--
--  Test mpz datatype
--
-- Compact output
\t
\a
SELECT gmp_version() > 10000;
t
--
-- mpz input and output functions
--
SELECT '0'::mpz;
0
SELECT '1'::mpz;
1
SELECT '-1'::mpz;
-1
SELECT '10'::mpz;
10
SELECT '-10'::mpz;
-10
SELECT '000001'::mpz;       -- padding zeros
1
SELECT '-000001'::mpz;
-1
SELECT '4294967295'::mpz;   -- limbs boundaries
4294967295
SELECT '4294967296'::mpz;
4294967296
SELECT '-4294967296'::mpz;
-4294967296
SELECT '-4294967297'::mpz;
-4294967297
SELECT '18446744073709551614'::mpz;
18446744073709551614
SELECT '18446744073709551615'::mpz;
18446744073709551615
SELECT '18446744073709551616'::mpz;
18446744073709551616
SELECT '18446744073709551617'::mpz;
18446744073709551617
SELECT '-18446744073709551615'::mpz;
-18446744073709551615
SELECT '-18446744073709551616'::mpz;
-18446744073709551616
SELECT '-18446744073709551617'::mpz;
-18446744073709551617
SELECT '-18446744073709551618'::mpz;
-18446744073709551618
SELECT '12345678901234567890123456789012345678901234567890123456789012345678901234567890'::mpz;
12345678901234567890123456789012345678901234567890123456789012345678901234567890
-- other bases
SELECT '0x10'::mpz, '010'::mpz, '0b10'::mpz;
16|8|2
SELECT mpz('10'), mpz('10', 16), mpz('10', 2);
10|16|2
SELECT mpz('10', 62);
62
SELECT mpz('10', 1);
ERROR:  invalid base for mpz input: 1
HINT:  base should be between 2 and 62
SELECT mpz('10', 63);
ERROR:  invalid base for mpz input: 63
HINT:  base should be between 2 and 62
SELECT mpz('10', 0), mpz('0x10', 0), mpz('010', 0), mpz('0b10', 0);
10|16|8|2
SELECT text(10::mpz);
10
SELECT text(10::mpz, 2);
1010
SELECT text(10::mpz, -2);
1010
SELECT text(255::mpz, 16);
ff
SELECT text((36 * 36 - 1)::mpz, 36);
zz
SELECT text((62 * 62 - 1)::mpz, 62);
zz
SELECT text((36 * 36 - 1)::mpz, -36);
ZZ
SELECT text(10::mpz, -37);
ERROR:  invalid base for mpz output: -37
HINT:  base should be between -36 and -2 or between 2 and 62
SELECT text(10::mpz, -1);
ERROR:  invalid base for mpz output: -1
HINT:  base should be between -36 and -2 or between 2 and 62
SELECT text(10::mpz, 0);
ERROR:  invalid base for mpz output: 0
HINT:  base should be between -36 and -2 or between 2 and 62
SELECT text(10::mpz, 1);
ERROR:  invalid base for mpz output: 1
HINT:  base should be between -36 and -2 or between 2 and 62
SELECT text(10::mpz, 63);
ERROR:  invalid base for mpz output: 63
HINT:  base should be between -36 and -2 or between 2 and 62
-- limited error
SELECT ('xx' || repeat('1234567890', 10))::mpz;
ERROR:  invalid input for mpz: "xx123456789012345678901234567890123456789012345678..."
SELECT mpz('xx' || repeat('1234567890', 10), 42);
ERROR:  invalid input for mpz base 42: "xx123456789012345678901234567890123456789012345678..."
--
-- mpz cast
--
SELECT 0::smallint::mpz, (-32768)::smallint::mpz, 32767::smallint::mpz;
0|-32768|32767
SELECT 0::integer::mpz, (-2147483648)::integer::mpz, 2147483647::integer::mpz;
0|-2147483648|2147483647
SELECT 0::bigint::mpz, (-9223372036854775808)::bigint::mpz, 9223372036854775807::bigint::mpz;
0|-9223372036854775808|9223372036854775807
