-- ATAN2()
-- Two parameter alias of atan2
CREATE OR REPLACE FUNCTION atan(double precision, double precision) 
RETURNS double precision AS $$
  SELECT pg_catalog.atan2($1, $2)
$$ IMMUTABLE STRICT LANGUAGE SQL;

-- CRC32()
CREATE OR REPLACE FUNCTION crc32(text)
RETURNS bigint AS $$
  DECLARE
    -- crc look up table
    -- based on the polynomial:
    -- x^32+x^26+x^23+x^22+x^16+x^12+x^11+x^10+x^8+x^7+x^5+x^4+x^2+x+1

    crc_lu bigint[256] := ARRAY[0, 1996959894, 3993919788, 2567524794, 
      124634137, 1886057615, 3915621685, 2657392035, 249268274, 2044508324, 
      3772115230, 2547177864, 162941995, 2125561021, 3887607047, 2428444049,
      498536548, 1789927666, 4089016648, 2227061214, 450548861, 1843258603,
      4107580753, 2211677639, 325883990, 1684777152, 4251122042, 
      2321926636, 335633487, 1661365465, 4195302755, 2366115317, 
      997073096, 1281953886, 3579855332, 2724688242, 1006888145, 
      1258607687, 3524101629, 2768942443, 901097722, 1119000684, 
      3686517206, 2898065728, 853044451, 1172266101, 3705015759, 
      2882616665, 651767980, 1373503546, 3369554304, 3218104598, 
      565507253, 1454621731, 3485111705, 3099436303, 671266974, 
      1594198024, 3322730930, 2970347812, 795835527, 1483230225, 
      3244367275, 3060149565, 1994146192, 31158534, 2563907772, 
      4023717930, 1907459465, 112637215, 2680153253, 3904427059, 
      2013776290, 251722036, 2517215374, 3775830040, 2137656763, 
      141376813, 2439277719, 3865271297, 1802195444, 476864866, 
      2238001368, 4066508878, 1812370925, 453092731, 2181625025, 
      4111451223, 1706088902, 314042704, 2344532202, 4240017532, 
      1658658271, 366619977, 2362670323, 4224994405, 1303535960, 
      984961486, 2747007092, 3569037538, 1256170817, 1037604311, 
      2765210733, 3554079995, 1131014506, 879679996, 2909243462, 
      3663771856, 1141124467, 855842277, 2852801631, 3708648649, 
      1342533948, 654459306, 3188396048, 3373015174, 1466479909, 
      544179635, 3110523913, 3462522015, 1591671054, 702138776, 
      2966460450, 3352799412, 1504918807, 783551873, 3082640443, 
      3233442989, 3988292384, 2596254646, 62317068, 1957810842, 
      3939845945, 2647816111, 81470997, 1943803523, 3814918930, 
      2489596804, 225274430, 2053790376, 3826175755, 2466906013, 
      167816743, 2097651377, 4027552580, 2265490386, 503444072, 
      1762050814, 4150417245, 2154129355, 426522225, 1852507879, 
      4275313526, 2312317920, 282753626, 1742555852, 4189708143, 
      2394877945, 397917763, 1622183637, 3604390888, 2714866558, 
      953729732, 1340076626, 3518719985, 2797360999, 1068828381, 
      1219638859, 3624741850, 2936675148, 906185462, 1090812512, 
      3747672003, 2825379669, 829329135, 1181335161, 3412177804, 
      3160834842, 628085408, 1382605366, 3423369109, 3138078467, 
      570562233, 1426400815, 3317316542, 2998733608, 733239954, 
      1555261956, 3268935591, 3050360625, 752459403, 1541320221, 
      2607071920, 3965973030, 1969922972, 40735498, 2617837225, 
      3943577151, 1913087877, 83908371, 2512341634, 3803740692, 
      2075208622, 213261112, 2463272603, 3855990285, 2094854071, 
      198958881, 2262029012, 4057260610, 1759359992, 534414190, 
      2176718541, 4139329115, 1873836001, 414664567, 2282248934, 
      4279200368, 1711684554, 285281116, 2405801727, 4167216745, 
      1634467795, 376229701, 2685067896, 3608007406, 1308918612, 
      956543938, 2808555105, 3495958263, 1231636301, 1047427035, 
      2932959818, 3654703836, 1088359270, 936918000, 2847714899, 
      3736837829, 1202900863, 817233897, 3183342108, 3401237130, 
      1404277552, 615818150, 3134207493, 3453421203, 1423857449, 
      601450431, 3009837614, 3294710456, 1567103746, 711928724, 
      3020668471, 3272380065, 1510334235, 755167117];
    crc bigint := 4294967295; -- must use bigint, because we don't have
                              -- an unsigned int32
    len int;
    data ALIAS FOR $1;
    tmp bigint;
    pos int := 1;
    c text;
    d bigint;
  BEGIN
    len = pg_catalog.length(data);
    WHILE len >= pos LOOP
        c := SUBSTRING(data FROM pos FOR 1);
        d := pg_catalog.ascii(c);
        pos = pos + 1;
        tmp = (crc # d) & 255;
        crc = crc_lu[tmp + 1] # (crc >> 8);
    END LOOP;
    crc := crc # 4294967295;
    RETURN crc;
  END
$$ IMMUTABLE STRICT LANGUAGE plpgsql;

