ceph/src/seastar/dpdk/lib/librte_sched/rte_approx.c

   1 /*-
   2  *   BSD LICENSE
   3  *
   4  *   Copyright(c) 2010-2014 Intel Corporation. All rights reserved.
   5  *   All rights reserved.
   6  *
   7  *   Redistribution and use in source and binary forms, with or without
   8  *   modification, are permitted provided that the following conditions
   9  *   are met:
  10  *
  11  *     * Redistributions of source code must retain the above copyright
  12  *       notice, this list of conditions and the following disclaimer.
  13  *     * Redistributions in binary form must reproduce the above copyright
  14  *       notice, this list of conditions and the following disclaimer in
  15  *       the documentation and/or other materials provided with the
  16  *       distribution.
  17  *     * Neither the name of Intel Corporation nor the names of its
  18  *       contributors may be used to endorse or promote products derived
  19  *       from this software without specific prior written permission.
  20  *
  21  *   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  22  *   "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  23  *   LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
  24  *   A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
  25  *   OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  26  *   SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
  27  *   LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  28  *   DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  29  *   THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  30  *   (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
  31  *   OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  32  */
  33
  34 #include <stdlib.h>
  35
  36 #include "rte_approx.h"
  37
  38 /*
  39  * Based on paper "Approximating Rational Numbers by Fractions" by Michal
  40  * Forisek forisek@dcs.fmph.uniba.sk
  41  *
  42  * Given a rational number alpha with 0 < alpha < 1 and a precision d, the goal
  43  * is to find positive integers p, q such that alpha - d < p/q < alpha + d, and
  44  * q is minimal.
  45  *
  46  * http://people.ksp.sk/~misof/publications/2007approx.pdf
  47  */
  48
  49 /* fraction comparison: compare (a/b) and (c/d) */
  50 static inline uint32_t
  51 less(uint32_t a, uint32_t b, uint32_t c, uint32_t d)
  52 {
  53         return a*d < b*c;
  54 }
  55
  56 static inline uint32_t
  57 less_or_equal(uint32_t a, uint32_t b, uint32_t c, uint32_t d)
  58 {
  59         return a*d <= b*c;
  60 }
  61
  62 /* check whether a/b is a valid approximation */
  63 static inline uint32_t
  64 matches(uint32_t a, uint32_t b,
  65         uint32_t alpha_num, uint32_t d_num, uint32_t denum)
  66 {
  67         if (less_or_equal(a, b, alpha_num - d_num, denum))
  68                 return 0;
  69
  70         if (less(a ,b, alpha_num + d_num, denum))
  71                 return 1;
  72
  73         return 0;
  74 }
  75
  76 static inline void
  77 find_exact_solution_left(uint32_t p_a, uint32_t q_a, uint32_t p_b, uint32_t q_b,
  78         uint32_t alpha_num, uint32_t d_num, uint32_t denum, uint32_t *p, uint32_t *q)
  79 {
  80         uint32_t k_num = denum * p_b - (alpha_num + d_num) * q_b;
  81         uint32_t k_denum = (alpha_num + d_num) * q_a - denum * p_a;
  82         uint32_t k = (k_num / k_denum) + 1;
  83
  84         *p = p_b + k * p_a;
  85         *q = q_b + k * q_a;
  86 }
  87
  88 static inline void
  89 find_exact_solution_right(uint32_t p_a, uint32_t q_a, uint32_t p_b, uint32_t q_b,
  90         uint32_t alpha_num, uint32_t d_num, uint32_t denum, uint32_t *p, uint32_t *q)
  91 {
  92         uint32_t k_num = - denum * p_b + (alpha_num - d_num) * q_b;
  93         uint32_t k_denum = - (alpha_num - d_num) * q_a + denum * p_a;
  94         uint32_t k = (k_num / k_denum) + 1;
  95
  96         *p = p_b + k * p_a;
