normal.go

package crazy

import "math"

// Normal adapts a Source to produce random numbers under a normal
// distribution.
type Normal struct {
	Source
	Mean, StdDev float64
}

// NewNormal creates a normal distribution drawing from the specified source
// with given mean and standard deviation.
func NewNormal(src Source, mean, stddev float64) Normal {
	return Normal{
		Source: src,
		Mean:   mean,
		StdDev: stddev,
	}
}

// Next generates a normal variate.
func (n Normal) Next() float64 {
	x := normalZig.GenNext(n.Source)
	return n.Mean + x*n.StdDev
}

func normalPDF(x float64) float64 {
	return math.Exp(-0.5 * x * x)
}

func normalTail(src Source) float64 {
	dist := Uniform0_1{src}
	for {
		x := -math.Log(dist.Next()) / normalR
		y := -math.Log(dist.Next())
		if y+y >= x*x {
			return x + normalR
		}
	}
}

var normalZig = Ziggurat{
	PDF:      normalPDF,
	Tail:     normalTail,
	Mirrored: true,
	K:        normalK,
	W:        normalW,
	F:        normalF,
}

const normalR = 4.0388498461095

var normalK = [1024]uint64{
	0x1e3e4a8bb4f969, 0x00000000000000, 0x181f29db804409, 0x1b5405b352f86e,
	0x1cb0a36a1f2595, 0x1d70cf1f08543f, 0x1dea3fdec95c06, 0x1e3dd13ea3711f,
	0x1e7ac893a08e18, 0x1ea9327c8026c9, 0x1ecdb2d523da52, 0x1eeb25f2755db1,
	0x1f03679c0bc516, 0x1f17ba339b0015, 0x1f28ffd70bf283, 0x1f37dbc4c52f7b,
	0x1f44c6c3ccd493, 0x1f501c1707a95a, 0x1f5a21fa11984b, 0x1f630f59b3e4a2,
	0x1f6b0fc75879ee, 0x1f724642d86756, 0x1f78cf3bfdf0b2, 0x1f7ec20a54817f,
	0x1f8432047bca75, 0x1f892f52b0ec52, 0x1f8dc78f86f1af, 0x1f92064407767c,
	0x1f95f548979015, 0x1f999d11599f25, 0x1f9d04eaf01bed, 0x1fa0332b3b9e8d,
	0x1fa32d58c32bba, 0x1fa5f84acbf75e, 0x1fa89843a9c534, 0x1fab11067580f1,
	0x1fad65e91365d5, 0x1faf99e33eb118, 0x1fb1af9b29dd9e, 0x1fb3a9702490cd,
	0x1fb58983a15ca6, 0x1fb751c0e399e9, 0x1fb903e38fa03a, 0x1fbaa17d4c9e56,
	0x1fbc2bfa9e9a72, 0x1fbda4a7182e32, 0x1fbf0cb0fdfea0, 0x1fc0652c7172ad,
	0x1fc1af163487b8, 0x1fc2eb5615adbe, 0x1fc41ac110297d, 0x1fc53e1b2b7e2b,
	0x1fc6561922bce0, 0x1fc76361db3ca1, 0x1fc8668fb11d50, 0x1fc960319f06f6,
	0x1fca50cc45cd32, 0x1fcb38dad7f552, 0x1fcc18cfec8ea5, 0x1fccf1163c5415,
	0x1fcdc2114ba767, 0x1fce8c1e039f9e, 0x1fcf4f933c1983, 0x1fd00cc23879c0,
	0x1fd0c3f7189988, 0x1fd175793f27b8, 0x1fd2218baea00d, 0x1fd2c86d5dd6f8,
	0x1fd36a5984fa74, 0x1fd40787e3cdd6, 0x1fd4a02d01cfc7, 0x1fd5347a68e59f,
	0x1fd5c49edb15ee, 0x1fd650c683ccb7, 0x1fd6d91b25168d, 0x1fd75dc44133ec,
	0x1fd7dee740dbea, 0x1fd85ca7967c19, 0x1fd8d726debb7d, 0x1fd94e84fe7f49,
	0x1fd9c2e03ea9be, 0x1fda345565c5f2, 0x1fdaa2ffcfce40, 0x1fdb0ef98436ae,
	0x1fdb785b4a60a6, 0x1fdbdf3cbc99c1, 0x1fdc43b459c453, 0x1fdca5d795c56f,
	0x1fdd05bae8d1aa, 0x1fdd6371ddaf92, 0x1fddbf0f1f04b2, 0x1fde18a483c02e,
	0x1fde70431ab464, 0x1fdec5fb356f5b, 0x1fdf19dc72608f, 0x1fdf6bf5c65954,
	0x1fdfbc55857404, 0x1fe00b096b6d11, 0x1fe0581ea37840, 0x1fe0a3a1cf9b69,
	0x1fe0ed9f0f9767, 0x1fe13622076726, 0x1fe17d35e55c22, 0x1fe1c2e567df1b,
	0x1fe2073ae2db30, 0x1fe24a4044d923, 0x1fe28bff1bd019, 0x1fe2cc8099b0bf,
	0x1fe30bcd98af57, 0x1fe349ee9f50e8, 0x1fe386ebe43f80, 0x1fe3c2cd51e913,
	0x1fe3fd9a89ec66, 0x1fe4375ae8570f, 0x1fe4701586b78b, 0x1fe4a7d13f05ff,
