source code
-- The Computer Language Benchmarks Game
-- https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
-- contributed by Mike Pall
-- requires LGMP "A GMP package for Lua 5.1"
-- with matrix optimization, courtesy of Wim Couwenberg
local g, aux = {}, {}
require"c-gmp"(g, aux)
local add, mul, div = g.mpz_add, g.mpz_mul_si, g.mpz_tdiv_q
local init, get = g.mpz_init_set_d, g.mpz_get_d
local u, v, w
local function produce(n1, n2, d, k)
mul(n1, 2*k-1, u)
add(n2, n2, v)
mul(n1, k-1, w)
add(u, v, n1)
mul(n2, k+2, u)
add(w, u, n2)
mul(d, 2*k+1, d)
end
local function extract(n1, n2, d, y)
mul(d, -10*y, u)
mul(n1, 10, n1)
add(n1, u, n1)
mul(n2, 10, n2)
add(n2, u, n2)
end
local function digit(n1, n2, d)
local y = get(div(n1, d, u))
if y == get(div(n2, d, v)) then return y end
end
-- Generate successive digits of PI.
local function pidigits(N)
local write = io.write
local k = 1
local n1, n2, d = init(4), init(3), init(1)
u, v, w = init(0), init(0), init(0)
local i = 0
while i < N do
local y = digit(n1, n2, d)
if y then
write(y)
i = i + 1; if i % 10 == 0 then write("\t:", i, "\n") end
extract(n1, n2, d, y)
else
produce(n1, n2, d, k)
k = k + 1
end
end
if i % 10 ~= 0 then write(string.rep(" ", 10 - N % 10), "\t:", N, "\n") end
end
local N = tonumber(arg and arg[1]) or 27
pidigits(N)