Perl 6 - python - ruby - c - 式の展開の注意点 - 浮動小数点数、数値計算、正確性、誤差 - ( @h_okumura 、 @shora_kujira16 ) Haruhiko Okumura さん、しょラーさんのツイートより

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)

追記: 2017/04/24

浮動小数点数の取扱いの注意点についてを perl 6、perl 5、python (python3)、ruby(2.4)、cでも試して結果を確認してみた。

@kagamihr @mkamimura 何が起きてるんだ？面白そう？と思ってコード眺めてみましたが、perl版のバグですね。間違えてfを2回呼んで比較してる。直せば他の言語と同じ結果っぽいです。
— kashi (@mkashi) 2017年4月28日

~~Perl 5と~~ Perl 6では、少なくとも試した範囲だと誤差は出ないみたい。他の言語とは浮動小数点数の実装方法が違ったりするからかなぁ。(実数について、有理数と無理数の実装が違って、有理数は正確になるような実装とか？)

コード(Emacs)

perl 6

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

sub f($p, $q) {
    (1 - $p) + $p * (1 - $q);
}
sub g($p, $q) {
    1 - $p * $q;
}

say '==, p, q, (1 - p) + p * (1 - q), 1 - p * q';
for 0..9 -> $p {
    for 0..9 -> $q {
        my $p0 = $p / 10;
        my $q0 = $q / 10;
        my $a1 = f($p0, $q0);
        my $a2 = g($p0, $q0);
        say $a1 == $a2, ", $p0, $q0, $a1, $a2";
    }
}

perl 5

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

sub f {
    my ($p, $q) = @_;
    (1 - $p) + $p * (1 - $q);
}
sub g {
    my ($p, $q) = @_;
    1 - $p * $q;
}

print "==, p, q, (1 - p) + p * (1 - q), 1 - p * q\n";

for my $p (0..9) {
    for my $q (0..9) {
        my $p0 = $p / 10.0;
        my $q0 = $q / 10.0;
        my $a1 = f($p0, $q0);
        my $a2 = g($p0, $q0);
        print $a1 == $a2 ? "True" : "False", ", $p0, $q0, $a1, $a2\n";
    }
}

python 3

#!/usr/bin/env python3
# -*- coding: utf-8 -*-


def f(p, q):
    return (1 - p) + p * (1 - q)


def g(p, q):
    return 1 - p * q

print('==, p, q, (1 - p) + p * (1 - q), 1 - p * q')
for p in range(10):
    for q in range(10):
        p0 = p / 10
        q0 = q / 10
        a1 = f(p0, q0)
        a2 = g(p0, q0)
        print('{0}, {1}, {2}, {3}, {4}'.format(a1 == a2, p0, q0, a1, a2))

ruby 2.4

#!/usr/bin/env ruby2.4
# -*- coding: utf-8 -*-

def f(p, q)
  (1 - p) + p * (1 - q)
end

def g(p, q)
  1 - p * q
end


puts '==, p, q, (1 - p) + p * (1 - q), 1 - p * q'
(0..9).each do |p|
  (0..9).each do |q|
    p0 = p / 10.0
    q0 = q / 10.0
    a1 = f p0, q0
    a2 = g p0, q0
    puts "#{a1 == a2}, #{p0}, #{q0}, #{a1}, #{a2}"
  end
end

#include <stdio.h>

double f(double p, double q) {
  return (1 - p) + p * (1 - q);
}

double g(double p, double q) {
  return 1 - p * q;
}

int main() {
  printf("bool, p, q, (1 - p) + p * (1 - q), 1 - p * q\n");
  for (double p = 0; p < 1; p += 0.1) {
    for (double q = 0; q < 1; q += 0.1) {
      double a1 = f(p, q);
      double a2 = g(p, q);
      printf("%s, %f, %f, %f, %f\n", a1 == a2 ? "true" : "false", p, q, a1, a2);
    }
  }
}

入出力結果(Terminal, REPL)

