Just another update
This commit is contained in:
Ingy döt Net
parent
a25938f123
commit
00a190b0a6
6591 changed files with 94363 additions and 23227 deletions
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@ -1,27 +1,40 @@
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Program Pi_Spigot;
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const
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n = 1000;
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len = 10*n div 3;
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var
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i, j, k, q, x, nines, predigit: integer;
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a: array[1..len] of longint;
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j, k, q, nines, predigit: integer;
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a: array[0..len] of longint;
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function OneLoop(i:integer):integer;
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var
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x: integer;
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begin
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{Only calculate as far as needed }
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{+16 for security digits ~5 decimals}
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i := i*10 div 3+16;
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IF i > len then
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i := len;
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result := 0;
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repeat {Work backwards}
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x := 10*a[i] + result*i;
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result := x div (2*i - 1);
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a[i] := x - result*(2*i - 1);//x mod (2*i - 1)
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dec(i);
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until i<= 0 ;
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end;
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begin
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for j := 1 to len do
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a[j] := 2; {Start with 2s}
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nines := 0;
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predigit := 0; {First predigit is a 0}
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for j := 1 to n do
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begin
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q := 0;
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for i := len downto 1 do {Work backwards}
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begin
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x := 10*a[i] + q*i;
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a[i] := x mod (2*i - 1);
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q := x div (2*i - 1);
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end;
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q := OneLoop(n-j);
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a[1] := q mod 10;
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q := q div 10;
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if q = 9 then
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@ -29,22 +42,22 @@ begin
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else
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if q = 10 then
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begin
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write(predigit+1);
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for k := 1 to nines do
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write(0); {zeros}
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predigit := 0;
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nines := 0
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write(predigit+1);
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for k := 1 to nines do
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write(0); {zeros}
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predigit := 0;
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nines := 0
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end
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else
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begin
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write(predigit);
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predigit := q;
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if nines <> 0 then
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begin
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for k := 1 to nines do
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write(9);
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nines := 0
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end
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write(predigit);
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predigit := q;
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if nines <> 0 then
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begin
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for k := 1 to nines do
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write(9);
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nines := 0
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end
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end
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end;
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writeln(predigit);
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@ -1,44 +1,41 @@
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use bigint;
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sub stream {
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my ($next, $safe, $prod, $cons, $z, $x) = @_;
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$x = $x->();
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sub {
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while (1) {
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my $y = $next->($z);
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if ($safe->($z, $y)) {
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$z = $prod->($z, $y);
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return $y;
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} else {
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$z = $cons->($z, $x->());
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}
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}
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sub pistream {
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my $digits = shift;
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my(@out, @a);
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my($b, $c, $d, $e, $f, $g, $i, $d4, $d3, $d2, $d1);
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my $outi = 0;
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$digits++;
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$b = $d = $e = $g = $i = 0;
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$f = 10000;
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$c = 14 * (int($digits/4)+2);
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@a = (20000000) x $c;
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print "3.";
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while (($b = $c -= 14) > 0 && $i < $digits) {
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$d = $e = $d % $f;
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while (--$b > 0) {
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$d = $d * $b + $a[$b];
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$g = ($b << 1) - 1;
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$a[$b] = ($d % $g) * $f;
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$d = int($d / $g);
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}
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$d4 = $e + int($d/$f);
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if ($d4 > 9999) {
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$d4 -= 10000;
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$out[$i-1]++;
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for ($b = $i-1; $out[$b] == 1; $b--) {
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$out[$b] = 0;
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$out[$b-1]++;
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}
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}
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$d3 = int($d4/10);
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$d2 = int($d3/10);
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$d1 = int($d2/10);
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$out[$i++] = $d1;
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$out[$i++] = $d2-$d1*10;
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$out[$i++] = $d3-$d2*10;
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$out[$i++] = $d4-$d3*10;
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print join "", @out[$i-15 .. $i-15+3] if $i >= 16;
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}
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# We've closed the spigot. Print the remainder without rounding.
