diff --git a/goldenposeidon/constants.go b/goldenposeidon/constants.go
index 1a952c4..a2b3c28 100644
--- a/goldenposeidon/constants.go
+++ b/goldenposeidon/constants.go
@@ -106,10 +106,817 @@ var (
 		0x4543d9df5476d3cb, 0xf172d73e004fc90d, 0xdfd1c4febcc81238, 0xbc8dfb627fe558fc,
 	}
 
+	c_opt = []uint64{
+		0xb585f766f2144405,
+		0x7746a55f43921ad7,
+		0xb2fb0d31cee799b4,
+		0xf6760a4803427d7,
+		0xe10d666650f4e012,
+		0x8cae14cb07d09bf1,
+		0xd438539c95f63e9f,
+		0xef781c7ce35b4c3d,
+		0xcdc4a239b0c44426,
+		0x277fa208bf337bff,
+		0xe17653a29da578a1,
+		0xc54302f225db2c76,
+		0xac6c9c2b4418dd61,
+		0xe0888eb1e8a01286,
+		0x813dbe952b98904e,
+		0xcc3033609c9cf175,
+		0x72cebc82a59c0f82,
+		0x8150d8525753e741,
+		0xb1122c74b268d66e,
+		0x7c6ddd482375aa2,
+		0xa4dd6f1ef49fb6af,
+		0xd33b0d5b4f7ccfe5,
+		0xc523112247209124,
+		0x464804200134c32d,
+		0xcd09dea180de4f2c,
+		0xadb069225c93e4e6,
+		0xbf01209b8a7c8534,
+		0xb1eb37d319913823,
+		0xdadf943b8d3e5a0d,
+		0x6d15f3cb7a3520ba,
+		0xf07af62b134ef181,
+		0x568355076c6b0de6,
+		0x31ca4bf93cab68b8,
+		0xfbad37a125735ba,
+		0x9d3a9caaf1ac9e0a,
+		0x4f265810f020c095,
+		0x6a84c9524e81a8bc,
+		0x68ba410537925c79,
+		0x422604631b34b07a,
+		0x28e3a001f62f8290,
+		0x3adfdccb8f734d41,
+		0x73503e539baec66a,
+		0xe8c1fd0142d9849c,
+		0xe204ac13660546c5,
+		0x8e2bb3ea97a40c53,
+		0xac2800d1bf56548c,
+		0x9494dca005d180d0,
+		0xf36e1d066383ef53,
+		0x8aa35b97a0e03c04,
+		0xcf42a59addbd1f0c,
+		0xa43ace89f8fdbd79,
+		0x37585d8c243870c,
+		0x4ab94ee3e26596fe,
+		0xcee3abbb50d57b23,
+		0xac91a7101a5ec55b,
+		0x9173aa8462280d2d,
+		0xaec1ca46ccb95105,
+		0x57b2f2845db61e4a,
+		0x95704158500c90c6,
+		0x66e023b0e6c9df5f,
+		0x315f63f4fec360ba,
+		0xf3009795713abcf1,
+		0xf4decc3fb00765ee,
+		0x32620ac918682d50,
+		0x49717d63a5fc742e,
+		0x153516f22014ea2d,
+		0xcc316380a2761fe4,
+		0x2e49b3f7076d203d,
+		0x44ac3e9bf0a2dc89,
+		0x49d1e388d8e35c,
+		0x53ec867cb39989fa,
+		0xd2c9bcc8d65f5a62,
+		0xc0cc930ee8540455,
+		0x40651e0872505e8,
+		0x168973b2ebafbe6c,
+		0x9c7eecb3b40581c2,
+		0x389473bcdfca97a2,
+		0xb1cb0b3abe9753ad,
+		0x41afceccffdb18e6,
+		0x7bf841e237ccd6c9,
+		0x6082a3f101fb888,
+		0x8c1a39196f4163cc,
+		0xb56664760c1c9476,
+		0x2a02ac020d1eb5a3,
+		0x6a9d48e8aa83605d,
+		0x8a0d2f5c4c9c51b2,
+		0x75fc65575b284ad4,
+		0xadaedf7d1ce2a8dd,
+		0x235bc889cc83968e,
+		0xa8c30cf1781738f5,
+		0x546b2a846753bcf8,
+		0x9b68e8c06c04bd25,
+		0x3fdf80794ebb443b,
+		0x92ca132a9bec5a45,
+		0x76133eecfd9bd1ff,
+		0x3fb0fd5381054812,
+		0xf15925978dbd52ff,
+		0x2ee289ac37f0e879,
+		0xd8af8654e9a2e659,
+		0x8595bbd7f34c5e8a,
+		0x206ddbf781e47b2,
+		0xe101a767854a2f97,
+		0xf4d4f0a01072c996,
+		0x197aec2894aab642,
+		0x8d0c3911220db49b,
+		0xa62a8bad609227ca,
+		0x1e4813a7e7b9cbce,
+		0x6b547528731244eb,
+		0xd08e48512bfea84e,
+		0xb2920c88d3885857,
+		0x1f0cd5d7a309fcc2,
+		0x99a0ea0842fdb4fb,
+		0xc227210554b6c53d,
+		0x70e5269708f6f3a9,
+		0xbe8f71c8c98bb3bd,
+		0xf96fb39adc4baaf6,
+		0x7f9a7555c60fc6c7,
+		0xccaa5446d71fe6a5,
+	}
+
+	p = [][]uint64{
+		{
+			0x19,
+			0x78566230aa7cc5d0,
+			0xdbf23e50005e7f24,
+			0xb4a02c5c826d523e,
+			0x466d8f66a8f9fed5,
+			0x68da2264f65ec3e,
+			0xb59f9ff0ac6d5d78,
+			0xcfb03c902d447551,
+			0x2044ce14eaf8f5d9,
+			0xfb9373c8481e0f0d,
+			0x72af70cdcb99214f,
+			0xe3ef40eacc6ff78d,
+		},
+		{
+			0xf,
+			0x817bd8a7869ed1b5,
+			0x819f2c14a8366b1f,
+			0x7a5cf5b7b922e946,
+			0x727eca45c8d7bb71,
+			0x605a82c52b5ad2f1,
+			0x59ccc4d5184bc93a,
+			0x66c8bab2096cfd38,
+			0xeb4c0ce280c3e935,
+			0x17f9202c16676b2f,
+			0x9b6e5164ed35d878,
+			0x6fadc9347faeee81,
+		},
+		{
+			0x29,
+			0xd267254bea1097f4,
+			0x2dc10fce3233f443,
+			0xfa9db0de2d852e7a,
+			0xde2a0516f8c9d943,
+			0xe6fdf23648931b99,
+			0x3743057c07a5dbfa,
+			0xa6fdb8ebccc51667,
+			0x2c4916605e3dea58,
+			0xe95c10ae32e05085,
+			0x97f9b7d2cfc2ade5,
+			0x9b6e5164ed35d878,
+		},
+		{
+			0x10,
+			0x60c33ebd1e023f0a,
+			0xdb6945a20d277091,
+			0x383dd77e07998487,
+			0xe04ea1957ad8305c,
+			0xd499fcbf63fbd266,
+			0x462269e4b04620a5,
+			0x63c9679d8572a867,
+			0x81c44e9699915693,
+			0x62ecbe05e02433fc,
+			0xe95c10ae32e05085,
+			0x17f9202c16676b2f,
+		},
+		{
+			0x2,
+			0xa89ef32ae1462322,
+			0x77c1a153e73659e8,
+			0x2aec981be4b62ed5,
+			0xb70fb5f2b4f1f85f,
+			0x7c66d474cd2087cb,
+			0x39302966be7df654,
