diff --git a/cmake/cpu_features.cmake b/cmake/cpu_features.cmake index a554992caf30..708a8492240a 100644 --- a/cmake/cpu_features.cmake +++ b/cmake/cpu_features.cmake @@ -65,9 +65,9 @@ elseif (ARCH_PPC64LE) # Note that gcc and clang have support for x86 SSE2 intrinsics when building for PowerPC option (POWER9 "Build for Power 9 CPU and above" 0) if(POWER9) - set (COMPILER_FLAGS "${COMPILER_FLAGS} -maltivec -mcpu=power9 -D__SSE2__=1 -DNO_WARN_X86_INTRINSICS") + set (COMPILER_FLAGS "${COMPILER_FLAGS} -maltivec -mcpu=power9 -D__SSE2__=1 -DNO_WARN_X86_INTRINSICS -DHAVE_POWER8=1 -DHAS_ALTIVEC=1") else () - set (COMPILER_FLAGS "${COMPILER_FLAGS} -maltivec -mcpu=power8 -D__SSE2__=1 -DNO_WARN_X86_INTRINSICS") + set (COMPILER_FLAGS "${COMPILER_FLAGS} -maltivec -mcpu=power8 -D__SSE2__=1 -DNO_WARN_X86_INTRINSICS -DHAVE_POWER8=1 -DHAS_ALTIVEC=1") endif () elseif (ARCH_AMD64) diff --git a/src/Common/HashTable/Hash.h b/src/Common/HashTable/Hash.h index f36ab5767666..daf24699dae1 100644 --- a/src/Common/HashTable/Hash.h +++ b/src/Common/HashTable/Hash.h @@ -44,10 +44,16 @@ inline DB::UInt64 intHash64(DB::UInt64 x) #include #endif +#if (defined(__PPC64__) || defined(__powerpc64__)) && __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ +#include "Common/HashTable/crc32_constants.h" +# include "Common/HashTable/vec_crc32.h" +#endif + + + #if defined(__aarch64__) && defined(__ARM_FEATURE_CRC32) #include #endif - /// NOTE: Intel intrinsic can be confusing. /// - https://code.google.com/archive/p/sse-intrinsics/wikis/PmovIntrinsicBug.wiki /// - https://stackoverflow.com/questions/15752770/mm-crc32-u64-poorly-defined @@ -57,6 +63,8 @@ inline DB::UInt64 intHashCRC32(DB::UInt64 x) return _mm_crc32_u64(-1ULL, x); #elif defined(__aarch64__) && defined(__ARM_FEATURE_CRC32) return __crc32cd(-1U, x); +#elif (defined(__PPC64__) || defined(__powerpc64__)) && __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ + return crc32_ppc(-1U, reinterpret_cast(&x), sizeof(x)); #else /// On other platforms we do not have CRC32. NOTE This can be confusing. /// NOTE: consider using intHash32() @@ -69,6 +77,8 @@ inline DB::UInt64 intHashCRC32(DB::UInt64 x, DB::UInt64 updated_value) return _mm_crc32_u64(updated_value, x); #elif defined(__aarch64__) && defined(__ARM_FEATURE_CRC32) return __crc32cd(static_cast(updated_value), x); +#elif (defined(__PPC64__) || defined(__powerpc64__)) && __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ + return crc32_ppc(updated_value, reinterpret_cast(&x), sizeof(x)); #else /// On other platforms we do not have CRC32. NOTE This can be confusing. return intHash64(x) ^ updated_value; diff --git a/src/Common/HashTable/clang_workaround.h b/src/Common/HashTable/clang_workaround.h new file mode 100644 index 000000000000..b3e94fcf8614 --- /dev/null +++ b/src/Common/HashTable/clang_workaround.h @@ -0,0 +1,87 @@ +#ifndef CLANG_WORKAROUND_H +#define CLANG_WORKAROUND_H + +/* + * These stubs fix clang incompatibilities with GCC builtins. + */ + +#ifndef __builtin_crypto_vpmsumw +#define __builtin_crypto_vpmsumw __builtin_crypto_vpmsumb +#endif +#ifndef __builtin_crypto_vpmsumd +#define __builtin_crypto_vpmsumd __builtin_crypto_vpmsumb +#endif + +static inline +__vector unsigned long long __attribute__((overloadable)) +vec_ld(int __a, const __vector unsigned long long* __b) +{ + return (__vector unsigned long long)__builtin_altivec_lvx(__a, __b); +} + +/* + * GCC __builtin_pack_vector_int128 returns a vector __int128_t but Clang + * does not recognize this type. On GCC this builtin is translated to a + * xxpermdi instruction that only moves the registers __a, __b instead generates + * a load. + * + * Clang has vec_xxpermdi intrinsics. It was implemented in 4.0.0. + */ +static inline +__vector unsigned long long __builtin_pack_vector (unsigned long __a, + unsigned long __b) +{ + #if defined(__BIG_ENDIAN__) + __vector unsigned long long __v = {__a, __b}; + #else + __vector unsigned long long __v = {__b, __a}; + #endif + return __v; +} + +/* + * Clang 7 changed the behavior of vec_xxpermdi in order to provide the same + * behavior of GCC. That means code adapted to Clang >= 7 does not work on + * Clang <= 6. So, fallback to __builtin_unpack_vector() on Clang <= 6. + */ +#if !defined vec_xxpermdi || __clang_major__ <= 6 + +static inline +unsigned long __builtin_unpack_vector (__vector unsigned long long __v, + int __o) +{ + return __v[__o]; +} + +#if defined(__BIG_ENDIAN__) +#define __builtin_unpack_vector_0(a) __builtin_unpack_vector ((a), 0) +#define __builtin_unpack_vector_1(a) __builtin_unpack_vector ((a), 1) +#else +#define __builtin_unpack_vector_0(a) __builtin_unpack_vector ((a), 1) +#define __builtin_unpack_vector_1(a) __builtin_unpack_vector ((a), 0) +#endif + +#else + +static inline +unsigned long __builtin_unpack_vector_0 (__vector unsigned long long __v) +{ + #if defined(__BIG_ENDIAN__) + return