status-im/c-kzg-4844
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Change the primitive root from 5 to 7 (#5)

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Ben Edgington 2021-06-11 14:22:47 +01:00 committed by GitHub
parent e23d7457b6
commit 32becfefcf
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GPG Key ID: 4AEE18F83AFDEB23
4 changed files with 67 additions and 67 deletions
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16
src/das_extension_test.c
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@ -26,14 +26,14 @@ void das_extension_test_known(void) {
fr_t *data; fr_t *data;
// The expected output (from go-kzg): // The expected output (from go-kzg):
const uint64_t expected_u[8][4] = { const uint64_t expected_u[8][4] = {
{0x740e9eb4cef44b7fL, 0xb66dfe6438d1316aL, 0xc62c567f7b9c5e97L, 0x5a4f75d3eb7951c4L}, {0xa0c43757db972d7dL, 0x79d15a1e0677962cL, 0xf678865c0c95fa6aL, 0x4e85fd4814f96825L},
{0x52617bb5c60d8fabL, 0x0e225ff8d6c658d9L, 0x73ce7b30718ed2aeL, 0x0d94457acc0cb888L}, {0xad9f844939f2705dL, 0x319e440c9f3b0325L, 0x4cbd29a60e160a28L, 0x665961d85d90c4c0L},
{0x8bf0614a310bb489L, 0xb14ca59c512a2a94L, 0xdfbbb4ba1802749cL, 0x199e317f3e242b82L}, {0x5f3ac8a72468d28bL, 0xede949e28383c5d2L, 0xaf6f84dd8708d8c9L, 0x2567aa0b14a41521L},
{0x98cbae3b8f66f769L, 0x69198f8ae9ed978dL, 0x360058041982845aL, 0x3171960f86bb881dL}, {0x25abe312b96aadadL, 0x4abf043f091ff417L, 0x43824b53e09536dbL, 0x195dbe06a28ca227L},
{0x8bf0614a310bb489L, 0xb14ca59c512a2a94L, 0xdfbbb4ba1802749cL, 0x199e317f3e242b82L}, {0x5f3ac8a72468d28bL, 0xede949e28383c5d2L, 0xaf6f84dd8708d8c9L, 0x2567aa0b14a41521L},
{0x52617bb5c60d8fabL, 0x0e225ff8d6c658d9L, 0x73ce7b30718ed2aeL, 0x0d94457acc0cb888L}, {0xad9f844939f2705dL, 0x319e440c9f3b0325L, 0x4cbd29a60e160a28L, 0x665961d85d90c4c0L},
{0x740e9eb4cef44b7fL, 0xb66dfe6438d1316aL, 0xc62c567f7b9c5e97L, 0x5a4f75d3eb7951c4L}, {0xa0c43757db972d7dL, 0x79d15a1e0677962cL, 0xf678865c0c95fa6aL, 0x4e85fd4814f96825L},
{0xc2735a57e47de950L, 0xa665548b548a12beL, 0x3040233ff907b7f0L, 0x2753864e0ac8841bL}}; {0x7f171458d2b071a9L, 0xd185bbb2a46cbd9bL, 0xa41aab0d02886e80L, 0x01cacceef58ccee9L}};
TEST_CHECK(C_KZG_OK == new_fft_settings(&fs, 4)); TEST_CHECK(C_KZG_OK == new_fft_settings(&fs, 4));
half = fs.max_width / 2; half = fs.max_width / 2;

60
src/fft_common.h
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@ -30,7 +30,7 @@
* The decimal values may be calculated with the following Python code: * The decimal values may be calculated with the following Python code:
* @code{.py} * @code{.py}
* MODULUS = 52435875175126190479447740508185965837690552500527637822603658699938581184513 * MODULUS = 52435875175126190479447740508185965837690552500527637822603658699938581184513
