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postgres/src/test/regress/sql/numeric.sql
Dean Rasheed 9428c001f6 Speed up numeric division by always using the "fast" algorithm. 
Formerly there were two internal functions in numeric.c to perform
numeric division, div_var() and div_var_fast(). div_var() performed
division exactly to a specified rscale using Knuth's long division
algorithm, while div_var_fast() used the algorithm from the "FM"
library, which approximates each quotient digit using floating-point
arithmetic, and computes a truncated quotient with DIV_GUARD_DIGITS
extra digits. div_var_fast() could be many times faster than
div_var(), but did not guarantee correct results in all cases, and was
therefore only suitable for use in transcendental functions, where
small errors are acceptable.

This commit merges div_var() and div_var_fast() together into a single
function with an extra "exact" boolean parameter, which can be set to
false if the caller is OK with an approximate result. The new function
uses the faster algorithm from the "FM" library, except that when
"exact" is true, it does not truncate the computation with
DIV_GUARD_DIGITS extra digits, but instead performs the full-precision
computation, subtracting off complete multiples of the divisor for
each quotient digit. However, it is able to retain most of the
performance benefits of div_var_fast(), by delaying the propagation of
carries, allowing the inner loop to be auto-vectorized.

Since this may still lead to an inaccurate result, when "exact" is
true, it then inspects the remainder and uses that to adjust the
quotient, if necessary, to make it correct. In practice, the quotient
rarely needs to be adjusted, and never by more than one in the final
digit, though it's difficult to prove that, so the code allows for
larger adjustments, just in case.

In addition, use base-NBASE^2 arithmetic and a 64-bit dividend array,
similar to mul_var(), so that the number of iterations of the outer
loop is roughly halved. Together with the faster algorithm, this makes
div_var() up to around 20 times as fast as the old Knuth algorithm
when "exact" is true, and up to 2 or 3 times as fast as the old
div_var_fast() function when "exact" is false.

Dean Rasheed, reviewed by Joel Jacobson.

Discussion: https://postgr.es/m/CAEZATCVHR10BPDJSANh0u2+Sg6atO3mD0G+CjKDNRMD-C8hKzQ@mail.gmail.com
2024-10-04 09:49:24 +01:00

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--
-- NUMERIC
--
CREATE TABLE num_data (id int4, val numeric(210,10));
CREATE TABLE num_exp_add (id1 int4, id2 int4, expected numeric(210,10));
CREATE TABLE num_exp_sub (id1 int4, id2 int4, expected numeric(210,10));
CREATE TABLE num_exp_div (id1 int4, id2 int4, expected numeric(210,10));
CREATE TABLE num_exp_mul (id1 int4, id2 int4, expected numeric(210,10));
CREATE TABLE num_exp_sqrt (id int4, expected numeric(210,10));
CREATE TABLE num_exp_ln (id int4, expected numeric(210,10));
CREATE TABLE num_exp_log10 (id int4, expected numeric(210,10));
CREATE TABLE num_exp_power_10_ln (id int4, expected numeric(210,10));
CREATE TABLE num_result (id1 int4, id2 int4, result numeric(210,10));
-- ******************************
-- * The following EXPECTED results are computed by bc(1)
-- * with a scale of 200
-- ******************************
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INSERT INTO num_exp_sub VALUES (7,9,'-58101680.954952580');
INSERT INTO num_exp_mul VALUES (7,9,'2069634775752159.035758700');
INSERT INTO num_exp_div VALUES (7,9,'3.33089171198810413382');
INSERT INTO num_exp_add VALUES (8,0,'74881');
INSERT INTO num_exp_sub VALUES (8,0,'74881');
INSERT INTO num_exp_mul VALUES (8,0,'0');
INSERT INTO num_exp_div VALUES (8,0,'NaN');
INSERT INTO num_exp_add VALUES (8,1,'74881');
INSERT INTO num_exp_sub VALUES (8,1,'74881');
INSERT INTO num_exp_mul VALUES (8,1,'0');
INSERT INTO num_exp_div VALUES (8,1,'NaN');
INSERT INTO num_exp_add VALUES (8,2,'-34263611.215397047');
INSERT INTO num_exp_sub VALUES (8,2,'34413373.215397047');
INSERT INTO num_exp_mul VALUES (8,2,'-2571300635581.146276407');
INSERT INTO num_exp_div VALUES (8,2,'-.00218067233500788615');
INSERT INTO num_exp_add VALUES (8,3,'74885.31');
INSERT INTO num_exp_sub VALUES (8,3,'74876.69');
INSERT INTO num_exp_mul VALUES (8,3,'322737.11');
INSERT INTO num_exp_div VALUES (8,3,'17373.78190255220417633410');
INSERT INTO num_exp_add VALUES (8,4,'7874342.4119');
INSERT INTO num_exp_sub VALUES (8,4,'-7724580.4119');
INSERT INTO num_exp_mul VALUES (8,4,'584031469984.4839');
INSERT INTO num_exp_div VALUES (8,4,'.00960079113741758956');
INSERT INTO num_exp_add VALUES (8,5,'91278.038491');
INSERT INTO num_exp_sub VALUES (8,5,'58483.961509');
INSERT INTO num_exp_mul VALUES (8,5,'1227826639.244571');
INSERT INTO num_exp_div VALUES (8,5,'4.56673929509287019456');
INSERT INTO num_exp_add VALUES (8,6,'168782.57763026');
INSERT INTO num_exp_sub VALUES (8,6,'-19020.57763026');
INSERT INTO num_exp_mul VALUES (8,6,'7031444034.53149906');
INSERT INTO num_exp_div VALUES (8,6,'.79744134113322314424');
INSERT INTO num_exp_add VALUES (8,7,'-82953604');
INSERT INTO num_exp_sub VALUES (8,7,'83103366');
INSERT INTO num_exp_mul VALUES (8,7,'-6217255985285');
INSERT INTO num_exp_div VALUES (8,7,'-.00090187120721280172');
INSERT INTO num_exp_add VALUES (8,8,'149762');
INSERT INTO num_exp_sub VALUES (8,8,'0');
INSERT INTO num_exp_mul VALUES (8,8,'5607164161');
INSERT INTO num_exp_div VALUES (8,8,'1.00000000000000000000');
INSERT INTO num_exp_add VALUES (8,9,'-24851923.045047420');
