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## [/] [zipcpu/] [trunk/] [rtl/] [core/] [**div.v**] - Rev 205

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//////////////////////////////////////////////////////////////////////////////// // // Filename: div.v // // Project: Zip CPU -- a small, lightweight, RISC CPU soft core // // 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. // Gisselquist Technology, LLC // //////////////////////////////////////////////////////////////////////////////// // // Copyright (C) 2015-2017, Gisselquist Technology, LLC // // 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 // by the Free Software Foundation, either version 3 of the License, or (at // your option) any later version. // // This program is distributed in the hope that it will be useful, but WITHOUT // ANY WARRANTY; without even the implied warranty of MERCHANTIBILITY or // FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License // 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, // http://www.gnu.org/licenses/gpl.html // // //////////////////////////////////////////////////////////////////////////////// // // // `include "cpudefs.v" // module div(i_clk, i_rst, i_wr, i_signed, i_numerator, i_denominator, o_busy, o_valid, o_err, o_quotient, o_flags); parameter BW=32, LGBW = 5; input i_clk, i_rst; // Input parameters input i_wr, i_signed; input [(BW-1):0] i_numerator, i_denominator; // Output parameters output reg o_busy, o_valid, o_err; output reg [(BW-1):0] o_quotient; output wire [3:0] o_flags; // r_busy is an internal busy register. It will clear one clock // before we are valid, so it can't be o_busy ... // reg r_busy; reg [(2*BW-2):0] r_divisor; reg [(BW-1):0] r_dividend; wire [(BW):0] diff; // , xdiff[(BW-1):0]; assign diff = r_dividend - r_divisor[(BW-1):0]; // assign xdiff= r_dividend - { 1'b0, r_divisor[(BW-1):1] }; reg r_sign, pre_sign, r_z, r_c, last_bit; reg [(LGBW-1):0] r_bit; reg zero_divisor; // 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; always @(posedge i_clk) if (i_rst) r_busy <= 1'b0; else if (i_wr) r_busy <= 1'b1; else if ((last_bit)||(zero_divisor)) 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; always @(posedge i_clk) if (i_rst) o_busy <= 1'b0; else if (i_wr) o_busy <= 1'b1; else if (((last_bit)&&(~r_sign))||(zero_divisor)) o_busy <= 1'b0; else if (~r_busy) 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) if (i_rst) o_valid <= 1'b0; else if (r_busy) begin if ((last_bit)||(zero_divisor)) o_valid <= (zero_divisor)||(!r_sign); end else if (r_sign) begin o_valid <= (!zero_divisor); // 1'b1; end else 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; always @(posedge i_clk) if((i_rst)||(o_valid)) o_err <= 1'b0; else if (((r_busy)||(r_sign))&&(zero_divisor)) o_err <= 1'b1; else 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; always @(posedge i_clk) if (r_busy) 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) if (i_wr) 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_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 // If we are doing a signed divide, then take the // absolute value of the dividend if (r_dividend[BW-1]) r_dividend <= -r_dividend; // The begin/end block is important so we don't lose // 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)]) r_divisor[(2*BW-2):(BW-1)] <= -r_divisor[(2*BW-2):(BW-1)]; end else if (r_busy) r_divisor <= { 1'b0, r_divisor[(2*BW-2):1] }; 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 o_quotient <= { o_quotient[(BW-2):0], 1'b0 }; if ((r_divisor[(2*BW-2):(BW)] == 0)&&(!diff[BW])) begin o_quotient[0] <= 1'b1; end end else if (r_sign) o_quotient <= -o_quotient; else o_quotient <= 0; // Set Carry on an exact divide // Perhaps nothing uses this, but ... well, I suppose we could remove // this logic eventually, just ... not yet. always @(posedge i_clk) 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 o_flags = { 1'b0, w_n, r_c, r_z }; endmodule

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