expo.go

package crazy

import "math"

// Exponential adapts a Source to generate random numbers under an exponential
// distribution.
type Exponential struct {
	Source
	Rate float64
}

// NewExponential creates an exponential distribution drawing from the
// specified source with given rate parameter.
func NewExponential(src Source, rate float64) Exponential {
	return Exponential{
		Source: src,
		Rate:   rate,
	}
}

// Next generates an exponential variate.
func (e Exponential) Next() float64 {
	x := expoZig.GenNext(e.Source)
	return x / e.Rate
}

func expoPDF(x float64) float64 {
	return math.Exp(-x)
}

func expoTail(src Source) float64 {
	return expoR - math.Log(Uniform0_1{src}.Next())
}

var expoZig = Ziggurat{
	PDF:      expoPDF,
	Tail:     expoTail,
	Mirrored: false,
	K:        expoK,
	W:        expoW,
	F:        expoF,
}

const expoR = 9.25616454426554

var expoK = [1024]uint64{
	0x1ce142c806bbca, 0x00000000000000, 0x13a2e8754d11d3, 0x1893ad94056903,
	0x1abdc2caab364d, 0x1bf0d5a059f05f, 0x1cb2dcb2afeca3, 0x1d382b88438efd,
	0x1d993d4a843892, 0x1de3005cdb9685, 0x1e1ce953a7aada, 0x1e4b8ff9b72624,
	0x1e71ef51692778, 0x1e920badc7caed, 0x1ead4eb647f2a7, 0x1ec4bd2917746d,
	0x1ed917afecf097, 0x1eeaefb117c710, 0x1efab4f0d45b99, 0x1f08bebea80034,
	0x1f15524a538575, 0x1f20a71a9a4950, 0x1f2aea428b997d, 0x1f3440b9fd4d2f,
	0x1f3cc91b7046c6, 0x1f449cf3d895f2, 0x1f4bd1c2ba0869, 0x1f5279bfcb493d,
	0x1f58a4751d7f8b, 0x1f5e5f388a575e, 0x1f63b58c3ad7e9, 0x1f68b16c08dc31,
	0x1f6d5b8c044fd9, 0x1f71bb8b55855b, 0x1f75d81def9dca, 0x1f79b72ef3a811,
	0x1f7d5dfd381a11, 0x1f80d133164bc9, 0x1f8414fa616be2, 0x1f872d0d3ad391,
	0x1f8a1cc452f503, 0x1f8ce72309a699, 0x1f8f8ee1ca4a4b, 0x1f921676eecb4a,
	0x1f94801e668bf9, 0x1f96cde05350f7, 0x1f990196c55b3a, 0x1f9b1cf2b8c1d3,
	0x1f9d2180705665, 0x1f9f10ab45ad4f, 0x1fa0ebc1020c8b, 0x1fa2b3f4d0ddf9,
	0x1fa46a61d9a972, 0x1fa6100d8d74de, 0x1fa7a5e9b19fcc, 0x1fa92cd630d2bd,
	0x1faaa5a2b95b8c, 0x1fac11102f446a, 0x1fad6fd1f79125, 0x1faec28f214fb0,
	0x1fb009e37086ff, 0x1fb146604e85bf, 0x1fb2788da29d0f, 0x1fb3a0ea95eeeb,
	0x1fb4bfee44a205, 0x1fb5d6085e829f, 0x1fb6e3a1b8d84e, 0x1fb7e91cd3015a,
	0x1fb8e6d64f34c0, 0x1fb9dd2560a263, 0x1fbacc5c3004f5, 0x1fbbb4c83799b7,
	0x1fbc96b29756b3, 0x1fbd726062201c, 0x1fbe4812e4a863, 0x1fbf1807e6940d,
	0x1fbfe279e66a1e, 0x1fc0a7a050cb6a, 0x1fc167afb35e94, 0x1fc222d9ebd331,
	0x1fc2d94e535488, 0x1fc38b39e6bbb7, 0x1fc438c76bc8fa, 0x1fc4e21f93a4fb,
	0x1fc587691ae4b6, 0x1fc628c8e7450b, 0x1fc6c662234def, 0x1fc760565808ea,
	0x1fc7f6c584f268, 0x1fc889ce3649dc, 0x1fc9198d99e17d, 0x1fc9a61f928b72,
	0x1fca2f9eca3fa7, 0x1fcab624c3132d, 0x1fcb39c9e717df, 0x1fcbbaa5973916,
	0x1fcc38ce39287b, 0x1fccb459446c6f, 0x1fcd2d5b4ea00f, 0x1fcda3e816f387,
	0x1fce181290fa48, 0x1fce89eceed388, 0x1fcef988aab890, 0x1fcf66f68ffb57,
	0x1fcfd246c37f46, 0x1fd03b88cbb500, 0x1fd0a2cb9821aa, 0x1fd1081d887932,
	0x1fd16b8c7352e7, 0x1fd1cd25ac7ec6, 0x1fd22cf60b01bf, 0x1fd28b09eebe86,
	0x1fd2e76d45d02f, 0x1fd3422b919b8a, 0x1fd39b4feb9bb3, 0x1fd3f2e509ee11,
	0x1fd448f543a1c2, 0x1fd49d8a94ce02, 0x1fd4f0aea27303, 0x1fd5426abe2867,
	0x1fd592c7e99c3d, 0x1fd5e1ced9e561, 0x1fd62f87faabb8, 0x1fd67bfb7128c6,