INSERT INTO num_exp_sub VALUES (8,9,'25001685.045047420');
INSERT INTO num_exp_mul VALUES (8,9,'-1866544013697.195857020');
INSERT INTO num_exp_div VALUES (8,9,'-.00300403532938582735');
INSERT INTO num_exp_add VALUES (9,0,'-24926804.045047420');
INSERT INTO num_exp_sub VALUES (9,0,'-24926804.045047420');
INSERT INTO num_exp_mul VALUES (9,0,'0');
INSERT INTO num_exp_div VALUES (9,0,'NaN');
INSERT INTO num_exp_add VALUES (9,1,'-24926804.045047420');
INSERT INTO num_exp_sub VALUES (9,1,'-24926804.045047420');
INSERT INTO num_exp_mul VALUES (9,1,'0');
INSERT INTO num_exp_div VALUES (9,1,'NaN');
INSERT INTO num_exp_add VALUES (9,2,'-59265296.260444467');
INSERT INTO num_exp_sub VALUES (9,2,'9411688.170349627');
INSERT INTO num_exp_mul VALUES (9,2,'855948866655588.453741509242968740');
INSERT INTO num_exp_div VALUES (9,2,'.72591434384152961526');
INSERT INTO num_exp_add VALUES (9,3,'-24926799.735047420');
INSERT INTO num_exp_sub VALUES (9,3,'-24926808.355047420');
INSERT INTO num_exp_mul VALUES (9,3,'-107434525.43415438020');
INSERT INTO num_exp_div VALUES (9,3,'-5783481.21694835730858468677');
INSERT INTO num_exp_add VALUES (9,4,'-17127342.633147420');
INSERT INTO num_exp_sub VALUES (9,4,'-32726265.456947420');
INSERT INTO num_exp_mul VALUES (9,4,'-194415646271340.1815956522980');
INSERT INTO num_exp_div VALUES (9,4,'-3.19596478892958416484');
INSERT INTO num_exp_add VALUES (9,5,'-24910407.006556420');
INSERT INTO num_exp_sub VALUES (9,5,'-24943201.083538420');
INSERT INTO num_exp_mul VALUES (9,5,'-408725765384.257043660243220');
INSERT INTO num_exp_div VALUES (9,5,'-1520.20159364322004505807');
INSERT INTO num_exp_add VALUES (9,6,'-24832902.467417160');
INSERT INTO num_exp_sub VALUES (9,6,'-25020705.622677680');
INSERT INTO num_exp_mul VALUES (9,6,'-2340666225110.29929521292692920');
INSERT INTO num_exp_div VALUES (9,6,'-265.45671195426965751280');
INSERT INTO num_exp_add VALUES (9,7,'-107955289.045047420');
INSERT INTO num_exp_sub VALUES (9,7,'58101680.954952580');
INSERT INTO num_exp_mul VALUES (9,7,'2069634775752159.035758700');
INSERT INTO num_exp_div VALUES (9,7,'.30021990699995814689');
INSERT INTO num_exp_add VALUES (9,8,'-24851923.045047420');
INSERT INTO num_exp_sub VALUES (9,8,'-25001685.045047420');
INSERT INTO num_exp_mul VALUES (9,8,'-1866544013697.195857020');
INSERT INTO num_exp_div VALUES (9,8,'-332.88556569820675471748');
INSERT INTO num_exp_add VALUES (9,9,'-49853608.090094840');
INSERT INTO num_exp_sub VALUES (9,9,'0');
INSERT INTO num_exp_mul VALUES (9,9,'621345559900192.420120630048656400');
INSERT INTO num_exp_div VALUES (9,9,'1.00000000000000000000');
COMMIT TRANSACTION;
BEGIN TRANSACTION;
INSERT INTO num_exp_sqrt VALUES (0,'0');
INSERT INTO num_exp_sqrt VALUES (1,'0');
INSERT INTO num_exp_sqrt VALUES (2,'5859.90547836712524903505');
INSERT INTO num_exp_sqrt VALUES (3,'2.07605394920266944396');
INSERT INTO num_exp_sqrt VALUES (4,'2792.75158435189147418923');
INSERT INTO num_exp_sqrt VALUES (5,'128.05092147657509145473');
INSERT INTO num_exp_sqrt VALUES (6,'306.43364311096782703406');
INSERT INTO num_exp_sqrt VALUES (7,'9111.99676251039939975230');
INSERT INTO num_exp_sqrt VALUES (8,'273.64392922189960397542');
INSERT INTO num_exp_sqrt VALUES (9,'4992.67503899937593364766');
COMMIT TRANSACTION;
BEGIN TRANSACTION;
INSERT INTO num_exp_ln VALUES (0,'NaN');
INSERT INTO num_exp_ln VALUES (1,'NaN');
INSERT INTO num_exp_ln VALUES (2,'17.35177750493897715514');
INSERT INTO num_exp_ln VALUES (3,'1.46093790411565641971');
INSERT INTO num_exp_ln VALUES (4,'15.86956523951936572464');
INSERT INTO num_exp_ln VALUES (5,'9.70485601768871834038');
INSERT INTO num_exp_ln VALUES (6,'11.45000246622944403127');
INSERT INTO num_exp_ln VALUES (7,'18.23469429965478772991');
INSERT INTO num_exp_ln VALUES (8,'11.22365546576315513668');
INSERT INTO num_exp_ln VALUES (9,'17.03145425013166006962');
COMMIT TRANSACTION;
BEGIN TRANSACTION;
INSERT INTO num_exp_log10 VALUES (0,'NaN');
INSERT INTO num_exp_log10 VALUES (1,'NaN');
INSERT INTO num_exp_log10 VALUES (2,'7.53578122160797276459');
INSERT INTO num_exp_log10 VALUES (3,'.63447727016073160075');
INSERT INTO num_exp_log10 VALUES (4,'6.89206461372691743345');
INSERT INTO num_exp_log10 VALUES (5,'4.21476541614777768626');
INSERT INTO num_exp_log10 VALUES (6,'4.97267288886207207671');
INSERT INTO num_exp_log10 VALUES (7,'7.91922711353275546914');
INSERT INTO num_exp_log10 VALUES (8,'4.87437163556421004138');
INSERT INTO num_exp_log10 VALUES (9,'7.39666659961986567059');
COMMIT TRANSACTION;
BEGIN TRANSACTION;
INSERT INTO num_exp_power_10_ln VALUES (0,'NaN');
INSERT INTO num_exp_power_10_ln VALUES (1,'NaN');
INSERT INTO num_exp_power_10_ln VALUES (2,'224790267919917955.13261618583642653184');
INSERT INTO num_exp_power_10_ln VALUES (3,'28.90266599445155957393');
INSERT INTO num_exp_power_10_ln VALUES (4,'7405685069594999.07733999469386277636');
INSERT INTO num_exp_power_10_ln VALUES (5,'5068226527.32127265408584640098');
INSERT INTO num_exp_power_10_ln VALUES (6,'281839893606.99372343357047819067');
INSERT INTO num_exp_power_10_ln VALUES (7,'1716699575118597095.42330819910640247627');
INSERT INTO num_exp_power_10_ln VALUES (8,'167361463828.07491320069016125952');
INSERT INTO num_exp_power_10_ln VALUES (9,'107511333880052007.04141124673540337457');
COMMIT TRANSACTION;
BEGIN TRANSACTION;
INSERT INTO num_data VALUES (0, '0');
INSERT INTO num_data VALUES (1, '0');
INSERT INTO num_data VALUES (2, '-34338492.215397047');
INSERT INTO num_data VALUES (3, '4.31');
INSERT INTO num_data VALUES (4, '7799461.4119');
INSERT INTO num_data VALUES (5, '16397.038491');
