Various fixes for binary expressions (#165)

The SQL standard states that arithmetic must result in the
"most specific type". This implementation is more correct, but is
incomplete. I'll keep the complete implementation for a later diff after
NUMERIC and DECIMAL has been included.

This also updates predicates to use the SQL-defined version instead of
the existing functions, adds some missing unary operators and fixes a
formatting error for some REAL values.

docs/numbers.rst

@@ -3,6 +3,26 @@ Numbers
 
 .. contents::
 
+Literals
+--------
+
+Different forms have implicit types:
+
+.. list-table::
+  :header-rows: 1
+
+  * - Description
+    - Examples
+    - Type
+
+  * - Integers
+    - ``123``, ``0``, ``-1234``
+    - ``BIGINT``
+
+  * - Floating-point (contains ``.``)
+    - ``12.3``, ``0.0001``, ``-12.0``
+    - ``DOUBLE PRECISION``
+
 Exact Numeric Types
 -------------------
 
@@ -98,6 +118,22 @@ Casting
     - ✅
     - ✅
 
+Arithmetic Operations
+---------------------
+
+Arithmetic operations (sometimes called binary operations) require the same type
+for both operands and return this same type. For example ``INTEGER + INTEGER``
+will result in an ``INTEGER``.
+
+When the type of the operands are different it will implicitly cast to the
+supertype of both. For numbers all supertypes are and in order: ``SMALLINT``,
+``INTEGER``, ``BIGINT``, ``REAL`` and ``DOUBLE PRECISION``.
+
+For example ``12 * 10.5`` is evaluated as the expression
+``BIGINT * DOUBLE PRECISION``. Since ``DOUBLE PRECISION`` is the only supertype
+for both, ``12`` must be implicitly cast to a ``DOUBLE PRECISION`` and the
+operation will yield as result as ``DOUBLE PRECISION``.
+
 Notes
 -----
 

tests/bigint.sql

@@ -64,52 +64,49 @@ SELECT CAST(x AS BOOLEAN) FROM foo;
 -- msg: INSERT 1
 -- error 42846: cannot coerce BIGINT to BOOLEAN
 
-VALUES CAST(123 AS BIGINT) + 53.7;
+VALUES CAST(123 AS BIGINT) + 53;
 -- COL1: 176
 
-VALUES 53.7 + CAST(123 AS BIGINT);
+VALUES 53 + CAST(123 AS BIGINT);
 -- COL1: 176
 
-VALUES CAST(5000000000000000000 AS BIGINT) + 5000000000000000000.7;
+VALUES CAST(5000000000000000000 AS BIGINT) + 5000000000000000000;
 -- error 22003: numeric value out of range
 
-VALUES 5000000000000000000.7 + CAST(5000000000000000000 AS BIGINT);
+VALUES 5000000000000000000 + CAST(5000000000000000000 AS BIGINT);
 -- error 22003: numeric value out of range
 
-VALUES CAST(123 AS BIGINT) - 53.7;
+VALUES CAST(123 AS BIGINT) - 53;
 -- COL1: 70
 
-VALUES 53.7 - CAST(123 AS BIGINT);
+VALUES 53 - CAST(123 AS BIGINT);
 -- COL1: -70
 
-VALUES CAST(-5000000000000000000 AS BIGINT) - 5000000000000000000.7;
+VALUES CAST(-5000000000000000000 AS BIGINT) - 5000000000000000000;
 -- error 22003: numeric value out of range
 
-VALUES -5000000000000000000.7 - CAST(5000000000000000000 AS BIGINT);
+VALUES -5000000000000000000 - CAST(5000000000000000000 AS BIGINT);
 -- error 22003: numeric value out of range
 
-VALUES CAST(123 AS BIGINT) * 53.7;
+VALUES CAST(123 AS BIGINT) * 53;
 -- COL1: 6519
 
-VALUES -53.7 * CAST(123 AS BIGINT);
+VALUES -53 * CAST(123 AS BIGINT);
 -- COL1: -6519
 
-VALUES CAST(-5000000000000000000 AS BIGINT) * 200000.7;
+VALUES CAST(-5000000000000000000 AS BIGINT) * 200000;
 -- error 22003: numeric value out of range
 
-VALUES -5000000000000000000.7 * CAST(5000000000000000000 AS BIGINT);
+VALUES -5000000000000000000 * CAST(5000000000000000000 AS BIGINT);
 -- error 22003: numeric value out of range
 
