Ramanujan's constant: Difference between revisions

In [{{FormulaeEntry|page=https://wiki.formulae.org/?script=examples/Ramanujan%27s_constant this] page you can see the solution of this task.}}

<langsyntaxhighlight lang="go">package main

}</langsyntaxhighlight>

J natively supports arithmetic types Boolean 0 1, integer 00 01 2 3 9, extended integer<ref>Taking a rational power of an extended integer produces a floating-point result whenever the denominator of the power is not 1.</ref> 9x, rational 1r2, floating point as c double, and complex numbers 2ad90 (radius 2, 90 angle in degrees). J does not natively support arbitrary precision decimal, or ternary. J can format a rationalsrational as arbitrary precision base 10 literals.

Rational arithmetic with series expansion therefor serves to compute Ramanujan's constant. We test for convergence in the base 10 literal expression over the required length. Exponential expansion of "long" rational numbers and the number of terms needed for "large" numbers is unwieldly. We divide by 8x, then raise the series sum to the 8th power. We also convert the rational exponent to a base 10 rational number of sufficient digits to reduce size. Tolerant continued fraction expansion reduces the magnitude of the exponent's numerator and denominator.

]RC=: +`%/ }: 1j1 (#!.1) 262537412640768743262537412640768743x 1 1333462407511 1 8 1 1 5 1 4 1 7 1 1 1 9 1 1 2 12 4 1 15 4 299 3 5 1 4 5 5 1 28 3 1 9 4 1 6 1 1 1 1 1 1 51 11 5 3 2 1 1 1 1 2 1 5 1 9 1x

yY =. y -. ' '

iX =. y0 (, i>. ]) '.'x

Iterms =. 'x'0 ,~ i {.$ y0x

Y=: rationalize_decimal1e_36 cf 37j34":1r8*P*S

262537412640768743.99999999999925005844602752370749735164389999999999992500711164316586918409066184

NB. ^

<langsyntaxhighlight lang="java">

<langsyntaxhighlight lang="julia">

<langsyntaxhighlight lang="perl">use strict;

}</langsyntaxhighlight>

<langsyntaxhighlight lang="perl">use strict;

{{libheader|Phix/mpfr}}

<syntaxhighlight lang="raku" perl6line>use Rat::Precise;

if ($mid <= $exp) { $low = $mid; $acc *×= $sqr }

else { $high = $mid; $acc *××= 1/$sqr }

given [ ($a + $g)/2, sqrt $a *× $g ] {

$z -= (.[0] - $a)**2 *× $n;

FatRat.new: sqrt($r.nude[0] *× 10**(D*2D×2) div $r.nude[1]), 10**D;

sub postfix:<!> (Int $n) { (constant f = 1, |[\*×] 1..*)[$n] }

my $Ramanujan = 𝑒**(π* × √163);

my $almost = 𝑒**(π* × √$heegner);

my $exact = $x**3³ + 744;

}</langsyntaxhighlight>

<syntaxhighlight lang="raku" perl6line>use Rat::Precise;

say "Ramanujan's constant to 32 decimal places:\n", $R.precise(32);</langsyntaxhighlight>

Instead of calculating &nbsp; <big> '''e''' </big> &nbsp; and &nbsp; <big><big><math>\pi</math></big></big> &nbsp; to some arbitrary length, &nbsp; it was easier to just include those two constants with &nbsp; '''201''' &nbsp; decimal digits &nbsp; (which is the amount of decimal digits used for the calculations). &nbsp; The results are displayed &nbsp; (right justified) &nbsp; with one -half of that number of decimal digits past the decimal point.

<langsyntaxhighlight lang="rexx">/*REXX pgm displays Ramanujan's constant to at least 100 decimal digits of precision. */

do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g) * .5; end /*k*/; return g</langsyntaxhighlight>

<langsyntaxhighlight lang="ruby">func ramanujan_const(x, decimals=32) {

})</langsyntaxhighlight>