INSERT INTO num_data VALUES (6, '93901.57763026');
INSERT INTO num_data VALUES (7, '-83028485');
INSERT INTO num_data VALUES (8, '74881');
INSERT INTO num_data VALUES (9, '-24926804.045047420');
COMMIT TRANSACTION;
-- ******************************
-- * Create indices for faster checks
-- ******************************
CREATE UNIQUE INDEX num_exp_add_idx ON num_exp_add (id1, id2);
CREATE UNIQUE INDEX num_exp_sub_idx ON num_exp_sub (id1, id2);
CREATE UNIQUE INDEX num_exp_div_idx ON num_exp_div (id1, id2);
CREATE UNIQUE INDEX num_exp_mul_idx ON num_exp_mul (id1, id2);
CREATE UNIQUE INDEX num_exp_sqrt_idx ON num_exp_sqrt (id);
CREATE UNIQUE INDEX num_exp_ln_idx ON num_exp_ln (id);
CREATE UNIQUE INDEX num_exp_log10_idx ON num_exp_log10 (id);
CREATE UNIQUE INDEX num_exp_power_10_ln_idx ON num_exp_power_10_ln (id);
VACUUM ANALYZE num_exp_add;
VACUUM ANALYZE num_exp_sub;
VACUUM ANALYZE num_exp_div;
VACUUM ANALYZE num_exp_mul;
VACUUM ANALYZE num_exp_sqrt;
VACUUM ANALYZE num_exp_ln;
VACUUM ANALYZE num_exp_log10;
VACUUM ANALYZE num_exp_power_10_ln;
-- ******************************
-- * Now check the behaviour of the NUMERIC type
-- ******************************
-- ******************************
-- * Addition check
-- ******************************
DELETE FROM num_result;
INSERT INTO num_result SELECT t1.id, t2.id, t1.val + t2.val
FROM num_data t1, num_data t2;
SELECT t1.id1, t1.id2, t1.result, t2.expected
FROM num_result t1, num_exp_add t2
WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
AND t1.result != t2.expected;
DELETE FROM num_result;
INSERT INTO num_result SELECT t1.id, t2.id, round(t1.val + t2.val, 10)
FROM num_data t1, num_data t2;
SELECT t1.id1, t1.id2, t1.result, round(t2.expected, 10) as expected
FROM num_result t1, num_exp_add t2
WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
AND t1.result != round(t2.expected, 10);
-- ******************************
-- * Subtraction check
-- ******************************
DELETE FROM num_result;
INSERT INTO num_result SELECT t1.id, t2.id, t1.val - t2.val
FROM num_data t1, num_data t2;
SELECT t1.id1, t1.id2, t1.result, t2.expected
FROM num_result t1, num_exp_sub t2
WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
AND t1.result != t2.expected;
DELETE FROM num_result;
INSERT INTO num_result SELECT t1.id, t2.id, round(t1.val - t2.val, 40)
FROM num_data t1, num_data t2;
SELECT t1.id1, t1.id2, t1.result, round(t2.expected, 40)
FROM num_result t1, num_exp_sub t2
WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
AND t1.result != round(t2.expected, 40);
-- ******************************
-- * Multiply check
-- ******************************
DELETE FROM num_result;
INSERT INTO num_result SELECT t1.id, t2.id, t1.val * t2.val
FROM num_data t1, num_data t2;
SELECT t1.id1, t1.id2, t1.result, t2.expected
FROM num_result t1, num_exp_mul t2
WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
AND t1.result != t2.expected;
DELETE FROM num_result;
INSERT INTO num_result SELECT t1.id, t2.id, round(t1.val * t2.val, 30)
FROM num_data t1, num_data t2;
SELECT t1.id1, t1.id2, t1.result, round(t2.expected, 30) as expected
FROM num_result t1, num_exp_mul t2
WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
AND t1.result != round(t2.expected, 30);
-- ******************************
-- * Division check
-- ******************************
DELETE FROM num_result;
INSERT INTO num_result SELECT t1.id, t2.id, t1.val / t2.val
FROM num_data t1, num_data t2
WHERE t2.val != '0.0';
SELECT t1.id1, t1.id2, t1.result, t2.expected
FROM num_result t1, num_exp_div t2
WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
AND t1.result != t2.expected;
DELETE FROM num_result;
INSERT INTO num_result SELECT t1.id, t2.id, round(t1.val / t2.val, 80)
FROM num_data t1, num_data t2
WHERE t2.val != '0.0';
SELECT t1.id1, t1.id2, t1.result, round(t2.expected, 80) as expected
FROM num_result t1, num_exp_div t2
WHERE t1.id1 = t2.id1 AND t1.id2 = t2.id2
AND t1.result != round(t2.expected, 80);
-- ******************************
-- * Square root check
-- ******************************
DELETE FROM num_result;
INSERT INTO num_result SELECT id, 0, SQRT(ABS(val))
FROM num_data;
SELECT t1.id1, t1.result, t2.expected
FROM num_result t1, num_exp_sqrt t2
WHERE t1.id1 = t2.id
AND t1.result != t2.expected;
-- ******************************
-- * Natural logarithm check
-- ******************************
DELETE FROM num_result;
INSERT INTO num_result SELECT id, 0, LN(ABS(val))
FROM num_data
WHERE val != '0.0';
SELECT t1.id1, t1.result, t2.expected
FROM num_result t1, num_exp_ln t2
WHERE t1.id1 = t2.id
AND t1.result != t2.expected;
-- ******************************
-- * Logarithm base 10 check
-- ******************************
DELETE FROM num_result;
INSERT INTO num_result SELECT id, 0, LOG(numeric '10', ABS(val))
FROM num_data
WHERE val != '0.0';
SELECT t1.id1, t1.result, t2.expected
FROM num_result t1, num_exp_log10 t2
WHERE t1.id1 = t2.id
AND t1.result != t2.expected;
-- ******************************
-- * POWER(10, LN(value)) check
-- ******************************
DELETE FROM num_result;
INSERT INTO num_result SELECT id, 0, POWER(numeric '10', LN(ABS(round(val,200))))
FROM num_data
WHERE val != '0.0';
SELECT t1.id1, t1.result, t2.expected
FROM num_result t1, num_exp_power_10_ln t2
WHERE t1.id1 = t2.id
AND t1.result != t2.expected;
-- ******************************
-- * Check behavior with Inf and NaN inputs. It's easiest to handle these
-- * separately from the num_data framework used above, because some input
-- * combinations will throw errors.