+			0xb827c807875511c0,
+			0xa4daffb3ffd0e78f,
+			0x81c44e9699915693,
+			0x2c4916605e3dea58,
+			0xeb4c0ce280c3e935,
+		},
+		{
+			0x1c,
+			0x6250f5f176d483e7,
+			0xaad1255d46e78f07,
+			0x8a00c7c83c762584,
+			0xc734f3829ed30b0c,
+			0xb1a0132288b1619b,
+			0x88685b4f0798dfd1,
+			0xfc02e869e21b72f8,
+			0xb827c807875511c0,
+			0x63c9679d8572a867,
+			0xa6fdb8ebccc51667,
+			0x66c8bab2096cfd38,
+		},
+		{
+			0xd,
+			0xe16a6c1dee3ba347,
+			0x13d316e45539aef4,
+			0x577e0472764f061d,
+			0x226a4dcf5db3316d,
+			0x3373035a3ca3dac6,
+			0x441f3a3747b5adb7,
+			0x88685b4f0798dfd1,
+			0x39302966be7df654,
+			0x462269e4b04620a5,
+			0x3743057c07a5dbfa,
+			0x59ccc4d5184bc93a,
+		},
+		{
+			0xd,
+			0xec9730136b7c2c05,
+			0xe1ecc5c21eec0646,
+			0x956d3c8b5528e064,
+			0x6df1d31fa84398f4,
+			0xf4898a1a3554ee49,
+			0x3373035a3ca3dac6,
+			0xb1a0132288b1619b,
+			0x7c66d474cd2087cb,
+			0xd499fcbf63fbd266,
+			0xe6fdf23648931b99,
+			0x605a82c52b5ad2f1,
+		},
+		{
+			0x27,
+			0x3cf7c3a39d94c236,
+			0x9e62c7d7b000cb0b,
+			0xe202be7ad7265af6,
+			0x82178371fa5fff69,
+			0x6df1d31fa84398f4,
+			0x226a4dcf5db3316d,
+			0xc734f3829ed30b0c,
+			0xb70fb5f2b4f1f85f,
+			0xe04ea1957ad8305c,
+			0xde2a0516f8c9d943,
+			0x727eca45c8d7bb71,
+		},
+		{
+			0x12,
+			0xb4707207455f57e3,
+			0x8e1de42b665c6706,
+			0xee7b04568203481,
+			0xe202be7ad7265af6,
+			0x956d3c8b5528e064,
+			0x577e0472764f061d,
+			0x8a00c7c83c762584,
+			0x2aec981be4b62ed5,
+			0x383dd77e07998487,
+			0xfa9db0de2d852e7a,
+			0x7a5cf5b7b922e946,
+		},
+		{
+			0x22,
+			0xaadb39e83e76a9e0,
+			0xcd9bf0bd292c5fda,
+			0x8e1de42b665c6706,
+			0x9e62c7d7b000cb0b,
+			0xe1ecc5c21eec0646,
+			0x13d316e45539aef4,
+			0xaad1255d46e78f07,
+			0x77c1a153e73659e8,
+			0xdb6945a20d277091,
+			0x2dc10fce3233f443,
+			0x819f2c14a8366b1f,
+		},
+		{
+			0x14,
+			0x32f8ae916e567d39,
+			0xaadb39e83e76a9e0,
+			0xb4707207455f57e3,
+			0x3cf7c3a39d94c236,
+			0xec9730136b7c2c05,
+			0xe16a6c1dee3ba347,
+			0x6250f5f176d483e7,
+			0xa89ef32ae1462322,
+			0x60c33ebd1e023f0a,
+			0xd267254bea1097f4,
+			0x817bd8a7869ed1b5,
+		},
+	}
+
+	s = []uint64{
+		0x19,
+		0x3d999c961b7c63b0,
+		0x814e82efcd172529,
+		0x2421e5d236704588,
+		0x887af7d4dd482328,
+		0xa5e9c291f6119b27,
+		0xbdc52b2676a4b4aa,
+		0x64832009d29bcf57,
+		0x9c4155174a552cc,
+		0x463f9ee03d290810,
+		0xc810936e64982542,
+		0x43b1c289f7bc3ac,
+		0x94877900674181c3,
+		0xc6c67cc37a2a2bbd,
+		0xd667c2055387940f,
+		0xba63a63e94b5ff0,
+		0x99460cc41b8f079f,
+		0x7ff02375ed524bb3,
+		0xea0870b47a8caf0e,
+		0xabcad82633b7bc9d,
+		0x3b8d135261052241,
+		0xfb4515f5e5b0d539,
+		0x3ee8011c2b37f77c,
+		0x19,
+		0x673655aae8be5a8b,
+		0xd510fe714f39fa10,
+		0x2c68a099b51c9e73,
+		0xa667bfa9aa96999d,
+		0x4d67e72f063e2108,
+		0xf84dde3e6acda179,
+		0x40f9cc8c08f80981,
+		0x5ead032050097142,
+		0x6591b02092d671bb,
+		0xe18c71963dd1b7,
+		0x8a21bcd24a14218a,
+		0xadef3740e71c726,
+		0xa37bf67c6f986559,
+		0xc6b16f7ed4fa1b00,
+		0x6a065da88d8bfc3c,
+		0x4cabc0916844b46f,
+		0x407faac0f02e78d1,
+		0x7a786d9cf0852cf,
+		0x42433fb6949a629a,
+		0x891682a147ce43b0,
+		0x26cfd58e7b003b55,
+		0x2bbf0ed7b657acb3,
+		0x19,
+		0x202800f4addbdc87,
+		0xe4b5bdb1cc3504ff,
+		0xbe32b32a825596e7,
+		0x8e0f68c5dc223b9a,
+		0x58022d9e1c256ce3,
+		0x584d29227aa073ac,
+		0x8b9352ad04bef9e7,
+		0xaead42a3f445ecbf,
+		0x3c667a1d833a3cca,
+		0xda6f61838efa1ffe,
+		0xe8f749470bd7c446,
+		0x481ac7746b159c67,
+		0xe367de32f108e278,
+		0x73f260087ad28bec,
+		0x5cfc82216bc1bdca,
+		0xcaccc870a2663a0e,
+		0xdb69cd7b4298c45d,
+		0x7bc9e0c57243e62d,
+		0x3cc51c5d368693ae,
+		0x366b4e8cc068895b,
+		0x2bd18715cdabbca4,
+		0xa752061c4f33b8cf,
+		0x19,
+		0xc5b85bab9e5b3869,
+		0x45245258aec51cf7,
+		0x16e6b8e68b931830,
+		0xe2ae0f051418112c,
+		0x470e26a0093a65b,
+		0x6bef71973a8146ed,
+		0x119265be51812daf,
+		0xb0be7356254bea2e,
+		0x8584defff7589bd7,
+		0x3c5fe4aeb1fb52ba,
+		0x9e7cd88acf543a5e,
+		0xb22d2432b72d5098,
+		0x9e18a487f44d2fe4,
+		0x4b39e14ce22abd3c,
+		0x9e77fde2eb315e0d,
+		0xca5e0385fe67014d,
+		0xc2cb99bf1b6bddb,
+		0x99ec1cd2a4460bfe,
+		0x8577a815a2ff843f,
+		0x7d80a6b4fd6518a5,
+		0xeb6c67123eab62cb,
+		0x8f7851650eca21a5,
+		0x19,
+		0x179be4bba87f0a8c,
+		0xacf63d95d8887355,
+		0x6696670196b0074f,
+		0xd99ddf1fe75085f9,
+		0xc2597881fef0283b,
+		0xcf48395ee6c54f14,
