github.com/m3db/m3@v1.5.1-0.20231129193456-75a402aa583b/src/query/graphite/ts/lttb_test.go

// Copyright (c) 2019 Uber Technologies, Inc.
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.

package ts

import (
	"math"
	"testing"
	"time"

	"github.com/m3db/m3/src/query/graphite/context"

	"github.com/stretchr/testify/require"
)

func TestLTTB(t *testing.T) {
	ctx := context.New()
	defer ctx.Close()

	seriesStart := time.Now()
	stepSize := 1000
	values := NewValues(ctx, stepSize, 10)
	for i := 0; i < values.Len(); i++ {
		values.SetValueAt(i, float64(i+1))
	}
	series := NewSeries(ctx, "foo", seriesStart, values)

	tests := []struct {
		startOffset     time.Duration
		endOffset       time.Duration
		threshold       int
		newStep         int
		resultThreshold int
	}{
		{
			startOffset: 0,
			endOffset:   0,
			threshold:   3,
			newStep:     stepSize * 4,
		},
		{
			startOffset: 0,
			endOffset:   0,
			newStep:     stepSize * 3,
			threshold:   4,
		},
		{
			startOffset: 0,
			endOffset:   0,
			newStep:     stepSize * 2,
			threshold:   5,
		},
		{
			startOffset:     0,
			endOffset:       0,
			newStep:         stepSize * 2,
			threshold:       6,
			resultThreshold: 5,
		},
		{
			startOffset:     0,
			endOffset:       0,
			newStep:         stepSize * 2,
			threshold:       7,
			resultThreshold: 5,
		},
	}

	for _, test := range tests {
		start := series.StartTime().Add(test.startOffset)
		end := series.EndTime().Add(test.endOffset)
		threshold := test.threshold
		millisPerStep := series.MillisPerStep()
		// Calculate the new millisPerStep if the length exceeds the limit on number of data points
		if (series.Len()) > threshold {
			samplingMultiplier := math.Ceil(float64(series.Len()) / float64(threshold))
			millisPerStep = int(samplingMultiplier * float64(series.MillisPerStep()))
		}

		result := LTTB(series, start, end, millisPerStep)
		require.NotNil(t, result)
		require.Equal(t, start, result.StartTime())
		require.False(t, end.After(result.EndTime()))
		require.True(t, end.After(result.StartTimeForStep(result.Len()-1)))

		require.Equal(t, series.Specification, result.Specification)
		require.Equal(t, series.Name(), result.Name())
		require.Equal(t, test.newStep, result.MillisPerStep())
		resultThreshold := test.threshold
		if test.resultThreshold > 0 {
			resultThreshold = test.resultThreshold
		}
		require.Equal(t, result.Len(), resultThreshold)

	}
}

func TestLTTBWithNull(t *testing.T) {
	ctx := context.New()
	defer ctx.Close()
	seriesStart := time.Now()
	stepSize := 1000
	values := NewValues(ctx, stepSize, len(data)/50)
	for i := 0; i < values.Len(); i++ {
		values.SetValueAt(i, data[i].Y)
	}

	values.SetValueAt(0, math.NaN())
	series := NewSeries(ctx, "foo", seriesStart, values)

	series = LTTB(series, series.StartTime(), series.EndTime(), 5000)
	require.True(t, math.IsNaN(series.ValueAt(0)))
	require.False(t, math.IsNaN(series.ValueAt(1)))
}

func TestLTTBAverage(t *testing.T) {
	ctx := context.New()
	defer ctx.Close()
	seriesStart := time.Now()
	values := NewValues(ctx, 1000, 8)
	values.SetValueAt(4, data[4].Y)

	series := NewSeries(ctx, "foo", seriesStart, values)

	series = LTTB(series, series.StartTime(), series.EndTime(), 3000)
	require.False(t, math.IsNaN(series.ValueAt(1)))
	require.InDelta(t, series.ValueAt(1), data[4].Y, 0.001)

	values = NewValues(ctx, 1000, 12)
	values.SetValueAt(7, data[7].Y)
	series = NewSeries(ctx, "foo", seriesStart, values)
	series = LTTB(series, series.StartTime(), series.EndTime(), 3000)
	require.False(t, math.IsNaN(series.ValueAt(2)))
	require.InDelta(t, series.ValueAt(2), data[7].Y, 0.001)
}