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print join "", @out[$i-15+4 .. $digits-2], "\n";
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}
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sub extr {
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use integer;
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my ($q, $r, $s, $t) = @{shift()};
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my $x = shift;
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($q * $x + $r) / ($s * $x + $t);
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}
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sub comp {
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my ($q, $r, $s, $t) = @{shift()};
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my ($u, $v, $w, $x) = @{shift()};
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[$q * $u + $r * $w,
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$q * $v + $r * $x,
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$s * $u + $t * $w,
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$s * $v + $t * $x];
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}
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my $pi_stream = stream
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sub { extr shift, 3 },
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sub { my ($z, $n) = @_; $n == extr $z, 4 },
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sub { my ($z, $n) = @_; comp([10, -10*$n, 0, 1], $z) },
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\&comp,
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[1, 0, 0, 1],
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sub { my $n = 0; sub { $n++; [$n, 4 * $n + 2, 0, 2 * $n + 1] } },
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;
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$|++;
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print $pi_stream->(), '.';
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print $pi_stream->() while 1;
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@ -1,55 +1,44 @@
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use Math::BigInt;
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use bigint;
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# Pi/4 = 4 arctan 1/5 - arctan 1/239
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# expanding it with Taylor series with what's probably the dumbest method
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my ($ds, $ns) = (1, 0);
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my ($n5, $d5) = (16 * (25 * 3 - 1), 3 * 5**3);
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my ($n2, $d2) = (4 * (239 * 239 * 3 - 1), 3 * 239**3);
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sub next_term {
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my ($coef, $p) = @_[1, 2];
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$_[0] /= ($p - 4) * ($p - 2);
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$_[0] *= $p * ($p + 2) * $coef**4;
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use bigint try=>"GMP";
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sub stream {
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my ($next, $safe, $prod, $cons, $z, $x) = @_;
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$x = $x->();
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sub {
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while (1) {
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my $y = $next->($z);
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if ($safe->($z, $y)) {
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$z = $prod->($z, $y);
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return $y;
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} else {
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$z = $cons->($z, $x->());
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}
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}
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}
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}
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my $p2 = 5;
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my $pow = 1;
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$| = 1;
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for (my $x = 5; ; $x += 4) {
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($ns, $ds) = ($ns * $d5 + $n5 * $pow * $ds, $ds * $d5);
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next_term($d5, 5, $x);
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$n5 = 16 * (5 * 5 * ($x + 2) - $x);
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while ($d5 > $d2) {
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($ns, $ds) = ($ns * $d2 - $n2 * $pow * $ds, $ds * $d2);
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$n2 = 4 * (239 * 239 * ($p2 + 2) - $p2);
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next_term($d2, 239, $p2);
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$p2 += 4;
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}
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my $ppow = 1;
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while ($pow * $n5 * 5**4 < $d5 && $pow * $n2 * $n2 * 239**4 < $d2) {
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$pow *= 10;
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$ppow *= 10;
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}
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if ($ppow > 1) {
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$ns *= $ppow;
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#FIX? my $out = $ns->bdiv($ds); # bugged?
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my $out = $ns / $ds;
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$ns %= $ds;
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$out = ("0" x (length($ppow) - length($out) - 1)) . $out;
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print $out;
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}
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if ( $p2 % 20 == 1) {
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my $g = Math::BigInt::bgcd($ds, $ns);
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$ds /= $g;
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$ns /= $g;
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}
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sub extr {
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use integer;
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my ($q, $r, $s, $t) = @{shift()};
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my $x = shift;
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($q * $x + $r) / ($s * $x + $t);
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}
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sub comp {
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my ($q, $r, $s, $t) = @{shift()};
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my ($u, $v, $w, $x) = @{shift()};
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[$q * $u + $r * $w,
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$q * $v + $r * $x,
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$s * $u + $t * $w,
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$s * $v + $t * $x];
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}
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my $pi_stream = stream
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sub { extr shift, 3 },
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sub { my ($z, $n) = @_; $n == extr $z, 4 },
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sub { my ($z, $n) = @_; comp([10, -10*$n, 0, 1], $z) },
