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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 Acos
// interval Acos(const interval& x);
// void testAcos();
static const interval AcosDomain(-1, 1, 0); // this interval needs 0 digits of precision
interval interval_algebra::Acos(const interval& x)
{
interval i = intersection(AcosDomain, x); // TODO: warn about interval violations
if (i.isEmpty()) {
return empty();
}
double v = 0; // value at which the min slope is attained, zero if it is present
int sign = 1; // whether we compute the difference between f(x) and f(x+ε) or f(x-ε), chosing
// the point that lies in the interval
if (!i.has(0)) { // if zero is not present, it's the bound closer to zero
v = minValAbs(i);
sign = signMinValAbs(i);
}
int precision = exactPrecisionUnary(acos, v, sign * pow(2, i.lsb()));
if ((precision == INT_MIN) || taylor_lsb) {
precision = floor(i.lsb() - (double)log2(1 - v * v) / 2);
}
return {acos(i.hi()), acos(i.lo()), precision};
}
void interval_algebra::testAcos()
{
analyzeUnaryMethod(10, 1000, "acos", interval(-1, 1, -1), acos, &interval_algebra::Acos);
analyzeUnaryMethod(10, 1000, "acos", interval(-1, 1, -5), acos, &interval_algebra::Acos);
analyzeUnaryMethod(10, 1000, "acos", interval(-1, 1, -10), acos, &interval_algebra::Acos);
analyzeUnaryMethod(10, 1000, "acos", interval(-1, 1, -15), acos, &interval_algebra::Acos);
analyzeUnaryMethod(10, 1000, "acos", interval(-1, 1, -20), acos, &interval_algebra::Acos);
// very fine input precision
/* analyzeUnaryMethod(10, 1000, "acos", interval(-1, 1, -100), acos, &interval_algebra::Acos);
analyzeUnaryMethod(10, 1000, "acos", interval(-1, -0.85, -100), acos, &interval_algebra::Acos);
analyzeUnaryMethod(10, 1000, "acos", interval(0.85, 1, -100), acos, &interval_algebra::Acos);
// out of bounds input interval
analyzeUnaryMethod(10, 1000, "acos", interval(-2, 2, -20), acos, &interval_algebra::Acos);*/
}
} // namespace itv
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