計算機科学のブログ

Building Abstractions with Data - Introduction to Data Abstraction - Extended Exercise: Interval Arithmetic - tolerance, uncertain number

Structure and Interpretation of Computer Programs: JavaScript Edition(Harold Abelson(著)、Gerald Jay Sussman(著)、Julie Sussman(著)、The MIT Press)のChapter 2(Building Abstractions with Data)、2.1(Introduction to Data Abstraction)、2.1.4(Extended Exercise: Interval Arithmetic)、Exercise 2.15解答を求めてみる。

コード

function math_abs(x) {
    return Math.abs(x);
}
function display(x) {
    return console.log(x);
}
function pair(x, y) {
    return [x, y];
}
function head(z) {
    return z[0];
}
function tail(z) {
    return z[1];
}
function make_interval(x, y) {
    return pair(x, y);
}
function lower_bound(i) {
    return head(i);
}
function upper_bound(i) {
    return tail(i);
}
function make_center_percent(c, p) {
    const w = math_abs(c) * p / 100;
    return make_interval(c - w, c + w);
}
function center(i) {
    return (lower_bound(i) + upper_bound(i)) / 2;
}
function percent(i) {
    const u = upper_bound(i);
    const m = center(i);
    return (u - m) / m * 100;
}
function add_interval(x, y) {
    return make_interval(
        lower_bound(x) + lower_bound(y),
        upper_bound(x) + upper_bound(y)
    );
}
function mul_interval(x, y) {
    const xl = lower_bound(x);
    const xu = upper_bound(x);
    const yl = lower_bound(y);
    const yu = upper_bound(y);
    if (xl < 0) {
        if (xu < 0) {
            if (yl < 0) {
                if (yu < 0) {
                    return make_interval(xu * yu, xl * yl);
                }
                return make_interval(xl * yu, xl * yl);
            }
            return make_interval(xl * yu, xu * yl);
        }
        if (yl < 0) {
            if (yu < 0) {
                return make_interval(xu * yl, xl * yl);
            }
            const p1 = xl * yu;
            const p2 = xu * yl;
            const p3 = xl * yl;
            const p4 = xu * yu;
            return make_interval(
                math_min(p1, p2),
                math_max(p3, p4)
            )
        }
        return make_interval(xl * yu, xu * yu);
    }
    if (yl < 0) {
        if (yu < 0) {
            return make_interval(xu * yl, xl * yu);
        }
        return make_interval(xu * yl, xu * yu);
    }
    return make_interval(xl * yl, xu * yu);
}
function div_interval(x, y) {
    return mul_interval(
        x,
        make_interval(
            1 / upper_bound(y),
            1 / lower_bound(y)
        )
    );
}
function par1(r1, r2) {
    return div_interval(
        mul_interval(r1, r2),
        add_interval(r1, r2)
    );
}
function par2(r1, r2) {
    const one = make_interval(1, 1);
    return div_interval(
        one,
        add_interval(
            div_interval(one, r1),
            div_interval(one, r2)
        )
    );
}


const interval = make_center_percent(100, 1);
const p1 = par1(interval, interval);
const p2 = par2(interval, interval);

display(interval);
display(p1);
display(par1(p1, p1));
display(p2);
display(par2(p2, p2));

入出力結果(Terminal, Zsh)

% node answer2.15.js
[ 99, 101 ]
[ 48.51980198019802, 51.52020202020203 ]
[ 22.847068643815813, 27.353071404595994 ]
[ 49.49999999999999, 50.5 ]
[ 24.749999999999996, 25.25 ]
%