-VALUES CAST(123 AS BIGINT) / 53.7;
+VALUES CAST(123 AS BIGINT) / 53;
 -- COL1: 2
 
-VALUES -123.7 / CAST(53 AS BIGINT);
+VALUES -123 / CAST(53 AS BIGINT);
 -- COL1: -2
 
-VALUES CAST(-5000000000000000000 AS BIGINT) / 0.02;
--- error 22012: division by zero
-
-VALUES -5000000000000000000.7 / CAST(3.2 AS BIGINT);
+VALUES -5000000000000000000 / CAST(3.2 AS BIGINT);
 -- COL1: -1666666666666666666
 
 VALUES CAST(-5000000000000000000 AS BIGINT) / 0;

tests/double-precision.sql

@@ -81,10 +81,10 @@ VALUES -53.7 * CAST(12.3 AS DOUBLE PRECISION);
 -- COL1: -660.51
 
 VALUES CAST(-300000.1 AS DOUBLE PRECISION) * 200000.7;
--- COL1: -6.000023e+1
+-- COL1: -6.000023e+10
 
 VALUES -300000.7 * CAST(200000.1 AS DOUBLE PRECISION);
--- COL1: -6.000017e+1
+-- COL1: -6.000017e+10
 
 VALUES CAST(1.23 AS DOUBLE PRECISION) / 53.7;
 -- COL1: 0.022905
@@ -93,7 +93,7 @@ VALUES -123.7 / CAST(53.1 AS DOUBLE PRECISION);
 -- COL1: -2.329567
 
 VALUES CAST(-300000000.5 AS DOUBLE PRECISION) / 0.02;
--- COL1: -1.500000e+1
+-- COL1: -1.500000e+10
 
 VALUES -90000.7 / CAST(3.2 AS DOUBLE PRECISION);
 -- COL1: -28125.21875

tests/integer.sql

@@ -54,52 +54,49 @@ SELECT CAST(x AS DOUBLE PRECISION) FROM foo;
 -- msg: INSERT 1
 -- COL1: 123
 
-VALUES CAST(123 AS INTEGER) + 53.7;
+VALUES CAST(123 AS INTEGER) + 53;
 -- COL1: 176
 
-VALUES 53.7 + CAST(123 AS INTEGER);
+VALUES 53 + CAST(123 AS INTEGER);
 -- COL1: 176
 
-VALUES CAST(500000000 AS INTEGER) + 2000000000.7;
+VALUES CAST(500000000 AS INTEGER) + 2000000000;
 -- error 22003: numeric value out of range
 
-VALUES 500000000.7 + CAST(2000000000 AS INTEGER);
+VALUES 500000000 + CAST(2000000000 AS INTEGER);
 -- error 22003: numeric value out of range
 
-VALUES CAST(123 AS INTEGER) - 53.7;
--- COL1: 69
+VALUES CAST(123 AS INTEGER) - 53;
+-- COL1: 70
 
-VALUES 53.7 - CAST(123 AS INTEGER);
--- COL1: -69
+VALUES 53 - CAST(123 AS INTEGER);
+-- COL1: -70
 
-VALUES CAST(-2000000000 AS INTEGER) - 500000000.7;
+VALUES CAST(-2000000000 AS INTEGER) - 500000000;
 -- error 22003: numeric value out of range
 
-VALUES -500000000.7 - CAST(2000000000 AS INTEGER);
+VALUES -500000000 - CAST(2000000000 AS INTEGER);
 -- error 22003: numeric value out of range
 
-VALUES CAST(123 AS INTEGER) * 53.7;
--- COL1: 6605
+VALUES CAST(123 AS INTEGER) * 53;
+-- COL1: 6519
 
-VALUES -53.7 * CAST(123 AS INTEGER);
--- COL1: -6605
+VALUES -53 * CAST(123 AS INTEGER);
+-- COL1: -6519
 
-VALUES CAST(-300000 AS INTEGER) * 200000.7;
+VALUES CAST(-300000 AS INTEGER) * 200000;
 -- error 22003: numeric value out of range
 
-VALUES -300000.7 * CAST(200000 AS INTEGER);
+VALUES -300000 * CAST(200000 AS INTEGER);
 -- error 22003: numeric value out of range
 
