Almkvist-Giullera formula for pi: Difference between revisions
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3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174503
────────────────────────────────────────────── ↑↑↑ the true pi to 160 fractional decimal digits (above) is ↑↑↑ ───────────────────────────────────────────────
</pre>
=={{header|RPL}}==
{{works with|HP|49}}
The starred formula can be implemented like this:
« → n
« 32 6 n * FACT *
532 n SQ * 126 n * + 9 + *
3 / n FACT 6 ^ /
» » '<span style="color:blue">ALMKV</span>' STO
or like that:
« → n '2^5*(6*n)!*(532*SQ(n)+126*n+9)/(3*n!^6)'
» '<span style="color:blue">ALMKV</span>' STO
which is more readable, although a little bit (0.6%) slower than the pure reverse Polish approach.
<code>LDIVN</code> is defined at [[Metallic ratios#RPL|Metallic ratios]]
« 0 → x t
« 0 1
'''WHILE''' DUP x ≤ '''REPEAT''' 4 * '''END'''
'''WHILE''' DUP 1 >
'''REPEAT''' 4 IQUOT
DUP2 + x SWAP - 't' STO
SWAP 2 IQUOT SWAP
'''IF''' t 0 ≥ '''THEN''' t 'x' STO SWAP OVER + SWAP '''END'''
'''END''' DROP
» » '<span style="color:blue">ISQRT</span>' STO
« -105 CF <span style="color:grey">@ set exact mode</span>
« n <span style="color:blue">ALMKV</span> » 'n' 0 9 1 SEQ
-1 → j
« 0 ""
'''DO''' SWAP 'j' INCR LOOK <span style="color:blue">ALMKV</span> 10 6 j * 3 + ^ / + EVAL
'''UNTIL''' DUP FXND <span style="color:blue">ISQRT</span> SWAP <span style="color:blue">ISQRT</span> 70 <span style="color:blue">LDIVN</span> ROT OVER ==
'''END'''
"π" →TAG NIP j "iterations" →TAG
» » '<span style="color:blue">TASK</span>' STO
{{out}}
<pre>
3: { 96 5122560 190722470400 7574824857600000 312546150372456000000 13207874703225491420651520 567273919793089083292259942400 24650600248172987140112763715584000 1080657854354639453670407474439566400000 47701779391594966287470570490839978880000000 }
2: π:"3.1415926535897932384626433832795028841971693993751058209749445923078164"
1: iterations:53
</pre>
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