## root / htools / Ganeti / HTools / Node.hs @ 8bc34c7b

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{-| Module describing a node. |
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All updates are functional (copy-based) and return a new node with |

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updated value. |

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-} |

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{- |

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Copyright (C) 2009, 2010, 2011, 2012 Google Inc. |

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This program is free software; you can redistribute it and/or modify |

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it under the terms of the GNU General Public License as published by |

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the Free Software Foundation; either version 2 of the License, or |

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(at your option) any later version. |

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This program is distributed in the hope that it will be useful, but |

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WITHOUT ANY WARRANTY; without even the implied warranty of |

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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |

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General Public License for more details. |

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You should have received a copy of the GNU General Public License |

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along with this program; if not, write to the Free Software |

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Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |

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02110-1301, USA. |

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-} |

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module Ganeti.HTools.Node |

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( Node(..) |

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, List |

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-- * Constructor |

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, create |

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-- ** Finalization after data loading |

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, buildPeers |

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, setIdx |

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, setAlias |

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, setOffline |

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, setXmem |

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, setFmem |

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, setPri |

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, setSec |

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, setMdsk |

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, setMcpu |

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, setPolicy |

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-- * Tag maps |

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, addTags |

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, delTags |

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, rejectAddTags |

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-- * Instance (re)location |

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, removePri |

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, removeSec |

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, addPri |

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, addPriEx |

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, addSec |

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, addSecEx |

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-- * Stats |

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, availDisk |

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, availMem |

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, availCpu |

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, iMem |

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, iDsk |

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, conflictingPrimaries |

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-- * Formatting |

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, defaultFields |

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, showHeader |

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, showField |

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, list |

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-- * Misc stuff |

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, AssocList |

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, AllocElement |

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, noSecondary |

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, computeGroups |

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) where |

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import Data.List hiding (group) |

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import qualified Data.Map as Map |

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import qualified Data.Foldable as Foldable |

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import Data.Ord (comparing) |

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import Text.Printf (printf) |

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import qualified Ganeti.HTools.Container as Container |

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import qualified Ganeti.HTools.Instance as Instance |

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import qualified Ganeti.HTools.PeerMap as P |

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import qualified Ganeti.HTools.Types as T |

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-- * Type declarations |

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-- | The tag map type. |

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type TagMap = Map.Map String Int |

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-- | The node type. |

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data Node = Node |

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{ name :: String -- ^ The node name |

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, alias :: String -- ^ The shortened name (for display purposes) |

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, tMem :: Double -- ^ Total memory (MiB) |

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, nMem :: Int -- ^ Node memory (MiB) |

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, fMem :: Int -- ^ Free memory (MiB) |

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, xMem :: Int -- ^ Unaccounted memory (MiB) |

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, tDsk :: Double -- ^ Total disk space (MiB) |

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, fDsk :: Int -- ^ Free disk space (MiB) |

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, tCpu :: Double -- ^ Total CPU count |

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, uCpu :: Int -- ^ Used VCPU count |

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, spindleCount :: Int -- ^ Node spindles (spindle_count node parameter) |

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, pList :: [T.Idx] -- ^ List of primary instance indices |

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, sList :: [T.Idx] -- ^ List of secondary instance indices |

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, idx :: T.Ndx -- ^ Internal index for book-keeping |

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, peers :: P.PeerMap -- ^ Pnode to instance mapping |

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, failN1 :: Bool -- ^ Whether the node has failed n1 |

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, rMem :: Int -- ^ Maximum memory needed for failover by |

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-- primaries of this node |

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, pMem :: Double -- ^ Percent of free memory |

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, pDsk :: Double -- ^ Percent of free disk |

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, pRem :: Double -- ^ Percent of reserved memory |

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, pCpu :: Double -- ^ Ratio of virtual to physical CPUs |

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, mDsk :: Double -- ^ Minimum free disk ratio |

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, loDsk :: Int -- ^ Autocomputed from mDsk low disk |

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-- threshold |

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, hiCpu :: Int -- ^ Autocomputed from mCpu high cpu |

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-- threshold |

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, hiSpindles :: Double -- ^ Auto-computed from policy spindle_ratio |

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-- and the node spindle count |

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, instSpindles :: Double -- ^ Spindles used by instances |

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, offline :: Bool -- ^ Whether the node should not be used for |

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-- allocations and skipped from score |

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-- computations |

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, utilPool :: T.DynUtil -- ^ Total utilisation capacity |

