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// ============================================================================
//        __
//   \\__/ o\    (C) 2006-2016  Robert Finch, Stratford
//    \  __ /    All rights reserved.
//     \/_//     robfinch<remove>@finitron.ca
//       ||
//
// 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/>.    
//
//	fpRound.v
//  - floating point rounding unit
//  - parameterized width
//  - IEEE 754 representation
//
//	This unit takes a normalized floating point number in an
// expanded format and rounds it according to the IEEE-754
// standard. NaN's and infinities are not rounded.
// This module has a single cycle latency.
//
// Mode
// 0:    round to nearest even
// 1:    round to zero (truncate)
// 2:    round towards +infinity
// 3:    round towards -infinity
// ============================================================================
//
module fpRound(rm, i, o);
parameter WID = 32;
localparam MSB = WID-1;
localparam EMSB = WID==80 ? 14 :
                  WID==64 ? 10 :
				  WID==52 ? 10 :
				  WID==48 ? 10 :
				  WID==44 ? 10 :
				  WID==42 ? 10 :
				  WID==40 ?  9 :
				  WID==32 ?  7 :
				  WID==24 ?  6 : 4;
localparam FMSB = WID==80 ? 63 :
                  WID==64 ? 51 :
				  WID==52 ? 39 :
				  WID==48 ? 35 :
				  WID==44 ? 31 :
				  WID==42 ? 29 :
				  WID==40 ? 28 :
				  WID==32 ? 22 :
				  WID==24 ? 15 : 9;
 
input [2:0] rm;			// rounding mode
input [WID+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[EMSB+FMSB+5:FMSB+5];
wire [FMSB+4:0] mo1 = i[FMSB+4:0];
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})
	4'd0:	rnd = (g & r) | (r & s);	// round to nearest even
	4'd1:	rnd = 0;					// round to zero (truncate)
	4'd2:	rnd = (r | s) & !so;		// round towards +infinity
	4'd3:	rnd = (r | s) & so;			// round towards -infinity
	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+2:0] rounded = {xo1,mo1[FMSB+4:2]} + rnd;
wire carry = mo1[FMSB+4] & !rounded[FMSB+2];
 
assign so = i[WID+3];
assign xo = rounded[MSB+2:FMSB+3];
 
always @(rnd or xo or carry or dn or rounded or mo1)
	casex({rnd,&xo,carry,dn})
	4'b0xx0:	mo = mo1[FMSB+3:3];		// not rounding, not denormalized, => hide MSB
	4'b0xx1:	mo = mo1[FMSB+4:4];		// not rounding, denormalized
	4'b1000:	mo = rounded[FMSB+1:1];	// exponent didn't change, number was normalized, => hide MSB
	4'b1001:	mo = rounded[FMSB+2:2];	// exponent didn't change, but number was denormalized, => retain MSB
	4'b1010:	mo = rounded[FMSB+2:2];	// exponent incremented (new MSB generated), number was normalized, => hide 'extra (FMSB+2)' MSB
	4'b1011:	mo = rounded[FMSB+2:2];	// exponent incremented (new MSB generated), number was denormalized, number became normalized, => hide 'extra (FMSB+2)' MSB
	4'b11xx:	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 = 32;
localparam MSB = WID-1;
localparam EMSB = WID==80 ? 14 :
                  WID==64 ? 10 :
				  WID==52 ? 10 :
				  WID==48 ? 10 :
				  WID==44 ? 10 :
				  WID==42 ? 10 :
				  WID==40 ?  9 :
				  WID==32 ?  7 :
				  WID==24 ?  6 : 4;
localparam FMSB = WID==80 ? 63 :
                  WID==64 ? 51 :
				  WID==52 ? 39 :
				  WID==48 ? 35 :
				  WID==44 ? 31 :
				  WID==42 ? 29 :
				  WID==40 ? 28 :
				  WID==32 ? 22 :
				  WID==24 ? 15 : 9;
 
input clk;
input ce;
input [1:0] rm;			// rounding mode
input [WID+2:0] 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
 
module fpRound_tb();
 
wire [31:0] o1,o2,o3,o4,o5,o6;
 
fpRound u1 (3'd1, 36'h0, o1);         // zero for zero
fpRound u2 (3'd1, 36'h444444444, o2); // 
fpRound u3 (3'd1, 36'h444444444, o3); // 
 
endmodule