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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 <functional>
#include <random>
#include "check.hh"
#include "interval_algebra.hh"
#include "interval_def.hh"
namespace itv {
//------------------------------------------------------------------------------------------
// Interval Cosh
// interval Cosh(const interval& x);
// void testCosh();
interval interval_algebra::Cosh(const interval& x)
{
if (x.isEmpty()) {
return empty();
}
double v = 0; // absolute lowest slope is at zero
if (x.hasZero()) {
int precision = exactPrecisionUnary(std::cosh, v, std::pow(2, x.lsb()));
if ((precision == INT_MIN) || taylor_lsb) {
precision = std::floor(2 * x.lsb() - 1); // cosh(u) - cosh(0) = u^2/2 + o(u^2)
}
return {1, std::max(std::cosh(x.lo()), std::cosh(x.hi())), precision};
}
int sign = 1;
// if zero is not included, lowest slope is at the boundary of lowest absolute value
if (x.lo() > 0) { // if the interval is entirely in the positives,
v = x.lo();
} else if (x.hi() < 0) { // if the interval is entirely in the negatives
v = x.hi();
sign = -1;
}
int precision = exactPrecisionUnary(cosh, v, sign * std::pow(2, x.lsb()));
if ((precision == INT_MIN) || taylor_lsb) {
precision = std::floor(
x.lsb() + std::log2(std::abs(sinh(v)))); // cosh(x+u) - cosh(x) = u sinh(x) + o(u)
}
return {std::min(std::cosh(x.lo()), std::cosh(x.hi())),
std::max(std::cosh(x.lo()), std::cosh(x.hi())), precision};
}
void interval_algebra::testCosh()
{
analyzeUnaryMethod(10, 1000, "cosh", interval(-10, 10, 0), std::cosh, &interval_algebra::Cosh);
analyzeUnaryMethod(10, 1000, "cosh", interval(-10, 10, -5), std::cosh, &interval_algebra::Cosh);
analyzeUnaryMethod(10, 1000, "cosh", interval(-10, 10, -10), std::cosh,
&interval_algebra::Cosh);
analyzeUnaryMethod(10, 1000, "cosh", interval(-10, 10, -15), std::cosh,
&interval_algebra::Cosh);
}
} // namespace itv
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