1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
|
--
-- FLOAT8
--
CREATE TABLE FLOAT8_TBL(f1 float8);
INSERT INTO FLOAT8_TBL(f1) VALUES (' 0.0 ');
INSERT INTO FLOAT8_TBL(f1) VALUES ('1004.30 ');
INSERT INTO FLOAT8_TBL(f1) VALUES (' -34.84');
INSERT INTO FLOAT8_TBL(f1) VALUES ('1.2345678901234e+200');
INSERT INTO FLOAT8_TBL(f1) VALUES ('1.2345678901234e-200');
-- test for underflow and overflow handling
SELECT '10e400'::float8;
SELECT '-10e400'::float8;
SELECT '10e-400'::float8;
SELECT '-10e-400'::float8;
-- test smallest normalized input
SELECT float8send('2.2250738585072014E-308'::float8);
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
INSERT INTO FLOAT8_TBL(f1) VALUES (' ');
INSERT INTO FLOAT8_TBL(f1) VALUES ('xyz');
INSERT INTO FLOAT8_TBL(f1) VALUES ('5.0.0');
INSERT INTO FLOAT8_TBL(f1) VALUES ('5 . 0');
INSERT INTO FLOAT8_TBL(f1) VALUES ('5. 0');
INSERT INTO FLOAT8_TBL(f1) VALUES (' - 3');
INSERT INTO FLOAT8_TBL(f1) VALUES ('123 5');
-- special inputs
SELECT 'NaN'::float8;
SELECT 'nan'::float8;
SELECT ' NAN '::float8;
SELECT 'infinity'::float8;
SELECT ' -INFINiTY '::float8;
-- bad special inputs
SELECT 'N A N'::float8;
SELECT 'NaN x'::float8;
SELECT ' INFINITY x'::float8;
SELECT 'Infinity'::float8 + 100.0;
SELECT 'Infinity'::float8 / 'Infinity'::float8;
SELECT '42'::float8 / 'Infinity'::float8;
SELECT 'nan'::float8 / 'nan'::float8;
SELECT 'nan'::float8 / '0'::float8;
SELECT 'nan'::numeric::float8;
SELECT * FROM FLOAT8_TBL;
SELECT f.* FROM FLOAT8_TBL f WHERE f.f1 <> '1004.3';
SELECT f.* FROM FLOAT8_TBL f WHERE f.f1 = '1004.3';
SELECT f.* FROM FLOAT8_TBL f WHERE '1004.3' > f.f1;
SELECT f.* FROM FLOAT8_TBL f WHERE f.f1 < '1004.3';
SELECT f.* FROM FLOAT8_TBL f WHERE '1004.3' >= f.f1;
SELECT f.* FROM FLOAT8_TBL f WHERE f.f1 <= '1004.3';
SELECT f.f1, f.f1 * '-10' AS x
FROM FLOAT8_TBL f
WHERE f.f1 > '0.0';
SELECT f.f1, f.f1 + '-10' AS x
FROM FLOAT8_TBL f
WHERE f.f1 > '0.0';
SELECT f.f1, f.f1 - '-10' AS x
FROM FLOAT8_TBL f
WHERE f.f1 > '0.0';
-- absolute value
SELECT f.f1, @f.f1 AS abs_f1
FROM FLOAT8_TBL f;
-- truncate
SELECT f.f1, trunc(f.f1) AS trunc_f1
FROM FLOAT8_TBL f;
-- round
SELECT f.f1, round(f.f1) AS round_f1
FROM FLOAT8_TBL f;
-- avoid bit-exact output here because operations may not be bit-exact.
SET extra_float_digits = 0;
-- square root
SELECT sqrt(float8 '64') AS eight;
SELECT |/ float8 '64' AS eight;
SELECT f.f1, |/f.f1 AS sqrt_f1
FROM FLOAT8_TBL f
WHERE f.f1 > '0.0';
-- power
SELECT power(float8 '144', float8 '0.5');
SELECT power(float8 'NaN', float8 '0.5');
SELECT power(float8 '144', float8 'NaN');
SELECT power(float8 'NaN', float8 'NaN');
SELECT power(float8 '-1', float8 'NaN');
SELECT power(float8 '1', float8 'NaN');
SELECT power(float8 'NaN', float8 '0');
SELECT power(float8 'inf', float8 '0');
SELECT power(float8 '-inf', float8 '0');
SELECT power(float8 '0', float8 'inf');
SELECT power(float8 '0', float8 '-inf');
SELECT power(float8 '1', float8 'inf');
SELECT power(float8 '1', float8 '-inf');
SELECT power(float8 '-1', float8 'inf');
SELECT power(float8 '-1', float8 '-inf');
SELECT power(float8 '0.1', float8 'inf');
SELECT power(float8 '-0.1', float8 'inf');
SELECT power(float8 '1.1', float8 'inf');
SELECT power(float8 '-1.1', float8 'inf');
SELECT power(float8 '0.1', float8 '-inf');
SELECT power(float8 '-0.1', float8 '-inf');
SELECT power(float8 '1.1', float8 '-inf');
SELECT power(float8 '-1.1', float8 '-inf');
SELECT power(float8 'inf', float8 '-2');
SELECT power(float8 'inf', float8 '2');
SELECT power(float8 'inf', float8 'inf');
SELECT power(float8 'inf', float8 '-inf');
-- Intel's icc misoptimizes the code that controls the sign of this result,
-- even with -mp1. Pending a fix for that, only test for "is it zero".