	0x1fd6c7311f02d3, 0x1fd71130a504bf, 0x1fd75a0165b486, 0x1fd7a1aa87ca39,
	0x1fd7e832f88942, 0x1fd82da16dfd80, 0x1fd871fc691dc8, 0x1fd8b54a37d537,
	0x1fd8f790f6f4b2, 0x1fd938d6940dd2, 0x1fd97920cf386c, 0x1fd9b8753cc3d3,
	0x1fd9f6d946d4e9, 0x1fda34522ef1e9, 0x1fda70e50f7cee, 0x1fdaac96dd1e02,
	0x1fdae76c681da3, 0x1fdb216a5db062, 0x1fdb5a9549347e, 0x1fdb92f1956210,
	0x1fdbca838d6e7c, 0x1fdc014f5e23c4, 0x1fdc375916ec52, 0x1fdc6ca4aad3c6,
	0x1fdca135f17d4d, 0x1fdcd510a80fff, 0x1fdd08387219c6, 0x1fdd3ab0da6926,
	0x1fdd6c7d53de73, 0x1fdd9da13a34ba, 0x1fddce1fd2c2dd, 0x1fddfdfc4d351d,
	0x1fde2d39c43f82, 0x1fde5bdb3e496a, 0x1fde89e3ae128a, 0x1fdeb755f351ad,
	0x1fdee434db4d7f, 0x1fdf1083216f9a, 0x1fdf3c436fd21a, 0x1fdf67785fc7fd,
	0x1fdf92247a607a, 0x1fdfbc4a38e58e, 0x1fdfe5ec0555f2, 0x1fe00f0c3adaaa,
	0x1fe037ad263860, 0x1fe05fd1063cae, 0x1fe0877a0c2794, 0x1fe0aeaa5c1128,
	0x1fe0d5640d4bc6, 0x1fe0fba92ac2c9, 0x1fe1217bb35607, 0x1fe146dd9a321c,
	0x1fe16bd0c725b9, 0x1fe1905716f40a, 0x1fe1b4725ba44e, 0x1fe1d8245ccec7,
	0x1fe1fb6ed7e715, 0x1fe21e53808417, 0x1fe240d400a56d, 0x1fe262f1f8f6b3,
	0x1fe284af011080, 0x1fe2a60ca7b754, 0x1fe2c70c731872, 0x1fe2e7afe104cc,
	0x1fe307f8672a07, 0x1fe327e77349b3, 0x1fe3477e6b6ebc, 0x1fe366beae2137,
	0x1fe385a9929884, 0x1fe3a44068ebe6, 0x1fe3c2847a4199, 0x1fe3e07708fc73,
	0x1fe3fe1950e81d, 0x1fe41b6c8763f6, 0x1fe43871db8ca3, 0x1fe4552a766464,
	0x1fe471977afa2c, 0x1fe48dba068f92, 0x1fe4a99330bd9d, 0x1fe4c5240b987e,
	0x1fe4e06da3d237, 0x1fe4fb7100dc40, 0x1fe5162f250832, 0x1fe530a90da77a,
	0x1fe54adfb32a2b, 0x1fe564d4093cdf, 0x1fe57e86fee5cb, 0x1fe597f97ea0f4,
	0x1fe5b12c6e7ba0, 0x1fe5ca20b02ef6, 0x1fe5e2d72139ee, 0x1fe5fb509afa74,
	0x1fe6138df2c5e8, 0x1fe62b8ffa00ea, 0x1fe643577e367b, 0x1fe65ae5492e80,
	0x1fe6723a2103a8, 0x1fe68956c838b2, 0x1fe6a03bfdcd2d, 0x1fe6b6ea7d5199,
	0x1fe6cd62fefb09, 0x1fe6e3a637b63c, 0x1fe6f9b4d93a30, 0x1fe70f8f921a3e,
	0x1fe725370dd7b3, 0x1fe73aabf4f2fd, 0x1fe74feeecfc5c, 0x1fe7650098a429,
	0x1fe779e197caaf, 0x1fe78e92878f9a, 0x1fe7a314026109, 0x1fe7b766a00a2d,
	0x1fe7cb8af5c19a, 0x1fe7df81963731, 0x1fe7f34b11a1b1, 0x1fe806e7f5cbf3,
	0x1fe81a58ce21d2, 0x1fe82d9e23bcbb, 0x1fe840b87d6ff7, 0x1fe853a85fd499,
	0x1fe8666e4d5531, 0x1fe8790ac63927, 0x1fe88b7e48afd9, 0x1fe89dc950db71,
	0x1fe8afec58db72, 0x1fe8c1e7d8d710, 0x1fe8d3bc470739, 0x1fe8e56a17c070,
	0x1fe8f6f1bd7c5e, 0x1fe90853a8e335, 0x1fe9199048d4d1, 0x1fe92aa80a71a4,
	0x1fe93b9b592372, 0x1fe94c6a9ea5d1, 0x1fe95d16430e79, 0x1fe96d9eacd569,
	0x1fe97e0440dcce, 0x1fe98e476278c9, 0x1fe99e68737701, 0x1fe9ae67d4260a,
	0x1fe9be45e35c9c, 0x1fe9ce02fe80ac, 0x1fe9dd9f818e4e, 0x1fe9ed1bc71e7a,
	0x1fe9fc78286da4, 0x1fea0bb4fd622f, 0x1fea1ad29c92c2, 0x1fea29d15b4c6b,
	0x1fea38b18d98b2, 0x1fea4773864375, 0x1fea561796e0b6, 0x1fea649e0fd23d,
	0x1fea7307404d1e, 0x1fea8153765f1f, 0x1fea8f82fef403, 0x1fea9d9625dab6,
	0x1feaab8d35ca5b, 0x1feab968786744, 0x1feac7283647c3, 0x1fead4ccb6f8f2,
	0x1feae256410352, 0x1feaefc519ef56, 0x1feafd198649db, 0x1feb0a53c9a87f,
	0x1feb177426ade9, 0x1feb247adf0df3, 0x1feb31683391c2, 0x1feb3e3c641bc8,
	0x1feb4af7afabb3, 0x1feb579a54623f, 0x1feb64248f8501, 0x1feb70969d820f,
