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`timescale 1ns / 1ps

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

//        __

//   \\__/ o\    (C) 2019  Robert Finch, Waterloo

//    \  __ /    All rights reserved.

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

//       ||

//

//      fpFMA.v

//              - floating point fused multiplier + adder

//              - 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

//      

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

module fpFMA (clk, ce, op, rm, a, b, c, o, 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 clk;

input ce;

input op;               // operation 0 = add, 1 = subtract

input [2:0] rm;

input  [WID:1] a, b, c;

output [EX:0] o;

output inf;

// 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}}};

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

// Clock #1

// - decode the input operands

// - derive basic information

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

wire sa1, sb1, sc1;                     // sign bit

wire [EMSB:0] xa1, xb1, xc1;     // exponent bits

wire [FMSB+1:0] fracta1, fractb1, fractc1;       // includes unhidden bit

wire a_dn1, b_dn1, c_dn1;                       // a/b is denormalized

wire aNan1, bNan1, cNan1;

wire az1, bz1, cz1;

wire aInf1, bInf1, cInf1;

reg op1;

wire xcInf1;

fpDecompReg #(WID) u1a (.clk(clk), .ce(ce), .i(a), .sgn(sa1), .exp(xa1), .fract(fracta1), .xz(a_dn1), .vz(az1), .inf(aInf1), .nan(aNan1) );

fpDecompReg #(WID) u1b (.clk(clk), .ce(ce), .i(b), .sgn(sb1), .exp(xb1), .fract(fractb1), .xz(b_dn1), .vz(bz1), .inf(bInf1), .nan(bNan1) );

fpDecompReg #(WID) u1c (.clk(clk), .ce(ce), .i(c), .sgn(sc1), .exp(xc1), .fract(fractc1), .xz(c_dn1), .vz(cz1), .inf(cInf1), .nan(cNan1) );

always @(posedge clk)

        if (ce) op1 <= op;

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

// Clock #2

// 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

// Form partial products (clocks 2 to 5)

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

reg abz2;

reg [EMSB+2:0] ex2;

reg [EMSB:0] xc2;

reg realOp2;

reg xcInf2;

always @(posedge clk)

        if (ce) abz2 <= az1|bz1;

always @(posedge clk)

        if (ce) ex2 <= (xa1|a_dn1) + (xb1|b_dn1) - bias;

always @(posedge clk)

        if (ce) xc2 <= (xc1|c_dn1);

always @(posedge clk)

        if (ce) xcInf2 = &xc1;

// Figure out which operation is really needed an add or

// subtract ?

// If the signs are the same, use the orignal op,

// otherwise flip the operation

//  a +  b = add,+

//  a + -b = sub, so of larger

// -a +  b = sub, so of larger

// -a + -b = add,-

//  a -  b = sub, so of larger

//  a - -b = add,+

// -a -  b = add,-

// -a - -b = sub, so of larger

always @(posedge clk)

        if (ce) realOp2 <= op1 ^ (sa1 ^ sb1) ^ sc1;

reg [FX:0] fract5;

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;

reg [127:0] fract3a;

reg [127:0] fract3b;

reg [127:0] fract3c;

reg [127:0] fract3d;

reg [127:0] fract4a;

reg [127:0] fract4b;

        always @(posedge clk)

        if (ce) begin

                p00 <= fracta1[15: 0] * fractb1[15: 0];

                p01 <= fracta1[31:16] * fractb1[15: 0];

                p02 <= fracta1[47:32] * fractb1[15: 0];

                p03 <= fracta1[63:48] * fractb1[15: 0];

                p10 <= fracta1[15: 0] * fractb1[31:16];

                p11 <= fracta1[31:16] * fractb1[31:16];

                p12 <= fracta1[47:32] * fractb1[31:16];

                p13 <= fracta1[63:48] * fractb1[31:16];

                p20 <= fracta1[15: 0] * fractb1[47:32];

                p21 <= fracta1[31:16] * fractb1[47:32];

                p22 <= fracta1[47:32] * fractb1[47:32];

                p23 <= fracta1[63:48] * fractb1[47:32];

                p30 <= fracta1[15: 0] * fractb1[63:48];

                p31 <= fracta1[31:16] * fractb1[63:48];

                p32 <= fracta1[47:32] * fractb1[63:48];