	0x1fe4de94ae663a, 0x1fe5146637c547, 0x1fe5494c0654b9, 0x1fe57d4c0fe5bf,
	0x1fe5b06c1725db, 0x1fe5e2b1adbf0c, 0x1fe61422365d09, 0x1fe644c2e69917,
	0x1fe67498c8cdf2, 0x1fe6a3a8bdd51a, 0x1fe6d1f77eaed3, 0x1fe6ff899e15f3,
	0x1fe72c638a00b6, 0x1fe758898d0f81, 0x1fe783ffcfeaab, 0x1fe7aeca5a9027,
	0x1fe7d8ed1591e8, 0x1fe8026bcb45dc, 0x1fe82b4a28e834, 0x1fe8538bbfb0ae,
	0x1fe87b3405db9e, 0x1fe8a24657a740, 0x1fe8c8c5f845fe, 0x1fe8eeb612c634,
	0x1fe91419baeff1, 0x1fe938f3ee1944, 0x1fe95d4793f180, 0x1fe981177f43ef,
	0x1fe9a4666eb25c, 0x1fe9c7370d67e2, 0x1fe9e98bf3c44b, 0x1fea0b67a8007a,
	0x1fea2ccc9ecc0f, 0x1fea4dbd3be4bd, 0x1fea6e3bd2a777, 0x1fea8e4aa69be8,
	0x1feaadebebfa4b, 0x1feacd21c82c13, 0x1feaebee524779, 0x1feb0a53938647,
	0x1feb285387b805, 0x1feb45f01dafcc, 0x1feb632b37adde, 0x1feb8006abc545,
	0x1feb9c84443da0, 0x1febb8a5bff13c, 0x1febd46cd2a7bb, 0x1febefdb256d57,
	0x1fec0af256e6f4, 0x1fec25b3fba31f, 0x1fec40219e681f, 0x1fec5a3cc07f32,
	0x1fec7406d9fd18, 0x1fec8d815a080a, 0x1feca6ada71b32, 0x1fecbf8d1f47ca,
	0x1fecd8211873e9, 0x1fecf06ae0972a, 0x1fed086bbdf533, 0x1fed2024ef563b,
	0x1fed3797ac3da1, 0x1fed4ec5251ea8, 0x1fed65ae838f64, 0x1fed7c54ea79fc,
	0x1fed92b9764c3b, 0x1feda8dd3d2593, 0x1fedbec14f0397, 0x1fedd466b5ecfd,
	0x1fede9ce761b3e, 0x1fedfef98e22d4, 0x1fee13e8f71a2b, 0x1fee289da4bf5a,
	0x1fee3d18859c9b, 0x1fee515a832ba1, 0x1fee656481f7cc, 0x1fee793761bf49,
	0x1fee8cd3fd932e, 0x1feea03b2bf68b, 0x1feeb36dbefc8f, 0x1feec66c8465b5,
	0x1feed93845bc16, 0x1feeebd1c86ed3, 0x1feefe39cdecb0, 0x1fef107113bde3,
	0x1fef2278539d12, 0x1fef3450438fa0, 0x1fef45f995fd32, 0x1fef5774f9c68b,
	0x1fef68c31a5bbb, 0x1fef79e49fd1a0, 0x1fef8ada2ef6ce, 0x1fef9ba46967da,
	0x1fefac43eda30a, 0x1fefbcb9571b77, 0x1fefcd053e4ba5, 0x1fefdd2838c792,
	0x1fefed22d94e3b, 0x1feffcf5afdaaf, 0x1ff00ca149b499, 0x1ff01c26318063,
	0x1ff02b84ef4ed5, 0x1ff03abe08ac52, 0x1ff049d200afa8, 0x1ff058c158086d,
	0x1ff0678c8d0d07, 0x1ff076341bc844, 0x1ff084b87e06a0, 0x1ff0931a2b6325,
	0x1ff0a1599953fa, 0x1ff0af773b3694, 0x1ff0bd73825ba2, 0x1ff0cb4ede1296,
	0x1ff0d909bbb4ed, 0x1ff0e6a486b127, 0x1ff0f41fa89576, 0x1ff1017b891a25,
	0x1ff10eb88e2bbb, 0x1ff11bd71bf4d9, 0x1ff128d794e7dd, 0x1ff135ba59c83a,
	0x1ff1427fc9b3a2, 0x1ff14f28422ae8, 0x1ff15bb41f1aaf, 0x1ff16823bae3e0,
	0x1ff174776e63ea, 0x1ff180af90fcc9, 0x1ff18ccc789ce2, 0x1ff198ce79c6a4,
	0x1ff1a4b5e79801, 0x1ff1b08313d1b4, 0x1ff1bc364ede58, 0x1ff1c7cfe7d957,
	0x1ff1d3502c95a9, 0x1ff1deb769a471, 0x1ff1ea05ea5b66, 0x1ff1f53bf8db20,
	0x1ff20059de1536, 0x1ff20b5fe1d23d, 0x1ff2164e4ab79f, 0x1ff221255e4d4c,
	0x1ff22be5610354, 0x1ff2368e963750, 0x1ff241214039b9, 0x1ff24b9da05312,
	0x1ff25603f6c902, 0x1ff2605482e340, 0x1ff26a8f82f072, 0x1ff274b5344ae2,
	0x1ff27ec5d35d1e, 0x1ff288c19ba681, 0x1ff292a8c7bf95, 0x1ff29c7b915e6d,
	0x1ff2a63a315ad3, 0x1ff2afe4dfb272, 0x1ff2b97bd38cd6, 0x1ff2c2ff433f61,
	0x1ff2cc6f645127, 0x1ff2d5cc6b7eaf, 0x1ff2df168cbda7, 0x1ff2e84dfb4081,
	0x1ff2f172e979f2, 0x1ff2fa85892070, 0x1ff303860b318c, 0x1ff30c749ff540,
	0x1ff3155177012e, 0x1ff31e1cbf3bc8, 0x1ff326d6a6df6a, 0x1ff32f7f5b7d5e,
	0x1ff338170a00d8, 0x1ff3409ddeb1de, 0x1ff34914053818, 0x1ff35179a89da4,