var data = []Point{
	{0, 29.357995947822218}, {1, 29.40932479606209}, {2, 29.28168582006162}, {3, 30.409965579108867}, {4, 30.7726859735917}, {5, 30.839942247539028}, {6, 30.760611642264667}, {7, 31.203663004229718}, {8, 31.38899603525572}, {9, 30.890299916955737},
	{10, 30.467811944911556}, {11, 30.596837868069542}, {12, 30.59789593509767}, {13, 30.19693062465079}, {14, 29.89081330734553}, {15, 29.54668002901058}, {16, 29.54890739422219}, {17, 30.53743760171474}, {18, 30.74066032317061}, {19, 30.3774450601516},
	{20, 30.095148889986568}, {21, 30.057979182917986}, {22, 30.364655421168525}, {23, 30.293450053773604}, {24, 30.14578230340987}, {25, 30.277772879951996}, {26, 30.3711931235659}, {27, 30.355932660992572}, {28, 29.994740831603046}, {29, 29.938012885023657},
	{30, 29.557268760451187}, {31, 29.16161297604625}, {32, 29.6921163421055}, {33, 30.246270628292226}, {34, 30.210955154680928}, {35, 29.382964668934058}, {36, 29.52892023906641}, {37, 29.719742065732202}, {38, 30.013856636945924}, {39, 29.818636169776926},
	{40, 27.931224826933345}, {41, 28.103057873678374}, {42, 28.276025902356782}, {43, 28.193497487789774}, {44, 28.22099171488288}, {45, 28.06872431241809}, {46, 27.239835885250365}, {47, 26.606504358317906}, {48, 27.220308136213916}, {49, 25.80790898978574},
	{50, 26.060334838062595}, {51, 25.89611036822564}, {52, 25.824433242208308}, {53, 25.89212193260212}, {54, 27.28963669872412}, {55, 27.208259984780806}, {56, 27.298211480886604}, {57, 27.056163307023077}, {58, 26.434701869643924}, {59, 26.21938188318228},
	{60, 26.402877759468772}, {61, 26.326019357967294}, {62, 27.592635104460253}, {63, 27.597468405434316}, {64, 27.533410081050647}, {65, 27.30713964830731}, {66, 27.170789712751404}, {67, 27.610166301145746}, {68, 27.619847332319885}, {69, 27.55974343996647},
	{70, 28.168803492093716}, {71, 28.284229862452584}, {72, 28.292638086760352}, {73, 28.523718178262335}, {74, 28.52268591410558}, {75, 28.576637206595993}, {76, 27.763715461946813}, {77, 27.48488075310065}, {78, 27.304006460281794}, {79, 26.902025619666333},
	{80, 26.690162079132378}, {81, 26.52277286738866}, {82, 26.09406789919051}, {83, 26.029039984983562}, {84, 26.145181108429618}, {85, 24.75335912549342}, {86, 24.787772395126176}, {87, 24.966652093726385}, {88, 25.33621421606084}, {89, 25.29283081429076},
	{90, 25.427452306231707}, {91, 25.34334450564347}, {92, 25.971939771661045}, {93, 25.907910638400836}, {94, 25.971895864171003}, {95, 26.448419417928317}, {96, 26.461057396494514}, {97, 26.332417666691025}, {98, 26.17395667752311}, {99, 25.318121919340044},
	{100, 26.092918888834987}, {101, 26.080903284583307}, {102, 26.65713935644778}, {103, 26.90227335392346}, {104, 27.14904791481757}, {105, 27.45775156727039}, {106, 28.476933177720472}, {107, 27.899526884805073}, {108, 27.274094274806096}, {109, 27.007320452528134},
	{110, 27.767594298696466}, {111, 28.669197835798027}, {112, 28.78287095361503}, {113, 28.744062941208348}, {114, 29.266136201836588}, {115, 29.29631346563548}, {116, 29.30576721224685}, {117, 28.92417256867908}, {118, 29.172020952087326}, {119, 29.36572118529946},
	{120, 29.407882394097168}, {121, 29.24581675687127}, {122, 30.374496989862006}, {123, 29.75867484229172}, {124, 29.724977349500893}, {125, 29.766232845230032}, {126, 29.755425025733203}, {127, 29.891515813029994}, {128, 29.224842590902917}, {129, 29.19894861750696},
	{130, 28.877260649054524}, {131, 29.100160763856657}, {132, 29.11303194254891}, {133, 29.471499370130353}, {134, 29.725430707066725}, {135, 29.875645922022283}, {136, 29.32336837740634}, {137, 29.659223458914788}, {138, 29.916122460150415}, {139, 29.947591268372232},
	{140, 29.912720660976237}, {141, 30.030001305562784}, {142, 30.01603062688162}, {143, 30.206305874273855}, {144, 29.654798308068155}, {145, 29.51005186796388}, {146, 29.479249298103124}, {147, 29.50465455692649}, {148, 28.668390496723326}, {149, 29.70235193454973},
	{150, 29.651621644229916}, {151, 29.514646394709878}, {152, 29.506006233800203}, {153, 29.85094476486748}, {154, 29.815453456016304}, {155, 29.942433471924208}, {156, 29.690047803042003}, {157, 29.081114874079432}, {158, 29.064499954878283}, {159, 29.17427761652929},
	{160, 28.48135454514647}, {161, 28.43614347392514}, {162, 28.615830690136196}, {163, 27.244815449582045}, {164, 28.030839937141593}, {165, 28.09433740820739}, {166, 28.134090510807432}, {167, 28.333335545414524}, {168, 28.187860385951467}, {169, 28.275647207865163},
	{170, 28.110663780904385}, {171, 27.941108395946074}, {172, 27.155839334130572}, {173, 27.486338387798014}, {174, 27.822551655905976}, {175, 27.863745721980674}, {176, 27.51492123912736}, {177, 27.83845450366903}, {178, 27.143346163904276}, {179, 26.470510229480666},
	{180, 27.030260699355054}, {181, 26.530046883178517}, {182, 26.061343714664623}, {183, 26.451944204073293}, {184, 26.430516873002972}, {185, 27.54560649645601}, {186, 27.607455732128237}, {187, 27.3151823435893}, {188, 27.015508353290546}, {189, 27.564104270774138},
	{190, 27.401004407024764}, {191, 27.158236015306873}, {192, 27.15560082391509}, {193, 27.052060260660955}, {194, 27.170854273897024}, {195, 27.764649442110628}, {196, 28.37485762180034}, {197, 28.693644963914128}, {198, 28.639988945921225}, {199, 28.55415913033328},
	{200, 28.227269873938933}, {201, 28.17193587609251}, {202, 28.326544342536973}, {203, 27.64207374329132}, {204, 28.28132114918632}, {205, 28.87895845286964}, {206, 28.188530355189847}, {207, 27.543826104728634}, {208, 27.518668557969406}, {209, 27.501005443892083},
