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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 <cassert>
#include <functional>
#include <random>
#include "check.hh"
#include "interval_algebra.hh"
#include "interval_def.hh"
namespace itv {
//------------------------------------------------------------------------------------------
// Interval Pow
// interval Pow(const interval& x, const interval& y);
// void testPow();
static const interval domainx = {0, HUGE_VAL, 0};
/**
* @brief Interval elevated to an integer power
*/
static interval ipow(const interval& x, int k)
{
assert(k >= 0);
if (k == 0) {
return interval{1, 1, 0};
}
// explicit expression because passing an anonymous function to exactPrecisionUnary is
// complicated
int precision = x.lsb() * k; // if x contains 0: finest precision is attained in 0
if (!x.hasZero()) {
double v = minValAbs(x);
int sign = signMinValAbs(x);
int p1 = k * (int)log2(abs(v));
int p2 = 0;
double u = pow(2, x.lsb()); // ulp
double delta = abs(pow(1 + sign * u / v, k) - 1);
if (delta == 0) { // in case of u << x
p2 = floor((double)log2(k) + x.lsb() -
(double)log2(abs(v))); // (1 + u/v)^k - 1 ≃ k*u/v if u/v very small
} else {
p2 = floor((double)log2(delta));
}
precision = p1 + p2;
}
if ((k & 1) == 0) {
// k is even
double z0 = std::pow(x.lo(), k);
double z1 = std::pow(x.hi(), k);
return {
x.hasZero()
? 0
: std::min(z0,
z1), // 0 is in the output interval only if it is in the input interval
std::max(z0, z1), precision};
}
// k is odd
return {std::pow(x.lo(), k), std::pow(x.hi(), k), precision};
}
/**
* @brief Interval elevated to an interval power
*/
interval interval_algebra::fPow(const interval& x, const interval& y)
{
if (x.isEmpty() || y.isEmpty()) {
return empty();
}
assert(x.lo() > 0);
// x all positive
return Exp(Mul(y, Log(x)));
}
interval interval_algebra::iPow(const interval& x, const interval& y)
{
if (x.isEmpty() || y.isEmpty()) {
return empty();
}
int y0 = std::max(0, saturatedIntCast(y.lo()));
int y1 = std::max(0, saturatedIntCast(y.hi()));
interval z = ipow(x, y0);
if (y1 > y0) {
// we have more than one integer exponent
z = reunion(z, ipow(x, y0 + 1));
z = reunion(z, ipow(x, y1 - 1));
z = reunion(z, ipow(x, y1));
}
return z;
}
interval interval_algebra::Pow(const interval& x, const interval& y)
{
interval z = empty();
interval xp = intersection(x, interval{nexttoward(0.0, 1.0), HUGE_VAL, 0});
interval xn = intersection(x, interval{-HUGE_VAL, nexttoward(0.0, -1.0), 0});
if (y.hasZero()) {
// x^0 = 1
z = reunion(z, interval(1, 1, 0));
}
if (x.hasZero()) {
// 0^y = 0
z = reunion(z, interval(0, 0, 0));
}
if (!xp.isEmpty()) {
z = reunion(z, fPow(xp, y));
}
if (!xn.isEmpty()) {
z = reunion(z, iPow(xn, y));
}
return z;
}
static double myfPow(double x, double y)
{
return std::pow(x, y);
}
static double myiPow(double x, double y)
{
return std::pow(x, int(y));
}
void interval_algebra::testPow()
{
/* analyzeBinaryMethod(10, 2000000, "iPow^2", interval(-100, 100), interval(2), myiPow,
&interval_algebra::iPow); analyzeBinaryMethod(10, 2000000, "iPow^3", interval(-100, 100),
interval(3), myiPow, &interval_algebra::iPow); analyzeBinaryMethod(10, 2000000, "iPow^2",
interval(-1, 1), interval(2), myiPow, &interval_algebra::iPow); analyzeBinaryMethod(10, 2000000,
"iPow^3", interval(-1, 1), interval(3), myiPow, &interval_algebra::iPow);*/
analyzeBinaryMethod(5, 2000000, "iPow2", interval(-100, 100, 0), interval(0, 200, 0), myiPow,
&interval_algebra::iPow);
analyzeBinaryMethod(5, 2000000, "iPow2", interval(-100, 100, -5), interval(0, 200, 0), myiPow,
&interval_algebra::iPow);
analyzeBinaryMethod(5, 2000000, "iPow2", interval(-100, 100, 0), interval(0, 200, -5), myiPow,
&interval_algebra::iPow);
analyzeBinaryMethod(5, 2000000, "iPow2", interval(-1, 1, 0), interval(1, 3, 0), myiPow,
&interval_algebra::iPow);
analyzeBinaryMethod(5, 2000000, "iPow2", interval(-1, 1, -5), interval(1, 3, 0), myiPow,
&interval_algebra::iPow);
analyzeBinaryMethod(5, 2000000, "iPow2", interval(-1, 1, 0), interval(1, 3, -5), myiPow,
&interval_algebra::iPow);
analyzeBinaryMethod(5, 2000000, "iPow2", interval(-1, 1), interval(1, 10), myiPow,
&interval_algebra::iPow);
analyzeBinaryMethod(5, 2000000, "iPow2", interval(-1, 1), interval(1, 10), myiPow,
&interval_algebra::iPow);
analyzeBinaryMethod(5, 2000000, "iPow2", interval(-1, 1), interval(1, 10), myiPow,
&interval_algebra::iPow);
/* analyzeBinaryMethod(10, 2000000, "fPow2", interval(1, 1000), interval(-10, 10), myfPow,
&interval_algebra::fPow); analyzeBinaryMethod(10, 2000000, "fPow2", interval(0.001, 1),
interval(-10, 10), myfPow, &interval_algebra::fPow); analyzeBinaryMethod(10, 2000000, "fPow2",
interval(0.001, 10), interval(-200, 200), myfPow, &interval_algebra::fPow);*/
}
} // namespace itv
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