	0x1ff359cef351c4, 0x1ff362140f2b93, 0x1ff36a49256c9a, 0x1ff3726e5ec365,
	0x1ff37a83e34e01, 0x1ff38289da9c72, 0x1ff38a806bb31a, 0x1ff39267bd0d12,
	0x1ff39a3ff49e7f, 0x1ff3a20937d6cb, 0x1ff3a9c3aba2e6, 0x1ff3b16f746f6b,
	0x1ff3b90cb62ac2, 0x1ff3c09b944738, 0x1ff3c81c31bd05, 0x1ff3cf8eb10c53,
	0x1ff3d6f3343f2f, 0x1ff3de49dceb77, 0x1ff3e592cc34be, 0x1ff3ecce22ce25,
	0x1ff3f3fc00fc28, 0x1ff3fb1c86966c, 0x1ff4022fd30974, 0x1ff4093605585e,
	0x1ff4102f3c1e8b, 0x1ff4171b959149, 0x1ff41dfb2f816b, 0x1ff424ce275cdf,
	0x1ff42b949a303c, 0x1ff4324ea4a849, 0x1ff438fc631377, 0x1ff43f9df1635b,
	0x1ff446336b2e1e, 0x1ff44cbcebafe4, 0x1ff4533a8dcc30, 0x1ff459ac6c0f40,
	0x1ff46012a0af5f, 0x1ff4666d458e38, 0x1ff46cbc743a19, 0x1ff4730045ef3d,
	0x1ff47938d39902, 0x1ff47f6635d322, 0x1ff4858884eae8, 0x1ff48b9fd8e052,
	0x1ff491ac496743, 0x1ff497adede899, 0x1ff49da4dd8351, 0x1ff4a3912f0d95,
	0x1ff4a972f915d8, 0x1ff4af4a51e3d7, 0x1ff4b5174f79aa, 0x1ff4bada0794c1,
	0x1ff4c0928faee5, 0x1ff4c640fcff32, 0x1ff4cbe5647b0d, 0x1ff4d17fdad710,
	0x1ff4d710748800, 0x1ff4dc9745c3ac, 0x1ff4e2146281d9, 0x1ff4e787de7d20,
	0x1ff4ecf1cd33c9, 0x1ff4f25241e8a6, 0x1ff4f7a94fa3e8, 0x1ff4fcf70933f1,
	0x1ff5023b812e1f, 0x1ff50776c9ef9a, 0x1ff50ca8f59e19, 0x1ff511d21628a4,
	0x1ff516f23d4859, 0x1ff51c097c8121, 0x1ff52117e52273, 0x1ff5261d884803,
	0x1ff52b1a76da79, 0x1ff5300ec19020, 0x1ff534fa78ed95, 0x1ff539ddad466f,
	0x1ff53eb86ebdeb, 0x1ff5438acd478c, 0x1ff54854d8a7bf, 0x1ff54d16a0747b,
	0x1ff551d03415df, 0x1ff55681a2c6ca, 0x1ff55b2afb9571, 0x1ff55fcc4d63fb,
	0x1ff56465a6e90c, 0x1ff568f716b059, 0x1ff56d80ab1b36, 0x1ff57202726122,
	0x1ff5767c7a904e, 0x1ff57aeed18e28, 0x1ff57f598517db, 0x1ff583bca2c2d6,
	0x1ff5881837fd4b, 0x1ff58c6c520eae, 0x1ff590b8fe1830, 0x1ff594fe49153e,
	0x1ff5993c3fdbf3, 0x1ff59d72ef1d94, 0x1ff5a1a2636704, 0x1ff5a5caa92134,
	0x1ff5a9ebcc9197, 0x1ff5ae05d9da92, 0x1ff5b218dcfbe5, 0x1ff5b624e1d31c,
	0x1ff5ba29f41bf8, 0x1ff5be281f70d3, 0x1ff5c21f6f4b0c, 0x1ff5c60fef036d,
	0x1ff5c9f9a9d288, 0x1ff5cddcaad120, 0x1ff5d1b8fcf885, 0x1ff5d58eab22f6,
	0x1ff5d95dc00bfc, 0x1ff5dd264650ca, 0x1ff5e0e8487091, 0x1ff5e4a3d0cce1,
	0x1ff5e858e9a9fc, 0x1ff5ec079d2f2d, 0x1ff5efaff5671e, 0x1ff5f351fc402d,
	0x1ff5f6edbb8cbd, 0x1ff5fa833d0387, 0x1ff5fe128a3fec, 0x1ff6019bacc241,
	0x1ff6051eadf020, 0x1ff6089b9714b1, 0x1ff60c127160fa, 0x1ff60f8345ec23,
	0x1ff612ee1db3c4, 0x1ff61653019c2a, 0x1ff619b1fa70a1, 0x1ff61d0b10e3b4,
	0x1ff6205e4d8f79, 0x1ff623abb8f5ce, 0x1ff626f35b80a2, 0x1ff62a353d822f,
	0x1ff62d71673541, 0x1ff630a7e0bd75, 0x1ff633d8b22772, 0x1ff63703e3692d,
	0x1ff63a297c6224, 0x1ff63d4984db99, 0x1ff640640488cc, 0x1ff64379030737,
	0x1ff6468887dec8, 0x1ff649929a8217, 0x1ff64c97424e9d, 0x1ff64f96868cee,
	0x1ff652906e70ec, 0x1ff655850119fd, 0x1ff6587445933f, 0x1ff65b5e42d3bc,
	0x1ff65e42ffbe9a, 0x1ff66122832352, 0x1ff663fcd3bddc, 0x1ff666d1f836e2,
	0x1ff669a1f723f1, 0x1ff66c6cd707a3, 0x1ff66f329e51d2, 0x1ff671f3535fc4,
	0x1ff674aefc7c57, 0x1ff677659fe02e, 0x1ff67a1743b1dd, 0x1ff67cc3ee0611,
	0x1ff67f6ba4dfbe, 0x1ff6820e6e3048, 0x1ff684ac4fd7a7, 0x1ff687454fa496,
	0x1ff689d97354b6, 0x1ff68c68c094b8, 0x1ff68ef33d0080, 0x1ff69178ee234f,
