Subversion Repositories fpu_double

The following describes the IEEE-Standard-754 compliant, double-precision floating point unit,

written in VHDL.  The module consists of the following files:

1.      fpu_double.vhd (top level)

2.      fpu_add.vhd

3.      fpu_sub.vhd

4.      fpu_mul.vhd

5.      fpu_div.vhd

6.      fpu_round.vhd

7.      fpu_exceptions.vhd

8.  fpupack.vhd

9.  comppack.vhd

And a testbench file is included, containing 50 test-case operations:

1.      fpu_double_TB.vhd

This unit has been extensively simulated, covering all 4 operations, rounding modes, exceptions

like underflow and overflow, and even the obscure corner cases, like when overflowing from

denormalized to normalized, and vice-versa.

The floating point unit supports denormalized numbers,

4 operations (add, subtract, multiply, divide), and 4 rounding

modes (nearest, zero, + inf, - inf).  The unit was synthesized with an

estimated frequency of 185 MHz, for a Virtex5 target device.  The synthesis results

are below.  fpu_double.vhd is the top-level module, and it contains the input

and output signals from the unit.

The input and output signals to the unit are the following:

1. clk  (global)

2. rst  (global)

2. enable   (set high, then low, to start operation)

3. rmode (rounding mode, 2 bits, 00 = nearest, 01 = zero,

                        10 = pos inf, 11 = neg inf)

4. fpu_op (operation code, 3 bits, 000 = add, 001 = subtract,

                        010 = multiply, 011 = divide, others are not used)

5. opa, opb (input operands, 64 bits, Big-endian order,

                        bit 63 = sign, bits 62-52 exponent, bits 51-0 mantissa)

6. out_fp   (output from operation, 64 bits, Big-endian order,

                        same ordering as inputs)

7. ready        (goes high when output is available)

8. underflow

9. overflow

10. inexact

11. exception - see IEEE 754 definition

12. invalid   - see IEEE 754 definition

The unit was designed to be synchronous with one global clock, and all of the

registers can be reset with an synchronous global reset.

When the inputs signals (a and b operands, fpu operation code, rounding mode code) are

available, set the enable input high, then set it low after 2 clock cycles.  When the

operation is complete and the output is available, the ready signal will go high.  To start

the next operation, set the enable input high.

Each operation takes the following amount of clock cycles to complete:

1.      addition :                      20 clock cycles

2.      subtraction:            21 clock cycles

3.      multiplication:         24 clock cycles

4.      division:                       71 clock cycles

This is longer than other floating point units, but supporting denormalized numbers

requires more signals and logic levels to accommodate gradual underflow.  The supported

clock speed of 185 MHz makes up for the large number of clock cycles required for each

operation to complete.  If you have a lower clock speed, the code can be changed to

reduce the number of registers and latency of each operation. I purposely increased the

number of logic levels to get the code to synthesize to a faster clock frequency, but of course,

this led to longer latency.  I guess it depends on your application what is more important.

The following output signals are also available: underflow, overflow, inexact, exception,

and invalid.  They are compliant with the IEEE-754 definition of each signal.  The unit

will handle QNaN and SNaN inputs per the standard.

I'm planning on adding more operations, like square root, sin, cos, tan, etc.,

so check back for updates.

Multiply:

The multiply module is written specifically for a Virtex5 target device.  The DSP48E slices

can perform a 25-bit by 18-bit Twos-complement multiply (24 by 17 unsigned multiply).  I broke up the multiply to

fit these DSP48E slices.  The breakdown is similar to the design in Figure 4-15 of the

Xilinx User Guide Document, "Virtex-5 FPGA XtremeDSP Design Considerations", also known as UG193.

You can find this document at xilinx.com by searching for "UG193".

Depending on your device, the multiply can be changed to match the bit-widths of the available

multipliers.  A total of 9 DSP48E slices are used to do the 53-bit by 53-bit multiply of 2

floating point numbers.

If you have any questions, please email me at: davidklun@gmail.com

Thanks,

David Lundgren

-----

Synthesis Results:

Performance Summary

*******************

Worst slack in design: -2.049

                   Requested     Estimated     Requested     Estimated                Clock        Clock

Starting Clock     Frequency     Frequency     Period        Period        Slack      Type         Group

----------------------------------------------------------------------------------------------------------------------

fpu_double|clk     300.0 MHz     185.8 MHz     3.333         5.382         -2.049     inferred     Inferred_clkgroup_0

======================================================================================================================

---------------------------------------

Resource Usage Report for fpu_double

Mapping to part: xc5vsx95tff1136-2

Cell usage:

DSP48E          9 uses

FD              3 uses

FDE             21 uses

FDR             587 uses

FDRE            3767 uses

FDRS            8 uses

FDRSE           51 uses

GND             6 uses

MUXCY           20 uses

MUXCY_L         598 uses

MUXF7           2 uses

VCC             6 uses

XORCY           497 uses

XORCY_L         5 uses

LUT1            187 uses

LUT2            742 uses

LUT3            1591 uses

LUT4            847 uses

LUT5            589 uses

LUT6            2613 uses

I/O ports: 206

I/O primitives: 205

IBUF           135 uses

OBUF           70 uses

BUFGP          1 use

I/O Register bits:                  0

Register bits not including I/Os:   4437 (7%)

Global Clock Buffers: 1 of 32 (3%)

Total load per clock:

   fpu_double|clk: 4446

Mapping Summary:

Total  LUTs: 6569 (11%)

Mapper successful!