SELECT 0::numeric::mpz, (-12345678901234567890)::numeric::mpz, 12345678901234567890::numeric::mpz;
0|-12345678901234567890|12345678901234567890
-- decimal are truncated
SELECT 123.10::numeric::mpz, 123.90::numeric::mpz;
123|123
SELECT (-123.10::numeric)::mpz, (-123.90::numeric)::mpz;
-123|-123
SELECT 'NaN'::numeric::mpz;
ERROR:  can't convert numeric value to mpz: "NaN"
SELECT 0.0::float4::mpz, 123.15::float4::mpz, 123.95::float4::mpz;
0|123|123
SELECT (1e36::float4)::mpz BETWEEN pow(10::mpz,36) - pow(10::mpz,30) AND pow(10::mpz,36) + pow(10::mpz,30);
t
SELECT (-1e36::float4)::mpz BETWEEN -pow(10::mpz,36) - pow(10::mpz,30) AND -pow(10::mpz,36) + pow(10::mpz,30);
t
SELECT 'NaN'::float4::mpz;
ERROR:  can't convert float value to mpz: "nan"
SELECT 'Infinity'::float4::mpz;
ERROR:  can't convert float value to mpz: "inf"
SELECT '-Infinity'::float4::mpz;
ERROR:  can't convert float value to mpz: "-inf"
SELECT 0.0::float8::mpz, 123.15::float8::mpz, 123.95::float8::mpz;
0|123|123
SELECT (1e307::float8)::mpz BETWEEN pow(10::mpz,307) - pow(10::mpz,307-15) AND pow(10::mpz,307) + pow(10::mpz,307-15);
t
SELECT (-1e307::float8)::mpz BETWEEN -pow(10::mpz,307) - pow(10::mpz,307-15) AND -pow(10::mpz,307) + pow(10::mpz,307-15);
t
SELECT 'NaN'::float8::mpz;
ERROR:  can't convert float value to mpz: "nan"
SELECT 'Infinity'::float8::mpz;
ERROR:  can't convert float value to mpz: "inf"
SELECT '-Infinity'::float8::mpz;
ERROR:  can't convert float value to mpz: "-inf"
SELECT 0::mpz, 1::mpz, (-1)::mpz;       -- automatic casts
0|1|-1
SELECT 1000000::mpz, (-1000000)::mpz;
1000000|-1000000
SELECT 1000000000::mpz, (-1000000000)::mpz;
1000000000|-1000000000
SELECT 1000000000000000::mpz, (-1000000000000000)::mpz;
1000000000000000|-1000000000000000
SELECT 1000000000000000000000000000000::mpz, (-1000000000000000000000000000000)::mpz;
1000000000000000000000000000000|-1000000000000000000000000000000
SELECT -1::mpz;       -- these take the unary minus to work
-1
SELECT -1000000::mpz;
-1000000
SELECT -1000000000::mpz;
-1000000000
SELECT -1000000000000000::mpz;
-1000000000000000
SELECT -1000000000000000000000000000000::mpz;
-1000000000000000000000000000000
SELECT 32767::mpz::int2;
32767
SELECT 32768::mpz::int2;
ERROR:  numeric value too big to be converted to int2 data type
SELECT (-32768)::mpz::int2;
-32768
SELECT (-32769)::mpz::int2;
ERROR:  numeric value too big to be converted to int2 data type
SELECT 2147483647::mpz::int4;
2147483647
SELECT 2147483648::mpz::int4;
ERROR:  numeric value too big to be converted to int4 data type
SELECT (-2147483648)::mpz::int4;
-2147483648
SELECT (-2147483649)::mpz::int4;
ERROR:  numeric value too big to be converted to int4 data type
SELECT 9223372036854775807::mpz::int8;
9223372036854775807
SELECT 9223372036854775808::mpz::int8;
ERROR:  numeric value too big to be converted to int8 data type
SELECT (-9223372036854775808)::mpz::int8;
-9223372036854775808
SELECT (-9223372036854775809)::mpz::int8;
ERROR:  numeric value too big to be converted to int8 data type
SELECT (2147483648)::mpz::int8;
2147483648
SELECT (-2147483648)::mpz::int8;