	0x1feb7cf0b9f3a6, 0x1feb89331fa3aa, 0x1feb955e088f28, 0x1feba171ade9b4,
	0x1febad6e4820c2, 0x1febb9540edee8, 0x1febc523390f11, 0x1febd0dbfcdfa0,
	0x1febdc7e8fc583, 0x1febe80b267f33, 0x1febf381f517ae, 0x1febfee32ee957,
	0x1fec0a2f06a0cf, 0x1fec1565ae3fbd, 0x1fec2087571f89, 0x1fec2b9431f408,
	0x1fec368c6ece1f, 0x1fec41703d1e52, 0x1fec4c3fcbb74e, 0x1fec56fb48d060,
	0x1fec61a2e207e6, 0x1fec6c36c465ae, 0x1fec76b71c5d4f, 0x1fec812415d072,
	0x1fec8b7ddc1116, 0x1fec95c499e3c1, 0x1fec9ff87981ad, 0x1fecaa19a49ae9,
	0x1fecb42844586c, 0x1fecbe24815e28, 0x1fecc80e83cd04, 0x1fecd1e67344dd,
	0x1fecdbac76e672, 0x1fece560b5554a, 0x1fecef0354b994, 0x1fecf8947ac1fc,
	0x1fed02144ca577, 0x1fed0b82ef2507, 0x1fed14e0868d78, 0x1fed1e2d36b915,
	0x1fed276923114f, 0x1fed30946e906a, 0x1fed39af3bc313, 0x1fed42b9acc9fa,
	0x1fed4bb3e35b5d, 0x1fed549e00c492, 0x1fed5d7825eb87, 0x1fed664273503c,
	0x1fed6efd090e34, 0x1fed77a806dde4, 0x1fed80438c1618, 0x1fed88cfb7ad55,
	0x1fed914ca83b2d, 0x1fed99ba7bf99b, 0x1feda21950c64a, 0x1fedaa694423e0,
	0x1fedb2aa733b41, 0x1fedbadcfadccc, 0x1fedc300f78190, 0x1fedcb16854c82,
	0x1fedd31dc00ba5, 0x1feddb16c33938, 0x1fede301a9fcd3, 0x1fedeade8f2c88,
	0x1fedf2ad8d4dfd, 0x1fedfa6ebe977d, 0x1fee02223cf109, 0x1fee09c821f567,
	0x1fee116086f321, 0x1fee18eb84ed8f, 0x1fee2069349dce, 0x1fee27d9ae73c1,
	0x1fee2f3d0a96ff, 0x1fee369360e7cb, 0x1fee3ddcc8ffff, 0x1fee45195a33f2,
	0x1fee4c492b9366, 0x1fee536c53ea62, 0x1fee5a82e9c215, 0x1fee618d0361ae,
	0x1fee688ab6cf37, 0x1fee6f7c19d064, 0x1fee766141eb64, 0x1fee7d3a4467b3,
	0x1fee8407364edc, 0x1fee8ac82c6d44, 0x1fee917d3b52ed, 0x1fee9826775433,
	0x1fee9ec3f48a8c, 0x1feea555c6d540, 0x1feeabdc01da1f, 0x1feeb256b9063a,
	0x1feeb8c5ff8e8b, 0x1feebf29e870ae, 0x1feec582867384, 0x1feecbcfec27df,
	0x1feed2122be928, 0x1feed84957de04, 0x1feede7581f8f2, 0x1feee496bbf8eb,
	0x1feeeaad1769fe, 0x1feef0b8a5a5e7, 0x1feef6b977d4ac, 0x1feefcaf9eed2a,
	0x1fef029b2bb5ae, 0x1fef087c2ec47f, 0x1fef0e52b88072, 0x1fef141ed92172,
	0x1fef19e0a0b108, 0x1fef1f981f0ae6, 0x1fef254563dd6c, 0x1fef2ae87eaa27,
	0x1fef30817ec656, 0x1fef3610735b68, 0x1fef3b956b677a, 0x1fef411075bdd0,
	0x1fef4681a10750, 0x1fef4be8fbc2fa, 0x1fef514694465d, 0x1fef569a78be09,
	0x1fef5be4b72e05, 0x1fef61255d723b, 0x1fef665c793eea, 0x1fef6b8a182112,
	0x1fef70ae477edc, 0x1fef75c914980a, 0x1fef7ada8c8659, 0x1fef7fe2bc3dea,
	0x1fef84e1b08da7, 0x1fef89d7761fa5, 0x1fef8ec4197987, 0x1fef93a7a6fce0,
	0x1fef98822ae78b, 0x1fef9d53b15411, 0x1fefa21c4639ff, 0x1fefa6dbf56e44,
	0x1fefab92caa386, 0x1fefb040d16a7e, 0x1fefb4e615324e, 0x1fefb982a148d3,
	0x1fefbe1680dafc, 0x1fefc2a1bef519, 0x1fefc724668333, 0x1fefcb9e825154,
	0x1fefd0101d0bda, 0x1fefd479413fc5, 0x1fefd8d9f95b02, 0x1fefdd324facb7,
	0x1fefe1824e658c, 0x1fefe5c9ff97f7, 0x1fefea096d387f, 0x1fefee40a11e06,
	0x1feff26fa5020e, 0x1feff6968280ff, 0x1feffab5431a67, 0x1feffecbf0313f,
	0x1ff002da930c2c, 0x1ff006e134d5bf, 0x1ff00adfde9cb5, 0x1ff00ed6995434,
	0x1ff012c56dd40c, 0x1ff016ac64d8ed, 0x1ff01a8b8704a9, 0x1ff01e62dcde6b,
	0x1ff022326ed2f3, 0x1ff025fa4534ca, 0x1ff029ba683c81, 0x1ff02d72e008e1,
	0x1ff03123b49f26, 0x1ff034ccedeb31, 0x1ff0386e93bfbf, 0x1ff03c08add698,
	0x1ff03f9b43d0c9, 0x1ff043265d36ce, 0x1ff046aa0178c7, 0x1ff04a2637eeaa,