                p33 <= fracta1[63:48] * fractb1[63:48];

        end

        always @(posedge clk)

        if (ce) begin

                fract3a <= {p33,p31,p20,p00};

                fract3b <= {p32,p12,p10,16'b0} + {p23,p03,p01,16'b0};

                fract3c <= {p22,p11,32'b0} + {p13,p02,32'b0};

                fract3d <= {p12,48'b0} + {p03,48'b0};

        end

        always @(posedge clk)

        if (ce) begin

                fract4a <= fract3a + fract3b;

                fract4b <= fract3c + fract3d;

        end

        always @(posedge clk)

        if (ce) begin

                fract5 <= fract4a + fract4b;

        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;

reg [71:0] fract3a;

reg [89:0] fract3b;

reg [107:0] fract3c;

reg [108:0] fract4a;

reg [108:0] fract4b;

        always @(posedge clk)

        if (ce) begin

                p00 <= fracta1[17: 0] * fractb1[17: 0];

                p01 <= fracta1[35:18] * fractb1[17: 0];

                p02 <= fracta1[52:36] * fractb1[17: 0];

                p10 <= fracta1[17: 0] * fractb1[35:18];

                p11 <= fracta1[35:18] * fractb1[35:18];

                p12 <= fracta1[52:36] * fractb1[35:18];

                p20 <= fracta1[17: 0] * fractb1[52:36];

                p21 <= fracta1[35:18] * fractb1[52:36];

                p22 <= fracta1[52:36] * fractb1[52:36];

        end

        always @(posedge clk)

        if (ce) begin

                fract3a <= {p02,p00};

                fract3b <= {p21,p10,18'b0} + {p12,p01,18'b0};

                fract3c <= {p22,p20,36'b0} + {p11,36'b0};

        end

        always @(posedge clk)

        if (ce) begin

                fract4a <= fract3a + fract3b;

                fract4b <= fract3c;

        end

        always @(posedge clk)

        if (ce) begin

                fract5 <= fract4a + fract4b;

        end

end

else if (WID==40) begin

reg [27:0] p00,p01,p02;

reg [27:0] p10,p11,p12;

reg [27:0] p20,p21,p22;

reg [79:0] fract3a;

reg [79:0] fract3b;

reg [79:0] fract3c;

reg [79:0] fract4a;

reg [79:0] fract4b;

        always @(posedge clk)

        if (ce) begin

                p00 <= fracta1[13: 0] * fractb1[13: 0];

                p01 <= fracta1[27:14] * fractb1[13: 0];

                p02 <= fracta1[39:28] * fractb1[13: 0];

                p10 <= fracta1[13: 0] * fractb1[27:14];

                p11 <= fracta1[27:14] * fractb1[27:14];

                p12 <= fracta1[39:28] * fractb1[27:14];

                p20 <= fracta1[13: 0] * fractb1[39:28];

                p21 <= fracta1[27:14] * fractb1[39:28];

                p22 <= fracta1[39:28] * fractb1[39:28];

        end

        always @(posedge clk)

        if (ce) begin

                fract3a <= {p02,p00};

                fract3b <= {p21,p10,18'b0} + {p12,p01,18'b0};

                fract3c <= {p22,p20,36'b0} + {p11,36'b0};

        end

        always @(posedge clk)

        if (ce) begin

                fract4a <= fract3a + fract3b;

                fract4b <= fract3c;

        end

        always @(posedge clk)

        if (ce) begin

                fract5 <= fract4a + fract4b;

        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;

reg [63:0] fract3a;

reg [63:0] fract3b;

reg [63:0] fract4;

        always @(posedge clk)

        if (ce) begin

                p00 <= fracta1[11: 0] * fractb1[11: 0];

                p01 <= fracta1[23:12] * fractb1[11: 0];

                p10 <= fracta1[11: 0] * fractb1[23:12];

                p11 <= fracta1[23:12] * fractb1[23:12];

        end

        always @(posedge clk)

        if (ce) begin

                fract3a <= {p11,p00};

                fract3b <= {p01,12'b0} + {p10,12'b0};

        end

        always @(posedge clk)

        if (ce) begin

                fract4 <= fract3a + fract3b;

        end

        always @(posedge clk)

        if (ce) begin

                fract5 <= fract4;

