source code
-- The Computer Language Benchmarks Game
-- https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
-- contributed by Mike Pall
-- requires LGMP which requires lua >= 5.1, < 5.4
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 q, r, s, t, u, v, w
-- Compose matrix with numbers on the right.
local function compose_r(bq, br, bs, bt)
mul(r, bs, u)
mul(r, bq, r)
mul(t, br, v)
add(r, v, r)
mul(t, bt, t)
add(t, u, t)
mul(s, bt, s)
mul(q, bs, u)
add(s, u, s)
mul(q, bq, q)
end
-- Compose matrix with numbers on the left.
local function compose_l(bq, br, bs, bt)
mul(r, bt, r)
mul(q, br, u)
add(r, u, r)
mul(t, bs, u)
mul(t, bt, t)
mul(s, br, v)
add(t, v, t)
mul(s, bq, s)
add(s, u, s)
mul(q, bq, q)
end
-- Extract one digit.
local function extract(j)
mul(q, j, u)
add(u, r, u)
mul(s, j, v)
add(v, t, v)
return get(div(u, v, w))
end
-- Generate successive digits of PI.
local function pidigits(N)
local write = io.write
local k = 1
q, r, s, t = init(1), init(0), init(0), init(1)
u, v, w = init(0), init(0), init(0)
local i = 0
while i < N do
local y = extract(3)
if y == extract(4) then
write(y)
i = i + 1; if i % 10 == 0 then write("\t:", i, "\n") end
compose_r(10, -10*y, 0, 1)
else
compose_l(k, 4*k+2, 0, 2*k+1)
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)