99a2dd955f
There is no reason for the DPDK libraries to all have 'librte_' prefix on the directory names. This prefix makes the directory names longer and also makes it awkward to add features referring to individual libraries in the build - should the lib names be specified with or without the prefix. Therefore, we can just remove the library prefix and use the library's unique name as the directory name, i.e. 'eal' rather than 'librte_eal' Signed-off-by: Bruce Richardson <bruce.richardson@intel.com>
321 lines
8.1 KiB
C
321 lines
8.1 KiB
C
/* SPDX-License-Identifier: BSD-3-Clause
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* Copyright(c) 2010-2014 Intel Corporation
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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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/* fraction comparison (64 bit version): compare (a/b) and (c/d) */
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static inline uint64_t
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less_64(uint64_t a, uint64_t b, uint64_t c, uint64_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 uint64_t
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less_or_equal_64(uint64_t a, uint64_t b, uint64_t c, uint64_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 (64 bit version) */
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static inline uint64_t
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matches_64(uint64_t a, uint64_t b,
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uint64_t alpha_num, uint64_t d_num, uint64_t denum)
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{
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if (less_or_equal_64(a, b, alpha_num - d_num, denum))
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return 0;
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if (less_64(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_64(uint64_t p_a, uint64_t q_a, uint64_t p_b, uint64_t q_b,
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uint64_t alpha_num, uint64_t d_num, uint64_t denum, uint64_t *p, uint64_t *q)
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{
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uint64_t k_num = denum * p_b - (alpha_num + d_num) * q_b;
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uint64_t k_denum = (alpha_num + d_num) * q_a - denum * p_a;
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uint64_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_64(uint64_t p_a, uint64_t q_a, uint64_t p_b, uint64_t q_b,
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uint64_t alpha_num, uint64_t d_num, uint64_t denum, uint64_t *p, uint64_t *q)
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{
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uint64_t k_num = -denum * p_b + (alpha_num - d_num) * q_b;
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uint64_t k_denum = -(alpha_num - d_num) * q_a + denum * p_a;
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uint64_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_64(uint64_t alpha_num, uint64_t d_num,
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uint64_t denum, uint64_t *p, uint64_t *q)
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{
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uint64_t p_a, q_a, p_b, q_b;
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/* check assumptions on the inputs */
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if (!((d_num > 0) && (d_num < alpha_num) &&
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(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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uint64_t new_p_a, new_q_a, new_p_b, new_q_b;
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uint64_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_64(p_b + x * p_a, q_b + x * q_a, alpha_num, d_num, denum);
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bb = matches_64(p_b + (x-1) * p_a, q_b + (x - 1) * q_a,
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alpha_num, d_num, denum);
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if (aa || bb) {
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find_exact_solution_left_64(p_a, q_a, p_b, q_b,
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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_64(p_b + x * p_a, q_b + x * q_a, alpha_num, d_num, denum);
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bb = matches_64(p_b + (x - 1) * p_a, q_b + (x - 1) * q_a,
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alpha_num, d_num, denum);
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if (aa || bb) {
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find_exact_solution_right_64(p_a, q_a, p_b, q_b,
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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_64(double alpha, double d, uint64_t *p, uint64_t *q)
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{
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uint64_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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if ((p == NULL) || (q == NULL))
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return -2;
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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 = (uint64_t) alpha;
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d_num = (uint64_t) d;
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/* Perform approximation */
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return find_best_rational_approximation_64(alpha_num, d_num, denum, p, q);
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}
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