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