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 # remainder
  27     for i in range(64, -1, -1): # negative ranges are weird...
  28
  29         R = (R<<2)|((D>>(i+i))&3)
  30
  31         if R >= 0:
  32             R -= ((Q<<2)|1) # -Q01
  33         else:
  34             R += ((Q<<2)|3) # +Q11
  35
  36         Q <<= 1
  37         if R >= 0:
  38             Q |= 1 # new Q
  39
  40     if R < 0:
  41         R = R + ((Q<<1)|1)
  42
  43     return Q, R
  44
  45
  46 # grabbed these from unit_test_single (convenience, this is just experimenting)
  47
  48 def get_mantissa(x):
  49     return 0x7fffff & x
  50
  51 def get_exponent(x):
  52     return ((x & 0x7f800000) >> 23) - 127
  53
  54 def set_exponent(x, e):
  55     return (x & ~0x7f800000) | ((e+127) << 23)
  56
  57 def get_sign(x):
  58     return ((x & 0x80000000) >> 31)
  59
  60 # convert FP32 to s/e/m
  61 def create_fp32(s, e, m):
  62     """ receive sign, exponent, mantissa, return FP32 """
  63     return set_exponent((s << 31) | get_mantissa(m))
  64
  65 # convert s/e/m to FP32
  66 def decode_fp32(x):
  67     """ receive FP32, return sign, exponent, mantissa """
  68     return get_sign(x), get_exponent(x), get_mantissa(x)
  69
  70
  71 # main function, takes mantissa and exponent as separate arguments
  72 # returns a tuple, sqrt'd mantissa, sqrt'd exponent
  73
  74 def main(mantissa, exponent):
  75     if exponent & 1 != 0:
  76         # shift mantissa up, subtract 1 from exp to compensate
  77         mantissa <<= 1
  78         exponent -= 1
  79     m, r = sqrt(mantissa)
  80     return m, r, exponent >> 1
  81
  82
  83 def fsqrt_test(x):
  84
  85     xbits = x.bits
  86     print ("x", x, type(x))
  87     sq_test = x.sqrt()
  88     print ("sqrt", sq_test)
  89
  90     print (xbits, type(xbits))
  91     s, e, m = decode_fp32(xbits)
  92     print("x decode", s, e, m, hex(m))
  93
  94     m |= 1<<23 # set top bit (the missing "1" from mantissa)
  95     m <<= 27
  96
  97     sm, sr, se = main(m, e)
  98     lowbits = sm & 0x3
  99     sm >>= 2
 100     sm = get_mantissa(sm)
 101     #sm += 2
 102     print("our  sqrt", s, se, sm, hex(sm), bin(sm), "lowbits", lowbits,
 103                                                     "rem", hex(sr))
 104     if lowbits >= 2:
 105         print ("probably needs rounding (+1 on mantissa)")
 106
 107     sq_xbits = sq_test.bits
 108     s, e, m = decode_fp32(sq_xbits)
 109     print ("sf32 sqrt", s, e, m, hex(m), bin(m))
 110     print ()
 111
 112 if __name__ == '__main__':
 113
 114     # quick test up to 1000 of two sqrt functions
 115     for Q in range(1, int(1e4)):
 116         print(Q, sqrt(Q), sqrtsimple(Q), int(Q**0.5))
 117         assert int(Q**0.5) == sqrtsimple(Q), "Q sqrtsimpl fail %d" % Q
 118         assert int(Q**0.5) == sqrt(Q)[0], "Q sqrt fail %d" % Q
 119
 120     # quick mantissa/exponent demo
 121     for e in range(26):
 122         for m in range(26):
 123             ms, mr, es = main(m, e)
 124             print("m:%d e:%d sqrt: m:%d-%d e:%d" % (m, e, ms, mr, es))
 125
 126     x = Float32(1234.123456789)
 127     fsqrt_test(x)
 128     x = Float32(32.1)
 129     fsqrt_test(x)
 130     x = Float32(16.0)
 131     fsqrt_test(x)
 132     x = Float32(8.0)
 133     fsqrt_test(x)
 134     x = Float32(8.5)
 135     fsqrt_test(x)
 136     x = Float32(3.14159265358979323)
 137     fsqrt_test(x)
 138     x = Float32(12.99392923123123)
 139     fsqrt_test(x)
 140     x = Float32(0.123456)
 141     fsqrt_test(x)
 142
 143 """
 144
 145 Notes:
 146 https://pdfs.semanticscholar.org/5060/4e9aff0e37089c4ab9a376c3f35761ffe28b.pdf
 147
 148 //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
 149 //
 150
 151 module testbench;
 152
 153 reg [15:0] sqr;
 154
 155 //Verilog function to find square root of a 32 bit number.
 156 //The output is 16 bit.
 157 function [15:0] sqrt;
 158     input [31:0] num;  //declare input
 159     //intermediate signals.
 160     reg [31:0] a;
 161     reg [15:0] q;
 162     reg [17:0] left,right,r;
 163     integer i;
 164 begin
 165     //initialize all the variables.
 166     a = num;
 167     q = 0;
 168     i = 0;
 169     left = 0;   //input to adder/sub
 170     right = 0;  //input to adder/sub
 171     r = 0;  //remainder
 172     //run the calculations for 16 iterations.
 173     for(i=0;i<16;i=i+1) begin
 174         right = {q,r[17],1'b1};
 175         left = {r[15:0],a[31:30]};
 176         a = {a[29:0],2'b00};    //left shift by 2 bits.
 177         if (r[17] == 1) //add if r is negative
 178             r = left + right;
 179         else    //subtract if r is positive
 180             r = left - right;
 181         q = {q[14:0],!r[17]};
 182     end
 183     sqrt = q;   //final assignment of output.
 184 end
 185 endfunction //end of Function
 186
 187
 188 c version (from paper linked from URL)
 189
 190 unsigned squart(D, r) /*Non-Restoring sqrt*/
 191     unsigned D; /*D:32-bit unsigned integer to be square rooted */
 192     int *r;
 193 {
 194     unsigned Q = 0; /*Q:16-bit unsigned integer (root)*/
 195     int R = 0; /*R:17-bit integer (remainder)*/
 196     int i;
 197     for (i = 15;i>=0;i--) /*for each root bit*/
 198     {
 199         if (R>=0)
 200         { /*new remainder:*/
 201             R = R<<2)|((D>>(i+i))&3);
 202             R = R-((Q<<2)|1); /*-Q01*/
 203         }
 204         else
 205         { /*new remainder:*/
 206             R = R<<2)|((D>>(i+i))&3);
 207             R = R+((Q<<2)|3); /*+Q11*/
 208         }
 209         if (R>=0) Q = Q<<1)|1; /*new Q:*/
 210         else Q = Q<<1)|0; /*new Q:*/
 211     }
 212
 213     /*remainder adjusting*/
 214     if (R<0) R = R+((Q<<1)|1);
 215     *r = R; /*return remainder*/
 216     return(Q); /*return root*/
 217 }
 218
 219 From wikipedia page:
 220
 221 short isqrt(short num) {
 222     short res = 0;
 223     short bit = 1 << 14; // The second-to-top bit is set: 1 << 30 for 32 bits
 224
 225     // "bit" starts at the highest power of four <= the argument.
 226     while (bit > num)
 227         bit >>= 2;
 228
 229     while (bit != 0) {
 230         if (num >= res + bit) {
 231             num -= res + bit;
 232             res = (res >> 1) + bit;
 233         }
 234         else
 235             res >>= 1;
 236         bit >>= 2;
 237     }
 238     return res;
 239 }
 240
 241 """