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\&comp,
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[1, 0, 0, 1],
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sub { my $n = 0; sub { $n++; [$n, 4 * $n + 2, 0, 2 * $n + 1] } },
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;
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$|++;
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print $pi_stream->(), '.';
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print $pi_stream->() while 1;
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54
Task/Pi/Perl/pi-3.pl
Normal file
54
Task/Pi/Perl/pi-3.pl
Normal file
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@ -0,0 +1,54 @@
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use bigint try=>"GMP"
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# Pi/4 = 4 arctan 1/5 - arctan 1/239
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# expanding it with Taylor series with what's probably the dumbest method
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my ($ds, $ns) = (1, 0);
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my ($n5, $d5) = (16 * (25 * 3 - 1), 3 * 5**3);
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my ($n2, $d2) = (4 * (239 * 239 * 3 - 1), 3 * 239**3);
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sub next_term {
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my ($coef, $p) = @_[1, 2];
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$_[0] /= ($p - 4) * ($p - 2);
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$_[0] *= $p * ($p + 2) * $coef**4;
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}
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my $p2 = 5;
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my $pow = 1;
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$| = 1;
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for (my $x = 5; ; $x += 4) {
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($ns, $ds) = ($ns * $d5 + $n5 * $pow * $ds, $ds * $d5);
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next_term($d5, 5, $x);
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$n5 = 16 * (5 * 5 * ($x + 2) - $x);
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while ($d5 > $d2) {
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($ns, $ds) = ($ns * $d2 - $n2 * $pow * $ds, $ds * $d2);
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$n2 = 4 * (239 * 239 * ($p2 + 2) - $p2);
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next_term($d2, 239, $p2);
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$p2 += 4;
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}
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my $ppow = 1;
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while ($pow * $n5 * 5**4 < $d5 && $pow * $n2 * $n2 * 239**4 < $d2) {
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$pow *= 10;
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$ppow *= 10;
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}
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if ($ppow > 1) {
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$ns *= $ppow;
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#FIX? my $out = $ns->bdiv($ds); # bugged?
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my $out = $ns / $ds;
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$ns %= $ds;
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$out = ("0" x (length($ppow) - length($out) - 1)) . $out;
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print $out;
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}
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if ( $p2 % 20 == 1) {
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my $g = Math::BigInt::bgcd($ds, $ns);
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$ds /= $g;
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$ns /= $g;
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}
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}
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18
Task/Pi/Perl/pi-4.pl
Normal file
18
Task/Pi/Perl/pi-4.pl
Normal file
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@ -0,0 +1,18 @@
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use ntheory qw/Pi/;
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say Pi(10000);
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use Math::Pari qw/setprecision Pi/;
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setprecision(10000);
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say Pi;
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use Math::MPFR;
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my $pi = Math::MPFR->new();
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Math::MPFR::Rmpfr_set_prec($pi, int(10000 * 3.322)+40);
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Math::MPFR::Rmpfr_const_pi($pi, 0);
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say Math::MPFR::Rmpfr_get_str($pi, 10, 10000, 0);
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use Math::BigFloat try=>"GMP"; # Slow without Math::BigInt::GMP installed
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say Math::BigFloat::bpi(10000); # For over ~2k digits, slower than AGM
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use Math::Big qw/pi/; # Very slow
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say pi(10000);
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19
Task/Pi/Racket/pi-1.rkt
Normal file
19
Task/Pi/Racket/pi-1.rkt
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@ -0,0 +1,19 @@
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#lang racket
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(require racket/generator)
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(define pidig
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(generator ()
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(let loop ([q 1] [r 0] [t 1] [k 1] [n 3] [l 3])
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(if (< (- (+ r (* 4 q)) t) (* n t))
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(begin (yield n)
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(loop (* q 10) (* 10 (- r (* n t))) t k
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(- (quotient (* 10 (+ (* 3 q) r)) t) (* 10 n))
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l))
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(loop (* q k) (* (+ (* 2 q) r) l) (* t l) (+ 1 k)
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(quotient (+ (* (+ 2 (* 7 k)) q) (* r l)) (* t l))
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(+ l 2))))))
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(for ([i (in-naturals)])
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(display (pidig))
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(when (zero? i) (display "." ))
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(when (zero? (modulo i 80)) (newline)))
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1
Task/Pi/Racket/pi-2.rkt
Normal file
1
Task/Pi/Racket/pi-2.rkt
Normal file
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@ -0,0 +1 @@
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3.14159265358979323846264338327950288419716939937510...
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@ -1,4 +0,0 @@
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#lang racket
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(require math/bigfloat)
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(bf-precision (exact-floor (/ (* 200 (log 10)) (log 2))))
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pi.bf
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