pipelined stages and abstracted overflow limit

src/FPA_module_test.sv

@@ -1,159 +1,207 @@
-module floating_add #(parameter N=16, M=4)(input_1, input_2, sum, diff);
+module floating_add #(parameter N=16, M=4)(input_1, input_2, sum, diff, clk, reset);
 	input logic [N-1:0] input_1, input_2;
+	input logic clk, reset;
 	output logic [N-1:0] sum;
 	output logic [M:0] diff;
 
-	logic flag_a;
-	logic flag_b;
-	logic [M:0] abs;
-	logic [N-3-M:0] res;
+//	logic flag_a;
+//	logic flag_b;
+//	logic [M:0] abs;
+//	logic [N-3-M:0] res;
+	logic [N-1:0] D0 [7:0];
+	logic [N-1:0] Q0 [7:0];
+	logic [N-1:0] Q1 [7:0];
+	logic [N-1:0] Q2 [7:0];
 	
 	// sign_x = x[N-1]
 	// exponent_x = x[N-2:N-2-M]
 	// mantissa_x = x[N-3-M:0]
 	
+	// Pipeline stage 0
+	always_comb
+		begin
+			D0[0] = input_1;
+			D0[1] = input_2;
+			D0[2] = 0 // sum
+			D0[3] = 0 // diff
+			D0[4] = 0 // flag_a
+			Do[5] = 0 // flag_b
+			D0[6] = 0 // abs
+			D0[7] = 0 // res
+		end
+		
+		pipe pipe_0(.clk(clk), .reset(reset), .D(D0), .Q(Q0));
+	
 	always_comb
 		begin
-			if (input_1[N-2:N-2-M] > input_2[N-2:N-2-M]) // If input 1 has the bigger exponent 
+			if (Q0[0][N-2:N-2-M] > Q0[1][N-2:N-2-M]) // If input 1 has the bigger exponent 
 				begin
 					// Flags input a as larger and calculates the absolute difference
-					flag_a = 1;
-					flag_b = 0;
-					abs = input_1[N-2:N-2-M] - input_2[N-2:N-2-M];
+					Q0]4] = 1;
+					Q0[5] = 0;
+					Q0[6] = Q0[0][N-2:N-2-M] - Q0[1][N-2:N-2-M];
 					// ASsigning overall sign of the output
-					sum[N-1] = input_1[N-1];
+					Q0[2][N-1] = Q0[0][N-1];
 					// Sets output to have the same exponent
-					sum[N-2:N-2-M] = input_1[N-2:N-2-M];
+					Q0[2][N-2:N-2-M] = Q0[0][N-2:N-2-M];
 				end
-			else if (input_2[N-2:N-2-M] > input_1[N-2:N-2-M]) // If input 2 has the bigger exponent
+			else if (Q0[1][N-2:N-2-M] > Q0[0][N-2:N-2-M]) // If input 2 has the bigger exponent
 				begin
 					// Similarly flags input b as larger and calculates the absolute difference
-					flag_a = 0;
-					flag_b = 1;
-					abs = input_2[N-2:N-2-M] - input_1[N-2:N-2-M];
+					Q0[4] = 0;
+					Q0[5] = 1;
+					Q0[6] = Q0[1][N-2:N-2-M] - Q0[0][N-2:N-2-M];
 					// ASsigning overall sign of the output
-					sum[N-1] = input_2[N-1];
+					Q0[2][N-1] = Q0[1][N-1];
 					// Sets ouput to have the same exponent
-					sum[N-2:N-2-M] = input_2[N-2:N-2-M];
+					Q0[2][N-2:N-2-M] = Q0[1][N-2:N-2-M];
 				end
 			else 
 				begin
 					// THe condition that both inputs have the same exponent
-					flag_a = 1;
-					flag_b = 1;
-					abs = 0;
+					Q0[4] = 1;
+					Q0[5] = 1;
+					Q0[6] = 0;
 					// ASsigning overall sign of the output based on size of the mantissa
-					if (input_1[N-3-M:0] >= input_2[N-3-M:0]) sum[N-1] = input_1[N-1];
-					else sum[N-1] = input_2[N-1];
-					sum[N-2:N-2-M] = input_1[N-2:N-2-M];
+					if (Q0[0][N-3-M:0] >= Q0[1][N-3-M:0]) sum[N-1] = Q0[0][N-1];
+					else Q0[2][N-1] = Q0[1][N-1];
+					Q0[2][N-2:N-2-M] = Q0[0][N-2:N-2-M];
 				end
-			diff = abs;
+			Q0[3] = Q0[6];
 		end
 		
