Java 使用哪种算法进行乘法运算？

Question

The list of possible algorithms for multiplication is quite long:

• Schoolbook long multiplication
• Karatsuba algorithm
• 3-way Toom–Cook multiplication
• k-way Toom–Cook multiplication
• Mixed-level Toom–Cook
• Schönhage–Strassen algorithm
• Fürer's algorithm

Which one is used by Java by default and why? When does it switch to a "better performance" algorithm?

Answer 1

Well... the * operator will use whatever the hardware provides. Java has no say in it.

But if you are talking about BigInteger.multiply(BigInteger) , the answer depends on the Java version. For Java 11 it uses:

• naive "long multiplication" for small numbers,
• Karatsuba algorithm for medium sized number, and
• 3-way Toom–Cook multiplication for large numbers.

The thresholds are Karatsuba for numbers represented by 80 to 239 int values, an 3-way Toom-Cook for >= 240 int values. The smaller of the numbers being multiplied controls the algorithm selection.

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Which one is used by Java by default and why?

Which ones? See above.

Why? Comments in the code imply that the thresholds were chosen empirically; ie someone did some systematic testing to determine which threshold values gave the best performance ¹ .

You can find more details by reading the source code ² .

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^{1 - The current implementation BigInteger implementation hasn't changed significantly since 2013, so it is possible that it doesn't incorporate more recent research results.
2 - Note that this link is to the latest version on Github.}