A Color Vision System for Embedded Robotics Applications

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Verilog FPGA integer divide function:

// serial_divide_uu.v  -- Serial division module
// Description: See description below (which suffices for IP core
//                                     specification document.)
// Copyright (C) 2002 John Clayton and OPENCORES.ORG (this Verilog version)
// This source file may be used and distributed without restriction provided
// that this copyright statement is not removed from the file and that any
// derivative work contains the original copyright notice and the associated
// disclaimer.
// This source file is free software; you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published
// by the Free Software Foundation;  either version 2.1 of the License, or
// (at your option) any later version.
// This source is distributed in the hope that it will be useful, but WITHOUT
// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 
// FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
// License for more details.
// You should have received a copy of the GNU Lesser General Public License
// along with this source.
// If not, download it from http://www.opencores.org/lgpl.shtml
// Author: John Clayton
// Date  : Jan. 30, 2003
// Update: Jan. 30, 2003  Copied this file from "vga_crosshair.v"
//                        Stripped out extraneous stuff.
// Update: Mar. 14, 2003  Added S_PP parameter, made some simple changes to
//                        implement quotient leading zero "skip" feature.
// Update: Mar. 24, 2003  Updated comments to improve readability.
// Description:
// This module performs a division operation serially, producing one bit of the
// answer per clock cycle.  The dividend and the divisor are both taken to be
// unsigned quantities.  The divider is conceived as an integer divider (as
// opposed to a divider for fractional quantities) but the user can configure
// the divider to divide fractional quantities as long as the position of the
// binary point is carefully monitored.
// The widths of the signals are configurable by parameters, as follows:
// M_PP = Bit width of the dividend
// N_PP = Bit width of the divisor
// R_PP = Remainder bits desired
// S_PP = Skipped quotient bits
// The skipped quotient bits parameter provides a way to prevent the divider
// from calculating the full M_PP+R_PP output bits, in case some of the leading
// bits are already known to be zero.  This is the case, for example, when
// dividing two quantities to obtain a result that is a fraction between 0 and 1
// (as when measuring PWM signals).  In that case the integer portion of the
// quotient is always zero, and therefore it need not be calculated.
// The divide operation is begun by providing a pulse on the divide_i input.
// The quotient is provided (M_PP+R_PP-S_PP) clock cycles later.
// The divide_i pulse stores the input parameters in registers, so they do
// not need to be maintained at the inputs throughout the operation of the module.
// If a divide_i pulse is given to the serial_divide_uu module during the time
// when it is already working on a previous divide operation, it will abort the
// operation it was doing, and begin working on the new one.
// The user is responsible for treating the results correctly.  The position
// of the binary point is not given, but it is understood that the integer part
// of the result is the M_PP most significant bits of the quotient output.
// The remaining R_PP least significant bits are the fractional part.
// This is illustrated graphically:
//     [ M_PP bits ][    R_PP bits]
//     [ S_PP bits    ][quotient_o]
// The quotient will consist of whatever bits are left after removing the S_PP
// most significant bits from the (M_PP+R_PP) result bits.
// Attempting to divide by zero will simply produce a result of all ones.
// This core is so simple, that no checking for this condition is provided.
// If the user is concerned about a possible divide by zero condition, he should
// compare the divisor to zero and flag that condition himself!
// The COUNT_WIDTH_PP parameter must be sized so that 2^COUNT_WIDTH_PP-1 is >=
// M_PP+R_PP-S_PP-1.  The unit terminates the divide operation when the count
// is equal to M_PP+R_PP-S_PP-1.
// The HELD_OUTPUT_PP parameter causes the unit to keep its output result in
// a register other than the one which it uses to compute the quotient.  This
// is useful for applications where the divider is used repeatedly and the
// previous divide result (quotient) must be stable during the computation of the
// next divide result.  Using the additional output register does incur some
// additional utilization of resources.

module serial_divide_uu (

parameter M_PP = 16;           // Size of dividend
parameter N_PP = 8;            // Size of divisor
parameter R_PP = 0;            // Size of remainder
parameter S_PP = 0;            // Skip this many bits (known leading zeros)
parameter COUNT_WIDTH_PP = 5;  // 2^COUNT_WIDTH_PP-1 >= (M_PP+R_PP-S_PP-1)
parameter HELD_OUTPUT_PP = 0;  // Set to 1 if stable output should be held
                               // from previous operation, during current
                               // operation.  Using this option will increase
                               // the resource utilization (costs extra
                               // d-flip-flops.)

// I/O declarations
input  clk_i;                           //
input  clk_en_i;
input  rst_i;                           // synchronous reset
input  divide_i;                        // starts division operation
input  [M_PP-1:0] dividend_i;           //
input  [N_PP-1:0] divisor_i;            //
output [M_PP+R_PP-S_PP-1:0] quotient_o; //
output done_o;                          // indicates completion of operation

//reg  [M_PP+R_PP-1:0] quotient_o;
reg  done_o;

// Internal signal declarations

reg  [M_PP+R_PP-1:0] grand_dividend;
reg  [M_PP+N_PP+R_PP-2:0] grand_divisor;
reg  [M_PP+R_PP-S_PP-1:0] quotient;
reg  [M_PP+R_PP-1:0] quotient_reg;       // Used exclusively for the held output
reg  [COUNT_WIDTH_PP-1:0] divide_count;

wire [M_PP+N_PP+R_PP-1:0] subtract_node; // Subtract node has extra "sign" bit
wire [M_PP+R_PP-1:0]      quotient_node; // Shifted version of quotient
wire [M_PP+N_PP+R_PP-2:0]  divisor_node; // Shifted version of grand divisor

// Module code

// Serial dividing module
always @(posedge clk_i)
  if (rst_i)
    grand_dividend <= 0;
    grand_divisor <= 0;
    divide_count <= 0;
    quotient <= 0;
    done_o <= 0;
  else if (clk_en_i)
    done_o <= 0;
    if (divide_i)       // Start a new division
      quotient <= 0;
      divide_count <= 0;
      // dividend placed initially so that remainder bits are zero...
      grand_dividend <= dividend_i << R_PP;
      // divisor placed initially for a 1 bit overlap with dividend...
      // But adjust it back by S_PP, to account for bits that are known
      // to be leading zeros in the quotient.
      grand_divisor  <= divisor_i << (N_PP+R_PP-S_PP-1);
    else if (divide_count == M_PP+R_PP-S_PP-1)
      if (~done_o) quotient <= quotient_node;      // final shift...
      if (~done_o) quotient_reg <= quotient_node;  // final shift (held output)
      done_o <= 1;                                 // Indicate done, just sit
    else                // Division in progress
      // If the subtraction yields a positive result, then store that result
      if (~subtract_node[M_PP+N_PP+R_PP-1]) grand_dividend <= subtract_node;
      // If the subtraction yields a positive result, then a 1 bit goes into 
      // the quotient, via a shift register
      quotient <= quotient_node;
      // shift the grand divisor to the right, to cut it in half next clock cycle
      grand_divisor <= divisor_node;
      // Advance the counter
      divide_count <= divide_count + 1;
  end  // End of else if clk_en_i
end // End of always block

assign subtract_node = {1'b0,grand_dividend} - {1'b0,grand_divisor};
assign quotient_node = 
assign divisor_node  = {1'b0,grand_divisor[M_PP+N_PP+R_PP-2:1]};

assign quotient_o = (HELD_OUTPUT_PP == 0)?quotient:quotient_reg;


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