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`timescale 1ns / 1ps
// ============================================================================
//        __
//   \\__/ o\    (C) 2006-2018  Robert Finch, Waterloo
//    \  __ /    All rights reserved.
//     \/_//     robfinch<remove>@finitron.ca
//       ||
//
//	fpMul.v
//		- floating point multiplier
//		- two cycle latency
//		- can issue every clock cycle
//		- 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
//
//	This multiplier/divider handles denormalized numbers.
//	The output format is of an internal expanded representation
//	in preparation to be fed into a normalization unit, then
//	rounding. Basically, it's the same as the regular format
//	except the mantissa is doubled in size, the leading two
//	bits of which are assumed to be whole bits.
//
//
//	Floating Point Multiplier
//
//	Properties:
//	+-inf * +-inf = -+inf	(this is handled by exOver)
//	+-inf * 0     = QNaN
//	
//	1 sign number
//	8 exponent
//	48 mantissa
//
// ============================================================================
 
module fpMul (clk, ce, a, b, o, sign_exe, inf, overflow, underflow);
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 clk;
input ce;
input  [WID:1] a, b;
output [EX:0] o;
output sign_exe;
output inf;
output overflow;
output underflow;
 
reg [EMSB:0] xo1;		// extra bit for sign
reg [FX:0] mo1;
 
// 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
reg [FX:0] fract1,fract1a;
wire [FX:0] fracto;
wire [EMSB+2:0] ex1;	// sum of exponents
wire [EMSB  :0] ex2;
 
// Decompose the operands
wire sa, sb;			// sign bit
wire [EMSB:0] xa, xb;	// exponent bits
wire [FMSB+1:0] fracta, fractb;
wire a_dn, b_dn;			// a/b is denormalized
wire aNan, bNan, aNan1, bNan1;
wire az, bz;
wire aInf, bInf, aInf1, bInf1;
 
 
// -----------------------------------------------------------
// First clock
// - decode the input operands
// - derive basic information
// - calculate exponent
// - calculate fraction
// -----------------------------------------------------------
 
fpDecomp #(WID) u1a (.i(a), .sgn(sa), .exp(xa), .fract(fracta), .xz(a_dn), .vz(az), .inf(aInf), .nan(aNan) );
fpDecomp #(WID) u1b (.i(b), .sgn(sb), .exp(xb), .fract(fractb), .xz(b_dn), .vz(bz), .inf(bInf), .nan(bNan) );
 
// Compute the sum of the exponents.
// correct the exponent for denormalized operands
// adjust the sum by the exponent offset (subtract 127)
// mul: ex1 = xa + xb,	result should always be < 1ffh
assign ex1 = (az|bz) ? 0 : (xa|a_dn) + (xb|b_dn) - bias;
 
generate
if (WID==80) begin
reg [31:0] p00,p01,p02,p03;
reg [31:0] p10,p11,p12,p13;
reg [31:0] p20,p21,p22,p23;
reg [31:0] p30,p31,p32,p33;
	always @(posedge clk)
	if (ce) begin
		p00 <= fracta[15: 0] * fractb[15: 0];
		p01 <= fracta[31:16] * fractb[15: 0];
		p02 <= fracta[47:32] * fractb[15: 0];
		p03 <= fracta[63:48] * fractb[15: 0];
 
		p10 <= fracta[15: 0] * fractb[31:16];
		p11 <= fracta[31:16] * fractb[31:16];
		p12 <= fracta[47:32] * fractb[31:16];
		p13 <= fracta[63:48] * fractb[31:16];
 
		p20 <= fracta[15: 0] * fractb[47:32];
		p21 <= fracta[31:16] * fractb[47:32];
		p22 <= fracta[47:32] * fractb[47:32];
		p23 <= fracta[63:48] * fractb[47:32];
 
		p30 <= fracta[15: 0] * fractb[63:48];
		p31 <= fracta[31:16] * fractb[63:48];
		p32 <= fracta[47:32] * fractb[63:48];
		p33 <= fracta[63:48] * fractb[63:48];
 
		fract1 <= 	              				{p03,48'b0} + {p02,32'b0} + {p01,16'b0} + p00 +
								  {p13,64'b0} + {p12,48'b0} + {p11,32'b0} + {p10,16'b0} +
					{p23,80'b0} + {p22,64'b0} + {p21,48'b0} + {p20,32'b0} +
      {p33,96'b0} + {p32,80'b0} + {p31,64'b0} + {p30,48'b0}
				;
	end
end
else if (WID==64) begin
reg [35:0] p00,p01,p02;
reg [35:0] p10,p11,p12;
reg [35:0] p20,p21,p22;
	always @(posedge clk)
	if (ce) begin
		p00 <= fracta[17: 0] * fractb[17: 0];
		p01 <= fracta[35:18] * fractb[17: 0];
		p02 <= fracta[52:36] * fractb[17: 0];
		p10 <= fracta[17: 0] * fractb[35:18];
		p11 <= fracta[35:18] * fractb[35:18];
		p12 <= fracta[52:36] * fractb[35:18];
		p20 <= fracta[17: 0] * fractb[52:36];
		p21 <= fracta[35:18] * fractb[52:36];
		p22 <= fracta[52:36] * fractb[52:36];
		fract1 <= 	                            {p02,36'b0} + {p01,18'b0} + p00 +
								  {p12,54'b0} + {p11,36'b0} + {p10,18'b0} +
					{p22,72'b0} + {p21,54'b0} + {p20,36'b0}
				;
	end
end
else if (WID==32) begin
reg [23:0] p00,p01,p02;
reg [23:0] p10,p11,p12;
reg [23:0] p20,p21,p22;
	always @(posedge clk)
	if (ce) begin
		p00 <= fracta[11: 0] * fractb[11: 0];
		p01 <= fracta[23:12] * fractb[11: 0];
		p10 <= fracta[11: 0] * fractb[23:12];
		p11 <= fracta[23:12] * fractb[23:12];
		fract1 <= {p11,p00} + {p01,12'b0} + {p10,12'b0};
	end
end
else begin
	always @(posedge clk)
    if (ce) begin
    	fract1a <= fracta * fractb;
        fract1 <= fract1a;
    end
end
endgenerate
 
