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Add trigonometric functions that work in degrees.

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The implementations go to some lengths to deliver exact results for values
where an exact result can be expected, such as sind(30) = 0.5 exactly.

Dean Rasheed, reviewed by Michael Paquier
This commit is contained in:
Tom Lane
2016-01-22 15:46:22 -05:00
parent fd5200c3dc
commit e1bd684a34
10 changed files with 860 additions and 9 deletions
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77
src/test/regress/expected/float8-exp-three-digits-win32.out
View File

@ -444,3 +444,80 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
| -1.2345678901234e-200
(5 rows)
-- test exact cases for trigonometric functions in degrees
SELECT x,
CASE WHEN sind(x) IN (-1,-0.5,0,0.5,1) THEN sind(x) END AS sind,
CASE WHEN cosd(x) IN (-1,-0.5,0,0.5,1) THEN cosd(x) END AS cosd,
CASE WHEN tand(x) IN ('-Infinity'::float8,-1,0,
1,'Infinity'::float8) THEN tand(x) END AS tand,
CASE WHEN cotd(x) IN ('-Infinity'::float8,-1,0,
1,'Infinity'::float8) THEN cotd(x) END AS cotd
FROM generate_series(0, 360, 15) AS t(x);
x | sind | cosd | tand | cotd
-----+------+------+-----------+-----------
0 | 0 | 1 | 0 | Infinity
15 | | | |
30 | 0.5 | | |
45 | | | 1 | 1
60 | | 0.5 | |
75 | | | |
90 | 1 | 0 | Infinity | 0
105 | | | |
120 | | -0.5 | |
135 | | | -1 | -1
150 | 0.5 | | |
165 | | | |
180 | 0 | -1 | -0 | -Infinity
195 | | | |
210 | -0.5 | | |
225 | | | 1 | 1
240 | | -0.5 | |
255 | | | |
270 | -1 | 0 | -Infinity | -0
285 | | | |
300 | | 0.5 | |
315 | | | -1 | -1
330 | -0.5 | | |
345 | | | |
360 | 0 | 1 | 0 | Infinity
(25 rows)
SELECT x,
CASE WHEN asind(x) IN (-90,-30,0,30,90) THEN asind(x) END AS asind,
CASE WHEN acosd(x) IN (0,60,90,120,180) THEN acosd(x) END AS acosd,
CASE WHEN atand(x) IN (-45,0,45) THEN atand(x) END AS atand
FROM (VALUES (-1), (-0.5), (0), (0.5), (1)) AS t(x);
x | asind | acosd | atand
------+-------+-------+-------
-1 | -90 | 180 | -45
-0.5 | -30 | 120 |
0 | 0 | 90 | 0
0.5 | 30 | 60 |
1 | 90 | 0 | 45
(5 rows)
SELECT atand('-Infinity'::float8) = -90;
?column?
----------
t
(1 row)
SELECT atand('Infinity'::float8) = 90;
?column?
----------
t
(1 row)
SELECT x, y,
CASE WHEN atan2d(y, x) IN (-90,0,90,180) THEN atan2d(y, x) END AS atan2d
FROM (SELECT 10*cosd(a), 10*sind(a)
FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);
x | y | atan2d
-----+-----+--------
10 | 0 | 0
0 | 10 | 90
-10 | 0 | 180
0 | -10 | -90
10 | 0 | 0
(5 rows)