	0x1ff693f9d977e4, 0x1ff696760468a4, 0x1ff698ed744fbd, 0x1ff69b602e774a,
	0x1ff69dce381973, 0x1ff6a037966094, 0x1ff6a29c4e675d, 0x1ff6a4fc6538f2,
	0x1ff6a757dfd10d, 0x1ff6a9aec31c20, 0x1ff6ac0113f771, 0x1ff6ae4ed7313c,
	0x1ff6b0981188d2, 0x1ff6b2dcc7aeb7, 0x1ff6b51cfe44be, 0x1ff6b758b9de28,
	0x1ff6b98ffeffc2, 0x1ff6bbc2d21fff, 0x1ff6bdf137a714, 0x1ff6c01b33ef17,
	0x1ff6c240cb4414, 0x1ff6c46201e42f, 0x1ff6c67edbffb6, 0x1ff6c8975db942,
	0x1ff6caab8b25cc, 0x1ff6ccbb684cc6, 0x1ff6cec6f92835, 0x1ff6d0ce41a4c9,
	0x1ff6d2d145a1f3, 0x1ff6d4d008f1fd, 0x1ff6d6ca8f5a20, 0x1ff6d8c0dc929d,
	0x1ff6dab2f446cf, 0x1ff6dca0da1544, 0x1ff6de8a918fcf, 0x1ff6e0701e3ba1,
	0x1ff6e251839158, 0x1ff6e42ec4fd17, 0x1ff6e607e5de9a, 0x1ff6e7dce98945,
	0x1ff6e9add3443d, 0x1ff6eb7aa64a73, 0x1ff6ed4365cabe, 0x1ff6ef0814e7e7,
	0x1ff6f0c8b6b8bd, 0x1ff6f2854e4827, 0x1ff6f43dde9531, 0x1ff6f5f26a9321,
	0x1ff6f7a2f52985, 0x1ff6f94f813440, 0x1ff6faf811839f, 0x1ff6fc9ca8dc62,
	0x1ff6fe3d49f7d2, 0x1ff6ffd9f783c7, 0x1ff70172b422bb, 0x1ff70307826bda,
	0x1ff7049864eb08, 0x1ff706255e20f5, 0x1ff707ae708327, 0x1ff709339e7c06,
	0x1ff70ab4ea6ae7, 0x1ff70c3256a41e, 0x1ff70dabe57101, 0x1ff70f21990ff8,
	0x1ff7109373b489, 0x1ff7120177875e, 0x1ff7136ba6a655, 0x1ff714d2032484,
	0x1ff716348f0a47, 0x1ff717934c5549, 0x1ff718ee3cf889, 0x1ff71a4562dc69,
	0x1ff71b98bfdeb2, 0x1ff71ce855d29d, 0x1ff71e342680dc, 0x1ff71f7c33a7a0,
	0x1ff720c07efaa4, 0x1ff722010a232d, 0x1ff7233dd6c019, 0x1ff72476e665de,
	0x1ff725ac3a9e96, 0x1ff726ddd4ea03, 0x1ff7280bb6bd90, 0x1ff72935e1845e,
	0x1ff72a5c569f44, 0x1ff72b7f1764d5, 0x1ff72c9e252165, 0x1ff72db981170a,
	0x1ff72ed12c7da6, 0x1ff72fe52882e4, 0x1ff730f5764a3f, 0x1ff7320216ed05,
	0x1ff7330b0b7a59, 0x1ff7341054f733, 0x1ff73511f45e68, 0x1ff7360feaa0a5,
	0x1ff7370a38a475, 0x1ff73800df4643, 0x1ff738f3df5857, 0x1ff739e339a2d9,
	0x1ff73aceeee3d2, 0x1ff73bb6ffcf2d, 0x1ff73c9b6d0eb2, 0x1ff73d7c37420b,
	0x1ff73e595efec1, 0x1ff73f32e4d03b, 0x1ff74008c937bd, 0x1ff740db0cac66,
	0x1ff741a9af9b2e, 0x1ff74274b266e5, 0x1ff7433c15682f, 0x1ff743ffd8ed83,
	0x1ff744bffd3b27, 0x1ff7457c828b2a, 0x1ff74635690d67, 0x1ff746eab0e779,
	0x1ff7479c5a34bd, 0x1ff7484a65064a, 0x1ff748f4d162ee, 0x1ff7499b9f4729,
	0x1ff74a3ecea523, 0x1ff74ade5f64ae, 0x1ff74b7a516339, 0x1ff74c12a473cd,
	0x1ff74ca7585f06, 0x1ff74d386ce30b, 0x1ff74dc5e1b386, 0x1ff74e4fb679a0,
	0x1ff74ed5ead3f3, 0x1ff74f587e5688, 0x1ff74fd7708ac9, 0x1ff75052c0ef7d,
	0x1ff750ca6ef8b9, 0x1ff7513e7a0fdb, 0x1ff751aee1937e, 0x1ff7521ba4d76f,
	0x1ff75284c324a4, 0x1ff752ea3bb930, 0x1ff7534c0dc837, 0x1ff753aa3879e4,
	0x1ff75404baeb5b, 0x1ff7545b942eac, 0x1ff754aec34aca, 0x1ff754fe473b79,
	0x1ff7554a1ef144, 0x1ff7559249516b, 0x1ff755d6c535da, 0x1ff75617916d16,
	0x1ff75654acba30, 0x1ff7568e15d4b3, 0x1ff756c3cb6898, 0x1ff756f5cc1631,
	0x1ff7572416721c, 0x1ff7574ea90531, 0x1ff75775824c6e, 0x1ff75798a0b8ea,
	0x1ff757b802afbc, 0x1ff757d3a689ee, 0x1ff757eb8a9465, 0x1ff757ffad0fd3,
	0x1ff758100c309b, 0x1ff7581ca61ec5, 0x1ff7582578f5e2, 0x1ff7582a82c4f9,
	0x1ff7582bc18e71, 0x1ff758293347fd, 0x1ff75822d5da7f, 0x1ff75818a721f5,
	0x1ff7580aa4ed62, 0x1ff757f8ccfeaf, 0x1ff757e31d0a9c, 0x1ff757c992b89c,
