Added info about highwater heap-memory use for the sortperf.py tests; + a
couple of minor edits elsewhere.
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@ -167,6 +167,34 @@ Comparison with Python's Samplesort Hybrid
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But timsort "should be" slower than samplesort on ~sort, so it's hard
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to count that it isn't on some boxes as a strike against it <wink>.
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+ Here's the highwater mark for the number of heap-based temp slots (4
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bytes each on this box) needed by each test, again with arguments
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"15 20 1":
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2**i *sort \sort /sort 3sort +sort %sort ~sort =sort !sort
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32768 16384 0 0 6256 0 10821 12288 0 16383
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65536 32766 0 0 21652 0 31276 24576 0 32767
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131072 65534 0 0 17258 0 58112 49152 0 65535
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262144 131072 0 0 35660 0 123561 98304 0 131071
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524288 262142 0 0 31302 0 212057 196608 0 262143
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1048576 524286 0 0 312438 0 484942 393216 0 524287
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Discussion: The tests that end up doing (close to) perfectly balanced
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merges (*sort, !sort) need all N//2 temp slots (or almost all). ~sort
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also ends up doing balanced merges, but systematically benefits a lot from
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the preliminary pre-merge searches described under "Merge Memory" later.
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%sort approaches having a balanced merge at the end because the random
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selection of elements to replace is expected to produce an out-of-order
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element near the midpoint. \sort, /sort, =sort are the trivial one-run
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cases, needing no merging at all. +sort ends up having one very long run
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and one very short, and so gets all the temp space it needs from the small
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temparray member of the MergeState struct (note that the same would be
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true if the new random elements were prefixed to the sorted list instead,
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but not if they appeared "in the middle"). 3sort approaches N//3 temp
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slots twice, but the run lengths that remain after 3 random exchanges
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clearly has very high variance.
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A detailed description of timsort follows.
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@ -460,13 +488,13 @@ Galloping with a Broken Leg
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---------------------------
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So why don't we always gallop? Because it can lose, on two counts:
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1. While we're willing to endure small per-run overheads, per-comparison
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1. While we're willing to endure small per-merge overheads, per-comparison
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overheads are a different story. Calling Yet Another Function per
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comparison is expensive, and gallop_left() and gallop_right() are
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too long-winded for sane inlining.
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2. Ignoring function-call overhead, galloping can-- alas --require more
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comparisons than linear one-at-time search, depending on the data.
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2. Galloping can-- alas --require more comparisons than linear one-at-time
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search, depending on the data.
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#2 requires details. If A[0] belongs before B[0], galloping requires 1
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compare to determine that, same as linear search, except it costs more
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