SQLite

/*
** Estimated quantities used for query planning are stored as 16-bit
** logarithms.  For quantity X, the value stored is 10*log2(X).  This
** gives a possible range of values of approximately 1.0e986 to 1e-986.
** But the allowed values are "grainy".  Not every value is representable.
** For example, quantities 16 and 17 are both represented by a LogEst
** of 40.  However, since LogEst quantatites are suppose to be estimates,
** of 40.  However, since LogEst quantaties are suppose to be estimates,
** not exact values, this imprecision is not a problem.
**
** "LogEst" is short for "Logarithimic Estimate".
** "LogEst" is short for "Logarithmic Estimate".
**
** Examples:
**      1 -> 0              20 -> 43          10000 -> 132
**      2 -> 10             25 -> 46          25000 -> 146
**      3 -> 16            100 -> 66        1000000 -> 199
**      4 -> 20           1000 -> 99        1048576 -> 200
**     10 -> 33           1024 -> 100    4294967296 -> 320

    if( b>a+49 ) return b;
    if( b>a+31 ) return b+1;
    return b+x[b-a];
  }
}

/*
** Convert an integer into a LogEst.  In other words, compute a
** good approximatation for 10*log2(x).
** Convert an integer into a LogEst.  In other words, compute an
** approximation for 10*log2(x).
*/
LogEst sqlite3LogEst(u64 x){
  static LogEst a[] = { 0, 2, 3, 5, 6, 7, 8, 9 };
  LogEst y = 40;
  if( x<8 ){
    if( x<2 ) return 0;
    while( x<8 ){  y -= 10; x <<= 1; }