In Object Constraint Language (OCL), the Double data type represents a floating-point number according to the IEEE 754 standard. Here's an explanation of the Double data type using OCL:

1. **Definition**: The Double data type in OCL represents double-precision floating-point numbers, which are decimal numbers with a higher precision compared to single-precision floating-point numbers (Float). Double precision means that these numbers have a higher range and more significant digits than single precision.

2. **Syntax**: In OCL, a Double variable can be declared like this:

  ```
  variableName: Real
  ```
  This declares a variable named `variableName` of type Real, which encompasses both Float and Double values.

3. **Range**: Double precision floating-point numbers typically have a range of approximately ±2.23 × 10^-308 to ±1.80 × 10^308 and provide about 15-16 decimal digits of precision.

4. **Operations**: OCL provides various mathematical operations that can be performed on Double values. These operations include addition, subtraction, multiplication, division, exponentiation, and more.

5. **Examples**:

  - Addition:
    ```
    let x: Real = 3.5;
    let y: Real = 2.25;
    let sum: Real = x + y;  -- sum will be 5.75
    ```

  - Multiplication:
    ```
    let a: Real = 2.5;
    let b: Real = 1.2;
    let product: Real = a * b;  -- product will be 3.0
    ```

  - Division:
    ```
    let numerator: Real = 5.0;
    let denominator: Real = 2.0;
    let quotient: Real = numerator / denominator;  -- quotient will be 2.5
    ```

  - Exponentiation:
    ```
    let base: Real = 2.0;
    let exponent: Integer = 3;
    let result: Real = base ^ exponent;  -- result will be 8.0
    ```

6. **Constraints**: Constraints involving Double values can be specified to enforce certain conditions. For instance, constraints may specify ranges within which Double values must fall or relationships between Double values and other attributes or variables.

7. **Precision and Approximation**: It's important to note that due to the nature of floating-point arithmetic, some calculations with Double values may result in approximation errors, especially when dealing with very large or very small numbers.

In summary, the Double data type in OCL represents double-precision floating-point numbers and supports various mathematical operations, enabling the specification of constraints and expressions involving real numbers with higher precision and a wider range.

See also: Number conversions