vec_xxpermdi(__v, __v, 0x0)[0]; + #else + return vec_xxpermdi(__v, __v, 0x3)[0]; + #endif +} + +static inline +unsigned long __builtin_unpack_vector_1 (__vector unsigned long long __v) +{ + #if defined(__BIG_ENDIAN__) + return vec_xxpermdi(__v, __v, 0x3)[0]; + #else + return vec_xxpermdi(__v, __v, 0x0)[0]; + #endif +} +#endif /* vec_xxpermdi */ + +#endif diff --git a/src/Common/HashTable/crc32_constants.h b/src/Common/HashTable/crc32_constants.h new file mode 100644 index 000000000000..f11750aeb367 --- /dev/null +++ b/src/Common/HashTable/crc32_constants.h @@ -0,0 +1,2032 @@ +/* +* +* THIS FILE IS GENERATED WITH +./crc32_constants -r -x 0x11EDC6F41 + +* This is from https://github.com/antonblanchard/crc32-vpmsum/ +* DO NOT MODIFY IT MANUALLY! +* +*/ + +#define CRC 0x1edc6f41 +#define CRC_XOR +#define REFLECT +#define MAX_SIZE_VALUE 32768 + +#ifndef __ASSEMBLER__ +#ifdef CRC_TABLE +static const unsigned int crc_table[] = { + 0x00000000, 0xf26b8303, 0xe13b70f7, 0x1350f3f4, + 0xc79a971f, 0x35f1141c, 0x26a1e7e8, 0xd4ca64eb, + 0x8ad958cf, 0x78b2dbcc, 0x6be22838, 0x9989ab3b, + 0x4d43cfd0, 0xbf284cd3, 0xac78bf27, 0x5e133c24, + 0x105ec76f, 0xe235446c, 0xf165b798, 0x030e349b, + 0xd7c45070, 0x25afd373, 0x36ff2087, 0xc494a384, + 0x9a879fa0, 0x68ec1ca3, 0x7bbcef57, 0x89d76c54, + 0x5d1d08bf, 0xaf768bbc, 0xbc267848, 0x4e4dfb4b, + 0x20bd8ede, 0xd2d60ddd, 0xc186fe29, 0x33ed7d2a, + 0xe72719c1, 0x154c9ac2, 0x061c6936, 0xf477ea35, + 0xaa64d611, 0x580f5512, 0x4b5fa6e6, 0xb93425e5, + 0x6dfe410e, 0x9f95c20d, 0x8cc531f9, 0x7eaeb2fa, + 0x30e349b1, 0xc288cab2, 0xd1d83946, 0x23b3ba45, + 0xf779deae, 0x05125dad, 0x1642ae59, 0xe4292d5a, + 0xba3a117e, 0x4851927d, 0x5b016189, 0xa96ae28a, + 0x7da08661, 0x8fcb0562, 0x9c9bf696, 0x6ef07595, + 0x417b1dbc, 0xb3109ebf, 0xa0406d4b, 0x522bee48, + 0x86e18aa3, 0x748a09a0, 0x67dafa54, 0x95b17957, + 0xcba24573, 0x39c9c670, 0x2a993584, 0xd8f2b687, + 0x0c38d26c, 0xfe53516f, 0xed03a29b, 0x1f682198, + 0x5125dad3, 0xa34e59d0, 0xb01eaa24, 0x42752927, + 0x96bf4dcc, 0x64d4cecf, 0x77843d3b, 0x85efbe38, + 0xdbfc821c, 0x2997011f, 0x3ac7f2eb, 0xc8ac71e8, + 0x1c661503, 0xee0d9600, 0xfd5d65f4, 0x0f36e6f7, + 0x61c69362, 0x93ad1061, 0x80fde395, 0x72966096, + 0xa65c047d, 0x5437877e, 0x4767748a, 0xb50cf789, + 0xeb1fcbad, 0x197448ae, 0x0a24bb5a, 0xf84f3859, + 0x2c855cb2, 0xdeeedfb1, 0xcdbe2c45, 0x3fd5af46, + 0x7198540d, 0x83f3d70e, 0x90a324fa, 0x62c8a7f9, + 0xb602c312, 0x44694011, 0x5739b3e5, 0xa55230e6, + 0xfb410cc2, 0x092a8fc1, 0x1a7a7c35, 0xe811ff36, + 0x3cdb9bdd, 0xceb018de, 0xdde0eb2a, 0x2f8b6829, + 0x82f63b78, 0x709db87b, 0x63cd4b8f, 0x91a6c88c, + 0x456cac67, 0xb7072f64, 0xa457dc90, 0x563c5f93, + 0x082f63b7, 0xfa44e0b4, 0xe9141340, 0x1b7f9043, + 0xcfb5f4a8, 0x3dde77ab, 0x2e8e845f, 0xdce5075c, + 0x92a8fc17, 0x60c37f14, 0x73938ce0, 0x81f80fe3, + 0x55326b08, 0xa759e80b, 0xb4091bff, 0x466298fc, + 0x1871a4d8, 0xea1a27db, 0xf94ad42f, 0x0b21572c, + 0xdfeb33c7, 0x2d80b0c4, 0x3ed04330, 0xccbbc033, + 0xa24bb5a6, 0x502036a5, 0x4370c551, 0xb11b4652, + 0x65d122b9, 0x97baa1ba, 0x84ea524e, 0x7681d14d, + 0x2892ed69, 0xdaf96e6a, 0xc9a99d9e, 0x3bc21e9d, + 0xef087a76, 0x1d63f975, 0x0e330a81, 0xfc588982, + 0xb21572c9, 0x407ef1ca, 0x532e023e, 0xa145813d, + 0x758fe5d6, 0x87e466d5, 0x94b49521, 0x66df1622, + 0x38cc2a06, 0xcaa7a905, 0xd9f75af1, 0x2b9cd9f2, + 0xff56bd19, 0x0d3d3e1a, 0x1e6dcdee, 0xec064eed, + 0xc38d26c4, 0x31e6a5c7, 0x22b65633, 0xd0ddd530, + 0x0417b1db, 0xf67c32d8, 0xe52cc12c, 0x1747422f, + 0x49547e0b, 0xbb3ffd08, 0xa86f0efc, 0x5a048dff, + 0x8ecee914, 0x7ca56a17, 0x6ff599e3, 0x9d9e1ae0, + 0xd3d3e1ab, 0x21b862a8, 0x32e8915c, 0xc083125f, + 0x144976b4, 0xe622f5b7, 0xf5720643, 0x07198540, + 0x590ab964, 0xab613a67, 0xb831c993, 0x4a5a4a90, + 0x9e902e7b, 0x6cfbad78, 0x7fab5e8c, 0x8dc0dd8f, + 0xe330a81a, 0x115b2b19, 0x020bd8ed, 0xf0605bee, + 0x24aa3f05, 0xd6c1bc06, 0xc5914ff2, 0x37faccf1, + 0x69e9f0d5, 0x9b8273d6, 0x88d28022, 0x7ab90321, + 0xae7367ca, 0x5c18e4c9, 0x4f48173d, 0xbd23943e, + 0xf36e6f75, 0x0105ec76, 0x12551f82, 0xe03e9c81, + 0x34f4f86a, 0xc69f7b69, 0xd5cf889d, 0x27a40b9e, + 0x79b737ba, 0x8bdcb4b9, 0x988c474d, 0x6ae7c44e, + 0xbe2da0a5, 0x4c4623a6, 0x5f16d052, 0xad7d5351,}; + +#endif /* CRC_TABLE */ +#ifdef POWER8_INTRINSICS + +/* Constants */ + +/* Reduce 262144 kbits to 1024 bits */ +static const __vector unsigned long long vcrc_const[255] + __attribute__((aligned (16))) = { +#ifdef __LITTLE_ENDIAN__ + /* x^261120 mod p(x)` << 1, x^261184 mod p(x)` << 1 */ + { 0x000000009c37c408, 0x00000000b6ca9e20 }, + /* x^260096 mod p(x)` << 1, x^260160 mod p(x)` << 1 */ + { 0x00000001b51df26c, 0x00000000350249a8 }, + /* x^259072 mod p(x)` << 1, x^259136 mod p(x)` << 1 */ + { 0x000000000724b9d0, 0x00000001862dac54 }, + /* x^258048 mod p(x)` << 1, x^258112 mod p(x)` << 1 */ + { 0x00000001c00532fe, 0x00000001d87fb48c }, + /* x^257024 mod p(x)` << 1, x^257088 mod p(x)` << 1 */ + { 0x00000000f05a9362, 0x00000001f39b699e }, + /* x^256000 