Page 349 - Programming Microcontrollers in C

334 Chapter 6 Large Microcontrollers

The convolution is little more than a series of dot products, one dot
product for each output sample. Therefore, if you have a function that
will calculate a dot product, it can also calculate a convolution.
An item of consequence is the use of modular arithmetic in calcu­
lation of the data addresses. Often times, it is desirable to traverse an
array and return to its beginning automatically when the end is reached.
Modular arithmetic allows this type of operation. When working in
combination with an unusual step value, modular arithmetic will per­
mit the collection of coefficients from a rectangular array placed in
linear memory space. Here the step value refers to one of the numbers
associated with the mac or the rmac instruction. These two values are
called xo and yo. This value is used to increment the address of the
corresponding register whenever data is loaded into either the H or the
I register. The location of the array in memory should be placed at
special location in memory. This location is discussed below. The ef­
fective address for the next value to be placed in the X after the value
is incremented by the xo register is given by
IX = (IX)&~XMASK | ((IX)+xo)&XMASK

Note that XMASK here is an 8-bit mask that defines the length of
the circular array. The array length must be a power of two less than
or equal to 256. The value placed in XMASK is one less than the array
length. When the contents of IX, or (IX), is anded with the comple­
ment of the sign extended value of XMASK, the value that is left is the
starting address of the array. The second term above causes the con­
tents in IX to be incremented. As the value in IX is replaced by
((IX)+ xo)&XMASK after each multiply and accumulate opera­
tion. Since XMASK must contain a number that is one less than a
power of two raised to the n: its least significant n bits are 1. The
value placed in IX is the address with the n least significant bits
masked off. When these two values are ORed together, an address is
created that will range from the beginning to the end of the array and
then back to the beginning in steps of xo. The requirements to make
this scheme work are:
1. The array length must be a power of two less than or equal to
256.
2. The array must begin on a specific address. This address is any
value where the least n bits are zero. Here n is determined by