-- ******************************
WITH v(x) AS
(VALUES('0'::numeric),('1'),('-1'),('4.2'),('inf'),('-inf'),('nan'))
SELECT x1, x2,
x1 + x2 AS sum,
x1 - x2 AS diff,
x1 * x2 AS prod
FROM v AS v1(x1), v AS v2(x2);
WITH v(x) AS
(VALUES('0'::numeric),('1'),('-1'),('4.2'),('inf'),('-inf'),('nan'))
SELECT x1, x2,
x1 / x2 AS quot,
x1 % x2 AS mod,
div(x1, x2) AS div
FROM v AS v1(x1), v AS v2(x2) WHERE x2 != 0;
SELECT 'inf'::numeric / '0';
SELECT '-inf'::numeric / '0';
SELECT 'nan'::numeric / '0';
SELECT '0'::numeric / '0';
SELECT 'inf'::numeric % '0';
SELECT '-inf'::numeric % '0';
SELECT 'nan'::numeric % '0';
SELECT '0'::numeric % '0';
SELECT div('inf'::numeric, '0');
SELECT div('-inf'::numeric, '0');
SELECT div('nan'::numeric, '0');
SELECT div('0'::numeric, '0');
WITH v(x) AS
(VALUES('0'::numeric),('1'),('-1'),('4.2'),('-7.777'),('inf'),('-inf'),('nan'))
SELECT x, -x as minusx, abs(x), floor(x), ceil(x), sign(x), numeric_inc(x) as inc
FROM v;
WITH v(x) AS
(VALUES('0'::numeric),('1'),('-1'),('4.2'),('-7.777'),('inf'),('-inf'),('nan'))
SELECT x, round(x), round(x,1) as round1, trunc(x), trunc(x,1) as trunc1
FROM v;
-- the large values fall into the numeric abbreviation code's maximal classes
WITH v(x) AS
(VALUES('0'::numeric),('1'),('-1'),('4.2'),('-7.777'),('1e340'),('-1e340'),
('inf'),('-inf'),('nan'),
('inf'),('-inf'),('nan'))
SELECT substring(x::text, 1, 32)
FROM v ORDER BY x;
WITH v(x) AS
(VALUES('0'::numeric),('1'),('4.2'),('inf'),('nan'))
SELECT x, sqrt(x)
FROM v;
SELECT sqrt('-1'::numeric);
SELECT sqrt('-inf'::numeric);
WITH v(x) AS
(VALUES('1'::numeric),('4.2'),('inf'),('nan'))
SELECT x,
log(x),
log10(x),
ln(x)
FROM v;
SELECT ln('0'::numeric);
SELECT ln('-1'::numeric);
SELECT ln('-inf'::numeric);
WITH v(x) AS
(VALUES('2'::numeric),('4.2'),('inf'),('nan'))
SELECT x1, x2,
log(x1, x2)
FROM v AS v1(x1), v AS v2(x2);
SELECT log('0'::numeric, '10');
SELECT log('10'::numeric, '0');
SELECT log('-inf'::numeric, '10');
SELECT log('10'::numeric, '-inf');
SELECT log('inf'::numeric, '0');
SELECT log('inf'::numeric, '-inf');
SELECT log('-inf'::numeric, 'inf');
WITH v(x) AS
(VALUES('0'::numeric),('1'),('2'),('4.2'),('inf'),('nan'))
SELECT x1, x2,
power(x1, x2)
FROM v AS v1(x1), v AS v2(x2) WHERE x1 != 0 OR x2 >= 0;
SELECT power('0'::numeric, '-1');
SELECT power('0'::numeric, '-inf');
SELECT power('-1'::numeric, 'inf');
SELECT power('-2'::numeric, '3');
SELECT power('-2'::numeric, '3.3');
SELECT power('-2'::numeric, '-1');
SELECT power('-2'::numeric, '-1.5');
SELECT power('-2'::numeric, 'inf');
SELECT power('-2'::numeric, '-inf');
SELECT power('inf'::numeric, '-2');
SELECT power('inf'::numeric, '-inf');
SELECT power('-inf'::numeric, '2');
SELECT power('-inf'::numeric, '3');
SELECT power('-inf'::numeric, '4.5');
SELECT power('-inf'::numeric, '-2');
SELECT power('-inf'::numeric, '-3');
SELECT power('-inf'::numeric, '0');
SELECT power('-inf'::numeric, 'inf');
SELECT power('-inf'::numeric, '-inf');
-- ******************************
-- * miscellaneous checks for things that have been broken in the past...
-- ******************************
-- numeric AVG used to fail on some platforms
SELECT AVG(val) FROM num_data;
SELECT MAX(val) FROM num_data;
SELECT MIN(val) FROM num_data;
SELECT STDDEV(val) FROM num_data;
SELECT VARIANCE(val) FROM num_data;
-- Check for appropriate rounding and overflow
CREATE TABLE fract_only (id int, val numeric(4,4));
INSERT INTO fract_only VALUES (1, '0.0');
INSERT INTO fract_only VALUES (2, '0.1');
INSERT INTO fract_only VALUES (3, '1.0'); -- should fail
INSERT INTO fract_only VALUES (4, '-0.9999');
INSERT INTO fract_only VALUES (5, '0.99994');
INSERT INTO fract_only VALUES (6, '0.99995'); -- should fail
INSERT INTO fract_only VALUES (7, '0.00001');
INSERT INTO fract_only VALUES (8, '0.00017');
INSERT INTO fract_only VALUES (9, 'NaN');
INSERT INTO fract_only VALUES (10, 'Inf'); -- should fail
INSERT INTO fract_only VALUES (11, '-Inf'); -- should fail
SELECT * FROM fract_only;
DROP TABLE fract_only;
-- Check conversion to integers
SELECT (-9223372036854775808.5)::int8; -- should fail
SELECT (-9223372036854775808.4)::int8; -- ok
SELECT 9223372036854775807.4::int8; -- ok
SELECT 9223372036854775807.5::int8; -- should fail
SELECT (-2147483648.5)::int4; -- should fail
SELECT (-2147483648.4)::int4; -- ok
SELECT 2147483647.4::int4; -- ok
SELECT 2147483647.5::int4; -- should fail
SELECT (-32768.5)::int2; -- should fail
SELECT (-32768.4)::int2; -- ok
SELECT 32767.4::int2; -- ok
SELECT 32767.5::int2; -- should fail
-- Check inf/nan conversion behavior
SELECT 'NaN'::float8::numeric;
SELECT 'Infinity'::float8::numeric;
SELECT '-Infinity'::float8::numeric;
SELECT 'NaN'::numeric::float8;
SELECT 'Infinity'::numeric::float8;
SELECT '-Infinity'::numeric::float8;
SELECT 'NaN'::float4::numeric;
SELECT 'Infinity'::float4::numeric;
SELECT '-Infinity'::float4::numeric;
SELECT 'NaN'::numeric::float4;
SELECT 'Infinity'::numeric::float4;
SELECT '-Infinity'::numeric::float4;
SELECT '42'::int2::numeric;
SELECT 'NaN'::numeric::int2;
SELECT 'Infinity'::numeric::int2;
SELECT '-Infinity'::numeric::int2;
SELECT 'NaN'::numeric::int4;
SELECT 'Infinity'::numeric::int4;
SELECT '-Infinity'::numeric::int4;
SELECT 'NaN'::numeric::int8;
SELECT 'Infinity'::numeric::int8;
SELECT '-Infinity'::numeric::int8;
-- Simple check that ceil(), floor(), and round() work correctly
CREATE TABLE ceil_floor_round (a numeric);
INSERT INTO ceil_floor_round VALUES ('-5.5');
INSERT INTO ceil_floor_round VALUES ('-5.499999');
INSERT INTO ceil_floor_round VALUES ('9.5');
INSERT INTO ceil_floor_round VALUES ('9.4999999');
INSERT INTO ceil_floor_round VALUES ('0.0');
INSERT INTO ceil_floor_round VALUES ('0.0000001');
INSERT INTO ceil_floor_round VALUES ('-0.000001');
SELECT a, ceil(a), ceiling(a), floor(a), round(a) FROM ceil_floor_round;
DROP TABLE ceil_floor_round;
-- Check rounding, it should round ties away from zero.
SELECT i as pow,
round((-2.5 * 10 ^ i)::numeric, -i),
round((-1.5 * 10 ^ i)::numeric, -i),
round((-0.5 * 10 ^ i)::numeric, -i),
round((0.5 * 10 ^ i)::numeric, -i),
round((1.5 * 10 ^ i)::numeric, -i),
round((2.5 * 10 ^ i)::numeric, -i)
FROM generate_series(-5,5) AS t(i);
-- Check limits of rounding before the decimal point
SELECT round(4.4e131071, -131071) = 4e131071;
SELECT round(4.5e131071, -131071) = 5e131071;
SELECT round(4.5e131071, -131072); -- loses all digits
SELECT round(5.5e131071, -131072); -- rounds up and overflows
SELECT round(5.5e131071, -131073); -- loses all digits
SELECT round(5.5e131071, -1000000); -- loses all digits
-- Check limits of rounding after the decimal point
SELECT round(5e-16383, 1000000) = 5e-16383;
SELECT round(5e-16383, 16383) = 5e-16383;
SELECT round(5e-16383, 16382) = 1e-16382;
SELECT round(5e-16383, 16381) = 0;
-- Check limits of trunc() before the decimal point
SELECT trunc(9.9e131071, -131071) = 9e131071;
SELECT trunc(9.9e131071, -131072); -- loses all digits
SELECT trunc(9.9e131071, -131073); -- loses all digits
SELECT trunc(9.9e131071, -1000000); -- loses all digits
-- Check limits of trunc() after the decimal point
SELECT trunc(5e-16383, 1000000) = 5e-16383;
SELECT trunc(5e-16383, 16383) = 5e-16383;
SELECT trunc(5e-16383, 16382) = 0;
-- Testing for width_bucket(). For convenience, we test both the
-- numeric and float8 versions of the function in this file.
