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 struct util_fast_udiv_info
  46 util_compute_fast_udiv_info(uint64_t D, unsigned num_bits, unsigned UINT_BITS)
  47 {
  48    /* The numerator must fit in a uint64_t */
  49    assert(num_bits > 0 && num_bits <= UINT_BITS);
  50    assert(D != 0);
  51
  52    /* The eventual result */
  53    struct util_fast_udiv_info result;
  54
  55
  56    /* The extra shift implicit in the difference between UINT_BITS and num_bits
  57     */
  58    const unsigned extra_shift = UINT_BITS - num_bits;
  59
  60    /* The initial power of 2 is one less than the first one that can possibly
  61     * work.
  62     */
  63    const uint64_t initial_power_of_2 = (uint64_t)1 << (UINT_BITS-1);
  64
  65    /* The remainder and quotient of our power of 2 divided by d */
  66    uint64_t quotient = initial_power_of_2 / D;
  67    uint64_t remainder = initial_power_of_2 % D;
  68
  69    /* ceil(log_2 D) */
  70    unsigned ceil_log_2_D;
  71
  72    /* The magic info for the variant "round down" algorithm */
  73    uint64_t down_multiplier = 0;
  74    unsigned down_exponent = 0;
  75    int has_magic_down = 0;
  76
  77    /* Compute ceil(log_2 D) */
  78    ceil_log_2_D = 0;
  79    uint64_t tmp;
  80    for (tmp = D; tmp > 0; tmp >>= 1)
  81       ceil_log_2_D += 1;
  82
  83
  84    /* Begin a loop that increments the exponent, until we find a power of 2
  85     * that works.
  86     */
  87    unsigned exponent;
  88    for (exponent = 0; ; exponent++) {
  89       /* Quotient and remainder is from previous exponent; compute it for this
  90        * exponent.
  91        */
  92       if (remainder >= D - remainder) {
  93          /* Doubling remainder will wrap around D */
  94          quotient = quotient * 2 + 1;
  95          remainder = remainder * 2 - D;
  96       } else {
  97          /* Remainder will not wrap */
  98          quotient = quotient * 2;
  99          remainder = remainder * 2;
 100       }
 101
 102       /* We're done if this exponent works for the round_up algorithm.
 103        * Note that exponent may be larger than the maximum shift supported,
 104        * so the check for >= ceil_log_2_D is critical.
 105        */
 106       if ((exponent + extra_shift >= ceil_log_2_D) ||
 107           (D - remainder) <= ((uint64_t)1 << (exponent + extra_shift)))
 108          break;
 109
 110       /* Set magic_down if we have not set it yet and this exponent works for
 111        * the round_down algorithm
 112        */
 113       if (!has_magic_down &&
 114           remainder <= ((uint64_t)1 << (exponent + extra_shift))) {
 115          has_magic_down = 1;
 116          down_multiplier = quotient;
 117          down_exponent = exponent;
 118       }
 119    }
 120
 121    if (exponent < ceil_log_2_D) {
 122       /* magic_up is efficient */
 123       result.multiplier = quotient + 1;
 124       result.pre_shift = 0;
 125       result.post_shift = exponent;
 126       result.increment = 0;
 127    } else if (D & 1) {
 128       /* Odd divisor, so use magic_down, which must have been set */
 129       assert(has_magic_down);
 130       result.multiplier = down_multiplier;
 131       result.pre_shift = 0;
 132       result.post_shift = down_exponent;
 133       result.increment = 1;
 134    } else {
 135       /* Even divisor, so use a prefix-shifted dividend */
 136       unsigned pre_shift = 0;
 137       uint64_t shifted_D = D;
 138       while ((shifted_D & 1) == 0) {
 139          shifted_D >>= 1;
 140          pre_shift += 1;
 141       }
 142       result = util_compute_fast_udiv_info(shifted_D, num_bits - pre_shift,
 143                                            UINT_BITS);
 144       /* expect no increment or pre_shift in this path */
 145       assert(result.increment == 0 && result.pre_shift == 0);
 146       result.pre_shift = pre_shift;
 147    }
 148    return result;
 149 }
 150
 151 static inline int64_t
 152 sign_extend(int64_t x, unsigned SINT_BITS)
 153 {
 154    return (x << (64 - SINT_BITS)) >> (64 - SINT_BITS);
 155 }
 156
 157 struct util_fast_sdiv_info
 158 util_compute_fast_sdiv_info(int64_t D, unsigned SINT_BITS)
 159 {
 160    /* D must not be zero. */
 161    assert(D != 0);
 162    /* The result is not correct for these divisors. */
 163    assert(D != 1 && D != -1);
 164
 165    /* Our result */
 166    struct util_fast_sdiv_info result;
 167
 168    /* Absolute value of D (we know D is not the most negative value since
 169     * that's a power of 2)
 170     */
 171    const uint64_t abs_d = (D < 0 ? -D : D);
 172
 173    /* The initial power of 2 is one less than the first one that can possibly
 174     * work */
 175    /* "two31" in Warren */
 176    unsigned exponent = SINT_BITS - 1;
 177    const uint64_t initial_power_of_2 = (uint64_t)1 << exponent;
 178
 179    /* Compute the absolute value of our "test numerator,"
 180     * which is the largest dividend whose remainder with d is d-1.
 181     * This is called anc in Warren.
 182     */
 183    const uint64_t tmp = initial_power_of_2 + (D < 0);
 184    const uint64_t abs_test_numer = tmp - 1 - tmp % abs_d;
 185
 186    /* Initialize our quotients and remainders (q1, r1, q2, r2 in Warren) */
 187    uint64_t quotient1 = initial_power_of_2 / abs_test_numer;
 188    uint64_t remainder1 = initial_power_of_2 % abs_test_numer;
 189    uint64_t quotient2 = initial_power_of_2 / abs_d;
 190    uint64_t remainder2 = initial_power_of_2 % abs_d;
 191    uint64_t delta;
 192
 193    /* Begin our loop */
 194    do {
 195       /* Update the exponent */
 196       exponent++;
 197
 198       /* Update quotient1 and remainder1 */
 199       quotient1 *= 2;
 200       remainder1 *= 2;
 201       if (remainder1 >= abs_test_numer) {
 202          quotient1 += 1;
 203          remainder1 -= abs_test_numer;
 204       }
 205
 206       /* Update quotient2 and remainder2 */
 207       quotient2 *= 2;
 208       remainder2 *= 2;
 209       if (remainder2 >= abs_d) {
 210          quotient2 += 1;
 211          remainder2 -= abs_d;
 212       }
 213
 214       /* Keep going as long as (2**exponent) / abs_d <= delta */
 215       delta = abs_d - remainder2;
 216    } while (quotient1 < delta || (quotient1 == delta && remainder1 == 0));
 217
 218    result.multiplier = sign_extend(quotient2 + 1, SINT_BITS);
 219    if (D < 0) result.multiplier = -result.multiplier;
 220    result.shift = exponent - SINT_BITS;
 221    return result;
 222 }