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tests & benchmarks for new integer-gmp import/export primitives
{-# LANGUAGE CPP, BangPatterns, MagicHash, UnliftedFFITypes, UnboxedTuples, ScopedTypeVariables #-}
-- | Tests/Benchmarks for new GHC.Integer.GMP.Internals.{import,export}Integer primitives
import Control.Monad
import Criterion.Main
import Data.Bits
import Data.ByteString.Short.Internal (ShortByteString(SBS))
import qualified Data.ByteString.Short.Internal as SBS
import Data.List
import GHC.Int
import GHC.Integer.GMP.Internals
import GHC.Prim
import GHC.Types
import GHC.Word
import System.Environment (getArgs)
import System.IO.Unsafe
import Test.QuickCheck
-- ByteArray helpers
data MBA = MBA { unMBA :: !(MutableByteArray# RealWorld) }
data BA = BA { unBA :: !ByteArray# }
packByteArray :: [Word8] -> IO BA
packByteArray ws = do
MBA mba <- newByteArray (int2Word# n)
forM_ (zip [0..] ws) $ \(I# i, w) -> do
writeByteArray mba i w
freezeByteArray mba
where
!(I# n) = length ws
lengthByteArray :: ByteArray# -> Word
lengthByteArray ba = W# (int2Word# (sizeofByteArray# ba))
unpackByteArray :: ByteArray# -> [Word8]
unpackByteArray ba | n == 0 = []
| otherwise = [ indexByteArray ba i | W# i <- [0 .. n-1] ]
where
n = lengthByteArray ba
newByteArray :: Word# -> IO MBA
newByteArray sz = IO $ \s -> case newByteArray# (word2Int# sz) s of (# s, arr #) -> (# s, MBA arr #)
freezeByteArray :: MutableByteArray# RealWorld -> IO BA
freezeByteArray arr = IO $ \s -> case unsafeFreezeByteArray# arr s of (# s, arr #) -> (# s, BA arr #)
indexByteArray :: ByteArray# -> Word# -> Word8
indexByteArray a# n# = W8# (indexWord8Array# a# (word2Int# n#))
writeByteArray :: MutableByteArray# RealWorld -> Int# -> Word8 -> IO ()
writeByteArray arr i (W8# w) = IO $ \s -> case writeWord8Array# arr i w s of s -> (# s, () #)
-- exportInteger wrappers
exportInteger' :: Integer -> MutableByteArray# RealWorld -> Word# -> Int# -> IO Word
exportInteger' i mba o e = IO $ \s -> case exportInteger i mba o e s of (# s', l #) -> (# s', W# l #)
exportInteger'' :: Integer -> IO BA
exportInteger'' i = do
MBA mba <- newByteArray n
_ <- exportInteger' i mba 0## -1#
freezeByteArray mba
where
!(W# n) = exportIntegerSize i
importInteger'' :: ByteArray# -> Integer
importInteger'' ba = importInteger ba 0## n -1#
where
!(W# n) = lengthByteArray ba
exportIntegerSize :: Integer -> Word
exportIntegerSize 0 = W# 0##
exportIntegerSize i = W# (sizeInBaseInteger i 256#)
-- short byte string wrappers
integerToSbs :: Integer -> SBS.ShortByteString
integerToSbs i = unsafePerformIO $ do
BA ba <- exportInteger'' i
return $! SBS.SBS ba
integerToSbsRef :: Integer -> SBS.ShortByteString
integerToSbsRef = SBS.pack . unroll
integerFromSbs :: SBS.ShortByteString -> Integer
integerFromSbs (SBS.SBS ba) = importInteger'' ba
integerFromSbsRef :: SBS.ShortByteString -> Integer
integerFromSbsRef = roll . SBS.unpack
-- criterion test
main :: IO ()
main = do
args <- getArgs
when (args == ["test"]) $ do
runTests
fail "tests finished"
-- buffer large enough to old all test-integers
MBA buf <- newByteArray 1024##
BA b8ba <- exportInteger'' b8int
BA b16ba <- exportInteger'' b16int
BA b32ba <- exportInteger'' b32int
BA b64ba <- exportInteger'' b64int
BA b128ba <- exportInteger'' b128int
assertBgroup b8int b8ba 8##
assertBgroup b16int b16ba 16##
assertBgroup b32int b32ba 32##
assertBgroup b64int b64ba 64##
assertBgroup b128int b128ba 128##
defaultMain
[ bgroup "64bit" (genBgroupRef b8int b8ba 8## buf ++
[ bench "sbs2int64" $ whnf sbs2int64 (SBS b8ba) ])
, bgroup "128bit" (genBgroupRef b16int b16ba 16## buf)
, bgroup "256bit" (genBgroup b32int b32ba 32## buf)
, bgroup "512bit" (genBgroup b64int b64ba 64## buf)
, bgroup "1024bit" (genBgroup b128int b128ba 128## buf)
]
where
{-# INLINE genBgroup #-}
genBgroup bXint bXba bXsz mbaBuf =
[ bench "id" $ whnf id bXint
, bench "exportIntegerSize" $ whnf exportIntegerSize bXint
, bench "exportInteger" $ whnfIO (exportInteger' bXint mbaBuf 0## -1#)
, bench "importInteger" $ whnf (\(BA ba) -> importInteger ba 0## bXsz -1#) (BA bXba)
, bench "roundtrip+alloc " $ whnfIO $ roundtrip bXint
, bench "int2sbs" $ whnf integerToSbs bXint
, bench "sbs2int" $ whnf integerFromSbs (SBS.SBS bXba)
]
{-# INLINE genBgroupRef #-}
genBgroupRef bXint bXba bXsz mbaBuf =
genBgroup bXint bXba bXsz mbaBuf ++
[ bench "int2sbs (naive)" $ whnf integerToSbsRef bXint
, bench "sbs2int (naive)" $ whnf integerFromSbsRef (SBS bXba)
]
assertBgroup bXint bXba bXsz = do
unless (exportIntegerSize bXint == W# bXsz) $
fail $ "exportIntegerSize mismatch for b" ++ show (W# bXsz) ++ "int"
unless (importInteger bXba 0## bXsz -1# == bXint) $
fail $ "importInteger mismatch for b" ++ show (W# bXsz) ++ "int"
return ()
b8int = mkXint 8
b16int = mkXint 16
b32int = mkXint 32
b64int = mkXint 64
b128int = mkXint 128
mkXint n = roll (map fromIntegral (take (n-1) [0xff .. ] ++ [0xff::Int]))
roundtrip j = do
BA ba <- exportInteger'' j
return (importInteger'' ba)
-- semi-fast 64bit primitive from binary package
sbs2int64 :: ShortByteString -> Integer
sbs2int64 = fromIntegral . word64le
{-# NOINLINE sbs2int64 #-}
word64le :: ShortByteString -> Word64
word64le = \s -> (fromIntegral (s `SBS.unsafeIndex` 7) `shiftL` 56) .|.
(fromIntegral (s `SBS.unsafeIndex` 6) `shiftL` 48) .|.
(fromIntegral (s `SBS.unsafeIndex` 5) `shiftL` 40) .|.
(fromIntegral (s `SBS.unsafeIndex` 4) `shiftL` 32) .|.
(fromIntegral (s `SBS.unsafeIndex` 3) `shiftL` 24) .|.
(fromIntegral (s `SBS.unsafeIndex` 2) `shiftL` 16) .|.
(fromIntegral (s `SBS.unsafeIndex` 1) `shiftL` 8) .|.
(fromIntegral (s `SBS.unsafeIndex` 0) )