$ ./sample1.pl6
==, p, q, (1 - p) + p * (1 - q), 1 - p * q
True, 0, 0, 1, 1
True, 0, 0.1, 1, 1
True, 0, 0.2, 1, 1
True, 0, 0.3, 1, 1
True, 0, 0.4, 1, 1
True, 0, 0.5, 1, 1
True, 0, 0.6, 1, 1
True, 0, 0.7, 1, 1
True, 0, 0.8, 1, 1
True, 0, 0.9, 1, 1
True, 0.1, 0, 1, 1
True, 0.1, 0.1, 0.99, 0.99
True, 0.1, 0.2, 0.98, 0.98
True, 0.1, 0.3, 0.97, 0.97
True, 0.1, 0.4, 0.96, 0.96
True, 0.1, 0.5, 0.95, 0.95
True, 0.1, 0.6, 0.94, 0.94
True, 0.1, 0.7, 0.93, 0.93
True, 0.1, 0.8, 0.92, 0.92
True, 0.1, 0.9, 0.91, 0.91
True, 0.2, 0, 1, 1
True, 0.2, 0.1, 0.98, 0.98
True, 0.2, 0.2, 0.96, 0.96
True, 0.2, 0.3, 0.94, 0.94
True, 0.2, 0.4, 0.92, 0.92
True, 0.2, 0.5, 0.9, 0.9
True, 0.2, 0.6, 0.88, 0.88
True, 0.2, 0.7, 0.86, 0.86
True, 0.2, 0.8, 0.84, 0.84
True, 0.2, 0.9, 0.82, 0.82
True, 0.3, 0, 1, 1
True, 0.3, 0.1, 0.97, 0.97
True, 0.3, 0.2, 0.94, 0.94
True, 0.3, 0.3, 0.91, 0.91
True, 0.3, 0.4, 0.88, 0.88
True, 0.3, 0.5, 0.85, 0.85
True, 0.3, 0.6, 0.82, 0.82
True, 0.3, 0.7, 0.79, 0.79
True, 0.3, 0.8, 0.76, 0.76
True, 0.3, 0.9, 0.73, 0.73
True, 0.4, 0, 1, 1
True, 0.4, 0.1, 0.96, 0.96
True, 0.4, 0.2, 0.92, 0.92
True, 0.4, 0.3, 0.88, 0.88
True, 0.4, 0.4, 0.84, 0.84
True, 0.4, 0.5, 0.8, 0.8
True, 0.4, 0.6, 0.76, 0.76
True, 0.4, 0.7, 0.72, 0.72
True, 0.4, 0.8, 0.68, 0.68
True, 0.4, 0.9, 0.64, 0.64
True, 0.5, 0, 1, 1
True, 0.5, 0.1, 0.95, 0.95
True, 0.5, 0.2, 0.9, 0.9
True, 0.5, 0.3, 0.85, 0.85
True, 0.5, 0.4, 0.8, 0.8
True, 0.5, 0.5, 0.75, 0.75
True, 0.5, 0.6, 0.7, 0.7
True, 0.5, 0.7, 0.65, 0.65
True, 0.5, 0.8, 0.6, 0.6
True, 0.5, 0.9, 0.55, 0.55
True, 0.6, 0, 1, 1
True, 0.6, 0.1, 0.94, 0.94
True, 0.6, 0.2, 0.88, 0.88
True, 0.6, 0.3, 0.82, 0.82
True, 0.6, 0.4, 0.76, 0.76
True, 0.6, 0.5, 0.7, 0.7
True, 0.6, 0.6, 0.64, 0.64
True, 0.6, 0.7, 0.58, 0.58
True, 0.6, 0.8, 0.52, 0.52
True, 0.6, 0.9, 0.46, 0.46
True, 0.7, 0, 1, 1
True, 0.7, 0.1, 0.93, 0.93
True, 0.7, 0.2, 0.86, 0.86
True, 0.7, 0.3, 0.79, 0.79
True, 0.7, 0.4, 0.72, 0.72
True, 0.7, 0.5, 0.65, 0.65
True, 0.7, 0.6, 0.58, 0.58
True, 0.7, 0.7, 0.51, 0.51
True, 0.7, 0.8, 0.44, 0.44
True, 0.7, 0.9, 0.37, 0.37
True, 0.8, 0, 1, 1
True, 0.8, 0.1, 0.92, 0.92
True, 0.8, 0.2, 0.84, 0.84
True, 0.8, 0.3, 0.76, 0.76
True, 0.8, 0.4, 0.68, 0.68
True, 0.8, 0.5, 0.6, 0.6
True, 0.8, 0.6, 0.52, 0.52
True, 0.8, 0.7, 0.44, 0.44
True, 0.8, 0.8, 0.36, 0.36
True, 0.8, 0.9, 0.28, 0.28
True, 0.9, 0, 1, 1
True, 0.9, 0.1, 0.91, 0.91
True, 0.9, 0.2, 0.82, 0.82
True, 0.9, 0.3, 0.73, 0.73
True, 0.9, 0.4, 0.64, 0.64
True, 0.9, 0.5, 0.55, 0.55
True, 0.9, 0.6, 0.46, 0.46
True, 0.9, 0.7, 0.37, 0.37
True, 0.9, 0.8, 0.28, 0.28
True, 0.9, 0.9, 0.19, 0.19
$ ./sample1.pl
==, p, q, (1 - p) + p * (1 - q), 1 - p * q
True, 0, 0, 1, 1
True, 0, 0.1, 1, 1
True, 0, 0.2, 1, 1
True, 0, 0.3, 1, 1
True, 0, 0.4, 1, 1
True, 0, 0.5, 1, 1
True, 0, 0.6, 1, 1
True, 0, 0.7, 1, 1
True, 0, 0.8, 1, 1
True, 0, 0.9, 1, 1
True, 0.1, 0, 1, 1
True, 0.1, 0.1, 0.99, 0.99
True, 0.1, 0.2, 0.98, 0.98
True, 0.1, 0.3, 0.97, 0.97
True, 0.1, 0.4, 0.96, 0.96
False, 0.1, 0.5, 0.95, 0.95
False, 0.1, 0.6, 0.94, 0.94
True, 0.1, 0.7, 0.93, 0.93
False, 0.1, 0.8, 0.92, 0.92
True, 0.1, 0.9, 0.91, 0.91
True, 0.2, 0, 1, 1
False, 0.2, 0.1, 0.98, 0.98
False, 0.2, 0.2, 0.96, 0.96
False, 0.2, 0.3, 0.94, 0.94
False, 0.2, 0.4, 0.92, 0.92
True, 0.2, 0.5, 0.9, 0.9
False, 0.2, 0.6, 0.88, 0.88
False, 0.2, 0.7, 0.86, 0.86
False, 0.2, 0.8, 0.84, 0.84
False, 0.2, 0.9, 0.82, 0.82
True, 0.3, 0, 1, 1
True, 0.3, 0.1, 0.97, 0.97
True, 0.3, 0.2, 0.94, 0.94
False, 0.3, 0.3, 0.91, 0.91
False, 0.3, 0.4, 0.88, 0.88
True, 0.3, 0.5, 0.85, 0.85
