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postgresql/src/test/regress/sql/numeric.sql
Dean Rasheed 4083f445c0 Improve the performance and accuracy of numeric sqrt() and ln(). 
Instead of using Newton's method to compute numeric square roots, use
the Karatsuba square root algorithm, which performs better for numbers
of all sizes. In practice, this is 3-5 times faster for inputs with
just a few digits and up to around 10 times faster for larger inputs.

Also, the new algorithm guarantees that the final digit of the result
is correctly rounded, since it computes an integer square root with
truncation, containing at least 1 extra decimal digit before rounding.
The former algorithm would occasionally round the wrong way because
it rounded both the intermediate and final results.

In addition, arrange for sqrt_var() to explicitly support negative
rscale values (rounding before the decimal point). This allows the
argument reduction phase of ln_var() to be optimised for large inputs,
since it only needs to compute square roots with a few more digits
than the final ln() result, rather than computing all the digits
before the decimal point. For very large inputs, this can be many
thousands of times faster.

In passing, optimise div_var_fast() in a couple of places where it was
doing unnecessary work.

Patch be me, reviewed by Tom Lane and Tels.

Discussion: https://postgr.es/m/CAEZATCV1A7+jD3P30Zu31KjaxeSEyOn3v9d6tYegpxcq3cQu-g@mail.gmail.com
2020-03-28 14:37:53 +00:00

