EvoApproxLib^LITE

/***
* This code is a part of EvoApproxLib library (ehw.fit.vutbr.cz/approxlib) distributed under The MIT License.
* When used, please cite the following article(s): V. Mrazek, Z. Vasicek, L. Sekanina, H. Jiang and J. Han, "Scalable Construction of Approximate Multipliers With Formally Guaranteed Worst Case Error" in IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 26, no. 11, pp. 2572-2576, Nov. 2018. doi: 10.1109/TVLSI.2018.2856362 
* This file contains a circuit from a sub-set of pareto optimal circuits with respect to the pwr and mre parameters
***/
// MAE% = 0.048 %
// MAE = 2040348 
// WCE% = 0.20 %
// WCE = 8404992 
// WCRE% = 100.00 %
// EP% = 100.00 %
// MRE% = 1.34 %
// MSE = 61508.569e8 
// PDK45_PWR = 0.512 mW
// PDK45_AREA = 872.9 um2
// PDK45_DELAY = 1.64 ns

module mult8_cgp14ep_ep65536_wc16384_2_csamcsa (
    A,
    B,
    O
);

input [7:0] A;
input [7:0] B;
output [15:0] O;

wire sig_225,sig_267,sig_268,sig_299,sig_300,sig_302,sig_328,sig_331;

assign sig_225 = B[7] & A[6];
assign sig_267 = B[6] & A[7];
assign sig_268 = B[7] & A[7];
assign sig_299 = sig_225 | sig_267;
assign sig_300 = sig_225 & sig_267;
assign sig_302 = sig_299 | sig_268;
assign sig_328 = sig_268 ^ sig_300;
assign sig_331 = sig_328 ^ sig_302;

assign O[15] = sig_268;
assign O[14] = sig_331;
assign O[13] = 1'b0;
assign O[12] = 1'b0;
assign O[11] = 1'b0;
assign O[10] = 1'b0;
assign O[9] = 1'b0;
assign O[8] = 1'b0;
assign O[7] = 1'b0;
assign O[6] = 1'b0;
assign O[5] = 1'b0;
assign O[4] = 1'b0;
assign O[3] = 1'b0;
assign O[2] = 1'b0;
assign O[1] = 1'b0;
assign O[0] = 1'b0;

endmodule


module trun8_tam00b ( A, B, O );
  input [7:0] A;
  input [7:0] B;
  output [15:0] O;

  wire C_1_0,C_1_1,C_1_2,C_1_3,C_1_4,C_1_5,C_1_6,C_2_0,C_2_1,C_2_2,C_2_3,C_2_4,C_2_5,C_2_6,C_3_0,C_3_1,C_3_2,C_3_3,C_3_4,C_3_5,C_3_6,C_4_0,C_4_1,C_4_2,C_4_3,C_4_4,C_4_5,C_4_6,C_5_0,C_5_1,C_5_2,C_5_3,C_5_4,C_5_5,C_5_6,C_6_0,C_6_1,C_6_2,C_6_3,C_6_4,C_6_5,C_6_6,C_7_0,C_7_1,C_7_2,C_7_3,C_7_4,C_7_5,C_7_6,S_0_0,S_0_1,S_0_2,S_0_3,S_0_4,S_0_5,S_0_6,S_0_7,S_1_0,S_1_1,S_1_2,S_1_3,S_1_4,S_1_5,S_1_6,S_1_7,S_2_0,S_2_1,S_2_2,S_2_3,S_2_4,S_2_5,S_2_6,S_2_7,S_3_0,S_3_1,S_3_2,S_3_3,S_3_4,S_3_5,S_3_6,S_3_7,S_4_0,S_4_1,S_4_2,S_4_3,S_4_4,S_4_5,S_4_6,S_4_7,S_5_0,S_5_1,S_5_2,S_5_3,S_5_4,S_5_5,S_5_6,S_5_7,S_6_0,S_6_1,S_6_2,S_6_3,S_6_4,S_6_5,S_6_6,S_6_7,S_7_0,S_7_1,S_7_2,S_7_3,S_7_4,S_7_5,S_7_6,S_7_7,S_8_0,S_8_1,S_8_2,S_8_3,S_8_4,S_8_5,S_8_6,S_8_7;