{-# INLINE word64le #-}
-- slow reference impl for order=-1# (i.e. LSBF)
unroll :: Integer -> [Word8]
unroll = unfoldr step . abs
where
step 0 = Nothing
step i = Just (fromIntegral i, i `shiftR` 8)
roll :: [Word8] -> Integer
roll = foldr unstep 0
where
unstep b a = a `shiftL` 8 .|. fromIntegral b
-- (un)roll via ByteArrays
unrollGMP :: Integer -> [Word8]
unrollGMP i = unpackByteArray (unBA (unsafePerformIO (exportInteger'' i)))
rollGMP :: [Word8] -> Integer
rollGMP ws = importInteger'' (unBA (unsafePerformIO (packByteArray ws)))
prop_unroll i = unrollGMP i == unroll i
prop_roll ws = rollGMP ws == roll ws
prop_unrollroll x = (unrollGMP . rollGMP) x == dropWhileEnd (==0) x
runTests :: IO ()
runTests = do
quickCheckWith stdArgs { maxSuccess = 1000000, maxSize = 200 } prop_unroll
quickCheckWith stdArgs { maxSuccess = 1000000, maxSize = 200 } prop_roll
quickCheckWith stdArgs { maxSuccess = 1000000, maxSize = 200 } prop_unrollroll
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<h1>criterion performance measurements</h1>
<h2>overview</h2>
<p><a href="#grokularation">want to understand this report?</a></p>
<div id="overview" class="ovchart" style="width:900px;height:100px;"></div>
<h2><a name="b0">64bit/id</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde0" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time0" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">8.493489777649111e-9</span></td>
<td><span class="time">8.499015573570184e-9</span></td>
<td><span class="citime">8.50897843982193e-9</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">2.2567841232466426e-11</span></td>
<td><span class="time">3.691847512995114e-11</span></td>
<td><span class="citime">5.837990630974678e-11</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999744e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b1">64bit/exportIntegerSize</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde1" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time1" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">2.90713057833843e-8</span></td>
<td><span class="time">2.9090500885395243e-8</span></td>
<td><span class="citime">2.9115860837687063e-8</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">9.019627379099151e-11</span></td>
<td><span class="time">1.1207721816313607e-10</span></td>
<td><span class="citime">1.4414249230944697e-10</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999999e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b2">64bit/exportInteger</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde2" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time2" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">5.3021220097214e-8</span></td>
<td><span class="time">5.3063510216107884e-8</span></td>
<td><span class="citime">5.3144105670656474e-8</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">1.7733325196644853e-10</span></td>
<td><span class="time">2.901917407108692e-10</span></td>
<td><span class="citime">5.315285938500462e-10</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999947e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b3">64bit/importInteger</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde3" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time3" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">4.7851791637589427e-8</span></td>
<td><span class="time">4.788173070089125e-8</span></td>
<td><span class="citime">4.793032410363496e-8</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">1.3076689610684273e-10</span></td>
<td><span class="time">1.9162289982503047e-10</span></td>
<td><span class="citime">2.8933707528632873e-10</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.89999999999983e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b4">64bit/roundtrip+alloc </a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde4" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time4" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">1.2451832112725267e-7</span></td>
<td><span class="time">1.2459030339520418e-7</span></td>
<td><span class="citime">1.246904131880275e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">3.3399268342026165e-10</span></td>
<td><span class="time">4.2704120484639685e-10</span></td>
<td><span class="citime">6.247440492568443e-10</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.9e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b5">64bit/int2sbs</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde5" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time5" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">8.797261179775463e-8</span></td>
<td><span class="time">8.809997533015615e-8</span></td>
<td><span class="citime">8.828963855369903e-8</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">5.85440932552031e-10</span></td>
<td><span class="time">7.817522788938959e-10</span></td>
<td><span class="citime">1.0266698510924335e-9</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.900000000000301e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b6">64bit/sbs2int</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde6" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time6" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">4.7842818284185286e-8</span></td>
<td><span class="time">4.7867337901323894e-8</span></td>
<td><span class="citime">4.7911172499887724e-8</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">1.1065598060886294e-10</span></td>
<td><span class="time">1.6321031481538823e-10</span></td>
