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///////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////
//
//
// Filename:    div.v
// Filename:    div.v
//
//
// Project:     Zip CPU -- a small, lightweight, RISC CPU soft core
// Project:     Zip CPU -- a small, lightweight, RISC CPU soft core
//
//
// Purpose:     Provide an Integer divide capability to the Zip CPU.
// Purpose:     Provide an Integer divide capability to the Zip CPU.  Provides
 
//              for both signed and unsigned divide.
 
//
 
// Steps:
 
//      i_rst   The DIVide unit starts in idle.  It can also be placed into an
 
//      idle by asserting the reset input.
 
//
 
//      i_wr    When i_rst is asserted, a divide begins.  On the next clock:
 
//
 
//        o_busy is set high so everyone else knows we are at work and they can
 
//              wait for us to complete.
 
//
 
//        pre_sign is set to true if we need to do a signed divide.  In this
 
//              case, we take a clock cycle to turn the divide into an unsigned
 
//              divide.
 
//
 
//        o_quotient, a place to store our result, is initialized to all zeros.
 
//
 
//        r_dividend is set to the numerator
 
//
 
//        r_divisor is set to 2^31 * the denominator (shift left by 31, or add
 
//              31 zeros to the right of the number.
 
//
 
//      pre_sign When true (clock cycle after i_wr), a clock cycle is used
 
//              to take the absolute value of the various arguments (r_dividend
 
//              and r_divisor), and to calculate what sign the output result
 
//              should be.
 
//
 
//
 
//      At this point, the divide is has started.  The divide works by walking
 
//      through every shift of the
 
//
 
//                  DIVIDEND    over the
 
//              DIVISOR
 
//
 
//      If the DIVISOR is bigger than the dividend, the divisor is shifted
 
//      right, and nothing is done to the output quotient.
 
//
 
//                  DIVIDEND
 
//               DIVISOR
 
//
 
//      This repeats, until DIVISOR is less than or equal to the divident, as in
 
//
 
//              DIVIDEND
 
//              DIVISOR
 
//
 
//      At this point, if the DIVISOR is less than the dividend, the
 
//      divisor is subtracted from the dividend, and the DIVISOR is again
 
//      shifted to the right.  Further, a '1' bit gets set in the output
 
//      quotient.
 
//
 
//      Once we've done this for 32 clocks, we've accumulated our answer into
 
//      the output quotient, and we can proceed to the next step.  If the
 
//      result will be signed, the next step negates the quotient, otherwise
 
//      it returns the result.
 
//
 
//      On the clock when we are done, o_busy is set to false, and o_valid set
 
//      to true.  (It is a violation of the ZipCPU internal protocol for both
 
//      busy and valid to ever be true on the same clock.  It is also a
 
//      violation for busy to be false with valid true thereafter.)
//
//
//
//
// Creator:     Dan Gisselquist, Ph.D.
// Creator:     Dan Gisselquist, Ph.D.
//              Gisselquist Technology, LLC
//              Gisselquist Technology, LLC
//
//
///////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////
//
//
// Copyright (C) 2015-2016, Gisselquist Technology, LLC
// Copyright (C) 2015-2017, Gisselquist Technology, LLC
//
//
// This program is free software (firmware): you can redistribute it and/or
// This program is free software (firmware): you can redistribute it and/or
// modify it under the terms of  the GNU General Public License as published
// modify it under the terms of  the GNU General Public License as published
// by the Free Software Foundation, either version 3 of the License, or (at
// by the Free Software Foundation, either version 3 of the License, or (at
// your option) any later version.
// your option) any later version.
Line 22... Line 81...
// This program is distributed in the hope that it will be useful, but WITHOUT
// This program is distributed in the hope that it will be useful, but WITHOUT
// ANY WARRANTY; without even the implied warranty of MERCHANTIBILITY or
// ANY WARRANTY; without even the implied warranty of MERCHANTIBILITY or
// FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
// FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
// for more details.
// for more details.
//
//
 
// You should have received a copy of the GNU General Public License along
 
// with this program.  (It's in the $(ROOT)/doc directory.  Run make with no
 
// target there if the PDF file isn't present.)  If not, see
 
// <http://www.gnu.org/licenses/> for a copy.
 