False, 0.3, 0.6, 0.82, 0.82
False, 0.3, 0.7, 0.79, 0.79
False, 0.3, 0.8, 0.76, 0.76
True, 0.3, 0.9, 0.73, 0.73
True, 0.4, 0, 1, 1
True, 0.4, 0.1, 0.96, 0.96
False, 0.4, 0.2, 0.92, 0.92
False, 0.4, 0.3, 0.88, 0.88
True, 0.4, 0.4, 0.84, 0.84
True, 0.4, 0.5, 0.8, 0.8
True, 0.4, 0.6, 0.76, 0.76
True, 0.4, 0.7, 0.72, 0.72
True, 0.4, 0.8, 0.68, 0.68
False, 0.4, 0.9, 0.64, 0.64
True, 0.5, 0, 1, 1
True, 0.5, 0.1, 0.95, 0.95
True, 0.5, 0.2, 0.9, 0.9
True, 0.5, 0.3, 0.85, 0.85
True, 0.5, 0.4, 0.8, 0.8
True, 0.5, 0.5, 0.75, 0.75
True, 0.5, 0.6, 0.7, 0.7
True, 0.5, 0.7, 0.65, 0.65
True, 0.5, 0.8, 0.6, 0.6
True, 0.5, 0.9, 0.55, 0.55
True, 0.6, 0, 1, 1
False, 0.6, 0.1, 0.94, 0.94
True, 0.6, 0.2, 0.88, 0.88
True, 0.6, 0.3, 0.82, 0.82
True, 0.6, 0.4, 0.76, 0.76
True, 0.6, 0.5, 0.7, 0.7
True, 0.6, 0.6, 0.64, 0.64
True, 0.6, 0.7, 0.58, 0.58
True, 0.6, 0.8, 0.52, 0.52
False, 0.6, 0.9, 0.46, 0.46
True, 0.7, 0, 1, 1
True, 0.7, 0.1, 0.93, 0.93
True, 0.7, 0.2, 0.86, 0.86
True, 0.7, 0.3, 0.79, 0.79
True, 0.7, 0.4, 0.72, 0.72
True, 0.7, 0.5, 0.65, 0.65
True, 0.7, 0.6, 0.58, 0.58
True, 0.7, 0.7, 0.51, 0.51
False, 0.7, 0.8, 0.44, 0.44
True, 0.7, 0.9, 0.37, 0.37
True, 0.8, 0, 1, 1
False, 0.8, 0.1, 0.92, 0.92
False, 0.8, 0.2, 0.84, 0.84
False, 0.8, 0.3, 0.76, 0.76
True, 0.8, 0.4, 0.68, 0.68
True, 0.8, 0.5, 0.6, 0.6
True, 0.8, 0.6, 0.52, 0.52
False, 0.8, 0.7, 0.44, 0.44
False, 0.8, 0.8, 0.36, 0.36
True, 0.8, 0.9, 0.28, 0.28
True, 0.9, 0, 1, 1
True, 0.9, 0.1, 0.91, 0.91
False, 0.9, 0.2, 0.82, 0.82
True, 0.9, 0.3, 0.73, 0.73
False, 0.9, 0.4, 0.64, 0.64
True, 0.9, 0.5, 0.55, 0.55
False, 0.9, 0.6, 0.46, 0.46
False, 0.9, 0.7, 0.37, 0.37
True, 0.9, 0.8, 0.28, 0.28
True, 0.9, 0.9, 0.19, 0.19
$ ./sample1.py
==, p, q, (1 - p) + p * (1 - q), 1 - p * q
True, 0.0, 0.0, 1.0, 1.0
True, 0.0, 0.1, 1.0, 1.0
True, 0.0, 0.2, 1.0, 1.0
True, 0.0, 0.3, 1.0, 1.0
True, 0.0, 0.4, 1.0, 1.0
True, 0.0, 0.5, 1.0, 1.0
True, 0.0, 0.6, 1.0, 1.0
True, 0.0, 0.7, 1.0, 1.0
True, 0.0, 0.8, 1.0, 1.0
True, 0.0, 0.9, 1.0, 1.0
True, 0.1, 0.0, 1.0, 1.0
True, 0.1, 0.1, 0.99, 0.99
True, 0.1, 0.2, 0.98, 0.98
True, 0.1, 0.3, 0.97, 0.97
True, 0.1, 0.4, 0.96, 0.96
False, 0.1, 0.5, 0.9500000000000001, 0.95
False, 0.1, 0.6, 0.9400000000000001, 0.94
True, 0.1, 0.7, 0.93, 0.93
False, 0.1, 0.8, 0.92, 0.9199999999999999
True, 0.1, 0.9, 0.91, 0.91
True, 0.2, 0.0, 1.0, 1.0
False, 0.2, 0.1, 0.9800000000000001, 0.98
False, 0.2, 0.2, 0.9600000000000001, 0.96
False, 0.2, 0.3, 0.9400000000000001, 0.94
False, 0.2, 0.4, 0.92, 0.9199999999999999
True, 0.2, 0.5, 0.9, 0.9
False, 0.2, 0.6, 0.8800000000000001, 0.88
False, 0.2, 0.7, 0.8600000000000001, 0.86
False, 0.2, 0.8, 0.8400000000000001, 0.84
False, 0.2, 0.9, 0.8200000000000001, 0.82
True, 0.3, 0.0, 1.0, 1.0
True, 0.3, 0.1, 0.97, 0.97
True, 0.3, 0.2, 0.94, 0.94
False, 0.3, 0.3, 0.9099999999999999, 0.91
False, 0.3, 0.4, 0.8799999999999999, 0.88
True, 0.3, 0.5, 0.85, 0.85
False, 0.3, 0.6, 0.82, 0.8200000000000001
False, 0.3, 0.7, 0.7899999999999999, 0.79
False, 0.3, 0.8, 0.7599999999999999, 0.76
True, 0.3, 0.9, 0.73, 0.73
True, 0.4, 0.0, 1.0, 1.0
True, 0.4, 0.1, 0.96, 0.96
False, 0.4, 0.2, 0.92, 0.9199999999999999
False, 0.4, 0.3, 0.8799999999999999, 0.88
True, 0.4, 0.4, 0.84, 0.84
True, 0.4, 0.5, 0.8, 0.8
True, 0.4, 0.6, 0.76, 0.76
True, 0.4, 0.7, 0.72, 0.72
True, 0.4, 0.8, 0.6799999999999999, 0.6799999999999999
False, 0.4, 0.9, 0.64, 0.6399999999999999
True, 0.5, 0.0, 1.0, 1.0
True, 0.5, 0.1, 0.95, 0.95
True, 0.5, 0.2, 0.9, 0.9
True, 0.5, 0.3, 0.85, 0.85
True, 0.5, 0.4, 0.8, 0.8
