Computing the digits of π in SQLite3

pi_spigot.sql

-- ref. https://xn--w6q13e505b.jp/program/spigot.html

create table consts as
  select 1000 ndigits;

.timer on

with a(i) as (
    select ndigits/4*14 from consts
    union all select i-1 from a where i>0
  ),
  loop(step, n, i, p, carry, digit, denom, nume, out) as (
    select 0
      , (select ndigits/4*14 from consts)       -- n
      , (select ndigits/4*14-1 from consts)     -- i
      , 0, 0, 0, 0                              -- p, carry, digit, denom
      , (select json_group_array(2000) from a)  -- nume
      , '_'                                     -- out
    union all select
      step + 1
      , case when i > 0 then n else n-14 end    -- n
      , case when i > 0 then i-p else n-15 end  -- i
      ,  case when i > 0 then 1-p else 0 end    -- p
      /* carry */
      , case when i > 0 then
          case when p = 0 then (carry * i + 10000 * json_extract(nume, '$['||i||']')) else carry / denom end
          else carry % 10000
        end
      /* digit */
      , case when i > 0 then digit else carry % 10000 end
      /* denom */ 
      , case when i > 0 and p = 0 then 2*i-1 else denom end
      /* nume */
      , case when i > 0 then
          case when p = 1 then json_set(nume, '$['||i||']', carry % denom) else  nume end
          else nume
        end
      /* out */
      , case when i > 0 then null else printf('%04d', digit + carry / 10000) end
    from loop
    where n > 0
  )
select
  replace(group_concat(out, ''), '_3', '3.') pi
from loop
where out is not null;

benchmarks

shell	time(sec)
v3.31.1 on WSL	44.328
WASM shell v3.39.0 on Chrome v102	116.029
WASM shell v3.39.0 on Firefox v100	127.253

wasm shell: https://www.sqlite.org/fiddle/