Almkvist-Giullera formula for pi: Difference between revisions
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3.1415926535897932384626433832795028841971693993751058209749445923078164
</pre>
=={{header|Haskell}}==
{{libheader|numbers}}
{{trans|Common Lisp}}
<lang haskell>import GHC.Integer
import Data.Number.CReal
import Text.Printf
-- Factorial for arbitrary-precision integers
facInteger :: Integer -> Integer
facInteger n = if n `leInteger` 1 then 1 else n `timesInteger` facInteger (n `minusInteger` 1)
-- Exponentiation for arbitrary-precision integers
powInteger :: Integer -> Integer -> Integer
powInteger 1 _ = 1
powInteger _ 0 = 1
powInteger b 1 = b
powInteger b e = b `timesInteger` powInteger b (e `minusInteger` 1)
-- The integral part of the Nth term in the Almkvist-Giullera series
integral :: Integer -> Integer
integral n =
let polynomial = (532 `timesInteger` n `timesInteger` n) `plusInteger` (126 `timesInteger` n) `plusInteger` 9
numerator = 32 `timesInteger` (facInteger (6 `timesInteger` n)) `timesInteger` polynomial
denominator = 3 `timesInteger` (powInteger (facInteger n) 6)
in numerator `divInteger` denominator
-- The exponent for 10 in the Nth term of the series
tenExponent :: Integer -> Integer
tenExponent n = 3 `minusInteger` (6 `timesInteger` (1 `plusInteger` n))
-- The Nth term in the series
almkvist'giullera :: Integer -> CReal
almkvist'giullera n = fromInteger (integral n) / fromInteger (powInteger 10 (abs (tenExponent n)))
-- The sum of the first N terms
a'g_sum :: Integer -> CReal
a'g_sum n = sum $ map almkvist'giullera [0 .. n]
-- The approximation of pi from the first N terms
a'g_pi :: Integer -> CReal
a'g_pi n = sqrt $ 1 / a'g_sum n
iterations = 52
main :: IO ()
main = do
(printf "N. %44s %4s %s\n" "Integral part of Nth term" "×10^" "=Actual value of Nth term")
mapM_ (\n -> printf "%d. %44d %4d %s\n" n (integral n) (tenExponent n) (showCReal 50 (almkvist'giullera n))) [0..9]
printf "\nPi after %d iterations:\n" iterations
putStrLn $ showCReal 70 $ a'g_pi iterations</lang>
{{Out}}
<pre>N. Integral part of Nth term ×10^ =Actual value of Nth term
0. 96 -3 0.096
1. 5122560 -9 0.00512256
2. 190722470400 -15 0.0001907224704
3. 7574824857600000 -21 0.0000075748248576
4. 312546150372456000000 -27 0.000000312546150372456
5. 13207874703225491420651520 -33 0.00000001320787470322549142065152
6. 567273919793089083292259942400 -39 0.0000000005672739197930890832922599424
7. 24650600248172987140112763715584000 -45 0.000000000024650600248172987140112763715584
8. 1080657854354639453670407474439566400000 -51 0.0000000000010806578543546394536704074744395664
9. 47701779391594966287470570490839978880000000 -57 0.00000000000004770177939159496628747057049083997888
Pi after 52 iterations:
3.1415926535897932384626433832795028841971693993751058209749445923078164</pre>
=={{header|Julia}}==
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