psiphon-tunnel-core/vendor/github.com/axiomhq/hyperloglog/beta.go

package hyperloglog

import (
	"fmt"
	"math"
)

var betaMap = map[uint8]func(float64) float64{
	4:  beta4,
	5:  beta5,
	6:  beta6,
	7:  beta7,
	8:  beta8,
	9:  beta9,
	10: beta10,
	11: beta11,
	12: beta12,
	13: beta13,
	14: beta14,
	15: beta15,
	16: beta16,
	17: beta17,
	18: beta18,
}

func beta(p uint8, ez float64) float64 {
	f, ok := betaMap[p]
	if !ok {
		panic(fmt.Sprintf("invalid precision %d", p))
	}
	return f(ez)
}

/*
p=4
[-0.582581413904517,-1.935300357560050,11.07932375 8035073,-22.131357446444323,22.505391846630037,-12 .000723834917984,3.220579408194167,-0.342225302271 235]
*/
func beta4(ez float64) float64 {
	zl := math.Log(ez + 1)
	return -0.582581413904517*ez +
		-1.935300357560050*zl +
		11.079323758035073*math.Pow(zl, 2) +
		-22.131357446444323*math.Pow(zl, 3) +
		22.505391846630037*math.Pow(zl, 4) +
		-12.000723834917984*math.Pow(zl, 5) +
		3.220579408194167*math.Pow(zl, 6) +
		-0.342225302271235*math.Pow(zl, 7)
}

/*
p=5
[-0.7518999460733967,-0.9590030077748760,5.5997371 322141607,-8.2097636999765520,6.5091254894472037,- 2.6830293734323729,0.5612891113138221,-0.046333162 2196545]
*/
func beta5(ez float64) float64 {
	zl := math.Log(ez + 1)
	return -0.7518999460733967*ez +
		-0.9590030077748760*zl +
		5.5997371322141607*math.Pow(zl, 2) +
		-8.2097636999765520*math.Pow(zl, 3) +
		6.5091254894472037*math.Pow(zl, 4) +
		-2.6830293734323729*math.Pow(zl, 5) +
		0.5612891113138221*math.Pow(zl, 6) +
		-0.0463331622196545*math.Pow(zl, 7)
}

/*
p=6
[29.8257900969619634,-31.3287083337725925,-10.5942 523036582283,-11.5720125689099618,3.81887543739074 92,-2.4160130328530811,0.4542208940970826,-0.05751 55452020420]
*/
func beta6(ez float64) float64 {
	zl := math.Log(ez + 1)
	return 29.8257900969619634*ez +
		-31.3287083337725925*zl +
		-10.5942523036582283*math.Pow(zl, 2) +
		-11.5720125689099618*math.Pow(zl, 3) +
		3.8188754373907492*math.Pow(zl, 4) +
		-2.4160130328530811*math.Pow(zl, 5) +
		0.4542208940970826*math.Pow(zl, 6) +
		-0.0575155452020420*math.Pow(zl, 7)
}

/*
p=7
[2.8102921290820060,-3.9780498518175995,1.31626800 41351582,-3.9252486335805901,2.0080835753946471,-0 .7527151937556955,0.1265569894242751,-0.0109946438726240]
*/
func beta7(ez float64) float64 {
	zl := math.Log(ez + 1)
	return 2.8102921290820060*ez +
		-3.9780498518175995*zl +
		1.3162680041351582*math.Pow(zl, 2) +
		-3.9252486335805901*math.Pow(zl, 3) +
		2.0080835753946471*math.Pow(zl, 4) +
		-0.7527151937556955*math.Pow(zl, 5) +
		0.1265569894242751*math.Pow(zl, 6) +
		-0.0109946438726240*math.Pow(zl, 7)
}

