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/* Copyright 2023 Yann ORLAREY
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include <algorithm>
#include <cmath>
#include <functional>
#include <random>
#include "check.hh"
#include "interval_algebra.hh"
#include "interval_def.hh"
namespace itv {
//------------------------------------------------------------------------------------------
// Interval Cos
// interval Cos(const interval& x);
// void testCos();
static double cosPi(double x)
{
return std::cos(x * M_PI);
}
interval interval_algebra::Cos(const interval& x)
{
if (x.isEmpty()) {
return empty();
}
int precision = exactPrecisionUnary(cos, 0, pow(2, x.lsb()));
if ((precision == INT_MIN) || taylor_lsb) {
precision =
2 * x.lsb() - 1; // if x.lsb() is so small that the automatic computation doesn't work
}
if (x.size() >= 2 * M_PI) {
return {-1, 1, precision};
}
// normalize input interval between 0..2 (corresponding to 0..2PI)
double l = fmod(x.lo(), 2 * M_PI);
if (l < 0) {
l += 2 * M_PI;
}
interval i(l, l + x.size(), x.lsb());
// compute the default boundaries
double a = cos(i.lo());
double b = cos(i.hi());
double lo = std::min(a, b);
double hi = std::max(a, b);
// check if integers are included
if (i.has(0) || i.has(2 * M_PI)) {
hi = 1;
}
if (i.has(1 * M_PI) || i.has(3 * M_PI)) {
lo = -1;
}
double v = 0; // value of the interval at which the finest precision is computed
if ((i.hi() < 1 * M_PI) ||
((i.lo() > 1 * M_PI) &&
i.hi() <
2 * M_PI)) { // if there are no integers in i, i.e i is included in ]0;1[ or ]1;2[
double delta_hi = std::ceil(x.hi() / M_PI) - x.hi() / M_PI;
double delta_lo = x.lo() / M_PI - floor(x.lo() / M_PI);
if (delta_hi < delta_lo) { // if the lowest slope is attained for the higher bound
v = x.hi();
} else { // ... for the lower bound
v = x.lo();
}
}
precision = exactPrecisionUnary(cos, v, pow(2, x.lsb()));
if ((precision == INT_MIN) || taylor_lsb) {
/* cos(x + u) - cos(x) = - u·sin(x) if x != 0
= - u^2/2 · cos(x) = -u^2/2 if x == 0*/
if (v != 0) {
precision = x.lsb() + (int)std::floor(std::log2(std::abs(sin(
v)))); // (int)floor(log2(M_PI*abs(cos(M_PI*v)))) + x.lsb();
} else {
precision = 2 * x.lsb() - 1; //- (int)floor(2*log2(M_PI));
}
}
return {lo, hi, precision};
}
void interval_algebra::testCos()
{
analyzeUnaryMethod(10, 40000, "cos", interval(0, 2 * M_PI, -3), std::cos,
&interval_algebra::Cos);
analyzeUnaryMethod(10, 40000, "cos", interval(0, M_PI, -5), std::cos, &interval_algebra::Cos);
analyzeUnaryMethod(10, 40000, "cos", interval(0, M_PI, -10), std::cos, &interval_algebra::Cos);
analyzeUnaryMethod(10, 40000, "cos", interval(0, M_PI, -15), std::cos, &interval_algebra::Cos);
analyzeUnaryMethod(10, 40000, "cos", interval(0, M_PI, -20), std::cos, &interval_algebra::Cos);
analyzeUnaryMethod(10, 40000, "cos", interval(0, M_PI, -24), std::cos, &interval_algebra::Cos);
}
} // namespace itv
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