SELECT power(float8 '-inf', float8 '-2') = '0';
SELECT power(float8 '-inf', float8 '-3');
SELECT power(float8 '-inf', float8 '2');
SELECT power(float8 '-inf', float8 '3');
SELECT power(float8 '-inf', float8 '3.5');
SELECT power(float8 '-inf', float8 'inf');
SELECT power(float8 '-inf', float8 '-inf');
-- take exp of ln(f.f1)
SELECT f.f1, exp(ln(f.f1)) AS exp_ln_f1
FROM FLOAT8_TBL f
WHERE f.f1 > '0.0';
-- cube root
SELECT ||/ float8 '27' AS three;
SELECT f.f1, ||/f.f1 AS cbrt_f1 FROM FLOAT8_TBL f;
SELECT * FROM FLOAT8_TBL;
SELECT f.f1 * '1e200' from FLOAT8_TBL f;
SELECT f.f1 ^ '1e200' from FLOAT8_TBL f;
SELECT 0 ^ 0 + 0 ^ 1 + 0 ^ 0.0 + 0 ^ 0.5;
SELECT ln(f.f1) from FLOAT8_TBL f where f.f1 = '0.0' ;
SELECT ln(f.f1) from FLOAT8_TBL f where f.f1 < '0.0' ;
SELECT f.f1 / '0.0' from FLOAT8_TBL f;
-- hyperbolic functions
-- we run these with extra_float_digits = 0 too, since different platforms
-- tend to produce results that vary in the last place.
SELECT sinh(float8 '1');
SELECT cosh(float8 '1');
SELECT tanh(float8 '1');
SELECT asinh(float8 '1');
SELECT acosh(float8 '2');
SELECT atanh(float8 '0.5');
-- test Inf/NaN cases for hyperbolic functions
SELECT sinh(float8 'infinity');
SELECT sinh(float8 '-infinity');
SELECT sinh(float8 'nan');
SELECT cosh(float8 'infinity');
SELECT cosh(float8 '-infinity');
SELECT cosh(float8 'nan');
SELECT tanh(float8 'infinity');
SELECT tanh(float8 '-infinity');
SELECT tanh(float8 'nan');
SELECT asinh(float8 'infinity');
SELECT asinh(float8 '-infinity');
SELECT asinh(float8 'nan');
-- acosh(Inf) should be Inf, but some mingw versions produce NaN, so skip test
-- SELECT acosh(float8 'infinity');
SELECT acosh(float8 '-infinity');
SELECT acosh(float8 'nan');
SELECT atanh(float8 'infinity');
SELECT atanh(float8 '-infinity');
SELECT atanh(float8 'nan');
RESET extra_float_digits;
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
INSERT INTO FLOAT8_TBL(f1) VALUES ('-10e400');
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e-400');
INSERT INTO FLOAT8_TBL(f1) VALUES ('-10e-400');
INSERT INTO FLOAT8_TBL(f1) VALUES ('0.0');
INSERT INTO FLOAT8_TBL(f1) VALUES ('-34.84');
INSERT INTO FLOAT8_TBL(f1) VALUES ('-1004.30');
INSERT INTO FLOAT8_TBL(f1) VALUES ('-1.2345678901234e+200');
INSERT INTO FLOAT8_TBL(f1) VALUES ('-1.2345678901234e-200');
-- test edge-case coercions to integer
SELECT '32767.4'::float8::int2;
SELECT '32767.6'::float8::int2;
SELECT '-32768.4'::float8::int2;
SELECT '-32768.6'::float8::int2;
SELECT '2147483647.4'::float8::int4;
SELECT '2147483647.6'::float8::int4;
SELECT '-2147483648.4'::float8::int4;
SELECT '-2147483648.6'::float8::int4;
SELECT '9223372036854773760'::float8::int8;
SELECT '9223372036854775807'::float8::int8;
SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
-- test exact cases for trigonometric functions in degrees
SELECT x,
sind(x),
sind(x) IN (-1,-0.5,0,0.5,1) AS sind_exact
FROM (VALUES (0), (30), (90), (150), (180),
(210), (270), (330), (360)) AS t(x);
SELECT x,
cosd(x),
cosd(x) IN (-1,-0.5,0,0.5,1) AS cosd_exact
FROM (VALUES (0), (60), (90), (120), (180),
(240), (270), (300), (360)) AS t(x);
SELECT x,
tand(x),
tand(x) IN ('-Infinity'::float8,-1,0,
1,'Infinity'::float8) AS tand_exact,
cotd(x),
cotd(x) IN ('-Infinity'::float8,-1,0,
1,'Infinity'::float8) AS cotd_exact
FROM (VALUES (0), (45), (90), (135), (180),
(225), (270), (315), (360)) AS t(x);
SELECT x,
atand(x),
atand(x) IN (-90,-45,0,45,90) AS atand_exact
FROM (VALUES ('-Infinity'::float8), (-1), (0), (1),
('Infinity'::float8)) AS t(x);
SELECT x, y,
atan2d(y, x),
atan2d(y, x) IN (-90,0,90,180) AS atan2d_exact
FROM (SELECT 10*cosd(a), 10*sind(a)
FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);
|