+		0x15226a8e4cd8d3b6,
+		0xc053297389af5d3b,
+		0x2c08893f0d1580e2,
+		0xed3cbcff6fcc5ba,
+		0xc82f510ecf81f6d0,
+		0x11ba9a1b81718c2a,
+		0x9f7d798a3323410c,
+		0xa821855c8c1cf5e5,
+		0x535e8d6fac0031b2,
+		0x404e7c751b634320,
+		0xa729353f6e55d354,
+		0x4db97d92e58bb831,
+		0xb53926c27897bf7d,
+		0x965040d52fe115c5,
+		0x9565fa41ebd31fd7,
+		0xaae4438c877ea8f4,
+		0x19,
+		0x94b06183acb715cc,
+		0x500392ed0d431137,
+		0x861cc95ad5c86323,
+		0x5830a443f86c4ac,
+		0x3b68225874a20a7c,
+		0x10b3309838e236fb,
+		0x9b77fc8bcd559e2c,
+		0xbdecf5e0cb9cb213,
+		0x30276f1221ace5fa,
+		0x7935dd342764a144,
+		0xeac6db520bb03708,
+		0x37f4e36af6073c6e,
+		0x4edc0918210800e9,
+		0xc44998e99eae4188,
+		0x9f4310d05d068338,
+		0x9ec7fe4350680f29,
+		0xc5b2c1fdc0b50874,
+		0xa01920c5ef8b2ebe,
+		0x59fa6f8bd91d58ba,
+		0x8bfc9eb89b515a82,
+		0xbe86a7a2555ae775,
+		0xcbb8bbaa3810babf,
+		0x19,
+		0x7186a80551025f8f,
+		0x622247557e9b5371,
+		0xc4cbe326d1ad9742,
+		0x55f1523ac6a23ea2,
+		0xa13dfe77a3d52f53,
+		0xe30750b6301c0452,
+		0x8bd488070a3a32b,
+		0xcd800caef5b72ae3,
+		0x83329c90f04233ce,
+		0xb5b99e6664a0a3ee,
+		0x6b0731849e200a7f,
+		0x577f9a9e7ee3f9c2,
+		0x88c522b949ace7b1,
+		0x82f07007c8b72106,
+		0x8283d37c6675b50e,
+		0x98b074d9bbac1123,
+		0x75c56fb7758317c1,
+		0xfed24e206052bc72,
+		0x26d7c3d1bc07dae5,
+		0xf88c5e441e28dbb4,
+		0x4fe27f9f96615270,
+		0x514d4ba49c2b14fe,
+		0x19,
+		0xec3fabc192b01799,
+		0x382b38cee8ee5375,
+		0x3bfb6c3f0e616572,
+		0x514abd0cf6c7bc86,
+		0x47521b1361dcc546,
+		0x178093843f863d14,
+		0xad1003c5d28918e7,
+		0x738450e42495bc81,
+		0xaf947c59af5e4047,
+		0x4653fb0685084ef2,
+		0x57fde2062ae35bf,
+		0xf02a3ac068ee110b,
+		0xa3630dafb8ae2d7,
+		0xce0dc874eaf9b55c,
+		0x9a95f6cff5b55c7e,
+		0x626d76abfed00c7b,
+		0xa0c1cf1251c204ad,
+		0xdaebd3006321052c,
+		0x3d4bd48b625a8065,
+		0x7f1e584e071f6ed2,
+		0x720574f0501caed3,
+		0xe3260ba93d23540a,
+		0x19,
+		0xe376678d843ce55e,
+		0x66f3860d7514e7fc,
+		0x7817f3dfff8b4ffa,
+		0x3929624a9def725b,
+		0x126ca37f215a80a,
+		0xfce2f5d02762a303,
+		0x1bc927375febbad7,
+		0x85b481e5243f60bf,
+		0x2d3c5f42a39c91a0,
+		0x811719919351ae8,
+		0xf669de0add993131,
+		0xab1cbd41d8c1e335,
+		0x9322ed4c0bc2df01,
+		0x51c3c0983d4284e5,
+		0x94178e291145c231,
+		0xfd0f1a973d6b2085,
+		0xd427ad96e2b39719,
+		0x8a52437fecaac06b,
+		0xdc20ee4b8c4c9a80,
+		0xa2c98e9549da2100,
+		0x1603fe12613db5b6,
+		0xe174929433c5505,
+		0x19,
+		0x7de38bae084da92d,
+		0x5b848442237e8a9b,
+		0xf6c705da84d57310,
+		0x31e6a4bdb6a49017,
+		0x889489706e5c5c0f,
+		0xe4a205459692a1b,
+		0xbac3fa75ee26f299,
+		0x5f5894f4057d755e,
+		0xb0dc3ecd724bb076,
+		0x5e34d8554a6452ba,
+		0x4f78fd8c1fdcc5f,
+		0x3d4eab2b8ef5f796,
+		0xcfff421583896e22,
+		0x4143cb32d39ac3d9,
+		0x22365051b78a5b65,
+		0x6f7fd010d027c9b6,
+		0xd9dd36fba77522ab,
+		0xa44cf1cb33e37165,
+		0x3fc83d3038c86417,
+		0xc4588d418e88d270,
+		0xce1320f10ab80fe2,
+		0xdb5eadbbec18de5d,
+		0x19,
+		0x4dd19c38779512ea,
+		0xdb79ba02704620e9,
+		0x92a29a3675a5d2be,
+		0xd5177029fe495166,
+		0xd32b3298a13330c1,
+		0x251c4a3eb2c5f8fd,
+		0xe1c48b26e0d98825,
+		0x3301d3362a4ffccb,
+		0x9bb6c88de8cd178,
+		0xdc05b676564f538a,
+		0x60192d883e473fee,
+		0x1183dfce7c454afd,
+		0x21cea4aa3d3ed949,
+		0xfce6f70303f2304,
+		0x19557d34b55551be,
+		0x4c56f689afc5bbc9,
+		0xa1e920844334f944,
+		0xbad66d423d2ec861,
+		0xf318c785dc9e0479,
+		0x99e2032e765ddd81,
+		0x400ccc9906d66f45,
+		0xe1197454db2e0dd9,
+		0x19,
+		0x16b9774801ac44a0,
+		0x3cb8411e786d3c8e,
+		0xa86e9cf505072491,
+		0x178928152e109ae,
+		0x5317b905a6e1ab7b,
+		0xda20b3be7f53d59f,
+		0xcb97dedecebee9ad,
+		0x4bd545218c59f58d,
+		0x77dc8d856c05a44a,
+		0x87948589e4f243fd,
+		0x7e5217af969952c2,
+		0x84d1ecc4d53d2ff1,
+		0xd8af8b9ceb4e11b6,
+		0x335856bb527b52f4,
+		0xc756f17fb59be595,
+		0xc0654e4ea5553a78,
+		0x9e9a46b61f2ea942,
+		0x14fc8b5b3b809127,
+		0xd7009f0f103be413,
+		0x3e0ee7b7a9fb4601,
+		0xa74e888922085ed7,
+		0xe80a7cde3d4ac526,
+		0x19,
+		0xbc58987d06a84e4d,
+		0xb5d420244c9cae3,
+		0xa3c4711b938c02c0,
+		0x3aace640a3e03990,
+		0x865a0f3249aacd8a,
+		0x8d00b2a7dbed06c7,
+		0x6eacb905beb7e2f8,
+		0x45322b216ec3ec7,
+		0xeb9de00d594828e6,
+		0x88c5f20df9e5c26,
+		0xf555f4112b19781f,
+		0x238aa6daa612186d,
+		0x9137a5c630bad4b4,
+		0xc7db3817870c5eda,
+		0x217e4f04e5718dc9,
+		0xcae814e2817bd99d,
+		0xe3292e7ab770a8ba,