  assign S_0_0 = (A[0] & B[0]);
  assign S_0_1 = (A[0] & B[1]);
  assign S_0_2 = (A[0] & B[2]);
  assign S_0_3 = (A[0] & B[3]);
  assign S_0_4 = (A[0] & B[4]);
  assign S_0_5 = (A[0] & B[5]);
  assign S_0_6 = (A[0] & B[6]);
  assign S_0_7 = (A[0] & B[7]);
  PDKGENHAX1 U13609 (.A(S_0_1), .B((A[1] & B[0])), .YS(S_1_0), .YC(C_1_0));
  PDKGENHAX1 U13610 (.A(S_0_2), .B((A[1] & B[1])), .YS(S_1_1), .YC(C_1_1));
  PDKGENHAX1 U13611 (.A(S_0_3), .B((A[1] & B[2])), .YS(S_1_2), .YC(C_1_2));
  PDKGENHAX1 U13612 (.A(S_0_4), .B((A[1] & B[3])), .YS(S_1_3), .YC(C_1_3));
  PDKGENHAX1 U13613 (.A(S_0_5), .B((A[1] & B[4])), .YS(S_1_4), .YC(C_1_4));
  PDKGENHAX1 U13614 (.A(S_0_6), .B((A[1] & B[5])), .YS(S_1_5), .YC(C_1_5));
  PDKGENHAX1 U13615 (.A(S_0_7), .B((A[1] & B[6])), .YS(S_1_6), .YC(C_1_6));
  assign S_1_7 = (A[1] & B[7]);
  PDKGENFAX1 U13617 (.A(S_1_1), .B(C_1_0), .C((A[2] & B[0])), .YS(S_2_0), .YC(C_2_0));
  PDKGENFAX1 U13618 (.A(S_1_2), .B(C_1_1), .C((A[2] & B[1])), .YS(S_2_1), .YC(C_2_1));
  PDKGENFAX1 U13619 (.A(S_1_3), .B(C_1_2), .C((A[2] & B[2])), .YS(S_2_2), .YC(C_2_2));
  PDKGENFAX1 U13620 (.A(S_1_4), .B(C_1_3), .C((A[2] & B[3])), .YS(S_2_3), .YC(C_2_3));
  PDKGENFAX1 U13621 (.A(S_1_5), .B(C_1_4), .C((A[2] & B[4])), .YS(S_2_4), .YC(C_2_4));
  PDKGENFAX1 U13622 (.A(S_1_6), .B(C_1_5), .C((A[2] & B[5])), .YS(S_2_5), .YC(C_2_5));
  PDKGENFAX1 U13623 (.A(S_1_7), .B(C_1_6), .C((A[2] & B[6])), .YS(S_2_6), .YC(C_2_6));
  assign S_2_7 = (A[2] & B[7]);
  PDKGENFAX1 U13625 (.A(S_2_1), .B(C_2_0), .C((A[3] & B[0])), .YS(S_3_0), .YC(C_3_0));
  PDKGENFAX1 U13626 (.A(S_2_2), .B(C_2_1), .C((A[3] & B[1])), .YS(S_3_1), .YC(C_3_1));
  PDKGENFAX1 U13627 (.A(S_2_3), .B(C_2_2), .C((A[3] & B[2])), .YS(S_3_2), .YC(C_3_2));
  PDKGENFAX1 U13628 (.A(S_2_4), .B(C_2_3), .C((A[3] & B[3])), .YS(S_3_3), .YC(C_3_3));
  PDKGENFAX1 U13629 (.A(S_2_5), .B(C_2_4), .C((A[3] & B[4])), .YS(S_3_4), .YC(C_3_4));
  PDKGENFAX1 U13630 (.A(S_2_6), .B(C_2_5), .C((A[3] & B[5])), .YS(S_3_5), .YC(C_3_5));
  PDKGENFAX1 U13631 (.A(S_2_7), .B(C_2_6), .C((A[3] & B[6])), .YS(S_3_6), .YC(C_3_6));
  assign S_3_7 = (A[3] & B[7]);
  PDKGENFAX1 U13633 (.A(S_3_1), .B(C_3_0), .C((A[4] & B[0])), .YS(S_4_0), .YC(C_4_0));
  PDKGENFAX1 U13634 (.A(S_3_2), .B(C_3_1), .C((A[4] & B[1])), .YS(S_4_1), .YC(C_4_1));
  PDKGENFAX1 U13635 (.A(S_3_3), .B(C_3_2), .C((A[4] & B[2])), .YS(S_4_2), .YC(C_4_2));
  PDKGENFAX1 U13636 (.A(S_3_4), .B(C_3_3), .C((A[4] & B[3])), .YS(S_4_3), .YC(C_4_3));
