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Diffstat (limited to 'lib/librte_sched/rte_approx.c')
| -rw-r--r-- | lib/librte_sched/rte_approx.c | 196 |
1 files changed, 196 insertions, 0 deletions
diff --git a/lib/librte_sched/rte_approx.c b/lib/librte_sched/rte_approx.c new file mode 100644 index 00000000..739f37d7 --- /dev/null +++ b/lib/librte_sched/rte_approx.c @@ -0,0 +1,196 @@ +/*- + * BSD LICENSE + * + * Copyright(c) 2010-2014 Intel Corporation. All rights reserved. + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * * Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * * Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * * Neither the name of Intel Corporation nor the names of its + * contributors may be used to endorse or promote products derived + * from this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR + * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT + * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT + * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE + * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include <stdlib.h> + +#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); +} |