	{210, 27.4034023213343}, {211, 27.81919230719886}, {212, 28.51752545491846}, {213, 28.45642871817993}, {214, 28.281434136230057}, {215, 28.955222450571647}, {216, 28.817758413114476}, {217, 28.512855374048605}, {218, 28.53649013938214}, {219, 28.037741647416063},
	{220, 28.758762367232816}, {221, 28.411225526795217}, {222, 28.081382658095393}, {223, 28.018197966678386}, {224, 27.669840575416934}, {225, 27.729482622798493}, {226, 27.44804950151258}, {227, 27.057357503159633}, {228, 27.02667664651584}, {229, 26.99034079421472},
	{230, 27.624460374012415}, {231, 26.6107079586933}, {232, 26.586632740266342}, {233, 26.50503068257422}, {234, 26.528094947562206}, {235, 27.42586110225183}, {236, 27.58607997646959}, {237, 27.119751888180552}, {238, 27.08687612699868}, {239, 26.50890594997075},
	{240, 27.31126847238326}, {241, 27.241646652930587}, {242, 27.206837899664286}, {243, 27.806910729195003}, {244, 27.943871889687294}, {245, 27.682133734768627}, {246, 27.717567280916626}, {247, 28.50754775235408}, {248, 28.522618646129153}, {249, 28.119450170073687},
	{250, 28.142446798473102}, {251, 27.493875384325104}, {252, 27.232866008532874}, {253, 26.815819408391537}, {254, 26.66806605894335}, {255, 26.832795316319906}, {256, 26.6709072973403}, {257, 26.805339614467922}, {258, 25.87709141573906}, {259, 25.78663848060838},
	{260, 26.292688529709856}, {261, 26.13540568260593}, {262, 26.950679537489023}, {263, 26.74360016328177}, {264, 25.880978465490344}, {265, 26.625349316487267}, {266, 27.726596358113618}, {267, 27.678660195691705}, {268, 27.712915567796777}, {269, 27.721698306913026},
	{270, 27.905267233295028}, {271, 27.957187159455156}, {272, 27.858194094400584}, {273, 28.081932932040928}, {274, 27.735044748607958}, {275, 27.032793497721116}, {276, 27.507939311361685}, {277, 27.574645954142067}, {278, 27.574051095225684}, {279, 27.759761781417595},
	{280, 27.365795276665352}, {281, 26.617667215269847}, {282, 26.798097033417232}, {283, 26.195989054524656}, {284, 26.976938134909243}, {285, 26.89198848346594}, {286, 27.147250351373707}, {287, 27.43948527543756}, {288, 28.0008367927751}, {289, 28.231697069321097},
	{290, 28.7967810312443}, {291, 29.512759843423506}, {292, 29.41555351035952}, {293, 30.70537467842703}, {294, 30.332009655179892}, {295, 30.368538690398843}, {296, 30.73440265654596}, {297, 30.967799052657455}, {298, 31.22392323854322}, {299, 31.122470949743033},
	{300, 31.140432351354303}, {301, 31.13729855237942}, {302, 30.716789453632746}, {303, 31.055606178854195}, {304, 31.025310612429436}, {305, 30.746317663776093}, {306, 31.16989662941391}, {307, 29.623226075091324}, {308, 29.11707721446215}, {309, 29.671462419401518},
	{310, 29.32656872224774}, {311, 29.360034344664133}, {312, 30.193073601940906}, {313, 30.051282853224887}, {314, 30.094809176026143}, {315, 30.62616938793058}, {316, 31.24738345775188}, {317, 31.288951935975373}, {318, 30.793680071961138}, {319, 30.855230722079575},
	{320, 30.172789122099953}, {321, 30.16588226960243}, {322, 30.02896795596743}, {323, 28.710256908027688}, {324, 28.788445957400086}, {325, 29.14084131034792}, {326, 29.154793392113767}, {327, 29.509956518244064}, {328, 29.919766479376083}, {329, 30.809790278228583},
	{330, 31.51994434827819}, {331, 31.14360887134284}, {332, 30.960009728867895}, {333, 31.007757592227232}, {334, 29.912529162927882}, {335, 30.430549132609936}, {336, 30.286270410087386}, {337, 30.29853067098949}, {338, 30.28484502358319}, {339, 30.2649148646112},
	{340, 30.269814084876984}, {341, 29.48743777656781}, {342, 29.25324229055582}, {343, 29.3224085984498}, {344, 28.845749148292715}, {345, 28.25734414947841}, {346, 28.22244460496951}, {347, 28.212727797755832}, {348, 28.099709252761244}, {349, 28.157686542165766},
	{350, 28.15110192590233}, {351, 28.242118337655835}, {352, 29.53367482995351}, {353, 29.532585019641683}, {354, 29.943653842668887}, {355, 28.64740678713178}, {356, 28.627878421859094}, {357, 28.85948017439502}, {358, 29.421837208187565}, {359, 29.213674689162733},
	{360, 29.588524659441383}, {361, 29.871736651370572}, {362, 29.97536581410366}, {363, 29.090848126781193}, {364, 29.07367624649577}, {365, 28.936182688349078}, {366, 28.478980562612755}, {367, 27.701450632319055}, {368, 27.70314463302395}, {369, 27.690633468393905},
	{370, 27.712418470005847}, {371, 28.04360951096915}, {372, 27.899319369636174}, {373, 27.67953057101954}, {374, 27.33713099741098}, {375, 27.715275282261704}, {376, 27.09457980740444}, {377, 26.564904718909652}, {378, 26.851805720484524}, {379, 27.17971899490677},
	{380, 27.203035420946204}, {381, 26.98833921789535}, {382, 27.3376969508508}, {383, 27.36673199620505}, {384, 27.22367712016426}, {385, 27.295774446517406}, {386, 27.24426813335004}, {387, 27.804345559349205}, {388, 27.81107241888124}, {389, 28.007141902081127},
	{390, 28.196204812447014}, {391, 27.570724094739713}, {392, 28.353947742891283}, {393, 28.264285808134655}, {394, 28.001544074943496}, {395, 28.073693599174273}, {396, 28.13948170648531}, {397, 27.7246917685699}, {398, 27.372056917732422}, {399, 26.76664288679182},
	{400, 26.726530330089947}, {401, 26.73659456496834}, {402, 26.35282363879538}, {403, 26.953655414803745}, {404, 27.037728660238816}, {405, 26.391122852260175}, {406, 26.45637305967239}, {407, 25.78486318168484}, {408, 25.92078676697798}, {409, 26.4970571420541},
	{410, 25.86809752383717}, {411, 26.534413662015773}, {412, 27.226357547185447}, {413, 26.71252553894152}, {414, 26.435002451423312}, {415, 26.921455461481504}, {416, 27.06045686220195}, {417, 27.09418382303274}, {418, 28.011098852919908}, {419, 27.896959438752912},
	{420, 27.914042725695705}, {421, 27.547368437091734}, {422, 26.710013475304418}, {423, 26.67332778875601}, {424, 26.624659424882857}, {425, 26.57172379809563}, {426, 26.846697174621756}, {427, 25.8834697613218}, {428, 26.0400273638686}, {429, 25.922770964698366},