-2147483648
SELECT (65536::mpz)::bigint;
65536
SELECT (65536::mpz*65536::mpz)::bigint;
4294967296
SELECT (65536::mpz*65536::mpz*65536::mpz)::bigint;
281474976710656
SELECT (65536::mpz*65536::mpz*65536::mpz*65536::mpz/2::mpz-1::mpz)::bigint;
9223372036854775807
SELECT (65536::mpz*65536::mpz*65536::mpz*65536::mpz/2::mpz)::bigint;
ERROR:  numeric value too big to be converted to int8 data type
SELECT (-65536::mpz)::bigint;
-65536
SELECT (-65536::mpz*65536::mpz)::bigint;
-4294967296
SELECT (-65536::mpz*65536::mpz*65536::mpz)::bigint;
-281474976710656
SELECT (-65536::mpz*65536::mpz*65536::mpz*65536::mpz/2::mpz+1::mpz)::bigint;
-9223372036854775807
SELECT (-65536::mpz*65536::mpz*65536::mpz*65536::mpz/2::mpz)::bigint;
-9223372036854775808
SELECT (65536::mpz)::numeric;
65536
SELECT (65536::mpz*65536::mpz)::numeric;
4294967296
SELECT (65536::mpz*65536::mpz*65536::mpz)::numeric;
281474976710656
SELECT (65536::mpz*65536::mpz*65536::mpz*65536::mpz)::numeric;
18446744073709551616
SELECT (65536::mpz*65536::mpz*65536::mpz*65536::mpz-1::mpz)::numeric;
18446744073709551615
SELECT (-65536::mpz)::numeric;
-65536
SELECT (-65536::mpz*65536::mpz)::numeric;
-4294967296
SELECT (-65536::mpz*65536::mpz*65536::mpz)::numeric;
-281474976710656
SELECT (-65536::mpz*65536::mpz*65536::mpz*65536::mpz)::numeric;
-18446744073709551616
SELECT (-65536::mpz*65536::mpz*65536::mpz*65536::mpz+1::mpz)::numeric;
-18446744073709551615
SELECT 0::mpz::float4, 123::mpz::float4, (-123::mpz)::float4;
0|123|-123
SELECT pow(10::mpz, 30)::float4, (-pow(10::mpz, 30))::float4;
1e+30|-1e+30
SELECT pow(10::mpz, 300)::float4, (-pow(10::mpz, 300))::float4;
Infinity|-Infinity
SELECT 0::mpz::float8, 123::mpz::float8, (-123::mpz)::float8;
0|123|-123
SELECT pow(10::mpz, 307)::float8, (-pow(10::mpz, 307))::float8;
1e+307|-1e+307
SELECT pow(10::mpz, 407)::float8, (-pow(10::mpz, 407))::float8;
Infinity|-Infinity
-- function-style casts
SELECT mpz('0'::varchar);
0
SELECT mpz('0'::int2);
0
SELECT mpz('0'::int4);
0
SELECT mpz('0'::int8);
0
SELECT mpz('0'::float4);
0
SELECT mpz('0'::float8);
0
SELECT mpz('0'::numeric);
0
SELECT text(0::mpz);
0
SELECT int2(0::mpz);
0
SELECT int4(0::mpz);
0
SELECT int8(0::mpz);
0
SELECT float4(0::mpz);
0
SELECT float8(0::mpz);
0
--
-- mpz arithmetic
--
SELECT -('0'::mpz), +('0'::mpz), -('1'::mpz), +('1'::mpz);
0|0|-1|1
SELECT -('12345678901234567890'::mpz), +('12345678901234567890'::mpz);
-12345678901234567890|12345678901234567890
SELECT abs('-1234567890'::mpz), abs('1234567890'::mpz);
1234567890|1234567890
SELECT sgn(0::mpz), sgn('-1234567890'::mpz), sgn('1234567890'::mpz);
0|-1|1
SELECT even(10::mpz), even(11::mpz);
t|f
SELECT odd(10::mpz), odd(11::mpz);
f|t
SELECT '1'::mpz + '2'::mpz;
3
SELECT '2'::mpz + '-4'::mpz;
-2
SELECT regexp_matches((
        ('1' || repeat('0', 1000))::mpz +
        ('2' || repeat('0', 1000))::mpz)::text,
    '^3(0000000000){100}$') IS NOT NULL;
t
SELECT '3'::mpz - '2'::mpz;
1
SELECT '3'::mpz - '5'::mpz;
-2
SELECT regexp_matches((
        ('5' || repeat('0', 1000))::mpz -
        ('2' || repeat('0', 1000))::mpz)::text,
