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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 Atan
// Calculates the principal value of the arc tangent of x; that is the value whose tangent is x.
// The return value is in the range [-pi/2, pi/2].
// interval Atan(const interval& x);
// void testAtan();
interval interval_algebra::Atan(const interval& x)
{
if (x.isEmpty()) {
return empty();
}
double v = maxValAbs(
x); // value at which the min slope is attained, here the bound of highest absolute value
int sign =
signMaxValAbs(x); // whether we compute the difference between f(v) and f(v+ε) or f(v-ε)
int precision = exactPrecisionUnary(atan, v, sign * pow(2, x.lsb()));
if ((precision == INT_MIN) || taylor_lsb) {
precision = floor(x.lsb() - (double)log2(1 + v * v));
}
return {atan(x.lo()), atan(x.hi()), precision};
}
void interval_algebra::testAtan()
{
analyzeUnaryMethod(10, 1000, "atan", interval(-100, 100, 0), atan, &interval_algebra::Atan);
analyzeUnaryMethod(10, 1000, "atan", interval(-100, 100, -5), atan, &interval_algebra::Atan);
analyzeUnaryMethod(10, 1000, "atan", interval(-100, 100, -10), atan, &interval_algebra::Atan);
analyzeUnaryMethod(10, 1000, "atan", interval(-100, 100, -15), atan, &interval_algebra::Atan);
analyzeUnaryMethod(10, 1000, "atan", interval(-100, 100, -20), atan, &interval_algebra::Atan);
}
} // namespace itv
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