197 lines
5.9 KiB
C
197 lines
5.9 KiB
C
/*-
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* BSD LICENSE
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*
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* Copyright(c) 2010-2014 Intel Corporation. All rights reserved.
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* * Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* * Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in
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* the documentation and/or other materials provided with the
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* distribution.
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* * Neither the name of Intel Corporation nor the names of its
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* contributors may be used to endorse or promote products derived
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* from this software without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#include <stdlib.h>
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#include "rte_approx.h"
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/*
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* Based on paper "Approximating Rational Numbers by Fractions" by Michal
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* Forisek forisek@dcs.fmph.uniba.sk
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*
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* Given a rational number alpha with 0 < alpha < 1 and a precision d, the goal
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* is to find positive integers p, q such that alpha - d < p/q < alpha + d, and
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* q is minimal.
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*
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* http://people.ksp.sk/~misof/publications/2007approx.pdf
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*/
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/* fraction comparison: compare (a/b) and (c/d) */
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static inline uint32_t
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less(uint32_t a, uint32_t b, uint32_t c, uint32_t d)
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{
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return (a*d < b*c);
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}
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static inline uint32_t
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less_or_equal(uint32_t a, uint32_t b, uint32_t c, uint32_t d)
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{
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return (a*d <= b*c);
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}
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/* check whether a/b is a valid approximation */
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static inline uint32_t
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matches(uint32_t a, uint32_t b,
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uint32_t alpha_num, uint32_t d_num, uint32_t denum)
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{
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if (less_or_equal(a, b, alpha_num - d_num, denum))
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return 0;
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if (less(a ,b, alpha_num + d_num, denum))
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return 1;
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return 0;
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}
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static inline void
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find_exact_solution_left(uint32_t p_a, uint32_t q_a, uint32_t p_b, uint32_t q_b,
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uint32_t alpha_num, uint32_t d_num, uint32_t denum, uint32_t *p, uint32_t *q)
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{
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uint32_t k_num = denum * p_b - (alpha_num + d_num) * q_b;
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uint32_t k_denum = (alpha_num + d_num) * q_a - denum * p_a;
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uint32_t k = (k_num / k_denum) + 1;
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*p = p_b + k * p_a;
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*q = q_b + k * q_a;
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}
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static inline void
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find_exact_solution_right(uint32_t p_a, uint32_t q_a, uint32_t p_b, uint32_t q_b,
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uint32_t alpha_num, uint32_t d_num, uint32_t denum, uint32_t *p, uint32_t *q)
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{
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uint32_t k_num = - denum * p_b + (alpha_num - d_num) * q_b;
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uint32_t k_denum = - (alpha_num - d_num) * q_a + denum * p_a;
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uint32_t k = (k_num / k_denum) + 1;
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*p = p_b + k * p_a;
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*q = q_b + k * q_a;
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}
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static int
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find_best_rational_approximation(uint32_t alpha_num, uint32_t d_num, uint32_t denum, uint32_t *p, uint32_t *q)
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{
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uint32_t p_a, q_a, p_b, q_b;
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/* check assumptions on the inputs */
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if (!((0 < d_num) && (d_num < alpha_num) && (alpha_num < denum) && (d_num + alpha_num < denum))) {
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return -1;
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}
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/* set initial bounds for the search */
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p_a = 0;
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q_a = 1;
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p_b = 1;
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q_b = 1;
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while (1) {
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uint32_t new_p_a, new_q_a, new_p_b, new_q_b;
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uint32_t x_num, x_denum, x;
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int aa, bb;
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/* compute the number of steps to the left */
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x_num = denum * p_b - alpha_num * q_b;
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x_denum = - denum * p_a + alpha_num * q_a;
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x = (x_num + x_denum - 1) / x_denum; /* x = ceil(x_num / x_denum) */
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/* check whether we have a valid approximation */
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aa = matches(p_b + x * p_a, q_b + x * q_a, alpha_num, d_num, denum);
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bb = matches(p_b + (x-1) * p_a, q_b + (x - 1) * q_a, alpha_num, d_num, denum);
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if (aa || bb) {
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find_exact_solution_left(p_a, q_a, p_b, q_b, alpha_num, d_num, denum, p, q);
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return 0;
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}
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/* update the interval */
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new_p_a = p_b + (x - 1) * p_a ;
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new_q_a = q_b + (x - 1) * q_a;
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new_p_b = p_b + x * p_a ;
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new_q_b = q_b + x * q_a;
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p_a = new_p_a ;
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q_a = new_q_a;
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p_b = new_p_b ;
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q_b = new_q_b;
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/* compute the number of steps to the right */
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x_num = alpha_num * q_b - denum * p_b;
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x_denum = - alpha_num * q_a + denum * p_a;
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x = (x_num + x_denum - 1) / x_denum; /* x = ceil(x_num / x_denum) */
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/* check whether we have a valid approximation */
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aa = matches(p_b + x * p_a, q_b + x * q_a, alpha_num, d_num, denum);
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bb = matches(p_b + (x - 1) * p_a, q_b + (x - 1) * q_a, alpha_num, d_num, denum);
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if (aa || bb) {
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find_exact_solution_right(p_a, q_a, p_b, q_b, alpha_num, d_num, denum, p, q);
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return 0;
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}
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/* update the interval */
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new_p_a = p_b + (x - 1) * p_a;
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new_q_a = q_b + (x - 1) * q_a;
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new_p_b = p_b + x * p_a;
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new_q_b = q_b + x * q_a;
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p_a = new_p_a;
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q_a = new_q_a;
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p_b = new_p_b;
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q_b = new_q_b;
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}
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}
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int rte_approx(double alpha, double d, uint32_t *p, uint32_t *q)
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{
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uint32_t alpha_num, d_num, denum;
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/* Check input arguments */
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if (!((0.0 < d) && (d < alpha) && (alpha < 1.0))) {
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return -1;
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}
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if ((p == NULL) || (q == NULL)) {
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return -2;
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}
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/* Compute alpha_num, d_num and denum */
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denum = 1;
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while (d < 1) {
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alpha *= 10;
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d *= 10;
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denum *= 10;
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}
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alpha_num = (uint32_t) alpha;
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d_num = (uint32_t) d;
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/* Perform approximation */
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return find_best_rational_approximation(alpha_num, d_num, denum, p, q);
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}
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