+		0x7bb36ef70b6b9482,
+		0x3c7835fb85bca2d3,
+		0xfe2cdf8ee3c25e86,
+		0x61b3915ad7274b20,
+		0xeab75ca7c918e4ef,
+		0x19,
+		0xa8cedbff1813d3a7,
+		0x50dcaee0fd27d164,
+		0xf1cb02417e23bd82,
+		0xfaf322786e2abe8b,
+		0x937a4315beb5d9b6,
+		0x1b18992921a11d85,
+		0x7d66c4368b3c497b,
+		0xe7946317a6b4e99,
+		0xbe4430134182978b,
+		0x3771e82493ab262d,
+		0xa671690d8095ce82,
+		0xd6e15ffc055e154e,
+		0xec67881f381a32bf,
+		0xfbb1196092bf409c,
+		0xdc9d2e07830ba226,
+		0x698ef3245ff7988,
+		0x194fae2974f8b576,
+		0x7a5d9bea6ca4910e,
+		0x7aebfea95ccdd1c9,
+		0xf9bd38a67d5f0e86,
+		0xfa65539de65492d8,
+		0xf0dfcbe7653ff787,
+		0x19,
+		0xb035585f6e929d9d,
+		0xba1579c7e219b954,
+		0xcb201cf846db4ba3,
+		0x287bf9177372cf45,
+		0xa350e4f61147d0a6,
+		0xd5d0ecfb50bcff99,
+		0x2e166aa6c776ed21,
+		0xe1e66c991990e282,
+		0x662b329b01e7bb38,
+		0x8aa674b36144d9a9,
+		0xcbabf78f97f95e65,
+		0xbd87ad390420258,
+		0xad8617bca9e33c8,
+		0xc00ad377a1e2666,
+		0xac6fc58b3f0518f,
+		0xc0cc8a892cc4173,
+		0xc210accb117bc21,
+		0xb73630dbb46ca18,
+		0xc8be4920cbd4a54,
+		0xbfe877a21be1690,
+		0xae790559b0ded81,
+		0xbf50db2f8d6ce31,
+		0x19,
+		0xeec24b15a06b53fe,
+		0xc8a7aa07c5633533,
+		0xefe9c6fa4311ad51,
+		0xb9173f13977109a1,
+		0x69ce43c9cc94aedc,
+		0xecf623c9cd118815,
+		0x28625def198c33c7,
+		0xccfc5f7de5c3636a,
+		0xf5e6c40f1621c299,
+		0xcec0e58c34cb64b1,
+		0xa868ea113387939f,
+		0xcf29427ff7c58,
+		0xbd9b3cf49eec8,
+		0xd1dc8aa81fb26,
+		0xbc792d5c394ef,
+		0xd2ae0b2266453,
+		0xd413f12c496c1,
+		0xc84128cfed618,
+		0xdb5ebd48fc0d4,
+		0xd1b77326dcb90,
+		0xbeb0ccc145421,
+		0xd10e5b22b11d1,
+		0x19,
+		0xd8dddbdc5ce4ef45,
+		0xacfc51de8131458c,
+		0x146bb3c0fe499ac0,
+		0x9e65309f15943903,
+		0x80d0ad980773aa70,
+		0xf97817d4ddbf0607,
+		0xe4626620a75ba276,
+		0xdfdc7fd6fc74f66,
+		0xf464864ad6f2bb93,
+		0x2d55e52a5d44414,
+		0xdd8de62487c40925,
+		0xe24c99adad8,
+		0xcf389ed4bc8,
+		0xe580cbf6966,
+		0xcde5fd7e04f,
+		0xe63628041b3,
+		0xe7e81a87361,
+		0xdabe78f6d98,
+		0xefb14cac554,
+		0xe5574743b10,
+		0xd05709f42c1,
+		0xe4690c96af1,
+		0x19,
+		0xc15acf44759545a3,
+		0xcbfdcf39869719d4,
+		0x33f62042e2f80225,
+		0x2599c5ead81d8fa3,
+		0xb306cb6c1d7c8d0,
+		0x658c80d3df3729b1,
+		0xe8d1b2b21b41429c,
+		0xa1b67f09d4b3ccb8,
+		0xe1adf8b84437180,
+		0xd593a5e584af47b,
+		0xa023d94c56e151c7,
+		0xf7157bc98,
+		0xe3006d948,
+		0xfa65811e6,
+		0xe0d127e2f,
+		0xfc18bfe53,
+		0xfd002d901,
+		0xeed6461d8,
+		0x1068562754,
+		0xfa0236f50,
+		0xe3af13ee1,
+		0xfa460f6d1,
+		0x19,
+		0x49026cc3a4afc5a6,
+		0xe06dff00ab25b91b,
+		0xab38c561e8850ff,
+		0x92c3c8275e105eeb,
+		0xb65256e546889bd0,
+		0x3c0468236ea142f6,
+		0xee61766b889e18f2,
+		0xa206f41b12c30415,
+		0x2fe9d756c9f12d1,
+		0xe9633210630cbf12,
+		0x1ffea9fe85a0b0b1,
+		0x11131738,
+		0xf56d588,
+		0x11050f86,
+		0xf848f4f,
+		0x111527d3,
+		0x114369a1,
+		0x106f2f38,
+		0x11e2ca94,
+		0x110a29f0,
+		0xfa9f5c1,
+		0x10f625d1,
+		0x19,
+		0x81d1ae8cc50240f3,
+		0xf4c77a079a4607d7,
+		0xed446b2315e3efc1,
+		0xb0a6b70915178c3,
+		0xb11ff3e089f15d9a,
+		0x1d4dba0b7ae9cc18,
+		0x65d74e2f43b48d05,
+		0xa2df8c6b8ae0804a,
+		0xa4e6f0a8c33348a6,
+		0xc0a26efc7be5669b,
+		0xa6b6582c547d0d60,
+		0x11f718,
+		0x10b6c8,
+		0x134a96,
+		0x10cf7f,
+		0x124d03,
+		0x13f8a1,
+		0x117c58,
+		0x132c94,
+		0x134fc0,
+		0x10a091,
+		0x128961,
+		0x19,
+		0x84afc741f1c13213,
+		0x2f8f43734fc906f3,
+		0xde682d72da0a02d9,
+		0xbb005236adb9ef2,
+		0x5bdf35c10a8b5624,
+		0x739a8a343950010,
+		0x52f515f44785cfbc,
+		0xcbaf4e5d82856c60,
+		0xac9ea09074e3e150,
+		0x8f0fa011a2035fb0,
+		0x1a37905d8450904a,
+		0x1300,
+		0x1750,
+		0x114e,
+		0x131f,
+		0x167b,
+		0x1371,
+		0x1230,
+		0x182c,
+		0x1368,
+		0xf31,
+		0x15c9,
+		0x19,
+		0x3abeb80def61cc85,
+		0x9d19c9dd4eac4133,
+		0x75a652d9641a985,
+		0x9daf69ae1b67e667,
+		0x364f71da77920a18,
+		0x50bd769f745c95b1,
+		0xf223d1180dbbf3fc,
+		0x2f885e584e04aa99,
+		0xb69a0fa70aea684a,
+		0x9584acaa6e062a0,
+		0xbc051640145b19b,
+		0x14,
+		0x22,
+		0x12,
+		0x27,
+		0xd,
+		0xd,
+		0x1c,
+		0x2,
+		0x10,
+		0x29,
+		0xf,
+	}
+
 	// C is a constant array of element
 	C []*ffg.Element
+	// C_OPT is a constant array of element
+	C_OPT []*ffg.Element
 	// M is a matrix
 	M [][]*ffg.Element
+	// P is a matrix
+	P [][]*ffg.Element
+	// S is a array of element
+	S []*ffg.Element
 )
 