77
src/test/regress/expected/float8-small-is-zero.out
View File

@ -442,3 +442,80 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
| -1.2345678901234e-200
(5 rows)
-- test exact cases for trigonometric functions in degrees
SELECT x,
CASE WHEN sind(x) IN (-1,-0.5,0,0.5,1) THEN sind(x) END AS sind,
CASE WHEN cosd(x) IN (-1,-0.5,0,0.5,1) THEN cosd(x) END AS cosd,
CASE WHEN tand(x) IN ('-Infinity'::float8,-1,0,
1,'Infinity'::float8) THEN tand(x) END AS tand,
CASE WHEN cotd(x) IN ('-Infinity'::float8,-1,0,
1,'Infinity'::float8) THEN cotd(x) END AS cotd
FROM generate_series(0, 360, 15) AS t(x);
x | sind | cosd | tand | cotd
-----+------+------+-----------+-----------
0 | 0 | 1 | 0 | Infinity
15 | | | |
30 | 0.5 | | |
45 | | | 1 | 1
60 | | 0.5 | |
75 | | | |
90 | 1 | 0 | Infinity | 0
105 | | | |
120 | | -0.5 | |
135 | | | -1 | -1
150 | 0.5 | | |
165 | | | |
180 | 0 | -1 | -0 | -Infinity
195 | | | |
210 | -0.5 | | |
225 | | | 1 | 1
240 | | -0.5 | |
255 | | | |
270 | -1 | 0 | -Infinity | -0
285 | | | |
300 | | 0.5 | |
315 | | | -1 | -1
330 | -0.5 | | |
345 | | | |
360 | 0 | 1 | 0 | Infinity
(25 rows)
SELECT x,
CASE WHEN asind(x) IN (-90,-30,0,30,90) THEN asind(x) END AS asind,
CASE WHEN acosd(x) IN (0,60,90,120,180) THEN acosd(x) END AS acosd,
CASE WHEN atand(x) IN (-45,0,45) THEN atand(x) END AS atand
FROM (VALUES (-1), (-0.5), (0), (0.5), (1)) AS t(x);
x | asind | acosd | atand
------+-------+-------+-------
-1 | -90 | 180 | -45
-0.5 | -30 | 120 |
0 | 0 | 90 | 0
0.5 | 30 | 60 |
1 | 90 | 0 | 45
(5 rows)
SELECT atand('-Infinity'::float8) = -90;
?column?
----------
t
(1 row)
SELECT atand('Infinity'::float8) = 90;
?column?
----------
t
(1 row)
SELECT x, y,
CASE WHEN atan2d(y, x) IN (-90,0,90,180) THEN atan2d(y, x) END AS atan2d
FROM (SELECT 10*cosd(a), 10*sind(a)
FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);
x | y | atan2d
-----+-----+--------
10 | 0 | 0
0 | 10 | 90
-10 | 0 | 180
0 | -10 | -90
10 | 0 | 0
(5 rows)

77
src/test/regress/expected/float8-small-is-zero_1.out
View File

@ -442,3 +442,80 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
| -1.2345678901234e-200
(5 rows)
-- test exact cases for trigonometric functions in degrees
SELECT x,
CASE WHEN sind(x) IN (-1,-0.5,0,0.5,1) THEN sind(x) END AS sind,
CASE WHEN cosd(x) IN (-1,-0.5,0,0.5,1) THEN cosd(x) END AS cosd,
CASE WHEN tand(x) IN ('-Infinity'::float8,-1,0,
1,'Infinity'::float8) THEN tand(x) END AS tand,
CASE WHEN cotd(x) IN ('-Infinity'::float8,-1,0,
1,'Infinity'::float8) THEN cotd(x) END AS cotd
FROM generate_series(0, 360, 15) AS t(x);
x | sind | cosd | tand | cotd
-----+------+------+-----------+-----------
0 | 0 | 1 | 0 | Infinity
15 | | | |
30 | 0.5 | | |
45 | | | 1 | 1
60 | | 0.5 | |
75 | | | |
90 | 1 | 0 | Infinity | 0
105 | | | |
120 | | -0.5 | |
135 | | | -1 | -1
150 | 0.5 | | |
165 | | | |
180 | 0 | -1 | -0 | -Infinity
195 | | | |
210 | -0.5 | | |
225 | | | 1 | 1
240 | | -0.5 | |
255 | | | |
270 | -1 | 0 | -Infinity | -0
285 | | | |
300 | | 0.5 | |
315 | | | -1 | -1
330 | -0.5 | | |
345 | | | |
360 | 0 | 1 | 0 | Infinity
(25 rows)
SELECT x,
CASE WHEN asind(x) IN (-90,-30,0,30,90) THEN asind(x) END AS asind,
CASE WHEN acosd(x) IN (0,60,90,120,180) THEN acosd(x) END AS acosd,
CASE WHEN atand(x) IN (-45,0,45) THEN atand(x) END AS atand
FROM (VALUES (-1), (-0.5), (0), (0.5), (1)) AS t(x);
x | asind | acosd | atand
------+-------+-------+-------
-1 | -90 | 180 | -45
-0.5 | -30 | 120 |
0 | 0 | 90 | 0
0.5 | 30 | 60 |
1 | 90 | 0 | 45
(5 rows)
SELECT atand('-Infinity'::float8) = -90;
?column?
----------
t
(1 row)
SELECT atand('Infinity'::float8) = 90;
?column?
----------
t
(1 row)
SELECT x, y,
CASE WHEN atan2d(y, x) IN (-90,0,90,180) THEN atan2d(y, x) END AS atan2d
FROM (SELECT 10*cosd(a), 10*sind(a)
FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);
x | y | atan2d
-----+-----+--------
10 | 0 | 0
0 | 10 | 90
-10 | 0 | 180
0 | -10 | -90
10 | 0 | 0
(5 rows)