  PDKGENFAX1 U13637 (.A(S_3_5), .B(C_3_4), .C((A[4] & B[4])), .YS(S_4_4), .YC(C_4_4));
  PDKGENFAX1 U13638 (.A(S_3_6), .B(C_3_5), .C((A[4] & B[5])), .YS(S_4_5), .YC(C_4_5));
  PDKGENFAX1 U13639 (.A(S_3_7), .B(C_3_6), .C((A[4] & B[6])), .YS(S_4_6), .YC(C_4_6));
  assign S_4_7 = (A[4] & B[7]);
  PDKGENFAX1 U13641 (.A(S_4_1), .B(C_4_0), .C((A[5] & B[0])), .YS(S_5_0), .YC(C_5_0));
  PDKGENFAX1 U13642 (.A(S_4_2), .B(C_4_1), .C((A[5] & B[1])), .YS(S_5_1), .YC(C_5_1));
  PDKGENFAX1 U13643 (.A(S_4_3), .B(C_4_2), .C((A[5] & B[2])), .YS(S_5_2), .YC(C_5_2));
  PDKGENFAX1 U13644 (.A(S_4_4), .B(C_4_3), .C((A[5] & B[3])), .YS(S_5_3), .YC(C_5_3));
  PDKGENFAX1 U13645 (.A(S_4_5), .B(C_4_4), .C((A[5] & B[4])), .YS(S_5_4), .YC(C_5_4));
  PDKGENFAX1 U13646 (.A(S_4_6), .B(C_4_5), .C((A[5] & B[5])), .YS(S_5_5), .YC(C_5_5));
  PDKGENFAX1 U13647 (.A(S_4_7), .B(C_4_6), .C((A[5] & B[6])), .YS(S_5_6), .YC(C_5_6));
  assign S_5_7 = (A[5] & B[7]);
  PDKGENFAX1 U13649 (.A(S_5_1), .B(C_5_0), .C((A[6] & B[0])), .YS(S_6_0), .YC(C_6_0));
  PDKGENFAX1 U13650 (.A(S_5_2), .B(C_5_1), .C((A[6] & B[1])), .YS(S_6_1), .YC(C_6_1));
  PDKGENFAX1 U13651 (.A(S_5_3), .B(C_5_2), .C((A[6] & B[2])), .YS(S_6_2), .YC(C_6_2));
  PDKGENFAX1 U13652 (.A(S_5_4), .B(C_5_3), .C((A[6] & B[3])), .YS(S_6_3), .YC(C_6_3));
  PDKGENFAX1 U13653 (.A(S_5_5), .B(C_5_4), .C((A[6] & B[4])), .YS(S_6_4), .YC(C_6_4));
  PDKGENFAX1 U13654 (.A(S_5_6), .B(C_5_5), .C((A[6] & B[5])), .YS(S_6_5), .YC(C_6_5));
  PDKGENFAX1 U13655 (.A(S_5_7), .B(C_5_6), .C((A[6] & B[6])), .YS(S_6_6), .YC(C_6_6));
  assign S_6_7 = (A[6] & B[7]);
  PDKGENFAX1 U13657 (.A(S_6_1), .B(C_6_0), .C((A[7] & B[0])), .YS(S_7_0), .YC(C_7_0));
  PDKGENFAX1 U13658 (.A(S_6_2), .B(C_6_1), .C((A[7] & B[1])), .YS(S_7_1), .YC(C_7_1));
  PDKGENFAX1 U13659 (.A(S_6_3), .B(C_6_2), .C((A[7] & B[2])), .YS(S_7_2), .YC(C_7_2));
  PDKGENFAX1 U13660 (.A(S_6_4), .B(C_6_3), .C((A[7] & B[3])), .YS(S_7_3), .YC(C_7_3));
  PDKGENFAX1 U13661 (.A(S_6_5), .B(C_6_4), .C((A[7] & B[4])), .YS(S_7_4), .YC(C_7_4));
  PDKGENFAX1 U13662 (.A(S_6_6), .B(C_6_5), .C((A[7] & B[5])), .YS(S_7_5), .YC(C_7_5));
  PDKGENFAX1 U13663 (.A(S_6_7), .B(C_6_6), .C((A[7] & B[6])), .YS(S_7_6), .YC(C_7_6));
  assign S_7_7 = (A[7] & B[7]);
  assign {S_8_7, S_8_6, S_8_5, S_8_4, S_8_3, S_8_2, S_8_1, S_8_0} = {C_7_6, C_7_5, C_7_4, C_7_3, C_7_2, C_7_1, C_7_0} + {S_7_7, S_7_6, S_7_5, S_7_4, S_7_3, S_7_2, S_7_1};
  assign O = {S_8_7,S_8_6,S_8_5,S_8_4,S_8_3,S_8_2,S_8_1,S_8_0,S_7_0,S_6_0,S_5_0,S_4_0,S_3_0,S_2_0,S_1_0,S_0_0};