-VALUES CAST(123 AS INTEGER) / 53.7;
+VALUES CAST(123 AS INTEGER) / 53;
 -- COL1: 2
 
-VALUES -123.7 / CAST(53 AS INTEGER);
+VALUES -123 / CAST(53 AS INTEGER);
 -- COL1: -2
 
-VALUES CAST(-300000000 AS INTEGER) / 0.02;
--- error 22003: numeric value out of range
-
-VALUES -90000.7 / CAST(3.2 AS INTEGER);
+VALUES -90000 / CAST(3.2 AS INTEGER);
 -- COL1: -30000
 
 VALUES CAST(-30000 AS INTEGER) / 0;

tests/real.sql

@@ -47,61 +47,61 @@ SELECT CAST(x AS DOUBLE PRECISION) FROM foo;
 -- msg: INSERT 1
 -- COL1: 123
 
-VALUES CAST(500000000.3 AS REAL) * 2000000000.7;
+VALUES CAST(500000000.3 AS REAL) * CAST(2000000000.7 AS REAL);
 -- COL1: 1e+18
 
-VALUES CAST(1.23 AS REAL) + 53.7;
+VALUES CAST(1.23 AS REAL) + CAST(53.7 AS REAL);
 -- COL1: 54.93
 
-VALUES 53.7 + CAST(1.23 AS REAL);
+VALUES CAST(53.7 AS REAL) + CAST(1.23 AS REAL);
 -- COL1: 54.93
 
-VALUES CAST(500000000 AS REAL) + 2000000000.7;
+VALUES CAST(500000000 AS REAL) + CAST(2000000000.7 AS REAL);
 -- COL1: 2.500000e+09
 
-VALUES 500000000.7 + CAST(2000000000 AS REAL);
+VALUES CAST(500000000.7 AS REAL) + CAST(2000000000 AS REAL);
 -- COL1: 2.500000e+09
 
-VALUES CAST(1.23 AS REAL) - 53.7;
+VALUES CAST(1.23 AS REAL) - CAST(53.7 AS REAL);
 -- COL1: -52.470001
 
-VALUES 53.7 - CAST(1.23 AS REAL);
+VALUES CAST(53.7 AS REAL) - CAST(1.23 AS REAL);
 -- COL1: 52.470001
 
-VALUES CAST(-2000000000.1 AS REAL) - 500000000.7;
+VALUES CAST(-2000000000.1 AS REAL) - CAST(500000000.7 AS REAL);
 -- COL1: -2.500000e+09
 
-VALUES -500000000.7 - CAST(2000000000.1 AS REAL);
+VALUES CAST(-500000000.7 AS REAL) - CAST(2000000000.1 AS REAL);
 -- COL1: -2.500000e+09
 
-VALUES CAST(12.3 AS REAL) * 53.7;
+VALUES CAST(12.3 AS REAL) * CAST(53.7 AS REAL);
 -- COL1: 660.51001
 
-VALUES -53.7 * CAST(12.3 AS REAL);
+VALUES CAST(-53.7 AS REAL) * CAST(12.3 AS REAL);
 -- COL1: -660.51001
 
-VALUES CAST(-300000.1 AS REAL) * 200000.7;
--- COL1: -0.6000023e+11
+VALUES CAST(-300000.1 AS REAL) * CAST(200000.7 AS REAL);
+-- COL1: -6.000023e+10
 
-VALUES -300000.7 * CAST(200000.1 AS REAL);
+VALUES CAST(-300000.7 AS REAL) * CAST(200000.1 AS REAL);
 -- COL1: -0.6000017e+11
 
-VALUES CAST(1.23 AS REAL) / 53.7;
+VALUES CAST(1.23 AS REAL) / CAST(53.7 AS REAL);
 -- COL1: 0.022905
 
-VALUES -123.7 / CAST(53.1 AS REAL);
+VALUES CAST(-123.7 AS REAL) / CAST(53.1 AS REAL);
 -- COL1: -2.329567
 
-VALUES CAST(-300000000.5 AS REAL) / 0.02;
--- COL1: -1.500000e+1
+VALUES CAST(-300000000.5 AS REAL) / CAST(0.02 AS REAL);
+-- COL1: -1.500000e+10
 
