## DSP M-Registers

This article is in response to No of Escape who wanted some info about how the M-registers worked on  the  DSP, particularly when using ring-buffers (that is, a buffer  that  automatically  loops around when you reach the end).

Once you get the idea,  using  the  registers  is pretty easy, so I'll launch straight in. Then I'll  introduce  some code to demonstrate the idea.

### M-Registers: Basics

According to Motorola, "M-Register" stands for "modifier register". An m-register's job is to take  an  effective  address that is used, then "modify" it to produce automatically a different effective result that is actually used.

There are 8 registers, named m0  to  m7.  Each one is coupled with the respective r-register, so m0 refers to r0  and so on. This is the same as the offset 'n'-registers. Each m-register is a 16-bit value.

There are 6 modes  of  addressing  that  an  address register can use, which are affected by the m-register. Here they are:-

 Type syntax address fetched  if using move new value of r0  after pipelining Postincrement by 1 (r0)+ r0 r0 + 1 Postdecrement by 1 (r0)- r0 r0 - 1 Postincrement by offset (r0)+n0 r0 r0 + n0 Postdecrement by offset (r0)-n0 r0 r0 - n0 Indexed by offset (r0+n0) r0 + n0 r0 Predecrement by 1 -(r0) r0 - 1 r0 - 1
There are two sets of  effective  addresses calculated by the instruction. The third column indicates  the  effective  address  where data is fetched from; the fourth column indicates the value of r0 after the instruction is executed and the pipelining has taken effect.

The m-registers affect both these two  sets  of  values if the register is set to the correct value.

#### M-Registers: Linear Operation

Normally an m-register has the value of  -1,  or \$FFFF. This means that it leaves all effective  addresses  unchanged.  This  is  called  the "linear modifier" by Motorola.

#### M-Registers: Modulo Operation

This is the mode used for  ring  buffers.  Here the m-register has a value between 1 and 32767. This causes  all effective addresses to be calculated to exist between a lower and upper bound address.
Let us assume that we want a ring buffer of size M, where M =  21.
Value in m-register = (M - 1) = 21 - 1 = 20
###### Lower Boundary
The lower boundary must have a base  address  of L, where the lower k bits of L are all zero.
'k' is calculated by finding the lowest value where 2^k >= M.

Another way of thinking of this  is  to  consider  the lowest value in the sequence 2,4,8,16,32,64,128,256...32768 which is greater than M.

So for our example 32 is the first  value greater than 21. This means that the lower boundary of our  range  must  be  a  multiple of 32, for example 0,32,64,96,128 etc.

###### Upper Boundary
The upper boundary is now (L + M - 1), since the base address is L and the size must be M.

##### Setting the boundaries
Once we have set the  size  of  the  ring  buffer,  the value of the lower boundary is set by the address "r"-register.
Let's say that we want our ring buffer to start at address 96.

move #20,m0             ;ring buffer size 21
move #96,r0             ;start of buffer is now 96

However (and this is important) our  buffer  still  starts at 96 if we use the following:

move #20,m0             ;ring buffer size 21
move #100,r0            ;start of buffer is now 96

For example, the in-built sine  table  has  256  entries and exists at address Y:\$100:

move #\$ff,m0
move #\$100,r0

In addition, the equivalent cosine table  starts at \$140, runs to \$1ff and then "wraps round" back to \$100 to  end at \$13f. We can handle the wrapping part automatically using:-

move #\$ff,m1
move #\$140,r1

Let us assume that an effective  address  of "ea" is calculated. Using modulo-modification, the new address will be:

Lower Boundary + ((ea - Lower Boundary) MOD buffersize)

where "buffersize" is the value in the m-regiser plus 1.
This works even when  the  "ea"  is  a  value  *lower*  than the Lower Boundary. The value wraps round to the top of the buffer.

MEMORY MAP:

LBUB      EA
|--------------------|--------V------------...

<---x---->
LB       EA2          UB
|--------V-----------|---------------------...

IMPORTANT NOTE:
If an n-register is used to create  an effective address, if Nn>M then the results are unpredictable and unreliable!

The exception to this  is  where  Nn  is  a  multiple  of 2^k that was mentioned before. eg. our buffer size is 21, and n0 = 32.

When using the (r0)+n0 addressing mode, this increases the value of r0 by n0, or the opposite for (r0)-n0.
This is useful when making the address "jump" to another block of ring buffers somewhere else!

#### Reverse-Carry Modifier

This is in operation when Mn = 0.  This is a complex operation used in things such as FFT generation.

Reverse carry  means  that  the  "carry"  value  used  in  addition is propagated (ie. passed on) from the Most Significant Bit (MSB) down to the Least Significant Bit (LSB).

Imagine a normal binary addition, let's  say  %1111+%0001. We start by adding the two LSB's: 1 and 1. This gives  us  2, or %10. We write "0" in our answer column and keep 1 as the "carry". Now we add the next two LSBs, plus our carry, and so on. The carry "propagates" upwards.

In "reverse carry" the opposite happens. Assume  that we add r0 and n0 using reverse carry. We can make it  easy by reversing all the bits of both r0 and n0, adding, then  reversing  all  the bits again. Not very useful?

Now, here's the interesting bit. If  Nn  =  2^k where k is any number, then the reverse carry addition is  equivalent to reversing the last k bits of r0, incrementing (adding 1)  and  then re-reversing the last k bits of r0 again. Apparently this  is  *very* useful when doing things
like "twiddle factors" with FFTs.

Interestingly(?), if we consider  a  setting  where  Nn  = 1024, using reverse carry repeatedly with the following code:

move    #output_buffer,r1
move    #0,r0
move    #0,m0           ; select reverse-carry
move    #512,n0         ; our reverse carry "increment"
do      #100,rc_loop
move   r0,x:(r1)+
lua    (r0)+n0,r0
nop; wait for pipeline
rc_loop:

... produces the following sequence:

0, 512, 256, 768, 128, 640 ... or in binary:

000000000
100000000
010000000
110000000
001000000
101000000
011000000

This may look  strange,  but  when  an  FFT  is  produced  the data is "scrambled". In the produced table, value  0  is  at  0, value 1 is at 512, value 2 at 256, and so on..

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