Optimize integer arithmetic #7553
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Fuse a multiplication operator followed by an addition operator. That will generally reduce the number of instructions compared to having separate operators.
We used to replace division by a power of two with a right shift only when the dividend was known to be a positive integer. Extend the implementation to do right shift when the range of the dividend is unknown.
Inline the code for right shift a small operand any number steps. We used to call a helper routine when the shift count exceeded the number of bits in a small.
The routine for squaring a big integer did not have all optimizations that the multiplication routine had.
This commit implements the Karatsuba algorithm in a way that reduces the number of additions, resulting in a measureable performance improvement for multiplication of large integers.
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This pull request optimizes some of the arithmetic operations for integers.
The most noticeable improvement is in multiplication of large integers. Consider this benchmark:
Its running time is dominated by multiplication of large integers. This PR reduces the running time from about 0.45 seconds down to about 0.32 seconds on my computer (an M1 MacBook Pro).