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In computer architecture, speedup is a number that measures the relative performance of two systems processing the same problem. More technically, it is the ...
Amdahl's Law demonstrates the theoretical maximum speedup of an overall system and the concept of diminishing returns. Plotted here is logarithmic parallelization vs linear speedup. If exactly 50% of the work can be parallelized, the best possible speedup is 2 times. If 95% of the work can be parallelized, the best possible speedup is 20 times.
In computational complexity theory, a speedup theorem is a theorem that for any algorithm (of a certain class) demonstrates the existence of a more efficient algorithm solving the same problem.
is the theoretical speedup of the program with parallelism (scaled speedup [2]); N {\displaystyle N} is the number of processors; s {\displaystyle s} and p {\displaystyle p} are the fractions of time spent executing the serial parts and the parallel parts of the program, respectively, on the parallel system, where s + p = 1 {\displaystyle s+p=1} .
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Instructions per second (IPS) is a measure of a computer's processor speed. For complex instruction set computers (CISCs), different instructions take different amounts of time, so the value measured depends on the instruction mix; even for comparing processors in the same family the IPS measurement can be problematic.
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In mathematics, Gödel's speed-up theorem, proved by Gödel , shows that there are theorems whose proofs can be drastically shortened by working in more powerful axiomatic systems. Kurt Gödel showed how to find explicit examples of statements in formal systems that are provable in that system but whose shortest proof is unimaginably long.