src/ieee754/fpsqrt/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 # quotient
  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 #normalization function
  84 def normalise(s, m, e, lowbits):
  85     if (lowbits >= 2):
  86         m += 1
  87     if get_mantissa(m) == ((1<<24)-1):
  88         e += 1
  89     #if the num is NaN, than adjust
  90     if (e == 128 & m !=0):
  91         z[31] = 1
  92         z[30:23] = 255
  93         z[22] = 1
  94         z[21:0] = 0
  95     #if the num is Inf, then adjust
  96     if (e == 128):
  97         z[31] = s
  98         z[30:23] = 255
  99         z[22:0] = 0
 100
 101     return s, m, e
 102
 103
 104 def fsqrt_test(x):
 105
 106     xbits = x.bits
 107     print ("x", x, type(x))
 108     sq_test = x.sqrt()
 109     print ("sqrt", sq_test)
 110
 111     print (xbits, type(xbits))
 112     s, e, m = decode_fp32(xbits)
 113     print("x decode", s, e, m, hex(m))
 114
 115     m |= 1<<23 # set top bit (the missing "1" from mantissa)
 116     m <<= 27
 117
 118     sm, sr, se = main(m, e)
 119     lowbits = sm & 0x3
 120     sm >>= 2
 121     sm = get_mantissa(sm)
 122     #sm += 2
 123
 124     s, sm, se = normalise(s, sm, se, lowbits)
 125
 126     print("our  sqrt", s, se, sm, hex(sm), bin(sm), "lowbits", lowbits,
 127                                                     "rem", hex(sr))
 128     if lowbits >= 2:
 129         print ("probably needs rounding (+1 on mantissa)")
 130
 131     sq_xbits = sq_test.bits
 132     s, e, m = decode_fp32(sq_xbits)
 133     print ("sf32 sqrt", s, e, m, hex(m), bin(m))
 134     print ()
 135
 136 if __name__ == '__main__':
 137
 138     # quick test up to 1000 of two sqrt functions
 139     for Q in range(1, int(1e4)):
 140         print(Q, sqrt(Q), sqrtsimple(Q), int(Q**0.5))
 141         assert int(Q**0.5) == sqrtsimple(Q), "Q sqrtsimpl fail %d" % Q
 142         assert int(Q**0.5) == sqrt(Q)[0], "Q sqrt fail %d" % Q
 143
 144     # quick mantissa/exponent demo
 145     for e in range(26):
 146         for m in range(26):
 147             ms, mr, es = main(m, e)
 148             print("m:%d e:%d sqrt: m:%d-%d e:%d" % (m, e, ms, mr, es))
 149
 150     x = Float32(1234.123456789)
 151     fsqrt_test(x)
 152     x = Float32(32.1)
 153     fsqrt_test(x)
 154     x = Float32(16.0)
 155     fsqrt_test(x)
 156     x = Float32(8.0)
 157     fsqrt_test(x)
 158     x = Float32(8.5)
 159     fsqrt_test(x)
 160     x = Float32(3.14159265358979323)
 161     fsqrt_test(x)
 162     x = Float32(12.99392923123123)
 163     fsqrt_test(x)
 164     x = Float32(0.123456)
 165     fsqrt_test(x)
 166
 167
 168
 169
 170 """
 171
 172 Notes:
 173 https://pdfs.semanticscholar.org/5060/4e9aff0e37089c4ab9a376c3f35761ffe28b.pdf
 174
 175 //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
 176 //
 177
 178 module testbench;
 179
 180 reg [15:0] sqr;
 181
 182 //Verilog function to find square root of a 32 bit number.
 183 //The output is 16 bit.
 184 function [15:0] sqrt;
 185     input [31:0] num;  //declare input
 186     //intermediate signals.
 187     reg [31:0] a;
 188     reg [15:0] q;
 189     reg [17:0] left,right,r;
 190     integer i;
 191 begin
 192     //initialize all the variables.
 193     a = num;
 194     q = 0;
 195     i = 0;
 196     left = 0;   //input to adder/sub
 197     right = 0;  //input to adder/sub
 198     r = 0;  //remainder
 199     //run the calculations for 16 iterations.
 200     for(i=0;i<16;i=i+1) begin
 201         right = {q,r[17],1'b1};
 202         left = {r[15:0],a[31:30]};
 203         a = {a[29:0],2'b00};    //left shift by 2 bits.
 204         if (r[17] == 1) //add if r is negative
 205             r = left + right;
 206         else    //subtract if r is positive
 207             r = left - right;
 208         q = {q[14:0],!r[17]};
 209     end
 210     sqrt = q;   //final assignment of output.
 211 end
 212 endfunction //end of Function
 213
 214
 215 c version (from paper linked from URL)
 216
 217 unsigned squart(D, r) /*Non-Restoring sqrt*/
 218     unsigned D; /*D:32-bit unsigned integer to be square rooted */
 219     int *r;
 220 {
 221     unsigned Q = 0; /*Q:16-bit unsigned integer (root)*/
 222     int R = 0; /*R:17-bit integer (remainder)*/
 223     int i;
 224     for (i = 15;i>=0;i--) /*for each root bit*/
 225     {
 226         if (R>=0)
 227         { /*new remainder:*/
 228             R = R<<2)|((D>>(i+i))&3);
 229             R = R-((Q<<2)|1); /*-Q01*/
 230         }
 231         else
 232         { /*new remainder:*/
 233             R = R<<2)|((D>>(i+i))&3);
 234             R = R+((Q<<2)|3); /*+Q11*/
 235         }
 236         if (R>=0) Q = Q<<1)|1; /*new Q:*/
 237         else Q = Q<<1)|0; /*new Q:*/
 238     }
 239
 240     /*remainder adjusting*/
 241     if (R<0) R = R+((Q<<1)|1);
 242     *r = R; /*return remainder*/
 243     return(Q); /*return root*/
 244 }
 245
 246 From wikipedia page:
 247
 248 short isqrt(short num) {
 249     short res = 0;
 250     short bit = 1 << 14; // The second-to-top bit is set: 1 << 30 for 32 bits
 251
 252     // "bit" starts at the highest power of four <= the argument.
 253     while (bit > num)
 254         bit >>= 2;
 255
 256     while (bit != 0) {
 257         if (num >= res + bit) {
 258             num -= res + bit;
 259             res = (res >> 1) + bit;
 260         }
 261         else
 262             res >>= 1;
 263         bit >>= 2;
 264     }
 265     return res;
 266 }
 267
 268 """