endmodule
module CLA32bit(a,b,c_in,sum,c_out);

input [31:0]a,b;
input c_in;
output [31:0]sum;
output c_out;

wire [31:0] sum_out,  p,  g;
wire [7:0] PPP, GGG;
wire [8:0] CC;

assign p[31:0] = a[31:0] ^ b[31:0];
assign g[31:0] = a[31:0] & b[31:0];

assign PPP[0]= p [3] & p [2] & p [1] & p [0];
assign PPP[1]= p [7] & p [6] & p [5] & p [4];
assign PPP[2]= p[11] & p[10] & p [9] & p [8];
assign PPP[3]= p[15] & p[14] & p[13] & p[12];
assign PPP[4]= p[19] & p[18] & p[17] & p[16];
assign PPP[5]= p[23] & p[22] & p[21] & p[20];
assign PPP[6]= p[27] & p[26] & p[25] & p[24];
assign PPP[7]= p[31] & p[30] & p[29] & p[28];

assign GGG[0]= g[3]  | (p [3] & g [2])  | (p [3] & p [2] & g [1])  | (p [3] & p [2] & p [1] & g [0]) ;
assign GGG[1]= g[7]  | (p [7] & g [6])  | (p [7] & p [6] & g [5])  | (p [7] & p [6] & p [5] & g [4]);
assign GGG[2]= g[11] | (p[11] & g[10])  | (p[11] & p[10] & g [9])  | (p[11] & p[10] & p [9] & g [8]);
assign GGG[3]= g[15] | (p[15] & g[14])  | (p[15] & p[14] & g[13])  | (p[15] & p[14] & p[13] & g[12]);
assign GGG[4]= g[19] | (p[19] & g[18])  | (p[19] & p[18] & g[17])  | (p[19] & p[18] & p[17] & g[16]);
assign GGG[5]= g[23] | (p[23] & g[22])  | (p[23] & p[22] & g[21])  | (p[23] & p[22] & p[21] & g[20]);
assign GGG[6]= g[27] | (p[27] & g[26])  | (p[27] & p[26] & g[25])  | (p[27] & p[26] & p[25] & g[24]);
assign GGG[7]= g[31] | (p[31] & g[30])  | (p[31] & p[30] & g[29])  | (p[31] & p[30] & p[29] & g[28]);
assign CC[0] = c_in;
assign CC[1] = GGG[0]  |  PPP[0]&  CC[0];
assign CC[2] = GGG[1]  |  PPP[1]&GGG[0]  |  PPP[1]&PPP[0]&  CC[0];
assign CC[3] = GGG[2]  |  PPP[2]&GGG[1]  |  PPP[2]&PPP[1]&GGG[0]  |  PPP[2]&PPP[1]&PPP[0]&  CC[0];
assign CC[4] = GGG[3]  |  PPP[3]&GGG[2]  |  PPP[3]&PPP[2]&GGG[1]  |  PPP[3]&PPP[2]&PPP[1]&GGG[0]  |  PPP[3]&PPP[2]&PPP[1]&PPP[0]&  CC[0];
assign CC[5] = GGG[4]  |  PPP[4]&GGG[3]  |  PPP[4]&PPP[3]&GGG[2]  |  PPP[4]&PPP[3]&PPP[2]&GGG[1]  |  PPP[4]&PPP[3]&PPP[2]&PPP[1]&GGG[0] |  PPP[4]&PPP[3]&PPP[2]&PPP[1]&PPP[0]&  CC[0];