/*
p=8
[1.00633544887550519,-2.00580666405112407,1.643697 49366514117,-2.70560809940566172,1.392099802442225 98,-0.46470374272183190,0.07384282377269775,-0.00578554885254223]
*/
func beta8(ez float64) float64 {
	zl := math.Log(ez + 1)
	return 1.00633544887550519*ez +
		-2.00580666405112407*zl +
		1.64369749366514117*math.Pow(zl, 2) +
		-2.70560809940566172*math.Pow(zl, 3) +
		1.39209980244222598*math.Pow(zl, 4) +
		-0.46470374272183190*math.Pow(zl, 5) +
		0.07384282377269775*math.Pow(zl, 6) +
		-0.00578554885254223*math.Pow(zl, 7)
}

/*
p=9
[-0.09415657458167959,-0.78130975924550528,1.71514 946750712460,-1.73711250406516338,0.86441508489048 924,-0.23819027465047218,0.03343448400269076,-0.00 207858528178157]
*/
func beta9(ez float64) float64 {
	zl := math.Log(ez + 1)
	return -0.09415657458167959*ez +
		-0.78130975924550528*zl +
		1.71514946750712460*math.Pow(zl, 2) +
		-1.73711250406516338*math.Pow(zl, 3) +
		0.86441508489048924*math.Pow(zl, 4) +
		-0.23819027465047218*math.Pow(zl, 5) +
		0.03343448400269076*math.Pow(zl, 6) +
		-0.00207858528178157*math.Pow(zl, 7)
}

/*
p=10
[-0.25935400670790054,-0.52598301999805808,1.48933 034925876839,-1.29642714084993571,0.62284756217221615,-0.15672326770251041,0.02054415903878563,-0.00 112488483925502]
*/
func beta10(ez float64) float64 {
	zl := math.Log(ez + 1)
	return -0.25935400670790054*ez +
		-0.52598301999805808*zl +
		1.48933034925876839*math.Pow(zl, 2) +
		-1.29642714084993571*math.Pow(zl, 3) +
		0.62284756217221615*math.Pow(zl, 4) +
		-0.15672326770251041*math.Pow(zl, 5) +
		0.02054415903878563*math.Pow(zl, 6) +
		-0.00112488483925502*math.Pow(zl, 7)
}

/*
p=11
[-4.32325553856025e-01,-1.08450736399632e-01,6.091 56550741120e-01,-1.65687801845180e-02,-7.958293410 87617e-02,4.71830602102918e-02,-7.81372902346934e- 03,5.84268708489995e-04]
*/
func beta11(ez float64) float64 {
	zl := math.Log(ez + 1)
	return -0.432325553856025*ez +
		-0.108450736399632*zl +
		0.609156550741120*math.Pow(zl, 2) +
		-0.0165687801845180*math.Pow(zl, 3) +
		-0.0795829341087617*math.Pow(zl, 4) +
		0.0471830602102918*math.Pow(zl, 5) +
		-0.00781372902346934*math.Pow(zl, 6) +
		0.000584268708489995*math.Pow(zl, 7)
}

/*
p=12
[-3.84979202588598e-01,1.83162233114364e-01,1.3039 6688841854e-01,7.04838927629266e-02,-8.95893971464 453e-03,1.13010036741605e-02,-1.94285569591290e-03 ,2.25435774024964e-04]
*/
func beta12(ez float64) float64 {
	zl := math.Log(ez + 1)
	return -0.384979202588598*ez +
		0.183162233114364*zl +
		0.130396688841854*math.Pow(zl, 2) +
		0.0704838927629266*math.Pow(zl, 3) +
		-0.0089589397146453*math.Pow(zl, 4) +
		0.0113010036741605*math.Pow(zl, 5) +
		-0.00194285569591290*math.Pow(zl, 6) +
		0.000225435774024964*math.Pow(zl, 7)
}

/*
p=13
[-0.41655270946462997,-0.22146677040685156,0.38862 131236999947,0.45340979746062371,-0.36264738324476 375,0.12304650053558529,-0.01701540384555510,0.001 02750367080838]
*/
func beta13(ez float64) float64 {
	zl := math.Log(ez + 1)
	return -0.41655270946462997*ez +
		-0.22146677040685156*zl +
		0.38862131236999947*math.Pow(zl, 2) +
		0.45340979746062371*math.Pow(zl, 3) +
		-0.36264738324476375*math.Pow(zl, 4) +
		0.12304650053558529*math.Pow(zl, 5) +
		-0.01701540384555510*math.Pow(zl, 6) +
		0.00102750367080838*math.Pow(zl, 7)
}

