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Check Machin-like formulas: Difference between revisions
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OK
Error: [[88, 1/172], [51, 1/239], [32, 1/682], [44, 1/5357], [68, 1/12944]]</pre>
=={{header|Perl}}==
<lang Perl>use Math::BigRat try=>"GMP";
sub taneval {
my($coef,$f) = @_;
$f = Math::BigRat->new($f) unless ref($f);
return 0 if $coef == 0;
return $f if $coef == 1;
return -taneval(-$coef, $f) if $coef < 0;
my($a,$b) = ( taneval($coef>>1, $f), taneval($coef-($coef>>1),$f) );
($a+$b)/(1-$a*$b);
}
sub tans {
my @xs=@_;
return taneval(@{$xs[0]}) if scalar(@xs)==1;
my($a,$b) = ( tans(@xs[0..($#xs>>1)]), tans(@xs[($#xs>>1)+1..$#xs]) );
($a+$b)/(1-$a*$b);
}
sub test {
printf "%5s (%s)\n", (tans(@_)==1)?"OK":"Error", join(" ",map{"[@$_]"} @_);
}
test([1,'1/2'], [1,'1/3']);
test([2,'1/3'], [1,'1/7']);
test([4,'1/5'], [-1,'1/239']);
test([5,'1/7'],[2,'3/79']);
test([5,'29/278'],[7,'3/79']);
test([1,'1/2'],[1,'1/5'],[1,'1/8']);
test([4,'1/5'],[-1,'1/70'],[1,'1/99']);
test([5,'1/7'],[4,'1/53'],[2,'1/4443']);
test([6,'1/8'],[2,'1/57'],[1,'1/239']);
test([8,'1/10'],[-1,'1/239'],[-4,'1/515']);
test([12,'1/18'],[8,'1/57'],[-5,'1/239']);
test([16,'1/21'],[3,'1/239'],[4,'3/1042']);
test([22,'1/28'],[2,'1/443'],[-5,'1/1393'],[-10,'1/11018']);
test([22,'1/38'],[17,'7/601'],[10,'7/8149']);
test([44,'1/57'],[7,'1/239'],[-12,'1/682'],[24,'1/12943']);
test([88,'1/172'],[51,'1/239'],[32,'1/682'],[44,'1/5357'],[68,'1/12943']);
test([88,'1/172'],[51,'1/239'],[32,'1/682'],[44,'1/5357'],[68,'1/12944']);</lang>
{{out}}
<pre> OK ([1 1/2] [1 1/3])
OK ([2 1/3] [1 1/7])
OK ([4 1/5] [-1 1/239])
OK ([5 1/7] [2 3/79])
OK ([5 29/278] [7 3/79])
OK ([1 1/2] [1 1/5] [1 1/8])
OK ([4 1/5] [-1 1/70] [1 1/99])
OK ([5 1/7] [4 1/53] [2 1/4443])
OK ([6 1/8] [2 1/57] [1 1/239])
OK ([8 1/10] [-1 1/239] [-4 1/515])
OK ([12 1/18] [8 1/57] [-5 1/239])
OK ([16 1/21] [3 1/239] [4 3/1042])
OK ([22 1/28] [2 1/443] [-5 1/1393] [-10 1/11018])
OK ([22 1/38] [17 7/601] [10 7/8149])
OK ([44 1/57] [7 1/239] [-12 1/682] [24 1/12943])
OK ([88 1/172] [51 1/239] [32 1/682] [44 1/5357] [68 1/12943])
Error ([88 1/172] [51 1/239] [32 1/682] [44 1/5357] [68 1/12944])</pre>
=={{header|Perl 6}}==
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