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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 <cmath>
#include <functional>
#include <random>
#include "check.hh"
#include "interval_algebra.hh"
#include "interval_def.hh"
namespace itv {
//------------------------------------------------------------------------------------------
// Interval Tan
// interval Tan(const interval& x);
// void testTan();
static double tanPi(double x)
{
return std::tan(x * M_PI);
}
interval interval_algebra::Tan(const interval& x)
{
if (x.isEmpty()) {
return empty();
}
if (x.size() >= M_PI) { // spans asymptotes and contains an integer multiple of pi
// std::cout << "Spanning more than one period" << std::endl;
int precision = exactPrecisionUnary(std::tan, 0, std::pow(2, x.lsb()));
if ((precision == INT_MIN) || taylor_lsb) {
precision = x.lsb();
}
return {-HUGE_VAL, HUGE_VAL, precision};
}
// normalize input interval between -PI/2..PI/2
double l = std::fmod(x.lo(), M_PI); // fractional part of x.lo()
interval i(l, l + x.size(), x.lsb());
double v = 0; // value at which the lowest slope is computed: 0 if present
int sign = 1;
if (i.lo() > 0) {
v = i.lo();
} else if (i.hi() < 0) {
v = i.hi();
sign = -1;
}
int precision = exactPrecisionUnary(std::tan, v, sign * std::pow(2, x.lsb()));
if ((precision == INT_MIN) || taylor_lsb) {
precision = std::floor(x.lsb() - 2. * (double)std::log2(std::cos(v)));
}
if (i.has(-M_PI_2) || i.has(M_PI_2)) { // asymptotes at PI/2
return {-HUGE_VAL, HUGE_VAL, precision};
}
double a = std::tan(i.lo());
double b = std::tan(i.hi());
double lo = std::min(a, b);
double hi = std::max(a, b);
return {lo, hi, precision};
}
void interval_algebra::testTan()
{
// analyzeUnaryMethod(20, 20000, "tan", interval(-5, 5, -2), std::tan, &interval_algebra::Tan);
analyzeUnaryMethod(20, 20000, "tan", interval(-5, 5, -5), std::tan, &interval_algebra::Tan);
// analyzeUnaryMethod(20, 20000, "tan", interval(-5, 5, -10), std::tan, &interval_algebra::Tan);
// analyzeUnaryMethod(20, 20000, "tan", interval(-5, 5, -15), std::tan, &interval_algebra::Tan);
}
} // namespace itv
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