pidigits Lua #7 program

source code

```-- The Computer Language Benchmarks Game
-- https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
-- contributed by Wim Couwenberg
--
-- requires LGMP which requires lua >= 5.1, < 5.4
--
-- 21 September 2008

local gmp, aux = {}, {}
require "c-gmp" (gmp, aux)
local init, get, set = gmp.mpz_init_set_d, gmp.mpz_get_d, gmp.mpz_set

--
-- Production:
--
-- [m11 m12]     [m11 m12][k  4*k+2]
-- [ 0  m22] <-- [ 0  m22][0  2*k+1]
--
local function produce(m11, m12, m22, k)
local p = 2*k + 1
mul(m12, p, m12)
mul(m11, k, m11)
mul(m22, p, m22)
end

--
-- Extraction:
--
-- [m11 m12]     [10 -10*d][m11 m12]
-- [ 0  m22] <-- [ 0   1  ][ 0  m22]
--
local function extract(m11, m12, m22, d)
submul(m12, m22, d)
mul(m11, 10, m11)
mul(m12, 10, m12)
end

--
-- Get integral part of p/q where
--
-- [p]   [m11 m12][d]
-- [q] = [ 0  m22][1]
--
local function digit(m11, m12, m22, d, tmp)
set(tmp, m12)
div(tmp, m22, tmp)
return get(tmp)
end

-- Generate successive digits of PI.
local function pidigits(N)
local write = io.write
local m11, m12, m22, tmp = init(1), init(0), init(1), init(0)
local k, i = 1, 0
while i < N do
local d = digit(m11, m12, m22, 3, tmp)
if d == digit(m11, m12, m22, 4, tmp) then
write(d)
extract(m11, m12, m22, d)
i = i + 1; if i % 10 == 0 then write("\t:", i, "\n") end
else
produce(m11, m12, m22, 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)

```

notes, command-line, and program output

```NOTES:
1994-2023 Lua.org, PUC-Rio

Sun, 26 May 2024 03:37:59 GMT

COMMAND LINE:
/opt/src/lua-5.4.6/install/bin/lua  pidigits.lua-7.lua 2000

PROGRAM FAILED

PROGRAM OUTPUT:

no file '/usr/local/share/lua/5.4/c-gmp.lua'
no file '/usr/local/share/lua/5.4/c-gmp/init.lua'
no file '/usr/local/lib/lua/5.4/c-gmp.lua'
no file '/usr/local/lib/lua/5.4/c-gmp/init.lua'
no file './c-gmp.lua'
no file './c-gmp/init.lua'
no file '/opt/src/luarocks/lib/lua/5.3/c-gmp.so'
stack traceback:
[C]: in function 'require'
pidigits.lua-7.lua:10: in main chunk
[C]: in ?
```