<td><span class="citime">2.942373197068945e-10</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999888e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b7">64bit/int2sbs (naive)</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde7" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time7" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">6.010263913452756e-7</span></td>
<td><span class="time">6.017455698745585e-7</span></td>
<td><span class="citime">6.028454045142897e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">3.169452523803957e-9</span></td>
<td><span class="time">4.489858207590987e-9</span></td>
<td><span class="citime">7.132697941369136e-9</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.900000000000093e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b8">64bit/sbs2int (naive)</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde8" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time8" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">5.988962902601429e-7</span></td>
<td><span class="time">6.002255918676336e-7</span></td>
<td><span class="citime">6.05446899735458e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">2.55325088142328e-9</span></td>
<td><span class="time">1.1811770685262606e-8</span></td>
<td><span class="citime">2.745151054791528e-8</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have moderate
(<span class="percent">0.12318123483502369</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b9">64bit/sbs2int64</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde9" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time9" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">1.169837319061317e-8</span></td>
<td><span class="time">1.1706053000839791e-8</span></td>
<td><span class="citime">1.1722062017010728e-8</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">3.2232689541964785e-11</span></td>
<td><span class="time">5.4380386219806304e-11</span></td>
<td><span class="citime">1.0666361612922766e-10</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999975e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b10">128bit/id</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde10" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time10" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">8.489605700390535e-9</span></td>
<td><span class="time">8.493566891961638e-9</span></td>
<td><span class="citime">8.498472201731045e-9</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">1.8952855118956175e-11</span></td>
<td><span class="time">2.2547847538145745e-11</span></td>
<td><span class="citime">2.6855110977584242e-11</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999924e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b11">128bit/exportIntegerSize</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde11" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time11" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">2.9152392981978234e-8</span></td>
<td><span class="time">2.9202041511963944e-8</span></td>
<td><span class="citime">2.9296338507213386e-8</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">2.158134343920494e-10</span></td>
<td><span class="time">3.3761899846171125e-10</span></td>
<td><span class="citime">6.058696071714365e-10</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.89999999999997e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b12">128bit/exportInteger</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde12" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time12" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">8.139403230977794e-8</span></td>
<td><span class="time">8.142960242518473e-8</span></td>
<td><span class="citime">8.148928117436722e-8</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">1.6333731559151237e-10</span></td>
<td><span class="time">2.3063590969184102e-10</span></td>
<td><span class="citime">4.01753817941565e-10</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999944e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b13">128bit/importInteger</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde13" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time13" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">8.90830970594282e-8</span></td>
<td><span class="time">8.91193837487907e-8</span></td>
<td><span class="citime">8.916297071885342e-8</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">1.7225914674181934e-10</span></td>
<td><span class="time">2.0266100764759287e-10</span></td>
<td><span class="citime">2.3618466481369846e-10</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999999e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b14">128bit/roundtrip+alloc </a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde14" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time14" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">1.9151741091975624e-7</span></td>
<td><span class="time">1.91886375561829e-7</span></td>
<td><span class="citime">1.9351693144563215e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">4.87162583546328e-10</span></td>
<td><span class="time">3.3698397093217758e-9</span></td>
<td><span class="citime">7.925969270282601e-9</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have moderate
(<span class="percent">0.10386979230816298</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b15">128bit/int2sbs</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde15" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time15" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">1.1619806792256568e-7</span></td>
