Number (Real, Integer)

Number is a generic term that stands for:

• Real field, variable or expression. The range for the Real data type is ±1.7e±308 (13 significant digits).
• Integer variable or expression. The range for the Integer data type is -2^31..(2^31)-1 (4-byte Integer, aka Long or Longint).

Compatibility

Usually when working with Integers, you handle Long values (4-byte Integer). However, there are two cases where Integers are stored as Shorts values (2-byte Integer), i.e. in the range -32,768..32,767 (2^15..(2^15)-1):

• Database fields with Integer type,
• Elements of arrays declared with ARRAY INTEGER.

These legacy data types are automatically converted in Longs when used in the 4D Language.

You can assign any Number data type to another; 4D does the conversion, truncating or rounding if necessary. However, when values are out of range, the conversion will not return a valid value. You can mix number data types in expressions.

Number literals

A numeric literal constant is written as a real number. Here are some examples of numeric constants:

27
123.76
0.0076

The default decimal separator is a period (.), regardless of the system language. If you have checked the "Use regional system settings" option in the Methods Page of the Preferences, you must use the separator defined in your system.

Negative numbers are specified with the minus sign (-). For example:

-27
-123.76
-0.0076

Number operators

Operation	Syntax	Returns	Expression	Value
Addition	Number + Number	Number	2 + 3	5
Subtraction	Number - Number	Number	3 – 2	1
Multiplication	Number * Number	Number	5 * 2	10
Division	Number / Number	Number	5 / 2	2.5
Longint division	Number \ Number	Number	5 \ 2	2
Modulo	Number % Number	Number	5 % 2	1
Exponentiation	Number ^ Number	Number	2 ^ 3	8
Equality	Number = Number	Boolean	10 = 10	True
			10 = 11	False
Inequality	Number # Number	Boolean	10 #11	True
			10 # 10	False
Greater than	Number > Number	Boolean	11 > 10	True
			10 > 11	False
Less than	Number < Number	Boolean	10 < 11	True
			11 < 10	False
Greater than or equal to	Number >= Number	Boolean	11 >= 10	True
			10 >= 11	False
Less than or equal to	Number <= Number	Boolean	10 <= 11	True
			11 <= 10	False

Modulo

The modulo operator % divides the first number by the second number and returns a whole number remainder. Here are some examples:

• 10 % 2 returns 0 because 10 is evenly divided by 2.
• 10 % 3 returns 1 because the remainder is 1.
• 10.5 % 2 returns 0 because the remainder is not a whole number.

warning

The modulo operator % returns significant values with numbers that are in the Long Integer range (from minus 2^31 to 2^31 minus one). To calculate the modulo with numbers outside of this range, use the Mod command.

Longint division

The longint division operator \ returns significant values with integer numbers only.

Real comparison

To compare two reals for equality, the 4D language actually compares the absolute value of the difference with epsilon. See the SET REAL COMPARISON LEVEL command.

note

For consistency, the 4D database engine always compares database fields of the real type using a 10^-6 value for epsilon and does not take the SET REAL COMPARISON LEVEL setting into account.

Precedence

The order in which an expression is evaluated is called precedence. 4D has a strict left-to-right precedence, in which algebraic order is not observed. For example:

 3+4*5

returns 35, because the expression is evaluated as 3 + 4, yielding 7, which is then multiplied by 5, with the final result of 35.

To override the left-to-right precedence, you MUST use parentheses. For example:

 3+(4*5)

returns 23 because the expression (4 * 5) is evaluated first, because of the parentheses. The result is 20, which is then added to 3 for the final result of 23.

Parentheses can be nested inside other sets of parentheses. Be sure that each left parenthesis has a matching right parenthesis to ensure proper evaluation of expressions. Lack of, or incorrect use of parentheses can cause unexpected results or invalid expressions. Furthermore, if you intend to compile your applications, you must have matching parentheses—the compiler detects a missing parenthesis as a syntax error.

Bitwise operators

The bitwise operators operates on (Long) Integers expressions or values.

If you pass a (Short) Integer or a Real value to a bitwise operator, 4D evaluates the value as a Long value before calculating the expression that uses the bitwise operator.

While using the bitwise operators, you must think about a Long value as an array of 32 bits. The bits are numbered from 0 to 31, from right to left.