mod p(x)` << 1, x^256064 mod p(x)` << 1 */ + { 0x00000001e1007970, 0x0000000101da11b4 }, + /* x^254976 mod p(x)` << 1, x^255040 mod p(x)` << 1 */ + { 0x00000000a57366ee, 0x00000001cab571e0 }, + /* x^253952 mod p(x)` << 1, x^254016 mod p(x)` << 1 */ + { 0x0000000192011284, 0x00000000c7020cfe }, + /* x^252928 mod p(x)` << 1, x^252992 mod p(x)` << 1 */ + { 0x0000000162716d9a, 0x00000000cdaed1ae }, + /* x^251904 mod p(x)` << 1, x^251968 mod p(x)` << 1 */ + { 0x00000000cd97ecde, 0x00000001e804effc }, + /* x^250880 mod p(x)` << 1, x^250944 mod p(x)` << 1 */ + { 0x0000000058812bc0, 0x0000000077c3ea3a }, + /* x^249856 mod p(x)` << 1, x^249920 mod p(x)` << 1 */ + { 0x0000000088b8c12e, 0x0000000068df31b4 }, + /* x^248832 mod p(x)` << 1, x^248896 mod p(x)` << 1 */ + { 0x00000001230b234c, 0x00000000b059b6c2 }, + /* x^247808 mod p(x)` << 1, x^247872 mod p(x)` << 1 */ + { 0x00000001120b416e, 0x0000000145fb8ed8 }, + /* x^246784 mod p(x)` << 1, x^246848 mod p(x)` << 1 */ + { 0x00000001974aecb0, 0x00000000cbc09168 }, + /* x^245760 mod p(x)` << 1, x^245824 mod p(x)` << 1 */ + { 0x000000008ee3f226, 0x000000005ceeedc2 }, + /* x^244736 mod p(x)` << 1, x^244800 mod p(x)` << 1 */ + { 0x00000001089aba9a, 0x0000000047d74e86 }, + /* x^243712 mod p(x)` << 1, x^243776 mod p(x)` << 1 */ + { 0x0000000065113872, 0x00000001407e9e22 }, + /* x^242688 mod p(x)` << 1, x^242752 mod p(x)` << 1 */ + { 0x000000005c07ec10, 0x00000001da967bda }, + /* x^241664 mod p(x)` << 1, x^241728 mod p(x)` << 1 */ + { 0x0000000187590924, 0x000000006c898368 }, + /* x^240640 mod p(x)` << 1, x^240704 mod p(x)` << 1 */ + { 0x00000000e35da7c6, 0x00000000f2d14c98 }, + /* x^239616 mod p(x)` << 1, x^239680 mod p(x)` << 1 */ + { 0x000000000415855a, 0x00000001993c6ad4 }, + /* x^238592 mod p(x)` << 1, x^238656 mod p(x)` << 1 */ + { 0x0000000073617758, 0x000000014683d1ac }, + /* x^237568 mod p(x)` << 1, x^237632 mod p(x)` << 1 */ + { 0x0000000176021d28, 0x00000001a7c93e6c }, + /* x^236544 mod p(x)` << 1, x^236608 mod p(x)` << 1 */ + { 0x00000001c358fd0a, 0x000000010211e90a }, + /* x^235520 mod p(x)` << 1, x^235584 mod p(x)` << 1 */ + { 0x00000001ff7a2c18, 0x000000001119403e }, + /* x^234496 mod p(x)` << 1, x^234560 mod p(x)` << 1 */ + { 0x00000000f2d9f7e4, 0x000000001c3261aa }, + /* x^233472 mod p(x)` << 1, x^233536 mod p(x)` << 1 */ + { 0x000000016cf1f9c8, 0x000000014e37a634 }, + /* x^232448 mod p(x)` << 1, x^232512 mod p(x)` << 1 */ + { 0x000000010af9279a, 0x0000000073786c0c }, + /* x^231424 mod p(x)` << 1, x^231488 mod p(x)` << 1 */ + { 0x0000000004f101e8, 0x000000011dc037f8 }, + /* x^230400 mod p(x)` << 1, x^230464 mod p(x)` << 1 */ + { 0x0000000070bcf184, 0x0000000031433dfc }, + /* x^229376 mod p(x)` << 1, x^229440 mod p(x)` << 1 */ + { 0x000000000a8de642, 0x000000009cde8348 }, + /* x^228352 mod p(x)` << 1, x^228416 mod p(x)` << 1 */ + { 0x0000000062ea130c, 0x0000000038d3c2a6 }, + /* x^227328 mod p(x)` << 1, x^227392 mod p(x)` << 1 */ + { 0x00000001eb31cbb2, 0x000000011b25f260 }, + /* x^226304 mod p(x)` << 1, x^226368 mod p(x)` << 1 */ + { 0x0000000170783448, 0x000000001629e6f0 }, + /* x^225280 mod p(x)` << 1, x^225344 mod p(x)` << 1 */ + { 0x00000001a684b4c6, 0x0000000160838b4c }, + /* x^224256 mod p(x)` << 1, x^224320 mod p(x)` << 1 */ + { 0x00000000253ca5b4, 0x000000007a44011c }, + /* x^223232 mod p(x)` << 1, x^223296 mod p(x)` << 1 */ + { 0x0000000057b4b1e2, 0x00000000226f417a }, + /* x^222208 mod p(x)` << 1, x^222272 mod p(x)` << 1 */ + { 0x00000000b6bd084c, 0x0000000045eb2eb4 }, + /* x^221184 mod p(x)` << 1, x^221248 mod p(x)` << 1 */ + { 0x0000000123c2d592, 0x000000014459d70c }, + /* x^220160 mod p(x)` << 1, x^220224 mod p(x)` << 1 */ + { 0x00000000159dafce, 0x00000001d406ed82 }, + /* x^219136 mod p(x)` << 1, x^219200 mod p(x)` << 1 */ + { 0x0000000127e1a64e, 0x0000000160c8e1a8 }, + /* x^218112 mod p(x)` << 1, x^218176 mod p(x)` << 1 */ + { 0x0000000056860754, 0x0000000027ba8098 }, + /* x^217088 mod p(x)` << 1, x^217152 mod p(x)` << 1 */ + { 0x00000001e661aae8, 0x000000006d92d018 }, + /* x^216064 mod p(x)` << 1, x^216128 mod p(x)` << 1 */ + { 0x00000000f82c6166, 0x000000012ed7e3f2 }, + /* x^215040 mod p(x)` << 1, x^215104 mod p(x)` << 1 */ + { 0x00000000c4f9c7ae, 0x000000002dc87788 }, + /* x^214016 mod p(x)` << 1, x^214080 mod p(x)` << 1 */ + { 0x0000000074203d20, 0x0000000018240bb8 }, + /* x^212992 mod p(x)` << 1, x^213056 mod p(x)` << 1 */ + { 0x0000000198173052, 0x000000001ad38158 }, + /* x^211968 mod p(x)` << 1, x^212032 mod p(x)` << 1 */ + { 0x00000001ce8aba54, 0x00000001396b78f2 }, + /* x^210944 mod p(x)` << 1, x^211008 mod p(x)` << 1 */ + { 0x00000001850d5d94, 0x000000011a681334 }, + /* x^209920 mod p(x)` << 1, x^209984 mod p(x)` << 1 */ + { 0x00000001d609239c, 0x000000012104732e }, + /* x^208896 mod p(x)` << 1, x^208960 mod p(x)` << 1 */ + { 0x000000001595f048, 0x00000000a140d90c }, + /* x^207872 mod p(x)` << 1, x^207936 mod p(x)` << 1 */ + { 