 func init() {
@@ -117,15 +924,28 @@ func init() {
 		C = append(C, ffg.NewElementFromUint64(c[i]))
 	}
 
+	for i := 0; i < len(c_opt); i++ {
+		C_OPT = append(C_OPT, ffg.NewElementFromUint64(c_opt[i]))
+	}
+
+	for i := 0; i < len(s); i++ {
+		S = append(S, ffg.NewElementFromUint64(s[i]))
+	}
+
 	for i := 0; i < mLen; i++ {
-		var row []*ffg.Element
+		var (
+			mRow []*ffg.Element
+			pRow []*ffg.Element
+		)
 		for j := 0; j < mLen; j++ {
-			ele := ffg.NewElementFromUint64(mcirc[(-i+j+mLen)%mLen])
+			ele := ffg.NewElementFromUint64(mcirc[(i-j+mLen)%mLen])
 			if i == j {
 				ele = ffg.NewElementFromUint64(mcirc[0] + mdiag[i])
 			}
-			row = append(row, ele)
+			mRow = append(mRow, ele)
+			pRow = append(pRow, ffg.NewElementFromUint64(p[i][j]))
 		}
-		M = append(M, row)
+		M = append(M, mRow)
+		P = append(P, pRow)
 	}
 }
diff --git a/goldenposeidon/poseidon.go b/goldenposeidon/poseidon.go
index c4be7ba..0340905 100644
--- a/goldenposeidon/poseidon.go
+++ b/goldenposeidon/poseidon.go
@@ -29,8 +29,15 @@ func ark(state []*ffg.Element, it int) {
 	}
 }
 
