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@@ -1,204 +1,156 @@
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-module floating_add #(parameter N=16, M=4)(input_1, input_2, sum, diff, clk, reset);
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+module floating_add #(parameter N=16, M=4)(input_1, input_2, sum, diff);
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input logic [N-1:0] input_1, input_2;
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- input logic clk, reset;
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output logic [N-1:0] sum;
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output logic [M:0] diff;
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-// logic flag_a;
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-// logic flag_b;
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-// logic [M:0] abs;
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-// logic [N-3-M:0] res;
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- logic [N-1:0] D0 [7:0];
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- logic [N-1:0] Q0 [7:0];
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- logic [N-1:0] Q1 [7:0];
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- logic [N-1:0] Q2 [7:0];
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+ logic flag_a;
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+ logic flag_b;
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+ logic [M:0] abs;
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+ logic [N-3-M:0] res;
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// sign_x = x[N-1]
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// exponent_x = x[N-2:N-2-M]
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// mantissa_x = x[N-3-M:0]
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- // Pipeline stage 0
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- always_comb
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- begin
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- D0[0] = input_1;
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- D0[1] = input_2;
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- D0[2] = 0 // sum
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- D0[3] = 0 // diff
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- D0[4] = 0 // flag_a
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- Do[5] = 0 // flag_b
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- D0[6] = 0 // abs
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- D0[7] = 0 // res
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- end
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-
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- pipe pipe_0(.clk(clk), .reset(reset), .D(D0), .Q(Q0));
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-
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always_comb
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begin
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- if (Q0[0][N-2:N-2-M] > Q0[1][N-2:N-2-M]) // If input 1 has the bigger exponent
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+ if (input_1[N-2:N-2-M] > input_2[N-2:N-2-M]) // If input 1 has the bigger exponent
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begin
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// Flags input a as larger and calculates the absolute difference
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- Q0]4] = 1;
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- Q0[5] = 0;
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- Q0[6] = Q0[0][N-2:N-2-M] - Q0[1][N-2:N-2-M];
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+ flag_a = 1;
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+ flag_b = 0;
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+ abs = input_1[N-2:N-2-M] - input_2[N-2:N-2-M];
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// ASsigning overall sign of the output
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- Q0[2][N-1] = Q0[0][N-1];
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+ sum[N-1] = input_1[N-1];
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// Sets output to have the same exponent
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- Q0[2][N-2:N-2-M] = Q0[0][N-2:N-2-M];
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+ sum[N-2:N-2-M] = input_1[N-2:N-2-M];
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end
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- else if (Q0[1][N-2:N-2-M] > Q0[0][N-2:N-2-M]) // If input 2 has the bigger exponent
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+ else if (input_2[N-2:N-2-M] > input_1[N-2:N-2-M]) // If input 2 has the bigger exponent
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begin
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// Similarly flags input b as larger and calculates the absolute difference
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- Q0[4] = 0;
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- Q0[5] = 1;
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- Q0[6] = Q0[1][N-2:N-2-M] - Q0[0][N-2:N-2-M];
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+ flag_a = 0;
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+ flag_b = 1;
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+ abs = input_2[N-2:N-2-M] - input_1[N-2:N-2-M];
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// ASsigning overall sign of the output
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- Q0[2][N-1] = Q0[1][N-1];
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+ sum[N-1] = input_2[N-1];
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// Sets ouput to have the same exponent
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- Q0[2][N-2:N-2-M] = Q0[1][N-2:N-2-M];
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+ sum[N-2:N-2-M] = input_2[N-2:N-2-M];
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end
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else
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begin
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// THe condition that both inputs have the same exponent
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- Q0[4] = 1;
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- Q0[5] = 1;
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- Q0[6] = 0;
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+ flag_a = 1;
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+ flag_b = 1;
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+ abs = 0;
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// ASsigning overall sign of the output based on size of the mantissa
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- if (Q0[0][N-3-M:0] >= Q0[1][N-3-M:0]) sum[N-1] = Q0[0][N-1];
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- else Q0[2][N-1] = Q0[1][N-1];
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- Q0[2][N-2:N-2-M] = Q0[0][N-2:N-2-M];
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+ if (input_1[N-3-M:0] >= input_2[N-3-M:0]) sum[N-1] = input_1[N-1];
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+ else sum[N-1] = input_2[N-1];
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+ sum[N-2:N-2-M] = input_1[N-2:N-2-M];