True, 0.5, 0.5, 0.75, 0.75
True, 0.5, 0.6, 0.7, 0.7
True, 0.5, 0.7, 0.65, 0.65
True, 0.5, 0.8, 0.6, 0.6
True, 0.5, 0.9, 0.55, 0.55
True, 0.6, 0.0, 1.0, 1.0
False, 0.6, 0.1, 0.9400000000000001, 0.94
True, 0.6, 0.2, 0.88, 0.88
True, 0.6, 0.3, 0.8200000000000001, 0.8200000000000001
True, 0.6, 0.4, 0.76, 0.76
True, 0.6, 0.5, 0.7, 0.7
True, 0.6, 0.6, 0.64, 0.64
True, 0.6, 0.7, 0.5800000000000001, 0.5800000000000001
True, 0.6, 0.8, 0.52, 0.52
False, 0.6, 0.9, 0.46, 0.45999999999999996
True, 0.7, 0.0, 1.0, 1.0
True, 0.7, 0.1, 0.93, 0.93
True, 0.7, 0.2, 0.86, 0.86
True, 0.7, 0.3, 0.79, 0.79
True, 0.7, 0.4, 0.72, 0.72
True, 0.7, 0.5, 0.65, 0.65
True, 0.7, 0.6, 0.5800000000000001, 0.5800000000000001
True, 0.7, 0.7, 0.51, 0.51
False, 0.7, 0.8, 0.44, 0.44000000000000006
True, 0.7, 0.9, 0.37, 0.37
True, 0.8, 0.0, 1.0, 1.0
False, 0.8, 0.1, 0.92, 0.9199999999999999
False, 0.8, 0.2, 0.8400000000000001, 0.84
False, 0.8, 0.3, 0.7599999999999999, 0.76
True, 0.8, 0.4, 0.6799999999999999, 0.6799999999999999
True, 0.8, 0.5, 0.6, 0.6
True, 0.8, 0.6, 0.52, 0.52
False, 0.8, 0.7, 0.44, 0.44000000000000006
False, 0.8, 0.8, 0.35999999999999993, 0.3599999999999999
True, 0.8, 0.9, 0.2799999999999999, 0.2799999999999999
True, 0.9, 0.0, 1.0, 1.0
True, 0.9, 0.1, 0.91, 0.91
False, 0.9, 0.2, 0.8200000000000001, 0.82
True, 0.9, 0.3, 0.73, 0.73
False, 0.9, 0.4, 0.64, 0.6399999999999999
True, 0.9, 0.5, 0.55, 0.55
False, 0.9, 0.6, 0.46, 0.45999999999999996
False, 0.9, 0.7, 0.37000000000000005, 0.37
True, 0.9, 0.8, 0.2799999999999999, 0.2799999999999999
True, 0.9, 0.9, 0.18999999999999995, 0.18999999999999995
$ ./sample1.rb 
==, p, q, (1 - p) + p * (1 - q), 1 - p * q
true, 0.0, 0.0, 1.0, 1.0
true, 0.0, 0.1, 1.0, 1.0
true, 0.0, 0.2, 1.0, 1.0
true, 0.0, 0.3, 1.0, 1.0
true, 0.0, 0.4, 1.0, 1.0
true, 0.0, 0.5, 1.0, 1.0
true, 0.0, 0.6, 1.0, 1.0
true, 0.0, 0.7, 1.0, 1.0
true, 0.0, 0.8, 1.0, 1.0
true, 0.0, 0.9, 1.0, 1.0
true, 0.1, 0.0, 1.0, 1.0
true, 0.1, 0.1, 0.99, 0.99
true, 0.1, 0.2, 0.98, 0.98
true, 0.1, 0.3, 0.97, 0.97
true, 0.1, 0.4, 0.96, 0.96
false, 0.1, 0.5, 0.9500000000000001, 0.95
false, 0.1, 0.6, 0.9400000000000001, 0.94
true, 0.1, 0.7, 0.93, 0.93
false, 0.1, 0.8, 0.92, 0.9199999999999999
true, 0.1, 0.9, 0.91, 0.91
true, 0.2, 0.0, 1.0, 1.0
false, 0.2, 0.1, 0.9800000000000001, 0.98
false, 0.2, 0.2, 0.9600000000000001, 0.96
false, 0.2, 0.3, 0.9400000000000001, 0.94
false, 0.2, 0.4, 0.92, 0.9199999999999999
true, 0.2, 0.5, 0.9, 0.9
false, 0.2, 0.6, 0.8800000000000001, 0.88
false, 0.2, 0.7, 0.8600000000000001, 0.86
false, 0.2, 0.8, 0.8400000000000001, 0.84
false, 0.2, 0.9, 0.8200000000000001, 0.82
true, 0.3, 0.0, 1.0, 1.0
true, 0.3, 0.1, 0.97, 0.97
true, 0.3, 0.2, 0.94, 0.94
false, 0.3, 0.3, 0.9099999999999999, 0.91
false, 0.3, 0.4, 0.8799999999999999, 0.88
true, 0.3, 0.5, 0.85, 0.85
false, 0.3, 0.6, 0.82, 0.8200000000000001
false, 0.3, 0.7, 0.7899999999999999, 0.79
false, 0.3, 0.8, 0.7599999999999999, 0.76
true, 0.3, 0.9, 0.73, 0.73
true, 0.4, 0.0, 1.0, 1.0
true, 0.4, 0.1, 0.96, 0.96
false, 0.4, 0.2, 0.92, 0.9199999999999999
false, 0.4, 0.3, 0.8799999999999999, 0.88
true, 0.4, 0.4, 0.84, 0.84
true, 0.4, 0.5, 0.8, 0.8
true, 0.4, 0.6, 0.76, 0.76
true, 0.4, 0.7, 0.72, 0.72
true, 0.4, 0.8, 0.6799999999999999, 0.6799999999999999
false, 0.4, 0.9, 0.64, 0.6399999999999999
true, 0.5, 0.0, 1.0, 1.0
true, 0.5, 0.1, 0.95, 0.95
true, 0.5, 0.2, 0.9, 0.9
true, 0.5, 0.3, 0.85, 0.85
true, 0.5, 0.4, 0.8, 0.8
true, 0.5, 0.5, 0.75, 0.75
true, 0.5, 0.6, 0.7, 0.7
true, 0.5, 0.7, 0.65, 0.65
true, 0.5, 0.8, 0.6, 0.6