Because each bit can equal 0 or 1, you can also think about a Long Integer value as a value where you can store 32 Boolean values. A bit equal to 1 means True and a bit equal to 0 means False.

An expression that uses a bitwise operator returns a Long value, except for the Bit Test operator, where the expression returns a Boolean value. The following table lists the bitwise operators and their syntax:

Operation	Operator	Syntax	Returns
Bitwise AND	&	Long & Long	Long
Bitwise OR (inclusive)	|	Long | Long	Long
Bitwise OR (exclusive)	^ |	Long ^ | Long	Long
Left Bit Shift	<<	Long << Long	Long (see note 1)
Right Bit Shift	>>	Long >> Long	Long (see note 1)
Bit Set	?+	Long ?+ Long	Long (see note 2)
Bit Clear	?-	Long ?- Long	Long (see note 2)
Bit Test	??	Long ?? Long	Boolean (see note 2)

Notes

1. For the Left Bit Shift and Right Bit Shift operations, the second operand indicates the number of positions by which the bits of the first operand will be shifted in the resulting value. Therefore, this second operand should be between 0 and 31. Note however, that shifting by 0 returns an unchanged value and shifting by more than 31 bits returns 0x00000000 because all the bits are lost. If you pass another value as second operand, the result is non-significant.
2. For the Bit Set, Bit Clear and Bit Test operations , the second operand indicates the number of the bit on which to act. Therefore, this second operand must be between 0 and 31; otherwise, the result of the expression is non-significant.

The following table lists the bitwise operators and their effects:

Operation	Description
Bitwise AND	Each resulting bit is the logical AND of the bits in the two operands. Here is the logical AND table: 1 & 1 --> 1 0 & 1 --> 0 1 & 0 --> 0 0 & 0 --> 0 In other words, the resulting bit is 1 if the two operand bits are 1; otherwise the resulting bit is 0.
Bitwise OR (inclusive)	Each resulting bit is the logical OR of the bits in the two operands.Here is the logical OR table: 1 | 1 --> 1 0 | 1 --> 1 1 | 0 --> 1 0 | 0 --> 0 In other words, the resulting bit is 1 if at least one of the two operand bits is 1; otherwise the resulting bit is 0.
Bitwise OR (exclusive)	Each resulting bit is the logical XOR of the bits in the two operands.Here is the logical XOR table: 1 ^ | 1 --> 0 0 ^ | 1 --> 1 1 ^ | 0 --> 1 0 ^ | 0 --> 0 In other words, the resulting bit is 1 if only one of the two operand bits is 1; otherwise the resulting bit is 0.
Left Bit Shift	The resulting value is set to the first operand value, then the resulting bits are shifted to the left by the number of positions indicated by the second operand. The bits on the left are lost and the new bits on the right are set to 0. Note: Taking into account only positive values, shifting to the left by N bits is the same as multiplying by 2^N.
Right Bit Shift	The resulting value is set to the first operand value, then the resulting bits are shifted to the right by the number of position indicated by the second operand. The bits on the right are lost and the new bits on the left are set to 0.Note: Taking into account only positive values, shifting to the right by N bits is the same as dividing by 2^N.
Bit Set	The resulting value is set to the first operand value, then the resulting bit, whose number is indicated by the second operand, is set to 1. The other bits are left unchanged.
Bit Clear	The resulting value is set to the first operand value, then the resulting bit, whose number is indicated by the second operand, is set to 0. The other bits are left unchanged.
Bit Test	Returns True if, in the first operand, the bit whose number is indicated by the second operand is equal to 1. Returns False if, in the first operand, the bit whose number is indicated by the second operand is equal to 0.

Examples

Operation	Example	Result
Bitwise AND	0x0000FFFF & 0xFF00FF00	0x0000FF00
Bitwise OR (inclusive)	0x0000FFFF | 0xFF00FF00	0xFF00FFFF
Bitwise OR (exclusive)	0x0000FFFF ^ | 0xFF00FF00	0xFF0000FF
Left Bit Shift	0x0000FFFF << 8	0x00FFFF00
Right Bit Shift	0x0000FFFF >> 8	0x000000FF
Bit Set	0x00000000 ?+ 16	0x00010000
Bit Clear	0x00010000 ?- 16	0x00000000
Bit Test	0x00010000 ?? 16	True