	{430, 26.550977646141284}, {431, 26.7196171595444}, {432, 26.57693368973477}, {433, 26.754937488902705}, {434, 26.68923906981248}, {435, 27.578054073124644}, {436, 28.491944955522996}, {437, 29.462067517762534}, {438, 29.049663449716007}, {439, 29.29125398211083},
	{440, 29.716399938469106}, {441, 29.697795912329543}, {442, 28.842426341018918}, {443, 27.995794268014496}, {444, 27.568707173494055}, {445, 27.572194900322412}, {446, 28.94876289646488}, {447, 28.827587778805206}, {448, 28.20122725800809}, {449, 28.982543824618322},
	{450, 28.98764510982713}, {451, 28.476638374330257}, {452, 27.8971845311884}, {453, 28.357599004387694}, {454, 29.550067169716076}, {455, 29.059986913307316}, {456, 29.44698201092504}, {457, 29.444893222605785}, {458, 30.2987283695555}, {459, 30.490753195685443},
	{460, 30.3712818585665}, {461, 31.03092246398632}, {462, 31.1306416649066}, {463, 31.204020755490298}, {464, 31.302761670091414}, {465, 31.287884426895985}, {466, 30.49414678626753}, {467, 30.9842218570926}, {468, 30.88247586217915}, {469, 31.65627890749247},
	{470, 31.300373482363312}, {471, 31.009412915052188}, {472, 31.135319385771062}, {473, 31.142947189076295}, {474, 31.095825728106682}, {475, 31.402733294236572}, {476, 31.348161546083656}, {477, 31.600766880442425}, {478, 31.51732023898528}, {479, 31.218212979786024},
	{480, 31.431310499487758}, {481, 31.536799819023997}, {482, 31.590576295671646}, {483, 31.49429616322668}, {484, 32.1816892011556}, {485, 32.61239327037908}, {486, 32.69902576477615}, {487, 32.89146487332367}, {488, 33.87564290993047}, {489, 33.89045560640269},
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	{1720, 42.15881862704277}, {1721, 42.73710053588433}, {1722, 42.348456207492845}, {1723, 42.096157824123665}, {1724, 41.92253556951924}, {1725, 41.917137854036646}, {1726, 41.97608613143687}, {1727, 41.72574431293022}, {1728, 41.24861627279633}, {1729, 41.87472943187815},
	{1730, 41.87568170648001}, {1731, 42.17909911414902}, {1732, 42.049177661936255}, {1733, 41.97474828244962}, {1734, 41.356541003497355}, {1735, 41.22195929777421}, {1736, 41.194030410051106}, {1737, 41.392479793475935}, {1738, 41.34843546848941}, {1739, 41.34402528705148},
	{1740, 42.07661962525981}, {1741, 41.52647896910617}, {1742, 41.44561097861686}, {1743, 40.958470191837534}, {1744, 41.037829903821645}, {1745, 41.07205195864329}, {1746, 41.46906637533652}, {1747, 41.49343224957735}, {1748, 40.610182804195105}, {1749, 41.017801824810185},
	{1750, 40.79059366319508}, {1751, 40.70441966049171}, {1752, 40.70503981535662}, {1753, 39.93683574905368}, {1754, 39.752239396736506}, {1755, 39.7645522699645}, {1756, 39.55588740392734}, {1757, 39.74727156272358}, {1758, 39.9737782466988}, {1759, 40.39693575020464},
	{1760, 40.216674372755165}, {1761, 40.25136763580497}, {1762, 39.38556407545778}, {1763, 39.26119592497736}, {1764, 39.16195286452751}, {1765, 38.86948923485995}, {1766, 39.61600974311452}, {1767, 39.39522112770508}, {1768, 39.514089866690526}, {1769, 39.45799756858736},
	{1770, 38.90570527579156}, {1771, 38.80478381534035}, {1772, 38.83322167157176}, {1773, 39.64297039815119}, {1774, 40.33223301684341}, {1775, 40.41694728495109}, {1776, 40.06020383799442}, {1777, 40.07361881200165}, {1778, 39.77916448556436}, {1779, 39.96893684870016},
	{1780, 40.57894081959218}, {1781, 39.89797496618613}, {1782, 39.35261558123242}, {1783, 39.36008989987693}, {1784, 38.0512977550727}, {1785, 38.264000581925124}, {1786, 38.26169623365976}, {1787, 39.10252385765842}, {1788, 39.27088966509622}, {1789, 39.15216453676914},
	{1790, 39.41049327702329}, {1791, 39.39907719439436}, {1792, 38.82328669157878}, {1793, 39.35804609496024}, {1794, 39.52870877903105}, {1795, 40.562208982859616}, {1796, 41.015089776340226}, {1797, 40.87083252184389}, {1798, 40.53994999420047}, {1799, 41.02575733506004},
	{1800, 41.17619373256442}, {1801, 41.19685023564847}, {1802, 40.98189573065346}, {1803, 41.159763360041595}, {1804, 41.59421552557119}, {1805, 41.20806640088285}, {1806, 40.414699831836835}, {1807, 39.92415966374783}, {1808, 39.62606546104271}, {1809, 39.857180263975444},
	{1810, 39.59080107893363}, {1811, 39.6974862276464}, {1812, 39.442229052918876}, {1813, 39.30199180817845}, {1814, 39.48025720867229}, {1815, 39.5287187420122}, {1816, 38.853563440015805}, {1817, 38.77749075357144}, {1818, 39.12960232658636}, {1819, 39.07838534119988},
	{1820, 39.149292277699324}, {1821, 39.00774814154133}, {1822, 38.63589451271645}, {1823, 38.95501568270912}, {1824, 38.4982817921926}, {1825, 39.10088500152322}, {1826, 39.59621160868451}, {1827, 39.45833354062081}, {1828, 39.59936421761144}, {1829, 39.57053924615646},
	{1830, 39.55660528183884}, {1831, 39.71569674116191}, {1832, 39.71328630121623}, {1833, 39.5500745849456}, {1834, 39.52081122302288}, {1835, 38.74032920127892}, {1836, 39.19864530117539}, {1837, 39.06947571924525}, {1838, 39.34422885689023}, {1839, 39.6353362225693},
	{1840, 40.71459696346432}, {1841, 40.66496952468566}, {1842, 41.006778236777826}, {1843, 40.98904213311685}, {1844, 40.108733704463795}, {1845, 39.422159369592656}, {1846, 39.23842350070322}, {1847, 37.531170184849564}, {1848, 38.05353522108415}, {1849, 38.31111320664359},
	{1850, 38.64900610422957}, {1851, 38.686484249347565}, {1852, 38.68434197825875}, {1853, 38.72332458907287}, {1854, 38.81119764084882}, {1855, 38.46493433585336}, {1856, 38.51556317974943}, {1857, 38.764010535750494}, {1858, 38.55294929767745}, {1859, 38.078366113942565},