true, 0.5, 0.9, 0.55, 0.55
true, 0.6, 0.0, 1.0, 1.0
false, 0.6, 0.1, 0.9400000000000001, 0.94
true, 0.6, 0.2, 0.88, 0.88
true, 0.6, 0.3, 0.8200000000000001, 0.8200000000000001
true, 0.6, 0.4, 0.76, 0.76
true, 0.6, 0.5, 0.7, 0.7
true, 0.6, 0.6, 0.64, 0.64
true, 0.6, 0.7, 0.5800000000000001, 0.5800000000000001
true, 0.6, 0.8, 0.52, 0.52
false, 0.6, 0.9, 0.46, 0.45999999999999996
true, 0.7, 0.0, 1.0, 1.0
true, 0.7, 0.1, 0.93, 0.93
true, 0.7, 0.2, 0.86, 0.86
true, 0.7, 0.3, 0.79, 0.79
true, 0.7, 0.4, 0.72, 0.72
true, 0.7, 0.5, 0.65, 0.65
true, 0.7, 0.6, 0.5800000000000001, 0.5800000000000001
true, 0.7, 0.7, 0.51, 0.51
false, 0.7, 0.8, 0.44, 0.44000000000000006
true, 0.7, 0.9, 0.37, 0.37
true, 0.8, 0.0, 1.0, 1.0
false, 0.8, 0.1, 0.92, 0.9199999999999999
false, 0.8, 0.2, 0.8400000000000001, 0.84
false, 0.8, 0.3, 0.7599999999999999, 0.76
true, 0.8, 0.4, 0.6799999999999999, 0.6799999999999999
true, 0.8, 0.5, 0.6, 0.6
true, 0.8, 0.6, 0.52, 0.52
false, 0.8, 0.7, 0.44, 0.44000000000000006
false, 0.8, 0.8, 0.35999999999999993, 0.3599999999999999
true, 0.8, 0.9, 0.2799999999999999, 0.2799999999999999
true, 0.9, 0.0, 1.0, 1.0
true, 0.9, 0.1, 0.91, 0.91
false, 0.9, 0.2, 0.8200000000000001, 0.82
true, 0.9, 0.3, 0.73, 0.73
false, 0.9, 0.4, 0.64, 0.6399999999999999
true, 0.9, 0.5, 0.55, 0.55
false, 0.9, 0.6, 0.46, 0.45999999999999996
false, 0.9, 0.7, 0.37000000000000005, 0.37
true, 0.9, 0.8, 0.2799999999999999, 0.2799999999999999
true, 0.9, 0.9, 0.18999999999999995, 0.18999999999999995
$ ./sample1
bool, p, q, (1 - p) + p * (1 - q), 1 - p * q
true, 0.000000, 0.000000, 1.000000, 1.000000
true, 0.000000, 0.100000, 1.000000, 1.000000
true, 0.000000, 0.200000, 1.000000, 1.000000
true, 0.000000, 0.300000, 1.000000, 1.000000
true, 0.000000, 0.400000, 1.000000, 1.000000
true, 0.000000, 0.500000, 1.000000, 1.000000
true, 0.000000, 0.600000, 1.000000, 1.000000
true, 0.000000, 0.700000, 1.000000, 1.000000
true, 0.000000, 0.800000, 1.000000, 1.000000
true, 0.000000, 0.900000, 1.000000, 1.000000
true, 0.000000, 1.000000, 1.000000, 1.000000
true, 0.100000, 0.000000, 1.000000, 1.000000
true, 0.100000, 0.100000, 0.990000, 0.990000
true, 0.100000, 0.200000, 0.980000, 0.980000
true, 0.100000, 0.300000, 0.970000, 0.970000
true, 0.100000, 0.400000, 0.960000, 0.960000
false, 0.100000, 0.500000, 0.950000, 0.950000
false, 0.100000, 0.600000, 0.940000, 0.940000
true, 0.100000, 0.700000, 0.930000, 0.930000
true, 0.100000, 0.800000, 0.920000, 0.920000
true, 0.100000, 0.900000, 0.910000, 0.910000
true, 0.100000, 1.000000, 0.900000, 0.900000
true, 0.200000, 0.000000, 1.000000, 1.000000
false, 0.200000, 0.100000, 0.980000, 0.980000
false, 0.200000, 0.200000, 0.960000, 0.960000
false, 0.200000, 0.300000, 0.940000, 0.940000
false, 0.200000, 0.400000, 0.920000, 0.920000
true, 0.200000, 0.500000, 0.900000, 0.900000
false, 0.200000, 0.600000, 0.880000, 0.880000
false, 0.200000, 0.700000, 0.860000, 0.860000
false, 0.200000, 0.800000, 0.840000, 0.840000
true, 0.200000, 0.900000, 0.820000, 0.820000
true, 0.200000, 1.000000, 0.800000, 0.800000
true, 0.300000, 0.000000, 1.000000, 1.000000
true, 0.300000, 0.100000, 0.970000, 0.970000
true, 0.300000, 0.200000, 0.940000, 0.940000
true, 0.300000, 0.300000, 0.910000, 0.910000
true, 0.300000, 0.400000, 0.880000, 0.880000
true, 0.300000, 0.500000, 0.850000, 0.850000
true, 0.300000, 0.600000, 0.820000, 0.820000
true, 0.300000, 0.700000, 0.790000, 0.790000
true, 0.300000, 0.800000, 0.760000, 0.760000
true, 0.300000, 0.900000, 0.730000, 0.730000
