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-- Some functions to calculate pi digits using mpz integers.
--
-- Reference:
-- https://web.archive.org/web/20111211140154/http://en.literateprograms.org/Pi_with_Machin's_formula_(Python)
--
-- Copyright (C) 2011-2020 Daniele Varrazzo
CREATE FUNCTION arccot(x mpz, unity mpz) RETURNS mpz
LANGUAGE plpgsql IMMUTABLE STRICT
AS $$
DECLARE
xp mpz := unity / x;
xp2 mpz := -(x ^ 2);
acc mpz := xp;
term mpz;
n mpz := 3;
BEGIN
LOOP
xp := xp / xp2;
term := xp / n;
EXIT WHEN term = 0;
acc := acc + term;
n := n + 2;
END LOOP;
RETURN acc;
END
$$;
CREATE FUNCTION pi_machin(ndigits integer) RETURNS mpz
LANGUAGE plpgsql IMMUTABLE STRICT
AS $$
DECLARE
unity mpz = 10::mpz ^ (ndigits + 10);
BEGIN
RETURN 4 * (
4 * arccot(5, unity)
- arccot(239, unity)
) / (10::mpz ^ 10);
END
$$;
CREATE FUNCTION pi_hwang_97(ndigits integer) RETURNS mpz
LANGUAGE plpgsql IMMUTABLE STRICT
AS $$
DECLARE
unity mpz = 10::mpz ^ (ndigits + 10);
BEGIN
RETURN 4 * (
183 * arccot(239, unity)
+ 32 * arccot(1023, unity)
- 68 * arccot(5832, unity)
+ 12 * arccot(110443, unity)
- 12 * arccot(4841182, unity)
- 100 * arccot(6826318, unity)
) / (10::mpz ^ 10);
END
$$;
CREATE FUNCTION pi_hwang_03(ndigits integer) RETURNS mpz
LANGUAGE plpgsql IMMUTABLE STRICT
AS $$
DECLARE
unity mpz = 10::mpz ^ (ndigits + 10);
BEGIN
RETURN 4 * (
183 * arccot(239, unity)
+ 32 * arccot(1023, unity)
- 68 * arccot(5832, unity)
+ 12 * arccot(113021, unity)
- 100 * arccot(6826318, unity)
- 12 * arccot(33366019650, unity)
+ 12 * arccot(43599522992503626068::mpz, unity)
) / (10::mpz ^ 10);
END
$$;
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