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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 addition
static double add(double x, double y)
{
return x + y;
}
static double addint(double x, double y)
{
return (int)x + (int)y;
}
interval interval_algebra::Add(const interval& x, const interval& y)
{
if (x.isEmpty() || y.isEmpty()) {
return empty();
}
if ((x.lsb() >= 0) && (y.lsb() >= 0)) { // if both intervals are integers
// if we're dealing with integers the interval has to wrap around 0
const int xlo = (int)x.lo();
const int xhi = (int)x.hi();
const int ylo = (int)y.lo();
const int yhi = (int)y.hi();
// detect wrapping
/* if (std::abs((double)xhi + (double)yhi) >= (double)INT_MAX
|| std::abs((double)xhi + (double)yhi) <= (double)INT_MIN
|| std::abs((double)xlo + (double)ylo) >= (double)INT_MAX
|| std::abs((double)xlo + (double)ylo) <= (double)INT_MIN)
return {(double) INT_MIN, (double) INT_MAX, std::min(x.lsb(), y.lsb())};*/
double lo = x.lo() + y.lo();
double hi = x.hi() + y.hi();
// if there is a discontinuity by the lower end of integers
if ((lo <= (double)INT_MIN - 1) && (hi >= (double)INT_MIN)) {
return {(double)INT_MIN, (double)INT_MAX, std::min(x.lsb(), y.lsb())};
}
// if there is a discontinuity by the higher end of integers
if ((lo <= (double)INT_MAX) && (hi >= (double)INT_MAX + 1)) {
return {(double)INT_MIN, (double)INT_MAX, std::min(x.lsb(), y.lsb())};
}
// if there is potential wrapping but no discontinuity
return {(double)(xlo + ylo), (double)(xhi + yhi), std::min(x.lsb(), y.lsb())};
}
return {x.lo() + y.lo(), x.hi() + y.hi(),
std::min(x.lsb(), y.lsb())}; // the result of an addition needs to be only as precise
// as the most precise of the operands
}
void interval_algebra::testAdd()
{
std::cout << "Testing add on regular intervals" << std::endl;
check("test algebra Add", Add(interval(0, 100), interval(10, 500)), interval(10, 600));
std::cout << "Testing add on positive intervals" << std::endl;
analyzeBinaryMethod(5, 2000, "add", interval(0, 10, 0), interval(0, 10, 0), add,
&interval_algebra::Add);
analyzeBinaryMethod(5, 2000, "add", interval(0, 10, -10), interval(0, 10, 0), add,
&interval_algebra::Add);
analyzeBinaryMethod(5, 2000, "add", interval(0, 10, 0), interval(0, 10, -10), add,
&interval_algebra::Add);
analyzeBinaryMethod(5, 2000, "add", interval(0, 10, -10), interval(0, 10, -10), add,
&interval_algebra::Add);
std::cout << "Testing add on negative intervals" << std::endl;
analyzeBinaryMethod(5, 2000, "add", interval(-10, 10, -5), interval(-10, 0, -5), add,
&interval_algebra::Add);
analyzeBinaryMethod(5, 2000, "add", interval(-10, 0, -5), interval(-10, 0, -5), add,
&interval_algebra::Add);
std::cout << "Testing add with wrapping" << std::endl;
analyzeBinaryMethod(10, 2000, "add", interval(0, pow(2, 31), 0), interval(0, pow(2, 31), 0),
addint, &interval_algebra::Add);
analyzeBinaryMethod(10, 2000, "add", interval((double)INT_MAX / 2, (double)INT_MAX, 0),
interval((double)INT_MAX / 2, (double)INT_MAX, 0), addint,
&interval_algebra::Add);
analyzeBinaryMethod(10, 2000, "add", interval((double)INT_MIN, (double)INT_MIN / 2, 0),
interval((double)INT_MAX / 2, (double)INT_MAX, 0), addint,
&interval_algebra::Add);
analyzeBinaryMethod(10, 2000, "add", interval((double)INT_MIN, (double)INT_MIN / 2, 0),
interval((double)INT_MIN, (double)INT_MIN / 2, 0), addint,
&interval_algebra::Add);
}
} // namespace itv
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