	{1860, 38.42988961361437}, {1861, 39.047014068329304}, {1862, 39.532635843081685}, {1863, 39.10571993423328}, {1864, 39.60131420080908}, {1865, 38.81680138357229}, {1866, 39.25082176080607}, {1867, 38.15677220409511}, {1868, 38.62555210254061}, {1869, 38.47132788365266},
	{1870, 38.487714681626166}, {1871, 38.39888830728324}, {1872, 37.54975105530615}, {1873, 36.620496899833185}, {1874, 36.76592939311881}, {1875, 36.77417927197788}, {1876, 36.78457313190018}, {1877, 36.726556157401774}, {1878, 37.19484339680942}, {1879, 37.12075085414386},
	{1880, 36.977258419880144}, {1881, 36.91078025788851}, {1882, 37.02130072401423}, {1883, 36.55535121811925}, {1884, 35.989467257305485}, {1885, 35.963032268137205}, {1886, 36.010752822606925}, {1887, 36.02787704722448}, {1888, 36.49326570398064}, {1889, 36.23934542841747},
	{1890, 35.87776015328743}, {1891, 35.09797528518658}, {1892, 35.077065290325194}, {1893, 35.311414001953885}, {1894, 34.57305509209034}, {1895, 34.6842074805997}, {1896, 34.80183031401632}, {1897, 35.47101264307737}, {1898, 35.17048394585489}, {1899, 35.089175368832215},
	{1900, 35.22509160122155}, {1901, 35.01261679236839}, {1902, 35.20621635881338}, {1903, 35.37294264170206}, {1904, 34.459027714667855}, {1905, 35.092154761591416}, {1906, 34.8517351148361}, {1907, 34.86550272062247}, {1908, 35.125600870401854}, {1909, 34.83446288221645},
	{1910, 34.78242112077965}, {1911, 34.31203602602105}, {1912, 34.279540168694986}, {1913, 35.1096803630126}, {1914, 34.514233849300744}, {1915, 34.53539867779291}, {1916, 34.279414052434674}, {1917, 34.36455267465703}, {1918, 34.10174900420402}, {1919, 34.41175163800032},
	{1920, 34.291999205288036}, {1921, 34.19594013042914}, {1922, 34.18838364564101}, {1923, 36.07392483120914}, {1924, 36.05098431555323}, {1925, 36.76095964181586}, {1926, 37.82863560027054}, {1927, 37.52980493319014}, {1928, 37.53527503569141}, {1929, 37.512668716830554},
	{1930, 37.11106227609642}, {1931, 37.349978643969806}, {1932, 37.20979207398837}, {1933, 37.29059943130983}, {1934, 37.12675552575493}, {1935, 37.34021255585861}, {1936, 37.33863802694112}, {1937, 36.93793225844994}, {1938, 36.96147855185145}, {1939, 37.079544775050316},
	{1940, 36.96800493367608}, {1941, 36.62130515314802}, {1942, 36.64654224799271}, {1943, 36.564393168165026}, {1944, 36.76798510268848}, {1945, 36.34484500467934}, {1946, 35.77622429269998}, {1947, 36.28861461359311}, {1948, 35.62308019530623}, {1949, 35.44131748549641},
	{1950, 34.85392909768805}, {1951, 34.55133668610086}, {1952, 35.092025906373635}, {1953, 34.768122961192404}, {1954, 35.02372314142307}, {1955, 35.11384033534372}, {1956, 35.09859916781124}, {1957, 35.63073140705392}, {1958, 35.47556248383545}, {1959, 34.87826460124942},
	{1960, 34.87959003890974}, {1961, 34.025365090862095}, {1962, 33.804380004654575}, {1963, 32.78020946544929}, {1964, 32.75918431846117}, {1965, 32.75851314921747}, {1966, 32.93198375479733}, {1967, 35.25828074460553}, {1968, 34.28240693566641}, {1969, 34.339864432373425},
	{1970, 34.12397376413126}, {1971, 34.79011341612875}, {1972, 34.64686103755323}, {1973, 34.599313028973235}, {1974, 34.53242934134927}, {1975, 34.606548457455425}, {1976, 34.83272344102554}, {1977, 34.49913157098365}, {1978, 34.70437557256804}, {1979, 35.19565588926615},
	{1980, 35.185492244262484}, {1981, 33.550787666460536}, {1982, 34.02484580154227}, {1983, 34.15044793215261}, {1984, 34.543313702949256}, {1985, 34.49383893491851}, {1986, 34.69468439935647}, {1987, 34.36140916945972}, {1988, 33.199535764838636}, {1989, 33.54089185371181},
	{1990, 33.25543526295492}, {1991, 33.126250139798344}, {1992, 32.1006804695537}, {1993, 32.11793625750763}, {1994, 31.547141310894098}, {1995, 31.358848538734513}, {1996, 30.96324192071878}, {1997, 31.081433577858583}, {1998, 31.004611604459708}, {1999, 30.86284767543519},
	{2000, 30.105433307161203}, {2001, 29.32024170286219}, {2002, 29.319658236582814}, {2003, 29.758958255855212}, {2004, 30.117663632341145}, {2005, 29.548890824528907}, {2006, 29.35044585015188}, {2007, 29.38762759040267}, {2008, 29.391950686507506}, {2009, 30.353380249710128},
	{2010, 29.46899984490753}, {2011, 29.33586115695675}, {2012, 29.36114381531963}, {2013, 29.256022938524392}, {2014, 29.207874497314503}, {2015, 29.266115045795534}, {2016, 29.11037246533442}, {2017, 29.98833975350206}, {2018, 29.827356428113166}, {2019, 29.196369679790173},
	{2020, 29.09133736287457}, {2021, 29.35398305475309}, {2022, 29.54604416792868}, {2023, 28.36216318117799}, {2024, 28.172545798424313}, {2025, 29.167896346989487}, {2026, 29.134747648857985}, {2027, 28.0133642954549}, {2028, 27.97694686027503}, {2029, 28.374194072568063},
	{2030, 28.37095153088029}, {2031, 28.388216858848796}, {2032, 27.992329533869835}, {2033, 27.367870148995426}, {2034, 27.251995482961384}, {2035, 27.746729670664767}, {2036, 27.679330290354688}, {2037, 28.028729073068334}, {2038, 28.028705243794963}, {2039, 28.350786367009555},
	{2040, 28.352026432670012}, {2041, 28.225867429505602}, {2042, 28.211139910084785}, {2043, 28.126532263542863}, {2044, 28.0111605756859}, {2045, 28.037986830307158}, {2046, 27.771048205304385}, {2047, 28.101282898505325}, {2048, 27.956754355558264}, {2049, 28.898451768426284},
	{2050, 28.33803560429799}, {2051, 28.51219696371789}, {2052, 28.687032331939648}, {2053, 28.519256261795114}, {2054, 28.534411822889545}, {2055, 28.475878463300383}, {2056, 28.425823720753847}, {2057, 28.531458363352172}, {2058, 28.371986321151727}, {2059, 27.281010674258564},
	{2060, 27.285423846392753}, {2061, 26.982970399775176}, {2062, 26.779917891194174}, {2063, 27.334018434853117}, {2064, 27.261844645356348}, {2065, 27.08643958372844}, {2066, 27.399456700893154}, {2067, 27.35064731231653}, {2068, 27.27964623953228}, {2069, 27.594268915970815},