    '^3(0000000000){100}$') IS NOT NULL;
t
SELECT '3'::mpz * '2'::mpz;
6
SELECT '3'::mpz * '-5'::mpz;
-15
SELECT regexp_matches((
        ('2' || repeat('0', 1000))::mpz *
        ('3' || repeat('0', 1000))::mpz)::text,
    '^6(00000000000000000000){100}$') IS NOT NULL;
t
-- PostgreSQL should apply the conventional precedence to operators
-- with the same name of the builtin operators.
SELECT '2'::mpz + '6'::mpz * '7'::mpz;  -- cit.
44
SELECT  '7'::mpz /  '3'::mpz;
2
SELECT '-7'::mpz /  '3'::mpz;
-2
SELECT  '7'::mpz / '-3'::mpz;
-2
SELECT '-7'::mpz / '-3'::mpz;
2
SELECT  '7'::mpz %  '3'::mpz;
1
SELECT '-7'::mpz %  '3'::mpz;
-1
SELECT  '7'::mpz % '-3'::mpz;
1
SELECT '-7'::mpz % '-3'::mpz;
-1
SELECT  '7'::mpz +/  '3'::mpz;
3
SELECT '-7'::mpz +/  '3'::mpz;
-2
SELECT  '7'::mpz +/ '-3'::mpz;
-2
SELECT '-7'::mpz +/ '-3'::mpz;
3
SELECT  '7'::mpz +%  '3'::mpz;
-2
SELECT '-7'::mpz +%  '3'::mpz;
-1
SELECT  '7'::mpz +% '-3'::mpz;
1
SELECT '-7'::mpz +% '-3'::mpz;
2
SELECT  '7'::mpz -/  '3'::mpz;
2
SELECT '-7'::mpz -/  '3'::mpz;
-3
SELECT  '7'::mpz -/ '-3'::mpz;
-3
SELECT '-7'::mpz -/ '-3'::mpz;
2
SELECT  '7'::mpz -%  '3'::mpz;
1
SELECT '-7'::mpz -%  '3'::mpz;
2
SELECT  '7'::mpz -% '-3'::mpz;
-2
SELECT '-7'::mpz -% '-3'::mpz;
-1
SELECT  '7'::mpz /  '0'::mpz;
ERROR:  division by zero
SELECT  '7'::mpz %  '0'::mpz;
ERROR:  division by zero
SELECT  '7'::mpz +/  '0'::mpz;
ERROR:  division by zero
SELECT  '7'::mpz +%  '0'::mpz;
ERROR:  division by zero
SELECT  '7'::mpz -/  '0'::mpz;
ERROR:  division by zero
SELECT  '7'::mpz -%  '0'::mpz;
ERROR:  division by zero
SELECT  '21'::mpz /! '7'::mpz;
3
SELECT  '10000000000'::mpz << 10;
10240000000000
SELECT  '10000000000'::mpz << 0;
10000000000
SELECT  '10000000000'::mpz << -1;
ERROR:  argument can't be negative
SELECT  '1027'::mpz >>   3;
128
SELECT '-1027'::mpz >>   3;
-128
SELECT  '1027'::mpz >>  -3;
ERROR:  argument can't be negative
SELECT  '1027'::mpz %>   3;
3
SELECT '-1027'::mpz %>   3;
-3
SELECT  '1027'::mpz %>  -3;
ERROR:  argument can't be negative
SELECT  '1027'::mpz +>>   3;
129
SELECT '-1027'::mpz +>>   3;
-128
SELECT  '1027'::mpz +>>  -3;
ERROR:  argument can't be negative
SELECT  '1027'::mpz +%>   3;
-5
SELECT '-1027'::mpz +%>   3;
-3
SELECT  '1027'::mpz +%>  -3;
ERROR:  argument can't be negative
SELECT  '1027'::mpz ->>   3;
128
SELECT '-1027'::mpz ->>   3;
-129
SELECT  '1027'::mpz ->>  -3;
ERROR:  argument can't be negative
SELECT  '1027'::mpz -%>   3;
3
SELECT '-1027'::mpz -%>   3;
5
SELECT  '1027'::mpz -%>  -3;
ERROR:  argument can't be negative
SELECT q, r from tdiv_qr( 7::mpz,  3::mpz);
2|1
SELECT q, r from tdiv_qr(-7::mpz,  3::mpz);
-2|-1
SELECT q, r from tdiv_qr( 7::mpz, -3::mpz);
-2|1
SELECT q, r from tdiv_qr(-7::mpz, -3::mpz);
2|-1
SELECT q, r from tdiv_qr( 7::mpz,  0::mpz);
ERROR:  division by zero
SELECT q, r from cdiv_qr( 7::mpz,  3::mpz);
3|-2
SELECT q, r from cdiv_qr(-7::mpz,  3::mpz);
-2|-1
SELECT q, r from cdiv_qr( 7::mpz, -3::mpz);
-2|1
SELECT q, r from cdiv_qr(-7::mpz, -3::mpz);
3|2
SELECT q, r from cdiv_qr( 7::mpz,  0::mpz);
ERROR:  division by zero
