src/add/fsqrt.py

   1 def sqrtsimple(num):
   2     res = 0
   3     bit = 1 << 14
   4
   5     while (bit > num):
   6         bit >>= 2
   7
   8     while (bit != 0):
   9         if (num >= res + bit):
  10             num -= res + bit
  11             res = (res >> 1) + bit
  12         else:
  13             res >>= 1
  14         bit >>= 2
  15
  16     return res
  17
  18
  19 def sqrt(num):
  20     D = num # D is input (from num)
  21     Q = 0
  22     R = 0
  23     r = 0 # remainder
  24     for i in range(15, -1, -1): # negative ranges are weird...
  25
  26         if (R>=0):
  27
  28             R = (R<<2)|((D>>(i+i))&3)
  29             R = R-((Q<<2)|1) #/*-Q01*/
  30
  31         else:
  32
  33             R = (R<<2)|((D>>(i+i))&3)
  34             R = R+((Q<<2)|3) #/*+Q11*/
  35
  36         if (R>=0):
  37             Q = (Q<<1)|1 #/*new Q:*/
  38         else:
  39             Q = (Q<<1)|0 #/*new Q:*/
  40
  41
  42     if (R<0):
  43         R = R+((Q<<1)|1)
  44         r = R
  45     return Q
  46
  47 def main(mantissa, exponent):
  48     if exponent & 1 != 0:
  49         return Q(sqrt(mantissa << 1), # shift mantissa up
  50                 ((exponent - 1) / 2)) # subtract 1 from exp to compensate
  51     else:
  52         return Q(sqrt(mantissa),      # mantissa as-is
  53                 (exponent / 2))       # no compensating needed on exp
  54
  55 for Q in range(1, int(1e7)):
  56     print(Q, sqrt(Q), sqrtsimple(Q), int(Q**0.5))
  57     assert int(Q**0.5) == sqrtsimple(Q), "Q sqrtsimpl fail %d" % Q
  58     assert int(Q**0.5) == sqrt(Q), "Q sqrt fail %d" % Q
  59 """
  60 //This is the main code of integer sqrt function found here:http://verilogcodes.blogspot.com/2017/11/a-verilog-function-for-finding-square-root.html
  61 //
  62
  63 module testbench;
  64
  65 reg [15:0] sqr;
  66
  67 //Verilog function to find square root of a 32 bit number.
  68 //The output is 16 bit.
  69 function [15:0] sqrt;
  70     input [31:0] num;  //declare input
  71     //intermediate signals.
  72     reg [31:0] a;
  73     reg [15:0] q;
  74     reg [17:0] left,right,r;
  75     integer i;
  76 begin
  77     //initialize all the variables.
  78     a = num;
  79     q = 0;
  80     i = 0;
  81     left = 0;   //input to adder/sub
  82     right = 0;  //input to adder/sub
  83     r = 0;  //remainder
  84     //run the calculations for 16 iterations.
  85     for(i=0;i<16;i=i+1) begin
  86         right = {q,r[17],1'b1};
  87         left = {r[15:0],a[31:30]};
  88         a = {a[29:0],2'b00};    //left shift by 2 bits.
  89         if (r[17] == 1) //add if r is negative
  90             r = left + right;
  91         else    //subtract if r is positive
  92             r = left - right;
  93         q = {q[14:0],!r[17]};
  94     end
  95     sqrt = q;   //final assignment of output.
  96 end
  97 endfunction //end of Function
  98
  99
 100 c version (from paper linked from URL)
 101
 102 unsigned squart(D, r) /*Non-Restoring sqrt*/
 103     unsigned D; /*D:32-bit unsigned integer to be square rooted */
 104     int *r;
 105 {
 106     unsigned Q = 0; /*Q:16-bit unsigned integer (root)*/
 107     int R = 0; /*R:17-bit integer (remainder)*/
 108     int i;
 109     for (i = 15;i>=0;i--) /*for each root bit*/
 110     {
 111         if (R>=0)
 112         { /*new remainder:*/
 113             R = R<<2)|((D>>(i+i))&3);
 114             R = R-((Q<<2)|1); /*-Q01*/
 115         }
 116         else
 117         { /*new remainder:*/
 118             R = R<<2)|((D>>(i+i))&3);
 119             R = R+((Q<<2)|3); /*+Q11*/
 120         }
 121         if (R>=0) Q = Q<<1)|1; /*new Q:*/
 122         else Q = Q<<1)|0; /*new Q:*/
 123     }
 124
 125     /*remainder adjusting*/
 126     if (R<0) R = R+((Q<<1)|1);
 127     *r = R; /*return remainder*/
 128     return(Q); /*return root*/
 129 }
 130
 131 From wikipedia page:
 132
 133 short isqrt(short num) {
 134     short res = 0;
 135     short bit = 1 << 14; // The second-to-top bit is set: 1 << 30 for 32 bits
 136
 137     // "bit" starts at the highest power of four <= the argument.
 138     while (bit > num)
 139         bit >>= 2;
 140
 141     while (bit != 0) {
 142         if (num >= res + bit) {
 143             num -= res + bit;
 144             res = (res >> 1) + bit;
 145         }
 146         else
 147             res >>= 1;
 148         bit >>= 2;
 149     }
 150     return res;
 151 }
 152
 153 """