Building Abstractions with Data - Introduction to Data Abstraction - Extended Exercise: Interval Arithmetic - signs of the endpoints
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 2.11解答を求めてみる。
コード
function display(x) {
return console.log(x);
}
function error(x) {
display(x);
return -1;
}
function math_min(...args) {
return Math.min(...args);
}
function math_max(...args) {
return Math.max(...args);
}
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(interval) {
return head(interval);
}
function upper_bound(interval) {
return tail(interval);
}
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);
}
const i1 = make_interval(-2, -1);
const i2 = make_interval(-1, 2);
const i3 = make_interval(1, 2);
display(mul_interval(i1, i1));
display(mul_interval(i1, i2));
display(mul_interval(i1, i3));
display(mul_interval(i2, i1));
display(mul_interval(i2, i2));
display(mul_interval(i2, i3));
display(mul_interval(i3, i1));
display(mul_interval(i3, i2));
display(mul_interval(i3, i3));
入出力結果(Terminal, Zsh)
% node answer2.11.js
[ 1, 4 ]
[ -4, 2 ]
[ -4, -1 ]
[ -4, 2 ]
[ -2, 4 ]
[ -2, 4 ]
[ -4, -1 ]
[ -2, 4 ]
[ 1, 4 ]
%