// parallel square root 32 bit input, 16 bit output
// sm basic building block is a subtractor multiplexer
// if u=0 then return x otherwise return x-y taking into account borrow
define sm(y, u, x, b, bout, dout)
circuits
 bout<=(~x&y&b) |(x&y&b)|(~x&y&~b)|(~x&~y&b) after 1ns;
 dout<=(((~x&y&~b)|(x&y&b)|(~x&~y&b)|(x&~y&~b))&u)|(x&~u) after 1ns;
end circuits;
end sm;

// special last layer, does not need u input or dout
define sml(y, x, b, bout)
circuits
 bout<=(~x&y&b) |(x&y&b)|(~x&y&~b)|(~x&~y&b) after 1ns;
end circuits;
end sml;

// special high order bit, produces u = ~bout
define smu(y, x, b, u)
circuits
 u<=~((~x&y&b) |(x&y&b)|(~x&y&~b)|(~x&~y&b)) after 1ns;
end circuits;
end smu;

// 32 bit input sqrt gives 16 bits out
define sqrt32(p[32], u[16])
signal b0[1];
signal b1[3];
signal b2[4];
signal b3[5];
signal b4[6];
signal b5[7];
signal b6[8];
signal b7[9];
signal b8[10];
signal b9[11];
signal b10[12];
signal b11[13];
signal b12[14];
signal b13[15];
signal b14[16];
signal b15[17];
signal x0[2];
signal x1[3];
signal x2[4];
signal x3[5];
signal x4[6];
signal x5[7];
signal x6[8];
signal x7[9];
signal x8[10];
signal x9[11];
signal x10[12];
signal x11[13];
signal x12[14];
signal x13[15];
signal x14[16];
signal ubar;

circuits

 b00   use sm(#b1,   u[15], p[30],  #b0,    b0[0],  x0[0]); 
 b01   use sm(#b0,   u[15], p[31],  b0[0],  ubar,   x0[1]);
 u[15]<=~ubar after 1ns;

 b10   use sm(#b1,   u[14], p[28],  #b0,    b1[0],  x1[0]); 
 b11   use sm(#b0,   u[14], p[29],  b1[0],  b1[1],  x1[1]);
 b12   use sm(u[15], u[14], x0[0],  b1[1],  b1[2],  x1[2]); 
 b13   use smu(#b0,         x0[1],  b1[2],  u[14]);

 b20   use sm(#b1,   u[13], p[26],  #b0,    b2[0],  x2[0]); 
 b21   use sm(#b0,   u[13], p[27],  b2[0],  b2[1],  x2[1]);
 b22   use sm(u[14], u[13], x1[0],  b2[1],  b2[2],  x2[2]); 
 b23   use sm(u[15], u[13], x1[1],  b2[2],  b2[3],  x2[3]); 
 b24   use smu(#b0,         x1[2],  b2[3],  u[13]);

 b30   use sm(#b1,   u[12], p[24],  #b0,    b3[0],  x3[0]);  
 b31   use sm(#b0,   u[12], p[25],  b3[0],  b3[1],  x3[1]);
 b32   use sm(u[13], u[12], x2[0],  b3[1],  b3[2],  x3[2]); 
 b33   use sm(u[14], u[12], x2[1],  b3[2],  b3[3],  x3[3]); 
 b34   use sm(u[15], u[12], x2[2],  b3[3],  b3[4],  x3[4]); 
 b35   use smu(#b0,         x2[3],  b3[4],  u[12]);

 b40   use sm(#b1,   u[11], p[22],  #b0,    b4[0],  x4[0]);  
 b41   use sm(#b0,   u[11], p[23],  b4[0],  b4[1],  x4[1]);
 b42   use sm(u[12], u[11], x3[0],  b4[1],  b4[2],  x4[2]); 
 b43   use sm(u[13], u[11], x3[1],  b4[2],  b4[3],  x4[3]); 
 b44   use sm(u[14], u[11], x3[2],  b4[3],  b4[4],  x4[4]); 
 b45   use sm(u[15], u[11], x3[3],  b4[4],  b4[5],  x4[5]); 
 b46   use smu(#b0,         x3[4],  b4[5],  u[11]);

 b50   use sm(#b1,   u[10], p[20],  #b0,    b5[0],  x5[0]);  
 b51   use sm(#b0,   u[10], p[21],  b5[0],  b5[1],  x5[1]);
 b52   use sm(u[11], u[10], x4[0],  b5[1],  b5[2],  x5[2]); 
 b53   use sm(u[12], u[10], x4[1],  b5[2],  b5[3],  x5[3]); 
 b54   use sm(u[13], u[10], x4[2],  b5[3],  b5[4],  x5[4]); 
 b55   use sm(u[14], u[10], x4[3],  b5[4],  b5[5],  x5[5]); 
 b56   use sm(u[15], u[10], x4[4],  b5[5],  b5[6],  x5[6]); 
 b57   use smu(#b0,         x4[5],  b5[6],  u[10]);

