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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