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`timescale 1ns / 1ps

// ============================================================================

//        __

//   \\__/ o\    (C) 2006-2018  Robert Finch, Waterloo

//    \  __ /    All rights reserved.

//     \/_//     robfinch<remove>@finitron.ca

//       ||

//

//      fpRound.v

//    - floating point rounding unit

//    - parameterized width

//    - IEEE 754 representation

//

//

// 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 3 of the License, or     

// (at your option) any later version.                                      

//                                                                          

// This source file 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 General Public License for more details.                             

//                                                                          

// You should have received a copy of the GNU General Public License        

// along with this program.  If not, see <http://www.gnu.org/licenses/>.    

//                                                                          

// ============================================================================

module fpRound(rm, i, o);

parameter WID = 128;

localparam MSB = WID-1;

localparam EMSB = WID==128 ? 14 :

                  WID==96 ? 14 :

                  WID==80 ? 14 :

                  WID==64 ? 10 :

                                  WID==52 ? 10 :

                                  WID==48 ? 11 :

                                  WID==44 ? 10 :

                                  WID==42 ? 10 :

                                  WID==40 ?  9 :

                                  WID==32 ?  7 :

                                  WID==24 ?  6 : 4;

localparam FMSB = WID==128 ? 111 :

                  WID==96 ? 79 :

                  WID==80 ? 63 :

                  WID==64 ? 51 :

                                  WID==52 ? 39 :

                                  WID==48 ? 34 :

                                  WID==44 ? 31 :

                                  WID==42 ? 29 :

                                  WID==40 ? 28 :

                                  WID==32 ? 22 :

                                  WID==24 ? 15 : 9;

input [2:0] rm;                  // rounding mode

input [MSB+3:0] i;               // intermediate format input

output [WID-1:0] o;              // rounded output

//------------------------------------------------------------

// variables

wire so;

wire [EMSB:0] xo;

reg  [FMSB:0] mo;

wire [EMSB:0] xo1 = i[MSB+2:FMSB+4];

wire [FMSB+3:0] mo1 = i[FMSB+3:0];

wire xInf = &xo1;

wire dn = !(|xo1);                      // denormalized input

assign o = {so,xo,mo};

wire g = i[2];  // guard bit: always the same bit for all operations

wire r = i[1];  // rounding bit

wire s = i[0];   // sticky bit

reg rnd;

// Compute the round bit

// Infinities and NaNs are not rounded!

always @(xInf,rm,g,r,s,so)

        case ({xInf,rm})

        3'd0:   rnd = (g & r) | (r & s);        // round to nearest even

        3'd1:   rnd = 0;                                 // round to zero (truncate)

        3'd2:   rnd = (r | s) & !so;            // round towards +infinity

        3'd3:   rnd = (r | s) & so;                     // round towards -infinity

        3'd4:   rnd = (r | s);

        default:        rnd = 0;                         // no rounding if exponent indicates infinite or NaN

        endcase

// round the number, check for carry

// note: inf. exponent checked above (if the exponent was infinite already, then no rounding occurs as rnd = 0)

// note: exponent increments if there is a carry (can only increment to infinity)

// performance note: use the carry chain to increment the exponent

wire [MSB:0] rounded = {xo1,mo1[FMSB+3:2]} + rnd;

wire carry = mo1[FMSB+3] & !rounded[FMSB+1];

assign so = i[MSB+3];

assign xo = rounded[MSB:FMSB+2];

always @(rnd or xo or carry or dn or rounded or mo1)

        casez({rnd,&xo,carry,dn})

        4'b0??0: mo = mo1[FMSB+2:2];             // not rounding, not denormalized, => hide MSB

        4'b0??1:        mo = mo1[FMSB+3:3];             // not rounding, denormalized

        4'b1000:        mo = rounded[FMSB  :0];  // exponent didn't change, number was normalized, => hide MSB

        4'b1001:        mo = rounded[FMSB+1:1]; // exponent didn't change, but number was denormalized, => retain MSB

        4'b1010:        mo = rounded[FMSB+1:1]; // exponent incremented (new MSB generated), number was normalized, => hide 'extra (FMSB+2)' MSB

        4'b1011:        mo = rounded[FMSB+1:1]; // exponent incremented (new MSB generated), number was denormalized, number became normalized, => hide 'extra (FMSB+2)' MSB

        4'b11??:        mo = 0;                                  // number became infinite, no need to check carry etc., rnd would be zero if input was NaN or infinite

        endcase

endmodule

// Round and register the output

module fpRoundReg(clk, ce, rm, i, o);

parameter WID = 128;

localparam MSB = WID-1;

localparam EMSB = WID==128 ? 14 :

                  WID==96 ? 14 :

                  WID==80 ? 14 :

                  WID==64 ? 10 :

                                  WID==52 ? 10 :

                                  WID==48 ? 11 :

                                  WID==44 ? 10 :

                                  WID==42 ? 10 :

                                  WID==40 ?  9 :

                                  WID==32 ?  7 :

                                  WID==24 ?  6 : 4;

localparam FMSB = WID==128 ? 111 :

                  WID==96 ? 79 :

                  WID==80 ? 63 :

                  WID==64 ? 51 :

                                  WID==52 ? 39 :

                                  WID==48 ? 34 :

                                  WID==44 ? 31 :

                                  WID==42 ? 29 :

                                  WID==40 ? 28 :

                                  WID==32 ? 22 :

                                  WID==24 ? 15 : 9;

input clk;

input ce;

input [2:0] rm;                  // rounding mode

input [MSB+3:0] i;               // expanded format input

output reg [WID-1:0] o;          // rounded output

wire [WID-1:0] o1;

fpRound #(WID) u1 (.rm(rm), .i(i), .o(o1) );

always @(posedge clk)

        if (ce)

                o <= o1;

endmodule