//
// License:     GPL, v3, as defined and found on www.gnu.org,
// License:     GPL, v3, as defined and found on www.gnu.org,
//              http://www.gnu.org/licenses/gpl.html
//              http://www.gnu.org/licenses/gpl.html
//
//
//
//
///////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////
 
//
//
//
// `include "cpudefs.v"
// `include "cpudefs.v"
//
//
module  div(i_clk, i_rst, i_wr, i_signed, i_numerator, i_denominator,
module  div(i_clk, i_rst, i_wr, i_signed, i_numerator, i_denominator,
                o_busy, o_valid, o_err, o_quotient, o_flags);
                o_busy, o_valid, o_err, o_quotient, o_flags);
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        assign  diff = r_dividend - r_divisor[(BW-1):0];
        assign  diff = r_dividend - r_divisor[(BW-1):0];
        // assign       xdiff= r_dividend - { 1'b0, r_divisor[(BW-1):1] };
        // assign       xdiff= r_dividend - { 1'b0, r_divisor[(BW-1):1] };
 
 
        reg             r_sign, pre_sign, r_z, r_c, last_bit;
        reg             r_sign, pre_sign, r_z, r_c, last_bit;
        reg     [(LGBW-1):0]     r_bit;
        reg     [(LGBW-1):0]     r_bit;
 
 
        reg     zero_divisor;
        reg     zero_divisor;
        initial zero_divisor = 1'b0;
 
        always @(posedge i_clk)
 
                zero_divisor <= (r_divisor == 0)&&(r_busy);
 
 
 
 
        // The Divide logic begins with r_busy.  We use r_busy to determine
 
        // whether or not the divide is in progress, vs being complete.
 
        // Here, we clear r_busy on any reset and set it on i_wr (the request
 
        // do to a divide).  The divide ends when we are on the last bit,
 
        // or equivalently when we discover we are dividing by zero.
        initial r_busy = 1'b0;
        initial r_busy = 1'b0;
        always @(posedge i_clk)
        always @(posedge i_clk)
                if (i_rst)
                if (i_rst)
                        r_busy <= 1'b0;
                        r_busy <= 1'b0;
                else if (i_wr)
                else if (i_wr)
                        r_busy <= 1'b1;
                        r_busy <= 1'b1;
                else if ((last_bit)||(zero_divisor))
                else if ((last_bit)||(zero_divisor))
                        r_busy <= 1'b0;
                        r_busy <= 1'b0;
 
 
 
        // o_busy is very similar to r_busy, save for some key differences.
 
        // Primary among them is that o_busy needs to (possibly) be true
 
        // for an extra clock after r_busy clears.  This would be that extra
 
        // clock where we negate the result (assuming a signed divide, and that
 
        // the result is supposed to be negative.)  Otherwise, the two are
 
        // identical.
        initial o_busy = 1'b0;
        initial o_busy = 1'b0;
        always @(posedge i_clk)
        always @(posedge i_clk)
                if (i_rst)
                if (i_rst)
                        o_busy <= 1'b0;
                        o_busy <= 1'b0;
                else if (i_wr)
                else if (i_wr)
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                else if (((last_bit)&&(~r_sign))||(zero_divisor))
                else if (((last_bit)&&(~r_sign))||(zero_divisor))
                        o_busy <= 1'b0;
                        o_busy <= 1'b0;
                else if (~r_busy)
                else if (~r_busy)
                        o_busy <= 1'b0;
                        o_busy <= 1'b0;
 
 
 
        // If we are asked to divide by zero, we need to halt.  The sooner
 
        // we halt and report the error, the better.  Hence, here we look
 
        // for a zero divisor while being busy.  The always above us will then
 
        // look at this and halt a divide in the middle if we are trying to
 
        // divide by zero.
 
