Numeric Types
Numeric Type Overview
Numeric types include the following types, which provide storage of varying sizes:
Numeric Type Promotion in Expressions
In expressions that use only integer types, Derby promotes the type of the result to at least INTEGER. In expressions that mix integer with noninteger types, Derby promotes the result of the expression to the highest type in the expression. Table 4 shows the promotion of data types in expressions.
Table 4. Type Promotion in Expressions
Largest Type That Appears in Expression  Resulting Type of Expression 

DOUBLE PRECISION  DOUBLE PRECISION 
REAL  DOUBLE PRECISION 
DECIMAL  DECIMAL 
BIGINT  BIGINT 
INTEGER  INTEGER 
SMALLINT  INTEGER 
For example:
 returns a double precision VALUES 1 + 1.0e0  returns a decimal VALUES 1 + 1.0  returns an integer VALUES CAST (1 AS INT) + CAST (1 AS INT)
Storing Values of One Numeric Data Type in Columns of Another Numeric Data Type
An attempt to put a floatingpoint type of a larger storage size into a location of a smaller size fails only if the value cannot be stored in the smallersize location. For example:
create table mytable (r REAL, d DOUBLE PRECISION); 0 rows inserted/updated/deleted INSERT INTO mytable (r, d) values (3.4028236E38, 3.4028235E38); ERROR X0X41: The number '3.4028236E38' is outside the range for the data type REAL.
You can store a floating point type in an INTEGER column; the fractional part of the number is truncated. For example:
INSERT INTO mytable(integer_column) values (1.09e0); 1 row inserted/updated/deleted SELECT integer_column FROM mytable; I  1
Integer types can always be placed successfully in approximate numeric values, although with the possible loss of some precision.
Integers can be stored in decimals if the DECIMAL precision is large enough for the value. For example:
ij> insert into mytable (decimal_column) VALUES (55555555556666666666); ERROR X0Y21: The number '55555555556666666666' is outside the range of the target DECIMAL/NUMERIC(5,2) datatype.
An attempt to put an integer value of a larger storage size into a location of a smaller size fails if the value cannot be stored in the smallersize location. For example:
INSERT INTO mytable (int_column) values 2147483648; ERROR 22003: The resulting value is outside the range for the data type INTEGER.
 Note:
 When truncating trailing digits from a NUMERIC value, Derby rounds down.
Scale for Decimal Arithmetic
SQL statements can involve arithmetic expressions that use decimal data types of different precisions (the total number of digits, both to the left and to the right of the decimal point) and scales (the number of digits of the fractional component). The precision and scale of the resulting decimal type depend on the precision and scale of the operands.
Given an arithmetic expression that involves two decimal operands:
 lp stands for the precision of the left operand
 rp stands for the precision of the right operand
 ls stands for the scale of the left operand
 rs stands for the scale of the right operand
Use the following formulas to determine the scale of the resulting data type for the following kinds of arithmetical expressions:

multiplication
ls + rs

division
31  lp + ls  rs

AVG()
max(max(ls, rs), 4)

all others
max(ls, rs)
For example, the scale of the resulting data type of the following expression is 27:
11.0/1111.33 // 31  3 + 1  2 = 27
Use the following formulas to determine the precision of the resulting data type for the following kinds of arithmetical expressions:

multiplication
lp + rp

addition
2 * (p  s) + s

division
lp  ls + rp + max(ls + rp  rs + 1, 4)

all others
max(lp  ls, rp  rs) + 1 + max(ls, rs)
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