--- /dev/null
+/*-
+ * 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);
+}
Code Review / deb_dpdk.git / blobdiff