* PRIMITIVE_ROOT = 5 * PRIMITIVE_ROOT = 7
* [pow(PRIMITIVE_ROOT, (MODULUS - 1) // (2**i), MODULUS) for i in range(32)] * [pow(PRIMITIVE_ROOT, (MODULUS - 1) // (2**i), MODULUS) for i in range(32)]
* @endcode * @endcode
* *
@ -45,35 +45,35 @@ static const uint64_t scale2_root_of_unity[][4] = {
{0x0000000000000001L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L}, {0x0000000000000001L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L},
{0xffffffff00000000L, 0x53bda402fffe5bfeL, 0x3339d80809a1d805L, 0x73eda753299d7d48L}, {0xffffffff00000000L, 0x53bda402fffe5bfeL, 0x3339d80809a1d805L, 0x73eda753299d7d48L},
{0x0001000000000000L, 0xec03000276030000L, 0x8d51ccce760304d0L, 0x0000000000000000L}, {0x0001000000000000L, 0xec03000276030000L, 0x8d51ccce760304d0L, 0x0000000000000000L},
{0x8dd702cb688bc087L, 0xa032824078eaa4feL, 0xa733b23a98ca5b22L, 0x3f96405d25a31660L}, {0x7228fd3397743f7aL, 0xb38b21c28713b700L, 0x8c0625cd70d77ce2L, 0x345766f603fa66e7L},
{0x95df4b360411fe73L, 0x1ef4e672ebc1e1bbL, 0x6e92a9c460afca4aL, 0x4f2c596e753e4fccL}, {0x53ea61d87742bcceL, 0x17beb312f20b6f76L, 0xdd1c0af834cec32cL, 0x20b1ce9140267af9L},
{0x9733f3a6ba60eaa6L, 0xbd7fdf9c77487ae7L, 0xd84f8612c8b6cc00L, 0x476fa2fb6162ffabL}, {0x360c60997369df4eL, 0xbf6e88fb4c38fb8aL, 0xb4bcd40e22f55448L, 0x50e0903a157988baL},
{0xd2fc5e69ac5db47fL, 0xa12a70a615d0b8e4L, 0x293b1d67bc8de5d9L, 0x0e4840ac57f86f5eL}, {0x8140d032f0a9ee53L, 0x2d967f4be2f95155L, 0x14a1e27164d8fdbdL, 0x45af6345ec055e4dL},
{0xb750da4cab28e208L, 0x501dff643be95635L, 0x8cbe2437f0b4b276L, 0x07d0c802a94a946eL}, {0x5130c2c1660125beL, 0x98d0caac87f5713cL, 0xb7c68b4d7fdd60d0L, 0x6898111413588742L},
{0x2cabadec2fe322b8L, 0x752c84f315412560L, 0x32a732ae1a3b0aefL, 0x2e95da59a33dcbf2L}, {0x4935bd2f817f694bL, 0x0a0865a899e8deffL, 0x6b368121ac0cf4adL, 0x4f9b4098e2e9f12eL},
{0x33811ea1fe0c65f4L, 0x15c1ad4c687f28a2L, 0xecfbede342dee7f4L, 0x1bb466679a5d88b1L}, {0x4541b8ff2ee0434eL, 0xd697168a3a6000feL, 0x39feec240d80689fL, 0x095166525526a654L},
{0xd58a5af42d010ff9L, 0x79efd6b0570bf109L, 0x3ed6d55a6350721dL, 0x2f27b09858f43cefL}, {0x3c28d666a5c2d854L, 0xea437f9626fc085eL, 0x8f4de02c0f776af3L, 0x325db5c3debf77a1L},
{0x74a1f6718c130477L, 0xa534af14b61e0abeL, 0xeb674a1a620890d7L, 0x43527a8bca252472L}, {0x4a838b5d59cd79e5L, 0x55ea6811be9c622dL, 0x09f1ca610a08f166L, 0x6d031f1b5c49c834L},
{0x450d9f977ea8ee05L, 0x565af17137d56fc0L, 0xe155cb4893f9e9acL, 0x110cebd0c8e9101bL}, {0xe206da11a5d36306L, 0x0ad1347b378fbf96L, 0xfc3e8acfe0f8245fL, 0x564c0a11a0f704f4L},
{0x23c9159959a0be92L, 0x87d188ce7a027759L, 0x70491431cab3c3ccL, 0x0ac00eb8b3f7f8daL}, {0x6fdd00bfc78c8967L, 0x146b58bc434906acL, 0x2ccddea2972e89edL, 0x485d512737b1da3dL},