        //
 
        // Note that this works off of the 2BW-1 length vector.  If we can
 
        // simplify that, it should simplify our logic as well.
 
        initial zero_divisor = 1'b0;
 
        always @(posedge i_clk)
 
                // zero_divisor <= (r_divisor == 0)&&(r_busy);
 
                if (i_rst)
 
                        zero_divisor <= 1'b0;
 
                else if (i_wr)
 
                        zero_divisor <= (i_denominator == 0);
 
                else if (!r_busy)
 
                        zero_divisor <= 1'b0;
 
 
 
        // o_valid is part of the ZipCPU protocol.  It will be set to true
 
        // anytime our answer is valid and may be used by the calling module.
 
        // Indeed, the ZipCPU will halt (and ignore us) once the i_wr has been
 
        // set until o_valid gets set.
 
        //
 
        // Here, we clear o_valid on a reset, and any time we are on the last
 
        // bit while busy (provided the sign is zero, or we are dividing by
 
        // zero).  Since o_valid is self-clearing, we don't need to clear
 
        // it on an i_wr signal.
 
        initial o_valid = 1'b0;
        always @(posedge i_clk)
        always @(posedge i_clk)
                if ((i_rst)||(i_wr))
                if (i_rst)
                        o_valid <= 1'b0;
                        o_valid <= 1'b0;
                else if (r_busy)
                else if (r_busy)
                begin
                begin
                        if ((last_bit)||(zero_divisor))
                        if ((last_bit)||(zero_divisor))
                                o_valid <= (zero_divisor)||(~r_sign);
                                o_valid <= (zero_divisor)||(!r_sign);
                end else if (r_sign)
                end else if (r_sign)
                begin
                begin
                        o_valid <= (~zero_divisor); // 1'b1;
                        o_valid <= (!zero_divisor); // 1'b1;
                end else
                end else
                        o_valid <= 1'b0;
                        o_valid <= 1'b0;
 
 
 
        // Division by zero error reporting.  Anytime we detect a zero divisor,
 
        // we set our output error, and then hold it until we are valid and
 
        // everything clears.
        initial o_err = 1'b0;
        initial o_err = 1'b0;
        always @(posedge i_clk)
        always @(posedge i_clk)
                if((i_rst)||(o_valid))
                if((i_rst)||(o_valid))
                        o_err <= 1'b0;
                        o_err <= 1'b0;
                else if (((r_busy)||(r_sign))&&(zero_divisor))
                else if (((r_busy)||(r_sign))&&(zero_divisor))
                        o_err <= 1'b1;
                        o_err <= 1'b1;
                else
                else
                        o_err <= 1'b0;
                        o_err <= 1'b0;
 
 
 
        // r_bit
 
        //
 
        // Keep track of which "bit" of our divide we are on.  This number
 
        // ranges from 31 down to zero.  On any write, we set ourselves to
 
        // 5'h1f.  Otherwise, while we are busy (but not within the pre-sign
 
        // adjustment stage), we subtract one from our value on every clock.
 
        always @(posedge i_clk)
 
                if ((r_busy)&&(!pre_sign))
 
                        r_bit <= r_bit + {(LGBW){1'b1}};
 
                else
 
                        r_bit <= {(LGBW){1'b1}};
 
 
 
        // last_bit
 
        //
 
        // This logic replaces a lot of logic that was inside our giant state
 
        // machine with ... something simpler.  In particular, we'll use this
 
        // logic to determine we are processing our last bit.  The only trick
 
        // is, this bit needs to be set whenever (r_busy) and (r_bit == 0),
 
        // hence we need to set on (r_busy) and (r_bit == 1) so as to be set
 
        // when (r_bit == 0).
        initial last_bit = 1'b0;
        initial last_bit = 1'b0;
        always @(posedge i_clk)
        always @(posedge i_clk)
                if ((i_wr)||(pre_sign)||(i_rst))
                if (r_busy)
                        last_bit <= 1'b0;
 
                else if (r_busy)
 
                        last_bit <= (r_bit == {{(LGBW-1){1'b0}},1'b1});
                        last_bit <= (r_bit == {{(LGBW-1){1'b0}},1'b1});
 
                else
 
                        last_bit <= 1'b0;
 
 
 
        // pre_sign
 
        //
 
        // This is part of the state machine.  pre_sign indicates that we need
 
        // a extra clock to take the absolute value of our inputs.  It need only
 
        // be true for the one clock, and then it must clear itself.
 
        initial pre_sign = 1'b0;
        always @(posedge i_clk)
        always @(posedge i_clk)
                // if (i_rst) r_busy <= 1'b0;
 
                // else
 
                if (i_wr)
                if (i_wr)
                begin
 
                        //
 
                        // Set our values upon an initial command.  Here's
 
                        // where we come in and start.
 