	0x1ff04d9b07d86c, 0x1ff05108785e39, 0x1ff0546e909096, 0x1ff057cd57689b,
	0x1ff05b24d3c814, 0x1ff05e750c79b4, 0x1ff061be08313c, 0x1ff064ffcd8ba6,
	0x1ff0683a630f4f, 0x1ff06b6dcf2c20, 0x1ff06e9a183bb5, 0x1ff071bf448182,
	0x1ff074dd5a2aff, 0x1ff077f45f4fc9, 0x1ff07b0459f1c8, 0x1ff07e0d4ffd57,
	0x1ff0810f474962, 0x1ff0840a45978e, 0x1ff086fe50945b, 0x1ff089eb6dd741,
	0x1ff08cd1a2e2d8, 0x1ff08fb0f524f4, 0x1ff0928969f6c7, 0x1ff0955b069cff,
	0x1ff09825d047e6, 0x1ff09ae9cc137f, 0x1ff09da6ff07a4, 0x1ff0a05d6e1824,
	0x1ff0a30d1e24dc, 0x1ff0a5b613f9d6, 0x1ff0a858544f64, 0x1ff0aaf3e3ca39,
	0x1ff0ad88c6fb83, 0x1ff0b017026104, 0x1ff0b29e9a652f, 0x1ff0b51f935f39,
	0x1ff0b799f19338, 0x1ff0ba0db93235, 0x1ff0bc7aee5a46, 0x1ff0bee19516a2,
	0x1ff0c141b15fb5, 0x1ff0c39b471b3b, 0x1ff0c5ee5a1c4e, 0x1ff0c83aee237d,
	0x1ff0ca8106dee0, 0x1ff0ccc0a7ea27, 0x1ff0cef9d4ceb1, 0x1ff0d12c91039d,
	0x1ff0d358dfedd9, 0x1ff0d57ec4e032, 0x1ff0d79e431b6b, 0x1ff0d9b75dce43,
	0x1ff0dbca18158d, 0x1ff0ddd674fc39, 0x1ff0dfdc777b66, 0x1ff0e1dc227a6c,
	0x1ff0e3d578ceef, 0x1ff0e5c87d3ce5, 0x1ff0e7b53276a5, 0x1ff0e99b9b1cf7,
	0x1ff0eb7bb9bf19, 0x1ff0ed5590dacb, 0x1ff0ef2922dc5d, 0x1ff0f0f6721eb8,
	0x1ff0f2bd80eb61, 0x1ff0f47e517a8b, 0x1ff0f638e5f319, 0x1ff0f7ed406aa9,
	0x1ff0f99b62e59b, 0x1ff0fb434f5716, 0x1ff0fce507a110, 0x1ff0fe808d9456,
	0x1ff10015e2f08b, 0x1ff101a5096437, 0x1ff1032e028cc1, 0x1ff104b0cff67a,
	0x1ff1062d731ca0, 0x1ff107a3ed695d, 0x1ff109144035cf, 0x1ff10a7e6cca04,
	0x1ff10be2745d03, 0x1ff10d405814c6, 0x1ff10e98190641, 0x1ff10fe9b8355e,
	0x1ff111353694fd, 0x1ff1127a9506f5, 0x1ff113b9d45c14, 0x1ff114f2f55418,
	0x1ff11625f89db3, 0x1ff11752ded684, 0x1ff11879a88b16, 0x1ff1199a5636db,
	0x1ff11ab4e8442a, 0x1ff11bc95f0c38, 0x1ff11cd7bad713, 0x1ff11ddffbdb9f,
	0x1ff11ee2223f8b, 0x1ff11fde2e1752, 0x1ff120d41f662a, 0x1ff121c3f61e06,
	0x1ff122adb21f86, 0x1ff123915339f5, 0x1ff1246ed92b39, 0x1ff12546439fd0,
	0x1ff126179232c1, 0x1ff126e2c46d93, 0x1ff127a7d9c842, 0x1ff12866d1a933,
	0x1ff1291fab6527, 0x1ff129d2663f2f, 0x1ff12a7f01689d, 0x1ff12b257c00f9,
	0x1ff12bc5d515f1, 0x1ff12c600ba346, 0x1ff12cf41e92c4, 0x1ff12d820cbc2d,
	0x1ff12e09d4e527, 0x1ff12e8b75c130, 0x1ff12f06edf185, 0x1ff12f7c3c0518,
	0x1ff12feb5e7874, 0x1ff1305453b5b0, 0x1ff130b71a1459, 0x1ff13113afd95b,
	0x1ff1316a1336ed, 0x1ff131ba424c7c, 0x1ff132043b2694, 0x1ff13247fbbec6,
	0x1ff1328581fb93, 0x1ff132bccbb054, 0x1ff132edd69d1d, 0x1ff13318a06ea6,
	0x1ff1333d26be31, 0x1ff1335b67116b, 0x1ff133735eda56, 0x1ff133850b7726,
	0x1ff133906a3229, 0x1ff133957841a6, 0x1ff1339432c7c0, 0x1ff1338c96d255,
	0x1ff1337ea15adf, 0x1ff1336a4f4653, 0x1ff1334f9d64ff, 0x1ff1332e887269,
	0x1ff133070d152b, 0x1ff132d927decd, 0x1ff132a4d54ba5, 0x1ff1326a11c2ae,
	0x1ff13228d99562, 0x1ff131e128ff97, 0x1ff13192fc2751, 0x1ff1313e4f1c9c,
	0x1ff130e31dd966, 0x1ff1308164414f, 0x1ff130191e2180, 0x1ff12faa473082,
	0x1ff12f34db0e0a, 0x1ff12eb8d542d2, 0x1ff12e36314068, 0x1ff12dacea60fc,
	0x1ff12d1cfbe731, 0x1ff12c8660fded, 0x1ff12be914b824, 0x1ff12b451210a4,
	0x1ff12a9a53e9e3, 0x1ff129e8d50dc7, 0x1ff12930902d73, 0x1ff128717fe108,
	0x1ff127ab9ea776, 0x1ff126dee6e63a, 0x1ff1260b52e926, 0x1ff12530dce227,