{0x13e96ade69583404L, 0x82c057275306243dL, 0x77e48bf529ca9f2aL, 0x50646ac81fe19595L}, {0x034d2ff22a5ad9e1L, 0xae4622f6a9152435L, 0xdc86b01c0d477fa6L, 0x56624634b500a166L},
{0xe6a354dda97eccd4L, 0x39929d2e88fbbc57L, 0xa22ba63dd6e7b1c8L, 0x42c22911f5f07f43L}, {0xfbd047e11279bb6eL, 0xc8d5f51db3f32699L, 0x483405417a0cbe39L, 0x3291357ee558b50dL},
{0x137b458acfc35f7aL, 0x0caba63a29c01b06L, 0x0409ee987a02402cL, 0x6709c6cd56aa725bL}, {0xd7118f85cd96b8adL, 0x67a665ae1fcadc91L, 0x88f39a78f1aeb578L, 0x2155379d12180caaL},
{0x10251f7d8831e03eL, 0x77d85a937ff858ecL, 0xebe905bd4fb9ac5cL, 0x05deb333f8727901L}, {0x08692405f3b70f10L, 0xcd7f2bd6d0711b7dL, 0x473a2eef772c33d6L, 0x224262332d8acbf4L},
{0xbf87b689b9009408L, 0x4f730e7ddd3ccc96L, 0xfd7f05ba4610300cL, 0x5ef5e8db0b8ac903L}, {0x6f421a7d8ef674fbL, 0xbb97a3bf30ce40fdL, 0x652f717ae1c34bb0L, 0x2d3056a530794f01L},
{0x6499688417cd0c14L, 0xa672867368812f7fL, 0x2e1d9a1922cc3253L, 0x3a689e83aa0a1d80L}, {0x194e8c62ecb38d9dL, 0xad8e16e84419c750L, 0xdf625e80d0adef90L, 0x520e587a724a6955L},
{0x20b53cbe41144deaL, 0x870c46fac2f0fcbdL, 0x556c35f6537d6971L, 0x3436287f5f686d91L}, {0xfece7e0e39898d4bL, 0x2f69e02d265e09d9L, 0xa57a6e07cb98de4aL, 0x03e1c54bcb947035L},
{0x007e082a436ba2e7L, 0x67c6630f9116e877L, 0x36f8f165fb4460f7L, 0x6eee34d57e7046e0L}, {0xcd3979122d3ea03aL, 0x46b3105f04db5844L, 0xc70d0874b0691d4eL, 0x47c8b5817018af4fL},
{0xc5b670eea53a56d1L, 0x127d1f4253037d7bL, 0x57d4257ea722c2e2L, 0x03ae26a333cbd838L}, {0xc6e7a6ffb08e3363L, 0xe08fec7c86389beeL, 0xf2d38f10fbb8d1bbL, 0x0abe6a5e5abcaa32L},
{0x1e91484876504cf8L, 0x55bbbf1eb63edd02L, 0xbcdafec84e55aa02L, 0x5145c4cd2dc0beb0L}, {0x5616c57de0ec9eaeL, 0xc631ffb2585a72dbL, 0x5121af06a3b51e3cL, 0x73560252aa0655b2L},
{0x5b90153a1ab70e2cL, 0x8deffa3175fb0ab8L, 0xc553ae2346900c95L, 0x1d31dcdc6bd3118cL}, {0x92cf4deb77bd779cL, 0x72cf6a8029b7d7bcL, 0x6e0bcd91ee762730L, 0x291cf6d68823e687L},
{0x801c894c59a2e8ebL, 0xbc535c5ce12fc974L, 0x95508d2747d39803L, 0x16d9d3cdac5d094fL}, {0xce32ef844e11a51eL, 0xc0ba12bb3da64ca5L, 0x0454dc1edc61a1a3L, 0x019fe632fd328739L},
{0x810fa372cca1d8beL, 0xc67b8c2882e0bfa7L, 0xdbb4edf0e2d35bc2L, 0x712d15805087c995L}, {0x531a11a0d2d75182L, 0x02c8118402867ddcL, 0x116168bffbedc11dL, 0x0a0a77a3b1980c0dL},
{0xeb162203fd88f133L, 0xac96c38ff010ea74L, 0x4307987fe64cfc70L, 0x350fe98d37b7a114L}, {0xe2d0a7869f0319edL, 0xb94f1101b1d7a628L, 0xece8ea224f31d25dL, 0x23397a9300f8f98bL},
{0xaba2f51842f2a254L, 0x4d7f3c3aa71efc0cL, 0x97ae418dd274a80aL, 0x2967385d5e3e7682L}, {0xd7b688830a4f2089L, 0x6558e9e3f6ac7b41L, 0x99e276b571905a7dL, 0x52dd465e2f094256L},
{0x75c55c7b575a0b79L, 0x3ba4a15774a7ded1L, 0xc3974d73a04fccf3L, 0x705aba4f4a939684L}, {0x474650359d8e211bL, 0x84d37b826214abc6L, 0x8da40c1ef2bb4598L, 0x0c83ea7744bf1beeL},