                        //
 
                        // r_busy <= 1'b1;
 
                        //
 
                        o_quotient <= 0;
 
                        r_bit <= {(LGBW){1'b1}};
 
                        r_divisor <= {  i_denominator, {(BW-1){1'b0}} };
 
                        r_dividend <=  i_numerator;
 
                        r_sign <= 1'b0;
 
                        pre_sign <= i_signed;
                        pre_sign <= i_signed;
 
                else
 
                        pre_sign <= 1'b0;
 
 
 
        // As a result of our operation, we need to set the flags.  The most
 
        // difficult of these is the "Z" flag indicating that the result is
 
        // zero.  Here, we'll use the same logic that sets the low-order
 
        // bit to clear our zero flag, and leave the zero flag set in all
 
        // other cases.  Well ... not quite.  If we need to flip the sign of
 
        // our value, then we can't quite clear the zero flag ... yet.
 
        always @(posedge i_clk)
 
                if((r_busy)&&(r_divisor[(2*BW-2):(BW)] == 0)&&(!diff[BW]))
 
                        // If we are busy, the upper bits of our divisor are
 
                        // zero (i.e., we got the shift right), and the top
 
                        // (carry) bit of the difference is zero (no overflow),
 
                        // then we could subtract our divisor from our dividend
 
                        // and hence we add a '1' to the quotient, while setting
 
                        // the zero flag to false.
 
                        r_z <= 1'b0;
 
                else if ((!r_busy)&&(!r_sign))
                        r_z <= 1'b1;
                        r_z <= 1'b1;
                end else if (pre_sign)
 
 
        // r_dividend
 
        // This is initially the numerator.  On a signed divide, it then becomes
 
        // the absolute value of the numerator.  We'll subtract from this value
 
        // the divisor shifted as appropriate for every output bit we are
 
        // looking for--just as with traditional long division.
 
        always @(posedge i_clk)
 
                if (pre_sign)
                begin
                begin
                        //
                        // If we are doing a signed divide, then take the
                        // Note that we only come in here, for one clock, if
                        // absolute value of the dividend
                        // our initial value may have been signed.  If we are
 
                        // doing an unsigned divide, we then skip this step.
 
                        //
 
                        r_sign <= ((r_divisor[(2*BW-2)])^(r_dividend[(BW-1)]));
 
                        // Negate our dividend if necessary so that it becomes
 
                        // a magnitude only value
 
                        if (r_dividend[BW-1])
                        if (r_dividend[BW-1])
                                r_dividend <= -r_dividend;
                                r_dividend <= -r_dividend;
                        // Do the same with the divisor--rendering it into
                        // The begin/end block is important so we don't lose
                        // a magnitude only.
                        // the fact that on an else we don't do anything.
 
                end else if((r_busy)&&(r_divisor[(2*BW-2):(BW)]==0)&&(!diff[BW]))
 
                        // This is the condition whereby we set a '1' in our
 
                        // output quotient, and we subtract the (current)
 
                        // divisor from our dividend.  (The difference is
 
                        // already kept in the diff vector above.)
 
                        r_dividend <= diff[(BW-1):0];
 
                else if (!r_busy)
 
                        // Once we are done, and r_busy is no longer high, we'll
 
                        // always accept new values into our dividend.  This
 
                        // guarantees that, when i_wr is set, the new value
 
                        // is already set as desired.
 
                        r_dividend <=  i_numerator;
 
 
 
        initial r_divisor = 0;
 
        always @(posedge i_clk)
 
                if (pre_sign)
 
                begin
                        if (r_divisor[(2*BW-2)])
                        if (r_divisor[(2*BW-2)])
                                r_divisor[(2*BW-2):(BW-1)] <= -r_divisor[(2*BW-2):(BW-1)];
                                r_divisor[(2*BW-2):(BW-1)]
                        //
                                        <= -r_divisor[(2*BW-2):(BW-1)];
                        // We only do this stage for a single clock, so go on
 
                        // with the rest of the divide otherwise.
 