	0x1ff1244f7ee906, 0x1ff1236732fb28, 0x1ff12277f2fb51, 0x1ff12181b8b164,
	0x1ff120847dca1f, 0x1ff11f803bd6d8, 0x1ff11e74ec4d3a, 0x1ff11d628886ff,
	0x1ff11c4909c1a8, 0x1ff11b28691e38, 0x1ff11a009fa0e6, 0x1ff118d1a630d6,
	0x1ff1179b7597ca, 0x1ff1165e0681d7, 0x1ff11519517d14, 0x1ff113cd4ef94a,
	0x1ff11279f747a3, 0x1ff1111f429a53, 0x1ff10fbd29044a, 0x1ff10e53a278d6,
	0x1ff10ce2a6cb50, 0x1ff10b6a2daec0, 0x1ff109ea2eb581, 0x1ff10862a150e7,
	0x1ff106d37cd0de, 0x1ff1053cb86389, 0x1ff1039e4b14e3, 0x1ff101f82bce57,
	0x1ff1004a51565d, 0x1ff0fe94b25013, 0x1ff0fcd7453ad1, 0x1ff0fb120071be,
	0x1ff0f944da2b66, 0x1ff0f76fc87945, 0x1ff0f592c1475c, 0x1ff0f3adba5bb6,
	0x1ff0f1c0a955fc, 0x1ff0efcb83aef3, 0x1ff0edce3eb80b, 0x1ff0ebc8cf9adc,
	0x1ff0e9bb2b58ad, 0x1ff0e7a546c9f0, 0x1ff0e587169dbe, 0x1ff0e3608f5956,
	0x1ff0e131a55790, 0x1ff0defa4cc858, 0x1ff0dcba79b01a, 0x1ff0da721fe739,
	0x1ff0d82133197a, 0x1ff0d5c7a6c56c, 0x1ff0d3656e3bd8, 0x1ff0d0fa7c9f1e,
	0x1ff0ce86c4e29c, 0x1ff0cc0a39ca0f, 0x1ff0c984cde8ea, 0x1ff0c6f673a1b7,
	0x1ff0c45f1d2566, 0x1ff0c1bebc72a5, 0x1ff0bf15435531, 0x1ff0bc62a3651e,
	0x1ff0b9a6ce0624, 0x1ff0b6e1b466e2, 0x1ff0b413478025, 0x1ff0b13b781421,
	0x1ff0ae5a36adb1, 0x1ff0ab6f739f8b, 0x1ff0a87b1f0373, 0x1ff0a57d28b970,
	0x1ff0a2758066ef, 0x1ff09f641575f3, 0x1ff09c48d71432, 0x1ff09923b43237,
	0x1ff095f49b827a, 0x1ff092bb7b787c, 0x1ff08f784247d0, 0x1ff08c2adde32f,
	0x1ff088d33bfb7e, 0x1ff0857149fed0, 0x1ff08204f51766, 0x1ff07e8e2a2aa6,
	0x1ff07b0cd5d812, 0x1ff07780e47835, 0x1ff073ea421b8e, 0x1ff07048da896e,
	0x1ff06c9c993ee0, 0x1ff068e5696d77, 0x1ff0652335fa27, 0x1ff06155e97c0f,
	0x1ff05d7d6e3b3d, 0x1ff05999ae2f72, 0x1ff055aa92fed7, 0x1ff051b005fcb1,
	0x1ff04da9f0280d, 0x1ff049983a2a63, 0x1ff0457acc5635, 0x1ff041518ea5a4,
	0x1ff03d1c68b8ff, 0x1ff038db41d549, 0x1ff0348e00e2ba, 0x1ff030348c6b33,
	0x1ff02bceca98b1, 0x1ff0275ca133ad, 0x1ff022ddf5a180, 0x1ff01e52ace2b3,
	0x1ff019baab914d, 0x1ff01515d5df14, 0x1ff010640f93c9, 0x1ff00ba53c0b50,
	0x1ff006d93e33de, 0x1ff001fff88c0b, 0x1feffd194d20e8, 0x1feff8251d8c04,
	0x1feff3234af162, 0x1fefee13b5fd6b, 0x1fefe8f63ee2d3, 0x1fefe3cac5586c,
	0x1fefde912896f6, 0x1fefd9494756d7, 0x1fefd3f2ffcdd5, 0x1fefce8e2facb1,
	0x1fefc91ab41cc8, 0x1fefc39869bd94, 0x1fefbe072ca228, 0x1fefb866d84e9f,
	0x1fefb2b747b579, 0x1fefacf85534e2, 0x1fefa729da93f9, 0x1fefa14bb0fff5,
	0x1fef9b5db10947, 0x1fef955fb2a0a3, 0x1fef8f518d13f9, 0x1fef8933170b5f,
	0x1fef83042685e3, 0x1fef7cc490d651, 0x1fef76742a9fda, 0x1fef7012c7d2b7,
	0x1fef69a03ba8a6, 0x1fef631c58a15f, 0x1fef5c86f07ee9, 0x1fef55dfd441e3,
	0x1fef4f26d425ab, 0x1fef485bbf9c74, 0x1fef417e654b41, 0x1fef3a8e9305c9,
	0x1fef338c15ca3d, 0x1fef2c76b9bcf3, 0x1fef254e4a2400, 0x1fef1e129162a5,
	0x1fef16c358f4ac, 0x1fef0f606969a0, 0x1fef07e98a5feb, 0x1fef005e827fd0,
	0x1feef8bf177645, 0x1feef10b0defaf, 0x1feee942299274, 0x1feee1642cf971,
	0x1feed970d9ae46, 0x1feed167f0237e, 0x1feec9492fae8f, 0x1feec1145681b2,
	0x1feeb8c921a58f, 0x1feeb0674cf2c6, 0x1feea7ee930b3e, 0x1fee9f5ead5355,
	0x1fee96b753ead6, 0x1fee8df83da5c4, 0x1fee85212004f2, 0x1fee7c31af2e64,
	0x1fee73299de581, 0x1fee6a089d8304, 0x1fee60ce5decc0, 0x1fee577a8d8d21,
	0x1fee4e0cd94a70, 0x1fee4484ec7dde, 0x1fee3ae270ea4b, 0x1fee31250eb2c6,