SELECT q, r from fdiv_qr( 7::mpz,  3::mpz);
2|1
SELECT q, r from fdiv_qr(-7::mpz,  3::mpz);
-3|2
SELECT q, r from fdiv_qr( 7::mpz, -3::mpz);
-3|-2
SELECT q, r from fdiv_qr(-7::mpz, -3::mpz);
2|-1
SELECT q, r from fdiv_qr( 7::mpz,  0::mpz);
ERROR:  division by zero
SELECT divisible(10::mpz, 3::mpz);
f
SELECT divisible(12::mpz, 3::mpz);
t
SELECT divisible(10::mpz, 0::mpz);
f
SELECT divisible(0::mpz, 0::mpz);
t
SELECT divisible_2exp(63::mpz, 3);
f
SELECT divisible_2exp(64::mpz, 3);
t
SELECT 10::mpz /? 3::mpz;
f
SELECT 12::mpz /? 3::mpz;
t
SELECT 10::mpz /? 0::mpz;
f
SELECT 0::mpz /? 0::mpz;
t
SELECT 63::mpz >>? 3;
f
SELECT 64::mpz >>? 3;
t
SELECT congruent(12::mpz, 16::mpz, 5::mpz);
f
SELECT congruent(12::mpz, 17::mpz, 5::mpz);
t
SELECT congruent(12::mpz, 11::mpz, 0::mpz);
f
SELECT congruent(12::mpz, 12::mpz, 0::mpz);
t
SELECT congruent_2exp(18::mpz, 41::mpz, 3);
f
SELECT congruent_2exp(18::mpz, 42::mpz, 3);
t
-- power operator/functions
SELECT 2::mpz ^ 10;
1024
SELECT 2::mpz ^ 0;
1
SELECT 2::mpz ^ -1;
ERROR:  argument can't be negative
SELECT pow(2::mpz, 10);
1024
SELECT pow(2::mpz, 0);
1
SELECT pow(2::mpz, -1);
ERROR:  argument can't be negative
SELECT powm(3::mpz, 2::mpz, 9::mpz);
0
SELECT powm(3::mpz, 2::mpz, 8::mpz);
1
SELECT powm(3::mpz, -1::mpz, 8::mpz);
ERROR:  argument can't be negative
SELECT powm(3::mpz, 2::mpz, 0::mpz);
ERROR:  division by zero
--
-- mpz ordering operators
--
select 1000::mpz =   999::mpz;
f
select 1000::mpz =  1000::mpz;
t
select 1000::mpz =  1001::mpz;
f
select 1000::mpz <>  999::mpz;
t
select 1000::mpz <> 1000::mpz;
f
select 1000::mpz <> 1001::mpz;
t
select 1000::mpz !=  999::mpz;
t
select 1000::mpz != 1000::mpz;
f
select 1000::mpz != 1001::mpz;
t
select 1000::mpz <   999::mpz;
f
select 1000::mpz <  1000::mpz;
f
select 1000::mpz <  1001::mpz;
t
select 1000::mpz <=  999::mpz;
f
select 1000::mpz <= 1000::mpz;
t
select 1000::mpz <= 1001::mpz;
t
select 1000::mpz >   999::mpz;
t
select 1000::mpz >  1000::mpz;
f
select 1000::mpz >  1001::mpz;
f
select 1000::mpz >=  999::mpz;
t
select 1000::mpz >= 1000::mpz;
t
select 1000::mpz >= 1001::mpz;
f
select mpz_cmp(1000::mpz,  999::mpz);
1
select mpz_cmp(1000::mpz, 1000::mpz);
0
select mpz_cmp(1000::mpz, 1001::mpz);
-1
-- Can create btree and hash indexes
create table test_mpz_idx (z mpz);
insert into test_mpz_idx select generate_series(1, 10000);
create index test_mpz_btree_idx on test_mpz_idx using btree (z);
set client_min_messages = error;
create index test_mpz_hash_idx on test_mpz_idx using hash (z);
reset client_min_messages;
-- Hash is compatible with builtins
select mpz_hash(0) = hashint4(0);
t
select mpz_hash(32767::int2) = hashint2(32767::int2);
t
select mpz_hash((-32768)::int2) = hashint2((-32768)::int2);
t
select mpz_hash(2147483647) = hashint4(2147483647);
t
select mpz_hash(-2147483648) = hashint4(-2147483648);
t
select mpz_hash(9223372036854775807) = hashint8(9223372036854775807);
t
select mpz_hash(-9223372036854775808) = hashint8(-9223372036854775808);
t
--
-- mpz aggregation
--
CREATE TABLE mpzagg(z mpz);
SELECT sum(z) FROM mpzagg;      -- NULL sum

