IQmath
C2000 Microcontroller Workshop - Numerical Concepts 8 - 19
IQmath Approach
32-bit IQmath Approach
y = mx + b
I8 Q24
I16 Q48
M
X
B
Y
>> 24
Align Binary
Point Of Multiply
I8 Q24
I8 Q24
sssssssssssssssssI16 Q24
I8 Q24
I8 Q24
Y = ((int64) M * (int64) X) >> Q + B;in C:
In the "IQmath" approach, rather then scaling the operands, which get added to or subtracted
from the multiplication result, we do the reverse. The multiplication result binary point is scaled
back such that it aligns to the operands, which are added to or subtracted from it. The C code
implementation of this is given by linear equation below:
int32 Y, M, X, B;
Y = ((int64) M * (int64) X) >> 24 + B;
The slide shows the implementation of the equation on a processor containing hardware that can
perform a 32x32 bit multiply, 32-bit addition/subtraction and 64-bit logical and arithmetic shifts
efficiently.
The key advantage of this approach is shown by what can then be done with the C and C++ com-
piler to simplify the coding of the linear equation example.
Let’s take an additional step and create a multiply function in C that performs the following oper-
ation:
int32 _IQ24mpy(int32 M, int32 X) { return ((int64) M * (int64) X) >> 24; }
The linear equation can then be written as follows:
Y = _IQ24mpy(M , X) + B;
Already we can see a marked improvement in the readability of the linear equation.
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