                        pre_sign <= 1'b0;
 
                end else if (r_busy)
                end else if (r_busy)
                begin
 
                        // While the divide is taking place, we examine each bit
 
                        // in turn here.
 
                        //
 
                        r_bit <= r_bit + {(LGBW){1'b1}}; // r_bit = r_bit - 1;
 
                        r_divisor <= { 1'b0, r_divisor[(2*BW-2):1] };
                        r_divisor <= { 1'b0, r_divisor[(2*BW-2):1] };
                        if (|r_divisor[(2*BW-2):(BW)])
                else
 
                        r_divisor <= {  i_denominator, {(BW-1){1'b0}} };
 
 
 
        // r_sign
 
        // is a flag for our state machine control(s).  r_sign will be set to
 
        // true any time we are doing a signed divide and the result must be
 
        // negative.  In that case, we take a final logic stage at the end of
 
        // the divide to negate the output.  This flag is what tells us we need
 
        // to do that.  r_busy will be true during the divide, then when r_busy
 
        // goes low, r_sign will be checked, then the idle/reset stage will have
 
        // been reached.  For this reason, we cannot set r_sign unless we are
 
        // up to something.
 
        initial r_sign = 1'b0;
 
        always @(posedge i_clk)
 
                if (pre_sign)
 
                        r_sign <= ((r_divisor[(2*BW-2)])^(r_dividend[(BW-1)]));
 
                else if (r_busy)
 
                        r_sign <= (r_sign)&&(!zero_divisor);
 
                else
 
                        r_sign <= 1'b0;
 
 
 
        always @(posedge i_clk)
 
                if (r_busy)
                        begin
                        begin
                        end else if (diff[BW])
                        o_quotient <= { o_quotient[(BW-2):0], 1'b0 };
 
                        if ((r_divisor[(2*BW-2):(BW)] == 0)&&(!diff[BW]))
                        begin
                        begin
                                // 
                                o_quotient[0] <= 1'b1;
                                // diff = r_dividend - r_divisor[(BW-1):0];
 
                                //
 
                                // If this value was negative, there wasn't
 
                                // enough value in the dividend to support
 
                                // pulling off a bit.  We'll move down a bit
 
                                // therefore and try again.
 
                                //
 
                        end else begin
 
                                //
 
                                // Put a '1' into our output accumulator.
 
                                // Subtract the divisor from the dividend,
 
                                // and then move on to the next bit
 
                                //
 
                                r_dividend <= diff[(BW-1):0];
 
                                o_quotient[r_bit[(LGBW-1):0]] <= 1'b1;
 
                                r_z <= 1'b0;
 
                        end
                        end
                        r_sign <= (r_sign)&&(~zero_divisor);
 
                end else if (r_sign)
                end else if (r_sign)
                begin
 
                        r_sign <= 1'b0;
 
                        o_quotient <= -o_quotient;
                        o_quotient <= -o_quotient;
                end
                else
 
                        o_quotient <= 0;
 
 
        // Set Carry on an exact divide
        // Set Carry on an exact divide
        wire    w_n;
        // Perhaps nothing uses this, but ... well, I suppose we could remove
 
        // this logic eventually, just ... not yet.
        always @(posedge i_clk)
        always @(posedge i_clk)
                r_c <= (r_busy)&&((diff == 0)||(r_dividend == 0));
                r_c <= (r_busy)&&((diff == 0)||(r_dividend == 0));
 
 
 
        // The last flag: Negative.  This flag is set assuming that the result
 
        // of the divide was negative (i.e., the high order bit is set).  This
 
        // will also be true of an unsigned divide--if the high order bit is
 
        // ever set upon completion.  Indeed, you might argue that there's no
 
        // logic involved.
 
        wire    w_n;
        assign w_n = o_quotient[(BW-1)];
        assign w_n = o_quotient[(BW-1)];
 
 
        assign o_flags = { 1'b0, w_n, r_c, r_z };
        assign o_flags = { 1'b0, w_n, r_c, r_z };
endmodule
endmodule
 
 
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