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end
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- Q0[3] = Q0[6];
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+ diff = abs;
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end
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- //Pipeline stage 1
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- pipe pipe_1(.clk(clk), .reset(reset), .D(Q0), .Q(Q1));
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-
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always_comb
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begin
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// Condition for overflow is that it sets the output to the larger input
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- if (Q1[6] > N-M-2) // Because size of mantissa is 10 bits and shifting by 10 would give 0
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+ if (abs > 9) // Because size of mantissa is 10 bits and shifting by 10 would give 0
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begin
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- if (Q1[4] & ~Q1[5]) Q1[2] = Q1[0]; // input 1 is larger and is translated to output
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- else if (~Q1[4] & Q1[5]) Q1[2] = Q1[1]; // input 2 is larger and is translated to output
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+ if (flag_a & ~flag_b) sum = input_1; // input 1 is larger and is translated to output
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+ else if (~flag_a & flag_b) sum = input_2; // input 2 is larger and is translated to output
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else // exponents are the same
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begin
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- if (Q1[0][N-3-M:0] >= Q1[1][N-3-M:0]) Q1[2] = Q1[0];// input 1 has the bigger mantissa
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- else Q1[2] = Q1[1]; // input 2 has the bigger mantissa
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+ if (input_1[N-3-M:0] >= input_2[N-3-M:0]) sum = input_1;// input 1 has the bigger mantissa
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+ else sum = input_2; // input 2 has the bigger mantissa
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end
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end
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else
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begin
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// Shifts the smaller input's mantissa to the right based on abs
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- if (Q1[4] & ~Q1[5])// If input 1 has the larger exponent
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+ if (flag_a & ~flag_b)// If input 1 has the larger exponent
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begin
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// If the signs of both inputs are the same you add, otherwise you subtract
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- if (Q1[0][N-1] == Q1[1][N-1])
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+ if (input_1[N-1] == input_2[N-1])
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begin
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- Q1[7] = Q1[0][N-3-M:0] + (Q1[1][N-3-M:0] >> Q1[6]-1); // Sum the mantissa
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- Q1[2][N-3-M:0] = Q1[7];
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+ res = input_1[N-3-M:0] + (input_2[N-3-M:0] >> abs-1); // Sum the mantissa
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+ sum[N-3-M:0] = res;
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end
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else
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begin
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- Q1[7] = Q1[0][N-3-M:0] - (Q1[1][N-3-M:0] >> Q1[6]-1); // Subtract the mantissas
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- Q1[2][N-3-M:0] = Q1[7];
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+ res = input_1[N-3-M:0] - (input_2[N-3-M:0] >> abs-1); // Subtract the mantissas
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+ sum[N-3-M:0] = res;
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end
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end
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- else if (~Q1[4] & Q1[5])
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+ else if (~flag_a & flag_b)
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begin
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// If the signs of both inputs are the same you add, otherwise you subtract
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- if (Q1[0][N-1] == Q1[1][N-1])
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+ if (input_1[N-1] == input_2[N-1])
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begin
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- Q1[7] = (Q1[0][N-3-M:0] >> Q1[6]-1) + Q1[1][N-3-M:0]; // Sum the mantissa
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- Q1[2][N-3-M:0] = Q1[7];
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+ res = (input_1[N-3-M:0] >> abs-1) + input_2[N-3-M:0]; // Sum the mantissa
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+ sum[N-3-M:0] = res;
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end
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else
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begin
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- Q1[7] = Q1[1][N-3-M:0] - (Q1[0][N-3-M:0] >> Q1[6]-1); // Subtract the mantissas
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- Q1[2][N-3-M:0] = Q1[7];
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+ res = input_2[N-3-M:0] - (input_1[N-3-M:0] >> abs-1); // Subtract the mantissas
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+ sum[N-3-M:0] = res;
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end
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end
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else
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begin
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- if (Q1[0][N-1] == Q1[1][N-1]) // If exponents and signs equal
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+ if (input_1[N-1] == input_2[N-1]) // If exponents and signs equal
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begin
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- Q1[7] = Q1[0][N-3-M:0] + Q1[1][N-3-M:0]; // Sum the mantissa
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- Q1[2][N-3-M:0] = Q1[7];
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+ res = input_1[N-3-M:0] + input_2[N-3-M:0]; // Sum the mantissa
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+ sum[N-3-M:0] = res;
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end
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else // In this case it will be a subtraction
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begin
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- if (Q1[0][N-3-M:0] > Q1[1][N-3-M:0]) // Which has the larger mantissa
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+ if (input_1[N-3-M:0] > input_2[N-3-M:0]) // Which has the larger mantissa