true, 0.300000, 1.000000, 0.700000, 0.700000
true, 0.400000, 0.000000, 1.000000, 1.000000
true, 0.400000, 0.100000, 0.960000, 0.960000
false, 0.400000, 0.200000, 0.920000, 0.920000
false, 0.400000, 0.300000, 0.880000, 0.880000
true, 0.400000, 0.400000, 0.840000, 0.840000
true, 0.400000, 0.500000, 0.800000, 0.800000
true, 0.400000, 0.600000, 0.760000, 0.760000
true, 0.400000, 0.700000, 0.720000, 0.720000
false, 0.400000, 0.800000, 0.680000, 0.680000
true, 0.400000, 0.900000, 0.640000, 0.640000
false, 0.400000, 1.000000, 0.600000, 0.600000
true, 0.500000, 0.000000, 1.000000, 1.000000
true, 0.500000, 0.100000, 0.950000, 0.950000
true, 0.500000, 0.200000, 0.900000, 0.900000
true, 0.500000, 0.300000, 0.850000, 0.850000
true, 0.500000, 0.400000, 0.800000, 0.800000
true, 0.500000, 0.500000, 0.750000, 0.750000
true, 0.500000, 0.600000, 0.700000, 0.700000
true, 0.500000, 0.700000, 0.650000, 0.650000
true, 0.500000, 0.800000, 0.600000, 0.600000
true, 0.500000, 0.900000, 0.550000, 0.550000
true, 0.500000, 1.000000, 0.500000, 0.500000
true, 0.600000, 0.000000, 1.000000, 1.000000
false, 0.600000, 0.100000, 0.940000, 0.940000
true, 0.600000, 0.200000, 0.880000, 0.880000
false, 0.600000, 0.300000, 0.820000, 0.820000
true, 0.600000, 0.400000, 0.760000, 0.760000
true, 0.600000, 0.500000, 0.700000, 0.700000
true, 0.600000, 0.600000, 0.640000, 0.640000
true, 0.600000, 0.700000, 0.580000, 0.580000
true, 0.600000, 0.800000, 0.520000, 0.520000
true, 0.600000, 0.900000, 0.460000, 0.460000
false, 0.600000, 1.000000, 0.400000, 0.400000
true, 0.700000, 0.000000, 1.000000, 1.000000
true, 0.700000, 0.100000, 0.930000, 0.930000
true, 0.700000, 0.200000, 0.860000, 0.860000
true, 0.700000, 0.300000, 0.790000, 0.790000
true, 0.700000, 0.400000, 0.720000, 0.720000
true, 0.700000, 0.500000, 0.650000, 0.650000
true, 0.700000, 0.600000, 0.580000, 0.580000
true, 0.700000, 0.700000, 0.510000, 0.510000
true, 0.700000, 0.800000, 0.440000, 0.440000
true, 0.700000, 0.900000, 0.370000, 0.370000
false, 0.700000, 1.000000, 0.300000, 0.300000
true, 0.800000, 0.000000, 1.000000, 1.000000
true, 0.800000, 0.100000, 0.920000, 0.920000
false, 0.800000, 0.200000, 0.840000, 0.840000
true, 0.800000, 0.300000, 0.760000, 0.760000
true, 0.800000, 0.400000, 0.680000, 0.680000
true, 0.800000, 0.500000, 0.600000, 0.600000
true, 0.800000, 0.600000, 0.520000, 0.520000
true, 0.800000, 0.700000, 0.440000, 0.440000
true, 0.800000, 0.800000, 0.360000, 0.360000
true, 0.800000, 0.900000, 0.280000, 0.280000
false, 0.800000, 1.000000, 0.200000, 0.200000
true, 0.900000, 0.000000, 1.000000, 1.000000
true, 0.900000, 0.100000, 0.910000, 0.910000
true, 0.900000, 0.200000, 0.820000, 0.820000
true, 0.900000, 0.300000, 0.730000, 0.730000
true, 0.900000, 0.400000, 0.640000, 0.640000
true, 0.900000, 0.500000, 0.550000, 0.550000
true, 0.900000, 0.600000, 0.460000, 0.460000
true, 0.900000, 0.700000, 0.370000, 0.370000
true, 0.900000, 0.800000, 0.280000, 0.280000
true, 0.900000, 0.900000, 0.190000, 0.190000
false, 0.900000, 1.000000, 0.100000, 0.100000
true, 1.000000, 0.000000, 1.000000, 1.000000
true, 1.000000, 0.100000, 0.900000, 0.900000
true, 1.000000, 0.200000, 0.800000, 0.800000
true, 1.000000, 0.300000, 0.700000, 0.700000
false, 1.000000, 0.400000, 0.600000, 0.600000
true, 1.000000, 0.500000, 0.500000, 0.500000
false, 1.000000, 0.600000, 0.400000, 0.400000
false, 1.000000, 0.700000, 0.300000, 0.300000
false, 1.000000, 0.800000, 0.200000, 0.200000
false, 1.000000, 0.900000, 0.100000, 0.100000
true, 1.000000, 1.000000, 0.000000, 0.000000
$

