Base convert functions for PostgreSQL

number_from_base.sql

-- SQL function to convert numbers from custom bases to numeric
-- requires PostgreSQL 9.3+

CREATE OR REPLACE FUNCTION number_from_base(num TEXT, base INTEGER)
  RETURNS NUMERIC
  LANGUAGE sql
  IMMUTABLE
  STRICT
AS $function$
SELECT sum(exp * cn)
FROM (
  SELECT base::NUMERIC ^ (row_number() OVER () - 1) exp,
         CASE
           WHEN ch BETWEEN '0' AND '9' THEN ascii(ch) - ascii('0')
           WHEN ch BETWEEN 'a' AND 'z' THEN 10 + ascii(ch) - ascii('a')
         END cn
  FROM regexp_split_to_table(reverse(lower(num)), '') ch(ch)
) sub
$function$;

number_to_base.sql

-- SQL function to convert bigints to custom bases
-- requires PostgreSQL 9.3+

CREATE OR REPLACE FUNCTION number_to_base(num BIGINT, base INTEGER)
  RETURNS TEXT
  LANGUAGE sql
  IMMUTABLE
  STRICT
AS $function$
WITH RECURSIVE n(i, n, r) AS (
    SELECT -1, num, 0
  UNION ALL
    SELECT i + 1, n / base, (n % base)::INT
    FROM n
    WHERE n > 0
)
SELECT string_agg(ch, '')
FROM (
  SELECT CASE
           WHEN r BETWEEN 0 AND 9 THEN r::TEXT
           WHEN r BETWEEN 10 AND 35 THEN chr(ascii('a') + r - 10)
           ELSE '%'
         END ch
  FROM n
  WHERE i >= 0
  ORDER BY i DESC
) ch
$function$;