boost::numeric::interval<int>(2): C++ Boost 区間演算ライブラリ 数学関数 ref: http://qiita.com/items/abcf31a7b1787604a4f4

output-for-test-interval-fun-math-0.txt

a         = [-1,3]
b         = [2,4]
min(a, b) = [-1,3]
max(a, b) = [2,4]
abs(a)    = [0,3]

output-for-test-interval-fun-math-1.txt

--- interval power functions ---
a              = [-1,3]
square(a)      = [0,9]
pow(a, 3)      = [-1,27]
b              = [2,4]
nth_root(b, 2) = [1.41421,2]
--- checking inclusion property ---
c = [-2,2.66667]
 k       d = c^k         e = d^(1/k)     inclusion
1       [-2,2.66667]    [-2,2.66667]        c  is a subset of e.
2       [0,7.11111]     [0,2.66667]     abs(c) is a subset of e.
3       [-8,18.963]     [-2,2.66667]        c  is a subset of e.
4       [0,50.5679]     [0,2.66667]     abs(c) is a subset of e.
5       [-32,134.848]   [-2,2.66667]        c  is a subset of e.

output-for-test-interval-fun-math-2.txt

a     = [1,2]
b     = [-3,4]
a / b = [-inf,inf]
negative part of a / b = [-inf,-0.333333]
positive part of a / b = [0.25,inf]

test-interval-fun-math-0.cpp

#include <iostream>
#include <boost/numeric/interval.hpp>
#include <boost/numeric/interval/io.hpp>

int main () {
    typedef double R;
    typedef boost::numeric::interval<R> IR;
    using std::cout;
    using std::endl;
    const IR a(-1, 3);
    const IR b(2, 4);
    cout << "a         = " << a << endl;
    cout << "b         = " << b << endl;
    cout << "min(a, b) = " << min(a, b) << endl;
    cout << "max(a, b) = " << max(a, b) << endl;
    cout << "abs(a)    = " << abs(a) << endl;
    return 0;
}

test-interval-fun-math-1.cpp

#include <iostream>
#include <boost/numeric/interval.hpp>
#include <boost/numeric/interval/io.hpp>

int main () {
    typedef double R;
    typedef boost::numeric::interval<R> IR;
    using std::cout;
    using std::endl;
    cout << "--- interval power functions ---" << endl;
    const IR a(-1, 3);
    cout << "a              = " << a << endl;
    cout << "square(a)      = " << square(a) << endl;
    cout << "pow(a, 3)      = " << pow(a, 3) << endl;
    const IR b(2, 4);
    cout << "b              = " << b << endl;
    cout << "nth_root(b, 2) = " << nth_root(b, 2) << endl;
    cout << "--- checking inclusion property ---" << endl;
    const IR c = IR(-6, 8) / 3.0;
    cout << "c = " << c << endl; 
    cout << " k \t d = c^k \t e = d^(1/k) \t inclusion" << endl;
    for ( int k = 1; k <= 5; k++ ) {
        const IR d = pow(c, k);
        const IR e = nth_root(d, k);
        cout << k << '\t' << d << '\t' << e << '\t';
        if (k % 2 == 1 && subset(c, e)) {
            cout << "    c  is a subset of e." << endl;
        } else if (k % 2 == 0 && subset(abs(c), e)) {
            cout << "abs(c) is a subset of e." << endl;
        } else {
            cout << endl;
        }
    }
    return 0;
}

test-interval-fun-math-2.cpp

#include <iostream>
#include <boost/numeric/interval.hpp>
#include <boost/numeric/interval/io.hpp>

int main () {
    typedef double R;
    typedef boost::numeric::interval<R> IR;
    using std::cout;
    using std::endl;
    const IR a(1, 2);
    const IR b(-3, 4);
    cout << "a     = " << a << endl;
    cout << "b     = " << b << endl;
    cout << "a / b = " << a / b << endl;
    bool parted = false;
    const IR c = division_part1(a, b, parted);
    const IR d = division_part2(a, b, parted);
    if (parted) {
        cout << "negative part of a / b = " << c << endl;
        cout << "positive part of a / b = " << d << endl;
    }
    return 0;
}

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