@kagamihr @mkamimura いえ、perl6は整数/整数を行なうと有理数型が作られるようです。加減乗除の範囲内では誤差なしで計算できそうです。(長い計算だと計算時間が大変なことになりそうですが。)
— kashi (@mkashi) 2017年4月28日

ということで、$p / 10 ではなく、10.0 で割ったり、1.0 を掛けたりしてみる。

コード(Emacs)

perl 6

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

sub f($p, $q) {
    (1 - $p) + $p * (1 - $q);
}
sub g($p, $q) {
    1 - $p * $q;
}

say '==, p, q, (1 - p) + p * (1 - q), 1 - p * q';
for 0..9 -> $p {
    for 0..9 -> $q {
        my $p0 = $p / 10.0;
        my $q0 = $q / 10.0;
        my $a1 = f($p0, $q0);
        my $a2 = g($p0, $q0);
        say $a1 == $a2, ", $p0, $q0, $a1, $a2";
    }
}

for 0..9 -> $p {
    for 0..9 -> $q {
        my $p0 = $p / 10 * 1.0;
        my $q0 = $q / 10 * 1.0;
        my $a1 = f($p0, $q0);
        my $a2 = g($p0, $q0);
        say $a1 == $a2, ", $p0, $q0, $a1, $a2";
    }
}

