add_pipe.v

module add_pipe #(
	parameter WIDTH = 64,
	parameter SLICE_WIDTH = 16,
) (
	input clk,
	input carry_in,
	input [0 +: WIDTH] x, y,
	output [0 +: WIDTH] z,
	output carry_out,
);

	/* round up */
	localparam SLICES = (WIDTH + SLICE_WIDTH - 1) / SLICE_WIDTH;
	localparam EXTRA_WIDTH = WIDTH - (SLICE_WIDTH * SLICES);
	
	reg [0 +: SLICE_WIDTH] sum[0 +: SLICES - 1][0 +: SLICES - 1];
	reg [0 +: EXTRA_WIDTH] extra[0 +: SLICES - 1];

	genvar i, j;
	always @(posedge clk) begin
		for (j = 0; j < SLICES - 1; j = j + 1) begin: add
			sum[0][j] <= x[j * SLICE_WIDTH +: SLICE_WIDTH] + y[j * SLICE_WIDTH +: SLICE_WIDTH] + ((j == 0) ? carry_in : 0);
		end
		extra[0] <= x[WIDTH - 1 -: EXTRA_WIDTH] + y[WIDTH - 1 -: EXTRA_WIDTH] + ((SLICES == 1) ? carry_in : 0);
	end

	/* Propagate the carry between each slice */
	always @(posedge clk) begin
		for (i = 1; i < SLICES - 1; i = i + 1) begin: stage
			for (j = 0; j < SLICES - 1; j = j + 1) begin: slice
				sum[i][j] <= sum[i - 1][j] + ((i == j) ? sum[i - 1][j - 1][SLICE_WIDTH] : 0);
			end
			extra[i] <= extra[i - 1];
		end
	end

	/* Assign output */
	for (j = 0; j < SLICES - 1; j = j + 1) begin: out
		assign z[j * SLICE_WIDTH +: SLICE_WIDTH] = sum[SLICES - 1][j];
	end
	assign { carry_out, z[WIDTH - 1 -: EXTRA_WIDTH] } = extra[SLICES - 1] + sum[SLICES - 1][SLICES - 1][SLICE_WIDTH];
endmodule