src/add/fsqrt.py

   1 from sfpy import Float32
   2
   3
   4 # XXX DO NOT USE, fails on num=65536.  wark-wark...
   5 def sqrtsimple(num):
   6     res = 0
   7     bit = 1
   8
   9     while (bit < num):
  10         bit <<= 2
  11
  12     while (bit != 0):
  13         if (num >= res + bit):
  14             num -= res + bit
  15             res = (res >> 1) + bit
  16         else:
  17             res >>= 1
  18         bit >>= 2
  19
  20     return res
  21
  22
  23 def sqrt(num):
  24     D = num # D is input (from num)
  25     Q = 0
  26     R = 0
  27     r = 0 # remainder
  28     for i in range(15, -1, -1): # negative ranges are weird...
  29
  30         if (R>=0):
  31
  32             R = (R<<2)|((D>>(i+i))&3)
  33             R = R-((Q<<2)|1) #/*-Q01*/
  34
  35         else:
  36
  37             R = (R<<2)|((D>>(i+i))&3)
  38             R = R+((Q<<2)|3) #/*+Q11*/
  39
  40         if (R>=0):
  41             Q = (Q<<1)|1 #/*new Q:*/
  42         else:
  43             Q = (Q<<1)|0 #/*new Q:*/
  44
  45
  46     if (R<0):
  47         R = R+((Q<<1)|1)
  48         r = R
  49     return Q
  50
  51
  52 # grabbed these from unit_test_single (convenience, this is just experimenting)
  53
  54 def get_mantissa(x):
  55     return 0x7fffff & x
  56
  57 def get_exponent(x):
  58     return ((x & 0x7f800000) >> 23) - 127
  59
  60 def set_exponent(x, e):
  61     return (x & ~0x7f800000) | ((e+127) << 23)
  62
  63 def get_sign(x):
  64     return ((x & 0x80000000) >> 31)
  65
  66 # convert FP32 to s/e/m
  67 def create_fp32(s, e, m):
  68     """ receive sign, exponent, mantissa, return FP32 """
  69     return set_exponent((s << 31) | get_mantissa(m))
  70
  71 # convert s/e/m to FP32
  72 def decode_fp32(x):
  73     """ receive FP32, return sign, exponent, mantissa """
  74     return get_sign(x), get_exponent(x), get_mantissa(x)
  75
  76
  77 # main function, takes mantissa and exponent as separate arguments
  78 # returns a tuple, sqrt'd mantissa, sqrt'd exponent
  79
  80 def main(mantissa, exponent):
  81     if exponent & 1 != 0:
  82         # shift mantissa up, subtract 1 from exp to compensate
  83         return sqrt(mantissa << 1), (exponent - 1) >> 1
  84     # mantissa as-is, no compensating needed on exp
  85     return sqrt(mantissa), (exponent >> 1)
  86
  87
  88 if __name__ == '__main__':
  89
  90     # quick test up to 1000 of two sqrt functions
  91     for Q in range(1, int(1e4)):
  92         print(Q, sqrt(Q), sqrtsimple(Q), int(Q**0.5))
  93         assert int(Q**0.5) == sqrtsimple(Q), "Q sqrtsimpl fail %d" % Q
  94         assert int(Q**0.5) == sqrt(Q), "Q sqrt fail %d" % Q
  95
  96     # quick mantissa/exponent demo
  97     for e in range(26):
  98         for m in range(26):
  99             ms, es = main(m, e)
 100             print("m:%d e:%d sqrt: m:%d e:%d" % (m, e, ms, es))
 101
 102     x = Float32(1234.123456789)
 103     xbits = x.bits
 104
 105     print (x, type(x))
 106     print (xbits, type(xbits))
 107     s, e, m = decode_fp32(xbits)
 108     print(s, e, m, hex(m))
 109
 110     se, sm = main(e, m)
 111     print("our  sqrt", s, se, sm, hex(sm), bin(sm))
 112
 113     sq_test = x.sqrt()
 114     sq_xbits = sq_test.bits
 115     s, e, m = decode_fp32(sq_xbits)
 116     print ("sf32 sqrt", s, e, m, hex(m), bin(m))
 117 """
 118
 119 Notes:
 120 https://pdfs.semanticscholar.org/5060/4e9aff0e37089c4ab9a376c3f35761ffe28b.pdf
 121
 122 //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
 123 //
 124
 125 module testbench;
 126
 127 reg [15:0] sqr;
 128
 129 //Verilog function to find square root of a 32 bit number.
 130 //The output is 16 bit.
 131 function [15:0] sqrt;
 132     input [31:0] num;  //declare input
 133     //intermediate signals.
 134     reg [31:0] a;
 135     reg [15:0] q;
 136     reg [17:0] left,right,r;
 137     integer i;
 138 begin
 139     //initialize all the variables.
 140     a = num;
 141     q = 0;
 142     i = 0;
 143     left = 0;   //input to adder/sub
 144     right = 0;  //input to adder/sub
 145     r = 0;  //remainder
 146     //run the calculations for 16 iterations.
 147     for(i=0;i<16;i=i+1) begin
 148         right = {q,r[17],1'b1};
 149         left = {r[15:0],a[31:30]};
 150         a = {a[29:0],2'b00};    //left shift by 2 bits.
 151         if (r[17] == 1) //add if r is negative
 152             r = left + right;
 153         else    //subtract if r is positive
 154             r = left - right;
 155         q = {q[14:0],!r[17]};
 156     end
 157     sqrt = q;   //final assignment of output.
 158 end
 159 endfunction //end of Function
 160
 161
 162 c version (from paper linked from URL)
 163
 164 unsigned squart(D, r) /*Non-Restoring sqrt*/
 165     unsigned D; /*D:32-bit unsigned integer to be square rooted */
 166     int *r;
 167 {
 168     unsigned Q = 0; /*Q:16-bit unsigned integer (root)*/
 169     int R = 0; /*R:17-bit integer (remainder)*/
 170     int i;
 171     for (i = 15;i>=0;i--) /*for each root bit*/
 172     {
 173         if (R>=0)
 174         { /*new remainder:*/
 175             R = R<<2)|((D>>(i+i))&3);
 176             R = R-((Q<<2)|1); /*-Q01*/
 177         }
 178         else
 179         { /*new remainder:*/
 180             R = R<<2)|((D>>(i+i))&3);
 181             R = R+((Q<<2)|3); /*+Q11*/
 182         }
 183         if (R>=0) Q = Q<<1)|1; /*new Q:*/
 184         else Q = Q<<1)|0; /*new Q:*/
 185     }
 186
 187     /*remainder adjusting*/
 188     if (R<0) R = R+((Q<<1)|1);
 189     *r = R; /*return remainder*/
 190     return(Q); /*return root*/
 191 }
 192
 193 From wikipedia page:
 194
 195 short isqrt(short num) {
 196     short res = 0;
 197     short bit = 1 << 14; // The second-to-top bit is set: 1 << 30 for 32 bits
 198
 199     // "bit" starts at the highest power of four <= the argument.
 200     while (bit > num)
 201         bit >>= 2;
 202
 203     while (bit != 0) {
 204         if (num >= res + bit) {
 205             num -= res + bit;
 206             res = (res >> 1) + bit;
 207         }
 208         else
 209             res >>= 1;
 210         bit >>= 2;
 211     }
 212     return res;
 213 }
 214
 215 """