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, utilLoad :: T.DynUtil -- ^ Sum of instance utilisation |

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, pTags :: TagMap -- ^ Map of primary instance tags and their count |

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, group :: T.Gdx -- ^ The node's group (index) |

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, iPolicy :: T.IPolicy -- ^ The instance policy (of the node's group) |

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} deriving (Show, Read, Eq) |

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instance T.Element Node where |

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nameOf = name |

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idxOf = idx |

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setAlias = setAlias |

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setIdx = setIdx |

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allNames n = [name n, alias n] |

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-- | A simple name for the int, node association list. |

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type AssocList = [(T.Ndx, Node)] |

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-- | A simple name for a node map. |

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type List = Container.Container Node |

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-- | A simple name for an allocation element (here just for logistic |

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-- reasons). |

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type AllocElement = (List, Instance.Instance, [Node], T.Score) |

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-- | Constant node index for a non-moveable instance. |

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noSecondary :: T.Ndx |

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noSecondary = -1 |

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-- * Helper functions |

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-- | Add a tag to a tagmap. |

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addTag :: TagMap -> String -> TagMap |

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addTag t s = Map.insertWith (+) s 1 t |

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-- | Add multiple tags. |

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addTags :: TagMap -> [String] -> TagMap |

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addTags = foldl' addTag |

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-- | Adjust or delete a tag from a tagmap. |

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delTag :: TagMap -> String -> TagMap |

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delTag t s = Map.update (\v -> if v > 1 |

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then Just (v-1) |

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else Nothing) |

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s t |

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-- | Remove multiple tags. |

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delTags :: TagMap -> [String] -> TagMap |

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delTags = foldl' delTag |

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-- | Check if we can add a list of tags to a tagmap. |

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rejectAddTags :: TagMap -> [String] -> Bool |

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rejectAddTags t = any (`Map.member` t) |

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-- | Check how many primary instances have conflicting tags. The |

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-- algorithm to compute this is to sum the count of all tags, then |

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-- subtract the size of the tag map (since each tag has at least one, |

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-- non-conflicting instance); this is equivalent to summing the |

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-- values in the tag map minus one. |

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conflictingPrimaries :: Node -> Int |

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conflictingPrimaries (Node { pTags = t }) = Foldable.sum t - Map.size t |

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-- * Initialization functions |

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-- | Create a new node. |

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-- |

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-- The index and the peers maps are empty, and will be need to be |

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-- update later via the 'setIdx' and 'buildPeers' functions. |

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create :: String -> Double -> Int -> Int -> Double |

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-> Int -> Double -> Bool -> Int -> T.Gdx -> Node |

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create name_init mem_t_init mem_n_init mem_f_init |

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dsk_t_init dsk_f_init cpu_t_init offline_init spindles_init |

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group_init = |

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Node { name = name_init |

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, alias = name_init |

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, tMem = mem_t_init |

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, nMem = mem_n_init |

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, fMem = mem_f_init |

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, tDsk = dsk_t_init |

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, fDsk = dsk_f_init |

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, tCpu = cpu_t_init |

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, spindleCount = spindles_init |

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, uCpu = 0 |

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, pList = [] |

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, sList = [] |

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, failN1 = True |

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, idx = -1 |

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, peers = P.empty |

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, rMem = 0 |

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, pMem = fromIntegral mem_f_init / mem_t_init |

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, pDsk = fromIntegral dsk_f_init / dsk_t_init |

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, pRem = 0 |

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, pCpu = 0 |

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, offline = offline_init |

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, xMem = 0 |

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, mDsk = T.defReservedDiskRatio |

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, loDsk = mDskToloDsk T.defReservedDiskRatio dsk_t_init |

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, hiCpu = mCpuTohiCpu (T.iPolicyVcpuRatio T.defIPolicy) cpu_t_init |

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, hiSpindles = computeHiSpindles (T.iPolicySpindleRatio T.defIPolicy) |

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spindles_init |

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, instSpindles = 0 |

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, utilPool = T.baseUtil |

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, utilLoad = T.zeroUtil |

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, pTags = Map.empty |

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, group = group_init |

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, iPolicy = T.defIPolicy |

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} |

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-- | Conversion formula from mDsk\/tDsk to loDsk. |

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mDskToloDsk :: Double -> Double -> Int |

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mDskToloDsk mval = floor . (mval *) |

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-- | Conversion formula from mCpu\/tCpu to hiCpu. |

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mCpuTohiCpu :: Double -> Double -> Int |

