Arithmetic-geometric mean/Calculate Pi: Difference between revisions
Arithmetic-geometric mean/Calculate Pi (view source)
Revision as of 01:37, 25 January 2024
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{{out}}
<pre>3.141592653589794</pre>
==={{header|IS-BASIC}}===
<syntaxhighlight lang="is-basic">100 PROGRAM "PI.bas"
110 LET DIGITS=10
120 LET AN,PN=1
130 LET BN=SQR(.5)
140 LET TN=.5^2
150 DO WHILE PN<=DIGITS
160 LET PREVAN=AN
170 LET AN=(BN+AN)/2
180 LET BN=SQR(BN*PREVAN)
190 LET PREVAN=PREVAN-AN
200 LET TN=TN-(PN*PREVAN^2)
210 LET PN=PN+PN
220 LOOP
230 PRINT (AN+BN)^2/(TN*4)</syntaxhighlight>
==={{header|True BASIC}}===
Line 566 ⟶ 582:
3.141592653589793238...81377399510065895288
</pre>
=={{header|EasyLang}}==
{{trans|FreeBASIC}}
<syntaxhighlight lang=easylang>
an = 1
bn = sqrt 0.5
tn = 0.25
pn = 1
while pn <= 5
prevAn = an
an = (bn + an) / 2
bn = sqrt (bn * prevAn)
prevAn -= an
tn -= (pn * prevAn * prevAn)
pn *= 2
.
mypi = (an + bn) * (an + bn) / (tn * 4)
numfmt 15 0
print mypi
</syntaxhighlight>
=={{header|Erlang}}==
{{trans|python}}
Line 646 ⟶ 682:
Iteration: 4 Diff: 3.05653257536554156111405386493810661E-0010 Pi: 3.14159265358979323846636060270664556
Iteration: 5 Diff: 3.71721942712928151094186846648146566E-0021 Pi: 3.14159265358979323846264338327951628
</pre>
=={{header|FutureBasic}}==
<syntaxhighlight lang="futurebasic">
double a, c, g, t, p
double apprpi
short i
// Initial values
a = 1
g = sqr(0.5)
p = 1
t = 0.25
//Iterate just 3 times
for i = 1 to 3
c = a
a = ( a + g ) / 2
g = sqr( c * g )
c -= a
t -= ( p * c^2 )
p *= 2
apprpi = (( a + g )^2) / ( t * 4 )
print "Iteration "i": ", apprpi
next
print "Actual value:",pi
handleevents
</syntaxhighlight>
{{output}}
<pre>
Iteration 1: 3.140579250522169
Iteration 2: 3.141592646213543
Iteration 3: 3.141592653589794
Actual value: 3.141592653589793
</pre>
Line 1,025 ⟶ 1,099:
pi[7, 100]
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628046852228654</syntaxhighlight>
=={{header|MATLAB}}==
{{trans|Julia}}
<syntaxhighlight lang="MATLAB">
clear all;close all;clc;
testMakePi();
function [a, g] = agm1step(x, y)
a = (x + y) / 2;
g = sqrt(x * y);
end
function [a, g, s, k] = approxPiStep(x, y, z, n)
[a, g] = agm1step(x, y);
k = n + 1;
s = z + 2^(k + 1) * (a^2 - g^2);
end
function pi_approx = approxPi(a, g, s)
pi_approx = 4 * a^2 / (1 - s);
end
function testMakePi()
digits(512); % Set the precision for variable-precision arithmetic
a = vpa(1.0);
g = 1 / sqrt(vpa(2.0));
s = vpa(0.0);
k = 0;
oldPi = vpa(0.0);
% Define a small value as a threshold for convergence
convergence_threshold = vpa(10)^(-digits);
fprintf(' k Error Result\n');
for i = 1:100
[a, g, s, k] = approxPiStep(a, g, s, k);
estPi = approxPi(a, g, s);
if abs(estPi - oldPi) < convergence_threshold
break;
end
oldPi = estPi;
err = abs(vpa(pi) - estPi);
fprintf('%4d%10.1e', i, double(err));
fprintf('%70.60f\n', double(estPi));
end
end
</syntaxhighlight>
{{out}}
<pre>
k Error Result
1 4.6e-02 3.187672642712108483920019352808594703674316406250000000000000
2 8.8e-05 3.141680293297653303596916884998790919780731201171875000000000
3 3.1e-10 3.141592653895446396461466065375134348869323730468750000000000
4 3.7e-21 3.141592653589793115997963468544185161590576171875000000000000
5 5.5e-43 3.141592653589793115997963468544185161590576171875000000000000
6 1.2e-86 3.141592653589793115997963468544185161590576171875000000000000
7 5.8e-174 3.141592653589793115997963468544185161590576171875000000000000
8 0.0e+00 3.141592653589793115997963468544185161590576171875000000000000
9 0.0e+00 3.141592653589793115997963468544185161590576171875000000000000
</pre>
=={{header|МК-61/52}}==
Line 1,038 ⟶ 1,173:
=={{header|Nim}}==
{{libheader|bignum}}
{{Trans|
<syntaxhighlight lang="nim">from math import sqrt
import times
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{{trans|Sidef}}
{{libheader|Wren-big}}
<syntaxhighlight lang="
var digits = 500
| |||