1. A floating point multiplier behavior model.
Project Step 10
A floating point multiplier behavior model.
1/8/ L25 Project Step 10 - Floating Point Adder
Copyright Joanne DeGroat, ECE, OSU

2. Model of a floating point multiplier
This exercise will once again be a high level behavioral model.
The code style will be algorithmic yet you will be working with the 32-bit data words.
As it is high level it is not intended for synthesis, rather as a reference model for the design.
It would be used to generate the reference output of the model that would be used for synthesis
1/8/ L25 Project Step 10 - Floating Point Adder
Copyright Joanne DeGroat, ECE, OSU

3. Copyright 2006 - Joanne DeGroat, ECE, OSU
Where to start?
THE INTERFACE!!!
Very simple
2 Data inputs A and B bits each in IEEE single precision
A latch signal to latch the inputs
A drive signal to latch the outputs
A results output C that is also IEEE single precision and 32-bits
1/8/ L25 Project Step 10 - Floating Point Adder
Copyright Joanne DeGroat, ECE, OSU

4. Copyright 2006 - Joanne DeGroat, ECE, OSU
Interface timing
Similar to other designs.
However, now 2 distinct cycle
The load cycle
The drive cycle
1/8/ L25 Project Step 10 - Floating Point Adder
Copyright Joanne DeGroat, ECE, OSU

5. Copyright 2006 - Joanne DeGroat, ECE, OSU
Recommended step 1
Get the interface working
Once you can pass the input straight to the output start the algorithm
This is a major step as you will be using a package that reads the test vectors from a file.
1/8/ L25 Project Step 10 - Floating Point Adder
Copyright Joanne DeGroat, ECE, OSU

6. Copyright 2006 - Joanne DeGroat, ECE, OSU
Reading from the file
The procedure is already compiled and in a package in LIBRARY ASSIGN that is located in directory ~degroat/ee762_assign
The procedure is hardcoded to read the vectors from the file fpm_vectors in this directory. You can see the vector file and copy it, but it will use the vectors in my file.
You will need to map to this library. You will not be able to see the code of concurrent procedure gen_vec which generates the test vectors and checks the result.
1/8/ L25 Project Step 10 - Floating Point Adder
Copyright Joanne DeGroat, ECE, OSU

7. Copyright 2006 - Joanne DeGroat, ECE, OSU
Mapping to the library
The library name will be ASSIGN
The testbench has a clause USE ASSIGN.fpm_test_vect.all
This procedure uses STD.TEXTIO.ALL for the file operations (info only)
In Modeltech you need to map to this library
/rcc4/homes/degroat/ee762_assign/assign
Testbench also has a signal yourname
1/8/ L25 Project Step 10 - Floating Point Adder
Copyright Joanne DeGroat, ECE, OSU

8. The rest of the algorithm
As this is behavioral it is easy to use if/else to handle all the special cases
NaN by all the other class results in NaN
IF (Ain=NaN or Bin=Nan) THEN out=NaN
ELSE
Only time you have to actually manipulate bits is for the Normalized x Normalized or Denormalized.
1/8/ L25 Project Step 10 - Floating Point Adder
Copyright Joanne DeGroat, ECE, OSU

9. Copyright 2006 - Joanne DeGroat, ECE, OSU
Manipulate bits
Need to do a multiplication of the mantissas
x.xxxxx…
x.xxxxx… where each is 24 bits
xx.xxxxx… giving 48 bit result which will need to be renormalized
Range of input is [0…2) i.e. from and including 0 to 2 but not including 2
Range of output is [0…4) which means you need to be aware of all the bits of the output
1/8/ L25 Project Step 10 - Floating Point Adder
Copyright Joanne DeGroat, ECE, OSU

10. Note on doing multiplication
This is a behavioral model
Several possible approaches to actually do the multiplication
One method – shift and add
Initialize a result vector (48-bits) to 0
Place the multiplicand into the least significant 24 bits of another 48-bit vector called prod_term.
Start with the lsb of the multiplier and repeat for each successive bit to the msb
If the bit of the multiplier is a 1 add the prod_term to the result.
Shift the prod_term 1 to the left with a 0 input as the lsb, i.e., x 2
Repeat
Output the result vector
1/8/ L25 Project Step 10 - Floating Point Adder
Copyright Joanne DeGroat, ECE, OSU

11. Renormalization of result
If result is in form 1x.xxxx
Shift right on fixed binary point and +1 to exponent giving 01.xxxxx
If result is in form 01.xxxx your are OK as is
If result is in form 00.00…1xxxx must shift left on fixed binary point until your leading 1 is to the left of the binary point, taking -1 from the exponent each time
Then look at exponent
1/8/ L25 Project Step 10 - Floating Point Adder
Copyright Joanne DeGroat, ECE, OSU

12. Copyright 2006 - Joanne DeGroat, ECE, OSU
Handling the exponent
Probably easiest to do a binary to integer conversion at the start for the exponent.
Then Exp_res = Exp_a + Exp_b – 127
After renormalization exponent must be between 0 and Adjust a necessary.
If >255 you have overflow to infinity.
If negative or 0 then you probably have a denormalized number or underflow
When in the 1 to 254 range do an integer to binary conversion
1/8/ L25 Project Step 10 - Floating Point Adder
Copyright Joanne DeGroat, ECE, OSU