/*
p=14
[-3.71009760230692e-01,9.78811941207509e-03,1.8579 6293324165e-01,2.03015527328432e-01,-1.16710521803 686e-01,4.31106699492820e-02,-5.99583540511831e-03 ,4.49704299509437e-04]
*/

func beta14(ez float64) float64 {
	zl := math.Log(ez + 1)
	return -0.371009760230692*ez +
		0.00978811941207509*zl +
		0.185796293324165*math.Pow(zl, 2) +
		0.203015527328432*math.Pow(zl, 3) +
		-0.116710521803686*math.Pow(zl, 4) +
		0.0431106699492820*math.Pow(zl, 5) +
		-0.00599583540511831*math.Pow(zl, 6) +
		0.000449704299509437*math.Pow(zl, 7)
}

/*
p=15
[-0.38215145543875273,-0.89069400536090837,0.37602 335774678869,0.99335977440682377,-0.65577441638318 956,0.18332342129703610,-0.02241529633062872,0.001 21399789330194]
*/
func beta15(ez float64) float64 {
	zl := math.Log(ez + 1)
	return -0.38215145543875273*ez +
		-0.89069400536090837*zl +
		0.37602335774678869*math.Pow(zl, 2) +
		0.99335977440682377*math.Pow(zl, 3) +
		-0.65577441638318956*math.Pow(zl, 4) +
		0.18332342129703610*math.Pow(zl, 5) +
		-0.02241529633062872*math.Pow(zl, 6) +
		0.00121399789330194*math.Pow(zl, 7)
}

/*
p=16
[-0.37331876643753059,-1.41704077448122989,0.407291 84796612533,1.56152033906584164,-0.99242233534286128,0.26064681399483092,-0.03053811369682807,0.00155770210179105]
*/
func beta16(ez float64) float64 {
	zl := math.Log(ez + 1)
	return -0.37331876643753059*ez +
		-1.41704077448122989*zl +
		0.40729184796612533*math.Pow(zl, 2) +
		1.56152033906584164*math.Pow(zl, 3) +
		-0.99242233534286128*math.Pow(zl, 4) +
		0.26064681399483092*math.Pow(zl, 5) +
		-0.03053811369682807*math.Pow(zl, 6) +
		0.00155770210179105*math.Pow(zl, 7)
}

/*
p=17
[-0.36775502299404605,0.53831422351377967,0.769702 89278767923,0.55002583586450560,-0.745755882611469 41,0.25711835785821952,-0.03437902606864149,0.0018 5949146371616]
*/
func beta17(ez float64) float64 {
	zl := math.Log(ez + 1)
	return -0.36775502299404605*ez +
		0.53831422351377967*zl +
		0.76970289278767923*math.Pow(zl, 2) +
		0.55002583586450560*math.Pow(zl, 3) +
		-0.74575588261146941*math.Pow(zl, 4) +
		0.25711835785821952*math.Pow(zl, 5) +
		-0.03437902606864149*math.Pow(zl, 6) +
		0.00185949146371616*math.Pow(zl, 7)
}

/*
p=18
[-0.36479623325960542,0.99730412328635032,1.553543 86230081221,1.25932677198028919,-1.533259482091101 63,0.47801042200056593,-0.05951025172951174,0.0029 1076804642205]
*/
func beta18(ez float64) float64 {
	zl := math.Log(ez + 1)
	return -0.36479623325960542*ez +
		0.99730412328635032*zl +
		1.55354386230081221*math.Pow(zl, 2) +
		1.25932677198028919*math.Pow(zl, 3) +
		-1.53325948209110163*math.Pow(zl, 4) +
		0.47801042200056593*math.Pow(zl, 5) +
		-0.05951025172951174*math.Pow(zl, 6) +
		0.00291076804642205*math.Pow(zl, 7)
}