	0x1ff757ac2ba2c2, 0x1ff7578ae555a4, 0x1ff75765bd5041, 0x1ff7573cb103e2,
	0x1ff7570fbdd403, 0x1ff756dee11630, 0x1ff756aa1811ee, 0x1ff75671600098,
	0x1ff75634b60d44, 0x1ff755f41754a0, 0x1ff755af80e4d7, 0x1ff75566efbd6d,
	0x1ff7551a60cf1e, 0x1ff754c9d0fbbe, 0x1ff754753d1618, 0x1ff7541ca1e1c6,
	0x1ff753bffc1313, 0x1ff7535f484ed3, 0x1ff752fa832a3f, 0x1ff75291a92ad1,
	0x1ff75224b6c619, 0x1ff751b3a8619c, 0x1ff7513e7a52a8, 0x1ff750c528de2c,
	0x1ff75047b0388f, 0x1ff74fc60c8586, 0x1ff74f4039d7e9, 0x1ff74eb6343187,
	0x1ff74e27f782fa, 0x1ff74d957fab78, 0x1ff74cfec878a7, 0x1ff74c63cda66c,
	0x1ff74bc48adebc, 0x1ff74b20fbb96c, 0x1ff74a791bbbfd, 0x1ff749cce6596a,
	0x1ff7491c56f1f6, 0x1ff7486768d2f6, 0x1ff747ae17369b, 0x1ff746f05d43be,
	0x1ff7462e360da5, 0x1ff745679c93cc, 0x1ff7449c8bc1ac, 0x1ff743ccfe6e81,
	0x1ff742f8ef5d0b, 0x1ff74220593b53, 0x1ff7414336a271, 0x1ff74061821644,
	0x1ff73f7b36053a, 0x1ff73e904cc80b, 0x1ff73da0c0a176, 0x1ff73cac8bbdfd,
	0x1ff73bb3a833a2, 0x1ff73ab61001a0, 0x1ff739b3bd101f, 0x1ff738aca92ff1,
	0x1ff737a0ce1a45, 0x1ff73690257059, 0x1ff7357aa8bb30, 0x1ff73460516b42,
	0x1ff7334118d82c, 0x1ff7321cf8405e, 0x1ff730f3e8c8c9, 0x1ff72fc5e37c89,
	0x1ff72e92e14c8d, 0x1ff72d5adb0f45, 0x1ff72c1dc98042, 0x1ff72adba53fde,
	0x1ff7299466d2df, 0x1ff7284806a216, 0x1ff726f67cfa02, 0x1ff7259fc20a6a,
	0x1ff72443cde5fc, 0x1ff722e29881e5, 0x1ff7217c19b568, 0x1ff72010493976,
	0x1ff71e9f1ea842, 0x1ff71d28917cd1, 0x1ff71bac99128b, 0x1ff71a2b2ca4c8,
	0x1ff718a4434e5a, 0x1ff71717d4091b, 0x1ff71585d5ad6d, 0x1ff713ee3ef1c5,
	0x1ff71251066a27, 0x1ff710ae2287ab, 0x1ff70f058997f4, 0x1ff70d5731c4b2,
	0x1ff70ba3111313, 0x1ff709e91d633c, 0x1ff708294c6fbc, 0x1ff7066393ccf7,
	0x1ff70497e8e898, 0x1ff702c64108f9, 0x1ff700ee914c89, 0x1ff6ff10cea92f,
	0x1ff6fd2cedebb0, 0x1ff6fb42e3b704, 0x1ff6f952a483b7, 0x1ff6f75c249f3f,
	0x1ff6f55f582b4b, 0x1ff6f35c331d18, 0x1ff6f152a93cba, 0x1ff6ef42ae2467,
	0x1ff6ed2c353fb9, 0x1ff6eb0f31caf1, 0x1ff6e8eb96d235, 0x1ff6e6c15730c8,
	0x1ff6e49065903c, 0x1ff6e258b467a8, 0x1ff6e01a35fad1, 0x1ff6ddd4dc5952,
	0x1ff6db88995dc0, 0x1ff6d9355eaccb, 0x1ff6d6db1db452, 0x1ff6d479c7aa7f,
	0x1ff6d2114d8cd3, 0x1ff6cfa1a01f30, 0x1ff6cd2aafeae3, 0x1ff6caac6d3da1,
	0x1ff6c826c82883, 0x1ff6c599b07efa, 0x1ff6c30515d5c0, 0x1ff6c068e781c1,
	0x1ff6bdc51496fd, 0x1ff6bb198be767, 0x1ff6b8663c01bb, 0x1ff6b5ab13304e,
	0x1ff6b2e7ff77d6, 0x1ff6b01cee962f, 0x1ff6ad49ce0117, 0x1ff6aa6e8ae4dd,
	0x1ff6a78b122313, 0x1ff6a49f505133, 0x1ff6a1ab31b737, 0x1ff69eaea24e32,
	0x1ff69ba98dbee0, 0x1ff6989bdf6021, 0x1ff6958582357e, 0x1ff6926660ed97,
	0x1ff68f3e65e08c, 0x1ff68c0d7b0e62, 0x1ff688d38a1d50, 0x1ff685907c5815,
	0x1ff682443aac35, 0x1ff67eeeada832, 0x1ff67b8fbd79b6, 0x1ff6782751ebb9,
	0x1ff674b5526495, 0x1ff67139a5e411, 0x1ff66db433015c, 0x1ff66a24dfe905,
	0x1ff6668b925adc, 0x1ff662e82fa7cb, 0x1ff65f3a9cafa1, 0x1ff65b82bdded0,
	0x1ff657c0772c16, 0x1ff653f3ac1625, 0x1ff6501c3fa12b, 0x1ff64c3a14545c,
	0x1ff6484d0c375a, 0x1ff6445508cf9b, 0x1ff64051eb1db8, 0x1ff63c43939aaa,
	0x1ff63829e234f5, 0x1ff63404b64dc3, 0x1ff62fd3eeb5ec, 0x1ff62b9769aae5,
	0x1ff6274f04d3a0, 0x1ff622fa9d3d57, 0x1ff61e9a0f583d, 0x1ff61a2d36f41f,