	0x1fee274c6c50d2, 0x1fee1d582e8a57, 0x1fee1347f86753, 0x1fee091b6b273b,
	0x1fedfed226360e, 0x1fedf46bc72111, 0x1fede9e7e98b3f, 0x1feddf4627215c,
	0x1fedd486178db0, 0x1fedc9a7506b60, 0x1fedbea965396e, 0x1fedb38be74d4d,
	0x1feda84e65c511, 0x1fed9cf06d7933, 0x1fed917188ede5, 0x1fed85d14043f3,
	0x1fed7a0f19292b, 0x1fed6e2a96c84e, 0x1fed622339b875, 0x1fed55f87fec02,
	0x1fed49a9e49ef6, 0x1fed3d36e044c3, 0x1fed309ee87582, 0x1fed23e16fda96,
	0x1fed16fde61aa9, 0x1fed09f3b7c502, 0x1fecfcc24e3c38, 0x1fecef690fa025,
	0x1fece1e75eb728, 0x1fecd43c9ad6a2, 0x1fecc6681fcaac, 0x1fecb86945bcf9,
	0x1fecaa3f611ae4, 0x1fec9be9c27a96, 0x1fec8d67b67f48, 0x1fec7eb885bc8a,
	0x1fec6fdb749894, 0x1fec60cfc32d86, 0x1fec5194ad299c, 0x1fec422969ae3c,
	0x1fec328d2b2de4, 0x1fec22bf1f48d6, 0x1fec12be6ea886, 0x1fec028a3cd9b4,
	0x1febf221a8252d, 0x1febe183c9670d, 0x1febd0afb3e495, 0x1febbfa4752065,
	0x1febae6114ad16, 0x1feb9ce493fe28, 0x1feb8b2dee3720, 0x1feb793c17f8d6,
	0x1feb670dff2cc5, 0x1feb54a28ace64, 0x1feb41f89ab255, 0x1feb2f0f074b67,
	0x1feb1be4a16d3d, 0x1feb0878320c91, 0x1feaf4c879fcef, 0x1feae0d431abbf,
	0x1feacc9a08d893, 0x1feab818a64a83, 0x1feaa34ea78281, 0x1fea8e3aa06a76,
	0x1fea78db1b010a, 0x1fea632e9701e4, 0x1fea4d33898a36, 0x1fea36e85cb96e,
	0x1fea204b6f4dd7, 0x1fea095b143cec, 0x1fe9f215924732, 0x1fe9da79238760,
	0x1fe9c283f4fc82, 0x1fe9aa34260ef2, 0x1fe99187c80fc6, 0x1fe9787cddb27f,
	0x1fe95f115a809d, 0x1fe945432246c2, 0x1fe92b10087b1e, 0x1fe91075cf9cab,
	0x1fe8f572288aef, 0x1fe8da02b1d5c3, 0x1fe8be24f704c2, 0x1fe8a1d66fd5d4,
	0x1fe885147f7262, 0x1fe867dc739aab, 0x1fe84a2b83c699, 0x1fe82bfed03b8b,
	0x1fe80d53611666, 0x1fe7ee2625493f, 0x1fe7ce73f18bd6, 0x1fe7ae397f3e29,
	0x1fe78d736b3c3c, 0x1fe76c1e34a225, 0x1fe74a363b7f7d, 0x1fe727b7bf790d,
	0x1fe7049ede57b6, 0x1fe6e0e792834b, 0x1fe6bc8db16825, 0x1fe6978ce9c603,
	0x1fe671e0c1e6c8, 0x1fe64b8495bb6e, 0x1fe6247394dd8a, 0x1fe5fca8c07372,
	0x1fe5d41ee8f51c, 0x1fe5aad0abcf7f, 0x1fe580b870e42c, 0x1fe555d067e2a0,
	0x1fe52a12857886, 0x1fe4fd7880561c, 0x1fe4cffbce0368, 0x1fe4a1959f82e4,
	0x1fe4723eddbde3, 0x1fe441f025b691, 0x1fe410a1c47b3a, 0x1fe3de4bb2d5ff,
	0x1fe3aae590b3cd, 0x1fe37666a03cda, 0x1fe340c5c09883, 0x1fe309f96855be,
	0x1fe2d1f79f70c1, 0x1fe298b5f8edc5, 0x1fe25e298c000b, 0x1fe22246ecb36a,
	0x1fe1e502240dd1, 0x1fe1a64ea79cf0, 0x1fe1661f506340, 0x1fe12466511634,
	0x1fe0e1152b9dfa, 0x1fe09c1ca5c586, 0x1fe0556cbd07ed, 0x1fe00cf49965e1,
	0x1fdfc2a27f2c03, 0x1fdf7663bf9023, 0x1fdf2824a8088b, 0x1fded7d0703d61,
	0x1fde855126705d, 0x1fde308f9a32f1, 0x1fddd973453e66, 0x1fdd7fe2323bfe,
	0x1fdd23c0e1452b, 0x1fdcc4f229dd06, 0x1fdc63571a1c4b, 0x1fdbfeced2c01b,
	0x1fdb97365fc177, 0x1fdb2c688d0f8b, 0x1fdabe3db6f92c, 0x1fda4c8b95c24b,
	0x1fd9d72503cfc4, 0x1fd95dd9bdbef4, 0x1fd8e0761ba5e9, 0x1fd85ec2c29c6d,
	0x1fd7d8844d8cda, 0x1fd74d7aec2468, 0x1fd6bd61f68cd8, 0x1fd627ef746325,
	0x1fd58cd3951ed5, 0x1fd4ebb817d1c2, 0x1fd4443f9fcda6, 0x1fd39604f3511c,
	0x1fd2e09a20dc3f, 0x1fd223878731c8, 0x1fd15e4abb4d94, 0x1fd0905546b5d4,
	0x1fcfb90b37769e, 0x1fced7c179c444, 0x1fcdebbbf19f89, 0x1fccf42b48d34f,
	0x1fcbf02a63233d, 0x1fcadebb6763a3, 0x1fc9bec4484712, 0x1fc88f0ab2ba29,
