LXR dpdk/lib/sched/rte

   1/* SPDX-License-Identifier: BSD-3-Clause
   2 * Copyright(c) 2010-2014 Intel Corporation
   3 */
   4
   5#include <stdlib.h>
   6
   7#include "rte_approx.h"
   8
   9/*
  10 * Based on paper "Approximating Rational Numbers by Fractions" by Michal
  11 * Forisek forisek@dcs.fmph.uniba.sk
  12 *
  13 * Given a rational number alpha with 0 < alpha < 1 and a precision d, the goal
  14 * is to find positive integers p, q such that alpha - d < p/q < alpha + d, and
  15 * q is minimal.
  16 *
  17 * http://people.ksp.sk/~misof/publications/2007approx.pdf
  18 */
  19
  20/* fraction comparison: compare (a/b) and (c/d) */
  21static inline uint32_t
  22less(uint32_t a, uint32_t b, uint32_t c, uint32_t d)
  23{
  24        return a*d < b*c;
  25}
  26
  27static inline uint32_t
  28less_or_equal(uint32_t a, uint32_t b, uint32_t c, uint32_t d)
  29{
  30        return a*d <= b*c;
  31}
  32
  33/* check whether a/b is a valid approximation */
  34static inline uint32_t
  35matches(uint32_t a, uint32_t b,
  36        uint32_t alpha_num, uint32_t d_num, uint32_t denum)
  37{
  38        if (less_or_equal(a, b, alpha_num - d_num, denum))
  39                return 0;
  40
  41        if (less(a ,b, alpha_num + d_num, denum))
  42                return 1;
  43
  44        return 0;
  45}
  46
  47static inline void
  48find_exact_solution_left(uint32_t p_a, uint32_t q_a, uint32_t p_b, uint32_t q_b,
  49        uint32_t alpha_num, uint32_t d_num, uint32_t denum, uint32_t *p, uint32_t *q)
  50{
  51        uint32_t k_num = denum * p_b - (alpha_num + d_num) * q_b;
  52        uint32_t k_denum = (alpha_num + d_num) * q_a - denum * p_a;
  53        uint32_t k = (k_num / k_denum) + 1;
  54
  55        *p = p_b + k * p_a;
  56        *q = q_b + k * q_a;
  57}
  58
  59static inline void
  60find_exact_solution_right(uint32_t p_a, uint32_t q_a, uint32_t p_b, uint32_t q_b,
  61        uint32_t alpha_num, uint32_t d_num, uint32_t denum, uint32_t *p, uint32_t *q)
  62{
  63        uint32_t k_num = - denum * p_b + (alpha_num - d_num) * q_b;
  64        uint32_t k_denum = - (alpha_num - d_num) * q_a + denum * p_a;
  65        uint32_t k = (k_num / k_denum) + 1;
  66
  67        *p = p_b + k * p_a;
  68        *q = q_b + k * q_a;
  69}
  70
  71static int
  72find_best_rational_approximation(uint32_t alpha_num, uint32_t d_num, uint32_t denum, uint32_t *p, uint32_t *q)
  73{
  74        uint32_t p_a, q_a, p_b, q_b;
  75
  76        /* check assumptions on the inputs */
  77        if (!((0 < d_num) && (d_num < alpha_num) && (alpha_num < denum) && (d_num + alpha_num < denum))) {
  78                return -1;
  79        }
  80
  81        /* set initial bounds for the search */
  82        p_a = 0;
  83        q_a = 1;
  84        p_b = 1;
  85        q_b = 1;
  86
  87        while (1) {
  88                uint32_t new_p_a, new_q_a, new_p_b, new_q_b;
  89                uint32_t x_num, x_denum, x;
  90                int aa, bb;
  91
  92                /* compute the number of steps to the left */
  93                x_num = denum * p_b - alpha_num * q_b;
  94                x_denum = - denum * p_a + alpha_num * q_a;
  95                x = (x_num + x_denum - 1) / x_denum; /* x = ceil(x_num / x_denum) */
  96
  97                /* check whether we have a valid approximation */
  98                aa = matches(p_b + x * p_a, q_b + x * q_a, alpha_num, d_num, denum);
  99                bb = matches(p_b + (x-1) * p_a, q_b + (x - 1) * q_a, alpha_num, d_num, denum);
 100                if (aa || bb) {
 101                        find_exact_solution_left(p_a, q_a, p_b, q_b, alpha_num, d_num, denum, p, q);
 102                        return 0;
 103                }
 104
 105                /* update the interval */
 106                new_p_a = p_b + (x - 1) * p_a ;
 107                new_q_a = q_b + (x - 1) * q_a;
 108                new_p_b = p_b + x * p_a ;