  97         *q = q_b + k * q_a;
  98 }
  99
 100 static int
 101 find_best_rational_approximation(uint32_t alpha_num, uint32_t d_num, uint32_t denum, uint32_t *p, uint32_t *q)
 102 {
 103         uint32_t p_a, q_a, p_b, q_b;
 104
 105         /* check assumptions on the inputs */
 106         if (!((0 < d_num) && (d_num < alpha_num) && (alpha_num < denum) && (d_num + alpha_num < denum))) {
 107                 return -1;
 108         }
 109
 110         /* set initial bounds for the search */
 111         p_a = 0;
 112         q_a = 1;
 113         p_b = 1;
 114         q_b = 1;
 115
 116         while (1) {
 117                 uint32_t new_p_a, new_q_a, new_p_b, new_q_b;
 118                 uint32_t x_num, x_denum, x;
 119                 int aa, bb;
 120
 121                 /* compute the number of steps to the left */
 122                 x_num = denum * p_b - alpha_num * q_b;
 123                 x_denum = - denum * p_a + alpha_num * q_a;
 124                 x = (x_num + x_denum - 1) / x_denum; /* x = ceil(x_num / x_denum) */
 125
 126                 /* check whether we have a valid approximation */
 127                 aa = matches(p_b + x * p_a, q_b + x * q_a, alpha_num, d_num, denum);
 128                 bb = matches(p_b + (x-1) * p_a, q_b + (x - 1) * q_a, alpha_num, d_num, denum);
 129                 if (aa || bb) {
 130                         find_exact_solution_left(p_a, q_a, p_b, q_b, alpha_num, d_num, denum, p, q);
 131                         return 0;
 132                 }
 133
 134                 /* update the interval */
 135                 new_p_a = p_b + (x - 1) * p_a ;
 136                 new_q_a = q_b + (x - 1) * q_a;
 137                 new_p_b = p_b + x * p_a ;
 138                 new_q_b = q_b + x * q_a;
 139
 140                 p_a = new_p_a ;
 141                 q_a = new_q_a;
 142                 p_b = new_p_b ;
 143                 q_b = new_q_b;
 144
 145                 /* compute the number of steps to the right */
 146                 x_num = alpha_num * q_b - denum * p_b;
 147                 x_denum = - alpha_num * q_a + denum * p_a;
 148                 x = (x_num + x_denum - 1) / x_denum; /* x = ceil(x_num / x_denum) */
 149
 150                 /* check whether we have a valid approximation */
 151                 aa = matches(p_b + x * p_a, q_b + x * q_a, alpha_num, d_num, denum);
 152                 bb = matches(p_b + (x - 1) * p_a, q_b + (x - 1) * q_a, alpha_num, d_num, denum);
 153                 if (aa || bb) {
 154                         find_exact_solution_right(p_a, q_a, p_b, q_b, alpha_num, d_num, denum, p, q);
 155                         return 0;
 156                  }
 157
 158                 /* update the interval */
 159                 new_p_a = p_b + (x - 1) * p_a;
 160                 new_q_a = q_b + (x - 1) * q_a;
 161                 new_p_b = p_b + x * p_a;
 162                 new_q_b = q_b + x * q_a;
 163
 164                 p_a = new_p_a;
 165                 q_a = new_q_a;
 166                 p_b = new_p_b;
 167                 q_b = new_q_b;
 168         }
 169 }
 170
 171 int rte_approx(double alpha, double d, uint32_t *p, uint32_t *q)
 172 {
 173         uint32_t alpha_num, d_num, denum;
 174
 175         /* Check input arguments */
 176         if (!((0.0 < d) && (d < alpha) && (alpha < 1.0))) {
 177                 return -1;
 178         }
 179
 180         if ((p == NULL) || (q == NULL)) {
 181                 return -2;
 182         }
 183
 184         /* Compute alpha_num, d_num and denum */
 185         denum = 1;
 186         while (d < 1) {
 187                 alpha *= 10;
 188                 d *= 10;
 189                 denum *= 10;
 190         }
 191         alpha_num = (uint32_t) alpha;
 192         d_num = (uint32_t) d;
 193
 194         /* Perform approximation */
 195         return find_best_rational_approximation(alpha_num, d_num, denum, p, q);
 196 }