 b60   use sm(#b1,   u[9],  p[18],  #b0,    b6[0],  x6[0]);  
 b61   use sm(#b0,   u[9],  p[19],  b6[0],  b6[1],  x6[1]);
 b62   use sm(u[10], u[9],  x5[0],  b6[1],  b6[2],  x6[2]); 
 b63   use sm(u[11], u[9],  x5[1],  b6[2],  b6[3],  x6[3]); 
 b64   use sm(u[12], u[9],  x5[2],  b6[3],  b6[4],  x6[4]); 
 b65   use sm(u[13], u[9],  x5[3],  b6[4],  b6[5],  x6[5]); 
 b66   use sm(u[14], u[9],  x5[4],  b6[5],  b6[6],  x6[6]); 
 b67   use sm(u[15], u[9],  x5[5],  b6[6],  b6[7],  x6[7]); 
 b68   use smu(#b0,         x5[6],  b6[7],  u[9]);

 b70   use sm(#b1,   u[8],  p[16],  #b0,    b7[0],  x7[0]);  
 b71   use sm(#b0,   u[8],  p[17],  b7[0],  b7[1],  x7[1]);
 b72   use sm(u[9],  u[8],  x6[0],  b7[1],  b7[2],  x7[2]); 
 b73   use sm(u[10], u[8],  x6[1],  b7[2],  b7[3],  x7[3]); 
 b74   use sm(u[11], u[8],  x6[2],  b7[3],  b7[4],  x7[4]); 
 b75   use sm(u[12], u[8],  x6[3],  b7[4],  b7[5],  x7[5]); 
 b76   use sm(u[13], u[8],  x6[4],  b7[5],  b7[6],  x7[6]); 
 b77   use sm(u[14], u[8],  x6[5],  b7[6],  b7[7],  x7[7]); 
 b78   use sm(u[15], u[8],  x6[6],  b7[7],  b7[8],  x7[8]); 
 b79   use smu(#b0,         x6[7],  b7[8],  u[8]);

 b80   use sm(#b1,   u[7],  p[14],  #b0,    b8[0],  x8[0]);  
 b81   use sm(#b0,   u[7],  p[15],  b8[0],  b8[1],  x8[1]);
 b82   use sm(u[8],  u[7],  x7[0],  b8[1],  b8[2],  x8[2]); 
 b83   use sm(u[9],  u[7],  x7[1],  b8[2],  b8[3],  x8[3]); 
 b84   use sm(u[10], u[7],  x7[2],  b8[3],  b8[4],  x8[4]); 
 b85   use sm(u[11], u[7],  x7[3],  b8[4],  b8[5],  x8[5]); 
 b86   use sm(u[12], u[7],  x7[4],  b8[5],  b8[6],  x8[6]); 
 b87   use sm(u[13], u[7],  x7[5],  b8[6],  b8[7],  x8[7]); 
 b88   use sm(u[14], u[7],  x7[6],  b8[7],  b8[8],  x8[8]); 
 b89   use sm(u[15], u[7],  x7[7],  b8[8],  b8[9],  x8[9]); 
 b810  use smu(#b0,         x7[8],  b8[9],  u[7]);

 b90   use sm(#b1,   u[6],  p[12],  #b0,    b9[0],  x9[0]);  
 b91   use sm(#b0,   u[6],  p[13],  b9[0],  b9[1],  x9[1]);
 b92   use sm(u[7],  u[6],  x8[0],  b9[1],  b9[2],  x9[2]); 
 b93   use sm(u[8],  u[6],  x8[1],  b9[2],  b9[3],  x9[3]); 
 b94   use sm(u[9],  u[6],  x8[2],  b9[3],  b9[4],  x9[4]); 
 b95   use sm(u[10], u[6],  x8[3],  b9[4],  b9[5],  x9[5]); 
 b96   use sm(u[11], u[6],  x8[4],  b9[5],  b9[6],  x9[6]); 
 b97   use sm(u[12], u[6],  x8[5],  b9[6],  b9[7],  x9[7]); 
 b98   use sm(u[13], u[6],  x8[6],  b9[7],  b9[8],  x9[8]); 
 b99   use sm(u[14], u[6],  x8[7],  b9[8],  b9[9],  x9[9]); 
 b910  use sm(u[15], u[6],  x8[8],  b9[9],  b9[10], x9[10]); 
 b911  use smu(#b0,         x8[9],  b9[10], u[6]);

