////////////////////////////////////////////////////////////////////////////////
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////////////////////////////////////////////////////////////////////////////////
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//
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//
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// Filename: convround.v
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// Filename: convround.v
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//
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//
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// Project: A General Purpose Pipelined FFT Implementation
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// Project: A General Purpose Pipelined FFT Implementation
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//
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//
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// Purpose: A convergent rounding routine, also known as banker's
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// Purpose: A convergent rounding routine, also known as banker's
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// rounding, Dutch rounding, Gaussian rounding, unbiased
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// rounding, Dutch rounding, Gaussian rounding, unbiased
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// rounding, or ... more, at least according to Wikipedia.
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// rounding, or ... more, at least according to Wikipedia.
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//
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//
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// This form of rounding works by rounding, when the direction is in
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// This form of rounding works by rounding, when the direction is in
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// question, towards the nearest even value.
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// question, towards the nearest even value.
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//
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//
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//
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//
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// Creator: Dan Gisselquist, Ph.D.
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// Creator: Dan Gisselquist, Ph.D.
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// Gisselquist Technology, LLC
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// Gisselquist Technology, LLC
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//
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//
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////////////////////////////////////////////////////////////////////////////////
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////////////////////////////////////////////////////////////////////////////////
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//
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//
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// Copyright (C) 2015-2018, Gisselquist Technology, LLC
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// Copyright (C) 2015-2018, Gisselquist Technology, LLC
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//
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//
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// This program is free software (firmware): you can redistribute it and/or
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// This file is part of the general purpose pipelined FFT project.
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// modify it under the terms of the GNU General Public License as published
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//
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// by the Free Software Foundation, either version 3 of the License, or (at
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// The pipelined FFT project is free software (firmware): you can redistribute
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// your option) any later version.
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// it and/or modify it under the terms of the GNU Lesser General Public License
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//
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// as published by the Free Software Foundation, either version 3 of the
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// This program is distributed in the hope that it will be useful, but WITHOUT
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// License, or (at your option) any later version.
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// ANY WARRANTY; without even the implied warranty of MERCHANTIBILITY or
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//
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// FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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// The pipelined FFT project is distributed in the hope that it will be useful,
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// for more details.
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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//
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// MERCHANTIBILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser
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// You should have received a copy of the GNU General Public License along
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// General Public License for more details.
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// with this program. (It's in the $(ROOT)/doc directory, run make with no
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//
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// target there if the PDF file isn't present.) If not, see
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// You should have received a copy of the GNU Lesser General Public License
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// along with this program. (It's in the $(ROOT)/doc directory. Run make
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// with no target there if the PDF file isn't present.) If not, see
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// <http://www.gnu.org/licenses/> for a copy.
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// <http://www.gnu.org/licenses/> for a copy.
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//
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//
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// License: GPL, v3, as defined and found on www.gnu.org,
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// License: LGPL, v3, as defined and found on www.gnu.org,
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// http://www.gnu.org/licenses/gpl.html
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// http://www.gnu.org/licenses/lgpl.html
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//
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//
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//
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//
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////////////////////////////////////////////////////////////////////////////////
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////////////////////////////////////////////////////////////////////////////////
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//
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//
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//
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//
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`default_nettype none
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`default_nettype none
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//
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//
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module convround(i_clk, i_ce, i_val, o_val);
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module convround(i_clk, i_ce, i_val, o_val);
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parameter IWID=16, OWID=8, SHIFT=0;
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parameter IWID=16, OWID=8, SHIFT=0;
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input i_clk, i_ce;
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input wire i_clk, i_ce;
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input signed [(IWID-1):0] i_val;
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input wire signed [(IWID-1):0] i_val;
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output reg signed [(OWID-1):0] o_val;
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output reg signed [(OWID-1):0] o_val;
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// Let's deal with three cases to be as general as we can be here
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// Let's deal with three cases to be as general as we can be here
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//
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//
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// 1. The desired output would lose no bits at all
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// 1. The desired output would lose no bits at all
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// 2. One bit would be dropped, so the rounding is simply
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// 2. One bit would be dropped, so the rounding is simply
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// adjusting the value to be the nearest even number in
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// adjusting the value to be the nearest even number in
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// cases of being halfway between two. If identically
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// cases of being halfway between two. If identically
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// equal to a number, we just leave it as is.
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// equal to a number, we just leave it as is.
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// 3. Two or more bits would be dropped. In this case, we round
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// 3. Two or more bits would be dropped. In this case, we round
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// normally unless we are rounding a value of exactly
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// normally unless we are rounding a value of exactly
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// halfway between the two. In the halfway case we round
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// halfway between the two. In the halfway case we round
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// to the nearest even number.
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// to the nearest even number.
