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

//        __

//   \\__/ 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 FPWIDth

//              - 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/>.    

//                                                                          

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

`include "fpConfig.sv"

module fpFMA (clk, ce, op, rm, a, b, c, o, under, over, inf, zero);

parameter FPWID = 128;

parameter MUL_LATENCY = FPWID==128 ? 16 :

                                                                                                FPWID==80 ? 16 :

                                                                                                FPWID==64 ? 16 :

                                                                                                FPWID==32 ?  5 :

                                                                                                1;

`include "fpSize.sv"

input clk;

input ce;

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

input [2:0] rm;

input  [MSB:0] a, b, c;

output [EX:0] o;

output under;

output over;

output inf;

output zero;

// 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;

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

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

fpDecompReg #(FPWID) 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;

wire [FX:0] fract17;

generate begin : gMults

// 16 clocks for multiply

if (FPWID==128) begin

        mult114x114 umul1 (clk, ce, {1'b0,fracta1}, {1'b0,fractb1}, fract17[FX-1:0]);

        assign fract17[FX] = 1'b0;

end

else if (FPWID==80) begin

        mult64x64 umul2 (.CLK(clk), .CE(ce), .A(fracta1), .B(fractb1), .P(fract17[FX-1:0]));

        assign fract17[FX] = 1'b0;

end

else if (FPWID==64) begin

        mult53x53 umul3 (.CLK(clk), .CE(ce), .A(fracta1), .B(fractb1), .P(fract17[FX-1:0]));

        assign fract17[FX] = 1'b0;

end

else if (FPWID==32) begin

        mult24x24 umul4 (.CLK(clk), .CE(ce), .A(fracta1), .B(fractb1), .P(fract17[FX-1:0]));

        assign fract17[FX] = 1'b0;

end

else begin

        reg [FX:0] fract17a;

        always @(posedge clk)

                if (ce) fract17a <= fracta1 * fractb1;

        assign fract17 = fract17a;

end

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

wire under5;

wire over5;

wire [EMSB+2:0] ex5;

wire [EMSB:0] xc5;

wire aInf5, bInf5;

wire aNan5, bNan5;

wire qNaNOut5;

vtdl u5a (.clk(clk), .ce(ce), .a(MUL_LATENCY-5), .d(ex4[EMSB+2]), .q(under5));

vtdl u5b (.clk(clk), .ce(ce), .a(MUL_LATENCY-5), .d((&ex4[EMSB:0] | ex4[EMSB+1]) & !ex4[EMSB+2]), .q(over5));

vtdl #(EMSB+3) u5c (.clk(clk), .ce(ce), .a(MUL_LATENCY-5), .d(ex4), .q(ex5));

vtdl #(EMSB+1) u5d (.clk(clk), .ce(ce), .a(MUL_LATENCY-5), .d(xc4), .q(xc5));

vtdl u2a (.clk(clk), .ce(ce), .a(MUL_LATENCY-2), .d(aInf1), .q(aInf5) );

vtdl u2b (.clk(clk), .ce(ce), .a(MUL_LATENCY-2), .d(bInf1), .q(bInf5) );

// determine when a NaN is output

wire [MSB:0] a5,b5;

vtdl u5 (.clk(clk), .ce(ce), .a(MUL_LATENCY-2), .d((aInf1&bz1)|(bInf1&az1)), .q(qNaNOut5) );

vtdl u14 (.clk(clk), .ce(ce), .a(MUL_LATENCY-2), .d(aNan1), .q(aNan5) );

vtdl u15 (.clk(clk), .ce(ce), .a(MUL_LATENCY-2), .d(bNan1), .q(bNan5) );

vtdl #(MSB+1) u16 (.clk(clk), .ce(ce), .a(MUL_LATENCY-1), .d(a), .q(a5) );

vtdl #(MSB+1) u17 (.clk(clk), .ce(ce), .a(MUL_LATENCY-1), .d(b), .q(b5) );

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

// Clock #6

// - figure multiplier mantissa output

// - figure multiplier exponent output

// - correct xponent and mantissa for exceptional conditions

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

reg [FX:0] mo6;

reg [EMSB+2:0] ex6;

reg [EMSB:0] xc6;

wire [FMSB+1:0] fractc6;

wire under6;

vtdl #(FMSB+2) u61 (.clk(clk), .ce(ce), .a(MUL_LATENCY-1), .d(fractc1), .q(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'b1,1'b1,a5[FMSB-1:0],{FMSB+1{1'b0}}};

    6'b01????:  mo6 <= {1'b1,1'b1,b5[FMSB-1:0],{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 <= fract17;

                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;             //0;            // underflow

                default:        ex6 <= ex5;             // 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 <= $signed(ex6) > $signed({2'b0,xc6});

always @(posedge clk)

        if (ce) xeq7 <= (ex6=={2'b0,xc6});

