How Stateflow Defines Fixed-Point Data :: Using Fixed-Point Data in Stateflow (Stateflow User's Guide)

Stateflow User's Guide

How Stateflow Defines Fixed-Point Data

The preceding example in What Is Fixed-Point Data? does not answer the question of how the values for the slope, , the quantized integer, , and the bias, , are implemented in Stateflow as integers. These values are implemented through the following:

Stateflow defines a fixed-point data's type from values that you specify.

You specify values for , , and the base integer type for . The available base types for are the unsigned integer types uint8, uint16, and uint32, and the signed integer types int8, int16, and int32. For specific instructions on how to enter fixed-point data, see Specifying Fixed-Point Data in Stateflow.

Notice that if a fixed-point number has a slope and a bias , it is equivalent to its quantized integer , and behaves exactly as its base integer type.

Stateflow implements an integer variable for the value of each fixed-point data in generated code.

This is the only part of a fixed-point number that varies in value. The quantities and are constant and appear only as literal numbers or expressions in generated code.

The slope, , is factored into an integer power of two, , and a coefficient, , such that and .

The powers of 2 are implemented as bit shifts, which are more efficient than multiply instructions. Setting avoids the computationally expensive multiply instructions for values of . This is referred to as binary-point-only scaling, which is implemented with bit shifts only, and is highly recommended.

Operations for fixed-point types are implemented with solutions for the quantized integer as described in Fixed-Point Operations.

To generate efficient code, the fixed-point promotion rules choose values for and that conveniently cancel out difficult terms in the solutions. See Addition (+) and Subtraction (-) and Multiplication (*) and Division (/).

Stateflow provides a special assignment operator (:=) and context-sensitive constants to help you maintain as much precision as possible in your fixed-point operations. See Assignment (=, :=) Operations and Fixed-Point Context-Sensitive Constants.

Any remaining numbers, such as the fractional slope, , that cannot be expressed as a pure integer or a power of 2, are converted into fixed-point numbers.

These remaining numbers can be computationally expensive in multiplication and division operations. That is why the practice of using binary-point-only scaling in which and is recommended.

During simulation, Stateflow detects when the result of a fixed-point operation overflows the capacity of its fixed-point type. See Overflow Detection for Fixed-Point Types.

Using Fixed-Point Data in Stateflow Specifying Fixed-Point Data in Stateflow