0x0000000042ccee08, 0x00000001b7215eda }, + /* x^206848 mod p(x)` << 1, x^206912 mod p(x)` << 1 */ + { 0x000000010a389d74, 0x00000001aaf1df3c }, + /* x^205824 mod p(x)` << 1, x^205888 mod p(x)` << 1 */ + { 0x000000012a840da6, 0x0000000029d15b8a }, + /* x^204800 mod p(x)` << 1, x^204864 mod p(x)` << 1 */ + { 0x000000001d181c0c, 0x00000000f1a96922 }, + /* x^203776 mod p(x)` << 1, x^203840 mod p(x)` << 1 */ + { 0x0000000068b7d1f6, 0x00000001ac80d03c }, + /* x^202752 mod p(x)` << 1, x^202816 mod p(x)` << 1 */ + { 0x000000005b0f14fc, 0x000000000f11d56a }, + /* x^201728 mod p(x)` << 1, x^201792 mod p(x)` << 1 */ + { 0x0000000179e9e730, 0x00000001f1c022a2 }, + /* x^200704 mod p(x)` << 1, x^200768 mod p(x)` << 1 */ + { 0x00000001ce1368d6, 0x0000000173d00ae2 }, + /* x^199680 mod p(x)` << 1, x^199744 mod p(x)` << 1 */ + { 0x0000000112c3a84c, 0x00000001d4ffe4ac }, + /* x^198656 mod p(x)` << 1, x^198720 mod p(x)` << 1 */ + { 0x00000000de940fee, 0x000000016edc5ae4 }, + /* x^197632 mod p(x)` << 1, x^197696 mod p(x)` << 1 */ + { 0x00000000fe896b7e, 0x00000001f1a02140 }, + /* x^196608 mod p(x)` << 1, x^196672 mod p(x)` << 1 */ + { 0x00000001f797431c, 0x00000000ca0b28a0 }, + /* x^195584 mod p(x)` << 1, x^195648 mod p(x)` << 1 */ + { 0x0000000053e989ba, 0x00000001928e30a2 }, + /* x^194560 mod p(x)` << 1, x^194624 mod p(x)` << 1 */ + { 0x000000003920cd16, 0x0000000097b1b002 }, + /* x^193536 mod p(x)` << 1, x^193600 mod p(x)` << 1 */ + { 0x00000001e6f579b8, 0x00000000b15bf906 }, + /* x^192512 mod p(x)` << 1, x^192576 mod p(x)` << 1 */ + { 0x000000007493cb0a, 0x00000000411c5d52 }, + /* x^191488 mod p(x)` << 1, x^191552 mod p(x)` << 1 */ + { 0x00000001bdd376d8, 0x00000001c36f3300 }, + /* x^190464 mod p(x)` << 1, x^190528 mod p(x)` << 1 */ + { 0x000000016badfee6, 0x00000001119227e0 }, + /* x^189440 mod p(x)` << 1, x^189504 mod p(x)` << 1 */ + { 0x0000000071de5c58, 0x00000000114d4702 }, + /* x^188416 mod p(x)` << 1, x^188480 mod p(x)` << 1 */ + { 0x00000000453f317c, 0x00000000458b5b98 }, + /* x^187392 mod p(x)` << 1, x^187456 mod p(x)` << 1 */ + { 0x0000000121675cce, 0x000000012e31fb8e }, + /* x^186368 mod p(x)` << 1, x^186432 mod p(x)` << 1 */ + { 0x00000001f409ee92, 0x000000005cf619d8 }, + /* x^185344 mod p(x)` << 1, x^185408 mod p(x)` << 1 */ + { 0x00000000f36b9c88, 0x0000000063f4d8b2 }, + /* x^184320 mod p(x)` << 1, x^184384 mod p(x)` << 1 */ + { 0x0000000036b398f4, 0x000000004138dc8a }, + /* x^183296 mod p(x)` << 1, x^183360 mod p(x)` << 1 */ + { 0x00000001748f9adc, 0x00000001d29ee8e0 }, + /* x^182272 mod p(x)` << 1, x^182336 mod p(x)` << 1 */ + { 0x00000001be94ec00, 0x000000006a08ace8 }, + /* x^181248 mod p(x)` << 1, x^181312 mod p(x)` << 1 */ + { 0x00000000b74370d6, 0x0000000127d42010 }, + /* x^180224 mod p(x)` << 1, x^180288 mod p(x)` << 1 */ + { 0x00000001174d0b98, 0x0000000019d76b62 }, + /* x^179200 mod p(x)` << 1, x^179264 mod p(x)` << 1 */ + { 0x00000000befc06a4, 0x00000001b1471f6e }, + /* x^178176 mod p(x)` << 1, x^178240 mod p(x)` << 1 */ + { 0x00000001ae125288, 0x00000001f64c19cc }, + /* x^177152 mod p(x)` << 1, x^177216 mod p(x)` << 1 */ + { 0x0000000095c19b34, 0x00000000003c0ea0 }, + /* x^176128 mod p(x)` << 1, x^176192 mod p(x)` << 1 */ + { 0x00000001a78496f2, 0x000000014d73abf6 }, + /* x^175104 mod p(x)` << 1, x^175168 mod p(x)` << 1 */ + { 0x00000001ac5390a0, 0x00000001620eb844 }, + /* x^174080 mod p(x)` << 1, x^174144 mod p(x)` << 1 */ + { 0x000000002a80ed6e, 0x0000000147655048 }, + /* x^173056 mod p(x)` << 1, x^173120 mod p(x)` << 1 */ + { 0x00000001fa9b0128, 0x0000000067b5077e }, + /* x^172032 mod p(x)` << 1, x^172096 mod p(x)` << 1 */ + { 0x00000001ea94929e, 0x0000000010ffe206 }, + /* x^171008 mod p(x)` << 1, x^171072 mod p(x)` << 1 */ + { 0x0000000125f4305c, 0x000000000fee8f1e }, + /* x^169984 mod p(x)` << 1, x^170048 mod p(x)` << 1 */ + { 0x00000001471e2002, 0x00000001da26fbae }, + /* x^168960 mod p(x)` << 1, x^169024 mod p(x)` << 1 */ + { 0x0000000132d2253a, 0x00000001b3a8bd88 }, + /* x^167936 mod p(x)` << 1, x^168000 mod p(x)` << 1 */ + { 0x00000000f26b3592, 0x00000000e8f3898e }, + /* x^166912 mod p(x)` << 1, x^166976 mod p(x)` << 1 */ + { 0x00000000bc8b67b0, 0x00000000b0d0d28c }, + /* x^165888 mod p(x)` << 1, x^165952 mod p(x)` << 1 */ + { 0x000000013a826ef2, 0x0000000030f2a798 }, + /* x^164864 mod p(x)` << 1, x^164928 mod p(x)` << 1 */ + { 0x0000000081482c84, 0x000000000fba1002 }, + /* x^163840 mod p(x)` << 1, x^163904 mod p(x)` << 1 */ + { 0x00000000e77307c2, 0x00000000bdb9bd72 }, + /* x^162816 mod p(x)` << 1, x^162880 mod p(x)` << 1 */ + { 0x00000000d4a07ec8, 0x0000000075d3bf5a }, + /* x^161792 mod p(x)` << 1, x^161856 mod p(x)` << 1 */ + { 0x0000000017102100, 0x00000000ef1f98a0 }, + /* x^160768 mod p(x)` << 1, x^160832 mod p(x)` << 1 */ + { 0x00000000db406486, 0x00000000689c7602 }, + /* x^159744 mod p(x)` << 1, x^159808 mod p(x)` << 1 */ + { 0x0000000192db7f88, 0x000000016d5fa5fe }, + /* x^158720 