INSERT INTO mpzagg SELECT generate_series(1, 100);
INSERT INTO mpzagg VALUES (NULL);
SELECT sum(z) FROM mpzagg;
5050
SELECT prod(z) FROM mpzagg;
93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
SELECT min(z) FROM mpzagg;
1
SELECT max(z) FROM mpzagg;
100
-- check correct values when the sortop kicks in
CREATE INDEX mpzagg_idx ON mpzagg(z);
SELECT min(z) FROM mpzagg;
1
SELECT max(z) FROM mpzagg;
100
SELECT bit_and(z) FROM mpzagg;
0
SELECT bit_and(z) FROM mpzagg WHERE z % 2 = 1;
1
SELECT bit_or(z) FROM mpzagg;
127
SELECT bit_or(z) FROM mpzagg WHERE z % 2 = 0;
126
SELECT bit_or(z) FROM mpzagg WHERE z = 1 or z = 2;
3
SELECT bit_xor(z) FROM mpzagg;
100
SELECT bit_xor(z) FROM mpzagg WHERE z = 1 or z = 2;
3
SELECT bit_xor(z) FROM mpzagg WHERE z = 1 or z = 2 or z = 3;
0
-- check aggregates work in windows functions too
CREATE TABLE test_mpz_win(z mpz);
INSERT INTO test_mpz_win SELECT generate_series(1,500);
SELECT DISTINCT z % 5, prod(z) OVER (PARTITION BY z % 5) FROM test_mpz_win ORDER BY 1;
0|736214027959609564214534807933509860360590478604140717816562255320550732004257967720125762877551166630104095572009682655334472656250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
1|4024980661396945255594437948691099096750750303522148939207253140343256389690134608552507750666273153464851186606092569064940061274937877687035835465562596381725444297753023206467590336262178237450463859369896155905624559845376
2|20916546636333781039819147945471434631041853197955027503272329909375076603172061212536955170894771081399258164490448681039306210750168807043358712676705447209588907620793116406518489750133917827418353041315415425444640641253376
3|78258648528733027168387470491499343638520216905903130597214530733536396165915793335397652314194905058465162496835320770455185720537199021723403297752439421984679965716575544045339560632302893082461947076538277070518358298853376
4|251546524835575501784021324366402680054179057461650771690723123931592596438400569072874480196699629786768776600250612669749873513568533129791068662565559263147495268772282292685896436853700130137800525196100073761792376099045376
--
-- mpz functions tests
--
SELECT sqrt(25::mpz);
5
SELECT sqrt(('1' || repeat('0',100))::mpz);
100000000000000000000000000000000000000000000000000
SELECT sqrt(0::mpz);
0
SELECT sqrt(-1::mpz);
ERROR:  argument can't be negative
SELECT root(27::mpz, 3);
3
SELECT root(('1' || repeat('0',100))::mpz, 3);
2154434690031883721759293566519350
SELECT root(0::mpz, 3);
0
SELECT root(27::mpz, 1);
27
SELECT root(27::mpz, 0);
ERROR:  argument must be positive
SELECT root(-27::mpz, 3);
ERROR:  argument can't be negative
SELECT root(27::mpz, -1);
ERROR:  argument can't be negative
select * from rootrem(1000::mpz,2) as rootrem;
31|39
select * from rootrem(1000::mpz,9) as rootrem;
2|488
select * from rootrem(('1' || repeat('0',100))::mpz,2);
100000000000000000000000000000000000000000000000000|0
select * from rootrem(('1' || repeat('0',100))::mpz,5);
100000000000000000000|0
select root from rootrem(1000::mpz, 2);
31
select rem from rootrem(1000::mpz, 2);
39
select * from sqrtrem(1000::mpz) as rootrem;
31|39
select * from sqrtrem(('1' || repeat('0',100))::mpz);
100000000000000000000000000000000000000000000000000|0
select root from sqrtrem(1000::mpz);
31
select rem from sqrtrem(1000::mpz);
39
select perfect_power(26::mpz);
f
select perfect_power(27::mpz);
t
select perfect_power(65535::mpz);
f
select perfect_power(65536::mpz);
t
select perfect_power(-65536::mpz);
f
select perfect_power(-65535::mpz);
f
select perfect_power(('1' || repeat('0',100))::mpz);
t
select perfect_power(('1' || repeat('0',10000))::mpz);
t
select perfect_power(('1' || repeat('0',10001))::mpz);
t
select perfect_power(('1' || repeat('0',10000))::mpz+1::mpz);
f
select perfect_square(0::mpz);
t
select perfect_square(1::mpz);
t
select perfect_square(-1::mpz);
f
select perfect_square(26::mpz);
f
select perfect_square(27::mpz);
f
select perfect_square(16777215::mpz);
f
select perfect_square(16777216::mpz);
t
select perfect_square(('1' || repeat('0',10000))::mpz);
t
select perfect_square(('1' || repeat('0',10000))::mpz+1::mpz);
f
--
-- Number Theoretic Functions
--
SELECT probab_prime(5::mpz, 2);
2
SELECT probab_prime(10::mpz, 2);
0
SELECT probab_prime(17::mpz, 2);
2
SELECT nextprime(5::mpz);
7
SELECT nextprime(10::mpz);
11
SELECT nextprime(100::mpz);
101
SELECT nextprime(1000::mpz);
1009
SELECT nextprime(0::mpz);
2
SELECT nextprime(-8::mpz);
2
SELECT gcd(3::mpz, 15::mpz);
3
SELECT gcd(17::mpz, 15::mpz);
1
SELECT gcd(12345::mpz, 54321::mpz);
3
SELECT gcd(10000000::mpz, 10000::mpz);
10000
SELECT g, s, t FROM gcdext(6::mpz, 15::mpz);
3|-2|1
SELECT lcm(3::mpz, 15::mpz);
15
SELECT lcm(17::mpz, 15::mpz);
255
SELECT lcm(12345::mpz, 54321::mpz);
223530915
SELECT invert(1::mpz,2::mpz);
1
SELECT invert(1::mpz,3::mpz);
1
SELECT invert(2::mpz,3::mpz);
2
SELECT invert(20::mpz,3::mpz);
2
SELECT invert(30::mpz,3::mpz);

