Karatsuba algorithm: Difference between revisions

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Implementation: Changed the calculation of the size of numbers in pseudocode. We need the max lenght of num1 or num2, not the minimum.
Implementation: format code
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The second argument of the split_at function specifies the number of digits to extract from the ''right'': for example, split_at("12345", 3) will extract the 3 final digits, giving: high="12", low="345".
 
<syntaxhighlight lang="Cc">
function karatsuba (num1, num2)
if (num1 < 10) or (num2 < 10)
return num1 × num2 /* fall back to traditional multiplication */
/* Calculates the size of the numbers. */
m = max (size_base10(num1), size_base10(num2))
m2 = floor (m / 2)
/* m2 = ceil (m / 2) will also work */
/* Split the digit sequences in the middle. */
high1, low1 = split_at (num1, m2)
high2, low2 = split_at (num2, m2)
/* 3 recursive calls made to numbers approximately half the size. */
z0 = karatsuba (low1, low2)
z1 = karatsuba (low1 + high1, low2 + high2)
z2 = karatsuba (high1, high2)
return (z2 × 10 ^ (m2 × 2)) + ((z1 - z2 - z0) × 10 ^ m2) + z0