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 # grabbed these from unit_test_single (convenience, this is just experimenting)
  49
  50 def get_mantissa(x):
  51     return 0x7fffff & x
  52
  53 def get_exponent(x):
  54     return ((x & 0x7f800000) >> 23) - 127
  55
  56 def set_exponent(x, e):
  57     return (x & ~0x7f800000) | ((e+127) << 23)
  58
  59 def get_sign(x):
  60     return ((x & 0x80000000) >> 31)
  61
  62
  63 def main(mantissa, exponent):
  64     if exponent & 1 != 0:
  65         return sqrt(mantissa << 1), # shift mantissa up
  66                 ((exponent - 1) / 2) # subtract 1 from exp to compensate
  67     return sqrt(mantissa),      # mantissa as-is
  68            (exponent / 2)       # no compensating needed on exp
  69
  70
  71 if __name__ == '__main__':
  72     for Q in range(1, int(1e7)):
  73         print(Q, sqrt(Q), sqrtsimple(Q), int(Q**0.5))
  74         assert int(Q**0.5) == sqrtsimple(Q), "Q sqrtsimpl fail %d" % Q
  75         assert int(Q**0.5) == sqrt(Q), "Q sqrt fail %d" % Q
  76
  77 """
  78 //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
  79 //
  80
  81 module testbench;
  82
  83 reg [15:0] sqr;
  84
  85 //Verilog function to find square root of a 32 bit number.
  86 //The output is 16 bit.
  87 function [15:0] sqrt;
  88     input [31:0] num;  //declare input
  89     //intermediate signals.
  90     reg [31:0] a;
  91     reg [15:0] q;
  92     reg [17:0] left,right,r;
  93     integer i;
  94 begin
  95     //initialize all the variables.
  96     a = num;
  97     q = 0;
  98     i = 0;
  99     left = 0;   //input to adder/sub
 100     right = 0;  //input to adder/sub
 101     r = 0;  //remainder
 102     //run the calculations for 16 iterations.
 103     for(i=0;i<16;i=i+1) begin
 104         right = {q,r[17],1'b1};
 105         left = {r[15:0],a[31:30]};
 106         a = {a[29:0],2'b00};    //left shift by 2 bits.
 107         if (r[17] == 1) //add if r is negative
 108             r = left + right;
 109         else    //subtract if r is positive
 110             r = left - right;
 111         q = {q[14:0],!r[17]};
 112     end
 113     sqrt = q;   //final assignment of output.
 114 end
 115 endfunction //end of Function
 116
 117
 118 c version (from paper linked from URL)
 119
 120 unsigned squart(D, r) /*Non-Restoring sqrt*/
 121     unsigned D; /*D:32-bit unsigned integer to be square rooted */
 122     int *r;
 123 {
 124     unsigned Q = 0; /*Q:16-bit unsigned integer (root)*/
 125     int R = 0; /*R:17-bit integer (remainder)*/
 126     int i;
 127     for (i = 15;i>=0;i--) /*for each root bit*/
 128     {
 129         if (R>=0)
 130         { /*new remainder:*/
 131             R = R<<2)|((D>>(i+i))&3);
 132             R = R-((Q<<2)|1); /*-Q01*/
 133         }
 134         else
 135         { /*new remainder:*/
 136             R = R<<2)|((D>>(i+i))&3);
 137             R = R+((Q<<2)|3); /*+Q11*/
 138         }
 139         if (R>=0) Q = Q<<1)|1; /*new Q:*/
 140         else Q = Q<<1)|0; /*new Q:*/
 141     }
 142
 143     /*remainder adjusting*/
 144     if (R<0) R = R+((Q<<1)|1);
 145     *r = R; /*return remainder*/
 146     return(Q); /*return root*/
 147 }
 148
 149 From wikipedia page:
 150
 151 short isqrt(short num) {
 152     short res = 0;
 153     short bit = 1 << 14; // The second-to-top bit is set: 1 << 30 for 32 bits
 154
 155     // "bit" starts at the highest power of four <= the argument.
 156     while (bit > num)
 157         bit >>= 2;
 158
 159     while (bit != 0) {
 160         if (num >= res + bit) {
 161             num -= res + bit;
 162             res = (res >> 1) + bit;
 163         }
 164         else
 165             res >>= 1;
 166         bit >>= 2;
 167     }
 168     return res;
 169 }
 170
 171 """