{0x8409a9ea14ebb608L, 0xfad0084e66bac611L, 0x04287254811c1dfbL, 0x086d072b23b30c29L}, {0x694341f608c9dd56L, 0xed3a181fabb30adcL, 0x1339a815da8b398fL, 0x2c6d4e4511657e1eL},
{0xb427c9b367e4756aL, 0xc7537fb902ebc38dL, 0x51de21becd6a205fL, 0x6064ab727923597dL}}; {0x63e7cb4906ffc93fL, 0xf070bb00e28a193dL, 0xad1715b02e5713b5L, 0x4b5371495990693fL}};
/** /**
* Stores the setup and parameters needed for performing FFTs. * Stores the setup and parameters needed for performing FFTs.

26
src/fft_fr_test.c
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@ -20,21 +20,21 @@
const uint64_t inv_fft_expected[][4] = { const uint64_t inv_fft_expected[][4] = {
{0x7fffffff80000008L, 0xa9ded2017fff2dffL, 0x199cec0404d0ec02L, 0x39f6d3a994cebea4L}, {0x7fffffff80000008L, 0xa9ded2017fff2dffL, 0x199cec0404d0ec02L, 0x39f6d3a994cebea4L},
{0x27325dd08ac4cee9L, 0xcbb94f168ddacca9L, 0x6843be68485784b1L, 0x5a6faf9039451673L},
{0x16d00224dcf9382cL, 0xfee079062d1eaa93L, 0x3ce49204a2235046L, 0x163147176461030eL},
{0x10d6917f04735deaL, 0x7e04a13731049a48L, 0x42cbd9ab89d7b1f7L, 0x60546bd624850b42L},
{0x80007fff80000000L, 0x1fe05202bb00adffL, 0x6045d26b3fd26e6bL, 0x39f6d3a994cebea4L},
{0xe3388d354a80ed91L, 0x5849af2fc2cd4521L, 0xe3a64f3f31971b0bL, 0x33f1dda75bc30526L},
{0x16cf0224dcf9382cL, 0x12dd7903b71baa93L, 0xaf92c5362c204b76L, 0x163147176461030dL},
{0xf9925986d0d25e90L, 0xcdf85d0a339d7782L, 0xee7a9a5f0410e423L, 0x2e0d216170831056L},
{0x7fffffff80000000L, 0xa9ded2017fff2dffL, 0x199cec0404d0ec02L, 0x39f6d3a994cebea4L},
{0x066da6782f2da170L, 0x85c546f8cc60e47cL, 0x44bf3da90590f3e1L, 0x45e085f1b91a6cf1L},
{0xe930fdda2306c7d4L, 0x40e02aff48e2b16bL, 0x83a712d1dd818c8fL, 0x5dbc603bc53c7a3aL},
{0x1cc772c9b57f126fL, 0xfb73f4d33d3116ddL, 0x4f9388c8d80abcf9L, 0x3ffbc9abcdda7821L},
{0x7fff7fff80000000L, 0x33dd520044fdadffL, 0xd2f4059cc9cf699aL, 0x39f6d3a994cebea3L},
{0xef296e7ffb8ca216L, 0xd5b902cbcef9c1b6L, 0xf06dfe5c7fca260dL, 0x13993b7d05187205L}, {0xef296e7ffb8ca216L, 0xd5b902cbcef9c1b6L, 0xf06dfe5c7fca260dL, 0x13993b7d05187205L},
{0xe930fdda2306c7d4L, 0x40e02aff48e2b16bL, 0x83a712d1dd818c8fL, 0x5dbc603bc53c7a3aL},
{0xf9925986d0d25e90L, 0xcdf85d0a339d7782L, 0xee7a9a5f0410e423L, 0x2e0d216170831056L},
{0x80007fff80000000L, 0x1fe05202bb00adffL, 0x6045d26b3fd26e6bL, 0x39f6d3a994cebea4L},
{0x27325dd08ac4cee9L, 0xcbb94f168ddacca9L, 0x6843be68485784b1L, 0x5a6faf9039451673L},
{0xe92ffdda2306c7d4L, 0x54dd2afcd2dfb16bL, 0xf6554603677e87beL, 0x5dbc603bc53c7a39L}, {0xe92ffdda2306c7d4L, 0x54dd2afcd2dfb16bL, 0xf6554603677e87beL, 0x5dbc603bc53c7a39L},
{0xd8cda22e753b3117L, 0x880454ec72238f55L, 0xcaf6199fc14a5353L, 0x197df7c2f05866d4L}}; {0x1cc772c9b57f126fL, 0xfb73f4d33d3116ddL, 0x4f9388c8d80abcf9L, 0x3ffbc9abcdda7821L},