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generate
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generate
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if (IWID == OWID) // In this case, the shift is irrelevant and
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if (IWID == OWID) // In this case, the shift is irrelevant and
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begin // cannot be applied. No truncation or rounding takes
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begin // cannot be applied. No truncation or rounding takes
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// effect here.
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// effect here.
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always @(posedge i_clk)
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always @(posedge i_clk)
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if (i_ce) o_val <= i_val[(IWID-1):0];
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if (i_ce) o_val <= i_val[(IWID-1):0];
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end else if (IWID-SHIFT == OWID)
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end else if (IWID-SHIFT == OWID)
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begin // No truncation or rounding, output drops no bits
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begin // No truncation or rounding, output drops no bits
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always @(posedge i_clk)
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always @(posedge i_clk)
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if (i_ce) o_val <= i_val[(IWID-SHIFT-1):0];
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if (i_ce) o_val <= i_val[(IWID-SHIFT-1):0];
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end else if (IWID-SHIFT-1 == OWID)
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end else if (IWID-SHIFT-1 == OWID)
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begin // Output drops one bit, can only add one or ... not.
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begin // Output drops one bit, can only add one or ... not.
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wire [(OWID-1):0] truncated_value, rounded_up;
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wire [(OWID-1):0] truncated_value, rounded_up;
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wire last_valid_bit, first_lost_bit;
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wire last_valid_bit, first_lost_bit;
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assign truncated_value=i_val[(IWID-1-SHIFT):(IWID-SHIFT-OWID)];
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assign truncated_value=i_val[(IWID-1-SHIFT):(IWID-SHIFT-OWID)];
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assign rounded_up=truncated_value + {{(OWID-1){1'b0}}, 1'b1 };
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assign rounded_up=truncated_value + {{(OWID-1){1'b0}}, 1'b1 };
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assign last_valid_bit = truncated_value[0];
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assign last_valid_bit = truncated_value[0];
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assign first_lost_bit = i_val[0];
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assign first_lost_bit = i_val[0];
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always @(posedge i_clk)
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always @(posedge i_clk)
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if (i_ce)
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if (i_ce)
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begin
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begin
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if (!first_lost_bit) // Round down / truncate
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if (!first_lost_bit) // Round down / truncate
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o_val <= truncated_value;
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o_val <= truncated_value;
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else if (last_valid_bit)// Round up to nearest
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else if (last_valid_bit)// Round up to nearest
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o_val <= rounded_up; // even value
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o_val <= rounded_up; // even value
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else // else round down to the nearest
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else // else round down to the nearest
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o_val <= truncated_value; // even value
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o_val <= truncated_value; // even value
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end
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end
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end else // If there's more than one bit we are dropping
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end else // If there's more than one bit we are dropping
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begin
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begin
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wire [(OWID-1):0] truncated_value, rounded_up;
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wire [(OWID-1):0] truncated_value, rounded_up;
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wire last_valid_bit, first_lost_bit;
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wire last_valid_bit, first_lost_bit;
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assign truncated_value=i_val[(IWID-1-SHIFT):(IWID-SHIFT-OWID)];
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assign truncated_value=i_val[(IWID-1-SHIFT):(IWID-SHIFT-OWID)];
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assign rounded_up=truncated_value + {{(OWID-1){1'b0}}, 1'b1 };
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assign rounded_up=truncated_value + {{(OWID-1){1'b0}}, 1'b1 };
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assign last_valid_bit = truncated_value[0];
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assign last_valid_bit = truncated_value[0];
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assign first_lost_bit = i_val[(IWID-SHIFT-OWID-1)];
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assign first_lost_bit = i_val[(IWID-SHIFT-OWID-1)];
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wire [(IWID-SHIFT-OWID-2):0] other_lost_bits;
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wire [(IWID-SHIFT-OWID-2):0] other_lost_bits;
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assign other_lost_bits = i_val[(IWID-SHIFT-OWID-2):0];
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assign other_lost_bits = i_val[(IWID-SHIFT-OWID-2):0];
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always @(posedge i_clk)
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always @(posedge i_clk)
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if (i_ce)
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if (i_ce)
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begin
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begin
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if (!first_lost_bit) // Round down / truncate
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if (!first_lost_bit) // Round down / truncate
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o_val <= truncated_value;
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o_val <= truncated_value;
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else if (|other_lost_bits) // Round up to
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else if (|other_lost_bits) // Round up to
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o_val <= rounded_up; // closest value
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o_val <= rounded_up; // closest value
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else if (last_valid_bit) // Round up to
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else if (last_valid_bit) // Round up to
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o_val <= rounded_up; // nearest even
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o_val <= rounded_up; // nearest even
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else // else round down to nearest even
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else // else round down to nearest even
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o_val <= truncated_value;
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o_val <= truncated_value;
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end
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end
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end
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end
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endgenerate
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endgenerate
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endmodule
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endmodule
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