// Status
wire under1, over1;
wire under = ex1[EMSB+2];	// exponent underflow
wire over = (&ex1[EMSB:0] | ex1[EMSB+1]) & !ex1[EMSB+2];
 
delay2 #(EMSB+1) u3 (.clk(clk), .ce(ce), .i(ex1[EMSB:0]), .o(ex2) );
delay2 u2a (.clk(clk), .ce(ce), .i(aInf), .o(aInf1) );
delay2 u2b (.clk(clk), .ce(ce), .i(bInf), .o(bInf1) );
delay2 u6  (.clk(clk), .ce(ce), .i(under), .o(under1) );
delay2 u7  (.clk(clk), .ce(ce), .i(over), .o(over1) );
 
// determine when a NaN is output
wire qNaNOut;
wire [WID-1:0] a1,b1;
delay2 u5 (.clk(clk), .ce(ce), .i((aInf&bz)|(bInf&az)), .o(qNaNOut) );
delay2 u14 (.clk(clk), .ce(ce), .i(aNan), .o(aNan1) );
delay2 u15 (.clk(clk), .ce(ce), .i(bNan), .o(bNan1) );
delay2 #(WID) u16 (.clk(clk), .ce(ce), .i(a), .o(a1) );
delay2 #(WID) u17 (.clk(clk), .ce(ce), .i(b), .o(b1) );
 
// -----------------------------------------------------------
// Second clock
// - correct xponent and mantissa for exceptional conditions
// -----------------------------------------------------------
 
wire so1;
delay3 u8 (.clk(clk), .ce(ce), .i(sa ^ sb), .o(so1) );// two clock delay!
 
always @(posedge clk)
	if (ce)
		casez({qNaNOut|aNan1|bNan1,aInf1,bInf1,over1,under1})
		5'b1????:	xo1 = infXp;	// qNaN - infinity * zero
		5'b01???:	xo1 = infXp;	// 'a' infinite
		5'b001??:	xo1 = infXp;	// 'b' infinite
		5'b0001?:	xo1 = infXp;	// result overflow
		5'b00001:	xo1 = ex2[EMSB:0];//0;		// underflow
		default:	xo1 = ex2[EMSB:0];	// situation normal
		endcase
 
always @(posedge clk)
	if (ce)
		casez({aNan1,bNan1,qNaNOut,aInf1,bInf1,over1})
		6'b1?????:  mo1 = {1'b1,a1[FMSB:0],{FMSB+1{1'b0}}};
        6'b01????:  mo1 = {1'b1,b1[FMSB:0],{FMSB+1{1'b0}}};
		6'b001???:	mo1 = {1'b1,qNaN|3'd4,{FMSB+1{1'b0}}};	// multiply inf * zero
		6'b0001??:	mo1 = 0;	// mul inf's
		6'b00001?:	mo1 = 0;	// mul inf's
		6'b000001:	mo1 = 0;	// mul overflow
		default:	mo1 = fract1;
		endcase
 
delay3 u10 (.clk(clk), .ce(ce), .i(sa & sb), .o(sign_exe) );
delay1 u11 (.clk(clk), .ce(ce), .i(over1),  .o(overflow) );
delay1 u12 (.clk(clk), .ce(ce), .i(over1),  .o(inf) );
delay1 u13 (.clk(clk), .ce(ce), .i(under1), .o(underflow) );
 
assign o = {so1,xo1,mo1};
 
endmodule
 
 
// Multiplier with normalization and rounding.
 
module fpMulnr(clk, ce, a, b, o, rm, sign_exe, inf, overflow, underflow);
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 clk;
input ce;
input  [MSB:0] a, b;
output [MSB:0] o;
input [2:0] rm;
output sign_exe;
output inf;
output overflow;
output underflow;
 
wire [EX:0] o1;
wire sign_exe1, inf1, overflow1, underflow1;
wire [MSB+3:0] fpn0;
 
fpMul       #(WID) u1 (clk, ce, a, b, o1, sign_exe1, inf1, overflow1, underflow1);
fpNormalize #(WID) u2(.clk(clk), .ce(ce), .under(underflow1), .i(o1), .o(fpn0) );
fpRoundReg  #(WID) u3(.clk(clk), .ce(ce), .rm(rm), .i(fpn0), .o(o) );
delay2      #(1)   u4(.clk(clk), .ce(ce), .i(sign_exe1), .o(sign_exe));
delay2      #(1)   u5(.clk(clk), .ce(ce), .i(inf1), .o(inf));
delay2      #(1)   u6(.clk(clk), .ce(ce), .i(overflow1), .o(overflow));
delay2      #(1)   u7(.clk(clk), .ce(ce), .i(underflow1), .o(underflow));
endmodule