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| R2011b Documentation → Fixed-Point Toolbox | |
Learn more about Fixed-Point Toolbox |
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fimath properties define the rules for performing arithmetic operations on fi objects. The fimath properties that govern fixed-point arithmetic operations can come from a fimath object or the global fimath. fimath objects and the global fimath have the following differences:
Individual fi objects can have a local fimath object. fi objects have a local fimath object when you specify fimath properties in a fi constructor or use dot notation to set any fimath object property of a fi object.
The global fimath is the set of fimath properties that fi constructors associate with, and fimath constructors return, when you do not specify any fimath properties in the constructor. When you use the sfi or ufi constructor or when you fail to specify any fimath properties in the fi constructor, the resulting fi object associates itself with the global fimath. It does not have a local fimath object. See Working with the Global fimath for more information.
To determine whether a fi object has a local fimath object or associates with the global fimath, use the isfimathlocal function.
The following sections discuss how fi objects with local fimath objects interact with fi objects associated with the global fimath.
In binary fixed-point operations such as c = a + b, the following rules apply:
If both a and b associate with the global fimath, the operation uses the global fimath to perform the fixed-point arithmetic. The output fi object c also associates with the global fimath.
If either a or b has a local fimath object, the operation uses that fimath object to perform the fixed-point arithmetic. The output fi object c has the same local fimath object as the input.
In unary fixed-point operations such as b = abs(a), the following rules apply:
If a associates with the global fimath, the operation uses the global fimath to perform the fixed-point arithmetic. The output fi object b also associates with the global fimath.
If a has a local fimath object, the operation uses that fimath object to perform the fixed-point arithmetic. The output fi object b has the same local fimath object as the input a.
When you specify a fimath object in the function call of a unary fixed-point operation, the operation uses the fimath object you specify to perform the fixed-point arithmetic. For example, when you use a syntax such as b = abs(a,F) or b = sqrt(a,F), the abs and sqrt operations use the fimath object F to compute intermediate quantities. The output fi object b always associates with the global fimath.
In fixed-point concatenation operations such as c = [a b], c = [a;b] and c = bitconcat(a,b), the following rule applies:
The fimath properties of the left-most fi object in the operation determine the fimath properties of the output fi object c.
For example, consider the following scenarios for the operation d = [a b c]:
If a is a fi object associated with the global fimath, the output fi object d also associates with the global fimath.
If a has a local fimath object, the output fi object d has the same local fimath object.
If a is not a fi object, the output fi object d inherits the fimath properties of the next left-most fi object. For example, if b is a fi object with a local fimath object, the output fi object d has the same local fimath object as the input fi object b.
The output of the fimath object operations add, mpy, and sub always associates with the global fimath. The operations use the fimath object you specify in the function call, but the output fi object never has a local fimath object.
Fixed-point operations performed with the MATLAB Function block use the same rules as fixed-point operations performed in MATLAB.
All input signals to the MATLAB Function block that you treat as fi objects associate with whatever you specify for the MATLAB Function block fimath parameter. When you set this parameter to Same as MATLAB, your fi objects associate with the global fimath. When you set the MATLAB Function block fimath parameter to Specify other, you can define your own set of fimath properties for all fi objects in the MATLAB Function block to associate with. You can choose to treat only fixed-point input signals as fi objects or both fixed-point and integer input signals as fi objects. See Using fimath Objects in MATLAB Function Blocks.
The fimath object and the global fimath encapsulate the math properties of Fixed-Point Toolbox software.
fi objects only have a local fimath object when you explicitly specify fimath properties in the fi constructor. When you use the sfi or ufi constructor or do not specify any fimath properties in the fi constructor, the resulting fi object associates itself with the global fimath.
a = fi(pi)
a =
3.1416
DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 16
FractionLength: 13
a.fimath
isfimathlocal(a)
ans =
RoundMode: nearest
OverflowMode: saturate
ProductMode: FullPrecision
MaxProductWordLength: 128
SumMode: FullPrecision
MaxSumWordLength: 128
ans =
0To perform arithmetic with +, -, .*, or * on two fi operands with local fimath objects, the local fimath objects must be identical. If one of the fi operands is associated with the global fimath, the fimath properties of the two operands need not be identical. See fimath Rules for Fixed-Point Arithmetic for more information.
