Sync

Task/Pi/Perl-6/pi.pl6

@@ -1,41 +1,33 @@
 # based on http://www.mathpropress.com/stan/bibliography/spigot.pdf
 
 sub stream(&next, &safe, &prod, &cons, $z is copy, @x) {
-    my $x-list = @x.iterator.list;
     gather loop {
-        my $y = next($z);
-        if safe($z, $y) {
-            take $y;
-            $z = prod($z, $y);
-        } else {
-            $z = cons($z, $x-list.shift);
-        }
+        $z = safe($z, my $y = next($z)) ??
+             prod($z, take $y)          !!
+             cons($z, @x[(state $)++])
     }
 }
 
 sub extr([$q, $r, $s, $t], $x) {
-    ($q * $x + $r) div ($s * $x + $t);
+    ($q * $x + $r) div ($s * $x + $t)
 }
 
-my $unit = [1, 0, 0, 1];
-
 sub comp([$q,$r,$s,$t], [$u,$v,$w,$x]) {
     [$q * $u + $r * $w,
      $q * $v + $r * $x,
      $s * $u + $t * $w,
-     $s * $v + $t * $x];
+     $s * $v + $t * $x]
 }
 
-sub pi-stream() {
+my @pi :=
     stream -> $z { extr($z, 3) },
            -> $z, $n { $n == extr($z, 4) },
            -> $z, $n { comp([10, -10*$n, 0, 1], $z) },
            &comp,
-           $unit,
+           <1 0 0 1>,
            (1..*).map: { [$_, 4 * $_ + 2, 0, 2 * $_ + 1] }
+
+loop {
+    print @pi.shift;
+    once print '.'
 }
-
-my @pi := pi-stream;
-
-print @pi[0], '.';
-print @pi[$_] for 1..*;

Task/Pi/Perl/pi-1.pl

@@ -0,0 +1,44 @@
+use bigint;
+sub stream {
+    my ($next, $safe, $prod, $cons, $z, $x) = @_;
+    $x = $x->();
+    sub {
+        while (1) {
+            my $y = $next->($z);
+            if ($safe->($z, $y)) {
+                $z = $prod->($z, $y);
+                return $y;
+            } else {
+                $z = $cons->($z, $x->());
+            }
+        }
+    }
+}
+
+sub extr {
+    use integer;
+    my ($q, $r, $s, $t) = @{shift()};
+    my $x = shift;
+    ($q * $x + $r) / ($s * $x + $t);
+}
+
+sub comp {
+    my ($q, $r, $s, $t) = @{shift()};
+    my ($u, $v, $w, $x) = @{shift()};
+    [$q * $u + $r * $w,
+     $q * $v + $r * $x,
+     $s * $u + $t * $w,
+     $s * $v + $t * $x];
+}
+
+my $pi_stream = stream
+    sub { extr shift, 3 },
+    sub { my ($z, $n) = @_; $n == extr $z, 4 },
+    sub { my ($z, $n) = @_; comp([10, -10*$n, 0, 1], $z) },
+    \&comp,
+    [1, 0, 0, 1],
+    sub { my $n = 0; sub { $n++; [$n, 4 * $n + 2, 0, 2 * $n + 1] } },
+;
+$|++;
+print $pi_stream->(), '.';
+print $pi_stream->() while 1;

Task/Pi/Perl/pi-2.pl

@@ -0,0 +1,55 @@
+use Math::BigInt;
+use bigint;
+
+# Pi/4 = 4 arctan 1/5 - arctan 1/239
+# expanding it with Taylor series with what's probably the dumbest method
+
+my ($ds, $ns) = (1, 0);
+my ($n5, $d5) = (16 * (25 * 3 - 1), 3 * 5**3);
+my ($n2, $d2) = (4 * (239 * 239 * 3 - 1), 3 * 239**3);
+
+sub next_term {
+	my ($coef, $p) = @_[1, 2];
+	$_[0] /= ($p - 4) * ($p - 2);
+	$_[0] *= $p * ($p + 2) * $coef**4;
+}
+
+my $p2 = 5;
+my $pow = 1;
+
+$| = 1;
+for (my $x = 5; ; $x += 4) {
+	($ns, $ds) = ($ns * $d5 + $n5 * $pow * $ds, $ds * $d5);
+
+	next_term($d5, 5, $x);
+	$n5 = 16 * (5 * 5 * ($x + 2) - $x);
+
+	while ($d5 > $d2) {
+		($ns, $ds) = ($ns * $d2 - $n2 * $pow * $ds, $ds * $d2);
+		$n2 = 4 * (239 * 239 * ($p2 + 2) - $p2);
+		next_term($d2, 239, $p2);
+		$p2 += 4;
+	}
+
+	my $ppow = 1;
+	while ($pow * $n5 * 5**4 < $d5 && $pow * $n2 * $n2 * 239**4 < $d2) {
+		$pow *= 10;
+		$ppow *= 10;
+	}
+
+	if ($ppow > 1) {
+		$ns *= $ppow;
+	#FIX?	my $out = $ns->bdiv($ds);   # bugged?
+		my $out = $ns / $ds;
+		$ns %= $ds;
+
+		$out = ("0" x (length($ppow) - length($out) - 1)) . $out;
+		print $out;
+	}
+
+	if ( $p2 % 20 == 1) {
+		my $g = Math::BigInt::bgcd($ds, $ns);
+		$ds /= $g;
+		$ns /= $g;
+	}
+}