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mCpuTohiCpu mval = floor . (mval *) |

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-- | Conversiojn formula from spindles and spindle ratio to hiSpindles. |

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computeHiSpindles :: Double -> Int -> Double |

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computeHiSpindles spindle_ratio = (spindle_ratio *) . fromIntegral |

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-- | Changes the index. |

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-- |

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-- This is used only during the building of the data structures. |

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setIdx :: Node -> T.Ndx -> Node |

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setIdx t i = t {idx = i} |

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-- | Changes the alias. |

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-- |

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-- This is used only during the building of the data structures. |

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setAlias :: Node -> String -> Node |

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setAlias t s = t { alias = s } |

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-- | Sets the offline attribute. |

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setOffline :: Node -> Bool -> Node |

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setOffline t val = t { offline = val } |

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-- | Sets the unnaccounted memory. |

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setXmem :: Node -> Int -> Node |

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setXmem t val = t { xMem = val } |

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-- | Sets the max disk usage ratio. |

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setMdsk :: Node -> Double -> Node |

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setMdsk t val = t { mDsk = val, loDsk = mDskToloDsk val (tDsk t) } |

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-- | Sets the max cpu usage ratio. This will update the node's |

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-- ipolicy, losing sharing (but it should be a seldomly done operation). |

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setMcpu :: Node -> Double -> Node |

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setMcpu t val = |

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let new_ipol = (iPolicy t) { T.iPolicyVcpuRatio = val } |

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in t { hiCpu = mCpuTohiCpu val (tCpu t), iPolicy = new_ipol } |

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-- | Sets the policy. |

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setPolicy :: T.IPolicy -> Node -> Node |

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setPolicy pol node = |

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node { iPolicy = pol |

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, hiCpu = mCpuTohiCpu (T.iPolicyVcpuRatio pol) (tCpu node) |

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, hiSpindles = computeHiSpindles (T.iPolicySpindleRatio pol) |

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(spindleCount node) |

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} |

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-- | Computes the maximum reserved memory for peers from a peer map. |

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computeMaxRes :: P.PeerMap -> P.Elem |

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computeMaxRes = P.maxElem |

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-- | Builds the peer map for a given node. |

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buildPeers :: Node -> Instance.List -> Node |

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buildPeers t il = |

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let mdata = map |

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(\i_idx -> let inst = Container.find i_idx il |

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mem = if Instance.usesSecMem inst |

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then Instance.mem inst |

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else 0 |

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in (Instance.pNode inst, mem)) |

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(sList t) |

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pmap = P.accumArray (+) mdata |

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new_rmem = computeMaxRes pmap |

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new_failN1 = fMem t <= new_rmem |

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new_prem = fromIntegral new_rmem / tMem t |

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in t {peers=pmap, failN1 = new_failN1, rMem = new_rmem, pRem = new_prem} |

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-- | Assigns an instance to a node as primary and update the used VCPU |

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-- count, utilisation data and tags map. |

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setPri :: Node -> Instance.Instance -> Node |

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setPri t inst = t { pList = Instance.idx inst:pList t |

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, uCpu = new_count |

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, pCpu = fromIntegral new_count / tCpu t |

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, utilLoad = utilLoad t `T.addUtil` Instance.util inst |

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, pTags = addTags (pTags t) (Instance.tags inst) |

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} |

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where new_count = Instance.applyIfOnline inst (+ Instance.vcpus inst) |

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(uCpu t ) |

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-- | Assigns an instance to a node as secondary without other updates. |

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setSec :: Node -> Instance.Instance -> Node |

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setSec t inst = t { sList = Instance.idx inst:sList t |

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, utilLoad = old_load { T.dskWeight = T.dskWeight old_load + |

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T.dskWeight (Instance.util inst) } |

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} |

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where old_load = utilLoad t |

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-- * Update functions |

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-- | Sets the free memory. |

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setFmem :: Node -> Int -> Node |

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setFmem t new_mem = |

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let new_n1 = new_mem <= rMem t |

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new_mp = fromIntegral new_mem / tMem t |

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in t { fMem = new_mem, failN1 = new_n1, pMem = new_mp } |

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-- | Removes a primary instance. |

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removePri :: Node -> Instance.Instance -> Node |

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removePri t inst = |

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let iname = Instance.idx inst |

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new_plist = delete iname (pList t) |

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new_mem = Instance.applyIfOnline inst (+ Instance.mem inst) (fMem t) |

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new_dsk = fDsk t + Instance.dsk inst |