77
src/test/regress/expected/float8.out
View File

@ -444,3 +444,80 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
| -1.2345678901234e-200
(5 rows)
-- test exact cases for trigonometric functions in degrees
SELECT x,
CASE WHEN sind(x) IN (-1,-0.5,0,0.5,1) THEN sind(x) END AS sind,
CASE WHEN cosd(x) IN (-1,-0.5,0,0.5,1) THEN cosd(x) END AS cosd,
CASE WHEN tand(x) IN ('-Infinity'::float8,-1,0,
1,'Infinity'::float8) THEN tand(x) END AS tand,
CASE WHEN cotd(x) IN ('-Infinity'::float8,-1,0,
1,'Infinity'::float8) THEN cotd(x) END AS cotd
FROM generate_series(0, 360, 15) AS t(x);
x | sind | cosd | tand | cotd
-----+------+------+-----------+-----------
0 | 0 | 1 | 0 | Infinity
15 | | | |
30 | 0.5 | | |
45 | | | 1 | 1
60 | | 0.5 | |
75 | | | |
90 | 1 | 0 | Infinity | 0
105 | | | |
120 | | -0.5 | |
135 | | | -1 | -1
150 | 0.5 | | |
165 | | | |
180 | 0 | -1 | -0 | -Infinity
195 | | | |
210 | -0.5 | | |
225 | | | 1 | 1
240 | | -0.5 | |
255 | | | |
270 | -1 | 0 | -Infinity | -0
285 | | | |
300 | | 0.5 | |
315 | | | -1 | -1
330 | -0.5 | | |
345 | | | |
360 | 0 | 1 | 0 | Infinity
(25 rows)
SELECT x,
CASE WHEN asind(x) IN (-90,-30,0,30,90) THEN asind(x) END AS asind,
CASE WHEN acosd(x) IN (0,60,90,120,180) THEN acosd(x) END AS acosd,
CASE WHEN atand(x) IN (-45,0,45) THEN atand(x) END AS atand
FROM (VALUES (-1), (-0.5), (0), (0.5), (1)) AS t(x);
x | asind | acosd | atand
------+-------+-------+-------
-1 | -90 | 180 | -45
-0.5 | -30 | 120 |
0 | 0 | 90 | 0
0.5 | 30 | 60 |
1 | 90 | 0 | 45
(5 rows)
SELECT atand('-Infinity'::float8) = -90;
?column?
----------
t
(1 row)
SELECT atand('Infinity'::float8) = 90;
?column?
----------
t
(1 row)
SELECT x, y,
CASE WHEN atan2d(y, x) IN (-90,0,90,180) THEN atan2d(y, x) END AS atan2d
FROM (SELECT 10*cosd(a), 10*sind(a)
FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);
x | y | atan2d
-----+-----+--------
10 | 0 | 0
0 | 10 | 90
-10 | 0 | 180
0 | -10 | -90
10 | 0 | 0
(5 rows)

24
src/test/regress/sql/float8.sql
View File

@ -167,3 +167,27 @@ INSERT INTO FLOAT8_TBL(f1) VALUES ('-1.2345678901234e+200');
INSERT INTO FLOAT8_TBL(f1) VALUES ('-1.2345678901234e-200');
SELECT '' AS five, * FROM FLOAT8_TBL;
-- test exact cases for trigonometric functions in degrees
SELECT x,
CASE WHEN sind(x) IN (-1,-0.5,0,0.5,1) THEN sind(x) END AS sind,
CASE WHEN cosd(x) IN (-1,-0.5,0,0.5,1) THEN cosd(x) END AS cosd,
CASE WHEN tand(x) IN ('-Infinity'::float8,-1,0,
1,'Infinity'::float8) THEN tand(x) END AS tand,
CASE WHEN cotd(x) IN ('-Infinity'::float8,-1,0,
1,'Infinity'::float8) THEN cotd(x) END AS cotd
FROM generate_series(0, 360, 15) AS t(x);
SELECT x,
CASE WHEN asind(x) IN (-90,-30,0,30,90) THEN asind(x) END AS asind,
CASE WHEN acosd(x) IN (0,60,90,120,180) THEN acosd(x) END AS acosd,
CASE WHEN atand(x) IN (-45,0,45) THEN atand(x) END AS atand
FROM (VALUES (-1), (-0.5), (0), (0.5), (1)) AS t(x);
SELECT atand('-Infinity'::float8) = -90;
SELECT atand('Infinity'::float8) = 90;
SELECT x, y,
CASE WHEN atan2d(y, x) IN (-90,0,90,180) THEN atan2d(y, x) END AS atan2d
FROM (SELECT 10*cosd(a), 10*sind(a)
FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);