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 #(1,32) u71 (.clk(clk), .ce(ce), .a(MUL_LATENCY), .d(az1), .q(az7));

vtdl #(1,32) u72 (.clk(clk), .ce(ce), .a(MUL_LATENCY), .d(bz1), .q(bz7));

vtdl #(1,32) u73 (.clk(clk), .ce(ce), .a(MUL_LATENCY), .d(cz1), .q(cz7));

vtdl #(1,32) u74 (.clk(clk), .ce(ce), .a(MUL_LATENCY-1), .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+2:0] ex8;

wire [EMSB:0] xc8;

wire xcInf8;

wire [2:0] rm8;

wire op8;

wire sa8, sc8;

delay2 #(EMSB+3) u81 (.clk(clk), .ce(ce), .i(ex6), .o(ex8));

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

vtdl #(1,32) u83 (.clk(clk), .ce(ce), .a(MUL_LATENCY-1), .d(xcInf2), .q(xcInf8));

vtdl #(3,32) u84 (.clk(clk), .ce(ce), .a(MUL_LATENCY+1), .d(rm), .q(rm8));

vtdl #(1,32) u85 (.clk(clk), .ce(ce), .a(MUL_LATENCY), .d(op1), .q(op8));

vtdl #(1,32) u86 (.clk(clk), .ce(ce), .a(MUL_LATENCY), .d(sa1 ^ sb1), .q(sa8));

vtdl #(1,32) u87 (.clk(clk), .ce(ce), .a(MUL_LATENCY), .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+2:0] ex9;

reg [EMSB+2:0] ex9a;

reg ex_gt_xc9;

reg [EMSB:0] xc9;

reg a_gt_c9;

wire [FX:0] mo9;

wire [FMSB+1:0] fractc9;

wire under9;

wire xeq9;

always @(posedge clk)

        if (ce) ex_gt_xc9 <= ex_gt_xc8;

always @(posedge clk)

        if (ce) a_gt_c9 <= a_gt_b8;

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));

delay2 u96 (.clk(clk), .ce(ce), .i(xeq7), .o(xeq9));

always @(posedge clk)

        if (ce) ex9 <= resZero8 ? 1'd0 : ex_gt_xc8 ? ex8 : {2'b0,xc8};

// Compute output sign

always @(posedge clk)

        if (ce)

        case ({resZero8,sa8,op8,sc8})   // synopsys full_case parallel_case

        4'b0000: so9 <= 0;                       // + + + = +

        4'b0001: so9 <= !a_gt_b8;       // + + - = sign of larger

        4'b0010: so9 <= !a_gt_b8;       // + - + = sign of larger

        4'b0011: so9 <= 0;                       // + - - = +

        4'b0100: so9 <= a_gt_b8;                // - + + = sign of larger

        4'b0101: so9 <= 1;                      // - + - = -

        4'b0110: so9 <= 1;                      // - - + = -

        4'b0111: so9 <= a_gt_b8;                // - - - = sign of larger

        4'b1000: so9 <= 0;                       //  A +  B, sign = +

        4'b1001: so9 <= rm8==3;         //  A + -B, sign = + unless rounding down

        4'b1010: so9 <= rm8==3;         //  A -  B, sign = + unless rounding down

        4'b1011: so9 <= 0;                       // +A - -B, sign = +

        4'b1100: so9 <= rm8==3;         // -A +  B, sign = + unless rounding down

        4'b1101: so9 <= 1;                      // -A + -B, sign = -

        4'b1110: so9 <= 1;                      // -A - +B, sign = -

        4'b1111: so9 <= rm8==3;         // -A - -B, sign = + unless rounding down

        endcase

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

// Clock #10

// Compute the difference in exponents, provides shift amount

// Note that ex9a will be negative for an underflow condition

// so it's added rather than subtracted from xc9 as -(-num)

// is the same as an add. The underflow is tracked rather than

// using extra bits in the exponent.

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

reg [EMSB+2:0] xdiff10;

reg [FX:0] mfs;

reg ops10;

// If the multiplier exponent was negative (underflowed) then

// the mantissa needs to be shifted right even more (until

// the exponent is zero. The total shift would be xc9-0-

// amount underflows which is xc9 + -ex9a.

always @(posedge clk)

        if (ce) xdiff10 <= ex_gt_xc9 ? ex9a - xc9

                                                                                : ex9a[EMSB+2] ? xc9 + (~ex9a+2'd1)

                                                                                : xc9 - ex9a;

// Determine which fraction to denormalize (the one with the

// smaller exponent is denormalized). If the exponents are equal

// denormalize the smaller fraction.

always @(posedge clk)

        if (ce) mfs <=

                xeq9 ? (a_gt_c9 ? {4'b0,fractc9,{FMSB+1{1'b0}}} : mo9)

                 : ex_gt_xc9 ? {4'b0,fractc9,{FMSB+1{1'b0}}} : mo9;

always @(posedge clk)

        if (ce) ops10 <= xeq9 ? (a_gt_c9 ? 1'b1 : 1'b0)

                                                                                                : (ex_gt_xc9 ? 1'b1 : 1'b0);

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

// Clock #11

// Limit the size of the shifter to only bits needed.

