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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 <iostream>
#include <random>
#include <utility>
#include "check.hh"
#include "interval_algebra.hh"
#include "interval_def.hh"
namespace itv {
// union of two floating point intervals
inline interval operator+(const interval& a, const interval& b)
{
if (a.isEmpty()) {
return b;
}
if (b.isEmpty()) {
return a;
}
return interval{std::min(a.lo(), b.lo()), std::max(a.hi(), b.hi()), std::min(a.lsb(), b.lsb())};
}
// negation of an interval
interval neg(interval x)
{
return interval{-x.hi(), -x.lo(), x.lsb()};
}
// join of two intervals
interval join(interval x, interval y)
{
if (x.isEmpty()) {
return y;
}
if (y.isEmpty()) {
return x;
}
return interval{std::min(x.lo(), y.lo()), std::max(x.hi(), y.hi()), std::min(x.lsb(), y.lsb())};
}
// split an interval into two intervals, negative and positive (or empty)
std::pair<interval, interval> split(interval x)
{
if (x.lo() >= 0) {
return {empty(), x};
}
if (x.hi() < 0) {
return {x, empty()};
}
return {interval{x.lo(), std::nexttoward(0.0, -1.0), x.lsb()}, interval{0.0, x.hi(), x.lsb()}};
}
// split an interval into two intervals, negative and positive (or empty)
std::pair<interval, interval> splitnz(interval x)
{
if (x.lo() >= 0) {
return {empty(), x};
}
if (x.hi() < 0) {
return {x, empty()};
}
return {interval{x.lo(), std::nexttoward(0.0, -1.0), x.lsb()},
interval{std::nexttoward(0.0, 1.0), x.hi(), x.lsb()}};
}
//------------------------------------------------------------------------------------------
// modulo function on intervals based on https://github.com/orlarey/interval-mod
//------------------------------------------------------------------------------------------
/**
* @brief resulting interval of fmod(x,y) for interval x and y
*
* @param x the interval we compute the modulo of
* @param y the divisor
* @return interval the resulting interval
*/
interval positiveFMod(const interval& x, const interval& y)
{
if (x.isEmpty() || y.isEmpty()) {
return empty();
}
int n = int(x.lo() / y.hi());
// std::cout << "n = " << n << std::endl;
int precision = std::min(x.lsb(), y.lsb());
// n == 0 obeys the same rules as the general case
/* if (n == 0) {
// prop: x.lo() < y.hi()
if (y.hi() > x.hi()) {
if (y.lo() > x.hi()) {
// prop: x < y => fmod(x,y) = x
return x;
}
// prop: y.lo() <= x.hi() < y.hi()
return interval{0.0, x.hi(), precision};
}
// prop: x.lo() < y.hi() <= x.hi()
return interval{0.0, nexttoward(y.hi(), 0), precision};
}*/
// prop: n > 0 && y.hi() <= x.lo()
double hi = x.hi() / (n + 1);
if (y.hi() <= hi) {
return interval{0.0, std::nexttoward(y.hi(), 0), precision};
}
// prop: y.hi() > hi
if (y.lo() <= hi) {
return interval{0.0, std::nexttoward(hi, 0), precision};
}
// prop : y.lo() > hi
// in that case, the quotient between x and y is constant and equal
return interval{x.lo() - n * y.hi(), x.hi() - n * y.lo(), precision};
}
// fmod of two signed intervals
interval interval_algebra::Mod(const interval& x, const interval& y)
{
auto [xn, xp] = split(x); // slipts x into a negative and a positive interval
auto [yn, yp] = splitnz(y); // slipts y into a negative and a positive interval (zero excluded)
// compute the 4 possible fmod of the 4 possible combinations of xn, xp, yn, yp
auto xnyn = neg(positiveFMod(neg(xn), neg(yn)));
auto xnyp = neg(positiveFMod(neg(xn), yp));
auto xpyn = positiveFMod(xp, neg(yn));
auto xpyp = positiveFMod(xp, yp);
// Make sure these 4 values are in the resulting interval
auto bb = singleton(std::fmod(x.hi(), y.hi())) + singleton(std::fmod(x.lo(), y.hi())) +
singleton(std::fmod(x.hi(), y.lo())) + singleton(std::fmod(x.lo(), y.lo()));
bb = interval{bb.lo(), bb.hi(), std::min(x.lsb(), y.lsb())};
// combine all the intervals
return bb + xnyn + xnyp + xpyn + xpyp;
}
void interval_algebra::testMod()
{
// check("test algebra Mod", Mod(interval(-100, 100), 1.0), interval(nextafter(-1.0, 0.0),
// nextafter(1.0, 0.0))); check("test algebra Mod", Mod(interval(0, 100), 2), interval(0,
// nextafter(2.0, 0))); check("test algebra Mod", Mod(interval(0, 100), -1.0), interval(0,
// nextafter(1.0, 0)));
/* check("test algebra Mod", Mod(interval(5, 7), interval(4, 4.5)), interval(0.5, 3));
check("test algebra Mod", Mod(interval(5, 7), interval(8, 10)), interval(5, 7));
check("test algebra Mod", Mod(interval(-7, 7), interval(8, 10)), interval(-7, 7));
check("test algebra Mod", Mod(interval(0, 100), interval(7, 7)), interval(0, nextafter(7.0,
0.0)));*/
// analyzeBinaryMethod(10, 10000, "mod", interval(0, 10, -5), interval(0, 10, -5), fmod,
// &interval_algebra::Mod);
analyzeBinaryMethod(10, 10000, "mod", interval(0, 10, 1), interval(0, 10, 0), std::fmod,
&interval_algebra::Mod);
/* analyzeBinaryMethod(10, 10000, "mod", interval(0, 10, 0), interval(0, 10, 0), fmod,
&interval_algebra::Mod); analyzeBinaryMethod(10, 10000, "mod", interval(0, 10, 0), interval(0,
10, -5), fmod, &interval_algebra::Mod);
analyzeBinaryMethod(10, 100000000, "mod", interval(3, 4, -3), interval(1.2, 1.4, -3), fmod,
&interval_algebra::Mod);*/
// analyzeBinaryMethod(10, 10000, "mod", interval(-10, 10, -5), interval(-10, 10, -5), fmod,
// &interval_algebra::Mod);
}
} // namespace itv
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