 109                new_q_b = q_b + x * q_a;
 110
 111                p_a = new_p_a ;
 112                q_a = new_q_a;
 113                p_b = new_p_b ;
 114                q_b = new_q_b;
 115
 116                /* compute the number of steps to the right */
 117                x_num = alpha_num * q_b - denum * p_b;
 118                x_denum = - alpha_num * q_a + denum * p_a;
 119                x = (x_num + x_denum - 1) / x_denum; /* x = ceil(x_num / x_denum) */
 120
 121                /* check whether we have a valid approximation */
 122                aa = matches(p_b + x * p_a, q_b + x * q_a, alpha_num, d_num, denum);
 123                bb = matches(p_b + (x - 1) * p_a, q_b + (x - 1) * q_a, alpha_num, d_num, denum);
 124                if (aa || bb) {
 125                        find_exact_solution_right(p_a, q_a, p_b, q_b, alpha_num, d_num, denum, p, q);
 126                        return 0;
 127                 }
 128
 129                /* update the interval */
 130                new_p_a = p_b + (x - 1) * p_a;
 131                new_q_a = q_b + (x - 1) * q_a;
 132                new_p_b = p_b + x * p_a;
 133                new_q_b = q_b + x * q_a;
 134
 135                p_a = new_p_a;
 136                q_a = new_q_a;
 137                p_b = new_p_b;
 138                q_b = new_q_b;
 139        }
 140}
 141
 142int rte_approx(double alpha, double d, uint32_t *p, uint32_t *q)
 143{
 144        uint32_t alpha_num, d_num, denum;
 145
 146        /* Check input arguments */
 147        if (!((0.0 < d) && (d < alpha) && (alpha < 1.0))) {
 148                return -1;
 149        }
 150
 151        if ((p == NULL) || (q == NULL)) {
 152                return -2;
 153        }
 154
 155        /* Compute alpha_num, d_num and denum */
 156        denum = 1;
 157        while (d < 1) {
 158                alpha *= 10;
 159                d *= 10;
 160                denum *= 10;
 161        }
 162        alpha_num = (uint32_t) alpha;
 163        d_num = (uint32_t) d;
 164
 165        /* Perform approximation */
 166        return find_best_rational_approximation(alpha_num, d_num, denum, p, q);
 167}
 168
 169/* fraction comparison (64 bit version): compare (a/b) and (c/d) */
 170static inline uint64_t
 171less_64(uint64_t a, uint64_t b, uint64_t c, uint64_t d)
 172{
 173        return a*d < b*c;
 174}
 175
 176static inline uint64_t
 177less_or_equal_64(uint64_t a, uint64_t b, uint64_t c, uint64_t d)
 178{
 179        return a*d <= b*c;
 180}
 181
 182/* check whether a/b is a valid approximation (64 bit version) */
 183static inline uint64_t
 184matches_64(uint64_t a, uint64_t b,
 185        uint64_t alpha_num, uint64_t d_num, uint64_t denum)
 186{
 187        if (less_or_equal_64(a, b, alpha_num - d_num, denum))
 188                return 0;
 189
 190        if (less_64(a, b, alpha_num + d_num, denum))
 191                return 1;
 192
 193        return 0;
 194}
 195
 196static inline void
 197find_exact_solution_left_64(uint64_t p_a, uint64_t q_a, uint64_t p_b, uint64_t q_b,
 198        uint64_t alpha_num, uint64_t d_num, uint64_t denum, uint64_t *p, uint64_t *q)
 199{
 200        uint64_t k_num = denum * p_b - (alpha_num + d_num) * q_b;
 201        uint64_t k_denum = (alpha_num + d_num) * q_a - denum * p_a;
 202        uint64_t k = (k_num / k_denum) + 1;
 203
 204        *p = p_b + k * p_a;
 205        *q = q_b + k * q_a;
 206}
 207
 208static inline void
 209find_exact_solution_right_64(uint64_t p_a, uint64_t q_a, uint64_t p_b, uint64_t q_b,
 210        uint64_t alpha_num, uint64_t d_num, uint64_t denum, uint64_t *p, uint64_t *q)
 211{
 212        uint64_t k_num = -denum * p_b + (alpha_num - d_num) * q_b;
 213        uint64_t k_denum = -(alpha_num - d_num) * q_a + denum * p_a;
 214        uint64_t k = (k_num / k_denum) + 1;
 215
 216        *p = p_b + k * p_a;
 217        *q = q_b + k * q_a;
 218}
 219
 220static int