mod p(x)` << 1, x^158784 mod p(x)` << 1 */ + { 0x000000018bf67b1e, 0x00000001d0d2b9ca }, + /* x^157696 mod p(x)` << 1, x^157760 mod p(x)` << 1 */ + { 0x000000007c09163e, 0x0000000041e7b470 }, + /* x^156672 mod p(x)` << 1, x^156736 mod p(x)` << 1 */ + { 0x000000000adac060, 0x00000001cbb6495e }, + /* x^155648 mod p(x)` << 1, x^155712 mod p(x)` << 1 */ + { 0x00000000bd8316ae, 0x000000010052a0b0 }, + /* x^154624 mod p(x)` << 1, x^154688 mod p(x)` << 1 */ + { 0x000000019f09ab54, 0x00000001d8effb5c }, + /* x^153600 mod p(x)` << 1, x^153664 mod p(x)` << 1 */ + { 0x0000000125155542, 0x00000001d969853c }, + /* x^152576 mod p(x)` << 1, x^152640 mod p(x)` << 1 */ + { 0x000000018fdb5882, 0x00000000523ccce2 }, + /* x^151552 mod p(x)` << 1, x^151616 mod p(x)` << 1 */ + { 0x00000000e794b3f4, 0x000000001e2436bc }, + /* x^150528 mod p(x)` << 1, x^150592 mod p(x)` << 1 */ + { 0x000000016f9bb022, 0x00000000ddd1c3a2 }, + /* x^149504 mod p(x)` << 1, x^149568 mod p(x)` << 1 */ + { 0x00000000290c9978, 0x0000000019fcfe38 }, + /* x^148480 mod p(x)` << 1, x^148544 mod p(x)` << 1 */ + { 0x0000000083c0f350, 0x00000001ce95db64 }, + /* x^147456 mod p(x)` << 1, x^147520 mod p(x)` << 1 */ + { 0x0000000173ea6628, 0x00000000af582806 }, + /* x^146432 mod p(x)` << 1, x^146496 mod p(x)` << 1 */ + { 0x00000001c8b4e00a, 0x00000001006388f6 }, + /* x^145408 mod p(x)` << 1, x^145472 mod p(x)` << 1 */ + { 0x00000000de95d6aa, 0x0000000179eca00a }, + /* x^144384 mod p(x)` << 1, x^144448 mod p(x)` << 1 */ + { 0x000000010b7f7248, 0x0000000122410a6a }, + /* x^143360 mod p(x)` << 1, x^143424 mod p(x)` << 1 */ + { 0x00000001326e3a06, 0x000000004288e87c }, + /* x^142336 mod p(x)` << 1, x^142400 mod p(x)` << 1 */ + { 0x00000000bb62c2e6, 0x000000016c5490da }, + /* x^141312 mod p(x)` << 1, x^141376 mod p(x)` << 1 */ + { 0x0000000156a4b2c2, 0x00000000d1c71f6e }, + /* x^140288 mod p(x)` << 1, x^140352 mod p(x)` << 1 */ + { 0x000000011dfe763a, 0x00000001b4ce08a6 }, + /* x^139264 mod p(x)` << 1, x^139328 mod p(x)` << 1 */ + { 0x000000007bcca8e2, 0x00000001466ba60c }, + /* x^138240 mod p(x)` << 1, x^138304 mod p(x)` << 1 */ + { 0x0000000186118faa, 0x00000001f6c488a4 }, + /* x^137216 mod p(x)` << 1, x^137280 mod p(x)` << 1 */ + { 0x0000000111a65a88, 0x000000013bfb0682 }, + /* x^136192 mod p(x)` << 1, x^136256 mod p(x)` << 1 */ + { 0x000000003565e1c4, 0x00000000690e9e54 }, + /* x^135168 mod p(x)` << 1, x^135232 mod p(x)` << 1 */ + { 0x000000012ed02a82, 0x00000000281346b6 }, + /* x^134144 mod p(x)` << 1, x^134208 mod p(x)` << 1 */ + { 0x00000000c486ecfc, 0x0000000156464024 }, + /* x^133120 mod p(x)` << 1, x^133184 mod p(x)` << 1 */ + { 0x0000000001b951b2, 0x000000016063a8dc }, + /* x^132096 mod p(x)` << 1, x^132160 mod p(x)` << 1 */ + { 0x0000000048143916, 0x0000000116a66362 }, + /* x^131072 mod p(x)` << 1, x^131136 mod p(x)` << 1 */ + { 0x00000001dc2ae124, 0x000000017e8aa4d2 }, + /* x^130048 mod p(x)` << 1, x^130112 mod p(x)` << 1 */ + { 0x00000001416c58d6, 0x00000001728eb10c }, + /* x^129024 mod p(x)` << 1, x^129088 mod p(x)` << 1 */ + { 0x00000000a479744a, 0x00000001b08fd7fa }, + /* x^128000 mod p(x)` << 1, x^128064 mod p(x)` << 1 */ + { 0x0000000096ca3a26, 0x00000001092a16e8 }, + /* x^126976 mod p(x)` << 1, x^127040 mod p(x)` << 1 */ + { 0x00000000ff223d4e, 0x00000000a505637c }, + /* x^125952 mod p(x)` << 1, x^126016 mod p(x)` << 1 */ + { 0x000000010e84da42, 0x00000000d94869b2 }, + /* x^124928 mod p(x)` << 1, x^124992 mod p(x)` << 1 */ + { 0x00000001b61ba3d0, 0x00000001c8b203ae }, + /* x^123904 mod p(x)` << 1, x^123968 mod p(x)` << 1 */ + { 0x00000000680f2de8, 0x000000005704aea0 }, + /* x^122880 mod p(x)` << 1, x^122944 mod p(x)` << 1 */ + { 0x000000008772a9a8, 0x000000012e295fa2 }, + /* x^121856 mod p(x)` << 1, x^121920 mod p(x)` << 1 */ + { 0x0000000155f295bc, 0x000000011d0908bc }, + /* x^120832 mod p(x)` << 1, x^120896 mod p(x)` << 1 */ + { 0x00000000595f9282, 0x0000000193ed97ea }, + /* x^119808 mod p(x)` << 1, x^119872 mod p(x)` << 1 */ + { 0x0000000164b1c25a, 0x000000013a0f1c52 }, + /* x^118784 mod p(x)` << 1, x^118848 mod p(x)` << 1 */ + { 0x00000000fbd67c50, 0x000000010c2c40c0 }, + /* x^117760 mod p(x)` << 1, x^117824 mod p(x)` << 1 */ + { 0x0000000096076268, 0x00000000ff6fac3e }, + /* x^116736 mod p(x)` << 1, x^116800 mod p(x)` << 1 */ + { 0x00000001d288e4cc, 0x000000017b3609c0 }, + /* x^115712 mod p(x)` << 1, x^115776 mod p(x)` << 1 */ + { 0x00000001eaac1bdc, 0x0000000088c8c922 }, + /* x^114688 mod p(x)` << 1, x^114752 mod p(x)` << 1 */ + { 0x00000001f1ea39e2, 0x00000001751baae6 }, + /* x^113664 mod p(x)` << 1, x^113728 mod p(x)` << 1 */ + { 0x00000001eb6506fc, 0x0000000107952972 }, + /* x^112640 mod p(x)` << 1, x^112704 mod p(x)` << 1 */ + { 0x000000010f806ffe, 0x0000000162b00abe }, + /* x^111616 mod p(x)` << 1, x^111680 mod p(x)` << 1 */ + { 0x000000010408481e, 0x000000000d7b404c }, + /* x^110592 mod p(x)` << 1, x^110656 mod p(x)` << 1 */ + { 