	{2070, 27.529530803142432}, {2071, 27.57032488737316}, {2072, 27.4481123592095}, {2073, 26.840190037017013}, {2074, 25.848284039508844}, {2075, 27.842568040851305}, {2076, 28.053732543316965}, {2077, 28.626766043264496}, {2078, 28.147220846160913}, {2079, 28.116929624170805},
	{2080, 28.006707726319842}, {2081, 28.30104291864807}, {2082, 28.33894272086177}, {2083, 28.44881078446907}, {2084, 28.407665090419357}, {2085, 29.120266868128827}, {2086, 29.3317588176526}, {2087, 29.665040474972592}, {2088, 29.513552545038365}, {2089, 29.692597123031344},
	{2090, 28.981378296214995}, {2091, 29.09551924330645}, {2092, 29.103036068928503}, {2093, 29.546315663547908}, {2094, 29.957633494290146}, {2095, 29.904489752089027}, {2096, 29.905243264397946}, {2097, 29.046115152161175}, {2098, 29.044952829872138}, {2099, 29.266240445467794},
	{2100, 29.59245009354912}, {2101, 29.711595098413557}, {2102, 30.01909364831503}, {2103, 30.02844709237877}, {2104, 29.95602684268363}, {2105, 29.966649831798698}, {2106, 29.870132199150568}, {2107, 30.054469107153587}, {2108, 30.00047327238945}, {2109, 29.56478041606059},
	{2110, 29.90146475387948}, {2111, 29.622907648647697}, {2112, 30.309630232664347}, {2113, 29.964474309001496}, {2114, 29.49100419801057}, {2115, 29.961421989896223}, {2116, 30.346134915473066}, {2117, 30.604426349400814}, {2118, 31.112159919665434}, {2119, 31.422724201504558},
	{2120, 31.585365400843976}, {2121, 31.996984724582912}, {2122, 32.01819220164321}, {2123, 29.835521461379106}, {2124, 30.096046165850005}, {2125, 30.103782504040677}, {2126, 30.053631787942646}, {2127, 29.906750519100672}, {2128, 29.906138940448397}, {2129, 29.852649788445774},
	{2130, 30.207615016068207}, {2131, 30.820165055355577}, {2132, 30.66806843164003}, {2133, 29.933937853455785}, {2134, 29.836930249713454}, {2135, 29.643987595361455}, {2136, 30.19074784312923}, {2137, 30.22542736675569}, {2138, 29.853735660522815}, {2139, 29.84557151500528},
	{2140, 29.839193019325773}, {2141, 31.156302724258683}, {2142, 31.25546101123808}, {2143, 31.108453918938817}, {2144, 30.666860514055692}, {2145, 30.645333186456657}, {2146, 30.170151295689198}, {2147, 30.295207809019463}, {2148, 30.8518824742632}, {2149, 31.113576998851187},
	{2150, 31.31604954619179}, {2151, 31.312585749752536}, {2152, 30.864704949670024}, {2153, 30.89452281143898}, {2154, 31.23342385585233}, {2155, 31.404784721717572}, {2156, 31.18805814717659}, {2157, 31.837154644201334}, {2158, 31.806849694846097}, {2159, 31.730917911346975},
	{2160, 31.640559706015285}, {2161, 31.04070924433706}, {2162, 29.808188744723488}, {2163, 30.56052952306829}, {2164, 30.606670887563382}, {2165, 30.40372997396476}, {2166, 30.720199473446222}, {2167, 30.76154769857017}, {2168, 30.970925562360136}, {2169, 31.019650519858754},
	{2170, 31.229380140618062}, {2171, 31.388864514313752}, {2172, 31.354301610850698}, {2173, 30.99276274081928}, {2174, 31.915179561018494}, {2175, 31.918576205835393}, {2176, 33.159103841393794}, {2177, 33.29787809852651}, {2178, 33.01252169346593}, {2179, 33.02073471727393},
	{2180, 32.99606635802466}, {2181, 33.00728410289347}, {2182, 34.05607738376311}, {2183, 33.15858774223605}, {2184, 33.43289159046996}, {2185, 33.4955768254167}, {2186, 33.49850941243009}, {2187, 33.6849166584474}, {2188, 33.94841513146962}, {2189, 33.30304766805812},
	{2190, 33.22108394356688}, {2191, 32.69882923499378}, {2192, 32.427937313925405}, {2193, 32.18858592278298}, {2194, 32.32103253993895}, {2195, 32.71485240989556}, {2196, 33.33520209595963}, {2197, 33.263196044170755}, {2198, 32.710035724800086}, {2199, 33.15410338967067},
	{2200, 33.49162431986145}, {2201, 33.710578425275074}, {2202, 33.32543853826808}, {2203, 33.25527764293191}, {2204, 33.46839755330703}, {2205, 33.683203814839125}, {2206, 33.73810431818219}, {2207, 33.26839137241745}, {2208, 32.870015366666216}, {2209, 33.00655626613422},
	{2210, 33.461231149892406}, {2211, 33.89423423998636}, {2212, 33.50309147431082}, {2213, 33.579287468108}, {2214, 33.66791505848393}, {2215, 34.38967435369897}, {2216, 36.28181224897229}, {2217, 36.88357351027984}, {2218, 36.84878280662571}, {2219, 37.47217008391058},
	{2220, 37.84817431115949}, {2221, 37.90417263033801}, {2222, 37.83987872444627}, {2223, 37.32997096688406}, {2224, 37.4853701637283}, {2225, 38.101980955554055}, {2226, 37.634879540380766}, {2227, 37.458475294951995}, {2228, 37.24084436632412}, {2229, 38.45249609002218},
	{2230, 37.85699416217567}, {2231, 37.35638525020401}, {2232, 37.34244352498811}, {2233, 37.61816197522845}, {2234, 37.16649173849021}, {2235, 37.47322953068236}, {2236, 37.2333430674181}, {2237, 37.14977263499141}, {2238, 36.93966508491671}, {2239, 37.069212698488194},
	{2240, 37.13031285412952}, {2241, 37.12637993171949}, {2242, 36.91777324959473}, {2243, 36.89130918063377}, {2244, 36.83287503871216}, {2245, 37.20202075141188}, {2246, 36.83524257279788}, {2247, 36.830944738890715}, {2248, 36.98000618572528}, {2249, 37.42482479721468},
	{2250, 37.63036405693426}, {2251, 36.667366298537495}, {2252, 36.752893008045845}, {2253, 36.353792852732994}, {2254, 36.68479700023098}, {2255, 36.69141503905663}, {2256, 36.87350479821814}, {2257, 36.165233755112176}, {2258, 35.733553198879285}, {2259, 35.48805636280678},
	{2260, 35.620206059835176}, {2261, 35.633174461262}, {2262, 35.8437425347841}, {2263, 35.9725442605288}, {2264, 35.30481451302577}, {2265, 34.799856216789664}, {2266, 35.20793503084299}, {2267, 35.15095956450417}, {2268, 35.52063000497536}, {2269, 35.7847373835048},