+// arkOpt computes Add-Round Key, from the paper https://eprint.iacr.org/2019/458.pdf
+func arkOpt(state []*ffg.Element, it int) {
+	for i := 0; i < len(state); i++ {
+		state[i].Add(state[i], C_OPT[it+i])
+	}
+}
+
 // mix returns [[matrix]] * [vector]
-func mix(state []*ffg.Element) []*ffg.Element {
+func mix(state []*ffg.Element, opt bool) []*ffg.Element {
 	mul := zero()
 	newState := make([]*ffg.Element, mLen)
 	for i := 0; i < mLen; i++ {
@@ -39,7 +46,11 @@ func mix(state []*ffg.Element) []*ffg.Element {
 	for i := 0; i < mLen; i++ {
 		newState[i].SetUint64(0)
 		for j := 0; j < mLen; j++ {
-			mul.Mul(M[i][j], state[j])
+			if opt {
+				mul.Mul(P[j][i], state[j])
+			} else {
+				mul.Mul(M[j][i], state[j])
+			}
 			newState[i].Add(newState[i], mul)
 		}
 	}
@@ -65,7 +76,61 @@ func Hash(inpBI [NROUNDSF]uint64, capBI [CAPLEN]uint64) ([CAPLEN]uint64, error)
 			exp7(state[0])
 		}
 
