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Combinational Circuits: IFFT, Types, Parameterization... Arvind

Combinational Circuits: IFFT, Types, Parameterization... Arvind Computer Science & Artificial Intelligence Lab Massachusetts Institute of Technology. Now we call this Guarded Atomic Actions. Bluespec: Two-Level Compilation. Bluespec (Objects, Types, Higher-order functions).

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Combinational Circuits: IFFT, Types, Parameterization... Arvind

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  1. Combinational Circuits: IFFT, Types, Parameterization... Arvind Computer Science & Artificial Intelligence Lab Massachusetts Institute of Technology http://csg.csail.mit.edu/arvind

  2. Now we call this Guarded Atomic Actions Bluespec: Two-Level Compilation Bluespec (Objects, Types, Higher-order functions) Lennart Augustsson @Sandburst 2000-2002 • Type checking • Massive partial evaluation and static elaboration Level 1 compilation Rules and Actions (Term Rewriting System) • Rule conflict analysis • Rule scheduling Level 2 synthesis James Hoe & Arvind @MIT 1997-2000 Object code (Verilog/C) http://csg.csail.mit.edu/arvind

  3. elaborate w/params Software Toolflow: Hardware Toolflow: source source compile .exe design1 design2 design3 run w/ params run w/ params run1 run3 run1 run1.1 run1 run1 run2.1 run1 run1 run3.1 run1 run1 … … … … Static Elaboration At compile time • Inline function calls and datatypes • Instantiate modules with specific parameters • Resolve polymorphism/overloading http://csg.csail.mit.edu/arvind

  4. + + Bfly4 in0 out0 Bfly4 - - Bfly4 out1 in1 Bfly4 Permute_1 x16 out2 in2 Bfly4 Bfly4 Bfly4 Permute_2 Permute_3 in3 out3 + + … … out4 in4 Bfly4 Bfly4 … … * t0 in63 out63 - - * t1 * t2 *j * t3 Combinational IFFT All numbers are complex and represented as two sixteen bit quantities. Fixed-point arithmetic is used to reduce area, power, ... http://csg.csail.mit.edu/arvind

  5. t0 t1 t2 t3 + + k0 k1 k2 k3 - - + + * - - * * *i * 4-way Butterfly Node function Vector#(4,Complex) Bfly4 (Vector#(4,Complex) t, Vector#(4,Complex) k); • BSV has a very strong notion of types • Every expression has a type. Either it is declared by the user or automatically deduced by the compiler • The compiler verifies that the type declarations are compatible http://csg.csail.mit.edu/arvind

  6. + + - - + + m z y * - - * * *i * BSV code: 4-way Butterfly function Vector#(4,Complex) Bfly4 (Vector#(4,Complex) t, Vector#(4,Complex) k); Vector#(4,Complex) m = newVector(), y = newVector(), z = newVector(); m[0] = k[0] * t[0]; m[1] = k[1] * t[1]; m[2] = k[2] * t[2]; m[3] = k[3] * t[3]; y[0] = m[0] + m[2]; y[1] = m[0] – m[2]; y[2] = m[1] + m[3]; y[3] = i*(m[1] – m[3]); z[0] = y[0] + y[2]; z[1] = y[1] + y[3]; z[2] = y[0] – y[2]; z[3] = y[1] – y[3]; return(z); endfunction Polymorphic code: works on any type of numbers for which *, + and - have been defined Note: Vector does not mean storage http://csg.csail.mit.edu/arvind

  7. Bfly4 in0 out0 Bfly4 Bfly4 in1 out1 Bfly4 Permute_1 x16 in2 out2 Bfly4 Bfly4 Bfly4 Permute_3 Permute_2 in3 out3 … … in4 out4 Bfly4 Bfly4 … … in63 out63 Combinational IFFT stage_f function repeat it three times http://csg.csail.mit.edu/arvind

  8. BSV Code: Combinational IFFT function Vector#(64, Complex) ifft (Vector#(64, Complex) in_data); //Declare vectors Vector#(4,Vector#(64, Complex)) stage_data = replicate(newVector); stage_data[0] = in_data; for (Integer stage = 0; stage < 3; stage = stage + 1) stage_data[stage+1] = stage_f(stage,stage_data[stage]); return(stage_data[3]); The for loop is unfolded and stage_f is inlined during static elaboration Note: no notion of loops or procedures during execution http://csg.csail.mit.edu/arvind

  9. BSV Code: Combinational IFFT- Unfolded function Vector#(64, Complex) ifft (Vector#(64, Complex) in_data); //Declare vectors Vector#(4,Vector#(64, Complex)) stage_data = replicate(newVector); stage_data[0] = in_data; for (Integer stage = 0; stage < 3; stage = stage + 1) stage_data[stage+1] = stage_f(stage,stage_data[stage]); return(stage_data[3]); stage_data[1] = stage_f(0,stage_data[0]); stage_data[2] = stage_f(1,stage_data[1]); stage_data[3] = stage_f(2,stage_data[2]); Stage_f can be inlined now; it could have been inlined before loop unfolding also. Does the order matter? http://csg.csail.mit.edu/arvind

  10. Bluespec Code for stage_f function Vector#(64, Complex) stage_f (Bit#(2) stage, Vector#(64, Complex) stage_in); begin for (Integer i = 0; i < 16; i = i + 1) begin Integer idx = i * 4; let twid = getTwiddle(stage, fromInteger(i)); let y = bfly4(twid, stage_in[idx:idx+3]); stage_temp[idx] = y[0]; stage_temp[idx+1] = y[1]; stage_temp[idx+2] = y[2]; stage_temp[idx+3] = y[3]; end //Permutation for (Integer i = 0; i < 64; i = i + 1) stage_out[i] = stage_temp[permute[i]]; end return(stage_out); http://csg.csail.mit.edu/arvind

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