projects / ceph.git / blame
| Commit | Line | Data |
|---|---|---|
| 9f95a23c TL |
1 | /* SPDX-License-Identifier: BSD-3-Clause |
| 2 | * Copyright(c) 2010-2014 Intel Corporation | |
| 7c673cae FG |
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) */ | |
| 21 | static inline uint32_t | |
| 22 | less(uint32_t a, uint32_t b, uint32_t c, uint32_t d) | |
| 23 | { | |
| 24 | return a*d < b*c; | |
| 25 | } | |
| 26 | ||
| 27 | static inline uint32_t | |
| 28 | less_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 */ | |
| 34 | static inline uint32_t | |
| 35 | matches(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 | ||
| 47 | static inline void | |
| 48 | find_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 | ||
| 59 | static inline void | |
| 60 | find_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 | ||
| 71 | static int | |
| 72 | find_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 | ||
| 142 | int 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 | } |