Perl 6 - Starting with the basics - Iteration(loop, Square Roots, infinite series, pi, Srinivasa Ramanujan)

Think Perl 6

開発環境

• macOS Sierra - Apple (OS)
• Emacs (Text Editor)
• Perl 6 (プログラミング言語)
• Rakudo(コンパイラ、実装)

Think Perl 6: How to Think Like a Computer Scientist (Laurent Rosenfeld(著)、Allen B. Downey(著)、Oreilly & Associates Inc)のPart 1(Starting with the basics)、Chapter 6(Iteration)の Exercises 6-1、6-2.を取り組んでみる。

Exercises 6-1、6-2.

コード(Emacs)

#!/usr/bin/env perl6
# -*- coding: utf-8 -*-

say '1.';

sub my-sqrt($a) {
    my $x = 1;
    while True {
        my $y = ($x + $a / $x) / 2;
        last if $y == $x;
        $x = $y;
    }
    $x;
}

sub test-sqaure-root {
    say 'a mysqrt(a) sqrt(a) diff';
    for 1..10 {
        my $x = my-sqrt($_);
        my $y = sqrt($_);
        say "$_ $x $y ", abs $x - $y;
    }
}

test-sqaure-root();

say '2.';

sub factorial($n) {
    return 1 if $n <= 1;
    $n * factorial($n - 1);
}

sub estimate-pi() {
    my $epsilon = 1e-15;
    my $sum = 0;
    my $k = 0;
    while True {
        my $term = factorial(4 * $k) * (1103 + 26390 * $k) /
        (factorial($k) ** 4 * 396 ** (4 * $k));
        $sum += $term;
        last if $term < $epsilon;
        $k += 1;
    }
    1 / (2 * sqrt(2) / 9801 * $sum);
}

say 'estimate-pi pi diff';
my $pi = estimate-pi;
say "$pi ", pi, ' ', abs $pi - pi;

入出力結果(Terminal, REPL)

$ ./sample1.pl
1.
a mysqrt(a) sqrt(a) diff
1 1 1 0
2 1.41421356237309 1.4142135623731 2.22044604925031e-16
3 1.7320508075688772935 1.73205080756888 0
4 2 2 0
5 2.236067977499790 2.23606797749979 0
6 2.44948974278318 2.44948974278318 0
7 2.64575131106459 2.64575131106459 0
8 2.82842712474619 2.82842712474619 4.44089209850063e-16
9 3.00000000000000000033 3 0
10 3.16227766016838 3.16227766016838 4.44089209850063e-16
2.
estimate-pi pi diff
3.14159265358979 3.14159265358979 0
$