Pi: Difference between revisions
add lambdatalk code
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3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745...
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=={{header|Lambdatalk}}==
1) We can build a lambdatalk function using the lib_BN javascript library.
<syntaxhighlight lang="scheme">
{require lib_BN}
{def genpi
{def genpi.loop
{lambda {:n :pi :q :r :t :i :z}
{if {> :z :n}
then :pi
else {let { {:n :n} {:pi :pi} {:q :q} {:r :r} {:t :t} {:i :i} {:z :z}
{:digit {BN./ {BN.+ {BN.* {BN.- {BN.* :i 27} 12} :q}
{BN.* :r 5} }
{BN.* :t 5} } }
{:u {BN.* {BN.+ {BN.* :i 3} 1}
{BN.* 3 {BN.+ {BN.* :i 3} 2} } } }
} {genpi.loop :n
{BN.+ :pi :digit}
{BN.* {BN.* :q 1}
{BN.* :i {BN.- {BN.* :i 2} 1} }}
{BN.* {BN.* :u 1}
{BN.+ {BN.* :q {BN.- {BN.* :i 5} 2} }
{BN.- :r {BN.* :t :digit} }}}
{BN.* :t :u}
{BN.+ :i 1}
{+ :z 1}} }}}}
{lambda {:n}
{genpi.loop :n # 1 180 60 2 0} }}
-> genpi
We can generate π with 72 digits in about 500ms.
{BN.DEC 72}
-> 72 digits
{genpi 60}
-> 3.141592653589793238462643383279502884197169399375105820974944592307816406
</syntaxhighlight>
To go further the best is to build a javascript primitive using the script special form.
<syntaxhighlight lang="scheme">
{script
LAMBDATALK.DICT["spigot"] = function() {
function generateDigitsOfPi(max) {
var pi = "";
var z = 0;
var q = 1n;
var r = 180n;
var t = 60n;
var i = 2n;
while (z < max) {
var digit = ((i * 27n - 12n) * q + r * 5n) / (t * 5n);
pi += digit;
var u = (i * 3n + 1n) * 3n * (i * 3n + 2n);
r = u * 10n * (q * (i * 5n - 2n) + (r - t * digit));
q = q * 10n * i * (i * 2n - 1n);
i = i + 1n;
t = t * u;
z++;
}
return pi
}
var args = arguments[0].trim();
return generateDigitsOfPi( args );
};
}
We can generate 1000 digits of π in about 70ms
3.{W.rest {spigot 100}}
-> 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198
</syntaxhighlight>
=={{header|Lasso}}==
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