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begin
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- Q1[7] = Q1[0][N-3-M:0] - Q1[1][N-3-M:0]; // Subtract the mantissa
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- Q1[2][N-3-M:0] = Q1[7];
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+ res = input_1[N-3-M:0] - input_2[N-3-M:0]; // Subtract the mantissa
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+ sum[N-3-M:0] = res;
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end
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- else if (Q1[0][N-3-M:0] < Q1[1][N-3-M:0])
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+ else if (input_1[N-3-M:0] < input_2[N-3-M:0])
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begin
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- Q1[7] = Q1[1][N-3-M:0] - Q1[0][N-3-M:0]; // Subtract the mantissa
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- Q1[2][N-3-M:0] = Q1[7];
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+ res = input_2[N-3-M:0] - input_1[N-3-M:0]; // Subtract the mantissa
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+ sum[N-3-M:0] = res;
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end
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- else Q1[7] = 0; // Both the exponent and the mantissa are equal so subtraction leads to 0
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- Q1[2][N-3-M:0] = Q1[7];
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+ else res = 0; // Both the exponent and the mantissa are equal so subtraction leads to 0
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+ sum[N-3-M:0] = res;
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end
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end
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end
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end
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-
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- //Final pipeline stage 2
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- pipe pipe2(.clk(clk), .reset(reset), .D(Q1), .Q(Q2));
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- assign sum = Q2[2];
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- assign diff = Q2[3];
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endmodule : floating_add
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-module floating_product #(parameter N=16, M=4)(input_1, input_2, product, clk, reset);
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+module floating_product #(parameter N=16, M=4)(input_1, input_2, product);
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input logic [N-1:0] input_1, input_2;
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- input logic clk, reset;
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output logic [N-1:0] product;
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// sign_x = x[N-1]
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// exponent_x = x[N-2:N-2-M]
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// mantissa_x = x[N-3-M:0]
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-// logic [N-2:N-2-M] sum;
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-// logic [2*(N-3-M):0] mult;
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- logic [2*(N-3-M):0] D0 [4:0];
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- logic [2*(N-3-M):0] Q0 [4:0];
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- logic [2*(N-3-M):0] Q1 [4:0];
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- logic [2*(N-3-M):0] Q2 [4:0];
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-
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- // First pipeline stage 0
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- assign D0[0] = input_1;
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- assign D0[1] = input_2;
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- assign D0[2] = 0; // product
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- assign D0[3] = 0; // sum
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- assign D0[4] = 0; // mult
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- pipe pipe0 #(N = 32, K = 4)(.clk(clk), .reset(reset), .D(D0), .Q(Q0));
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+ logic [N-2:N-2-M] sum;
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+ logic [2*(N-3-M):0] mult;
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// We have assigned an {M+1} bit exponent so we must have a 2^{M} offset
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- assign Q0[3] = Q0[0][N-2:N-2-M] + Q0[1][N-2:N-2-M];
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- assign Q0[2][N-2:N-2-M] = Q0[3] - (1'b1 << M) + 2;
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-
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- // Second pipeline stage 1
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- pipe pipe1 #(N = 32, K = 4)(.clk(clk), .reset(reset), .D(Q0), .Q(Q1));
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+ assign sum = input_1[N-2:N-2-M] + input_2[N-2:N-2-M];
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+ assign product[N-2:N-2-M] = sum - (1'b1 << M) + 2;
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always_comb
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begin
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// Setting the mantissa of the output
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- Q1[4] = Q1[0][N-3-M:0] * Q1[1][N-3-M:0];
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- if (Q1[4][N-3-M]) Q1[2][N-3-M:0] = Q1[4][2*(N-3-M):2*(N-3-M)-9];
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- else Q1[2][N-3-M:0] = Q1[4][2*(N-3-M):2*(N-3-M)-9] << 1;
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- Q1[2][N-1] = Q1[0][N-1] ^ Q1[1][N-1];
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+ mult = input_1[N-3-M:0] * input_2[N-3-M:0];
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+ if (mult[N-3-M]) product[N-3-M:0] = mult[2*(N-3-M):2*(N-3-M)-9];
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+ else product[N-3-M:0] = mult[2*(N-3-M):2*(N-3-M)-9] << 1;
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+ product[N-1] = input_1[N-1] ^ input_2[N-1];
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end
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-
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- // Final Pipeline Stage 2
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- pipe pipe2 #(N = 32, K = 4)(.clk(clk), .reset(reset), .D(Q1), .Q(Q2));
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- assign product = Q2[2][N-1:0];
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endmodule : floating_product
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-module pipe #(parameter N = 16, K = 7)pipe(clk, reset, D, Q);
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+module pipe #(parameter N=16)(clk, reset, Q, D);
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input logic clk, reset;
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input logic [N-1:0] D [K:0];
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output reg [N-1:0] Q [K:0];
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