select jacobi(2::mpz, 3::mpz);
-1
select jacobi(5::mpz, 3::mpz);
-1
select jacobi(5::mpz, 10::mpz);
0
select jacobi(5::mpz, 20::mpz);
0
select jacobi(5::mpz, 200::mpz);
0
select legendre(2::mpz, 3::mpz);
-1
select legendre(5::mpz, 3::mpz);
-1
select legendre(5::mpz, 10::mpz);
0
select legendre(5::mpz, 20::mpz);
0
select legendre(5::mpz, 200::mpz);
0
select kronecker(2::mpz, 3::mpz);
-1
select kronecker(5::mpz, 3::mpz);
-1
select kronecker(5::mpz, 10::mpz);
0
select kronecker(5::mpz, 20::mpz);
0
select kronecker(5::mpz, 200::mpz);
0
select remove(40::mpz, 5::mpz); 
8
select remove(43::mpz, 5::mpz); 
43
select remove(48::mpz, 6::mpz); 
8
select remove(48::mpz, 3::mpz); 
16
select fac(0);
1
select fac(1);
1
select fac(10);
3628800
select fac(100);
93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
select fac(-1);
ERROR:  argument can't be negative
select bin(0::mpz, 0);
1
select bin(7::mpz, 2);
21
select bin(-2::mpz, 1);
-2
select bin(2::mpz, -1);
ERROR:  argument can't be negative
select fib(0);
0
select fib(1);
1
select fib(10);
55
select fib(-1);
ERROR:  argument can't be negative
select fn, fnsub1 from fib2(0);
0|1
select fn, fnsub1 from fib2(1);
1|0
select fn, fnsub1 from fib2(2);
1|1
select fn, fnsub1 from fib2(10);
55|34
select fn, fnsub1 from fib2(-1);
ERROR:  argument can't be negative
select lucnum(0);
2
select lucnum(1);
1
select lucnum(10);
123
select lucnum(-1);
ERROR:  argument can't be negative
select ln, lnsub1 from lucnum2(0);
2|-1
select ln, lnsub1 from lucnum2(1);
1|2
select ln, lnsub1 from lucnum2(2);
3|1
select ln, lnsub1 from lucnum2(10);
123|76
select ln, lnsub1 from lucnum2(-1);
ERROR:  argument can't be negative
--
-- Logic and bit fiddling functions and operators
--
SELECT text('0b10001'::mpz & '0b01001'::mpz, 2);
1
SELECT text('0b10001'::mpz | '0b01001'::mpz, 2);
11001
SELECT text('0b10001'::mpz # '0b01001'::mpz, 2);
11000
SELECT com(10::mpz);
-11
SELECT popcount('0b101010'::mpz);
3
SELECT popcount(0::mpz);
0
SELECT popcount(-1::mpz) = gmp_max_bitcnt();
t
SELECT hamdist('0b101010'::mpz, '0b101100'::mpz);
2
SELECT hamdist(0::mpz, -1::mpz) = gmp_max_bitcnt();
t
SELECT scan0('0b110110'::mpz, 1);
3
SELECT scan0('0b110110'::mpz, 3);
3
SELECT scan0(-1::mpz, 2) = gmp_max_bitcnt();
t
SELECT scan0(0::mpz, -1);
ERROR:  argument doesn't fit into a bitcount type
SELECT scan0(0::mpz, (2^64)::numeric::mpz);
ERROR:  argument doesn't fit into a bitcount type
SELECT scan1('0b110110'::mpz, 1);
1
SELECT scan1('0b110110'::mpz, 3);
4
SELECT scan1(1::mpz, 2) = gmp_max_bitcnt();
t
SELECT scan1(0::mpz, -1);
ERROR:  argument doesn't fit into a bitcount type
SELECT scan1(0::mpz, (2^64)::numeric::mpz);
ERROR:  argument doesn't fit into a bitcount type
SELECT text(setbit('0b1010'::mpz, 0), 2);
1011
SELECT text(setbit('0b1010'::mpz, 1), 2);
1010
SELECT setbit(0::mpz, -1);
ERROR:  argument doesn't fit into a bitcount type
SELECT setbit(0::mpz, (2^64)::numeric::mpz);
ERROR:  argument doesn't fit into a bitcount type
SELECT text(clrbit('0b1010'::mpz, 0), 2);
1010
SELECT text(clrbit('0b1010'::mpz, 1), 2);
1000
SELECT clrbit(0::mpz, -1);
ERROR:  argument doesn't fit into a bitcount type
SELECT clrbit(0::mpz, (2^64)::numeric::mpz);
ERROR:  argument doesn't fit into a bitcount type
SELECT text(combit('0b1010'::mpz, 0), 2);
1011
SELECT text(combit('0b1010'::mpz, 1), 2);
1000
SELECT combit(0::mpz, -1);
ERROR:  argument doesn't fit into a bitcount type
SELECT combit(0::mpz, (2^64)::numeric::mpz);
ERROR:  argument doesn't fit into a bitcount type
SELECT tstbit('0b1010'::mpz, 0);
0
SELECT tstbit('0b1010'::mpz, 1);
1
SELECT tstbit(0::mpz, -1);
ERROR:  argument doesn't fit into a bitcount type
SELECT tstbit(0::mpz, (2^64)::numeric::mpz);
ERROR:  argument doesn't fit into a bitcount type
--
-- Random numbers
--
-- Errors
SELECT rrandomb(128);
ERROR:  random state not initialized
SELECT urandomb(128);
ERROR:  random state not initialized
SELECT randseed(123456::mpz);
ERROR:  random state not initialized
-- Correct sequence
SELECT randinit();

