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// ============================================================================
//        __
//   \\__/ o\    (C) 2006-2020  Robert Finch, Waterloo
//    \  __ /    All rights reserved.
//     \/_//     robfinch<remove>@finitron.ca
//       ||
//
//      fpMultiply.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
//
// ============================================================================

import fp::*;

module fpMultiply(clk, ce, a, b, o, sign_exe, inf, overflow, underflow);
input clk;
input ce;
input  [MSB:0] 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 u1a (.i(a), .sgn(sa), .exp(xa), .fract(fracta), .xz(a_dn), .vz(az), .inf(aInf), .nan(aNan) );
fpDecomp 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 (FPWID==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 (FPWID==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 (FPWID==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 [FPWID-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 #(FPWID) u16 (.clk(clk), .ce(ce), .i(a), .o(a1) );
delay2 #(FPWID) 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);
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       #(FPWID) u1 (clk, ce, a, b, o1, sign_exe1, inf1, overflow1, underflow1);
fpNormalize #(FPWID) u2(.clk(clk), .ce(ce), .under_i(underflow1), .i(o1), .o(fpn0) );
fpRound     #(FPWID) 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