        end

end

else begin

reg [FX:0] p00;

reg [FX:0] fract3;

reg [FX:0] fract4;

        always @(posedge clk)

    if (ce) begin

        p00 <= fracta1 * fractb1;

    end

        always @(posedge clk)

    if (ce)

        fract3 <= p00;

        always @(posedge clk)

    if (ce)

        fract4 <= fract3;

        always @(posedge clk)

    if (ce)

        fract5 <= fract4;

end

endgenerate

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

// Clock #3

// Select zero exponent

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

reg [EMSB+2:0] ex3;

reg [EMSB:0] xc3;

always @(posedge clk)

        if (ce) ex3 <= abz2 ? 1'd0 : ex2;

always @(posedge clk)

        if (ce) xc3 <= xc2;

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

// Clock #4

// Generate partial products.

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

reg [EMSB+2:0] ex4;

reg [EMSB:0] xc4;

always @(posedge clk)

        if (ce) ex4 <= ex3;

always @(posedge clk)

        if (ce) xc4 <= xc3;

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

// Clock #5

// Sum partial products (above)

// compute multiplier overflow and underflow

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

// Status

reg under5;

reg over5;

reg [EMSB:0] ex5;

reg [EMSB:0] xc5;

wire aInf5, bInf5;

wire aNan5, bNan5;

wire qNaNOut5;

always @(posedge clk)

        if (ce) under5 <= ex4[EMSB+2];

always @(posedge clk)

        if (ce) over5 <= (&ex4[EMSB:0] | ex4[EMSB+1]) & !ex4[EMSB+2];

always @(posedge clk)

        if (ce) ex5 <= ex4[EMSB:0];

always @(posedge clk)

        if (ce) xc5 <= xc4;

delay4 u2a (.clk(clk), .ce(ce), .i(aInf1), .o(aInf5) );

delay4 u2b (.clk(clk), .ce(ce), .i(bInf1), .o(bInf5) );

// determine when a NaN is output

wire [WID-1:0] a5,b5;

delay4 u5 (.clk(clk), .ce(ce), .i((aInf1&bz1)|(bInf1&az1)), .o(qNaNOut5) );

delay4 u14 (.clk(clk), .ce(ce), .i(aNan1), .o(aNan5) );

delay4 u15 (.clk(clk), .ce(ce), .i(bNan1), .o(bNan5) );

delay5 #(WID) u16 (.clk(clk), .ce(ce), .i(a), .o(a5) );

delay5 #(WID) u17 (.clk(clk), .ce(ce), .i(b), .o(b5) );

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

// Clock #6

// - figure multiplier mantissa output

// - figure multiplier exponent output

// - correct xponent and mantissa for exceptional conditions

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

reg [FX:0] mo6;

reg [EMSB:0] ex6;

reg [EMSB:0] xc6;

reg exinf6;

wire [FMSB+1:0] fractc6;

delay5 #(FMSB+2) u61 (.clk(clk), .ce(ce), .i(fractc1), .o(fractc6) );

delay1 u62 (.clk(clk), .ce(ce), .i(under5), .o(under6));

always @(posedge clk)

        if (ce) xc6 <= xc5;

always @(posedge clk)

        if (ce)

                casez({aNan5,bNan5,qNaNOut5,aInf5,bInf5,over5})

                6'b1?????:  mo6 <= {1'b1,a5[FMSB:0],{FMSB+1{1'b0}}};

    6'b01????:  mo6 <= {1'b1,b5[FMSB:0],{FMSB+1{1'b0}}};

                6'b001???:      mo6 <= {1'b1,qNaN|3'd4,{FMSB+1{1'b0}}}; // multiply inf * zero

                6'b0001??:      mo6 <= 0;        // mul inf's

                6'b00001?:      mo6 <= 0;        // mul inf's

                6'b000001:      mo6 <= 0;        // mul overflow

                default:        mo6 <= fract5;

                endcase

always @(posedge clk)

        if (ce)

                casez({qNaNOut5|aNan5|bNan5,aInf5,bInf5,over5,under5})