<td><span class="time">1.1625786909702237e-7</span></td>
<td><span class="citime">1.1635136107398992e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">2.756446155253544e-10</span></td>
<td><span class="time">3.7637857838070594e-10</span></td>
<td><span class="citime">6.16878596451239e-10</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999855e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b16">128bit/sbs2int</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde16" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time16" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">8.322364321200609e-8</span></td>
<td><span class="time">8.327923875574809e-8</span></td>
<td><span class="citime">8.336795077861436e-8</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">2.4945109243845663e-10</span></td>
<td><span class="time">3.543717981361297e-10</span></td>
<td><span class="citime">5.329813091737339e-10</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999999e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b17">128bit/int2sbs (naive)</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde17" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time17" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">1.1289055436675007e-6</span></td>
<td><span class="time">1.1314140747492046e-6</span></td>
<td><span class="citime">1.140996771607653e-6</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">5.349808942059254e-9</span></td>
<td><span class="time">2.1971395660994104e-8</span></td>
<td><span class="citime">5.076414375657355e-8</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have moderate
(<span class="percent">0.12299779864993411</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b18">128bit/sbs2int (naive)</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde18" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time18" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">1.3051648576041322e-6</span></td>
<td><span class="time">1.305836194129498e-6</span></td>
<td><span class="citime">1.3066424253772492e-6</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">3.2631108094546167e-9</span></td>
<td><span class="time">3.77412992857166e-9</span></td>
<td><span class="citime">4.432852101233779e-9</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999813e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b19">256bit/id</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde19" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time19" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">8.495557749901523e-9</span></td>
<td><span class="time">8.51113570017339e-9</span></td>
<td><span class="citime">8.571867129494133e-9</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">2.0306077979413937e-11</span></td>
<td><span class="time">1.4440749315808284e-10</span></td>
<td><span class="citime">3.410923794740004e-10</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have slight
(<span class="percent">9.457230296632305e-2</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b20">256bit/exportIntegerSize</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde20" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time20" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">2.9103803527565737e-8</span></td>
<td><span class="time">2.9168376254113452e-8</span></td>
<td><span class="citime">2.942983940123735e-8</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">1.2163210580921445e-10</span></td>
<td><span class="time">5.780843826617008e-10</span></td>
<td><span class="citime">1.3513043078019636e-9</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have moderate
(<span class="percent">0.1232772220953047</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b21">256bit/exportInteger</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde21" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time21" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">1.5416067848960214e-7</span></td>
<td><span class="time">1.542173471745489e-7</span></td>
<td><span class="citime">1.5428930149161948e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">2.707087070430719e-10</span></td>
<td><span class="time">3.267257008044739e-10</span></td>
<td><span class="citime">3.9998761648662984e-10</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999999e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b22">256bit/importInteger</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde22" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time22" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">1.2762505278616996e-7</span></td>
<td><span class="time">1.2767963127621257e-7</span></td>
<td><span class="citime">1.2774592718219667e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">2.589446187092335e-10</span></td>
<td><span class="time">3.0876951367115334e-10</span></td>
<td><span class="citime">3.6993163710488554e-10</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999754e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b23">256bit/roundtrip+alloc </a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde23" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time23" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">3.2156560286204583e-7</span></td>
<td><span class="time">3.218454114025387e-7</span></td>
<td><span class="citime">3.2232906937834946e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">1.250041543148922e-9</span></td>
<td><span class="time">1.836203631858919e-9</span></td>
