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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 Sin
// interval Sin(const interval& x);
// void testSin();
static double sinPi(double x)
{
return std::sin(x * M_PI);
}
interval interval_algebra::Sin(const interval& x)
{
if (x.isEmpty()) {
return empty();
}
int precision = exactPrecisionUnary(sin, 0.5, std::pow(2, x.lsb()));
if ((precision == INT_MIN) || taylor_lsb) {
precision =
2 * x.lsb() - 1; // if x.lsb() is so small that the automatic computation doesn't work
}
if (x.size() >= 2 * M_PI) {
return {-1, 1, precision};
}
// normalize input interval between 0..2
double l = std::fmod(x.lo(), 2 * M_PI);
if (l < 0) {
l += 2 * M_PI;
}
interval i(l, l + x.size(), x.lsb());
// compute the default boundaries
double a = std::sin(i.lo());
double b = std::sin(i.hi());
double lo = std::min(a, b);
double hi = std::max(a, b);
// check if integers are included
if (i.has(M_PI_2) || i.has(5 * M_PI_2)) {
hi = 1;
}
if (i.has(3 * M_PI_2) || i.has(7 * M_PI_2)) {
lo = -1;
}
double v = M_PI_2; // value of the interval at which the finest precision is computed
// defaults at 0.5, interchangeable with any other half-integer
// precision if we don't hit the half integers
if (i.hi() < M_PI_2) {
v = x.hi();
} else if (((i.lo() > M_PI_2) && (i.hi() < 3 * M_PI_2)) ||
((i.lo() > 3 * M_PI_2) && (i.hi() < 2.5 * M_PI))) {
double delta_hi = std::ceil(i.hi() / M_PI + 0.5) - i.hi() / M_PI;
double delta_lo = i.lo() / M_PI - std::floor(i.lo() / M_PI - 0.5);
if (delta_lo > delta_hi) { // if i.hi is closer to its higher half-integer than i.lo() to
// its lower half-integer
v = x.hi();
} else {
v = x.lo();
}
}
precision = exactPrecisionUnary(std::sin, v, std::pow(2, x.lsb()));
if ((precision == INT_MIN) || taylor_lsb) {
if (v != 0.5 * M_PI) {
precision = x.lsb() + (int)std::floor(std::log2(std::abs(std::cos(
v)))); // (int)floor(log2(M_PI*cos(M_PI*v))) + x.lsb();
} else {
precision = 2 * x.lsb() - 1; // - (int)floor(2*log2(M_PI));
}
}
return {lo, hi, precision};
}
void interval_algebra::testSin()
{
// analyzeUnaryMethod(5, 20000, "sin", interval(-1, 1, -3), std::sin, &interval_algebra::Sin);
analyzeUnaryMethod(10, 40000, "sin", interval(0, 2 * M_PI, -3), std::sin,
&interval_algebra::Sin);
analyzeUnaryMethod(10, 40000, "sin", interval(0, 2 * M_PI, -5), std::sin,
&interval_algebra::Sin);
analyzeUnaryMethod(10, 40000, "sin", interval(0, 2 * M_PI, -10), std::sin,
&interval_algebra::Sin);
analyzeUnaryMethod(10, 40000, "sin", interval(0, 2 * M_PI, -15), std::sin,
&interval_algebra::Sin);
analyzeUnaryMethod(10, 40000, "sin", interval(0, 2 * M_PI, -20), std::sin,
&interval_algebra::Sin);
analyzeUnaryMethod(10, 40000, "sin", interval(0, 2 * M_PI, -24), std::sin,
&interval_algebra::Sin);
}
} // namespace itv
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