	0x1ff615b3ef3ce8, 0x1ff6112e12b713, 0x1ff60c9b7b3c00, 0x1ff607fc01f632,
	0x1ff6034f7f5d75, 0x1ff5fe95cb32e3, 0x1ff5f9cebc7cd8, 0x1ff5f4fa2982be,
	0x1ff5f017e7c8c3, 0x1ff5eb27cc0b70, 0x1ff5e629aa3b1b, 0x1ff5e11d557743,
	0x1ff5dc02a009c3, 0x1ff5d6d95b61e0, 0x1ff5d1a1580f3e, 0x1ff5cc5a65bca7,
	0x1ff5c704532aaf, 0x1ff5c19eee2a33, 0x1ff5bc2a0396a9, 0x1ff5b6a55f5050,
	0x1ff5b110cc362c, 0x1ff5ab6c141fd7, 0x1ff5a5b6ffd727, 0x1ff59ff15711a2,
	0x1ff59a1ae069be, 0x1ff594336157f4, 0x1ff58e3a9e2b92, 0x1ff588305a0368,
	0x1ff5821456c627, 0x1ff57be6551a9a, 0x1ff575a6145f8d, 0x1ff56f5352a388,
	0x1ff568edcc9c3a, 0x1ff562753d9da7, 0x1ff55be95f910f, 0x1ff55549eaeb8b,
	0x1ff54e9696a459, 0x1ff547cf182ae8, 0x1ff540f3235c80, 0x1ff53a026a79a3,
	0x1ff532fc9e1b10, 0x1ff52be16d266d, 0x1ff524b084c292, 0x1ff51d69904b6f,
	0x1ff5160c394592, 0x1ff50e9827513e, 0x1ff5070d001d15, 0x1ff4ff6a67584e,
	0x1ff4f7affea47a, 0x1ff4efdd6586c6, 0x1ff4e7f23958bf, 0x1ff4dfee153892,
	0x1ff4d7d091f8be, 0x1ff4cf99460f37, 0x1ff4c747c583f1, 0x1ff4bedba1dece,
	0x1ff4b6546a14e7, 0x1ff4adb1aa7531, 0x1ff4a4f2ec9465, 0x1ff49c17b73838,
	0x1ff4931f8e41d1, 0x1ff48a09f29772, 0x1ff480d6620d53, 0x1ff47784574d9d,
	0x1ff46e1349bf86, 0x1ff46482ad6d7c, 0x1ff45ad1f2ea57, 0x1ff45100873586,
	0x1ff4470dd39e2d, 0x1ff43cf93da529, 0x1ff432c226dde4, 0x1ff42867eccdff,
	0x1ff41de9e8cbaa, 0x1ff413476fdaaf, 0x1ff4087fd2881c, 0x1ff3fd925cc472,
	0x1ff3f27e55bc50, 0x1ff3e742ffaf8e, 0x1ff3dbdf97c69c, 0x1ff3d05355e633,
	0x1ff3c49d6c811e, 0x1ff3b8bd086824, 0x1ff3acb15097e4, 0x1ff3a079660494,
	0x1ff39414636388, 0x1ff387815cf25c, 0x1ff37abf603bae, 0x1ff36dcd73d93f,
	0x1ff360aa97335f, 0x1ff35355c23d7b, 0x1ff345cde52fa6, 0x1ff33811e83cff,
	0x1ff32a20ab46b7, 0x1ff31bf9058b9d, 0x1ff30d99c553f1, 0x1ff2ff01af994e,
	0x1ff2f02f7faa77, 0x1ff2e121e6cacd, 0x1ff2d1d78bcd30, 0x1ff2c24f0aa9fc,
	0x1ff2b286f40ff7, 0x1ff2a27dccefc9, 0x1ff292320e01bd, 0x1ff281a2234579,
	0x1ff270cc6b7b45, 0x1ff25faf379689, 0x1ff24e48ca291a, 0x1ff23c9756c6e6,
	0x1ff22a99016188, 0x1ff2184bdd9b42, 0x1ff205adee10dd, 0x1ff1f2bd2399d8,
	0x1ff1df775c7e47, 0x1ff1cbda63a1c6, 0x1ff1b7e3efa2bd, 0x1ff1a391a1ed42,
	0x1ff18ee105c0be, 0x1ff179cf8f277f, 0x1ff1645a99df44, 0x1ff14e7f6831b7,
	0x1ff1383b21bbd2, 0x1ff1218ad222e8, 0x1ff10a6b67b62c, 0x1ff0f2d9b1fb37,
	0x1ff0dad260242a, 0x1ff0c251ff6dc6, 0x1ff0a954f963be, 0x1ff08fd792096b,
	0x1ff075d5e5e4c3, 0x1ff05b4be7e977, 0x1ff040355f41b4, 0x1ff0248de4f201,
	0x1ff00850e1554c, 0x1fefeb79896e21, 0x1fefce02dc0989, 0x1fefafe79eb009,
	0x1fef91225a608c, 0x1fef71ad5810eb, 0x1fef51829cef30, 0x1fef309be65e4d,
	0x1fef0ef2a5a86b, 0x1feeec7ffb607f, 0x1feec93cb26c08, 0x1feea5213aad4d,
	0x1fee8025a34587, 0x1fee5a4194658e, 0x1fee336c48a2ab, 0x1fee0b9c85c3fe,
	0x1fede2c894fbb8, 0x1fedb8e63a7e12, 0x1fed8deaac662b, 0x1fed61ca88d768,
	0x1fed3479cb47be, 0x1fed05ebc0dd34, 0x1fecd612fbc640, 0x1feca4e14571c2,
	0x1fec72478f8813, 0x1fec3e35e382d9, 0x1fec089b50bcfa, 0x1febd165d8cf35,
	0x1feb98825a0821, 0x1feb5ddc77c7ff, 0x1feb215e808137, 0x1feae2f15115db,
	0x1feaa27c354088, 0x1fea5fe4c4ab79, 0x1fea1b0ebc4b44, 0x1fe9d3dbd38321,
	0x1fe98a2b8c864e, 0x1fe93ddaff54db, 0x1fe8eec49e9910, 0x1fe89cbff58d03,
