- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
- * * 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
+ * * 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
- * * Neither the name of Intel Corporation nor the names of its
- * contributors may be used to endorse or promote products derived
+ * * Neither the name of Intel Corporation nor the names of its
+ * contributors may be used to endorse or promote products derived
- *
- * 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
+ *
+ * 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
* Forisek forisek@dcs.fmph.uniba.sk
*
* Given a rational number alpha with 0 < alpha < 1 and a precision d, the goal
* Forisek forisek@dcs.fmph.uniba.sk
*
* Given a rational number alpha with 0 < alpha < 1 and a precision d, the goal
less(uint32_t a, uint32_t b, uint32_t c, uint32_t d)
{
less(uint32_t a, uint32_t b, uint32_t c, uint32_t d)
{
}
static inline uint32_t
less_or_equal(uint32_t a, uint32_t b, uint32_t c, uint32_t d)
{
}
static inline uint32_t
less_or_equal(uint32_t a, uint32_t b, uint32_t c, uint32_t d)
{
uint32_t alpha_num, uint32_t d_num, uint32_t denum)
{
if (less_or_equal(a, b, alpha_num - d_num, denum))
uint32_t alpha_num, uint32_t d_num, uint32_t denum)
{
if (less_or_equal(a, b, alpha_num - d_num, denum))
if (less(a ,b, alpha_num + d_num, denum))
return 1;
if (less(a ,b, alpha_num + d_num, denum))
return 1;
-static inline void
-find_exact_solution_left(uint32_t p_a, uint32_t q_a, uint32_t p_b, uint32_t q_b,
+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;
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,
*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 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;
{
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;
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;
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;
}
/* check assumptions on the inputs */
if (!((0 < d_num) && (d_num < alpha_num) && (alpha_num < denum) && (d_num + alpha_num < denum))) {
return -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;
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) */
/* 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);
/* 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);
find_exact_solution_left(p_a, q_a, p_b, q_b, alpha_num, d_num, denum, p, q);
return 0;
}
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;
/* update the interval */
new_p_a = p_b + (x - 1) * p_a ;
new_q_a = q_b + (x - 1) * q_a;
find_exact_solution_right(p_a, q_a, p_b, q_b, alpha_num, d_num, denum, p, q);
return 0;
}
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;
/* 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;
int rte_approx(double alpha, double d, uint32_t *p, uint32_t *q)
{
uint32_t alpha_num, d_num, denum;
int rte_approx(double alpha, double d, uint32_t *p, uint32_t *q)
{
uint32_t alpha_num, d_num, denum;
- return find_best_rational_approximation(alpha_num, d_num, denum, p, q);
+ return find_best_rational_approximation(alpha_num, d_num, denum, p, q);