-- errors
SELECT width_bucket(5.0, 3.0, 4.0, 0);
SELECT width_bucket(5.0, 3.0, 4.0, -5);
SELECT width_bucket(3.5, 3.0, 3.0, 888);
SELECT width_bucket(5.0::float8, 3.0::float8, 4.0::float8, 0);
SELECT width_bucket(5.0::float8, 3.0::float8, 4.0::float8, -5);
SELECT width_bucket(3.5::float8, 3.0::float8, 3.0::float8, 888);
SELECT width_bucket('NaN', 3.0, 4.0, 888);
SELECT width_bucket(0::float8, 'NaN', 4.0::float8, 888);
SELECT width_bucket(2.0, 3.0, '-inf', 888);
SELECT width_bucket(0::float8, '-inf', 4.0::float8, 888);
-- normal operation
CREATE TABLE width_bucket_test (operand_num numeric, operand_f8 float8);
COPY width_bucket_test (operand_num) FROM stdin;
-5.2
-0.0000000001
0.000000000001
1
1.99999999999999
2
2.00000000000001
3
4
4.5
5
5.5
6
7
8
9
9.99999999999999
10
10.0000000000001
\.
UPDATE width_bucket_test SET operand_f8 = operand_num::float8;
SELECT
operand_num,
width_bucket(operand_num, 0, 10, 5) AS wb_1,
width_bucket(operand_f8, 0, 10, 5) AS wb_1f,
width_bucket(operand_num, 10, 0, 5) AS wb_2,
width_bucket(operand_f8, 10, 0, 5) AS wb_2f,
width_bucket(operand_num, 2, 8, 4) AS wb_3,
width_bucket(operand_f8, 2, 8, 4) AS wb_3f,
width_bucket(operand_num, 5.0, 5.5, 20) AS wb_4,
width_bucket(operand_f8, 5.0, 5.5, 20) AS wb_4f,
width_bucket(operand_num, -25, 25, 10) AS wb_5,
width_bucket(operand_f8, -25, 25, 10) AS wb_5f
FROM width_bucket_test;
-- Check positive and negative infinity: we require
-- finite bucket bounds, but allow an infinite operand
SELECT width_bucket(0.0::numeric, 'Infinity'::numeric, 5, 10); -- error
SELECT width_bucket(0.0::numeric, 5, '-Infinity'::numeric, 20); -- error
SELECT width_bucket('Infinity'::numeric, 1, 10, 10),
width_bucket('-Infinity'::numeric, 1, 10, 10);
SELECT width_bucket(0.0::float8, 'Infinity'::float8, 5, 10); -- error
SELECT width_bucket(0.0::float8, 5, '-Infinity'::float8, 20); -- error
SELECT width_bucket('Infinity'::float8, 1, 10, 10),
width_bucket('-Infinity'::float8, 1, 10, 10);
DROP TABLE width_bucket_test;
-- Simple test for roundoff error when results should be exact
SELECT x, width_bucket(x::float8, 10, 100, 9) as flt,
width_bucket(x::numeric, 10, 100, 9) as num
FROM generate_series(0, 110, 10) x;
SELECT x, width_bucket(x::float8, 100, 10, 9) as flt,
width_bucket(x::numeric, 100, 10, 9) as num
FROM generate_series(0, 110, 10) x;
-- Another roundoff-error hazard
SELECT width_bucket(0, -1e100::numeric, 1, 10);
SELECT width_bucket(0, -1e100::float8, 1, 10);
SELECT width_bucket(1, 1e100::numeric, 0, 10);
SELECT width_bucket(1, 1e100::float8, 0, 10);
-- Check cases that could trigger overflow or underflow within the calculation
SELECT oper, low, high, cnt, width_bucket(oper, low, high, cnt)
FROM
(SELECT 1.797e+308::float8 AS big, 5e-324::float8 AS tiny) as v,
LATERAL (VALUES
(10.5::float8, -big, big, 1),
(10.5::float8, -big, big, 2),
(10.5::float8, -big, big, 3),
(big / 4, -big / 2, big / 2, 10),
(10.5::float8, big, -big, 1),
(10.5::float8, big, -big, 2),
(10.5::float8, big, -big, 3),
(big / 4, big / 2, -big / 2, 10),
(0, 0, tiny, 4),
(tiny, 0, tiny, 4),
(0, 0, 1, 2147483647),
(1, 1, 0, 2147483647)
) as sample(oper, low, high, cnt);
-- These fail because the result would be out of int32 range:
SELECT width_bucket(1::float8, 0, 1, 2147483647);
SELECT width_bucket(0::float8, 1, 0, 2147483647);
--
-- TO_CHAR()
--
SELECT to_char(val, '9G999G999G999G999G999')
FROM num_data;
SELECT to_char(val, '9G999G999G999G999G999D999G999G999G999G999')
FROM num_data;
SELECT to_char(val, '9999999999999999.999999999999999PR')
FROM num_data;
SELECT to_char(val, '9999999999999999.999999999999999S')
FROM num_data;
SELECT to_char(val, 'MI9999999999999999.999999999999999') FROM num_data;
SELECT to_char(val, 'FMS9999999999999999.999999999999999') FROM num_data;
SELECT to_char(val, 'FM9999999999999999.999999999999999THPR') FROM num_data;
SELECT to_char(val, 'SG9999999999999999.999999999999999th') FROM num_data;
SELECT to_char(val, '0999999999999999.999999999999999') FROM num_data;
SELECT to_char(val, 'S0999999999999999.999999999999999') FROM num_data;
SELECT to_char(val, 'FM0999999999999999.999999999999999') FROM num_data;
SELECT to_char(val, 'FM9999999999999999.099999999999999') FROM num_data;
SELECT to_char(val, 'FM9999999999990999.990999999999999') FROM num_data;
SELECT to_char(val, 'FM0999999999999999.999909999999999') FROM num_data;
SELECT to_char(val, 'FM9999999990999999.099999999999999') FROM num_data;
SELECT to_char(val, 'L9999999999999999.099999999999999') FROM num_data;
SELECT to_char(val, 'FM9999999999999999.99999999999999') FROM num_data;
SELECT to_char(val, 'S 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 . 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9') FROM num_data;
SELECT to_char(val, 'FMS 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 . 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9') FROM num_data;
SELECT to_char(val, E'99999 "text" 9999 "9999" 999 "\\"text between quote marks\\"" 9999') FROM num_data;
SELECT to_char(val, '999999SG9999999999') FROM num_data;
SELECT to_char(val, 'FM9999999999999999.999999999999999') FROM num_data;
SELECT to_char(val, '9.999EEEE') FROM num_data;
SELECT to_char(val, 'FMRN') FROM num_data;
WITH v(val) AS
(VALUES('0'::numeric),('-4.2'),('4.2e9'),('1.2e-5'),('inf'),('-inf'),('nan'))
SELECT val,
to_char(val, '9.999EEEE') as numeric,
to_char(val::float8, '9.999EEEE') as float8,
to_char(val::float4, '9.999EEEE') as float4
FROM v;
WITH v(exp) AS
(VALUES(-16379),(-16378),(-1234),(-789),(-45),(-5),(-4),(-3),(-2),(-1),(0),
(1),(2),(3),(4),(5),(38),(275),(2345),(45678),(131070),(131071))
SELECT exp,
to_char(('1.2345e'||exp)::numeric, '9.999EEEE') as numeric
FROM v;
WITH v(val) AS
(VALUES('0'::numeric),('-4.2'),('4.2e9'),('1.2e-5'),('inf'),('-inf'),('nan'))
SELECT val,
to_char(val, 'MI9999999999.99') as numeric,
