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 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167``` ```/* SPDX-License-Identifier: BSD-3-Clause * Copyright(c) 2010-2014 Intel Corporation */ #include #include "rte_approx.h" /* * Based on paper "Approximating Rational Numbers by Fractions" by Michal * Forisek forisek@dcs.fmph.uniba.sk * * Given a rational number alpha with 0 < alpha < 1 and a precision d, the goal * is to find positive integers p, q such that alpha - d < p/q < alpha + d, and * q is minimal. * * http://people.ksp.sk/~misof/publications/2007approx.pdf */ /* fraction comparison: compare (a/b) and (c/d) */ static inline uint32_t less(uint32_t a, uint32_t b, uint32_t c, uint32_t d) { return a*d < b*c; } static inline uint32_t less_or_equal(uint32_t a, uint32_t b, uint32_t c, uint32_t d) { return a*d <= b*c; } /* check whether a/b is a valid approximation */ static inline uint32_t matches(uint32_t a, uint32_t b, uint32_t alpha_num, uint32_t d_num, uint32_t denum) { if (less_or_equal(a, b, alpha_num - d_num, denum)) return 0; if (less(a ,b, alpha_num + d_num, denum)) return 1; return 0; } static inline void find_exact_solution_left(uint32_t p_a, uint32_t q_a, uint32_t p_b, uint32_t q_b, uint32_t alpha_num, uint32_t d_num, uint32_t denum, uint32_t *p, uint32_t *q) { uint32_t k_num = denum * p_b - (alpha_num + d_num) * q_b; uint32_t k_denum = (alpha_num + d_num) * q_a - denum * p_a; uint32_t k = (k_num / k_denum) + 1; *p = p_b + k * p_a; *q = q_b + k * q_a; } static inline void find_exact_solution_right(uint32_t p_a, uint32_t q_a, uint32_t p_b, uint32_t q_b, uint32_t alpha_num, uint32_t d_num, uint32_t denum, uint32_t *p, uint32_t *q) { uint32_t k_num = - denum * p_b + (alpha_num - d_num) * q_b; uint32_t k_denum = - (alpha_num - d_num) * q_a + denum * p_a; uint32_t k = (k_num / k_denum) + 1; *p = p_b + k * p_a; *q = q_b + k * q_a; } static int find_best_rational_approximation(uint32_t alpha_num, uint32_t d_num, uint32_t denum, uint32_t *p, uint32_t *q) { uint32_t p_a, q_a, p_b, q_b; /* check assumptions on the inputs */ if (!((0 < d_num) && (d_num < alpha_num) && (alpha_num < denum) && (d_num + alpha_num < denum))) { return -1; } /* set initial bounds for the search */ p_a = 0; q_a = 1; p_b = 1; q_b = 1; while (1) { uint32_t new_p_a, new_q_a, new_p_b, new_q_b; uint32_t x_num, x_denum, x; int aa, bb; /* compute the number of steps to the left */ x_num = denum * p_b - alpha_num * q_b; x_denum = - denum * p_a + alpha_num * q_a; x = (x_num + x_denum - 1) / x_denum; /* x = ceil(x_num / x_denum) */ /* check whether we have a valid approximation */ aa = matches(p_b + x * p_a, q_b + x * q_a, alpha_num, d_num, denum); bb = matches(p_b + (x-1) * p_a, q_b + (x - 1) * q_a, alpha_num, d_num, denum); if (aa || bb) { find_exact_solution_left(p_a, q_a, p_b, q_b, alpha_num, d_num, denum, p, q); return 0; } /* update the interval */ new_p_a = p_b + (x - 1) * p_a ; new_q_a = q_b + (x - 1) * q_a; new_p_b = p_b + x * p_a ; new_q_b = q_b + x * q_a; p_a = new_p_a ; q_a = new_q_a; p_b = new_p_b ; q_b = new_q_b; /* compute the number of steps to the right */ x_num = alpha_num * q_b - denum * p_b; x_denum = - alpha_num * q_a + denum * p_a; x = (x_num + x_denum - 1) / x_denum; /* x = ceil(x_num / x_denum) */ /* check whether we have a valid approximation */ aa = matches(p_b + x * p_a, q_b + x * q_a, alpha_num, d_num, denum); bb = matches(p_b + (x - 1) * p_a, q_b + (x - 1) * q_a, alpha_num, d_num, denum); if (aa || bb) { find_exact_solution_right(p_a, q_a, p_b, q_b, alpha_num, d_num, denum, p, q); return 0; } /* update the interval */ new_p_a = p_b + (x - 1) * p_a; new_q_a = q_b + (x - 1) * q_a; new_p_b = p_b + x * p_a; new_q_b = q_b + x * q_a; p_a = new_p_a; q_a = new_q_a; p_b = new_p_b; q_b = new_q_b; } } int rte_approx(double alpha, double d, uint32_t *p, uint32_t *q) { uint32_t alpha_num, d_num, denum; /* Check input arguments */ if (!((0.0 < d) && (d < alpha) && (alpha < 1.0))) { return -1; } if ((p == NULL) || (q == NULL)) { return -2; } /* Compute alpha_num, d_num and denum */ denum = 1; while (d < 1) { alpha *= 10; d *= 10; denum *= 10; } alpha_num = (uint32_t) alpha; d_num = (uint32_t) d; /* Perform approximation */ return find_best_rational_approximation(alpha_num, d_num, denum, p, q); } ```