	0x1fc74e2f41599a, 0x1fc5faa7cc7e95, 0x1fc492b8a3f8da, 0x1fc3146c720d64,
	0x1fc17d8a75a29c, 0x1fbfcb8aaa2a0f, 0x1fbdfb8754ba16, 0x1fbc0a2b43eb4b,
	0x1fb9f39bd71f30, 0x1fb7b35d938f7c, 0x1fb54431a09a74, 0x1fb29fe9eb39c4,
	0x1fafbf30d51c86, 0x1fac9940155db5, 0x1fa923809add97, 0x1fa5510a7e2e33,
	0x1fa111f7d6ccf2, 0x1f9c5276a7d6ff, 0x1f96f97b763f40, 0x1f90e6e48f5fd7,
	0x1f89f0c02df865, 0x1f81df33180649, 0x1f78661cee4357, 0x1f6d1ade61b01f,
	0x1f5f632ea2dce6, 0x1f4e56c35fc3f7, 0x1f38862a92f170, 0x1f1b862fe29563,
	0x1ef2e7b5562b19, 0x1eb584cfe7bbe6, 0x1e4cc4bf01d278, 0x1d6bfb46d88c28,
}

var expoW = [1024]float64{
	1.13866300213877813e-15, 3.50242056868416685e-18, 5.70764952751972552e-18, 7.43157304507964198e-18,
	8.89301382714102794e-18, 1.01849930256090362e-17, 1.13566120763560199e-17, 1.24373330462895014e-17,
	1.34464053055239106e-17, 1.43971940744360142e-17, 1.52994122305171874e-17, 1.61603734793054288e-17,
	1.69857437005156817e-17, 1.77800154948490313e-17, 1.85468208790794572e-17, 1.92891447096363812e-17,
	2.00094747399575766e-17, 2.07099098388363480e-17, 2.13922397691885634e-17, 2.20580051413288253e-17,
	2.27085432365339685e-17, 2.33450235613893963e-17, 2.39684758075173161e-17, 2.45798121063206663e-17,
	2.51798449374771436e-17, 2.57693016838210481e-17, 2.63488365683286212e-17, 2.69190405257174441e-17,
	2.74804494286134748e-17, 2.80335509910373130e-17, 2.85787905998030641e-17, 2.91165762702436677e-17,
	2.96472828815662770e-17, 3.01712558156409405e-17, 3.06888140986687519e-17, 3.12002531261801955e-17,
	3.17058470368832284e-17, 3.22058507890550994e-17, 3.27005019837409651e-17, 3.31900224714507652e-17,
	3.36746197729291870e-17, 3.41544883396033694e-17, 3.46298106752513256e-17, 3.51007583370977331e-17,
	3.55674928317893002e-17, 3.60301664194168814e-17, 3.64889228368475191e-17, 3.69438979500361947e-17,
	3.73952203436478575e-17, 3.78430118551906078e-17, 3.82873880599043852e-17, 3.87284587118362003e-17,
	3.91663281458397442e-17, 3.96010956446438125e-17, 4.00328557746248912e-17, 4.04616986934806411e-17,
	4.08877104326225461e-17, 4.13109731567783096e-17, 4.17315654030096701e-17, 4.21495623011038930e-17,
	4.25650357770807539e-17, 4.29780547413678012e-17, 4.33886852630308135e-17, 4.37969907313005329e-17,
	4.42030320055085859e-17, 4.46068675544319532e-17, 4.50085535859453662e-17, 4.54081441677920346e-17,
	4.58056913402044554e-17, 4.62012452210367440e-17, 4.65948541040075780e-17, 4.69865645505969950e-17,
	4.73764214760904961e-17, 4.77644682302191072e-17, 4.81507466728040892e-17, 4.85352972447789544e-17,
	4.89181590349291082e-17, 4.92993698426600875e-17, 4.96789662370792738e-17, 5.00569836126519279e-17,
	5.04334562416710039e-17, 5.08084173237606483e-17, 5.11818990326155613e-17, 5.15539325601623859e-17,
	5.19245481583145717e-17, 5.22937751784789536e-17, 5.26616421089601042e-17, 5.30281766103974008e-17,
	5.33934055493597026e-17, 5.37573550302132608e-17, 5.41200504253700168e-17, 5.44815164040155802e-17,
	5.48417769594092893e-17, 5.52008554348419563e-17, 5.55587745483310531e-17, 5.59155564161275402e-17,
	5.62712225751033443e-17, 5.66257940040840001e-17, 5.69792911441864214e-17, 5.73317339182178903e-17,