-- FORMAT()
-- FIXME: Only handles numbers with integer part up to 21 digits
--
-- MySQL has some bugs with long numbers, but they're not worth replicating:
-- format(9999999999999999999999999999999999999999999999999999999999999999, 10)
--  --> last group has four nines!
-- format(9999999999999999999999999999999999999999999999999999999999999999999999999, 1);
--  --> last group has five nines and no decmial zero
CREATE OR REPLACE FUNCTION format(numeric, integer)
RETURNS text AS $$
  SELECT pg_catalog.to_char(pg_catalog.round($1, $2), 'FM999,999,999,999,999,999,990'
    operator(pg_catalog.||)
      case when $2 > 0 then
        '.' operator(pg_catalog.||) pg_catalog.repeat('0', $2)
      else '' end)
$$ IMMUTABLE STRICT LANGUAGE SQL;

-- LN(), LOG()
-- Not reimplemented but note that PostgreSQL has an error on -ve values,
-- but MySQL just returns NULL.

-- LOG2()
CREATE OR REPLACE FUNCTION log2(numeric)
RETURNS numeric AS $$
  SELECT CASE WHEN $1 > 0 THEN pg_catalog.log(2, $1) ELSE NULL END
$$ IMMUTABLE STRICT LANGUAGE SQL;

-- LOG10()
CREATE OR REPLACE FUNCTION log10(numeric)
RETURNS numeric AS $$
  SELECT CASE WHEN $1 > 0 THEN pg_catalog.log(10, $1) ELSE NULL END
$$ IMMUTABLE STRICT LANGUAGE SQL;

-- MOD()
-- PostgreSQL has all MOD usage the same as MySQL EXCEPT this will not work:
--
-- SELECT 29 MOD 9;

-- RAND()
CREATE OR REPLACE FUNCTION rand() RETURNS double precision AS $$
  SELECT pg_catalog.random()
$$ VOLATILE LANGUAGE SQL;

CREATE OR REPLACE FUNCTION rand(integer) RETURNS double precision AS $$
  SELECT pg_catalog.setseed($1); 
  SELECT pg_catalog.random()
$$ VOLATILE LANGUAGE SQL;

-- SQRT()
-- Not reimplemented but note that PostgreSQL has an error on -ve values,
-- but MySQL just returns NULL.

-- TRUNCATE()
CREATE OR REPLACE FUNCTION truncate(numeric, integer)
RETURNS numeric AS $$
  SELECT pg_catalog.trunc($1, $2)
$$ IMMUTABLE STRICT LANGUAGE SQL;