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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_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;
-- ******************************
-- * 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 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');
SELECT * FROM fract_only;
DROP TABLE fract_only;
-- Check inf/nan conversion behavior
SELECT 'NaN'::float8::numeric;
SELECT 'Infinity'::float8::numeric;
SELECT '-Infinity'::float8::numeric;
SELECT 'NaN'::float4::numeric;
SELECT 'Infinity'::float4::numeric;
SELECT '-Infinity'::float4::numeric;
-- 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);
-- 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);
-- 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;
-- for float8 only, check positive and negative infinity: we require
-- finite bucket bounds, but allow an infinite operand
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;
-- TO_CHAR()
--
SELECT '' AS to_char_1, to_char(val, '9G999G999G999G999G999')
FROM num_data;
SELECT '' AS to_char_2, to_char(val, '9G999G999G999G999G999D999G999G999G999G999')
FROM num_data;
SELECT '' AS to_char_3, to_char(val, '9999999999999999.999999999999999PR')
FROM num_data;
SELECT '' AS to_char_4, to_char(val, '9999999999999999.999999999999999S')
FROM num_data;
SELECT '' AS to_char_5, to_char(val, 'MI9999999999999999.999999999999999') FROM num_data;
SELECT '' AS to_char_6, to_char(val, 'FMS9999999999999999.999999999999999') FROM num_data;
SELECT '' AS to_char_7, to_char(val, 'FM9999999999999999.999999999999999THPR') FROM num_data;
SELECT '' AS to_char_8, to_char(val, 'SG9999999999999999.999999999999999th') FROM num_data;
SELECT '' AS to_char_9, to_char(val, '0999999999999999.999999999999999') FROM num_data;
SELECT '' AS to_char_10, to_char(val, 'S0999999999999999.999999999999999') FROM num_data;
SELECT '' AS to_char_11, to_char(val, 'FM0999999999999999.999999999999999') FROM num_data;
SELECT '' AS to_char_12, to_char(val, 'FM9999999999999999.099999999999999') FROM num_data;
SELECT '' AS to_char_13, to_char(val, 'FM9999999999990999.990999999999999') FROM num_data;
SELECT '' AS to_char_14, to_char(val, 'FM0999999999999999.999909999999999') FROM num_data;
SELECT '' AS to_char_15, to_char(val, 'FM9999999990999999.099999999999999') FROM num_data;
SELECT '' AS to_char_16, to_char(val, 'L9999999999999999.099999999999999') FROM num_data;
SELECT '' AS to_char_17, to_char(val, 'FM9999999999999999.99999999999999') FROM num_data;
SELECT '' AS to_char_18, 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 '' AS to_char_19, 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 '' AS to_char_20, to_char(val, E'99999 "text" 9999 "9999" 999 "\\"text between quote marks\\"" 9999') FROM num_data;
SELECT '' AS to_char_21, to_char(val, '999999SG9999999999') FROM num_data;
SELECT '' AS to_char_22, to_char(val, 'FM9999999999999999.999999999999999') FROM num_data;
SELECT '' AS to_char_23, to_char(val, '9.999EEEE') FROM num_data;
SELECT '' AS to_char_24, to_char('100'::numeric, 'FM999.9');
SELECT '' AS to_char_25, to_char('100'::numeric, 'FM999.');
SELECT '' AS to_char_26, to_char('100'::numeric, 'FM999');
-- Check parsing of literal text in a format string
SELECT '' AS to_char_27, to_char('100'::numeric, 'foo999');
SELECT '' AS to_char_28, to_char('100'::numeric, 'f\oo999');
SELECT '' AS to_char_29, to_char('100'::numeric, 'f\\oo999');
SELECT '' AS to_char_30, to_char('100'::numeric, 'f\"oo999');
SELECT '' AS to_char_31, to_char('100'::numeric, 'f\\"oo999');
SELECT '' AS to_char_32, to_char('100'::numeric, 'f"ool"999');
SELECT '' AS to_char_33, to_char('100'::numeric, 'f"\ool"999');
SELECT '' AS to_char_34, to_char('100'::numeric, 'f"\\ool"999');
SELECT '' AS to_char_35, to_char('100'::numeric, 'f"ool\"999');
SELECT '' AS to_char_36, to_char('100'::numeric, 'f"ool\\"999');
-- TO_NUMBER()
--
SET lc_numeric = 'C';
SELECT '' AS to_number_1, to_number('-34,338,492', '99G999G999');
SELECT '' AS to_number_2, to_number('-34,338,492.654,878', '99G999G999D999G999');
SELECT '' AS to_number_3, to_number('<564646.654564>', '999999.999999PR');
SELECT '' AS to_number_4, to_number('0.00001-', '9.999999S');
SELECT '' AS to_number_5, to_number('5.01-', 'FM9.999999S');
SELECT '' AS to_number_5, to_number('5.01-', 'FM9.999999MI');
SELECT '' AS to_number_7, to_number('5 4 4 4 4 8 . 7 8', '9 9 9 9 9 9 . 9 9');
SELECT '' AS to_number_8, to_number('.01', 'FM9.99');
SELECT '' AS to_number_9, to_number('.0', '99999999.99999999');
SELECT '' AS to_number_10, to_number('0', '99.99');
SELECT '' AS to_number_11, to_number('.-01', 'S99.99');
SELECT '' AS to_number_12, to_number('.01-', '99.99S');
SELECT '' AS to_number_13, to_number(' . 0 1-', ' 9 9 . 9 9 S');
SELECT '' AS to_number_14, to_number('34,50','999,99');
SELECT '' AS to_number_15, to_number('123,000','999G');
SELECT '' AS to_number_16, to_number('123456','999G999');
SELECT '' AS to_number_17, to_number('$1234.56','L9,999.99');
SELECT '' AS to_number_18, to_number('$1234.56','L99,999.99');
SELECT '' AS to_number_19, to_number('$1,234.56','L99,999.99');
SELECT '' AS to_number_20, to_number('1234.56','L99,999.99');
SELECT '' AS to_number_21, to_number('1,234.56','L99,999.99');
SELECT '' AS to_number_22, to_number('42nd', '99th');
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');
-- 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 ');
SELECT * FROM num_input_test;
--
-- Test some corner cases for multiplication
--
select 4790999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999;
select 4789999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999;
select 4770999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999;
select 4769999999999999999999999999999999999999999999999999999999999999999999999999999999999999 * 9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999;
--
-- 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;
--
-- 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;
select 3.789 ^ 35;
select 1.2 ^ 345;
select 0.12 ^ (-20);
-- cases that used to error out
select 0.12 ^ (-25);
select 0.5678 ^ (-85);
--
-- 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));
-- 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);
-- 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(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(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(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 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)) 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)) AS v(a, b);
SELECT lcm(9999 * (10::numeric)^131068 + (10::numeric^131068 - 1), 2); -- overflow
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