gistfile1.txt

log2_integer_recur(x, integer_result, error, multiplier, level):
 if x > multiplier:
   x = log2_integer_recur(x, integer_result, error, multiplier*multiplier, level*2)
   while x > multiplier:
     x := x / multiplier
     integer_result := integer_result + level
   return x  
 else:
  return x
  
log2_integer(x, integer_result, error):
 multiplier = 2
 if x > 2:
   x = log2_integer_recur(x, integer_result, error, multiplier*multiplier, 2):
   while x > 2:
     x := x / 2
     integer_result := integer_result + 1
   error = x
 else:
   error = x

log2(x):
 result = 0
 rem = 0
 i = 0
 log2_integer(x, i, rem) ; integer exponent stored in i, the remaining error from trial division stored in rem
 result += i ; accumulate result
 m = truncate(rem * 2^29) ; fixedpoint base. scale rem with a huge number then truncate
 log2_integer(m, i) ;get the integer exponent from m stored in i
 i -= 29 ; by the identity log(x / y) = log(x) - log(y), subtract log2(2^29) from the previous iteration
 result += i
 return result