-VALUES -90000.7 / CAST(3.2 AS REAL);
+VALUES CAST(-90000.7 AS REAL) / CAST(3.2 AS REAL);
 -- COL1: -28125.21875
 
-VALUES CAST(-30000.5 AS REAL) / 0;
+VALUES CAST(-30000.5 AS REAL) / CAST(0 AS REAL);
 -- error 22012: division by zero
 
-VALUES -90000.5 / CAST(0.1 AS REAL);
+VALUES CAST(-90000.5 AS REAL) / CAST(0.1 AS REAL);
 -- COL1: -900005
 
 CREATE TABLE foo (x REAL);

tests/smallint.sql

@@ -47,56 +47,50 @@ SELECT CAST(x AS DOUBLE PRECISION) FROM foo;
 -- msg: INSERT 1
 -- COL1: 123
 
-VALUES CAST(123 AS SMALLINT) + 53.7;
+VALUES CAST(123 AS SMALLINT) + CAST(53 AS SMALLINT);
 -- COL1: 176
 
-VALUES 53.7 + CAST(123 AS SMALLINT);
+VALUES CAST(53 AS SMALLINT) + CAST(123 AS SMALLINT);
 -- COL1: 176
 
-VALUES CAST(30000 AS SMALLINT) + 20000.7;
+VALUES CAST(30000 AS SMALLINT) + CAST(20000 AS SMALLINT);
 -- error 22003: numeric value out of range
 
-VALUES 30000.7 + CAST(20000 AS SMALLINT);
+VALUES CAST(30000 AS SMALLINT) + CAST(20000 AS SMALLINT);
 -- error 22003: numeric value out of range
 
-VALUES CAST(123 AS SMALLINT) - 53.7;
--- COL1: 69
+VALUES CAST(123 AS SMALLINT) - CAST(53 AS SMALLINT);
+-- COL1: 70
 
-VALUES 53.7 - CAST(123 AS SMALLINT);
--- COL1: -69
+VALUES CAST(53 AS SMALLINT) - CAST(123 AS SMALLINT);
+-- COL1: -70
 
-VALUES CAST(-30000 AS SMALLINT) - 20000.7;
+VALUES CAST(-30000 AS SMALLINT) - CAST(20000 AS SMALLINT);
 -- error 22003: numeric value out of range
 
-VALUES -30000.7 - CAST(20000 AS SMALLINT);
+VALUES CAST(-30000 AS SMALLINT) - CAST(20000 AS SMALLINT);
 -- error 22003: numeric value out of range
 
-VALUES CAST(123 AS SMALLINT) * 53.7;
--- COL1: 6605
+VALUES CAST(123 AS SMALLINT) * CAST(53 AS SMALLINT);
+-- COL1: 6519
 
-VALUES -53.7 * CAST(123 AS SMALLINT);
--- COL1: -6605
+VALUES CAST(-53 AS SMALLINT) * CAST(123 AS SMALLINT);
+-- COL1: -6519
 
-VALUES CAST(-30000 AS SMALLINT) * 20000.7;
+VALUES CAST(-30000 AS SMALLINT) * CAST(20000 AS SMALLINT);
 -- error 22003: numeric value out of range
 
-VALUES -30000.7 * CAST(20000 AS SMALLINT);
+VALUES CAST(-30000 AS SMALLINT) * CAST(20000 AS SMALLINT);
 -- error 22003: numeric value out of range
 
-VALUES CAST(123 AS SMALLINT) / 53.7;
+VALUES CAST(123 AS SMALLINT) / CAST(53 AS SMALLINT);
 -- COL1: 2
 
-VALUES -123.7 / CAST(53 AS SMALLINT);
+VALUES CAST(-123 AS SMALLINT) / CAST(53 AS SMALLINT);
 -- COL1: -2
 
-VALUES CAST(-30000 AS SMALLINT) / 0.02;
--- error 22003: numeric value out of range
-
-VALUES -90000.7 / CAST(3.2 AS SMALLINT);
--- COL1: -30000
-
-VALUES CAST(-30000 AS SMALLINT) / 0;
+VALUES CAST(-30000 AS SMALLINT) / CAST(0 AS SMALLINT);
 -- error 22012: division by zero
 
-VALUES -90000 / CAST(0.1 AS SMALLINT);
+VALUES CAST(-30000 AS SMALLINT) / CAST(0.1 AS SMALLINT);
 -- error 22012: division by zero