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(64, -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, r
  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         mantissa <<= 1
  84         exponent -= 1
  85     m, r = sqrt(mantissa)
  86     return m, r, exponent >> 1
  87
  88
  89 def fsqrt_test(x):
  90
  91     xbits = x.bits
  92     print ("x", x, type(x))
  93     sq_test = x.sqrt()
  94     print ("sqrt", sq_test)
  95
  96     print (xbits, type(xbits))
  97     s, e, m = decode_fp32(xbits)
  98     print("x decode", s, e, m, hex(m))
  99
 100     m |= 1<<23 # set top bit (the missing "1" from mantissa)
 101     m <<= 27
 102
 103     sm, sr, se = main(m, e)
 104     lowbits = sm & 0x3
 105     sm >>= 2
 106     sm = get_mantissa(sm)
 107     #sm += 2
 108     print("our  sqrt", s, se, sm, hex(sm), bin(sm), "lowbits", lowbits,
 109                                                     "rem", hex(sr))
 110     if lowbits >= 2:
 111         print ("probably needs rounding (+1 on mantissa)")
 112
 113     sq_xbits = sq_test.bits
 114     s, e, m = decode_fp32(sq_xbits)
 115     print ("sf32 sqrt", s, e, m, hex(m), bin(m))
 116     print ()
 117
 118 if __name__ == '__main__':
 119
 120     # quick test up to 1000 of two sqrt functions
 121     for Q in range(1, int(1e4)):
 122         print(Q, sqrt(Q), sqrtsimple(Q), int(Q**0.5))
 123         assert int(Q**0.5) == sqrtsimple(Q), "Q sqrtsimpl fail %d" % Q
 124         assert int(Q**0.5) == sqrt(Q)[0], "Q sqrt fail %d" % Q
 125
 126     # quick mantissa/exponent demo
 127     for e in range(26):
 128         for m in range(26):
 129             ms, mr, es = main(m, e)
 130             print("m:%d e:%d sqrt: m:%d-%d e:%d" % (m, e, ms, mr, es))
 131
 132     x = Float32(1234.123456789)
 133     fsqrt_test(x)
 134     x = Float32(32.1)
 135     fsqrt_test(x)
 136     x = Float32(16.0)
 137     fsqrt_test(x)
 138     x = Float32(8.0)
 139     fsqrt_test(x)
 140     x = Float32(8.5)
 141     fsqrt_test(x)
 142     x = Float32(3.14159265358979323)
 143     fsqrt_test(x)
 144     x = Float32(12.99392923123123)
 145     fsqrt_test(x)
 146     x = Float32(0.123456)
 147     fsqrt_test(x)
 148
 149 """
 150
 151 Notes:
 152 https://pdfs.semanticscholar.org/5060/4e9aff0e37089c4ab9a376c3f35761ffe28b.pdf
 153
 154 //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
 155 //
 156
 157 module testbench;
 158
 159 reg [15:0] sqr;
 160
 161 //Verilog function to find square root of a 32 bit number.
 162 //The output is 16 bit.
 163 function [15:0] sqrt;
 164     input [31:0] num;  //declare input
 165     //intermediate signals.
 166     reg [31:0] a;
 167     reg [15:0] q;
 168     reg [17:0] left,right,r;
 169     integer i;
 170 begin
 171     //initialize all the variables.
 172     a = num;
 173     q = 0;
 174     i = 0;
 175     left = 0;   //input to adder/sub
 176     right = 0;  //input to adder/sub
 177     r = 0;  //remainder
 178     //run the calculations for 16 iterations.
 179     for(i=0;i<16;i=i+1) begin
 180         right = {q,r[17],1'b1};
 181         left = {r[15:0],a[31:30]};
 182         a = {a[29:0],2'b00};    //left shift by 2 bits.
 183         if (r[17] == 1) //add if r is negative
 184             r = left + right;
 185         else    //subtract if r is positive
 186             r = left - right;
 187         q = {q[14:0],!r[17]};
 188     end
 189     sqrt = q;   //final assignment of output.
 190 end
 191 endfunction //end of Function
 192
 193
 194 c version (from paper linked from URL)
 195
 196 unsigned squart(D, r) /*Non-Restoring sqrt*/
 197     unsigned D; /*D:32-bit unsigned integer to be square rooted */
 198     int *r;
 199 {
 200     unsigned Q = 0; /*Q:16-bit unsigned integer (root)*/
 201     int R = 0; /*R:17-bit integer (remainder)*/
 202     int i;
 203     for (i = 15;i>=0;i--) /*for each root bit*/
 204     {
 205         if (R>=0)
 206         { /*new remainder:*/
 207             R = R<<2)|((D>>(i+i))&3);
 208             R = R-((Q<<2)|1); /*-Q01*/
 209         }
 210         else
 211         { /*new remainder:*/
 212             R = R<<2)|((D>>(i+i))&3);
 213             R = R+((Q<<2)|3); /*+Q11*/
 214         }
 215         if (R>=0) Q = Q<<1)|1; /*new Q:*/
 216         else Q = Q<<1)|0; /*new Q:*/
 217     }
 218
 219     /*remainder adjusting*/
 220     if (R<0) R = R+((Q<<1)|1);
 221     *r = R; /*return remainder*/
 222     return(Q); /*return root*/
 223 }
 224
 225 From wikipedia page:
 226
 227 short isqrt(short num) {
 228     short res = 0;
 229     short bit = 1 << 14; // The second-to-top bit is set: 1 << 30 for 32 bits
 230
 231     // "bit" starts at the highest power of four <= the argument.
 232     while (bit > num)
 233         bit >>= 2;
 234
 235     while (bit != 0) {
 236         if (num >= res + bit) {
 237             num -= res + bit;
 238             res = (res >> 1) + bit;
 239         }
 240         else
 241             res >>= 1;
 242         bit >>= 2;
 243     }
 244     return res;
 245 }
 246
 247 """