<td><span class="citime">3.310554570634696e-9</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.900000000000124e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b24">256bit/int2sbs</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde24" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time24" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">1.894102444788588e-7</span></td>
<td><span class="time">1.8953620835296307e-7</span></td>
<td><span class="citime">1.8973975867126186e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">5.644415572915788e-10</span></td>
<td><span class="time">8.020604618147665e-10</span></td>
<td><span class="citime">1.1583212841766418e-9</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999798e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b25">256bit/sbs2int</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde25" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time25" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">1.2791868658259622e-7</span></td>
<td><span class="time">1.2801464643519175e-7</span></td>
<td><span class="citime">1.2820471482489878e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">3.9519595170561984e-10</span></td>
<td><span class="time">6.678037672485837e-10</span></td>
<td><span class="citime">1.132999467602317e-9</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.900000000000216e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b26">512bit/id</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde26" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time26" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">8.494850660584339e-9</span></td>
<td><span class="time">8.499703713832797e-9</span></td>
<td><span class="citime">8.507620771038968e-9</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">2.0892300118892186e-11</span></td>
<td><span class="time">3.1225424672619246e-11</span></td>
<td><span class="citime">4.7874328645026565e-11</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.9e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b27">512bit/exportIntegerSize</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde27" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time27" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">2.910154664797489e-8</span></td>
<td><span class="time">2.9129061331003868e-8</span></td>
<td><span class="citime">2.9165397515462004e-8</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">1.3038357723205095e-10</span></td>
<td><span class="time">1.615700919063536e-10</span></td>
<td><span class="citime">2.092114317896882e-10</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.900000000000063e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b28">512bit/exportInteger</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde28" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time28" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">2.818027189241117e-7</span></td>
<td><span class="time">2.818955738117344e-7</span></td>
<td><span class="citime">2.8200822863862933e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">4.4253000561762996e-10</span></td>
<td><span class="time">5.225999612260979e-10</span></td>
<td><span class="citime">6.197574364502625e-10</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999725e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b29">512bit/importInteger</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde29" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time29" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">2.2349889083378652e-7</span></td>
<td><span class="time">2.2367619578976409e-7</span></td>
<td><span class="citime">2.2403727275178498e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">7.204929208829124e-10</span></td>
<td><span class="time">1.242608787737259e-9</span></td>
<td><span class="citime">2.1733839129275453e-9</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999968e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b30">512bit/roundtrip+alloc </a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde30" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time30" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">5.325299622574905e-7</span></td>
<td><span class="time">5.327438946041442e-7</span></td>
<td><span class="citime">5.330055106666175e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">1.0293471343012023e-9</span></td>
<td><span class="time">1.2041226204420305e-9</span></td>
<td><span class="citime">1.4004694132122348e-9</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999897e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b31">512bit/int2sbs</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde31" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time31" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">3.1621307663335426e-7</span></td>
<td><span class="time">3.163371891327578e-7</span></td>
<td><span class="citime">3.1648275317526855e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">5.955428446504431e-10</span></td>
<td><span class="time">6.879260636301623e-10</span></td>
<td><span class="citime">7.950534793787999e-10</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999938e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b32">512bit/sbs2int</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde32" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time32" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">2.2351505632370398e-7</span></td>
<td><span class="time">2.239913540733571e-7</span></td>