{0x7fffffff80000000L, 0xa9ded2017fff2dffL, 0x199cec0404d0ec02L, 0x39f6d3a994cebea4L},
{0xe3388d354a80ed91L, 0x5849af2fc2cd4521L, 0xe3a64f3f31971b0bL, 0x33f1dda75bc30526L},
{0x16d00224dcf9382cL, 0xfee079062d1eaa93L, 0x3ce49204a2235046L, 0x163147176461030eL},
{0xd8cda22e753b3117L, 0x880454ec72238f55L, 0xcaf6199fc14a5353L, 0x197df7c2f05866d4L},
{0x7fff7fff80000000L, 0x33dd520044fdadffL, 0xd2f4059cc9cf699aL, 0x39f6d3a994cebea3L},
{0x066da6782f2da170L, 0x85c546f8cc60e47cL, 0x44bf3da90590f3e1L, 0x45e085f1b91a6cf1L},
{0x16cf0224dcf9382cL, 0x12dd7903b71baa93L, 0xaf92c5362c204b76L, 0x163147176461030dL},
{0x10d6917f04735deaL, 0x7e04a13731049a48L, 0x42cbd9ab89d7b1f7L, 0x60546bd624850b42L}};
void compare_sft_fft(void) { void compare_sft_fft(void) {
// Initialise: ascending values of i (could be anything), and arbitrary size // Initialise: ascending values of i (could be anything), and arbitrary size

32
src/zero_poly_test.c
View File

@ -25,32 +25,32 @@ bool exists[16] = {true, false, false, true, false, true, true, false,
false, false, true, true, false, true, false, true}; false, false, true, true, false, true, false, true};
uint64_t expected_eval_u64[16][4] = { uint64_t expected_eval_u64[16][4] = {
{0xf675fcb368535efaL, 0xe702bee472f5a74cL, 0xb2f500c4418d44d8L, 0x204089b477319517L}, {0xfd5a5130b97ce0c3L, 0xb4748a4cb0f90e6dL, 0x12a1ab34b25b18c1L, 0x5a5ac0c81c9f7ea8L},
{0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L}, {0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L},
{0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L}, {0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L},
{0x2be1bf25823353ecL, 0xe98177cae115131bL, 0xe0de4495f16788fbL, 0x37e5487beb15a91eL}, {0xaa385cbce3dd1657L, 0x2fdab57a38bdb514L, 0x20e022e205dafa53L, 0x14077dd3f5d996b1L},
{0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L}, {0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L},
{0xa8fd50243ec6f6daL, 0xb5863f0c04559733L, 0xbb55a8d735b8ceafL, 0x15856a55a6ba245bL}, {0x194018614b6f7276L, 0xdf2b18f870532376L, 0x1ff427cd5b583fe6L, 0x014d6444ff03dd09L},
{0x40d8d622337027e7L, 0xd0c41e3defe394e5L, 0x25d1a6848cfbe861L, 0x6615977f56ab9ad1L}, {0xcc84c2de684c0ddeL, 0xf1e7ab32aa830d02L, 0x967bf35a2a691f20L, 0x046109731cdf0d3cL},
{0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L}, {0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L},
{0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L}, {0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L},
{0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L}, {0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L},