 b100  use sm(#b1,   u[5],  p[10],  #b0,     b10[0],   x10[0]);  
 b101  use sm(#b0,   u[5],  p[11],  b10[0],  b10[1],   x10[1]);
 b102  use sm(u[6],  u[5],  x9[0],  b10[1],  b10[2],   x10[2]); 
 b103  use sm(u[7],  u[5],  x9[1],  b10[2],  b10[3],   x10[3]); 
 b104  use sm(u[8],  u[5],  x9[2],  b10[3],  b10[4],   x10[4]); 
 b105  use sm(u[9],  u[5],  x9[3],  b10[4],  b10[5],   x10[5]); 
 b106  use sm(u[10], u[5],  x9[4],  b10[5],  b10[6],   x10[6]); 
 b107  use sm(u[11], u[5],  x9[5],  b10[6],  b10[7],   x10[7]); 
 b108  use sm(u[12], u[5],  x9[6],  b10[7],  b10[8],   x10[8]); 
 b109  use sm(u[13], u[5],  x9[7],  b10[8],  b10[9],   x10[9]); 
 b1010 use sm(u[14], u[5],  x9[8],  b10[9],  b10[10],  x10[10]); 
 b1011 use sm(u[15], u[5],  x9[9],  b10[10], b10[11],  x10[11]); 
 b1012 use smu(#b0,         x9[10], b10[11], u[5]);

 b110  use sm(#b1,   u[4],  p[8],    #b0,     b11[0],   x11[0]);  
 b111  use sm(#b0,   u[4],  p[9],    b11[0],  b11[1],   x11[1]);
 b112  use sm(u[5],  u[4],  x10[0],  b11[1],  b11[2],   x11[2]); 
 b113  use sm(u[6],  u[4],  x10[1],  b11[2],  b11[3],   x11[3]); 
 b114  use sm(u[7],  u[4],  x10[2],  b11[3],  b11[4],   x11[4]); 
 b115  use sm(u[8],  u[4],  x10[3],  b11[4],  b11[5],   x11[5]); 
 b116  use sm(u[9],  u[4],  x10[4],  b11[5],  b11[6],   x11[6]); 
 b117  use sm(u[10], u[4],  x10[5],  b11[6],  b11[7],   x11[7]); 
 b118  use sm(u[11], u[4],  x10[6],  b11[7],  b11[8],   x11[8]); 
 b119  use sm(u[12], u[4],  x10[7],  b11[8],  b11[9],   x11[9]); 
 b1110 use sm(u[13], u[4],  x10[8],  b11[9],  b11[10],  x11[10]); 
 b1111 use sm(u[14], u[4],  x10[9],  b11[10], b11[11],  x11[11]); 
 b1112 use sm(u[15], u[4],  x10[10], b11[11], b11[12],  x11[12]); 
 b1113 use smu(#b0,         x10[11], b11[12], u[4]);

 b120  use sm(#b1,   u[3],  p[6],    #b0,     b12[0],   x12[0]);  
 b121  use sm(#b0,   u[3],  p[7],    b12[0],  b12[1],   x12[1]);
 b122  use sm(u[4],  u[3],  x11[0],  b12[1],  b12[2],   x12[2]); 
 b123  use sm(u[5],  u[3],  x11[1],  b12[2],  b12[3],   x12[3]); 
 b124  use sm(u[6],  u[3],  x11[2],  b12[3],  b12[4],   x12[4]); 
 b125  use sm(u[7],  u[3],  x11[3],  b12[4],  b12[5],   x12[5]); 
 b126  use sm(u[8],  u[3],  x11[4],  b12[5],  b12[6],   x12[6]); 
 b127  use sm(u[9],  u[3],  x11[5],  b12[6],  b12[7],   x12[7]); 
 b128  use sm(u[10], u[3],  x11[6],  b12[7],  b12[8],   x12[8]); 
 b129  use sm(u[11], u[3],  x11[7],  b12[8],  b12[9],   x12[9]); 
 b1210 use sm(u[12], u[3],  x11[8],  b12[9],  b12[10],  x12[10]); 
 b1211 use sm(u[13], u[3],  x11[9],  b12[10], b12[11],  x12[11]); 
 b1212 use sm(u[14], u[3],  x11[10], b12[11], b12[12],  x12[12]); 
 b1213 use sm(u[15], u[3],  x11[11], b12[12], b12[13],  x12[13]); 
 b1214 use smu(#b0,         x11[12], b12[13], u[3]);