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new_mp = fromIntegral new_mem / tMem t |

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new_dp = fromIntegral new_dsk / tDsk t |

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new_failn1 = new_mem <= rMem t |

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new_ucpu = Instance.applyIfOnline inst |

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(\x -> x - Instance.vcpus inst) (uCpu t) |

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new_rcpu = fromIntegral new_ucpu / tCpu t |

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new_load = utilLoad t `T.subUtil` Instance.util inst |

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in t { pList = new_plist, fMem = new_mem, fDsk = new_dsk |

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, failN1 = new_failn1, pMem = new_mp, pDsk = new_dp |

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, uCpu = new_ucpu, pCpu = new_rcpu, utilLoad = new_load |

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, pTags = delTags (pTags t) (Instance.tags inst) } |

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-- | Removes a secondary instance. |

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removeSec :: Node -> Instance.Instance -> Node |

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removeSec t inst = |

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let iname = Instance.idx inst |

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cur_dsk = fDsk t |

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pnode = Instance.pNode inst |

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new_slist = delete iname (sList t) |

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new_dsk = if Instance.usesLocalStorage inst |

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then cur_dsk + Instance.dsk inst |

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else cur_dsk |

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old_peers = peers t |

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old_peem = P.find pnode old_peers |

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new_peem = if Instance.usesSecMem inst |

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then old_peem - Instance.mem inst |

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else old_peem |

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new_peers = if new_peem > 0 |

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then P.add pnode new_peem old_peers |

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else P.remove pnode old_peers |

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old_rmem = rMem t |

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new_rmem = if old_peem < old_rmem |

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then old_rmem |

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else computeMaxRes new_peers |

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new_prem = fromIntegral new_rmem / tMem t |

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new_failn1 = fMem t <= new_rmem |

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new_dp = fromIntegral new_dsk / tDsk t |

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old_load = utilLoad t |

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new_load = old_load { T.dskWeight = T.dskWeight old_load - |

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T.dskWeight (Instance.util inst) } |

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in t { sList = new_slist, fDsk = new_dsk, peers = new_peers |

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, failN1 = new_failn1, rMem = new_rmem, pDsk = new_dp |

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, pRem = new_prem, utilLoad = new_load } |

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-- | Adds a primary instance (basic version). |

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addPri :: Node -> Instance.Instance -> T.OpResult Node |

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addPri = addPriEx False |

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-- | Adds a primary instance (extended version). |

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addPriEx :: Bool -- ^ Whether to override the N+1 and |

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-- other /soft/ checks, useful if we |

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-- come from a worse status |

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-- (e.g. offline) |

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-> Node -- ^ The target node |

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-> Instance.Instance -- ^ The instance to add |

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-> T.OpResult Node -- ^ The result of the operation, |

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-- either the new version of the node |

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-- or a failure mode |

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addPriEx force t inst = |

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let iname = Instance.idx inst |

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uses_disk = Instance.usesLocalStorage inst |

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cur_dsk = fDsk t |

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new_mem = Instance.applyIfOnline inst |

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(\x -> x - Instance.mem inst) (fMem t) |

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new_dsk = if uses_disk |

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then cur_dsk - Instance.dsk inst |

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else cur_dsk |

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new_failn1 = new_mem <= rMem t |

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new_ucpu = Instance.applyIfOnline inst (+ Instance.vcpus inst) (uCpu t) |

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new_pcpu = fromIntegral new_ucpu / tCpu t |

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new_dp = fromIntegral new_dsk / tDsk t |

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l_cpu = T.iPolicyVcpuRatio $ iPolicy t |

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new_load = utilLoad t `T.addUtil` Instance.util inst |

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inst_tags = Instance.tags inst |

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old_tags = pTags t |

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strict = not force |

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in case () of |

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_ | new_mem <= 0 -> T.OpFail T.FailMem |

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| uses_disk && new_dsk <= 0 -> T.OpFail T.FailDisk |

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| uses_disk && mDsk t > new_dp && strict -> T.OpFail T.FailDisk |

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| new_failn1 && not (failN1 t) && strict -> T.OpFail T.FailMem |

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| l_cpu >= 0 && l_cpu < new_pcpu && strict -> T.OpFail T.FailCPU |

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| rejectAddTags old_tags inst_tags -> T.OpFail T.FailTags |

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| otherwise -> |

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let new_plist = iname:pList t |

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new_mp = fromIntegral new_mem / tMem t |

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r = t { pList = new_plist, fMem = new_mem, fDsk = new_dsk |