0x0000000188260534, 0x00000000763b13d4 }, + /* x^109568 mod p(x)` << 1, x^109632 mod p(x)` << 1 */ + { 0x0000000058fc73e0, 0x00000000f6dc22d8 }, + /* x^108544 mod p(x)` << 1, x^108608 mod p(x)` << 1 */ + { 0x00000000391c59b8, 0x000000007daae060 }, + /* x^107520 mod p(x)` << 1, x^107584 mod p(x)` << 1 */ + { 0x000000018b638400, 0x000000013359ab7c }, + /* x^106496 mod p(x)` << 1, x^106560 mod p(x)` << 1 */ + { 0x000000011738f5c4, 0x000000008add438a }, + /* x^105472 mod p(x)` << 1, x^105536 mod p(x)` << 1 */ + { 0x000000008cf7c6da, 0x00000001edbefdea }, + /* x^104448 mod p(x)` << 1, x^104512 mod p(x)` << 1 */ + { 0x00000001ef97fb16, 0x000000004104e0f8 }, + /* x^103424 mod p(x)` << 1, x^103488 mod p(x)` << 1 */ + { 0x0000000102130e20, 0x00000000b48a8222 }, + /* x^102400 mod p(x)` << 1, x^102464 mod p(x)` << 1 */ + { 0x00000000db968898, 0x00000001bcb46844 }, + /* x^101376 mod p(x)` << 1, x^101440 mod p(x)` << 1 */ + { 0x00000000b5047b5e, 0x000000013293ce0a }, + /* x^100352 mod p(x)` << 1, x^100416 mod p(x)` << 1 */ + { 0x000000010b90fdb2, 0x00000001710d0844 }, + /* x^99328 mod p(x)` << 1, x^99392 mod p(x)` << 1 */ + { 0x000000004834a32e, 0x0000000117907f6e }, + /* x^98304 mod p(x)` << 1, x^98368 mod p(x)` << 1 */ + { 0x0000000059c8f2b0, 0x0000000087ddf93e }, + /* x^97280 mod p(x)` << 1, x^97344 mod p(x)` << 1 */ + { 0x0000000122cec508, 0x000000005970e9b0 }, + /* x^96256 mod p(x)` << 1, x^96320 mod p(x)` << 1 */ + { 0x000000000a330cda, 0x0000000185b2b7d0 }, + /* x^95232 mod p(x)` << 1, x^95296 mod p(x)` << 1 */ + { 0x000000014a47148c, 0x00000001dcee0efc }, + /* x^94208 mod p(x)` << 1, x^94272 mod p(x)` << 1 */ + { 0x0000000042c61cb8, 0x0000000030da2722 }, + /* x^93184 mod p(x)` << 1, x^93248 mod p(x)` << 1 */ + { 0x0000000012fe6960, 0x000000012f925a18 }, + /* x^92160 mod p(x)` << 1, x^92224 mod p(x)` << 1 */ + { 0x00000000dbda2c20, 0x00000000dd2e357c }, + /* x^91136 mod p(x)` << 1, x^91200 mod p(x)` << 1 */ + { 0x000000011122410c, 0x00000000071c80de }, + /* x^90112 mod p(x)` << 1, x^90176 mod p(x)` << 1 */ + { 0x00000000977b2070, 0x000000011513140a }, + /* x^89088 mod p(x)` << 1, x^89152 mod p(x)` << 1 */ + { 0x000000014050438e, 0x00000001df876e8e }, + /* x^88064 mod p(x)` << 1, x^88128 mod p(x)` << 1 */ + { 0x0000000147c840e8, 0x000000015f81d6ce }, + /* x^87040 mod p(x)` << 1, x^87104 mod p(x)` << 1 */ + { 0x00000001cc7c88ce, 0x000000019dd94dbe }, + /* x^86016 mod p(x)` << 1, x^86080 mod p(x)` << 1 */ + { 0x00000001476b35a4, 0x00000001373d206e }, + /* x^84992 mod p(x)` << 1, x^85056 mod p(x)` << 1 */ + { 0x000000013d52d508, 0x00000000668ccade }, + /* x^83968 mod p(x)` << 1, x^84032 mod p(x)` << 1 */ + { 0x000000008e4be32e, 0x00000001b192d268 }, + /* x^82944 mod p(x)` << 1, x^83008 mod p(x)` << 1 */ + { 0x00000000024120fe, 0x00000000e30f3a78 }, + /* x^81920 mod p(x)` << 1, x^81984 mod p(x)` << 1 */ + { 0x00000000ddecddb4, 0x000000010ef1f7bc }, + /* x^80896 mod p(x)` << 1, x^80960 mod p(x)` << 1 */ + { 0x00000000d4d403bc, 0x00000001f5ac7380 }, + /* x^79872 mod p(x)` << 1, x^79936 mod p(x)` << 1 */ + { 0x00000001734b89aa, 0x000000011822ea70 }, + /* x^78848 mod p(x)` << 1, x^78912 mod p(x)` << 1 */ + { 0x000000010e7a58d6, 0x00000000c3a33848 }, + /* x^77824 mod p(x)` << 1, x^77888 mod p(x)` << 1 */ + { 0x00000001f9f04e9c, 0x00000001bd151c24 }, + /* x^76800 mod p(x)` << 1, x^76864 mod p(x)` << 1 */ + { 0x00000000b692225e, 0x0000000056002d76 }, + /* x^75776 mod p(x)` << 1, x^75840 mod p(x)` << 1 */ + { 0x000000019b8d3f3e, 0x000000014657c4f4 }, + /* x^74752 mod p(x)` << 1, x^74816 mod p(x)` << 1 */ + { 0x00000001a874f11e, 0x0000000113742d7c }, + /* x^73728 mod p(x)` << 1, x^73792 mod p(x)` << 1 */ + { 0x000000010d5a4254, 0x000000019c5920ba }, + /* x^72704 mod p(x)` << 1, x^72768 mod p(x)` << 1 */ + { 0x00000000bbb2f5d6, 0x000000005216d2d6 }, + /* x^71680 mod p(x)` << 1, x^71744 mod p(x)` << 1 */ + { 0x0000000179cc0e36, 0x0000000136f5ad8a }, + /* x^70656 mod p(x)` << 1, x^70720 mod p(x)` << 1 */ + { 0x00000001dca1da4a, 0x000000018b07beb6 }, + /* x^69632 mod p(x)` << 1, x^69696 mod p(x)` << 1 */ + { 0x00000000feb1a192, 0x00000000db1e93b0 }, + /* x^68608 mod p(x)` << 1, x^68672 mod p(x)` << 1 */ + { 0x00000000d1eeedd6, 0x000000000b96fa3a }, + /* x^67584 mod p(x)` << 1, x^67648 mod p(x)` << 1 */ + { 0x000000008fad9bb4, 0x00000001d9968af0 }, + /* x^66560 mod p(x)` << 1, x^66624 mod p(x)` << 1 */ + { 0x00000001884938e4, 0x000000000e4a77a2 }, + /* x^65536 mod p(x)` << 1, x^65600 mod p(x)` << 1 */ + { 0x00000001bc2e9bc0, 0x00000000508c2ac8 }, + /* x^64512 mod p(x)` << 1, x^64576 mod p(x)` << 1 */ + { 0x00000001f9658a68, 0x0000000021572a80 }, + /* x^63488 mod p(x)` << 1, x^63552 mod p(x)` << 1 */ + { 0x000000001b9224fc, 0x00000001b859daf2 }, + /* x^62464 mod p(x)` << 1, x^62528 mod p(x)` << 1 */ + { 0x0000000055b2fb84, 0x000000016f788474 }, + /* x^61440 mod p(x)` << 1, x^61504 mod p(x)` << 1 */ + { 0x000000018b090348, 