src/add/fsqrt.py

   1 # XXX DO NOT USE, fails on num=65536.  wark-wark...
   2 def sqrtsimple(num):
   3     res = 0
   4     bit = 1
   5
   6     while (bit < num):
   7         bit <<= 2
   8
   9     while (bit != 0):
  10         if (num >= res + bit):
  11             num -= res + bit
  12             res = (res >> 1) + bit
  13         else:
  14             res >>= 1
  15         bit >>= 2
  16
  17     return res
  18
  19
  20 def sqrt(num):
  21     D = num # D is input (from num)
  22     Q = 0
  23     R = 0
  24     r = 0 # remainder
  25     for i in range(15, -1, -1): # negative ranges are weird...
  26
  27         if (R>=0):
  28
  29             R = (R<<2)|((D>>(i+i))&3)
  30             R = R-((Q<<2)|1) #/*-Q01*/
  31
  32         else:
  33
  34             R = (R<<2)|((D>>(i+i))&3)
  35             R = R+((Q<<2)|3) #/*+Q11*/
  36
  37         if (R>=0):
  38             Q = (Q<<1)|1 #/*new Q:*/
  39         else:
  40             Q = (Q<<1)|0 #/*new Q:*/
  41
  42
  43     if (R<0):
  44         R = R+((Q<<1)|1)
  45         r = R
  46     return Q
  47
  48
  49 # grabbed these from unit_test_single (convenience, this is just experimenting)
  50
  51 def get_mantissa(x):
  52     return 0x7fffff & x
  53
  54 def get_exponent(x):
  55     return ((x & 0x7f800000) >> 23) - 127
  56
  57 def set_exponent(x, e):
  58     return (x & ~0x7f800000) | ((e+127) << 23)
  59
  60 def get_sign(x):
  61     return ((x & 0x80000000) >> 31)
  62
  63 # convert FP32 to s/e/m
  64 def create_fp32(s, e, m):
  65     """ receive sign, exponent, mantissa, return FP32 """
  66     return set_exponent((s << 31) | get_mantissa(m))
  67
  68 # convert s/e/m to FP32
  69 def decode_fp32(x):
  70     """ receive FP32, return sign, exponent, mantissa """
  71     return get_sign(x), get_exponent(x), get_mantissa(x)
  72
  73
  74 # main function, takes mantissa and exponent as separate arguments
  75 # returns a tuple, sqrt'd mantissa, sqrt'd exponent
  76
  77 def main(mantissa, exponent):
  78     if exponent & 1 != 0:
  79         # shift mantissa up, subtract 1 from exp to compensate
  80         return sqrt(mantissa << 1), (exponent - 1) >> 1
  81     # mantissa as-is, no compensating needed on exp
  82     return sqrt(mantissa), (exponent >> 1)
  83
  84
  85 if __name__ == '__main__':
  86
  87     # quick test up to 1000 of two sqrt functions
  88     for Q in range(1, int(1e4)):
  89         print(Q, sqrt(Q), sqrtsimple(Q), int(Q**0.5))
  90         assert int(Q**0.5) == sqrtsimple(Q), "Q sqrtsimpl fail %d" % Q
  91         assert int(Q**0.5) == sqrt(Q), "Q sqrt fail %d" % Q
  92
  93     # quick mantissa/exponent demo
  94     for e in range(26):
  95         for m in range(26):
  96             ms, es = main(m, e)
  97             print("m:%d e:%d sqrt: m:%d e:%d" % (m, e, ms, es))
  98
  99 """
 100
 101 Notes:
 102 https://pdfs.semanticscholar.org/5060/4e9aff0e37089c4ab9a376c3f35761ffe28b.pdf
 103
 104 //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
 105 //
 106
 107 module testbench;
 108
 109 reg [15:0] sqr;
 110
 111 //Verilog function to find square root of a 32 bit number.
 112 //The output is 16 bit.
 113 function [15:0] sqrt;
 114     input [31:0] num;  //declare input
 115     //intermediate signals.
 116     reg [31:0] a;
 117     reg [15:0] q;
 118     reg [17:0] left,right,r;
 119     integer i;
 120 begin
 121     //initialize all the variables.
 122     a = num;
 123     q = 0;
 124     i = 0;
 125     left = 0;   //input to adder/sub
 126     right = 0;  //input to adder/sub
 127     r = 0;  //remainder
 128     //run the calculations for 16 iterations.
 129     for(i=0;i<16;i=i+1) begin
 130         right = {q,r[17],1'b1};
 131         left = {r[15:0],a[31:30]};
 132         a = {a[29:0],2'b00};    //left shift by 2 bits.
 133         if (r[17] == 1) //add if r is negative
 134             r = left + right;
 135         else    //subtract if r is positive
 136             r = left - right;
 137         q = {q[14:0],!r[17]};
 138     end
 139     sqrt = q;   //final assignment of output.
 140 end
 141 endfunction //end of Function
 142
 143
 144 c version (from paper linked from URL)
 145
 146 unsigned squart(D, r) /*Non-Restoring sqrt*/
 147     unsigned D; /*D:32-bit unsigned integer to be square rooted */
 148     int *r;
 149 {
 150     unsigned Q = 0; /*Q:16-bit unsigned integer (root)*/
 151     int R = 0; /*R:17-bit integer (remainder)*/
 152     int i;
 153     for (i = 15;i>=0;i--) /*for each root bit*/
 154     {
 155         if (R>=0)
 156         { /*new remainder:*/
 157             R = R<<2)|((D>>(i+i))&3);
 158             R = R-((Q<<2)|1); /*-Q01*/
 159         }
 160         else
 161         { /*new remainder:*/
 162             R = R<<2)|((D>>(i+i))&3);
 163             R = R+((Q<<2)|3); /*+Q11*/
 164         }
 165         if (R>=0) Q = Q<<1)|1; /*new Q:*/
 166         else Q = Q<<1)|0; /*new Q:*/
 167     }
 168
 169     /*remainder adjusting*/
 170     if (R<0) R = R+((Q<<1)|1);
 171     *r = R; /*return remainder*/
 172     return(Q); /*return root*/
 173 }
 174
 175 From wikipedia page:
 176
 177 short isqrt(short num) {
 178     short res = 0;
 179     short bit = 1 << 14; // The second-to-top bit is set: 1 << 30 for 32 bits
 180
 181     // "bit" starts at the highest power of four <= the argument.
 182     while (bit > num)
 183         bit >>= 2;
 184
 185     while (bit != 0) {
 186         if (num >= res + bit) {
 187             num -= res + bit;
 188             res = (res >> 1) + bit;
 189         }
 190         else
 191             res >>= 1;
 192         bit >>= 2;
 193     }
 194     return res;
 195 }
 196
 197 """