	0x1fe847a15ded0d, 0x1fe7ef39acd24e, 0x1fe79355d51f26, 0x1fe733be7dec95,
	0x1fe6d0378b20ea, 0x1fe6687f96032e, 0x1fe5fc4f53381e, 0x1fe58b58e31928,
	0x1fe5154708be3a, 0x1fe499bc4359d8, 0x1fe41851c4a2c7, 0x1fe390963decfc,
	0x1fe3020c7c359c, 0x1fe26c29c9b0d3, 0x1fe1ce54094389, 0x1fe127df7d9d7d,
	0x1fe0780c2a3655, 0x1fdfbe02b80705, 0x1fdef8d0c228c6, 0x1fde2764671edb,
	0x1fdd4886f1e212, 0x1fdc5ad660fb45, 0x1fdb5cbd80ed3b, 0x1fda4c6a383af4,
	0x1fd927c1841e8c, 0x1fd7ec507a1247, 0x1fd697396681f0, 0x1fd5251bcca40f,
	0x1fd391f592d6f4, 0x1fd1d8faf7a490, 0x1fcff461e8ca45, 0x1fcddd1bd07028,
	0x1fcb8a769788b3, 0x1fc8f199f36e14, 0x1fc604d032640d, 0x1fc2b28000dbca,
	0x1fbee3ac0cc16a, 0x1fba79b024d12d, 0x1fb54abd9de691, 0x1faf1c31164e6c,
	0x1fa79908ab5576, 0x1f9e40f74adba6, 0x1f92485b7f7ce4, 0x1f82566f32613d,
	0x1f6beeb86a3986, 0x1f49e14c562fc1, 0x1f0f1b3f87a334, 0x1e8d218970e9f8,
}

var normalW = [1024]float64{
	4.74447736997673454e-16, 1.49950672584574354e-17, 1.98925244441675334e-17, 2.32931734656154252e-17,
	2.59805409399221482e-17, 2.82390849337205807e-17, 3.02072404382168115e-17, 3.19637756999175384e-17,
	3.35581847741996873e-17, 3.50237918907125268e-17, 3.63842088069319060e-17, 3.76568359621902072e-17,
	3.88549029674455544e-17, 3.99887271404885479e-17, 4.10665260620887388e-17, 4.20949623559874980e-17,
	4.30795206891502077e-17, 4.40247757990233704e-17, 4.49345875327002910e-17, 4.58122456815039448e-17,
	4.66605794695609696e-17, 4.74820416413924252e-17, 4.82787739593837055e-17, 4.90526588719055837e-17,
	4.98053607414183723e-17, 5.05383590857482273e-17, 5.12529756349615950e-17, 5.19503965463335850e-17,
	5.26316907899034361e-17, 5.32978254770334355e-17, 5.39496787274974680e-17, 5.45880505387522068e-17,
	5.52136720216588931e-17, 5.58272132912632662e-17, 5.64292902430992755e-17, 5.70204704004093791e-17,
	5.76012779824455802e-17, 5.81721983162684134e-17, 5.87336816924484999e-17, 5.92861467474938743e-17,
	5.98299834416924934e-17, 6.03655556896294455e-17, 6.08932036913414661e-17, 6.14132460044681435e-17,
	6.19259813915100218e-17, 6.24316904711406697e-17, 6.29306371982363009e-17, 6.34230701937148089e-17,
	6.39092239422872284e-17, 6.43893198737117100e-17, 6.48635673410207942e-17, 6.53321645073973591e-17,
	6.57952991518495417e-17, 6.62531494025336163e-17, 6.67058844054618932e-17, 6.71536649353770298e-17,
	6.75966439547528951e-17, 6.80349671261725714e-17, 6.84687732827198133e-17, 6.88981948604878165e-17,
	6.93233582968452103e-17, 6.97443843976946282e-17, 7.01613886766060445e-17, 7.05744816683965032e-17,
	7.09837692194563100e-17, 7.13893527568816509e-17, 7.17913295382624915e-17, 7.21897928837879015e-17,
	7.25848323921652097e-17, 7.29765341417029167e-17, 7.33649808777767593e-17, 7.37502521877819875e-17,
	7.41324246645715269e-17, 7.45115720592869447e-17, 7.48877654244062334e-17, 7.52610732477584599e-17,
	7.56315615781880504e-17, 7.59992941434922814e-17, 7.63643324612008193e-17, 7.67267359427181052e-17,
	7.70865619913048833e-17, 7.74438660943359153e-17, 7.77987019102345971e-17, 7.81511213504527397e-17,
	7.85011746568341703e-17, 7.88489104746738531e-17, 7.91943759217598825e-17, 7.95376166536632234e-17,
