotient1 += 1;
 205          remainder1 -= abs_test_numer;
 206       }
 207
 208       /* Update quotient2 and remainder2 */
 209       quotient2 *= 2;
 210       remainder2 *= 2;
 211       if (remainder2 >= abs_d) {
 212          quotient2 += 1;
 213          remainder2 -= abs_d;
 214       }
 215
 216       /* Keep going as long as (2**exponent) / abs_d <= delta */
 217       delta = abs_d - remainder2;
 218    } while (quotient1 < delta || (quotient1 == delta && remainder1 == 0));
 219
 220    result.multiplier = quotient2 + 1;
 221    if (D < 0) result.multiplier = -result.multiplier;
 222    result.shift = exponent - SINT_BITS;
 223    return result;
 224 }