Example Code
The following Python program computes the binary logarithm using the recursive method outlined above, showing the steps along the way: (This code fails when finding the binary logarithm of any number 2^n where n is any integer.)
def lg(x): ip = 0 rem = x # Integer part while rem<1: ip -= 1 rem *= 2 while rem>=2: ip += 1 rem /= 2 print("lg(%g) = %d + lg(%g)" % (x, ip, rem)) # Brackets required for Python 3 # Fractional part res = ip + frac_lg(rem) return res def frac_lg(x, fp=1.0, tol=1e-10): assert 1<=x<2 # terminate the recursion if we're close enough if fpSince Python does not optimize tail recursion, this can be implemented more efficiently with iteration. Here is an iterative version of the same algorithm in Perl:
sub lg { my $x = shift; my $tol = shift || 1e-13; my $res = 0.0; while ($x < 1) { $res -= 1; $x *= 2; } while ($x >= 2) { $res += 1; $x /= 2; } my $fp = 1.0; while ($fp >= $tol) { $fp /= 2; $x *= $x; if ($x >= 2) { $x /= 2; $res += $fp; } } $res } printf "x = %g\nlg(x) = %g\n", 4.5, lg(4.5);Read more about this topic: Binary Logarithm
Famous quotes containing the word code:
“Many people will say to working mothers, in effect, “I don’t think you can have it all.” The phrase for “have it all” is code for “have your cake and eat it too.” What these people really mean is that achievement in the workplace has always come at a price—usually a significant personal price; conversely, women who stayed home with their children were seen as having sacrificed a great deal of their own ambition for their families.”
—Anne C. Weisberg (20th century)
“Hollywood keeps before its child audiences a string of glorified young heroes, everyone of whom is an unhesitating and violent Anarchist. His one answer to everything that annoys him or disparages his country or his parents or his young lady or his personal code of manly conduct is to give the offender a “sock” in the jaw.... My observation leads me to believe that it is not the virtuous people who are good at socking jaws.”
—George Bernard Shaw (1856–1950)