	5.76831417491886752e-17, 5.80335335779871866e-17, 5.83829278802635728e-17, 5.87313426825644027e-17,
	5.90787955777588901e-17, 5.94253037397940196e-17, 5.97708839378140594e-17, 6.01155525496774833e-17,
	6.04593255749024622e-17, 6.08022186470701729e-17, 6.11442470457132772e-17, 6.14854257077155906e-17,
	6.18257692382471985e-17, 6.21652919212578466e-17, 6.25040077295503742e-17, 6.28419303344544295e-17,
	6.31790731151195959e-17, 6.35154491674463330e-17, 6.38510713126714457e-17, 6.41859521056246471e-17,
	6.45201038426711684e-17, 6.48535385693550682e-17, 6.51862680877568281e-17, 6.55183039635782105e-17,
	6.58496575329665713e-17, 6.61803399090902991e-17, 6.65103619884764002e-17, 6.68397344571204976e-17,
	6.71684677963794495e-17, 6.74965722886556345e-17, 6.78240580228820122e-17, 6.81509348998165384e-17,
	6.84772126371536022e-17, 6.88029007744605938e-17, 6.91280086779465688e-17, 6.94525455450699849e-17,
	6.97765204089922405e-17, 7.00999421428830436e-17, 7.04228194640838963e-17, 7.07451609381350078e-17,
	7.10669749826714292e-17, 7.13882698711932909e-17, 7.17090537367152949e-17, 7.20293345752999490e-17,
	7.23491202494792634e-17, 7.26684184915689645e-17, 7.29872369068795414e-17, 7.33055829768278701e-17,
	7.36234640619532022e-17, 7.39408874048411141e-17, 7.42578601329588457e-17, 7.45743892614052207e-17,
	7.48904816955783273e-17, 7.52061442337639926e-17, 7.55213835696477749e-17, 7.58362062947534310e-17,
	7.61506189008102266e-17, 7.64646277820518860e-17, 7.67782392374492908e-17, 7.70914594728795881e-17,
	7.74042946032335713e-17, 7.77167506544637473e-17, 7.80288335655749535e-17, 7.83405491905595321e-17,
	7.86519033002790468e-17, 7.89629015842941934e-17, 7.92735496526446554e-17, 7.95838530375807270e-17,
	7.98938171952481110e-17, 8.02034475073275782e-17, 8.05127492826308455e-17, 8.08217277586542374e-17,
	8.11303881030913265e-17, 8.14387354153060087e-17, 8.17467747277673049e-17, 8.20545110074468898e-17,
	8.23619491571807650e-17, 8.26690940169961470e-17, 8.29759503654045216e-17, 8.32825229206620955e-17,
	8.35888163419985706e-17, 8.38948352308151647e-17, 8.42005841318529637e-17, 8.45060675343323331e-17,
	8.48112898730644100e-17, 8.51162555295354792e-17, 8.54209688329649217e-17, 8.57254340613377475e-17,
	8.60296554424122665e-17, 8.63336371547037247e-17, 8.66373833284446306e-17, 8.69408980465223419e-17,
	8.72441853453947103e-17, 8.75472492159843547e-17, 8.78500936045520899e-17, 8.81527224135503018e-17,
	8.84551395024566624e-17, 8.87573486885888013e-17, 8.90593537479005498e-17, 8.93611584157600782e-17,
	8.96627663877107150e-17, 8.99641813202145720e-17, 9.02654068313798122e-17, 9.05664465016717829e-17,
	9.08673038746084713e-17, 9.11679824574408223e-17, 9.14684857218181801e-17, 9.17688171044394437e-17,
	9.20689800076901207e-17, 9.23689778002657626e-17, 9.26688138177820984e-17, 9.29684913633723879e-17,
	9.32680137082719675e-17, 9.35673840923907163e-17, 9.38666057248735546e-17, 9.41656817846492320e-17,
	9.44646154209679607e-17, 9.47634097539278079e-17, 9.50620678749905365e-17, 9.53605928474868584e-17,
	9.56589877071115063e-17, 9.59572554624083708e-17, 9.62553990952459616e-17, 9.65534215612833288e-17,
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}