<td><span class="citime">2.2593484307901981e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">7.955122132300985e-10</span></td>
<td><span class="time">4.26639873363785e-9</span></td>
<td><span class="citime">9.96632743452913e-9</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have moderate
(<span class="percent">0.1227214250671564</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b33">1024bit/id</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde33" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time33" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">8.558593169275592e-9</span></td>
<td><span class="time">8.586459183306166e-9</span></td>
<td><span class="citime">8.657458011395862e-9</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">1.0680794049536878e-10</span></td>
<td><span class="time">2.139079669456941e-10</span></td>
<td><span class="citime">4.5187665817925383e-10</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have moderate
(<span class="percent">0.18992942387230288</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b34">1024bit/exportIntegerSize</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde34" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time34" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">2.9103859344967398e-8</span></td>
<td><span class="time">2.913011767932298e-8</span></td>
<td><span class="citime">2.9161627680549687e-8</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">1.2579455366427028e-10</span></td>
<td><span class="time">1.4734500970339652e-10</span></td>
<td><span class="citime">1.726663772765088e-10</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.89999999999986e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b35">1024bit/exportInteger</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde35" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time35" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">5.372088157735769e-7</span></td>
<td><span class="time">5.374875541885132e-7</span></td>
<td><span class="citime">5.379970620818626e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">1.0972993762272864e-9</span></td>
<td><span class="time">1.866035009810465e-9</span></td>
<td><span class="citime">2.984195137277654e-9</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999859e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b36">1024bit/importInteger</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde36" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time36" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">4.0357602730846807e-7</span></td>
<td><span class="time">4.0382085812319323e-7</span></td>
<td><span class="citime">4.042551413540753e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">9.768724472231083e-10</span></td>
<td><span class="time">1.6270158103776352e-9</span></td>
<td><span class="citime">2.590404052976798e-9</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999885e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b37">1024bit/roundtrip+alloc </a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde37" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time37" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">9.671666598788938e-7</span></td>
<td><span class="time">9.677258555649118e-7</span></td>
<td><span class="citime">9.692162641506587e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">2.1248356528588745e-9</span></td>
<td><span class="time">4.357913011564874e-9</span></td>
<td><span class="citime">9.20378151262326e-9</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.9e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b38">1024bit/int2sbs</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde38" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time38" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">5.719231672240519e-7</span></td>
<td><span class="time">5.72158403198789e-7</span></td>
<td><span class="citime">5.724462213325853e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">1.1204160173048417e-9</span></td>
<td><span class="time">1.3312383707384217e-9</span></td>
<td><span class="citime">1.624739205041223e-9</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.9e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b39">1024bit/sbs2int</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde39" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time39" class="timechart"
style="width:450px;height:278px;"></div></td>
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>Mean execution time</td>
<td><span class="citime">4.0345760684739785e-7</span></td>
<td><span class="time">4.036523137311066e-7</span></td>
<td><span class="citime">4.0399013017434183e-7</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="citime">8.839609345246568e-10</span></td>
<td><span class="time">1.2834925709157631e-9</span></td>
<td><span class="citime">2.2889774654535744e-9</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have no
(<span class="percent">9.899999999999841e-3</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="grokularation">understanding this report</a></h2>
<p>In this report, each function benchmarked by criterion is assigned
a section of its own. In each section, we display two charts, each
with an <i>x</i> axis that represents measured execution time.
These charts are active; if you hover your mouse over data points
and annotations, you will see more details.</p>
<ul>
<li>The chart on the left is a
<a href="http://en.wikipedia.org/wiki/Kernel_density_estimation">kernel