	{2270, 35.4149729701676}, {2271, 35.20790810237125}, {2272, 35.015963290895314}, {2273, 35.152141159882405}, {2274, 34.7677733076443}, {2275, 34.48805775061282}, {2276, 34.48754941675096}, {2277, 34.31241590281594}, {2278, 34.39912341428924}, {2279, 34.214813920779555},
	{2280, 34.28073309875244}, {2281, 33.48991097769715}, {2282, 33.48007351832354}, {2283, 34.358913453235225}, {2284, 34.81847331063591}, {2285, 35.01545093767003}, {2286, 35.522962489940845}, {2287, 35.4137445712856}, {2288, 36.11012685056512}, {2289, 36.22211408792958},
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	{4640, 46.47744540724059}, {4641, 46.43460283813155}, {4642, 46.176535515295534}, {4643, 46.1267773587671}, {4644, 46.07078753090914}, {4645, 45.90463206174146}, {4646, 45.55249821676164}, {4647, 46.10452178892155}, {4648, 46.657238306997954}, {4649, 46.676446405868745},
	{4650, 46.61931105547808}, {4651, 46.75145539959066}, {4652, 47.15614626698322}, {4653, 47.87910231233235}, {4654, 47.90315790426083}, {4655, 48.13748706690984}, {4656, 48.14012518669324}, {4657, 48.12478834534791}, {4658, 47.721710829839914}, {4659, 47.75882142791673},
	{4660, 48.62175299672685}, {4661, 49.44973560609625}, {4662, 49.45655590836775}, {4663, 49.467384079074314}, {4664, 49.36632082510971}, {4665, 49.361539089859946}, {4666, 48.923792508100405}, {4667, 48.82936960309324}, {4668, 48.696827533051106}, {4669, 49.021992536039356},
	{4670, 48.88792946529902}, {4671, 49.049698787091685}, {4672, 49.08423254107231}, {4673, 48.92829127058939}, {4674, 48.38289408354073}, {4675, 48.92579198716452}, {4676, 48.49132529951036}, {4677, 48.54115658361094}, {4678, 48.22070675260601}, {4679, 47.92838519785814},
	{4680, 47.732252711009075}, {4681, 45.99113534110142}, {4682, 44.72899549055614}, {4683, 44.55687451719093}, {4684, 44.55628471776198}, {4685, 44.44930616361875}, {4686, 44.69514501843518}, {4687, 44.08997798757562}, {4688, 44.326776424034165}, {4689, 44.5246373562509},
	{4690, 44.77024206609575}, {4691, 44.41279660589304}, {4692, 44.29090624408688}, {4693, 43.49452874948875}, {4694, 43.31906915186023}, {4695, 42.936317507114055}, {4696, 42.887727362033345}, {4697, 42.05490971051252}, {4698, 42.14072479814179}, {4699, 40.804558836186786},
	{4700, 41.48316460835661}, {4701, 41.52072176780903}, {4702, 41.5348100852975}, {4703, 41.75692669456157}, {4704, 41.49643711525131}, {4705, 42.35954965911466}, {4706, 42.254443486387316}, {4707, 42.346428230827634}, {4708, 42.26152211995296}, {4709, 42.978169988498536},
	{4710, 42.523208465380144}, {4711, 42.92136840228886}, {4712, 42.491877240874906}, {4713, 42.43808793916936}, {4714, 42.31386731961688}, {4715, 42.40503671098323}, {4716, 41.51956996493458}, {4717, 41.51666400077679}, {4718, 41.47426644424032}, {4719, 41.642970570173034},
	{4720, 41.62187072416654}, {4721, 41.15180912858265}, {4722, 41.894760156551904}, {4723, 42.092594714290364}, {4724, 42.27635546119988}, {4725, 42.69832068724076}, {4726, 42.980504524777594}, {4727, 45.87658310035213}, {4728, 43.6183451512828}, {4729, 43.92197152986545},
	{4730, 43.97403155795249}, {4731, 43.83776224600831}, {4732, 44.01998787494774}, {4733, 43.74137827823208}, {4734, 43.51842058845427}, {4735, 43.28245959362667}, {4736, 42.931398042043796}, {4737, 42.81785284737095}, {4738, 43.3507423739577}, {4739, 42.53626377548142},
	{4740, 43.32318432190919}, {4741, 44.1194336467924}, {4742, 44.256900789761175}, {4743, 44.471678262389915}, {4744, 44.52826323886761}, {4745, 44.28324388592612}, {4746, 44.23885158768107}, {4747, 44.118008732018836}, {4748, 44.126076154771745}, {4749, 43.920419005974225},
	{4750, 43.47296751071649}, {4751, 43.54310189974708}, {4752, 43.53066942512155}, {4753, 44.49097326057114}, {4754, 44.60107183314088}, {4755, 42.77090560264186}, {4756, 42.99334677650617}, {4757, 42.929199954491246}, {4758, 42.4663653797701}, {4759, 42.63510417353381},
	{4760, 41.15252150405892}, {4761, 41.65062666173321}, {4762, 41.63569595747878}, {4763, 41.80167602812174}, {4764, 41.54305663974481}, {4765, 41.09851635788159}, {4766, 40.44563966701578}, {4767, 40.533880450251715}, {4768, 40.8690019227734}, {4769, 40.88937124246862},
	{4770, 41.183809565163905}, {4771, 41.23702889676266}, {4772, 41.98448907911279}, {4773, 41.95032094100293}, {4774, 41.831147917269575}, {4775, 41.61384516565436}, {4776, 41.337855349523466}, {4777, 41.31691388756026}, {4778, 41.00824360651651}, {4779, 40.66303052923502},
	{4780, 40.75233960523218}, {4781, 40.74691723991323}, {4782, 41.224220277952135}, {4783, 41.24176898114373}, {4784, 41.19227291002064}, {4785, 41.455618057185966}, {4786, 41.793314227583664}, {4787, 41.169085632598424}, {4788, 41.147687532911064}, {4789, 41.308688926534245},
	{4790, 41.159786924004884}, {4791, 41.8142881123724}, {4792, 41.552546791536315}, {4793, 41.63707209178867}, {4794, 41.36580909924643}, {4795, 40.810470695252555}, {4796, 40.90861666010221}, {4797, 40.9449761604474}, {4798, 41.15181950532048}, {4799, 41.13789218005914},
	{4800, 41.08509141277718}, {4801, 41.05365891335565}, {4802, 40.980911652896054}, {4803, 41.734203454889105}, {4804, 41.31916007992194}, {4805, 41.4215682147432}, {4806, 41.51414417468774}, {4807, 42.37111482324612}, {4808, 42.70943804743709}, {4809, 42.666757607996296},
	{4810, 42.12147053040958}, {4811, 42.464100810348334}, {4812, 42.62139441696377}, {4813, 41.94637435030276}, {4814, 41.99684563449916}, {4815, 42.54816794861336}, {4816, 42.28223265087694}, {4817, 42.24550930900591}, {4818, 42.282491306075286}, {4819, 42.58423495563741},
	{4820, 41.359861111288104}, {4821, 42.10481353702761}, {4822, 42.24941093960088}, {4823, 41.19941990664588}, {4824, 41.21364184446058}, {4825, 41.72506184259513}, {4826, 42.53601771160175}, {4827, 42.67420054464686}, {4828, 42.76426057329836}, {4829, 42.78798548069922},