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

reg [7:0] xdif11;

always @(posedge clk)

        if (ce) xdif11 <= xdiff10 > FX+3 ? FX+3 : xdiff10;

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

// Clock #12

// Determine the sticky bit

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

wire sticky, sticky12;

wire [FX:0] mfs12;

wire [7:0] xdif12;

generate

begin

if (FPWID==128)

    redor128 u121 (.a(xdif11), .b({mfs,2'b0}), .o(sticky) );

else if (FPWID==80)

    redor80 u121 (.a(xdif11), .b({mfs,2'b0}), .o(sticky) );

else if (FPWID==64)

    redor64 u121 (.a(xdif11), .b({mfs,2'b0}), .o(sticky) );

else if (FPWID==32)

    redor32 u121 (.a(xdif11), .b({mfs,2'b0}), .o(sticky) );

end

endgenerate

// register inputs to shifter and shift

delay1 #(1)    u122(.clk(clk), .ce(ce), .i(sticky), .o(sticky12) );

delay1 #(8)    u123(.clk(clk), .ce(ce), .i(xdif11),   .o(xdif12) );

delay2 #(FX+1) u124(.clk(clk), .ce(ce), .i(mfs), .o(mfs12) );

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

// Clock #13

// - denormalize operand (shift right)

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

reg [FX+2:0] mfs13;

wire [FX:0] mo13;

wire ex_gt_xc13;

wire [FMSB+1:0] fractc13;

wire ops13;

delay4 #(FX+1) u131 (.clk(clk), .ce(ce), .i(mo9), .o(mo13));

delay4 u132 (.clk(clk), .ce(ce), .i(ex_gt_xc9), .o(ex_gt_xc13));

vtdl #(FMSB+2) u133 (.clk(clk), .ce(ce), .a(4'd3), .d(fractc9), .q(fractc13));

delay3 u134 (.clk(clk), .ce(ce), .i(ops10), .o(ops13));

always @(posedge clk)

        if (ce) mfs13 <= ({mfs12,2'b0} >> xdif12)|sticky12;

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

// Clock #14

// Sort operands

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

reg [FX+2:0] oa, ob;

wire a_gt_b14;

vtdl #(1) u141 (.clk(clk), .ce(ce), .a(4'd5), .d(a_gt_b8), .q(a_gt_b14));

always @(posedge clk)

        if (ce) oa <= ops13 ? {mo13,2'b00} : mfs13;

always @(posedge clk)

        if (ce) ob <= ops13 ? mfs13 : {fractc13,{FMSB+1{1'b0}},2'b00};

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

// Clock #15

// - Sort operands

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

reg [FX+2:0] oaa, obb;

wire realOp15;

wire [EMSB:0] ex15;

wire [EMSB:0] ex9c = ex9[EMSB+1] ? infXp : ex9[EMSB:0];

wire overflow15;

vtdl #(1) u151 (.clk(clk), .ce(ce), .a(4'd7), .d(realOp7), .q(realOp15));

vtdl #(EMSB+1) u152 (.clk(clk), .ce(ce), .a(4'd5), .d(ex9c), .q(ex15));

vtdl #(EMSB+1) u153 (.clk(clk), .ce(ce), .a(4'd5), .d(ex9[EMSB+1]| &ex9[EMSB:0]), .q(overflow15));

always @(posedge clk)

        if (ce) oaa <= a_gt_b14 ? oa : ob;

always @(posedge clk)

        if (ce) obb <= a_gt_b14 ? ob : oa;

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

// Clock #16

// - perform add/subtract

// - addition can generate an extra bit, subtract can't go negative

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

reg [FX+3:0] mab;

wire [FX:0] mo16;

wire [FMSB+1:0] fractc16;

wire Nan16;

wire cNan16;

wire aInf16, cInf16;

wire op16;

wire exinf16;

vtdl #(1) u161 (.clk(clk), .ce(ce), .a(4'd10), .d(qNaNOut5|aNan5|bNan5), .q(Nan16));

vtdl #(1) u162 (.clk(clk), .ce(ce), .a(4'd14), .d(cNan1), .q(cNan16));

vtdl #(1) u163 (.clk(clk), .ce(ce), .a(4'd9), .d(&ex6), .q(aInf16));

vtdl #(1) u164 (.clk(clk), .ce(ce), .a(4'd14), .d(cInf1), .q(cInf16));

vtdl #(1) u165 (.clk(clk), .ce(ce), .a(4'd14), .d(op1), .q(op16));

delay3 #(FX+1) u166 (.clk(clk), .ce(ce), .i(mo13), .o(mo16));

vtdl #(FMSB+2) u167 (.clk(clk), .ce(ce), .a(4'd6), .d(fractc9), .q(fractc16));

delay1 u169 (.clk(clk), .ce(ce), .i(&ex15), .o(exinf16));

always @(posedge clk)

        if (ce) mab <= realOp15 ? oaa - obb : oaa + obb;

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

// Clock #17

// - adjust for Nans

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