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