to_char(val::float8, 'MI9999999999.99') as float8,
to_char(val::float4, 'MI9999999999.99') as float4
FROM v;
WITH v(val) AS
(VALUES('0'::numeric),('-4.2'),('4.2e9'),('1.2e-5'),('inf'),('-inf'),('nan'))
SELECT val,
to_char(val, 'MI99.99') as numeric,
to_char(val::float8, 'MI99.99') as float8,
to_char(val::float4, 'MI99.99') as float4
FROM v;
SELECT to_char('100'::numeric, 'FM999.9');
SELECT to_char('100'::numeric, 'FM999.');
SELECT to_char('100'::numeric, 'FM999');
SELECT to_char('12345678901'::float8, 'FM9999999999D9999900000000000000000');
SELECT to_char('100'::numeric, 'rn');
SELECT to_char('1234'::numeric, 'rn');
SELECT to_char('1235'::float4, 'rn');
SELECT to_char('1236'::float8, 'rn');
SELECT to_char('1237'::float8, 'fmrn');
SELECT to_char('100e9'::numeric, 'RN');
SELECT to_char('100e9'::float4, 'RN');
SELECT to_char('100e9'::float8, 'RN');
SELECT to_char(1234.56::numeric, '99999V99');
SELECT to_char(1234.56::float4, '99999V99');
SELECT to_char(1234.56::float8, '99999V99');
-- Check parsing of literal text in a format string
SELECT to_char('100'::numeric, 'foo999');
SELECT to_char('100'::numeric, 'f\oo999');
SELECT to_char('100'::numeric, 'f\\oo999');
SELECT to_char('100'::numeric, 'f\"oo999');
SELECT to_char('100'::numeric, 'f\\"oo999');
SELECT to_char('100'::numeric, 'f"ool"999');
SELECT to_char('100'::numeric, 'f"\ool"999');
SELECT to_char('100'::numeric, 'f"\\ool"999');
SELECT to_char('100'::numeric, 'f"ool\"999');
SELECT to_char('100'::numeric, 'f"ool\\"999');
-- TO_NUMBER()
--
SET lc_numeric = 'C';
SELECT to_number('-34,338,492', '99G999G999');
SELECT to_number('-34,338,492.654,878', '99G999G999D999G999');
SELECT to_number('<564646.654564>', '999999.999999PR');
SELECT to_number('0.00001-', '9.999999S');
SELECT to_number('5.01-', 'FM9.999999S');
SELECT to_number('5.01-', 'FM9.999999MI');
SELECT to_number('5 4 4 4 4 8 . 7 8', '9 9 9 9 9 9 . 9 9');
SELECT to_number('.01', 'FM9.99');
SELECT to_number('.0', '99999999.99999999');
SELECT to_number('0', '99.99');
SELECT to_number('.-01', 'S99.99');
SELECT to_number('.01-', '99.99S');
SELECT to_number(' . 0 1-', ' 9 9 . 9 9 S');
SELECT to_number('34,50','999,99');
SELECT to_number('123,000','999G');
SELECT to_number('123456','999G999');
SELECT to_number('$1234.56','L9,999.99');
SELECT to_number('$1234.56','L99,999.99');
SELECT to_number('$1,234.56','L99,999.99');
SELECT to_number('1234.56','L99,999.99');
SELECT to_number('1,234.56','L99,999.99');
SELECT to_number('42nd', '99th');
SELECT to_number('123456', '99999V99');
RESET lc_numeric;
--
-- Input syntax
--
CREATE TABLE num_input_test (n1 numeric);
-- good inputs
INSERT INTO num_input_test(n1) VALUES (' 123');
INSERT INTO num_input_test(n1) VALUES (' 3245874 ');
INSERT INTO num_input_test(n1) VALUES (' -93853');
INSERT INTO num_input_test(n1) VALUES ('555.50');
INSERT INTO num_input_test(n1) VALUES ('-555.50');
INSERT INTO num_input_test(n1) VALUES ('NaN ');
INSERT INTO num_input_test(n1) VALUES (' nan');
INSERT INTO num_input_test(n1) VALUES (' inf ');
INSERT INTO num_input_test(n1) VALUES (' +inf ');
INSERT INTO num_input_test(n1) VALUES (' -inf ');
INSERT INTO num_input_test(n1) VALUES (' Infinity ');
INSERT INTO num_input_test(n1) VALUES (' +inFinity ');
INSERT INTO num_input_test(n1) VALUES (' -INFINITY ');
INSERT INTO num_input_test(n1) VALUES ('12_000_000_000');
INSERT INTO num_input_test(n1) VALUES ('12_000.123_456');
INSERT INTO num_input_test(n1) VALUES ('23_000_000_000e-1_0');
INSERT INTO num_input_test(n1) VALUES ('.000_000_000_123e1_0');
INSERT INTO num_input_test(n1) VALUES ('.000_000_000_123e+1_1');
INSERT INTO num_input_test(n1) VALUES ('0b10001110111100111100001001010');
INSERT INTO num_input_test(n1) VALUES (' -0B_1010_1011_0101_0100_1010_1001_1000_1100_1110_1011_0001_1111_0000_1010_1101_0010 ');
INSERT INTO num_input_test(n1) VALUES (' +0o112402761777 ');
INSERT INTO num_input_test(n1) VALUES ('-0O0012_5524_5230_6334_3167_0261');
INSERT INTO num_input_test(n1) VALUES ('-0x0000000000000000000000000deadbeef');
INSERT INTO num_input_test(n1) VALUES (' 0X_30b1_F33a_6DF0_bD4E_64DF_9BdA_7D15 ');
-- bad inputs
INSERT INTO num_input_test(n1) VALUES (' ');
INSERT INTO num_input_test(n1) VALUES (' 1234 %');
INSERT INTO num_input_test(n1) VALUES ('xyz');
INSERT INTO num_input_test(n1) VALUES ('- 1234');
INSERT INTO num_input_test(n1) VALUES ('5 . 0');
INSERT INTO num_input_test(n1) VALUES ('5. 0 ');
INSERT INTO num_input_test(n1) VALUES ('');
INSERT INTO num_input_test(n1) VALUES (' N aN ');
INSERT INTO num_input_test(n1) VALUES ('+NaN');
INSERT INTO num_input_test(n1) VALUES ('-NaN');
INSERT INTO num_input_test(n1) VALUES ('+ infinity');
INSERT INTO num_input_test(n1) VALUES ('_123');
INSERT INTO num_input_test(n1) VALUES ('123_');
INSERT INTO num_input_test(n1) VALUES ('12__34');
INSERT INTO num_input_test(n1) VALUES ('123_.456');
INSERT INTO num_input_test(n1) VALUES ('123._456');
INSERT INTO num_input_test(n1) VALUES ('1.2e_34');
INSERT INTO num_input_test(n1) VALUES ('1.2e34_');
INSERT INTO num_input_test(n1) VALUES ('1.2e3__4');
INSERT INTO num_input_test(n1) VALUES ('0b1112');
INSERT INTO num_input_test(n1) VALUES ('0c1112');
INSERT INTO num_input_test(n1) VALUES ('0o12345678');
INSERT INTO num_input_test(n1) VALUES ('0x1eg');
INSERT INTO num_input_test(n1) VALUES ('0x12.34');
INSERT INTO num_input_test(n1) VALUES ('0x__1234');
INSERT INTO num_input_test(n1) VALUES ('0x1234_');
INSERT INTO num_input_test(n1) VALUES ('0x12__34');
SELECT * FROM num_input_test;
-- Also try it with non-error-throwing API
SELECT pg_input_is_valid('34.5', 'numeric');
SELECT pg_input_is_valid('34xyz', 'numeric');
SELECT pg_input_is_valid('1e400000', 'numeric');
SELECT * FROM pg_input_error_info('1e400000', 'numeric');
SELECT pg_input_is_valid('1234.567', 'numeric(8,4)');