-		state = mix(state)
+		state = mix(state, false)
+	}
+
+	return [CAPLEN]uint64{
+		state[0].ToUint64Regular(),
+		state[1].ToUint64Regular(),
+		state[2].ToUint64Regular(),
+		state[3].ToUint64Regular(),
+	}, nil
+}
+
+// NeptuneHash computes the hash for the given inputs
+func NeptuneHash(inpBI [NROUNDSF]uint64, capBI [CAPLEN]uint64) ([CAPLEN]uint64, error) {
+	state := make([]*ffg.Element, mLen)
+	for i := 0; i < NROUNDSF; i++ {
+		state[i] = ffg.NewElement().SetUint64(inpBI[i])
+	}
+	for i := 0; i < CAPLEN; i++ {
+		state[i+NROUNDSF] = ffg.NewElement().SetUint64(capBI[i])
+	}
+
+	for i := 0; i < mLen; i++ {
+		state[i].Add(state[i], C_OPT[i])
+	}
+
+	for r := 0; r < NROUNDSF/2; r++ {
+		exp7state(state)
+		arkOpt(state, (r+1)*mLen)
+		state = mix(state, r == NROUNDSF/2-1)
+	}
+
+	for r := 0; r < NROUNDSP; r++ {
+		exp7(state[0])
+		state[0].Add(state[0], C_OPT[(NROUNDSF/2+1)*mLen+r])
+
+		s0 := zero()
+		mul := zero()
+		mul.Mul(S[(mLen*2-1)*r], state[0])
+		s0.Add(s0, mul)
+		for i := 1; i < mLen; i++ {
+			mul.Mul(S[(mLen*2-1)*r+i], state[i])
+			s0.Add(s0, mul)
+			mul.Mul(S[(mLen*2-1)*r+mLen+i-1], state[0])
+			state[i].Add(state[i], mul)
+		}
+		state[0] = s0
+	}
+
+	for r := 0; r < NROUNDSF/2; r++ {
+		exp7state(state)
+		if r < NROUNDSF/2-1 {
+			arkOpt(state, (NROUNDSF/2+1+r)*mLen+NROUNDSP)
+		}
+
+		state = mix(state, false)
 	}
 