+		//Pipeline stage 1
+		pipe pipe_1(.clk(clk), .reset(reset), .D(Q0), .Q(Q1));
+		
 	always_comb
 		begin
 			// Condition for overflow is that it sets the output to the larger input
-			if (abs > 9) // Because size of mantissa is 10 bits and shifting by 10 would give 0
+			if (Q1[6] > N-M-2) // Because size of mantissa is 10 bits and shifting by 10 would give 0
 				begin
-					if (flag_a & ~flag_b) sum = input_1; // input 1 is larger and is translated to output
-					else if (~flag_a & flag_b) sum = input_2; // input 2 is larger and is translated to output
+					if (Q1[4] & ~Q1[5]) Q1[2] = Q1[0]; // input 1 is larger and is translated to output
+					else if (~Q1[4] & Q1[5]) Q1[2] = Q1[1]; // input 2 is larger and is translated to output
 					else // exponents are the same
 						begin
-							if (input_1[N-3-M:0] >= input_2[N-3-M:0]) sum = input_1;// input 1 has the bigger mantissa
-							else sum = input_2; // input 2 has the bigger mantissa
+							if (Q1[0][N-3-M:0] >= Q1[1][N-3-M:0]) Q1[2] = Q1[0];// input 1 has the bigger mantissa
+							else Q1[2] = Q1[1]; // input 2 has the bigger mantissa
 						end
 				end
 			else
 				begin
 					// Shifts the smaller input's mantissa to the right based on abs
-					if (flag_a & ~flag_b)// If input 1 has the larger exponent
+					if (Q1[4] & ~Q1[5])// If input 1 has the larger exponent
 						begin
 							// If the signs of both inputs are the same you add, otherwise you subtract
-							if (input_1[N-1] == input_2[N-1])
+							if (Q1[0][N-1] == Q1[1][N-1])
 								begin
-									res = input_1[N-3-M:0] + (input_2[N-3-M:0] >> abs-1); // Sum the mantissa
-									sum[N-3-M:0] = res;
+									Q1[7] = Q1[0][N-3-M:0] + (Q1[1][N-3-M:0] >> Q1[6]-1); // Sum the mantissa
+									Q1[2][N-3-M:0] = Q1[7];
 								end
 							else
 								begin
-									res = input_1[N-3-M:0] - (input_2[N-3-M:0] >> abs-1); // Subtract the mantissas
-									sum[N-3-M:0] = res;
+									Q1[7] = Q1[0][N-3-M:0] - (Q1[1][N-3-M:0] >> Q1[6]-1); // Subtract the mantissas
+									Q1[2][N-3-M:0] = Q1[7];
 								end
 						end
-					else if (~flag_a & flag_b)
+					else if (~Q1[4] & Q1[5])
 						begin
 							// If the signs of both inputs are the same you add, otherwise you subtract
-							if (input_1[N-1] == input_2[N-1])
+							if (Q1[0][N-1] == Q1[1][N-1])
 								begin
-									res = (input_1[N-3-M:0] >> abs-1) + input_2[N-3-M:0]; // Sum the mantissa
-									sum[N-3-M:0] = res;
+									Q1[7] = (Q1[0][N-3-M:0] >> Q1[6]-1) + Q1[1][N-3-M:0]; // Sum the mantissa
+									Q1[2][N-3-M:0] = Q1[7];
 								end
 							else
 								begin
-									res = input_2[N-3-M:0] - (input_1[N-3-M:0] >> abs-1); // Subtract the mantissas
-									sum[N-3-M:0] = res;
+									Q1[7] = Q1[1][N-3-M:0] - (Q1[0][N-3-M:0] >> Q1[6]-1); // Subtract the mantissas
+									Q1[2][N-3-M:0] = Q1[7];
 								end
 						end
 					else
 						begin 
-							if (input_1[N-1] == input_2[N-1]) // If exponents and signs equal
+							if (Q1[0][N-1] == Q1[1][N-1]) // If exponents and signs equal
 								begin
-									res = input_1[N-3-M:0] + input_2[N-3-M:0]; // Sum the mantissa
-									sum[N-3-M:0] = res;
+									Q1[7] = Q1[0][N-3-M:0] + Q1[1][N-3-M:0]; // Sum the mantissa
+									Q1[2][N-3-M:0] = Q1[7];
 								end
 							else // In this case it will be a subtraction
 								begin
-									if (input_1[N-3-M:0] > input_2[N-3-M:0]) // Which has the larger mantissa 
+									if (Q1[0][N-3-M:0] > Q1[1][N-3-M:0]) // Which has the larger mantissa 
 										begin
-											res = input_1[N-3-M:0] - input_2[N-3-M:0]; // Subtract the mantissa
-											sum[N-3-M:0] = res;
+											Q1[7] = Q1[0][N-3-M:0] - Q1[1][N-3-M:0]; // Subtract the mantissa
+											Q1[2][N-3-M:0] = Q1[7];
 										end
-									else if (input_1[N-3-M:0] < input_2[N-3-M:0])
+									else if (Q1[0][N-3-M:0] < Q1[1][N-3-M:0])
 										begin
-											res = input_2[N-3-M:0] - input_1[N-3-M:0]; // Subtract the mantissa
-											sum[N-3-M:0] = res;
+											Q1[7] = Q1[1][N-3-M:0] - Q1[0][N-3-M:0]; // Subtract the mantissa
+											Q1[2][N-3-M:0] = Q1[7];
 										end
-									else res = 0; // Both the exponent and the mantissa are equal so subtraction leads to 0
-									sum[N-3-M:0] = res;
+									else Q1[7] = 0; // Both the exponent and the mantissa are equal so subtraction leads to 0
+									Q1[2][N-3-M:0] = Q1[7];
 								end
 						end
 				end
 		end
+		
+		//Final pipeline stage 2
+		pipe pipe2(.clk(clk), .reset(reset), .D(Q1), .Q(Q2));
+		assign sum = Q2[2];
+		assign diff = Q2[3];
 endmodule : floating_add
 
