]>
Commit | Line | Data |
---|---|---|
7c673cae FG |
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 | } |