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Unformatted text preview: part was and how much it sped up. Consider a system where executing some application requires time ÌÓÐ . Suppose, some part of the system requires a fraction « of this time, and that we improve its performance by a factor of . That is, the component originally required time «ÌÓÐ , and it now requires time ´«ÌÓÐ µ . The overall execution time will be: ÌÒ Û From this, we can compute the speedup Ë « ÌÓÐ ÌÓÐ « ´½ µ ´½ «ÌÓÐ µ·« ·´ µ ÌÓÐ ÌÒ Û as: ´½ Ë « ½ µ· « (5.1) As an example, consider the case where a part of the system that initially consumed 60% of the time (« ¼ ) is sped up by a factor of 3 ( ½¼). Then we get a speedup of ½ ¼ ·¼ ¿ ½ . Thus, even though we made a substantial improvement to a major part of the system, our net speedup was significantly less. This is the major insight of Amdahl’s Law—to significantly speed up the entire system, we must improve the speed of a very large fraction of the overall system. Practice Problem 5.7: The ma...
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