	{4830, 42.76148923124109}, {4831, 43.55500018064631}, {4832, 43.52818564137662}, {4833, 43.71030227628026}, {4834, 43.69559859751488}, {4835, 42.75390903216747}, {4836, 42.95452875778498}, {4837, 43.365066775687346}, {4838, 43.36814790382736}, {4839, 43.89333739845817},
	{4840, 43.989916759215}, {4841, 43.56253598246386}, {4842, 43.377743454747105}, {4843, 42.924400615882426}, {4844, 43.12304670119044}, {4845, 42.58288520924721}, {4846, 42.6192440085378}, {4847, 42.65060540788467}, {4848, 42.41222623035344}, {4849, 41.646360968682984},
	{4850, 41.424134917273825}, {4851, 41.10868413269653}, {4852, 41.172396017699}, {4853, 41.36004588804885}, {4854, 40.800077988280925}, {4855, 40.86912290176179}, {4856, 39.88125368753376}, {4857, 40.413562336579986}, {4858, 40.30739366800392}, {4859, 40.4448665834484},
	{4860, 40.67992036846289}, {4861, 39.19323041879348}, {4862, 38.934776988261994}, {4863, 38.6635282389286}, {4864, 38.018950718551935}, {4865, 38.04674518139207}, {4866, 38.01853292656019}, {4867, 37.71021607139222}, {4868, 38.422846767406455}, {4869, 38.450019969893354},
	{4870, 38.3997470792123}, {4871, 38.34361998177123}, {4872, 39.091980399463395}, {4873, 39.5198852558182}, {4874, 39.5472385581927}, {4875, 39.52236007766908}, {4876, 39.37969949452826}, {4877, 40.222868236832014}, {4878, 39.66661286220836}, {4879, 40.283042854444616},
	{4880, 40.229716416585205}, {4881, 40.445190873458}, {4882, 41.20372788803875}, {4883, 41.40919784184403}, {4884, 41.40205136110032}, {4885, 41.489596657482274}, {4886, 41.63320805924114}, {4887, 41.74501472339082}, {4888, 41.59463339227347}, {4889, 41.89165418164628},
	{4890, 42.429906756721266}, {4891, 42.51566334270849}, {4892, 42.43112651097444}, {4893, 42.65573412390896}, {4894, 42.5649774287204}, {4895, 42.20578627338075}, {4896, 42.19905186404266}, {4897, 42.063060621486514}, {4898, 40.8631606909062}, {4899, 41.4015851042295},
	{4900, 40.88944459737443}, {4901, 41.365721619037295}, {4902, 40.08190763242786}, {4903, 40.11091422145917}, {4904, 40.97087104137605}, {4905, 41.15805729486192}, {4906, 41.27896864220977}, {4907, 41.170130110377485}, {4908, 41.019095916064586}, {4909, 41.19823454109512},
	{4910, 40.71222352487721}, {4911, 40.604096585580145}, {4912, 40.22428726447587}, {4913, 38.86084836942058}, {4914, 38.70041746310922}, {4915, 38.8194506164692}, {4916, 38.64467182897344}, {4917, 38.639870243656844}, {4918, 38.929014450694986}, {4919, 38.80087908949201},
	{4920, 38.474735694735124}, {4921, 38.66300047873025}, {4922, 38.684455038039566}, {4923, 38.29265621342109}, {4924, 38.49017410077791}, {4925, 38.88748571310341}, {4926, 39.34561928924596}, {4927, 39.41078759839496}, {4928, 39.753432401888055}, {4929, 39.66725496587569},
	{4930, 39.64503039721447}, {4931, 39.74434633216348}, {4932, 39.24422485817575}, {4933, 39.357176347703124}, {4934, 39.083868743073175}, {4935, 38.77958154299146}, {4936, 38.784739437051876}, {4937, 38.84416930772779}, {4938, 38.531983904133995}, {4939, 38.13839982421345},
	{4940, 38.19834116299139}, {4941, 38.384878790359856}, {4942, 37.41788048991505}, {4943, 38.32825078053794}, {4944, 37.27571543485687}, {4945, 37.381643210593964}, {4946, 37.139400383368596}, {4947, 37.686425234248986}, {4948, 37.603432975092}, {4949, 37.64359097418195},
	{4950, 37.23329232367846}, {4951, 36.994849462220934}, {4952, 36.826705097979186}, {4953, 36.10850429296769}, {4954, 36.10515278531009}, {4955, 36.27585866868438}, {4956, 35.877106950223286}, {4957, 35.06902417472288}, {4958, 35.68954496717155}, {4959, 34.429975016070486},
	{4960, 33.9039081124664}, {4961, 34.50994734260132}, {4962, 34.24726508634311}, {4963, 34.27196566995411}, {4964, 34.53854603237626}, {4965, 33.18029169046981}, {4966, 33.74849740086445}, {4967, 33.7660814446232}, {4968, 33.690731394344716}, {4969, 33.75687045286519},
	{4970, 33.94382441333488}, {4971, 33.56341790269826}, {4972, 33.64387610469928}, {4973, 33.603199106999526}, {4974, 33.55490176741914}, {4975, 33.76379562158691}, {4976, 33.76315401597445}, {4977, 32.8267558087521}, {4978, 32.45241276131267}, {4979, 32.55733463964615},
	{4980, 33.319801723754786}, {4981, 33.59341126615778}, {4982, 33.73081923269426}, {4983, 34.37346764688176}, {4984, 35.07176548766099}, {4985, 35.37591959109057}, {4986, 35.471233571041964}, {4987, 35.13016122517179}, {4988, 34.65099719562258}, {4989, 34.37111074112498},
	{4990, 34.51523331821902}, {4991, 34.357189444832144}, {4992, 34.36407537164143}, {4993, 34.34124435265085}, {4994, 34.71701325993874}, {4995, 34.535111124444725}, {4996, 34.12819607955428}, {4997, 33.476805201968794}, {4998, 33.21364571883214}, {4999, 34.07622604782128},
}

// Point is a point on a line
type Point struct {
	X float64
	Y float64
}

func BenchmarkLTTB(b *testing.B) {
	ctx := context.New()
	defer ctx.Close()

	seriesStart := time.Now()
	stepSize := 1000
	values := NewValues(ctx, stepSize, len(data))
	for i := 0; i < values.Len(); i++ {
		values.SetValueAt(i, data[i].Y)
	}
	series := NewSeries(ctx, "foo", seriesStart, values)

	for i := 0; i < b.N; i++ {
		LTTB(series, series.StartTime(), series.EndTime(), 5000)
	}
}

func BenchmarkAverage(b *testing.B) {
	ctx := context.New()
	defer ctx.Close()

	seriesStart := time.Now()
	stepSize := 1000
	values := NewValues(ctx, stepSize, len(data))
	for i := 0; i < values.Len(); i++ {
		values.SetValueAt(i, data[i].Y)
	}
	series := NewSeries(ctx, "foo", seriesStart, values)

	for i := 0; i < b.N; i++ {
		series.IntersectAndResize(series.StartTime(), series.EndTime(), 5000, Avg)
	}
}