0x00000001b438810e }, + /* x^60416 mod p(x)` << 1, x^60480 mod p(x)` << 1 */ + { 0x000000011ccbd5ea, 0x0000000095ddc6f2 }, + /* x^59392 mod p(x)` << 1, x^59456 mod p(x)` << 1 */ + { 0x0000000007ae47f8, 0x00000001d977c20c }, + /* x^58368 mod p(x)` << 1, x^58432 mod p(x)` << 1 */ + { 0x0000000172acbec0, 0x00000000ebedb99a }, + /* x^57344 mod p(x)` << 1, x^57408 mod p(x)` << 1 */ + { 0x00000001c6e3ff20, 0x00000001df9e9e92 }, + /* x^56320 mod p(x)` << 1, x^56384 mod p(x)` << 1 */ + { 0x00000000e1b38744, 0x00000001a4a3f952 }, + /* x^55296 mod p(x)` << 1, x^55360 mod p(x)` << 1 */ + { 0x00000000791585b2, 0x00000000e2f51220 }, + /* x^54272 mod p(x)` << 1, x^54336 mod p(x)` << 1 */ + { 0x00000000ac53b894, 0x000000004aa01f3e }, + /* x^53248 mod p(x)` << 1, x^53312 mod p(x)` << 1 */ + { 0x00000001ed5f2cf4, 0x00000000b3e90a58 }, + /* x^52224 mod p(x)` << 1, x^52288 mod p(x)` << 1 */ + { 0x00000001df48b2e0, 0x000000000c9ca2aa }, + /* x^51200 mod p(x)` << 1, x^51264 mod p(x)` << 1 */ + { 0x00000000049c1c62, 0x0000000151682316 }, + /* x^50176 mod p(x)` << 1, x^50240 mod p(x)` << 1 */ + { 0x000000017c460c12, 0x0000000036fce78c }, + /* x^49152 mod p(x)` << 1, x^49216 mod p(x)` << 1 */ + { 0x000000015be4da7e, 0x000000009037dc10 }, + /* x^48128 mod p(x)` << 1, x^48192 mod p(x)` << 1 */ + { 0x000000010f38f668, 0x00000000d3298582 }, + /* x^47104 mod p(x)` << 1, x^47168 mod p(x)` << 1 */ + { 0x0000000039f40a00, 0x00000001b42e8ad6 }, + /* x^46080 mod p(x)` << 1, x^46144 mod p(x)` << 1 */ + { 0x00000000bd4c10c4, 0x00000000142a9838 }, + /* x^45056 mod p(x)` << 1, x^45120 mod p(x)` << 1 */ + { 0x0000000042db1d98, 0x0000000109c7f190 }, + /* x^44032 mod p(x)` << 1, x^44096 mod p(x)` << 1 */ + { 0x00000001c905bae6, 0x0000000056ff9310 }, + /* x^43008 mod p(x)` << 1, x^43072 mod p(x)` << 1 */ + { 0x00000000069d40ea, 0x00000001594513aa }, + /* x^41984 mod p(x)` << 1, x^42048 mod p(x)` << 1 */ + { 0x000000008e4fbad0, 0x00000001e3b5b1e8 }, + /* x^40960 mod p(x)` << 1, x^41024 mod p(x)` << 1 */ + { 0x0000000047bedd46, 0x000000011dd5fc08 }, + /* x^39936 mod p(x)` << 1, x^40000 mod p(x)` << 1 */ + { 0x0000000026396bf8, 0x00000001675f0cc2 }, + /* x^38912 mod p(x)` << 1, x^38976 mod p(x)` << 1 */ + { 0x00000000379beb92, 0x00000000d1c8dd44 }, + /* x^37888 mod p(x)` << 1, x^37952 mod p(x)` << 1 */ + { 0x000000000abae54a, 0x0000000115ebd3d8 }, + /* x^36864 mod p(x)` << 1, x^36928 mod p(x)` << 1 */ + { 0x0000000007e6a128, 0x00000001ecbd0dac }, + /* x^35840 mod p(x)` << 1, x^35904 mod p(x)` << 1 */ + { 0x000000000ade29d2, 0x00000000cdf67af2 }, + /* x^34816 mod p(x)` << 1, x^34880 mod p(x)` << 1 */ + { 0x00000000f974c45c, 0x000000004c01ff4c }, + /* x^33792 mod p(x)` << 1, x^33856 mod p(x)` << 1 */ + { 0x00000000e77ac60a, 0x00000000f2d8657e }, + /* x^32768 mod p(x)` << 1, x^32832 mod p(x)` << 1 */ + { 0x0000000145895816, 0x000000006bae74c4 }, + /* x^31744 mod p(x)` << 1, x^31808 mod p(x)` << 1 */ + { 0x0000000038e362be, 0x0000000152af8aa0 }, + /* x^30720 mod p(x)` << 1, x^30784 mod p(x)` << 1 */ + { 0x000000007f991a64, 0x0000000004663802 }, + /* x^29696 mod p(x)` << 1, x^29760 mod p(x)` << 1 */ + { 0x00000000fa366d3a, 0x00000001ab2f5afc }, + /* x^28672 mod p(x)` << 1, x^28736 mod p(x)` << 1 */ + { 0x00000001a2bb34f0, 0x0000000074a4ebd4 }, + /* x^27648 mod p(x)` << 1, x^27712 mod p(x)` << 1 */ + { 0x0000000028a9981e, 0x00000001d7ab3a4c }, + /* x^26624 mod p(x)` << 1, x^26688 mod p(x)` << 1 */ + { 0x00000001dbc672be, 0x00000001a8da60c6 }, + /* x^25600 mod p(x)` << 1, x^25664 mod p(x)` << 1 */ + { 0x00000000b04d77f6, 0x000000013cf63820 }, + /* x^24576 mod p(x)` << 1, x^24640 mod p(x)` << 1 */ + { 0x0000000124400d96, 0x00000000bec12e1e }, + /* x^23552 mod p(x)` << 1, x^23616 mod p(x)` << 1 */ + { 0x000000014ca4b414, 0x00000001c6368010 }, + /* x^22528 mod p(x)` << 1, x^22592 mod p(x)` << 1 */ + { 0x000000012fe2c938, 0x00000001e6e78758 }, + /* x^21504 mod p(x)` << 1, x^21568 mod p(x)` << 1 */ + { 0x00000001faed01e6, 0x000000008d7f2b3c }, + /* x^20480 mod p(x)` << 1, x^20544 mod p(x)` << 1 */ + { 0x000000007e80ecfe, 0x000000016b4a156e }, + /* x^19456 mod p(x)` << 1, x^19520 mod p(x)` << 1 */ + { 0x0000000098daee94, 0x00000001c63cfeb6 }, + /* x^18432 mod p(x)` << 1, x^18496 mod p(x)` << 1 */ + { 0x000000010a04edea, 0x000000015f902670 }, + /* x^17408 mod p(x)` << 1, x^17472 mod p(x)` << 1 */ + { 0x00000001c00b4524, 0x00000001cd5de11e }, + /* x^16384 mod p(x)` << 1, x^16448 mod p(x)` << 1 */ + { 0x0000000170296550, 0x000000001acaec54 }, + /* x^15360 mod p(x)` << 1, x^15424 mod p(x)` << 1 */ + { 0x0000000181afaa48, 0x000000002bd0ca78 }, + /* x^14336 mod p(x)` << 1, x^14400 mod p(x)` << 1 */ + { 0x0000000185a31ffa, 0x0000000032d63d5c }, + /* x^13312 mod p(x)` << 1, x^13376 mod p(x)` << 1 */ + { 0x000000002469f608, 0x000000001c6d4e4c }, + /* x^12288 mod p(x)` << 1, x^12352 mod p(x)` << 1 */ + { 0x000000006980102a, 0x0000000106a60b92 }, + /* x^11264 mod p(x)` << 