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
  48 def main(mantissa, exponent):
  49     if exponent & 1 != 0:
  50         return sqrt(mantissa << 1), # shift mantissa up
  51                 ((exponent - 1) / 2) # subtract 1 from exp to compensate
  52     return sqrt(mantissa),      # mantissa as-is
  53            (exponent / 2)       # no compensating needed on exp
  54
  55
  56 if __name__ == '__main__':
  57     for Q in range(1, int(1e7)):
  58         print(Q, sqrt(Q), sqrtsimple(Q), int(Q**0.5))
  59         assert int(Q**0.5) == sqrtsimple(Q), "Q sqrtsimpl fail %d" % Q
  60         assert int(Q**0.5) == sqrt(Q), "Q sqrt fail %d" % Q
  61
  62 """
  63 //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
  64 //
  65
  66 module testbench;
  67
  68 reg [15:0] sqr;
  69
  70 //Verilog function to find square root of a 32 bit number.
  71 //The output is 16 bit.
  72 function [15:0] sqrt;
  73     input [31:0] num;  //declare input
  74     //intermediate signals.
  75     reg [31:0] a;
  76     reg [15:0] q;
  77     reg [17:0] left,right,r;
  78     integer i;
  79 begin
  80     //initialize all the variables.
  81     a = num;
  82     q = 0;
  83     i = 0;
  84     left = 0;   //input to adder/sub
  85     right = 0;  //input to adder/sub
  86     r = 0;  //remainder
  87     //run the calculations for 16 iterations.
  88     for(i=0;i<16;i=i+1) begin
  89         right = {q,r[17],1'b1};
  90         left = {r[15:0],a[31:30]};
  91         a = {a[29:0],2'b00};    //left shift by 2 bits.
  92         if (r[17] == 1) //add if r is negative
  93             r = left + right;
  94         else    //subtract if r is positive
  95             r = left - right;
  96         q = {q[14:0],!r[17]};
  97     end
  98     sqrt = q;   //final assignment of output.
  99 end
 100 endfunction //end of Function
 101
 102
 103 c version (from paper linked from URL)
 104
 105 unsigned squart(D, r) /*Non-Restoring sqrt*/
 106     unsigned D; /*D:32-bit unsigned integer to be square rooted */
 107     int *r;
 108 {
 109     unsigned Q = 0; /*Q:16-bit unsigned integer (root)*/
 110     int R = 0; /*R:17-bit integer (remainder)*/
 111     int i;
 112     for (i = 15;i>=0;i--) /*for each root bit*/
 113     {
 114         if (R>=0)
 115         { /*new remainder:*/
 116             R = R<<2)|((D>>(i+i))&3);
 117             R = R-((Q<<2)|1); /*-Q01*/
 118         }
 119         else
 120         { /*new remainder:*/
 121             R = R<<2)|((D>>(i+i))&3);
 122             R = R+((Q<<2)|3); /*+Q11*/
 123         }
 124         if (R>=0) Q = Q<<1)|1; /*new Q:*/
 125         else Q = Q<<1)|0; /*new Q:*/
 126     }
 127
 128     /*remainder adjusting*/
 129     if (R<0) R = R+((Q<<1)|1);
 130     *r = R; /*return remainder*/
 131     return(Q); /*return root*/
 132 }
 133
 134 From wikipedia page:
 135
 136 short isqrt(short num) {
 137     short res = 0;
 138     short bit = 1 << 14; // The second-to-top bit is set: 1 << 30 for 32 bits
 139
 140     // "bit" starts at the highest power of four <= the argument.
 141     while (bit > num)
 142         bit >>= 2;
 143
 144     while (bit != 0) {
 145         if (num >= res + bit) {
 146             num -= res + bit;
 147             res = (res >> 1) + bit;
 148         }
 149         else
 150             res >>= 1;
 151         bit >>= 2;
 152     }
 153     return res;
 154 }
 155
 156 """