 b130  use sm(#b1,   u[2],  p[4],    #b0,     b13[0],   x13[0]);  
 b131  use sm(#b0,   u[2],  p[5],    b13[0],  b13[1],   x13[1]);
 b132  use sm(u[3],  u[2],  x12[0],  b13[1],  b13[2],   x13[2]); 
 b133  use sm(u[4],  u[2],  x12[1],  b13[2],  b13[3],   x13[3]); 
 b134  use sm(u[5],  u[2],  x12[2],  b13[3],  b13[4],   x13[4]); 
 b135  use sm(u[6],  u[2],  x12[3],  b13[4],  b13[5],   x13[5]); 
 b136  use sm(u[7],  u[2],  x12[4],  b13[5],  b13[6],   x13[6]); 
 b137  use sm(u[8],  u[2],  x12[5],  b13[6],  b13[7],   x13[7]); 
 b138  use sm(u[9],  u[2],  x12[6],  b13[7],  b13[8],   x13[8]); 
 b139  use sm(u[10], u[2],  x12[7],  b13[8],  b13[9],   x13[9]); 
 b1310 use sm(u[11], u[2],  x12[8],  b13[9],  b13[10],  x13[10]); 
 b1311 use sm(u[12], u[2],  x12[9],  b13[10], b13[11],  x13[11]); 
 b1312 use sm(u[13], u[2],  x12[10], b13[11], b13[12],  x13[12]); 
 b1313 use sm(u[14], u[2],  x12[11], b13[12], b13[13],  x13[13]); 
 b1314 use sm(u[15], u[2],  x12[12], b13[13], b13[14],  x13[14]); 
 b1315 use smu(#b0,         x12[13], b13[14], u[2]);

 b140  use sm(#b1,   u[1],  p[2],    #b0,     b14[0],   x14[0]);  
 b141  use sm(#b0,   u[1],  p[3],    b14[0],  b14[1],   x14[1]);
 b142  use sm(u[2],  u[1],  x13[0],  b14[1],  b14[2],   x14[2]); 
 b143  use sm(u[3],  u[1],  x13[1],  b14[2],  b14[3],   x14[3]); 
 b144  use sm(u[4],  u[1],  x13[2],  b14[3],  b14[4],   x14[4]); 
 b145  use sm(u[5],  u[1],  x13[3],  b14[4],  b14[5],   x14[5]); 
 b146  use sm(u[6],  u[1],  x13[4],  b14[5],  b14[6],   x14[6]); 
 b147  use sm(u[7],  u[1],  x13[5],  b14[6],  b14[7],   x14[7]); 
 b148  use sm(u[8],  u[1],  x13[6],  b14[7],  b14[8],   x14[8]); 
 b149  use sm(u[9],  u[1],  x13[7],  b14[8],  b14[9],   x14[9]); 
 b1410 use sm(u[10], u[1],  x13[8],  b14[9],  b14[10],  x14[10]); 
 b1411 use sm(u[11], u[1],  x13[9],  b14[10], b14[11],  x14[11]); 
 b1412 use sm(u[12], u[1],  x13[10], b14[11], b14[12],  x14[12]); 
 b1413 use sm(u[13], u[1],  x13[11], b14[12], b14[13],  x14[13]); 
 b1414 use sm(u[14], u[1],  x13[12], b14[13], b14[14],  x14[14]); 
 b1415 use sm(u[15], u[1],  x13[13], b14[14], b14[15],  x14[15]); 
 b1416 use smu(#b0,         x13[14], b14[15], u[1]);

 b150  use sml(#b1,         p[0],    #b0,     b15[0]); 
 b151  use sml(#b0,         p[1],    b15[0],  b15[1]);
 b152  use sml(u[1],        x14[0],  b15[1],  b15[2]); 
 b153  use sml(u[2],        x14[1],  b15[2],  b15[3]); 
 b154  use sml(u[3],        x14[2],  b15[3],  b15[4]); 
 b155  use sml(u[4],        x14[3],  b15[4],  b15[5]); 
 b156  use sml(u[5],        x14[4],  b15[5],  b15[6]); 
 b157  use sml(u[6],        x14[5],  b15[6],  b15[7]); 
 b158  use sml(u[7],        x14[6],  b15[7],  b15[8]); 
 b159  use sml(u[8],        x14[7],  b15[8],  b15[9]); 
 b1510 use sml(u[9],        x14[8],  b15[9],  b15[10]); 
 b1511 use sml(u[10],       x14[9],  b15[10], b15[11]); 
 b1512 use sml(u[11],       x14[10], b15[11], b15[12]); 
 b1513 use sml(u[12],       x14[11], b15[12], b15[13]); 
 b1514 use sml(u[13],       x14[12], b15[13], b15[14]); 
 b1515 use sml(u[14],       x14[13], b15[14], b15[15]); 
 b1516 use sml(u[15],       x14[14], b15[15], b15[16]); 
 b1517 use smu(#b0,         x14[15], b15[16], u[0]);
end circuits;
end sqrt32;

signal p[32] <= #h00000001;
signal u[16];
circuits
 s32 use sqrt32(p, u);
end circuits;