                5'b1????:       ex6 <= infXp;   // qNaN - infinity * zero

                5'b01???:       ex6 <= infXp;   // 'a' infinite

                5'b001??:       ex6 <= infXp;   // 'b' infinite

                5'b0001?:       ex6 <= infXp;   // result overflow

                5'b00001:       ex6 <= ex5[EMSB:0];//0;          // underflow

                default:        ex6 <= ex5[EMSB:0];      // situation normal

                endcase

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

// Clock #7

// - prep for addition, determine greater operand

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

reg ex_gt_xc7;

reg xeq7;

reg ma_gt_mc7;

reg meq7;

wire az7, bz7, cz7;

wire realOp7;

// which has greater magnitude ? Used for sign calc

always @(posedge clk)

        if (ce) ex_gt_xc7 <= (ex6 > xc6) && !under6;

always @(posedge clk)

        if (ce) xeq7 <= (ex6==xc6) && !under6;

always @(posedge clk)

        if (ce) ma_gt_mc7 <= mo6 > {fractc6,{FMSB+1{1'b0}}};

always @(posedge clk)

        if (ce) meq7 <= mo6 == {fractc6,{FMSB+1{1'b0}}};

vtdl #(1) u71 (.clk(clk), .ce(ce), .a(4'd5), .d(az1), .q(az7));

vtdl #(1) u72 (.clk(clk), .ce(ce), .a(4'd5), .d(bz1), .q(bz7));

vtdl #(1) u73 (.clk(clk), .ce(ce), .a(4'd5), .d(cz1), .q(cz7));

vtdl #(1) u74 (.clk(clk), .ce(ce), .a(4'd4), .d(realOp2), .q(realOp7));

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

// Clock #8

// - prep for addition, determine greater operand

// - determine if result will be zero

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

reg a_gt_b8;

reg resZero8;

reg ex_gt_xc8;

wire [EMSB:0] ex8;

wire [EMSB:0] xc8;

wire xcInf8;

wire [2:0] rm8;

wire op8;

wire sa8, sb8, sc8;

delay2 #(EMSB+1) u81 (.clk(clk), .ce(ce), .i(ex6), .o(ex8));

delay2 #(EMSB+1) u82 (.clk(clk), .ce(ce), .i(xc6), .o(xc8));

vtdl #(1) u83 (.clk(clk), .ce(ce), .a(4'd5), .d(xcInf2), .q(xcInf8));

vtdl #(3) u84 (.clk(clk), .ce(ce), .a(4'd7), .d(rm), .q(rm8));

vtdl #(1) u85 (.clk(clk), .ce(ce), .a(4'd6), .d(op1), .q(op8));

vtdl #(1) u86 (.clk(clk), .ce(ce), .a(4'd7), .d(sa1 ^ sb1), .q(sa8));

vtdl #(1) u87 (.clk(clk), .ce(ce), .a(4'd7), .d(sc1), .q(sc8));

always @(posedge clk)

        if (ce) ex_gt_xc8 <= ex_gt_xc7;

always @(posedge clk)

        if (ce)

                a_gt_b8 <= ex_gt_xc7 || (xeq7 && ma_gt_mc7);

// Find out if the result will be zero.

always @(posedge clk)

        if (ce)

                resZero8 <= (realOp7 & xeq7 & meq7) ||  // subtract, same magnitude

                           ((az7 | bz7) & cz7);         // a or b zero and c zero

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

// CLock #9

// Compute output exponent and sign

//

// The output exponent is the larger of the two exponents,

// unless a subtract operation is in progress and the two

// numbers are equal, in which case the exponent should be

// zero.

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

reg so9;

reg [EMSB:0] ex9;

reg [EMSB:0] ex9a;

reg ex_gt_xc9;

reg [EMSB:0] xc9;

wire [FX:0] mo9;

wire [FMSB+1:0] fractc9;

wire under9;

always @(posedge clk)

        if (ce) ex_gt_xc9 <= ex_gt_xc8;

always @(posedge clk)

        if (ce) xc9 <= xc8;

always @(posedge clk)

        if (ce) ex9a <= ex8;

delay3 #(FX+1) u93 (.clk(clk), .ce(ce), .i(mo6), .o(mo9));

delay3 #(FMSB+2) u94 (.clk(clk), .ce(ce), .i(fractc6), .o(fractc9));

delay3 u95 (.clk(clk), .ce(ce), .i(under6), .o(under9));

always @(posedge clk)

        if (ce) ex9 <= resZero8 ? 0 : ex_gt_xc8 ? ex8 : xc8;