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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 Sqrt
// interval Sqrt(const interval& x);
// void testSqrt();
static const interval SqrtDomain(0, HUGE_VAL, 0);
interval interval_algebra::Sqrt(const interval& x)
{
interval i = intersection(SqrtDomain, x);
if (i.isEmpty()) {
return empty();
}
/* if (i.lo() < 0) {
return {}; // sqrt of negative numbers
}*/
// lowest slope at the highest bound of the interval
int precision = exactPrecisionUnary(sqrt, i.hi(), -pow(2, i.lsb()));
if ((precision == INT_MIN) || taylor_lsb) {
if (i.hi() == 0) {
precision = floor(i.lsb() / 2);
} else {
precision = floor(i.lsb() - log2(i.hi()) - 1); // sqrt(x+u) - sqrt(x) = 1/2 u/sqrt(x)
}
}
return {sqrt(i.lo()), sqrt(i.hi()), precision};
}
void interval_algebra::testSqrt()
{
// analyzeUnaryMethod(10, 1000, "sqrt", interval(0, 10), sqrt, &interval_algebra::Sqrt);
analyzeUnaryMethod(10, 1000, "sqrt", interval(0, 10, 0), sqrt, &interval_algebra::Sqrt);
analyzeUnaryMethod(10, 1000, "sqrt", interval(0, 10, -5), sqrt, &interval_algebra::Sqrt);
analyzeUnaryMethod(10, 1000, "sqrt", interval(0, 10, -10), sqrt, &interval_algebra::Sqrt);
analyzeUnaryMethod(10, 1000, "sqrt", interval(0, 10, -15), sqrt, &interval_algebra::Sqrt);
analyzeUnaryMethod(10, 1000, "sqrt", interval(0, 10, -20), sqrt, &interval_algebra::Sqrt);
}
} // namespace itv
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