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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 inverse
static double inv(double x)
{
if (x == 0) {
return HUGE_VAL;
}
return 1 / x;
}
interval interval_algebra::Inv(const interval& x)
{
if (x.isEmpty()) {
return empty();
}
int sign = signMaxValAbs(x);
double v = maxValAbs(x); // precision is computed at the bound with the highest absolute value
// if v is infinite, this means that images of interval elements will get closer and closer
// but since we're writing the fixed-point numbers on at most 31 bits of MSB
// we can take the max number to be an integer bound
// and this one will give a finite precision, unlike a floating-point infinity
if (std::isinf(v)) {
v = (sign == -1) ? INT_MAX : INT_MIN;
}
int precision = exactPrecisionUnary(inv, v, sign * std::pow(2, x.lsb()));
if ((precision == INT_MIN) || taylor_lsb) {
precision =
std::floor(x.lsb() - 2 * std::log2(std::abs(v))); // 1/(x+u) - 1/x = -u/x^2 + o(u)
}
// precision = std::max(precision, -31);
if ((x.hi() < 0) || (x.lo() >= 0)) {
return {1.0 / x.hi(), 1.0 / x.lo(), precision};
}
if (x.hi() == 0 && x.lo() < 0) {
return {-HUGE_VAL, 1.0 / x.lo(), precision};
// normally, we don't divide by 0
// so the bounds of the image interval are not infinity but 1/ulp
// return {-pow(2, -x.lsb()), 1.0 / x.lo(), precision};
}
if (x.lo() == 0 && x.hi() > 0) {
return {1 / x.hi(), HUGE_VAL, precision};
// return {1 / x.hi(), pow(2, -x.lsb()), precision};
}
return {-HUGE_VAL, HUGE_VAL, precision};
// return {-pow(2, -x.lsb()), pow(2, -x.lsb()), precision};
}
void interval_algebra::testInv()
{
/* check("test algebra Inv", Inv(interval(-16, -4)), interval(-1. / 4., -1. / 16.));
check("test algebra Inv", Inv(interval(4, 16)), interval(1.0 / 16, 0.25));
check("test algebra Inv", Inv(interval(0, 10)), interval(0.1, +HUGE_VAL));
check("test algebra Inv", Inv(interval(-10, 0)), interval(-HUGE_VAL, -0.1));
check("test algebra Inv", Inv(interval(-20, +20)), interval(-HUGE_VAL, +HUGE_VAL));
check("test algebra Inv", Inv(interval(0, 0)), interval(+HUGE_VAL, +HUGE_VAL));*/
analyzeUnaryMethod(10, 2000, "inv", interval(-16, -4, -5), inv, &interval_algebra::Inv);
analyzeUnaryMethod(10, 2000, "inv", interval(4, 16, -5), inv, &interval_algebra::Inv);
analyzeUnaryMethod(10, 2000, "inv", interval(0, 10, -5), inv, &interval_algebra::Inv);
analyzeUnaryMethod(10, 2000, "inv", interval(-10, 0, -5), inv, &interval_algebra::Inv);
analyzeUnaryMethod(10, 2000, "inv", interval(-20, 20, -5), inv, &interval_algebra::Inv);
// analyzeUnaryMethod(10, 2000, "inv", interval(0, 0, -5), inv, &interval_algebra::Inv);
// analyzeUnaryMethod(10, 2000, "inv", interval(-10, 0, -5), inv, &interval_algebra::Inv);
}
} // namespace itv
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