SELECT urandomb(128);
157222500695008773376422121395749431412
SELECT urandomb(128);
134920890566235299823285762767211707848
-- Re-initialization
SELECT randinit();

SELECT urandomb(128);
157222500695008773376422121395749431412
SELECT urandomb(128);
134920890566235299823285762767211707848
SELECT randinit_mt();

SELECT urandomb(128);
157222500695008773376422121395749431412
SELECT urandomb(128);
134920890566235299823285762767211707848
SELECT randinit_lc_2exp(1103515245, 12345, 32);

SELECT urandomb(128);
208667253088805722654994525601019085254
SELECT urandomb(128);
261232200431476629202778117829285035860
SELECT randinit_lc_2exp_size(64);

SELECT urandomb(128);
249447876620907321381460515833516635592
SELECT urandomb(128);
22936434003400892378378850487313686779
-- A failed initialization leaves the state as it was before
SELECT randinit();

SELECT urandomb(128);
157222500695008773376422121395749431412
SELECT randinit_lc_2exp_size(8192);
ERROR:  failed to initialized random state with size 8192
SELECT urandomb(128);
134920890566235299823285762767211707848
-- Seeding
SELECT randinit();

SELECT randseed(123456::mpz);

SELECT urandomb(128);
138901051744608890087912541094105168008
SELECT urandomb(128);
95807093925713229772160210272764553732
SELECT randseed(123456::mpz);

SELECT urandomb(128);
138901051744608890087912541094105168008
SELECT urandomb(128);
95807093925713229772160210272764553732
SELECT randinit();

SELECT randseed(123456::mpz);

SELECT text(rrandomb(128), 2);
11111111111111111111111111111100000011111111111111111111111000001111111111111111111111111111111110000000000000000000000000000000
SELECT text(rrandomb(128), 2);
11111111111111111111111111111111111111111000000000000000000000000000000000000000000000000000000000011110000000000000000000000000
SELECT randseed(123456::mpz);

SELECT text(rrandomb(128), 2);
11111111111111111111111111111100000011111111111111111111111000001111111111111111111111111111111110000000000000000000000000000000
SELECT text(rrandomb(128), 2);
11111111111111111111111111111111111111111000000000000000000000000000000000000000000000000000000000011110000000000000000000000000
SELECT randinit();

SELECT randseed(123456::mpz);

SELECT urandomm(1000000::mpz);
112776
SELECT urandomm(1000000::mpz);
928797
SELECT randseed(123456::mpz);

SELECT urandomm(1000000::mpz);
112776
SELECT urandomm(1000000::mpz);
928797