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Processor L1 cache size performance impact

I was wondering how much the L1 cache size improves performance, because there are modern cpus that have 512kb,258kb,128kb of L1 cache and will, let's say doubling the L1 cache of let's say an i5 haswell cpu or fx piledriver cpu give much better performance?
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    To a certain point, maybe
    The problem is.
    Faster cache=smaller cache
    Bigger cache=slower cache
    Thats why there is l1,l2,l3 cache
    The cache is also related to cpu performance.
    Giving super large/fast to a crappy core will still give crappy performance. The other way is also true
    Thus, i believe the size of cache is optimized for the cpu. without bottleneck on both side.
    So larger cache cpu generally relates to stronger core., but to conclude, i do believe increasing cache will improve performance untill one side caps
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