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:
“... the self respect of individuals ought to make them demand of their leaders conformity with an agreed-upon code of ethics and moral conduct.”
—Mary Barnett Gilson (1877?)
“Wise Draco comes, deep in the midnight roll
Of black artillery; he comes, though late;
In code corroborating Calvins 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 Republics faith implied,
Which holds that Man is naturally good,
Andmoreis Natures Roman, never to be
scourged.”
—Herman Melville (18191891)