 
 
-module floating_product #(parameter N=16, M=4)(input_1, input_2, product);
+module floating_product #(parameter N=16, M=4)(input_1, input_2, product, clk, reset);
 	input logic [N-1:0] input_1, input_2;
+	input logic clk, reset;
 	output logic [N-1:0] product;
 
 	// sign_x = x[N-1]
 	// exponent_x = x[N-2:N-2-M]
 	// mantissa_x = x[N-3-M:0]
 
-	logic [N-2:N-2-M] sum;
-	logic [2*(N-3-M):0] mult;
+//	logic [N-2:N-2-M] sum;
+//	logic [2*(N-3-M):0] mult;
+	logic [2*(N-3-M):0] D0 [4:0];
+	logic [2*(N-3-M):0] Q0 [4:0];
+	logic [2*(N-3-M):0] Q1 [4:0];
+	logic [2*(N-3-M):0] Q2 [4:0];
+	
+	// First pipeline stage 0
+	assign D0[0] = input_1;
+	assign D0[1] = input_2;
+	assign D0[2] = 0; // product
+	assign D0[3] = 0; // sum
+	assign D0[4] = 0; // mult
+	pipe pipe0 #(N = 32, K = 4)(.clk(clk), .reset(reset), .D(D0), .Q(Q0));
 
 	// We have assigned an {M+1} bit exponent so we must have a 2^{M} offset
-	assign sum = input_1[N-2:N-2-M] + input_2[N-2:N-2-M];
-	assign product[N-2:N-2-M] = sum - (1'b1 << M) + 2;
+	assign Q0[3] = Q0[0][N-2:N-2-M] + Q0[1][N-2:N-2-M];
+	assign Q0[2][N-2:N-2-M] = Q0[3] - (1'b1 << M) + 2;
+	
+	// Second pipeline stage 1
+	pipe pipe1 #(N = 32, K = 4)(.clk(clk), .reset(reset), .D(Q0), .Q(Q1));
 
 	always_comb
 		begin
 				// Setting the mantissa of the output
-				mult = input_1[N-3-M:0] * input_2[N-3-M:0];
-				if (mult[N-3-M]) product[N-3-M:0] = mult[2*(N-3-M):2*(N-3-M)-9];
-				else product[N-3-M:0] = mult[2*(N-3-M):2*(N-3-M)-9] << 1;
-				product[N-1] = input_1[N-1] ^ input_2[N-1];
+				Q1[4] = Q1[0][N-3-M:0] * Q1[1][N-3-M:0];
+				if (Q1[4][N-3-M]) Q1[2][N-3-M:0] = Q1[4][2*(N-3-M):2*(N-3-M)-9];
+				else Q1[2][N-3-M:0] = Q1[4][2*(N-3-M):2*(N-3-M)-9] << 1;
+				Q1[2][N-1] = Q1[0][N-1] ^ Q1[1][N-1];
 		end
+		
+		// Final Pipeline Stage 2
+		pipe pipe2 #(N = 32, K = 4)(.clk(clk), .reset(reset), .D(Q1), .Q(Q2));
+		assign product = Q2[2][N-1:0];
 endmodule : floating_product
 
 
 
-module pipe #(parameter N=16)pipe(clk, reset, Q, D);
+module pipe #(parameter N = 16, K = 7)pipe(clk, reset, D, Q);
 	input logic clk, reset;
-	input logic [N-1:0] D;
-	output reg [N-1:0] Q;
+	input logic [N-1:0] D [K:0];
+	output reg [N-1:0] Q [K:0];
 	reg [N-1:0] in_pipe;
 	
 	always @(posedge clk or negedge reset)