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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 Asin
// Calculates the principal value of the arc sine of x; that is the value whose sine is x.
// the return value is in the range [-pi/2, pi/2].
// interval Asin(const interval& x);
// void testAsin();
static const interval domain(-1, 1, 0); // this interval needs 0 digits of precision
interval interval_algebra::Asin(const interval& x)
{
interval i = intersection(domain, x);
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(v) and f(v+ε) or f(v-ε)
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(asin, v, sign * pow(2, i.lsb()));
if ((precision == INT_MIN) || taylor_lsb) {
precision = floor(x.lsb() - (double)log2(1 - v * v) / 2);
}
return {asin(i.lo()), asin(i.hi()), precision};
}
void interval_algebra::testAsin()
{
analyzeUnaryMethod(10, 1000, "asin", interval(-1, 1, 0), asin, &interval_algebra::Asin);
analyzeUnaryMethod(10, 1000, "asin", interval(-1, 1, -5), asin, &interval_algebra::Asin);
analyzeUnaryMethod(10, 1000, "asin", interval(-1, 1, -10), asin, &interval_algebra::Asin);
analyzeUnaryMethod(10, 1000, "asin", interval(-1, 1, -15), asin, &interval_algebra::Asin);
analyzeUnaryMethod(10, 1000, "asin", interval(-1, 1, -20), asin, &interval_algebra::Asin);
/* analyzeUnaryMethod(10, 1000, "asin", interval(-1, 1, 30), asin, &interval_algebra::Asin);
analyzeUnaryMethod(10, 1000, "asin", interval(-1, 1, -35), asin, &interval_algebra::Asin);
analyzeUnaryMethod(10, 1000, "asin", interval(-1, 1, -40), asin, &interval_algebra::Asin);
analyzeUnaryMethod(10, 1000, "asin", interval(-1, 1, -45), asin, &interval_algebra::Asin);
analyzeUnaryMethod(10, 1000, "asin", interval(-1, 1, -50), asin, &interval_algebra::Asin);*/
}
} // namespace itv
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