SELECT pg_input_is_valid('1234.567', 'numeric(7,4)');
SELECT * FROM pg_input_error_info('1234.567', 'numeric(7,4)');
SELECT * FROM pg_input_error_info('0x1234.567', 'numeric');
--
-- Test precision and scale typemods
--
CREATE TABLE num_typemod_test (
millions numeric(3, -6),
thousands numeric(3, -3),
units numeric(3, 0),
thousandths numeric(3, 3),
millionths numeric(3, 6)
);
\d num_typemod_test
-- rounding of valid inputs
INSERT INTO num_typemod_test VALUES (123456, 123, 0.123, 0.000123, 0.000000123);
INSERT INTO num_typemod_test VALUES (654321, 654, 0.654, 0.000654, 0.000000654);
INSERT INTO num_typemod_test VALUES (2345678, 2345, 2.345, 0.002345, 0.000002345);
INSERT INTO num_typemod_test VALUES (7654321, 7654, 7.654, 0.007654, 0.000007654);
INSERT INTO num_typemod_test VALUES (12345678, 12345, 12.345, 0.012345, 0.000012345);
INSERT INTO num_typemod_test VALUES (87654321, 87654, 87.654, 0.087654, 0.000087654);
INSERT INTO num_typemod_test VALUES (123456789, 123456, 123.456, 0.123456, 0.000123456);
INSERT INTO num_typemod_test VALUES (987654321, 987654, 987.654, 0.987654, 0.000987654);
INSERT INTO num_typemod_test VALUES ('NaN', 'NaN', 'NaN', 'NaN', 'NaN');
SELECT scale(millions), * FROM num_typemod_test ORDER BY millions;
-- invalid inputs
INSERT INTO num_typemod_test (millions) VALUES ('inf');
INSERT INTO num_typemod_test (millions) VALUES (999500000);
INSERT INTO num_typemod_test (thousands) VALUES (999500);
INSERT INTO num_typemod_test (units) VALUES (999.5);
INSERT INTO num_typemod_test (thousandths) VALUES (0.9995);
INSERT INTO num_typemod_test (millionths) VALUES (0.0009995);
--
-- Test some corner cases for multiplication
--
select 4790999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999;
select 4789999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999;
select 4770999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999;
select 4769999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999;
select trim_scale((0.1 - 2e-16383) * (0.1 - 3e-16383));
--
-- Test some corner cases for division
--
select 999999999999999999999::numeric/1000000000000000000000;
select div(999999999999999999999::numeric,1000000000000000000000);
select mod(999999999999999999999::numeric,1000000000000000000000);
select div(-9999999999999999999999::numeric,1000000000000000000000);
select mod(-9999999999999999999999::numeric,1000000000000000000000);
select div(-9999999999999999999999::numeric,1000000000000000000000)*1000000000000000000000 + mod(-9999999999999999999999::numeric,1000000000000000000000);
select mod (70.0,70) ;
select div (70.0,70) ;
select 70.0 / 70 ;
select 12345678901234567890 % 123;
select 12345678901234567890 / 123;
select div(12345678901234567890, 123);
select div(12345678901234567890, 123) * 123 + 12345678901234567890 % 123;
select 8e9000 - div(8e18000 - 1, 9e9000 - 1) * 9;
select 7328412092 - div(53705623790171816464 - 1, 7328412092);
select div(539913372912345678, 539913372912345678);
--
-- Test some corner cases for square root
--
select sqrt(1.000000000000003::numeric);
select sqrt(1.000000000000004::numeric);
select sqrt(96627521408608.56340355805::numeric);
select sqrt(96627521408608.56340355806::numeric);
select sqrt(515549506212297735.073688290367::numeric);
select sqrt(515549506212297735.073688290368::numeric);
select sqrt(8015491789940783531003294973900306::numeric);
select sqrt(8015491789940783531003294973900307::numeric);
--
-- Test code path for raising to integer powers
--
select 10.0 ^ -2147483648 as rounds_to_zero;
select 10.0 ^ -2147483647 as rounds_to_zero;
select 10.0 ^ 2147483647 as overflows;
select 117743296169.0 ^ 1000000000 as overflows;
-- cases that used to return inaccurate results
select 3.789 ^ 21.0000000000000000;
select 3.789 ^ 35.0000000000000000;
select 1.2 ^ 345;
select 0.12 ^ (-20);
select 1.000000000123 ^ (-2147483648);
select coalesce(nullif(0.9999999999 ^ 23300000000000, 0), 0) as rounds_to_zero;
select round(((1 - 1.500012345678e-1000) ^ 1.45e1003) * 1e1000);
-- cases that used to error out
select 0.12 ^ (-25);
select 0.5678 ^ (-85);
select coalesce(nullif(0.9999999999 ^ 70000000000000, 0), 0) as underflows;
-- negative base to integer powers
select (-1.0) ^ 2147483646;
select (-1.0) ^ 2147483647;
select (-1.0) ^ 2147483648;
select (-1.0) ^ 1000000000000000;
select (-1.0) ^ 1000000000000001;
-- integer powers of 10
select n, 10.0 ^ n as "10^n", (10.0 ^ n) * (10.0 ^ (-n)) = 1 as ok
from generate_series(-20, 20) n;
--
-- Tests for raising to non-integer powers
--
-- special cases
select 0.0 ^ 0.0;
select (-12.34) ^ 0.0;
select 12.34 ^ 0.0;
select 0.0 ^ 12.34;
-- NaNs
select 'NaN'::numeric ^ 'NaN'::numeric;
select 'NaN'::numeric ^ 0;
select 'NaN'::numeric ^ 1;
select 0 ^ 'NaN'::numeric;
select 1 ^ 'NaN'::numeric;
-- invalid inputs
select 0.0 ^ (-12.34);
select (-12.34) ^ 1.2;
-- cases that used to generate inaccurate results
select 32.1 ^ 9.8;
select 32.1 ^ (-9.8);
select 12.3 ^ 45.6;
select 12.3 ^ (-45.6);
-- big test
select 1.234 ^ 5678;
--
-- Tests for EXP()
--
-- special cases
select exp(0.0);
select exp(1.0);
select exp(1.0::numeric(71,70));
select exp('nan'::numeric);
select exp('inf'::numeric);
select exp('-inf'::numeric);
select coalesce(nullif(exp(-5000::numeric), 0), 0) as rounds_to_zero;
select coalesce(nullif(exp(-10000::numeric), 0), 0) as underflows;
-- cases that used to generate inaccurate results
select exp(32.999);
select exp(-32.999);
select exp(123.456);
select exp(-123.456);
-- big test
select exp(1234.5678);
--
-- Tests for generate_series
--
select * from generate_series(0.0::numeric, 4.0::numeric);
select * from generate_series(0.1::numeric, 4.0::numeric, 1.3::numeric);
select * from generate_series(4.0::numeric, -1.5::numeric, -2.2::numeric);
-- Trigger errors
select * from generate_series(-100::numeric, 100::numeric, 0::numeric);