 221find_best_rational_approximation_64(uint64_t alpha_num, uint64_t d_num,
 222        uint64_t denum, uint64_t *p, uint64_t *q)
 223{
 224        uint64_t p_a, q_a, p_b, q_b;
 225
 226        /* check assumptions on the inputs */
 227        if (!((d_num > 0) && (d_num < alpha_num) &&
 228                (alpha_num < denum) && (d_num + alpha_num < denum))) {
 229                return -1;
 230        }
 231
 232        /* set initial bounds for the search */
 233        p_a = 0;
 234        q_a = 1;
 235        p_b = 1;
 236        q_b = 1;
 237
 238        while (1) {
 239                uint64_t new_p_a, new_q_a, new_p_b, new_q_b;
 240                uint64_t x_num, x_denum, x;
 241                int aa, bb;
 242
 243                /* compute the number of steps to the left */
 244                x_num = denum * p_b - alpha_num * q_b;
 245                x_denum = -denum * p_a + alpha_num * q_a;
 246                x = (x_num + x_denum - 1) / x_denum; /* x = ceil(x_num / x_denum) */
 247
 248                /* check whether we have a valid approximation */
 249                aa = matches_64(p_b + x * p_a, q_b + x * q_a, alpha_num, d_num, denum);
 250                bb = matches_64(p_b + (x-1) * p_a, q_b + (x - 1) * q_a,
 251                        alpha_num, d_num, denum);
 252                if (aa || bb) {
 253                        find_exact_solution_left_64(p_a, q_a, p_b, q_b,
 254                                alpha_num, d_num, denum, p, q);
 255                        return 0;
 256                }
 257
 258                /* update the interval */
 259                new_p_a = p_b + (x - 1) * p_a;
 260                new_q_a = q_b + (x - 1) * q_a;
 261                new_p_b = p_b + x * p_a;
 262                new_q_b = q_b + x * q_a;
 263
 264                p_a = new_p_a;
 265                q_a = new_q_a;
 266                p_b = new_p_b;
 267                q_b = new_q_b;
 268
 269                /* compute the number of steps to the right */
 270                x_num = alpha_num * q_b - denum * p_b;
 271                x_denum = -alpha_num * q_a + denum * p_a;
 272                x = (x_num + x_denum - 1) / x_denum; /* x = ceil(x_num / x_denum) */
 273
 274                /* check whether we have a valid approximation */
 275                aa = matches_64(p_b + x * p_a, q_b + x * q_a, alpha_num, d_num, denum);
 276                bb = matches_64(p_b + (x - 1) * p_a, q_b + (x - 1) * q_a,
 277                        alpha_num, d_num, denum);
 278                if (aa || bb) {
 279                        find_exact_solution_right_64(p_a, q_a, p_b, q_b,
 280                                alpha_num, d_num, denum, p, q);
 281                        return 0;
 282                }
 283
 284                /* update the interval */
 285                new_p_a = p_b + (x - 1) * p_a;
 286                new_q_a = q_b + (x - 1) * q_a;
 287                new_p_b = p_b + x * p_a;
 288                new_q_b = q_b + x * q_a;
 289
 290                p_a = new_p_a;
 291                q_a = new_q_a;
 292                p_b = new_p_b;
 293                q_b = new_q_b;
 294        }
 295}
 296
 297int rte_approx_64(double alpha, double d, uint64_t *p, uint64_t *q)
 298{
 299        uint64_t alpha_num, d_num, denum;
 300
 301        /* Check input arguments */
 302        if (!((0.0 < d) && (d < alpha) && (alpha < 1.0)))
 303                return -1;
 304
 305        if ((p == NULL) || (q == NULL))
 306                return -2;
 307
 308        /* Compute alpha_num, d_num and denum */
 309        denum = 1;
 310        while (d < 1) {
 311                alpha *= 10;
 312                d *= 10;
 313                denum *= 10;
 314        }
 315        alpha_num = (uint64_t) alpha;
 316        d_num = (uint64_t) d;
 317
 318        /* Perform approximation */
 319        return find_best_rational_approximation_64(alpha_num, d_num, denum, p, q);
 320}
 321