Arithmetic-geometric mean/Calculate Pi: Difference between revisions
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m (→version 2: added wording to the REXX version 2 section header, added/changed whitespace and comments, added a template for the output sections.) |
m (→{{header|REXX}}: added whitespace and comments, used a template for the output sections.) |
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=={{header|REXX}}== |
=={{header|REXX}}== |
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{{trans|Ruby}} |
{{trans|Ruby}} |
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Programming note: the number of digits to be used in the calculations can be specified on the C.L. ('''c'''ommand '''l'''ine). |
Programming note: the number of digits to be used in the calculations can be specified on the C.L. ('''c'''ommand '''l'''ine). |
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Whatever number of digits used, the actual number of digits is five larger than specified, and then the result is rounded to the requested number of digits. |
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===version 1=== |
===version 1=== |
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<lang rexx>/*REXX program calculates the value of pi using the AGM algorithm. */ |
<lang rexx>/*REXX program calculates the value of pi using the AGM algorithm. */ |
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parse arg d .; if d=='' | d=="," then d= |
parse arg d .; if d=='' | d=="," then d= 500 /*D not specified? Then use default. */ |
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numeric digits d+5 /*set the numeric decimal digits to D+5*/ |
numeric digits d+5 /*set the numeric decimal digits to D+5*/ |
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z=1/4; |
z= 1/4; a= 1; g= sqrt(1/2) /*calculate some initial values. */ |
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n=1 |
n= 1 |
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do j=1 until a==old; old= a /*keep calculating until no more noise.*/ |
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x= (a+g) * .5; g= sqrt(a*g) /*calculate the next set of terms. */ |
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z= z - n*(x-a)**2; n= n+n; a= x /*Z is used in the final calculation. */ |
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end /*j*/ /* [↑] stop if A equals OLD. */ |
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pi=a**2 / z |
pi= a**2 / z /*compute the finished value of pi. */ |
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numeric digits d /*set the numeric decimal digits to D.*/ |
numeric digits d /*set the numeric decimal digits to D.*/ |
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say pi / 1 /*display the computed value of pi. */ |
say pi / 1 /*display the computed value of pi. */ |
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exit |
exit 0 /*stick a fork in it, we're all done. */ |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); numeric digits; h=d+6 |
sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); numeric digits; h=d+6 |
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Programming note: the '''sqrt''' subroutine (above) is optimized for larger ''digits''. |
Programming note: the '''sqrt''' subroutine (above) is optimized for larger ''digits''. |
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{{out|output|text= when using the default number of digits: <tt> 500 </tt>}} |
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<pre> |
<pre> |
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3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491 |
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491 |
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