select * from generate_series(-100::numeric, 100::numeric, 'nan'::numeric);
select * from generate_series('nan'::numeric, 100::numeric, 10::numeric);
select * from generate_series(0::numeric, 'nan'::numeric, 10::numeric);
select * from generate_series('inf'::numeric, 'inf'::numeric, 10::numeric);
select * from generate_series(0::numeric, 'inf'::numeric, 10::numeric);
select * from generate_series(0::numeric, '42'::numeric, '-inf'::numeric);
-- Checks maximum, output is truncated
select (i / (10::numeric ^ 131071))::numeric(1,0)
from generate_series(6 * (10::numeric ^ 131071),
9 * (10::numeric ^ 131071),
10::numeric ^ 131071) as a(i);
-- Check usage with variables
select * from generate_series(1::numeric, 3::numeric) i, generate_series(i,3) j;
select * from generate_series(1::numeric, 3::numeric) i, generate_series(1,i) j;
select * from generate_series(1::numeric, 3::numeric) i, generate_series(1,5,i) j;
--
-- Tests for LN()
--
-- Invalid inputs
select ln(-12.34);
select ln(0.0);
-- Some random tests
select ln(1.2345678e-28);
select ln(0.0456789);
select ln(0.349873948359354029493948309745709580730482050975);
select ln(0.99949452);
select ln(1.00049687395);
select ln(1234.567890123456789);
select ln(5.80397490724e5);
select ln(9.342536355e34);
--
-- Tests for LOG() (base 10)
--
-- invalid inputs
select log(-12.34);
select log(0.0);
-- some random tests
select log(1.234567e-89);
select log(3.4634998359873254962349856073435545);
select log(9.999999999999999999);
select log(10.00000000000000000);
select log(10.00000000000000001);
select log(590489.45235237);
--
-- Tests for LOG() (arbitrary base)
--
-- invalid inputs
select log(-12.34, 56.78);
select log(-12.34, -56.78);
select log(12.34, -56.78);
select log(0.0, 12.34);
select log(12.34, 0.0);
select log(1.0, 12.34);
-- some random tests
select log(1.23e-89, 6.4689e45);
select log(0.99923, 4.58934e34);
select log(1.000016, 8.452010e18);
select log(3.1954752e47, 9.4792021e-73);
--
-- Tests for scale()
--
select scale(numeric 'NaN');
select scale(numeric 'inf');
select scale(NULL::numeric);
select scale(1.12);
select scale(0);
select scale(0.00);
select scale(1.12345);
select scale(110123.12475871856128);
select scale(-1123.12471856128);
select scale(-13.000000000000000);
--
-- Tests for min_scale()
--
select min_scale(numeric 'NaN') is NULL; -- should be true
select min_scale(numeric 'inf') is NULL; -- should be true
select min_scale(0); -- no digits
select min_scale(0.00); -- no digits again
select min_scale(1.0); -- no scale
select min_scale(1.1); -- scale 1
select min_scale(1.12); -- scale 2
select min_scale(1.123); -- scale 3
select min_scale(1.1234); -- scale 4, filled digit
select min_scale(1.12345); -- scale 5, 2 NDIGITS
select min_scale(1.1000); -- 1 pos in NDIGITS
select min_scale(1e100); -- very big number
--
-- Tests for trim_scale()
--
select trim_scale(numeric 'NaN');
select trim_scale(numeric 'inf');
select trim_scale(1.120);
select trim_scale(0);
select trim_scale(0.00);
select trim_scale(1.1234500);
select trim_scale(110123.12475871856128000);
select trim_scale(-1123.124718561280000000);
select trim_scale(-13.00000000000000000000);
select trim_scale(1e100);
--
-- Tests for SUM()
--
-- cases that need carry propagation
SELECT SUM(9999::numeric) FROM generate_series(1, 100000);
SELECT SUM((-9999)::numeric) FROM generate_series(1, 100000);
--
-- Tests for VARIANCE()
--
CREATE TABLE num_variance (a numeric);
INSERT INTO num_variance VALUES (0);
INSERT INTO num_variance VALUES (3e-500);
INSERT INTO num_variance VALUES (-3e-500);
INSERT INTO num_variance VALUES (4e-500 - 1e-16383);
INSERT INTO num_variance VALUES (-4e-500 + 1e-16383);
-- variance is just under 12.5e-1000 and so should round down to 12e-1000
SELECT trim_scale(variance(a) * 1e1000) FROM num_variance;
-- check that parallel execution produces the same result
BEGIN;
ALTER TABLE num_variance SET (parallel_workers = 4);
SET LOCAL parallel_setup_cost = 0;
SET LOCAL max_parallel_workers_per_gather = 4;
SELECT trim_scale(variance(a) * 1e1000) FROM num_variance;
ROLLBACK;
-- case where sum of squares would overflow but variance does not
DELETE FROM num_variance;
INSERT INTO num_variance SELECT 9e131071 + x FROM generate_series(1, 5) x;
SELECT variance(a) FROM num_variance;
-- check that parallel execution produces the same result
BEGIN;
ALTER TABLE num_variance SET (parallel_workers = 4);
SET LOCAL parallel_setup_cost = 0;
SET LOCAL max_parallel_workers_per_gather = 4;
SELECT variance(a) FROM num_variance;
ROLLBACK;
DROP TABLE num_variance;
--
-- Tests for GCD()
--
SELECT a, b, gcd(a, b), gcd(a, -b), gcd(-b, a), gcd(-b, -a)
FROM (VALUES (0::numeric, 0::numeric),
(0::numeric, numeric 'NaN'),
(0::numeric, 46375::numeric),
(433125::numeric, 46375::numeric),
(43312.5::numeric, 4637.5::numeric),
(4331.250::numeric, 463.75000::numeric),
('inf', '0'),
('inf', '42'),
('inf', 'inf')
) AS v(a, b);
--
-- Tests for LCM()
--
SELECT a,b, lcm(a, b), lcm(a, -b), lcm(-b, a), lcm(-b, -a)
FROM (VALUES (0::numeric, 0::numeric),
(0::numeric, numeric 'NaN'),
(0::numeric, 13272::numeric),
(13272::numeric, 13272::numeric),
(423282::numeric, 13272::numeric),
(42328.2::numeric, 1327.2::numeric),
(4232.820::numeric, 132.72000::numeric),
('inf', '0'),
('inf', '42'),
('inf', 'inf')
) AS v(a, b);
SELECT lcm(9999 * (10::numeric)^131068 + (10::numeric^131068 - 1), 2); -- overflow
--
-- Tests for factorial
--
SELECT factorial(4);
SELECT factorial(15);
SELECT factorial(100000);
SELECT factorial(0);
SELECT factorial(-4);
--
-- Tests for pg_lsn()
--
SELECT pg_lsn(23783416::numeric);
SELECT pg_lsn(0::numeric);
SELECT pg_lsn(18446744073709551615::numeric);
SELECT pg_lsn(-1::numeric);
SELECT pg_lsn(18446744073709551616::numeric);
SELECT pg_lsn('NaN'::numeric);
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