	7.98786769255199909e-17, 8.02175996505322284e-17, 8.05544264553965537e-17, 8.08891977328541654e-17,
	8.12219526915416622e-17, 8.15527294033093489e-17, 8.18815648481611505e-17, 8.22084949569601272e-17,
	8.25335546520325750e-17, 8.28567778857952906e-17, 8.31781976775214191e-17, 8.34978461483526289e-17,
	8.38157545546582758e-17, 8.41319533198352248e-17, 8.44464720646359403e-17, 8.47593396361067142e-17,
	8.50705841352126876e-17, 8.53802329432211436e-17, 8.56883127469103091e-17, 8.59948495626664423e-17,
	8.62998687595283339e-17, 8.66033950812341692e-17, 8.69054526673231507e-17, 8.72060650733402476e-17,
	8.75052552901901087e-17, 8.78030457626832078e-17, 8.80994584073148199e-17, 8.83945146293149688e-17,
	8.86882353390052602e-17, 8.89806409674966714e-17, 8.92717514817601226e-17, 8.95615863991000534e-17,
	8.98501648010593776e-17, 9.01375053467829477e-17, 9.04236262858645734e-17, 9.07085454707019519e-17,
	9.09922803683819417e-17, 9.12748480721179123e-17, 9.15562653122592837e-17, 9.18365484668927203e-17,
	9.21157135720530599e-17, 9.23937763315613461e-17, 9.26707521265065175e-17, 9.29466560243859386e-17,
	9.32215027879200085e-17, 9.34953068835544793e-17, 9.37680824896640050e-17, 9.40398435044695816e-17,
	9.43106035536817829e-17, 9.45803759978813803e-17, 9.48491739396480449e-17, 9.51170102304477559e-17,
	9.53838974772884575e-17, 9.56498480491536385e-17, 9.59148740832225374e-17, 9.61789874908857124e-17,
	9.64421999635639259e-17, 9.67045229783381953e-17, 9.69659678033983937e-17, 9.72265455033173770e-17,
	9.74862669441574773e-17, 9.77451427984157614e-17, 9.80031835498141046e-17, 9.82603994979400724e-17,
	9.85168007627442285e-17, 9.87723972888990225e-17, 9.90271988500247306e-17, 9.92812150527869959e-17,
	9.95344553408709128e-17, 9.97869289988361404e-17, 1.00038645155857078e-16, 1.00289612789352646e-16,
	1.00539840728509293e-16, 1.00789337657701088e-16, 1.01038112119810637e-16, 1.01286172519454187e-16,
	1.01533527126114272e-16, 1.01780184077183157e-16, 1.02026151380920064e-16, 1.02271436919325215e-16,
	1.02516048450933459e-16, 1.02759993613530225e-16, 1.03003279926792351e-16, 1.03245914794856472e-16,
	1.03487905508817134e-16, 1.03729259249157121e-16, 1.03969983088112181e-16, 1.04210083991972242e-16,
	1.04449568823321212e-16, 1.04688444343217438e-16, 1.04926717213316494e-16, 1.05164393997938393e-16,
	1.05401481166080830e-16, 1.05637985093380197e-16, 1.05873912064022036e-16, 1.06109268272602417e-16,
	1.06344059825941985e-16, 1.06578292744853757e-16, 1.06811972965866535e-16, 1.07045106342904891e-16,
	1.07277698648927354e-16, 1.07509755577523864e-16, 1.07741282744473731e-16, 1.07972285689265456e-16,
	1.08202769876579329e-16, 1.08432740697733980e-16, 1.08662203472098044e-16, 1.08891163448467797e-16,
	1.09119625806411894e-16, 1.09347595657584053e-16, 1.09575078047004702e-16, 1.09802077954312416e-16,
	1.10028600294985997e-16, 1.10254649921538112e-16, 1.10480231624681227e-16, 1.10705350134466619e-16,
	1.10930010121397184e-16, 1.11154216197514961e-16, 1.11377972917463705e-16, 1.11601284779527719e-16,
	1.11824156226646909e-16, 1.12046591647409526e-16, 1.12268595377022417e-16, 1.12490171698260027e-16,
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}