入出力結果(Terminal, REPL)

$ ./sample2.pl6
==, p, q, (1 - p) + p * (1 - q), 1 - p * q
True, 0, 0, 1, 1
True, 0, 0.1, 1, 1
True, 0, 0.2, 1, 1
True, 0, 0.3, 1, 1
True, 0, 0.4, 1, 1
True, 0, 0.5, 1, 1
True, 0, 0.6, 1, 1
True, 0, 0.7, 1, 1
True, 0, 0.8, 1, 1
True, 0, 0.9, 1, 1
True, 0.1, 0, 1, 1
True, 0.1, 0.1, 0.99, 0.99
True, 0.1, 0.2, 0.98, 0.98
True, 0.1, 0.3, 0.97, 0.97
True, 0.1, 0.4, 0.96, 0.96
True, 0.1, 0.5, 0.95, 0.95
True, 0.1, 0.6, 0.94, 0.94
True, 0.1, 0.7, 0.93, 0.93
True, 0.1, 0.8, 0.92, 0.92
True, 0.1, 0.9, 0.91, 0.91
True, 0.2, 0, 1, 1
True, 0.2, 0.1, 0.98, 0.98
True, 0.2, 0.2, 0.96, 0.96
True, 0.2, 0.3, 0.94, 0.94
True, 0.2, 0.4, 0.92, 0.92
True, 0.2, 0.5, 0.9, 0.9
True, 0.2, 0.6, 0.88, 0.88
True, 0.2, 0.7, 0.86, 0.86
True, 0.2, 0.8, 0.84, 0.84
True, 0.2, 0.9, 0.82, 0.82
True, 0.3, 0, 1, 1
True, 0.3, 0.1, 0.97, 0.97
True, 0.3, 0.2, 0.94, 0.94
True, 0.3, 0.3, 0.91, 0.91
True, 0.3, 0.4, 0.88, 0.88
True, 0.3, 0.5, 0.85, 0.85
True, 0.3, 0.6, 0.82, 0.82
True, 0.3, 0.7, 0.79, 0.79
True, 0.3, 0.8, 0.76, 0.76
True, 0.3, 0.9, 0.73, 0.73
True, 0.4, 0, 1, 1
True, 0.4, 0.1, 0.96, 0.96
True, 0.4, 0.2, 0.92, 0.92
True, 0.4, 0.3, 0.88, 0.88
True, 0.4, 0.4, 0.84, 0.84
True, 0.4, 0.5, 0.8, 0.8
True, 0.4, 0.6, 0.76, 0.76
True, 0.4, 0.7, 0.72, 0.72
True, 0.4, 0.8, 0.68, 0.68
True, 0.4, 0.9, 0.64, 0.64
True, 0.5, 0, 1, 1
True, 0.5, 0.1, 0.95, 0.95
True, 0.5, 0.2, 0.9, 0.9
True, 0.5, 0.3, 0.85, 0.85
True, 0.5, 0.4, 0.8, 0.8
True, 0.5, 0.5, 0.75, 0.75
True, 0.5, 0.6, 0.7, 0.7
True, 0.5, 0.7, 0.65, 0.65
True, 0.5, 0.8, 0.6, 0.6
True, 0.5, 0.9, 0.55, 0.55
True, 0.6, 0, 1, 1
True, 0.6, 0.1, 0.94, 0.94
True, 0.6, 0.2, 0.88, 0.88
True, 0.6, 0.3, 0.82, 0.82
True, 0.6, 0.4, 0.76, 0.76
True, 0.6, 0.5, 0.7, 0.7
True, 0.6, 0.6, 0.64, 0.64
True, 0.6, 0.7, 0.58, 0.58
True, 0.6, 0.8, 0.52, 0.52
True, 0.6, 0.9, 0.46, 0.46
True, 0.7, 0, 1, 1
True, 0.7, 0.1, 0.93, 0.93
True, 0.7, 0.2, 0.86, 0.86
True, 0.7, 0.3, 0.79, 0.79
True, 0.7, 0.4, 0.72, 0.72
True, 0.7, 0.5, 0.65, 0.65
True, 0.7, 0.6, 0.58, 0.58
True, 0.7, 0.7, 0.51, 0.51
True, 0.7, 0.8, 0.44, 0.44
True, 0.7, 0.9, 0.37, 0.37
True, 0.8, 0, 1, 1
True, 0.8, 0.1, 0.92, 0.92
True, 0.8, 0.2, 0.84, 0.84
True, 0.8, 0.3, 0.76, 0.76
True, 0.8, 0.4, 0.68, 0.68
True, 0.8, 0.5, 0.6, 0.6
True, 0.8, 0.6, 0.52, 0.52
True, 0.8, 0.7, 0.44, 0.44
True, 0.8, 0.8, 0.36, 0.36
True, 0.8, 0.9, 0.28, 0.28
True, 0.9, 0, 1, 1
True, 0.9, 0.1, 0.91, 0.91
True, 0.9, 0.2, 0.82, 0.82
True, 0.9, 0.3, 0.73, 0.73
True, 0.9, 0.4, 0.64, 0.64
True, 0.9, 0.5, 0.55, 0.55
True, 0.9, 0.6, 0.46, 0.46
True, 0.9, 0.7, 0.37, 0.37
True, 0.9, 0.8, 0.28, 0.28
True, 0.9, 0.9, 0.19, 0.19
True, 0, 0, 1, 1
True, 0, 0.1, 1, 1
True, 0, 0.2, 1, 1
True, 0, 0.3, 1, 1
True, 0, 0.4, 1, 1
True, 0, 0.5, 1, 1
True, 0, 0.6, 1, 1
True, 0, 0.7, 1, 1
True, 0, 0.8, 1, 1
True, 0, 0.9, 1, 1
True, 0.1, 0, 1, 1
True, 0.1, 0.1, 0.99, 0.99
True, 0.1, 0.2, 0.98, 0.98
True, 0.1, 0.3, 0.97, 0.97
True, 0.1, 0.4, 0.96, 0.96
True, 0.1, 0.5, 0.95, 0.95
True, 0.1, 0.6, 0.94, 0.94
True, 0.1, 0.7, 0.93, 0.93
True, 0.1, 0.8, 0.92, 0.92
True, 0.1, 0.9, 0.91, 0.91
True, 0.2, 0, 1, 1
True, 0.2, 0.1, 0.98, 0.98
True, 0.2, 0.2, 0.96, 0.96
True, 0.2, 0.3, 0.94, 0.94
True, 0.2, 0.4, 0.92, 0.92
True, 0.2, 0.5, 0.9, 0.9
True, 0.2, 0.6, 0.88, 0.88
True, 0.2, 0.7, 0.86, 0.86
True, 0.2, 0.8, 0.84, 0.84
True, 0.2, 0.9, 0.82, 0.82
True, 0.3, 0, 1, 1
True, 0.3, 0.1, 0.97, 0.97
True, 0.3, 0.2, 0.94, 0.94
True, 0.3, 0.3, 0.91, 0.91
True, 0.3, 0.4, 0.88, 0.88
True, 0.3, 0.5, 0.85, 0.85
True, 0.3, 0.6, 0.82, 0.82
True, 0.3, 0.7, 0.79, 0.79
True, 0.3, 0.8, 0.76, 0.76
True, 0.3, 0.9, 0.73, 0.73
True, 0.4, 0, 1, 1
True, 0.4, 0.1, 0.96, 0.96
True, 0.4, 0.2, 0.92, 0.92
True, 0.4, 0.3, 0.88, 0.88
True, 0.4, 0.4, 0.84, 0.84
True, 0.4, 0.5, 0.8, 0.8
True, 0.4, 0.6, 0.76, 0.76
True, 0.4, 0.7, 0.72, 0.72
True, 0.4, 0.8, 0.68, 0.68
True, 0.4, 0.9, 0.64, 0.64
True, 0.5, 0, 1, 1
True, 0.5, 0.1, 0.95, 0.95
True, 0.5, 0.2, 0.9, 0.9
True, 0.5, 0.3, 0.85, 0.85
True, 0.5, 0.4, 0.8, 0.8
True, 0.5, 0.5, 0.75, 0.75
True, 0.5, 0.6, 0.7, 0.7
True, 0.5, 0.7, 0.65, 0.65
True, 0.5, 0.8, 0.6, 0.6
True, 0.5, 0.9, 0.55, 0.55
True, 0.6, 0, 1, 1
True, 0.6, 0.1, 0.94, 0.94
True, 0.6, 0.2, 0.88, 0.88
True, 0.6, 0.3, 0.82, 0.82
True, 0.6, 0.4, 0.76, 0.76
True, 0.6, 0.5, 0.7, 0.7
True, 0.6, 0.6, 0.64, 0.64
True, 0.6, 0.7, 0.58, 0.58
True, 0.6, 0.8, 0.52, 0.52
True, 0.6, 0.9, 0.46, 0.46
True, 0.7, 0, 1, 1
True, 0.7, 0.1, 0.93, 0.93
True, 0.7, 0.2, 0.86, 0.86
True, 0.7, 0.3, 0.79, 0.79
True, 0.7, 0.4, 0.72, 0.72
True, 0.7, 0.5, 0.65, 0.65
True, 0.7, 0.6, 0.58, 0.58
True, 0.7, 0.7, 0.51, 0.51
True, 0.7, 0.8, 0.44, 0.44
True, 0.7, 0.9, 0.37, 0.37
True, 0.8, 0, 1, 1
True, 0.8, 0.1, 0.92, 0.92
True, 0.8, 0.2, 0.84, 0.84
True, 0.8, 0.3, 0.76, 0.76
True, 0.8, 0.4, 0.68, 0.68
True, 0.8, 0.5, 0.6, 0.6
True, 0.8, 0.6, 0.52, 0.52
True, 0.8, 0.7, 0.44, 0.44
True, 0.8, 0.8, 0.36, 0.36
True, 0.8, 0.9, 0.28, 0.28
True, 0.9, 0, 1, 1
True, 0.9, 0.1, 0.91, 0.91
True, 0.9, 0.2, 0.82, 0.82
True, 0.9, 0.3, 0.73, 0.73
True, 0.9, 0.4, 0.64, 0.64
True, 0.9, 0.5, 0.55, 0.55
True, 0.9, 0.6, 0.46, 0.46
True, 0.9, 0.7, 0.37, 0.37
True, 0.9, 0.8, 0.28, 0.28
True, 0.9, 0.9, 0.19, 0.19
$ perl6
You may want to `zef install Readline` or `zef install Linenoise` or use rlwrap for a line editor

To exit type 'exit' or '^D'
> (1).WHAT
(Int)
> (1.0).WHAT
(Rat)
> (pi).WHAT
(Num)
> (sqrt 2).WHAT
(Num)
> (1.234567890234567890234567890234567890234567890234567890234567890234567890234567890234567890234567890).WHAT
(Rat)
> exit
$

Perl 6 は他の言語と違って、1が正確な整数、1.0が丸め誤差が発生する可能性のある実数というわけではなく、1.0を正確な有理数として扱ってくれるみたい。ということで、表記可能(計算結果ではなく直接入力可能)な実数(1.2とか)は全て正確な有理数として扱ってくれるみたい。

Kamimura's blog

2017年4月19日水曜日

Perl 6 - python - ruby - c - 式の展開の注意点 - 浮動小数点数、数値計算、正確性、誤差 - ( @h_okumura 、 @shora_kujira16 ) Haruhiko Okumura さん、しょラーさんのツイートより

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