a = fi(pi);
b = fi(8);
isequal(a.fimath, b.fimath)
ans =
1
a + b
ans =
11.1416
DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 19
FractionLength: 13
To perform arithmetic with +, -, .*, or *, two fi operands must also have the same data type. For example, you can perform addition on two fi objects with data type double, but not on an object with data type double and one with data type single:
a = fi(3, 'DataType', 'double') a = 3 DataTypeMode: Double b = fi(27, 'DataType', 'double') b = 27 DataTypeMode: Double a + b ans = 30 DataTypeMode: Double c = fi(12, 'DataType', 'single') c = 12 DataTypeMode: Single a + c ??? Math operations are not allowed on FI objects with different data types.
Fixed-point fi object operands do not have to have the same scaling. You can perform binary math operations on a fi object with a fixed-point data type and a fi object with a scaled doubles data type. In this sense, the scaled double data type acts as a fixed-point data type:
a = fi(pi)
a =
3.1416
DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 16
FractionLength: 13
b = fi(magic(2), ...
'DataTypeMode', 'Scaled double: binary point scaling')
b =
1 3
4 2
DataTypeMode: Scaled double: binary point scaling
Signedness: Signed
WordLength: 16
FractionLength: 12
a + b
ans =
4.1416 6.1416
7.1416 5.1416
DataTypeMode: Scaled double: binary point scaling
Signedness: Signed
WordLength: 18
FractionLength: 13
Use the divide function to perform division with doubles, singles, or binary point-only scaling fi objects.
Fixed-Point Toolbox software supports fixed-point arithmetic using the fimath object or the global fimath for all binary point-only signals. The toolbox also supports arithmetic for [Slope Bias] signals with the following restrictions:
[Slope Bias] signals must be real.
You must set the SumMode and ProductMode properties of the governing fimath to 'SpecifyPrecision' for sum and multiply operations, respectively.
You must set the CastBeforeSum property of the governing fimath to 'true'.
Fixed-Point Toolbox does not support the divide function for [Slope Bias] signals.
f = fimath('SumMode', 'SpecifyPrecision', ... 'SumFractionLength', 16) f = RoundMode: nearest OverflowMode: saturate ProductMode: FullPrecision MaxProductWordLength: 128 SumMode: SpecifyPrecision SumWordLength: 32 SumFractionLength: 16 CastBeforeSum: true a = fi(pi, 'fimath', f) a = 3.1416 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 13 RoundMode: nearest OverflowMode: saturate ProductMode: FullPrecision MaxProductWordLength: 128 SumMode: SpecifyPrecision SumWordLength: 32 SumFractionLength: 16 CastBeforeSum: true b = fi(22, true, 16, 2^-8, 3, 'fimath', f) b = 22 DataTypeMode: Fixed-point: slope and bias scaling Signedness: Signed WordLength: 16 Slope: 0.00390625 Bias: 3 RoundMode: nearest OverflowMode: saturate ProductMode: FullPrecision MaxProductWordLength: 128 SumMode: SpecifyPrecision SumWordLength: 32 SumFractionLength: 16 CastBeforeSum: true a + b ans = 25.1416 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 32 FractionLength: 16 RoundMode: nearest OverflowMode: saturate ProductMode: FullPrecision MaxProductWordLength: 128 SumMode: SpecifyPrecision SumWordLength: 32 SumFractionLength: 16 CastBeforeSum: true
Setting the SumMode and ProductMode properties to SpecifyPrecision are mutually exclusive except when performing the * operation between matrices. In this case, you must set both the SumMode and ProductMode properties to SpecifyPrecision for [Slope Bias] signals. Doing so is necessary because the * operation performs both sum and multiply operations to calculate the result.
 | fimath Object Properties | Using fimath to Specify Rounding and Overflow Modes |  |
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