density estimate</a> (also known as a KDE) of time
measurements. This graphs the probability of any given time
measurement occurring. A spike indicates that a measurement of a
particular time occurred; its height indicates how often that
measurement was repeated.</li>
<li>The chart on the right is the raw data from which the kernel
density estimate is built. Measurements are displayed on
the <i>y</i> axis in the order in which they occurred.</li>
</ul>
<p>Under the charts is a small table displaying the mean and standard
deviation of the measurements. We use a statistical technique
called
the <a href="http://en.wikipedia.org/wiki/Bootstrapping_(statistics)">bootstrap</a>
to provide confidence intervals on our estimates of these values.
The bootstrap-derived upper and lower bounds on the mean and
standard deviation let you see how accurate we believe those
estimates to be. (Hover the mouse over the table headers to see
the confidence levels.)</p>
<p>A noisy benchmarking environment can cause some or many
measurements to fall far from the mean. These outlying
measurements can have a significant inflationary effect on the
estimate of the standard deviation. We calculate and display an
estimate of the extent to which the standard deviation has been
inflated by outliers.</p>
<script type="text/javascript">
$(function () {
function mangulate(number, name, mean, times, kdetimes, kdepdf) {
var meanSecs = mean;
var units = $.timeUnits(mean);
var scale = units[0];
units = units[1];
mean *= scale;
kdetimes = $.scaleBy(scale, kdetimes);
var ts = $.scaleBy(scale, times);
var kq = $("#kde" + number);
var k = $.plot(kq,
[{ label: name + " time densities",
data: $.zip(kdetimes, kdepdf),
}],
{ xaxis: { tickFormatter: $.unitFormatter(units) },
yaxis: { ticks: false },
grid: { borderColor: "#777",
hoverable: true, markings: [ { color: '#6fd3fb',
lineWidth: 1.5, xaxis: { from: mean, to: mean } } ] },
});
var o = k.pointOffset({ x: mean, y: 0});
kq.append('<div class="meanlegend" title="' + $.renderTime(meanSecs) +
'" style="position:absolute;left:' + (o.left + 4) +
'px;bottom:139px;">mean</div>');
var timepairs = new Array(ts.length);
for (var i = 0; i < ts.length; i++)
timepairs[i] = [ts[i],i];
$.plot($("#time" + number),
[{ label: name + " times",
data: timepairs }],
{ points: { show: true },
grid: { borderColor: "#777", hoverable: true },
xaxis: { min: kdetimes[0], max: kdetimes[kdetimes.length-1],
tickFormatter: $.unitFormatter(units) },
yaxis: { ticks: false },
});
$.addTooltip("#kde" + number, function(x,y) { return x + ' ' + units; });
$.addTooltip("#time" + number, function(x,y) { return x + ' ' + units; });
};
mangulate(0, "64bit/id",
8.499015573570184e-9,
[8.493859533510001e-9,8.588352697959546e-9,8.485642736601345e-9,8.477425939692689e-9,8.48769693582851e-9,8.512347326554478e-9,8.477425939692689e-9,8.485642736601345e-9,8.512347326554478e-9,8.485642736601345e-9,8.485642736601345e-9,8.477425939692689e-9,8.547268713416266e-9,8.48769693582851e-9,8.477425939692689e-9,8.512347326554478e-9,8.485642736601345e-9,8.479480138919854e-9,8.512347326554478e-9,8.512347326554478e-9,8.485642736601345e-9,8.48769693582851e-9,8.53905191650761e-9,8.477425939692689e-9,8.477425939692689e-9,8.479480138919854e-9,8.520564123463133e-9,8.512347326554478e-9,8.48769693582851e-9,8.504130529645822e-9,8.477425939692689e-9,8.485642736601345e-9,8.479480138919854e-9,8.545214514189101e-9,8.485642736601345e-9,8.479480138919854e-9,8.512347326554478e-9,8.477425939692689e-9,8.48769693582851e-9,8.477425939692689e-9,8.512347326554478e-9,8.485642736601345e-9,8.48769693582851e-9,8.477425939692689e-9,8.485642736601345e-9,8.512347326554478e-9,8.48769693582851e-9,8.512347326554478e-9,8.477425939692689e-9,8.477425939692689e-9,8.48769693582851e-9,8.512347326554478e-9,8.485642736601345e-9,8.479480138919854e-9,8.571919104142234e-9,8.485642736601345e-9,8.48769693582851e-9,8.477425939692689e-9,8.512347326554478e-9,8.477425939692689e-9,8.48769693582851e-9,8.512347326554478e-9,8.485642736601345e-9,8.485642736601345e-9,8.48769693582851e-9,8.547268713416266e-9,8.477425939692689e-9,8.477425939692689e-9,8.512347326554478e-9,8.48769693582851e-9,8.485642736601345e-9,8.512347326554478e-9,8.512347326554478e-9,8.477425939692689e-9,8.477425939692689e-9,8.701333655453565e-9,8.485642736601345e-9,8.48769693582851e-9,8.485642736601345e-9,8.520564123463133e-9,8.512347326554478e-9,8.477425939692689e-9,8.512347326554478e-9,8.485642736601345e-9,8.477425939692689e-9,8.477425939692689e-9,8.545214514189101e-9,8.477425939692689e-9,8.48769693582851e-9,8.512347326554478e-9,8.485642736601345e-9,8.479480138919854e-9,8.477425939692689e-9,8.520564123463133e-9,8.477425939692689e-9,8.485642736601345e-9,8.477425939692689e-9,8.477425939692689e-9,8.711604651589386e-9,8.479480138919854e-9,],
