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10.3 Speed efficiency
Speed efficiency is obtained by the combination of the following tricks and algorithms:
- Small integers, being represented as immediate values, don’t require memory access, just a couple of instructions for each elementary operation.
-
The kernel of CLN has been written in assembly language for some CPUs
(
i386,m68k,sparc,mips,arm). - On all CPUs, CLN may be configured to use the superefficient low-level routines from GNU GMP version 3.
-
For large numbers, CLN uses, instead of the standard
O(N^2)algorithm, the Karatsuba multiplication, which is an algorithm. - For very large numbers (more than 12000 decimal digits), CLN uses multiplication, which is an asymptotically optimal multiplication algorithm.
- These fast multiplication algorithms also give improvements in the speed of division and radix conversion.
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