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)
“Wise Draco comes, deep in the midnight roll
Of black artillery; he comes, though late;
In code corroborating Calvin’s creed
And cynic tyrannies of honest kings;
He comes, nor parlies; and the Town, redeemed,
Gives thanks devout; nor, being thankful, heeds
The grimy slur on the Republic’s faith implied,
Which holds that Man is naturally good,
And—more—is Nature’s Roman, never to be
scourged.”
—Herman Melville (1819–1891)