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[-1.4111327504458645e7,4.3821666713150606e7,-7.843028381864604e7,1.2291310036455616e8,-1.8599743640658867e8,2.8553012352666205e8,-4.645324513727033e8,8.527238015413662e8,-2.0185373008654854e9,1.2161232237436132e10,9.950413545244183e10,3.901208822363763e10,5944083.292863488,8.915224493389578e9,8.057703803703581e10,6.185307481260991e10,4.824708166231643e9,2.1768102875189334e8,3.617119829379114e9,6.828385307322004e8,-3.8858796829216355e8,8.182453010172199e8,3.2501736582650514e9,1.2385615078708797e9,-1.747632018813737e9,9.325091485467047e9,7.029505116360239e10,9.363822711420635e9,-1.8815152691799946e9,2.169172867304004e9,1.0710789000197802e10,1.7203776237310317e9,-4.42007474977912e8,2.545803658965452e8,-1.8196795363774168e8,1.5307238771492767e8,-1.7055698947895315e8,5.460902309593298e8,3.6756455551081114e9,4.408529363604741e8,6.744540963788916e8,8.454272214195536e9,8.32972232436086e9,8.414637906299715e8,-1.2707787970125811e8,5.687192620282112e7,-3.3679783814898685e7,2.1202185938149706e7,-1.1276005810592543e7,-179569.96140591623,1.944976849724044e7,-7.010996753027783e7,4.7362726825426555e8,3.7144825979416175e9,4.788814758548695e8,-8.127865161637133e7,3.8193978664013095e7,-3.025603007310711e7,3.973085294697396e7,-8.438556095374449e7,4.8362795447388536e8,3.70798336772454e9,4.8204953551329714e8,-8.070685362600452e7,3.259904748072507e7,-1.6474132977752503e7,9165124.743255012,-5270764.497800501,2978915.876657359,-1538684.3606987656,592108.5383352744,49485.03062852231,-493349.8963109999,804152.9443381062,-1022762.7128462696,1176018.5064696863,-1282117.4851039622,1353734.3591763405,-1399904.4887360798,1427201.814713069,-1440499.0317232325,1443472.0200586144,-1438943.270269026,1429121.537397088,-1415773.3869810626,1400349.532850363,-1384081.169418034,1368056.814898961,-1353287.3725264245,1340765.5536145798,-1331525.16794416,1326705.9556344047,-1327630.671950708,1335903.2977543685,-1353541.0773302391,1383159.5906543303,-1428241.1091640277,1493535.516406936,-1585676.7081245051,1714158.6878238893,-1892931.4720540221,2143105.5181905003,-2497727.033987996,3010626.1903401753,-3773784.42316577,4953911.168440527,-6876607.141292538,1.0243683169946443e7,-1.6790148724756386e7,3.1790655101538867e7,-7.819256328770769e7,4.7683859200990725e8,3.7177215152643113e9,4.655570075084417e8,-4.845411364445548e7,-4.745155837311536e7,4.645470120704057e8,3.71874671033034e9,4.757897705874224e8,-7.711061192119075e7,3.0664479707713757e7,-1.5606387692690799e7,8985778.970383508,-5523490.531079638,3478079.913754091,-2138414.919047271,1165096.754177179,-370443.3456886965,]);
mangulate(1, "64bit/exportIntegerSize",
2.9090500885395243e-8,
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mangulate(2, "64bit/exportInteger",
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mangulate(4, "64bit/roundtrip+alloc ",
1.2459030339520418e-7,
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mangulate(8, "64bit/sbs2int (naive)",
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mangulate(9, "64bit/sbs2int64",
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mangulate(10, "128bit/id",
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mangulate(11, "128bit/exportIntegerSize",
2.9202041511963944e-8,
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mangulate(12, "128bit/exportInteger",
8.142960242518473e-8,
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mangulate(13, "128bit/importInteger",
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mangulate(14, "128bit/roundtrip+alloc ",
1.91886375561829e-7,
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mangulate(16, "128bit/sbs2int",
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mangulate(17, "128bit/int2sbs (naive)",
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mangulate(18, "128bit/sbs2int (naive)",
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mangulate(19, "256bit/id",
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mangulate(20, "256bit/exportIntegerSize",
2.9168376254113452e-8,
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mangulate(21, "256bit/exportInteger",
1.542173471745489e-7,
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mangulate(22, "256bit/importInteger",
1.2767963127621257e-7,
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mangulate(23, "256bit/roundtrip+alloc ",
3.218454114025387e-7,
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mangulate(24, "256bit/int2sbs",
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mangulate(25, "256bit/sbs2int",
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mangulate(27, "512bit/exportIntegerSize",
2.9129061331003868e-8,
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mangulate(28, "512bit/exportInteger",
2.818955738117344e-7,
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mangulate(29, "512bit/importInteger",
2.2367619578976409e-7,
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mangulate(30, "512bit/roundtrip+alloc ",
5.327438946041442e-7,
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mangulate(31, "512bit/int2sbs",
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mangulate(32, "512bit/sbs2int",
2.239913540733571e-7,
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mangulate(34, "1024bit/exportIntegerSize",
2.913011767932298e-8,
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mangulate(35, "1024bit/exportInteger",
5.374875541885132e-7,
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mangulate(36, "1024bit/importInteger",
4.0382085812319323e-7,
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mangulate(37, "1024bit/roundtrip+alloc ",
9.677258555649118e-7,
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mangulate(38, "1024bit/int2sbs",
5.72158403198789e-7,
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mangulate(39, "1024bit/sbs2int",
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</div>
</div>
<div id="footer">
<div class="body">
<div class="footfirst">
<h2>colophon</h2>
<p>This report was created using the
<a href="http://hackage.haskell.org/package/criterion">criterion</a>
benchmark execution and performance analysis tool.</p>
<p>Criterion is developed and maintained
by <a href="http://www.serpentine.com/blog/">Bryan O'Sullivan</a>.</p>
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