///
/// It rounds ``f`` to a float with 64 bit significand and multiplies it by the best approximation
/// of `10^e` (in the same floating point format). This is often enough to get the correct result.
-/// However, when the result is close to halfway between two adjecent (ordinary) floats, the
+/// However, when the result is close to halfway between two adjacent (ordinary) floats, the
/// compound rounding error from multiplying two approximation means the result may be off by a
/// few bits. When this happens, the iterative Algorithm R fixes things up.
///
//
// Therefore, when the rounded-off bits are != 0.5 ULP, they decide the rounding
// on their own. When they are equal and the remainder is non-zero, the value still
- // needs to be rounded up. Only when the rounded off bits are 1/2 and the remainer
+ // needs to be rounded up. Only when the rounded off bits are 1/2 and the remainder
// is zero, we have a half-to-even situation.
let bits = x.bit_length();
let lsb = bits - T::sig_bits() as usize;