Building Abstractions with Data - Introduction to Data Abstraction - Extended Exercise: Interval Arithmetic - division, error
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 2.10の解答を求めてみる。
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 p1 = lower_bound(x) * lower_bound(y);
const p2 = lower_bound(x) * upper_bound(y);
const p3 = upper_bound(x) * lower_bound(y);
const p4 = upper_bound(x) * upper_bound(y);
return make_interval(
math_min(p1, p2, p3, p4),
math_max(p1, p2, p3, p4)
)
}
function div_interval(x, y) {
const p1 = upper_bound(y);
const p2 = lower_bound(y);
return p1 * p2 <= 0 ?
error("spans zero error") :
mul_interval(
x,
make_interval(
1 / p1,
1 / p2
)
);
}
const x = make_interval(1, 2);
const y = make_interval(-1, 2);
display(x);
display(y);
display(mul_interval(x, y));
display(div_interval(x, y));
入出力結果(Terminal, Zsh)
% node answer2.10.js
[ 1, 2 ]
[ -1, 2 ]
[ -2, 4 ]
spans zero error
-1
%