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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 Exp
// interval Exp(const interval& x);
// void testExp();
interval interval_algebra::Exp(const interval& x)
{
if (x.isEmpty()) {
return empty();
}
// lowest slope is attained at the lowest boundary
// int precision = exactPrecisionUnary(exp, x.lo(), pow(2, x.lsb()));
double delta = exp(pow(2, x.lsb())) - 1;
int p1 = floor(x.lo() * log2(M_E)); // log2(exp(x.lo()))
int p2 = 0;
if (delta == 0) { // avoid absorption of 2^l into v
p2 = x.lsb(); // exp(v) - 1 ≃ v if v very small, so delta2 ≃ pow(2, x.lsb())
} else {
p2 = floor((double)log2(delta));
}
int precision = p1 + p2;
return {exp(x.lo()), exp(x.hi()), precision};
}
void interval_algebra::testExp()
{
analyzeUnaryMethod(10, 100000, "exp", interval(-100, 10, 0), exp, &interval_algebra::Exp);
analyzeUnaryMethod(10, 100000, "exp", interval(-100, 10, -3), exp, &interval_algebra::Exp);
analyzeUnaryMethod(10, 100000, "exp", interval(-100, 10, -6), exp, &interval_algebra::Exp);
analyzeUnaryMethod(10, 100000, "exp", interval(-100, 10, -9), exp, &interval_algebra::Exp);
analyzeUnaryMethod(10, 100000, "exp", interval(-100, 10, -12), exp, &interval_algebra::Exp);
analyzeUnaryMethod(10, 100000, "exp", interval(-100, 10, -15), exp, &interval_algebra::Exp);
analyzeUnaryMethod(10, 100000, "exp", interval(-100, 10, -18), exp, &interval_algebra::Exp);
}
} // namespace itv
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