////
/// @author Takeru Suzuki
////

/// Returns the natural logarithm of a number.
/// @since 1.12.0 - The Sith
/// @param {Number} $x
/// @return {Number} - modified number
/// @example
///   log(2)  // 0.69315
///   log(10) // 2.30259
@function log($x) {
	@if $x <= 0 {
		@return 0 / 0;
	}

	$k: nth(frexp($x / $sqrt2), 2);
	$x: $x / ldexp(1, $k);
	$x: ($x - 1) / ($x + 1);
	$x2: $x * $x;
	$i: 1;
	$s: $x;
	$sp: null;

	@while $sp != $s {
		$x: $x * $x2;
		$i: $i + 2;
		$sp: $s;
		$s: $s + $x / $i;
	}

	@return $ln2 * $k + 2 * $s;
}