 	return [CAPLEN]uint64{
diff --git a/goldenposeidon/poseidon_test.go b/goldenposeidon/poseidon_test.go
index cd108d6..8cdae83 100644
--- a/goldenposeidon/poseidon_test.go
+++ b/goldenposeidon/poseidon_test.go
@@ -1,6 +1,7 @@
 package poseidon
 
 import (
+	"fmt"
 	"testing"
 
 	"github.com/stretchr/testify/assert"
@@ -8,13 +9,24 @@ import (
 
 const prime uint64 = 18446744069414584321
 
-func TestPoseidonHash(t *testing.T) {
+func compareHash(inpBI [NROUNDSF]uint64, capBI [CAPLEN]uint64) ([CAPLEN]uint64, error) {
+	h, err := Hash(inpBI, capBI)
+	h1, _ := NeptuneHash(inpBI, capBI)
+
+	if h != h1 {
+		return h, fmt.Errorf("Not same")
+	}
+
+	return h, err
+}
+
+func TestPoseidonHashCompare(t *testing.T) {
 	b0 := uint64(0)
 	b1 := uint64(1)
 	bm1 := prime - 1
 	bM := prime
 
-	h, err := Hash([NROUNDSF]uint64{b0, b0, b0, b0, b0, b0, b0, b0}, [CAPLEN]uint64{b0, b0, b0, b0})
+	h, err := compareHash([NROUNDSF]uint64{b0, b0, b0, b0, b0, b0, b0, b0}, [CAPLEN]uint64{b0, b0, b0, b0})
 	assert.Nil(t, err)
 	assert.Equal(t,
 		[CAPLEN]uint64{
@@ -25,7 +37,7 @@ func TestPoseidonHash(t *testing.T) {
 		}, h,
 	)
 
-	h, err = Hash([NROUNDSF]uint64{b1, b1, b1, b1, b1, b1, b1, b1}, [CAPLEN]uint64{b1, b1, b1, b1})
+	h, err = compareHash([NROUNDSF]uint64{b1, b1, b1, b1, b1, b1, b1, b1}, [CAPLEN]uint64{b1, b1, b1, b1})
 	assert.Nil(t, err)
 	assert.Equal(t,
 		[CAPLEN]uint64{
@@ -36,7 +48,7 @@ func TestPoseidonHash(t *testing.T) {
 		}, h,
 	)
 
-	h, err = Hash([NROUNDSF]uint64{b1, b1, b1, b1, b1, b1, b1, b1}, [CAPLEN]uint64{b1, b1, b1, b1})
+	h, err = compareHash([NROUNDSF]uint64{b1, b1, b1, b1, b1, b1, b1, b1}, [CAPLEN]uint64{b1, b1, b1, b1})
 	assert.Nil(t, err)
 	assert.Equal(t,
 		[CAPLEN]uint64{
@@ -47,7 +59,7 @@ func TestPoseidonHash(t *testing.T) {
 		}, h,
 	)
 
-	h, err = Hash(
+	h, err = compareHash(
 		[NROUNDSF]uint64{bm1, bm1, bm1, bm1, bm1, bm1, bm1, bm1},
 		[CAPLEN]uint64{bm1, bm1, bm1, bm1},
 	)
@@ -61,7 +73,7 @@ func TestPoseidonHash(t *testing.T) {
 		}, h,
 	)
 
-	h, err = Hash([NROUNDSF]uint64{bM, bM, bM, bM, bM, bM, bM, bM}, [CAPLEN]uint64{b0, b0, b0, b0})
+	h, err = compareHash([NROUNDSF]uint64{bM, bM, bM, bM, bM, bM, bM, bM}, [CAPLEN]uint64{b0, b0, b0, b0})
 	assert.Nil(t, err)
 	assert.Equal(t,
 		[CAPLEN]uint64{
@@ -72,7 +84,7 @@ func TestPoseidonHash(t *testing.T) {
 		}, h,
 	)
 
-	h, err = Hash([NROUNDSF]uint64{
+	h, err = compareHash([NROUNDSF]uint64{
 		uint64(923978),
 		uint64(235763497586),
 		uint64(9827635653498),
@@ -92,3 +104,21 @@ func TestPoseidonHash(t *testing.T) {
 		}, h,
 	)
 }
+
+func BenchmarkPoseidonHash(b *testing.B) {
+	inp := [NROUNDSF]uint64{1, 2, 3, 4, 5, 6, 7, 8}
+	cap := [CAPLEN]uint64{10, 11, 12, 13}
+
+	for i := 0; i < b.N; i++ {
+		Hash(inp, cap) //nolint:errcheck,gosec
+	}
+}
+
+func BenchmarkPoseidonNeptuneHash(b *testing.B) {
+	inp := [NROUNDSF]uint64{1, 2, 3, 4, 5, 6, 7, 8}
+	cap := [CAPLEN]uint64{10, 11, 12, 13}
+
+	for i := 0; i < b.N; i++ {
+		Hash(inp, cap) //nolint:errcheck,gosec
+	}
+}
diff --git a/poseidon/poseidon_test.go b/poseidon/poseidon_test.go
index b9a0234..86a2d37 100644
--- a/poseidon/poseidon_test.go
+++ b/poseidon/poseidon_test.go
@@ -213,6 +213,27 @@ func BenchmarkPoseidonHash8Inputs(b *testing.B) {
 	}
 }
 
+func BenchmarkPoseidonHash12Inputs(b *testing.B) {
+	bigArray12 := []*big.Int{
+		big.NewInt(1),
+		big.NewInt(2),
+		big.NewInt(3),
+		big.NewInt(4),
+		big.NewInt(5),
+		big.NewInt(6),
+		big.NewInt(7),
+		big.NewInt(8),
+		big.NewInt(9),
+		big.NewInt(10),
+		big.NewInt(11),
+		big.NewInt(12),
+	}
+
+	for i := 0; i < b.N; i++ {
+		Hash(bigArray12) //nolint:errcheck,gosec
+	}
+}
+
 func BenchmarkPoseidonHash16Inputs(b *testing.B) {
 	bigArray16 := []*big.Int{
 		big.NewInt(1),