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, failN1 = new_failn1, pMem = new_mp, pDsk = new_dp |

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, uCpu = new_ucpu, pCpu = new_pcpu |

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, utilLoad = new_load |

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, pTags = addTags old_tags inst_tags } |

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in T.OpGood r |

434 | |

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-- | Adds a secondary instance (basic version). |

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addSec :: Node -> Instance.Instance -> T.Ndx -> T.OpResult Node |

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addSec = addSecEx False |

438 | |

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-- | Adds a secondary instance (extended version). |

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addSecEx :: Bool -> Node -> Instance.Instance -> T.Ndx -> T.OpResult Node |

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addSecEx force t inst pdx = |

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let iname = Instance.idx inst |

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old_peers = peers t |

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old_mem = fMem t |

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new_dsk = fDsk t - Instance.dsk inst |

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secondary_needed_mem = if Instance.usesSecMem inst |

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then Instance.mem inst |

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else 0 |

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new_peem = P.find pdx old_peers + secondary_needed_mem |

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new_peers = P.add pdx new_peem old_peers |

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new_rmem = max (rMem t) new_peem |

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new_prem = fromIntegral new_rmem / tMem t |

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new_failn1 = old_mem <= new_rmem |

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new_dp = fromIntegral new_dsk / tDsk t |

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old_load = utilLoad t |

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new_load = old_load { T.dskWeight = T.dskWeight old_load + |

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T.dskWeight (Instance.util inst) } |

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strict = not force |

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in case () of |

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_ | not (Instance.hasSecondary inst) -> T.OpFail T.FailDisk |

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| new_dsk <= 0 -> T.OpFail T.FailDisk |

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| mDsk t > new_dp && strict -> T.OpFail T.FailDisk |

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| secondary_needed_mem >= old_mem && strict -> T.OpFail T.FailMem |

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| new_failn1 && not (failN1 t) && strict -> T.OpFail T.FailMem |

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| otherwise -> |

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let new_slist = iname:sList t |

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r = t { sList = new_slist, fDsk = new_dsk |

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, peers = new_peers, failN1 = new_failn1 |

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, rMem = new_rmem, pDsk = new_dp |

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, pRem = new_prem, utilLoad = new_load } |

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in T.OpGood r |

472 | |

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-- * Stats functions |

474 | |

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-- | Computes the amount of available disk on a given node. |

476 |
availDisk :: Node -> Int |

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availDisk t = |

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let _f = fDsk t |

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_l = loDsk t |

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in if _f < _l |

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then 0 |

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else _f - _l |

483 | |

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-- | Computes the amount of used disk on a given node. |

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iDsk :: Node -> Int |

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iDsk t = truncate (tDsk t) - fDsk t |

487 | |

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-- | Computes the amount of available memory on a given node. |

