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

//        __

//   \\__/ o\    (C) 2006-2020  Robert Finch, Waterloo

//    \  __ /    All rights reserved.

//     \/_//     robfinch@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 .

//

//      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