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`timescale 1ns / 1ps

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

//        __

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

//    \  __ /    All rights reserved.

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

//       ||

//

//      fpSqrt.v

//    - floating point square root

//    - 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/>.    

//                                                                          

//      Floating Point Multiplier / Divider

//

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

module fpSqrt(rst, clk, ce, ld, a, o, done);

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;

localparam FX = (FMSB+2)*2-1;   // the MSB of the expanded fraction

localparam EX = FX + 1 + EMSB + 1 + 1 - 1;

input rst;

input clk;

input ce;

input ld;

input [MSB:0] a;

output [EX:0] o;

output done;

// registered outputs

reg sign_exe;

reg inf;

reg     overflow;

reg     underflow;

wire so;

wire [EMSB:0] xo;

wire [FX:0] mo;

// constants

wire [EMSB:0] infXp = {EMSB+1{1'b1}};    // infinite / NaN - all ones

// The following is the value for an exponent of zero, with the offset

// eg. 8'h7f for eight bit exponent, 11'h7ff for eleven bit exponent, etc.

wire [EMSB:0] bias = {1'b0,{EMSB{1'b1}}};        //2^0 exponent

// The following is a template for a quiet nan. (MSB=1)

wire [FMSB:0] qNaN  = {1'b1,{FMSB{1'b0}}};

// variables

wire [EMSB+2:0] ex1;     // sum of exponents

wire [FX:0] sqrto;

// Operands

wire sa;                        // sign bit

wire [EMSB:0] xa;        // exponent bits

wire [FMSB+1:0] fracta;

wire a_dn;                      // a/b is denormalized

wire az;

wire aInf;

wire aNan;

wire done1;

wire [7:0] lzcnt;

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

// - decode the input operand

// - derive basic information

// - calculate exponent

// - calculate fraction

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

fpDecomp #(WID) u1

(

        .i(a),

        .sgn(sa),

        .exp(xa),

        .fract(fracta),

        .xz(a_dn),

        .vz(az),

        .inf(aInf),

        .nan(aNan)

);

assign ex1 = xa + 8'd1;

assign so = 1'b0;                               // square root of positive numbers only

assign xo = (ex1 >> 1) + (bias >> 1);   // divide by 2 cuts the bias in half, so 1/2 of it is added back in.

assign mo = aNan ? {1'b1,a[FMSB:0],{FMSB+1{1'b0}}} : (sqrto << 36);

wire [FMSB+2:0] fracta1 = ex1[0] ? {1'b0,fracta} << 1 : {2'b0,fracta};

isqrt #(FX+1) u2

(

        .rst(rst),

        .clk(clk),

        .ce(ce),

        .ld(ld),

        .a({fracta1,{FMSB+1{1'b0}}}),

        .o(sqrto),

        .done(done)

);

assign o = aNan ? {sa,xa,mo} : {so,xo,mo};

endmodule

module fpSqrtnr(rst, clk, ce, ld, a, o, rm, done, inf);

parameter WID=32;

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;

localparam FX = (FMSB+2)*2-1;   // the MSB of the expanded fraction

localparam EX = FX + 1 + EMSB + 1 + 1 - 1;

input rst;

input clk;

input ce;

input ld;

input  [MSB:0] a;

output [MSB:0] o;

input [2:0] rm;

output done;

output inf;

wire [EX:0] o1;

wire inf1;

wire [MSB+3:0] fpn0;

wire done1;

fpSqrt      #(WID) u1 (rst, clk, ce, ld, a, o1, done1);

fpNormalize #(WID) u2(.clk(clk), .ce(ce), .under(1'b0), .i(o1), .o(fpn0) );

fpRoundReg  #(WID) u3(.clk(clk), .ce(ce), .rm(rm), .i(fpn0), .o(o) );

delay2      #(1)   u5(.clk(clk), .ce(ce), .i(inf1), .o(inf));

delay2          #(1)   u8(.clk(clk), .ce(ce), .i(done1), .o(done));

endmodule