489 |
availMem :: Node -> Int |

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availMem t = |

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let _f = fMem t |

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_l = rMem t |

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in if _f < _l |

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then 0 |

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else _f - _l |

496 | |

497 |
-- | Computes the amount of available memory on a given node. |

498 |
availCpu :: Node -> Int |

499 |
availCpu t = |

500 |
let _u = uCpu t |

501 |
_l = hiCpu t |

502 |
in if _l >= _u |

503 |
then _l - _u |

504 |
else 0 |

505 | |

506 |
-- | The memory used by instances on a given node. |

507 |
iMem :: Node -> Int |

508 |
iMem t = truncate (tMem t) - nMem t - xMem t - fMem t |

509 | |

510 |
-- * Display functions |

511 | |

512 |
-- | Return a field for a given node. |

513 |
showField :: Node -- ^ Node which we're querying |

514 |
-> String -- ^ Field name |

515 |
-> String -- ^ Field value as string |

516 |
showField t field = |

517 |
case field of |

518 |
"idx" -> printf "%4d" $ idx t |

519 |
"name" -> alias t |

520 |
"fqdn" -> name t |

521 |
"status" -> case () of |

522 |
_ | offline t -> "-" |

523 |
| failN1 t -> "*" |

524 |
| otherwise -> " " |

525 |
"tmem" -> printf "%5.0f" $ tMem t |

526 |
"nmem" -> printf "%5d" $ nMem t |

527 |
"xmem" -> printf "%5d" $ xMem t |

528 |
"fmem" -> printf "%5d" $ fMem t |

529 |
"imem" -> printf "%5d" $ iMem t |

530 |
"rmem" -> printf "%5d" $ rMem t |

531 |
"amem" -> printf "%5d" $ fMem t - rMem t |

532 |
"tdsk" -> printf "%5.0f" $ tDsk t / 1024 |

533 |
"fdsk" -> printf "%5d" $ fDsk t `div` 1024 |

534 |
"tcpu" -> printf "%4.0f" $ tCpu t |

535 |
"ucpu" -> printf "%4d" $ uCpu t |

536 |
"pcnt" -> printf "%3d" $ length (pList t) |

537 |
"scnt" -> printf "%3d" $ length (sList t) |

538 |
"plist" -> show $ pList t |

539 |
"slist" -> show $ sList t |

540 |
"pfmem" -> printf "%6.4f" $ pMem t |

541 |
"pfdsk" -> printf "%6.4f" $ pDsk t |

542 |
"rcpu" -> printf "%5.2f" $ pCpu t |

543 |
"cload" -> printf "%5.3f" uC |

544 |
"mload" -> printf "%5.3f" uM |

545 |
"dload" -> printf "%5.3f" uD |

546 |
"nload" -> printf "%5.3f" uN |

547 |
"ptags" -> intercalate "," . map (uncurry (printf "%s=%d")) . |

548 |
Map.toList $ pTags t |

549 |
"peermap" -> show $ peers t |

550 |
_ -> T.unknownField |

551 |
where |

552 |
T.DynUtil { T.cpuWeight = uC, T.memWeight = uM, |

553 |
T.dskWeight = uD, T.netWeight = uN } = utilLoad t |

554 | |

555 |
-- | Returns the header and numeric propery of a field. |

556 |
showHeader :: String -> (String, Bool) |

557 |
showHeader field = |

558 |
case field of |

559 |
"idx" -> ("Index", True) |

560 |
"name" -> ("Name", False) |

561 |
"fqdn" -> ("Name", False) |

562 |
"status" -> ("F", False) |

563 |
"tmem" -> ("t_mem", True) |

564 |
"nmem" -> ("n_mem", True) |

565 |
"xmem" -> ("x_mem", True) |

566 |
"fmem" -> ("f_mem", True) |

567 |
"imem" -> ("i_mem", True) |

568 |
"rmem" -> ("r_mem", True) |

569 |
"amem" -> ("a_mem", True) |

570 |
"tdsk" -> ("t_dsk", True) |

571 |
"fdsk" -> ("f_dsk", True) |

572 |
"tcpu" -> ("pcpu", True) |

573 |
"ucpu" -> ("vcpu", True) |

574 |
"pcnt" -> ("pcnt", True) |

575 |
"scnt" -> ("scnt", True) |

576 |
"plist" -> ("primaries", True) |

577 |
"slist" -> ("secondaries", True) |

578 |
"pfmem" -> ("p_fmem", True) |

579 |
"pfdsk" -> ("p_fdsk", True) |

580 |
"rcpu" -> ("r_cpu", True) |

581 |
"cload" -> ("lCpu", True) |

582 |
"mload" -> ("lMem", True) |

583 |
"dload" -> ("lDsk", True) |

584 |
"nload" -> ("lNet", True) |

585 |
"ptags" -> ("PrimaryTags", False) |

586 |
"peermap" -> ("PeerMap", False) |

587 |
-- TODO: add node fields (group.uuid, group) |

588 |
_ -> (T.unknownField, False) |

589 | |

590 |
-- | String converter for the node list functionality. |

591 |
list :: [String] -> Node -> [String] |

592 |
list fields t = map (showField t) fields |

593 | |

594 |
-- | Constant holding the fields we're displaying by default. |

595 |
defaultFields :: [String] |

596 |
defaultFields = |

597 |
[ "status", "name", "tmem", "nmem", "imem", "xmem", "fmem" |

598 |
, "rmem", "tdsk", "fdsk", "tcpu", "ucpu", "pcnt", "scnt" |

599 |
, "pfmem", "pfdsk", "rcpu" |

600 |
, "cload", "mload", "dload", "nload" ] |

601 | |

602 |
-- | Split a list of nodes into a list of (node group UUID, list of |

603 |
-- associated nodes). |

604 |
computeGroups :: [Node] -> [(T.Gdx, [Node])] |

605 |
computeGroups nodes = |

606 |
let nodes' = sortBy (comparing group) nodes |

607 |
nodes'' = groupBy (\a b -> group a == group b) nodes' |

608 |
in map (\nl -> (group (head nl), nl)) nodes'' |