assign CC[6] = GGG[5]  |  PPP[5]&GGG[4]  |  PPP[5]&PPP[4]&GGG[3]  |  PPP[5]&PPP[4]&PPP[3]&GGG[2]  |  PPP[5]&PPP[4]&PPP[3]&PPP[2]&GGG[1] |  PPP[5]&PPP[4]&PPP[3]&PPP[2]&PPP[1]&GGG[0] |  PPP[5]&PPP[4]&PPP[3]&PPP[2]&PPP[1]&PPP[0]& CC[0];
assign CC[7] = GGG[6]  | PPP[6]&GGG[5]  |  PPP[6]&PPP[5]&GGG[4]  |  PPP[6]&PPP[5]&PPP[4]&GGG[3]  |  PPP[6]&PPP[5]&PPP[4]&PPP[3]&GGG[2]  |  PPP[6]&PPP[5]&PPP[4]&PPP[3]&PPP[2]&GGG[1] |  PPP[6]&PPP[5]&PPP[4]&PPP[3]&PPP[2]&PPP[1]&GGG[0] |  PPP[6]&PPP[5]&PPP[4]&PPP[3]&PPP[2]&PPP[1]&PPP[0] & CC[0];
assign CC[8] = GGG[7] | PPP[7]&GGG[6]  | PPP[7]&PPP[6]&GGG[5]  |  PPP[7]&PPP[6]&PPP[5]&GGG[4]  |  PPP[7]&PPP[6]&PPP[5]&PPP[4]&GGG[3]  |  PPP[7]&PPP[6]&PPP[5]&PPP[4]&PPP[3]&GGG[2]  |  PPP[7]&PPP[6]&PPP[5]&PPP[4]&PPP[3]&PPP[2]&GGG[1] |  PPP[7]&PPP[6]&PPP[5]&PPP[4]&PPP[3]&PPP[2]&PPP[1]&GGG[0] |  PPP[7]&PPP[6]&PPP[5]&PPP[4]&PPP[3]&PPP[2]&PPP[1]&PPP[0] & CC[0];
cla_4bit cla4bit1(.aa(a  [3:0]),  .bb(b  [3:0]),  .cin(CC[0]),   .pp(p  [3:0]),  .gg(g  [3:0]),   .summ(sum  [3:0]));
cla_4bit cla4bit2(.aa(a  [7:4]),  .bb(b  [7:4]),  .cin(CC[1]),   .pp(p  [7:4]),  .gg(g  [7:4]),   .summ(sum  [7:4]));
cla_4bit cla4bit3(.aa(a [11:8]),  .bb(b [11:8]),  .cin(CC[2]),   .pp(p [11:8]),  .gg(g [11:8]),   .summ(sum [11:8]));
cla_4bit cla4bit4(.aa(a[15:12]),  .bb(b[15:12]),  .cin(CC[3]),   .pp(p[15:12]),  .gg(g[15:12]),   .summ(sum[15:12]));
cla_4bit cla4bit5(.aa(a[19:16]),  .bb(b[19:16]),  .cin(CC[4]),   .pp(p[19:16]),  .gg(g[19:16]),   .summ(sum[19:16]));
cla_4bit cla4bit6(.aa(a[23:20]),  .bb(b[23:20]),  .cin(CC[5]),   .pp(p[23:20]),  .gg(g[23:20]),   .summ(sum[23:20]));
cla_4bit cla4bit7(.aa(a[27:24]),  .bb(b[27:24]),  .cin(CC[6]),   .pp(p[27:24]),  .gg(g[27:24]),   .summ(sum[27:24]));
cla_4bit cla4bit8(.aa(a[31:28]),  .bb(b[31:28]),  .cin(CC[7]),   .pp(p[31:28]),  .gg(g[31:28]),   .summ(sum[31:28]));