{0x19b6d37343ac8596L, 0x9ac16b5b3f0c39eaL, 0x1938f2cc6f656899L, 0x2bc6a69eab7ebeadL}, {0x96cddd2924212afbL, 0xeaa4c1f51421d8d8L, 0x3ae969cfa34d0ed1L, 0x6b6c5e876bc3916dL},
{0x75ceddca83d9b1e4L, 0x69917e9ccac289bcL, 0x7564f74fd58cc97aL, 0x7215036c8f20939fL}, {0x449310802f74ad49L, 0x47c940979163037aL, 0x10d311564afb9b2aL, 0x269b8531c369bafbL},
{0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L}, {0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L},
{0x0088e6ba87233593L, 0xcc4a412d77455e7eL, 0x06ce406c147ada85L, 0x44275d7e26f9392cL}, {0xd9af75fe35c16cf1L, 0x068bb140cea92f75L, 0xe769811965e10a47L, 0x48ed97e6745612f2L},
{0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L}, {0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L},
{0x05ced2791378da2bL, 0xd16275df7a713f92L, 0x0cd24cf43668722dL, 0x22635b695b0fd198L}}; {0x7ef1f59bb1677685L, 0x33a637296680e8ceL, 0xaaf62b3f6e016709L, 0x454a299178a4dba9L}};
uint64_t expected_poly_u64[16][4] = { uint64_t expected_poly_u64[16][4] = {
{0x6a20b4c8fbee018eL, 0x34c8bd90143c7a43L, 0xc4a72e43a8f20dbbL, 0x24c14de4b45f2d7bL}, {0xac159e2688bd4333L, 0x3bfef0f00df2ec88L, 0x561dcd0fd4d314d9L, 0x533bd8c1e977024eL},
{0xba227dc25dab47c2L, 0xfa1cdd366cf44de2L, 0x2920a9a04dd15d06L, 0x0174305e712df7baL}, {0x18bc6eedc010ef8dL, 0xc731a3eb4ea2ab70L, 0x5c2589357ae121a8L, 0x04f9108d308f7016L},
{0xa3c8b170d759d6c4L, 0x846e2f5bfc241b81L, 0x1e4c5e807b5793eeL, 0x0758eca45c6dec8aL}, {0x232759f49556ac08L, 0x9776fe2e9f4c613cL, 0x74d5bed4eb2de960L, 0x1f6cf6719bfa0e68L},
{0x2c280194f3795affL, 0x55035b9ba568dd4fL, 0x91dda79960525b60L, 0x3fbfd2edd4a105f3L}, {0xf2f3461e8ab1ae34L, 0xeb220fcc11ef1c80L, 0x7a4637d3a637739bL, 0x19901a58cd177c53L},
{0x537cca635e26d630L, 0xaed6c42a88801d8fL, 0x41b2fdf16c422f7dL, 0x1d45a831fe3bf66eL}, {0x9340f62465a1f4feL, 0xd9cb3ea6de494a11L, 0xee92ebc763cdff5dL, 0x5443e89811b5b9f5L},
{0x037b0169fc698ffdL, 0xe982a4842fc849f0L, 0xdd398294c762e031L, 0x4092c5b8416d2c2fL}, {0x269a255e2e4e48a4L, 0xfadae7a89d9b2f2bL, 0xb5515799b41e1a88L, 0x2e990979a0ffcee5L},
{0x19d4cdbb82bb00fbL, 0x5f31525ea0987c51L, 0xe80dcdb499dca94aL, 0x3aae0972562d375fL}, {0x1c2f3a5759088c29L, 0x2a958d654cf1795fL, 0x9ca121fa43d152d1L, 0x1425239535953093L},
{0x91757d97669b7cc0L, 0x8e9c261ef753ba83L, 0x747c849bb4e1e1d8L, 0x02472328ddfa1df6L}, {0x4c634e2d63ad89fdL, 0xd6ea7bc7da4ebe1aL, 0x9730a8fb88c7c895L, 0x1a01ffae0477c2a8L},
{0x0000000000000001L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L}, {0x0000000000000001L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L},
{0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L}, {0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L},
{0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L}, {0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L, 0x0000000000000000L},