1. A Floating Point Divider for Complex Numbers in the NIOS II Presented by John-Marc Desmarais Authors: Philipp Digeser, Marco Tubolino, Martin Klemm, Daniel Shapiro and Miodrag Bolic Email: {dshap092, mbolic}@site.uottawa.ca

2. Overview  Floating point division  Instruction Set Extensions (ISE)  NIOS II processor  Instruction hardware  Software interface  Experiment  Conclusion carg.site.uottawa.ca CARG 2010

3. Floating Point Division carg.site.uottawa.ca CARG 2010 Unlike real multiplication or real division, mathematical operations for complex numbers are usually provided by slow software. Consider complex division: Slow

4. Floating Point Division Fast complex dividers are necessary to drive an increasing number of applications such as signal processing systems for image and audio manipulation, GPS, and multi-antenna systems. Example: STSDAS offers math libraries for image analysis, including stsdas.analysis.fourier.carith, which is used to multiply or divide two complex images 1. carg.site.uottawa.ca CARG 2010 1 http://stsdas.stsci.edu/cgibin/gethelp.cgi?carith.hlp

5. Instruction Set Extensions carg.site.uottawa.ca ISE (Instruction Set Extensions) Instruction-Set Extensions, as the name implies, involves the addition of custom instructions to a processor’s instruction set. CARG 2010 Many market processors allow for the addition of these internal custom instructions: 1.Tensilica Xtensa (VLIW) 2.Altera NIOS II 3.Xilinx Microblaze 4.MIPS CorExtend In recent years there has been much research into the area of automatic identification of Instruction Set Extensions.

6. Instruction Set Extensions carg.site.uottawa.ca ISE (Instruction Set Extensions) These automated efforts vary in their approach. Some look at the functional C level of the program where hotspot functions are identified. Others look lower at the basic construct of the program as data and control flow graphs. CARG 2010 + />> x y z Modify ISA Add Custom Hardware Modify Compiler, ASM & LD Regenerate Custom Program

7. Instruction Set Extensions carg.site.uottawa.ca An ISE candidate has limited IO access to the register file. The instruction width also poses an IO barrier. Possible Remedies: 1.Multiport Register File 2.Register File Replication 3.Shadow Registers 4.Multicycle Reads (Altera’s NIOS II) 5.Dedicated Data Links (Microblaze) CARG 2010 Solution (Pozzi05): We use multicycle reads/writes from/to the register bank in order to squeeze several operands into the two input- one-output register file.

8. NIOS II Processor carg.site.uottawa.ca CARG 2010 Generic custom instruction datapathOur custom logic block

9. Instruction Hardware carg.site.uottawa.ca CARG 2010  We can see in these figures that a sequence of three calls to the custom instruction results in a complex operation with four inputs and two outputs. Cycles

10. Instruction Hardware carg.site.uottawa.ca CARG 2010 Operation when n=0 above, n=1 at right.

11. Software Interface carg.site.uottawa.ca CARG 2010 The designed hardware for complex division can be used easily in assembly (by inline) or C/C++ code as shown below:

12. Experiment carg.site.uottawa.ca CARG 2010 We used a NIOS II processor and a PLL as the starting point for the design.

13. Experiment carg.site.uottawa.ca CARG 2010

14. Conclusion CARG 2010 carg.site.uottawa.ca We designed a complex divider instruction set extension for the NIOS II This instruction was able to accelerate the execution of code that uses complex division In the future we would like to implement additional complex operations, and publish the core on OPENCORES.org Applications can be accelerated with instruction set extensions, and complex division is one case where there is a tangible benefit.