2021-08-26 00:39:48 +00:00
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# calculators
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Some extra information on the more complex topics (:
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2021-08-26 01:42:17 +00:00
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## Karatsuba Algorithm
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2021-08-26 00:39:48 +00:00
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### Useful Links
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- [Wikipedia](https://en.wikipedia.org/wiki/Karatsuba_algorithm)
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- [An amazing video on the topic](https://youtu.be/cCKOl5li6YM)
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### The Pseudocode
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```
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function karatsuba (num1, num2)
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if (num1 < 10) or (num2 < 10)
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return num1 × num2 /* fall back to traditional multiplication */
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/* Calculates the size of the numbers. */
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m = min (size_base10(num1), size_base10(num2))
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m2 = floor (m / 2)
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/* m2 = ceil (m / 2) will also work */
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/* Split the digit sequences in the middle. */
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high1, low1 = split_at (num1, m2)
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high2, low2 = split_at (num2, m2)
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/* 3 recursive calls made to numbers approximately half the size. */
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z0 = karatsuba (low1, low2)
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z1 = karatsuba (low1 + high1, low2 + high2)
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z2 = karatsuba (high1, high2)
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return (z2 × 10 ^ (m2 × 2)) + ((z1 - z2 - z0) × 10 ^ m2) + z0
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```
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