assign c_out=CC[8];

endmodule
module cla_4bit(aa,bb,cin,summ,pp,gg);
input  [3:0] aa,bb,pp,gg;  
input cin;
output [3:0] summ;

wire [3:0] c;

   assign c[0] = cin;
   assign c[1] = gg[0] | (pp[0] & c[0]);
   assign c[2] = gg[1] | (pp[1] & gg[0]) | (pp[1] & pp[0] & c[0]);
   assign c[3] = gg[2] | (pp[2] & gg[1]) | (pp[2] & pp[1] & gg[0])| (pp[2] & pp[1] & pp[0] & c[0]);

   assign summ[3:0] = pp[3:0]  ^  c[3:0];
endmodule

`timescale 1ns/100ps
module mul16u_1UG ( input[15:0] A,
                   input[15:0] B,
                   output [31:0] O
                 );

wire [15:0] ll,lh,hl,hh;
wire [31:0] llhhlh_sum;
wire [31:0] shifted_llhh, shifted_lh, shifted_hl;

localparam MAX1 = 15;
localparam MIN1 = 8;

localparam MAX2 = 7;
localparam MIN2 = 0;

mult8_cgp14ep_ep65536_wc16384_2_csamcsa LxL (.A(A[MAX2:MIN2]), .B(B[MAX2:MIN2]), .O(ll));
mult8_cgp14ep_ep65536_wc16384_2_csamcsa HxL (.A(A[MAX1:MIN1]), .B(B[MAX2:MIN2]), .O(hl));
mult8_cgp14ep_ep65536_wc16384_2_csamcsa LxH (.A(A[MAX2:MIN2]), .B(B[MAX1:MIN1]), .O(lh));
trun8_tam00b HxH (.A(A[MAX1:MIN1]), .B(B[MAX1:MIN1]), .O(hh));

assign shifted_llhh = { hh, ll }; 
assign shifted_lh = { {8{1'b0}}, lh, {8{1'b0}}}; 
assign shifted_hl = { {8{1'b0}}, hl, {8{1'b0}}};
CLA32bit LLHHLH (.a(shifted_llhh), .b(shifted_lh), .c_in(1'b0), .sum(llhhlh_sum), .c_out());
CLA32bit SUMO (.a(llhhlh_sum), .b(shifted_hl), .c_in(1'b0), .sum(O), .c_out());

endmodule


/* mod */
module PDKGENFAX1( input A, input B, input C, output YS, output YC );
    assign YS = (A ^ B) ^ C;
    assign YC = (A & B) | (B & C) | (A & C);
endmodule
/* mod */
module PDKGENHAX1( input A, input B, output YS, output YC );
    assign YS = A ^ B;
    assign YC = A & B;
endmodule