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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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  , 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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  , 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 -> 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 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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       , 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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       , 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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-- | 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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-- | 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
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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
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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
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-- * Stats functions
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-- | Computes the amount of available disk on a given node.
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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
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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
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-- | Computes the amount of available memory on a given node.
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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
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-- | Computes the amount of available memory on a given node.
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availCpu :: Node -> Int
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availCpu t =
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  let _u = uCpu t
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      _l = hiCpu t
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  in if _l >= _u
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       then _l - _u
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       else 0
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-- | The memory used by instances on a given node.
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iMem :: Node -> Int
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iMem t = truncate (tMem t) - nMem t - xMem t - fMem t
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-- * Display functions
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-- | Return a field for a given node.
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showField :: Node   -- ^ Node which we're querying
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          -> String -- ^ Field name
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          -> String -- ^ Field value as string
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showField t field =
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  case field of
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    "idx"  -> printf "%4d" $ idx t
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    "name" -> alias t
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    "fqdn" -> name t
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    "status" -> case () of
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                  _ | offline t -> "-"
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                    | failN1 t -> "*"
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                    | otherwise -> " "
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    "tmem" -> printf "%5.0f" $ tMem t
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    "nmem" -> printf "%5d" $ nMem t
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    "xmem" -> printf "%5d" $ xMem t
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    "fmem" -> printf "%5d" $ fMem t
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    "imem" -> printf "%5d" $ iMem t
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    "rmem" -> printf "%5d" $ rMem t
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    "amem" -> printf "%5d" $ fMem t - rMem t
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    "tdsk" -> printf "%5.0f" $ tDsk t / 1024
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    "fdsk" -> printf "%5d" $ fDsk t `div` 1024
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    "tcpu" -> printf "%4.0f" $ tCpu t
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    "ucpu" -> printf "%4d" $ uCpu t
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    "pcnt" -> printf "%3d" $ length (pList t)
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    "scnt" -> printf "%3d" $ length (sList t)
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    "plist" -> show $ pList t
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    "slist" -> show $ sList t
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    "pfmem" -> printf "%6.4f" $ pMem t
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    "pfdsk" -> printf "%6.4f" $ pDsk t
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    "rcpu"  -> printf "%5.2f" $ pCpu t
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    "cload" -> printf "%5.3f" uC
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    "mload" -> printf "%5.3f" uM
529 fd7a7c73 Iustin Pop
    "dload" -> printf "%5.3f" uD
530 fd7a7c73 Iustin Pop
    "nload" -> printf "%5.3f" uN
531 fd7a7c73 Iustin Pop
    "ptags" -> intercalate "," . map (uncurry (printf "%s=%d")) .
532 fd7a7c73 Iustin Pop
               Map.toList $ pTags t
533 fd7a7c73 Iustin Pop
    "peermap" -> show $ peers t
534 fd7a7c73 Iustin Pop
    _ -> T.unknownField
535 fd7a7c73 Iustin Pop
  where
536 fd7a7c73 Iustin Pop
    T.DynUtil { T.cpuWeight = uC, T.memWeight = uM,
537 fd7a7c73 Iustin Pop
                T.dskWeight = uD, T.netWeight = uN } = utilLoad t
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-- | Returns the header and numeric propery of a field.
540 76354e11 Iustin Pop
showHeader :: String -> (String, Bool)
541 76354e11 Iustin Pop
showHeader field =
542 fd7a7c73 Iustin Pop
  case field of
543 fd7a7c73 Iustin Pop
    "idx" -> ("Index", True)
544 fd7a7c73 Iustin Pop
    "name" -> ("Name", False)
545 fd7a7c73 Iustin Pop
    "fqdn" -> ("Name", False)
546 fd7a7c73 Iustin Pop
    "status" -> ("F", False)
547 fd7a7c73 Iustin Pop
    "tmem" -> ("t_mem", True)
548 fd7a7c73 Iustin Pop
    "nmem" -> ("n_mem", True)
549 fd7a7c73 Iustin Pop
    "xmem" -> ("x_mem", True)
550 fd7a7c73 Iustin Pop
    "fmem" -> ("f_mem", True)
551 fd7a7c73 Iustin Pop
    "imem" -> ("i_mem", True)
552 fd7a7c73 Iustin Pop
    "rmem" -> ("r_mem", True)
553 fd7a7c73 Iustin Pop
    "amem" -> ("a_mem", True)
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    "tdsk" -> ("t_dsk", True)
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    "fdsk" -> ("f_dsk", True)
556 fd7a7c73 Iustin Pop
    "tcpu" -> ("pcpu", True)
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    "ucpu" -> ("vcpu", True)
558 fd7a7c73 Iustin Pop
    "pcnt" -> ("pcnt", True)
559 fd7a7c73 Iustin Pop
    "scnt" -> ("scnt", True)
560 fd7a7c73 Iustin Pop
    "plist" -> ("primaries", True)
561 fd7a7c73 Iustin Pop
    "slist" -> ("secondaries", True)
562 fd7a7c73 Iustin Pop
    "pfmem" -> ("p_fmem", True)
563 fd7a7c73 Iustin Pop
    "pfdsk" -> ("p_fdsk", True)
564 fd7a7c73 Iustin Pop
    "rcpu"  -> ("r_cpu", True)
565 fd7a7c73 Iustin Pop
    "cload" -> ("lCpu", True)
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    "mload" -> ("lMem", True)
567 fd7a7c73 Iustin Pop
    "dload" -> ("lDsk", True)
568 fd7a7c73 Iustin Pop
    "nload" -> ("lNet", True)
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    "ptags" -> ("PrimaryTags", False)
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    "peermap" -> ("PeerMap", False)
571 fd7a7c73 Iustin Pop
    -- TODO: add node fields (group.uuid, group)
572 fd7a7c73 Iustin Pop
    _ -> (T.unknownField, False)
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-- | String converter for the node list functionality.
575 76354e11 Iustin Pop
list :: [String] -> Node -> [String]
576 76354e11 Iustin Pop
list fields t = map (showField t) fields
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-- | Constant holding the fields we're displaying by default.
579 76354e11 Iustin Pop
defaultFields :: [String]
580 76354e11 Iustin Pop
defaultFields =
581 fd7a7c73 Iustin Pop
  [ "status", "name", "tmem", "nmem", "imem", "xmem", "fmem"
582 fd7a7c73 Iustin Pop
  , "rmem", "tdsk", "fdsk", "tcpu", "ucpu", "pcnt", "scnt"
583 fd7a7c73 Iustin Pop
  , "pfmem", "pfdsk", "rcpu"
584 fd7a7c73 Iustin Pop
  , "cload", "mload", "dload", "nload" ]
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586 d8bcd0a8 Iustin Pop
-- | Split a list of nodes into a list of (node group UUID, list of
587 525bfb36 Iustin Pop
-- associated nodes).
588 10ef6b4e Iustin Pop
computeGroups :: [Node] -> [(T.Gdx, [Node])]
589 d8bcd0a8 Iustin Pop
computeGroups nodes =
590 d8bcd0a8 Iustin Pop
  let nodes' = sortBy (comparing group) nodes
591 d8bcd0a8 Iustin Pop
      nodes'' = groupBy (\a b -> group a == group b) nodes'
592 d8bcd0a8 Iustin Pop
  in map (\nl -> (group (head nl), nl)) nodes''