{"id":2773,"date":"2019-07-16T15:00:05","date_gmt":"2019-07-16T15:00:05","guid":{"rendered":"https:\/\/nenadnoveljic.com\/blog\/?p=2773"},"modified":"2020-10-08T14:27:41","modified_gmt":"2020-10-08T14:27:41","slug":"io-sort-cost-calculation-2","status":"publish","type":"post","link":"https:\/\/nenadnoveljic.com\/blog\/io-sort-cost-calculation-2\/","title":{"rendered":"IO Sort Cost Calculation (2)"},"content":{"rendered":"

In my previous blog post<\/a> I described the IO costing for sort operation. It turned out that the calculation functions are central and used in other scenarios as well, like full table scan (FTS); as such, they are definitely worth giving it a second look.<\/p>\n

So I did a similar low-level analysis for FTS and deduced more generic formulae.<\/p>\n

Expectedly, scaled IO cost<\/i> depends on the number of blocks:<\/p>\n

<\/a><\/p>\n

(1) <\/span>   <\/span>\"\begin{equation*} <\/p>\n

Both +1<\/i> are really just the safeguards against multiplication\/division by zero, which would lead the whole cost calculation astray. But, as normally, blocks >> 1 and cost >>1, the equation 1<\/a> can be approximated as follows:<\/p>\n

<\/a><\/p>\n

(2) <\/span>   <\/span>\"\begin{equation*} <\/p>\n

where<\/p>\n

<\/a><\/p>\n

(3) <\/span>   <\/span>\"\begin{equation*} <\/p>\n

In the equation above, we can recognize the single-block read time (SREADTIM) in the numerator and multi-block read time (MREADTIM) in the denominator.<\/p>\n

<\/a><\/p>\n

(4) <\/span>   <\/span>\"\begin{equation*} <\/p>\n

<\/a><\/p>\n

(5) <\/span>   <\/span>\"\begin{equation*} <\/p>\n

Consequently, io scale factor<\/i> can be expressed by the means of SREAD and MREADTIM:<\/p>\n

<\/a><\/p>\n

(6) <\/span>   <\/span>\"\begin{equation*} <\/p>\n

Everything gets perfectly clear after combining the equations 2<\/a> and 6<\/a>, i.e. expressing also scaled io cost<\/i> as a function of SREADTIME and MREADTIM:<\/p>\n

<\/a><\/p>\n

(7) <\/span>   <\/span>\"\begin{equation*} <\/p>\n

That’s a well known formula documented in [Lewis 2006]<\/a>. Simply put, the cost calculated in the equation 7<\/a> is the total multi-block read time divided by a single-block read time. Or, in other words, to paraphrase Jonathan Lewis<\/a>: “the cost is total predicted time, expressed in units of the single-block read time”.<\/p>\n

After having sorted out the general formula, I revisited the IO sort cost calculation. Predictably, the io scale factor<\/i> calculation is just a variant of the general calculation with a special value for MBRC:<\/p>\n

(8) <\/span>   <\/span>\"\begin{equation*}<\/p>\n

This means that the optimizer always foresees 64k IOs for sort. Consequently, the MBRC is simply the number of blocks that fit in 64k.<\/p>\n

For FTS, the total IO cost equals scaled io cost<\/i>.<\/p>\n

<\/a><\/p>\n

(9) <\/span>   <\/span>\"\begin{equation*} <\/p>\n

But for sort, the total IO cost contains other components as well:<\/p>\n

<\/a><\/p>\n

(10) <\/span>   <\/span>\"\begin{equation*} <\/p>\n

Multiplying scaled IO cost<\/i> by two might mean that the data has to be read twice.<\/p>\n

But what’s the rationale behind adding blocks<\/i>? I don’t know. Both summands are expressed in different units anyway. I mean scaled io cost<\/i> is measured in “single-block read time”, and blocks<\/i> don’t have any units at all. And precisely this oddity is the reason why the sort cost significantly changes with the block size.<\/p>\n

Related blog post:<\/p>\n

IO Sort Cost Calculation<\/a><\/p>\n

References:<\/p>\n

[Lewis 2006]<\/a> Jonathan Lewis<\/a>. (2006). Cost-Based Oracle Fundamentals<\/p>\n

Updates on October 8, 2020<\/h1>\n

floor<\/i> on the fraction was missing in the formula for io_scale_factor. This became apparent when I tried to apply it to Jonathan Lewis’ model for investigating an index FFS cost anomaly<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

Interpreting formulae; comparison to full table scan calculation Continue Reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[11,5,32],"tags":[],"class_list":["post-2773","post","type-post","status-publish","format-standard","hentry","category-cost-based-optimizer","category-oracle","category-sort"],"yoast_head":"\nIO Sort Cost Calculation (2) - All-round Database Topics<\/title>\n<meta name=\"description\" content=\"Interpreting formulae; comparison to full table scan calculation\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/nenadnoveljic.com\/blog\/io-sort-cost-calculation-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"IO Sort Cost Calculation (2) - All-round Database Topics\" \/>\n<meta property=\"og:description\" content=\"Interpreting formulae; 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