1, x^11328 mod p(x)` << 1 */ + { 0x0000000111ea9ca8, 0x00000000d3855e12 }, + /* x^10240 mod p(x)` << 1, x^10304 mod p(x)` << 1 */ + { 0x00000001bd1d29ce, 0x00000000e3125636 }, + /* x^9216 mod p(x)` << 1, x^9280 mod p(x)` << 1 */ + { 0x00000001b34b9580, 0x000000009e8f7ea4 }, + /* x^8192 mod p(x)` << 1, x^8256 mod p(x)` << 1 */ + { 0x000000003076054e, 0x00000001c82e562c }, + /* x^7168 mod p(x)` << 1, x^7232 mod p(x)` << 1 */ + { 0x000000012a608ea4, 0x00000000ca9f09ce }, + /* x^6144 mod p(x)` << 1, x^6208 mod p(x)` << 1 */ + { 0x00000000784d05fe, 0x00000000c63764e6 }, + /* x^5120 mod p(x)` << 1, x^5184 mod p(x)` << 1 */ + { 0x000000016ef0d82a, 0x0000000168d2e49e }, + /* x^4096 mod p(x)` << 1, x^4160 mod p(x)` << 1 */ + { 0x0000000075bda454, 0x00000000e986c148 }, + /* x^3072 mod p(x)` << 1, x^3136 mod p(x)` << 1 */ + { 0x000000003dc0a1c4, 0x00000000cfb65894 }, + /* x^2048 mod p(x)` << 1, x^2112 mod p(x)` << 1 */ + { 0x00000000e9a5d8be, 0x0000000111cadee4 }, + /* x^1024 mod p(x)` << 1, x^1088 mod p(x)` << 1 */ + { 0x00000001609bc4b4, 0x0000000171fb63ce } +#else /* __LITTLE_ENDIAN__ */ + /* x^261120 mod p(x)` << 1, x^261184 mod p(x)` << 1 */ + { 0x00000000b6ca9e20, 0x000000009c37c408 }, + /* x^260096 mod p(x)` << 1, x^260160 mod p(x)` << 1 */ + { 0x00000000350249a8, 0x00000001b51df26c }, + /* x^259072 mod p(x)` << 1, x^259136 mod p(x)` << 1 */ + { 0x00000001862dac54, 0x000000000724b9d0 }, + /* x^258048 mod p(x)` << 1, x^258112 mod p(x)` << 1 */ + { 0x00000001d87fb48c, 0x00000001c00532fe }, + /* x^257024 mod p(x)` << 1, x^257088 mod p(x)` << 1 */ + { 0x00000001f39b699e, 0x00000000f05a9362 }, + /* x^256000 mod p(x)` << 1, x^256064 mod p(x)` << 1 */ + { 0x0000000101da11b4, 0x00000001e1007970 }, + /* x^254976 mod p(x)` << 1, x^255040 mod p(x)` << 1 */ + { 0x00000001cab571e0, 0x00000000a57366ee }, + /* x^253952 mod p(x)` << 1, x^254016 mod p(x)` << 1 */ + { 0x00000000c7020cfe, 0x0000000192011284 }, + /* x^252928 mod p(x)` << 1, x^252992 mod p(x)` << 1 */ + { 0x00000000cdaed1ae, 0x0000000162716d9a }, + /* x^251904 mod p(x)` << 1, x^251968 mod p(x)` << 1 */ + { 0x00000001e804effc, 0x00000000cd97ecde }, + /* x^250880 mod p(x)` << 1, x^250944 mod p(x)` << 1 */ + { 0x0000000077c3ea3a, 0x0000000058812bc0 }, + /* x^249856 mod p(x)` << 1, x^249920 mod p(x)` << 1 */ + { 0x0000000068df31b4, 0x0000000088b8c12e }, + /* x^248832 mod p(x)` << 1, x^248896 mod p(x)` << 1 */ + { 0x00000000b059b6c2, 0x00000001230b234c }, + /* x^247808 mod p(x)` << 1, x^247872 mod p(x)` << 1 */ + { 0x0000000145fb8ed8, 0x00000001120b416e }, + /* x^246784 mod p(x)` << 1, x^246848 mod p(x)` << 1 */ + { 0x00000000cbc09168, 0x00000001974aecb0 }, + /* x^245760 mod p(x)` << 1, x^245824 mod p(x)` << 1 */ + { 0x000000005ceeedc2, 0x000000008ee3f226 }, + /* x^244736 mod p(x)` << 1, x^244800 mod p(x)` << 1 */ + { 0x0000000047d74e86, 0x00000001089aba9a }, + /* x^243712 mod p(x)` << 1, x^243776 mod p(x)` << 1 */ + { 0x00000001407e9e22, 0x0000000065113872 }, + /* x^242688 mod p(x)` << 1, x^242752 mod p(x)` << 1 */ + { 0x00000001da967bda, 0x000000005c07ec10 }, + /* x^241664 mod p(x)` << 1, x^241728 mod p(x)` << 1 */ + { 0x000000006c898368, 0x0000000187590924 }, + /* x^240640 mod p(x)` << 1, x^240704 mod p(x)` << 1 */ + { 0x00000000f2d14c98, 0x00000000e35da7c6 }, + /* x^239616 mod p(x)` << 1, x^239680 mod p(x)` << 1 */ + { 0x00000001993c6ad4, 0x000000000415855a }, + /* x^238592 mod p(x)` << 1, x^238656 mod p(x)` << 1 */ + { 0x000000014683d1ac, 0x0000000073617758 }, + /* x^237568 mod p(x)` << 1, x^237632 mod p(x)` << 1 */ + { 0x00000001a7c93e6c, 0x0000000176021d28 }, + /* x^236544 mod p(x)` << 1, x^236608 mod p(x)` << 1 */ + { 0x000000010211e90a, 0x00000001c358fd0a }, + /* x^235520 mod p(x)` << 1, x^235584 mod p(x)` << 1 */ + { 0x000000001119403e, 0x00000001ff7a2c18 }, + /* x^234496 mod p(x)` << 1, x^234560 mod p(x)` << 1 */ + { 0x000000001c3261aa, 0x00000000f2d9f7e4 }, + /* x^233472 mod p(x)` << 1, x^233536 mod p(x)` << 1 */ + { 0x000000014e37a634, 0x000000016cf1f9c8 }, + /* x^232448 mod p(x)` << 1, x^232512 mod p(x)` << 1 */ + { 0x0000000073786c0c, 0x000000010af9279a }, + /* x^231424 mod p(x)` << 1, x^231488 mod p(x)` << 1 */ + { 0x000000011dc037f8, 0x0000000004f101e8 }, + /* x^230400 mod p(x)` << 1, x^230464 mod p(x)` << 1 */ + { 0x0000000031433dfc, 0x0000000070bcf184 }, + /* x^229376 mod p(x)` << 1, x^229440 mod p(x)` << 1 */ + { 0x000000009cde8348, 0x000000000a8de642 }, + /* x^228352 mod p(x)` << 1, x^228416 mod p(x)` << 1 */ + { 0x0000000038d3c2a6, 0x0000000062ea130c }, + /* x^227328 mod p(x)` << 1, x^227392 mod p(x)` << 1 */ + { 0x000000011b25f260, 0x00000001eb31cbb2 }, + /* x^226304 mod p(x)` << 1, x^226368 mod p(x)` << 1 */ + { 0x000000001629e6f0, 0x0000000170783448 }, + /* x^225280 mod p(x)` << 1, x^225344 mod p(x)` << 1 */ + { 0x0000000160838b4c, 0x00000001a684b4c6 }, + /* x^224256 mod p(x)` << 1, x^224320 mod p(x)` << 1 */ + { 0x000000007a44011c, 0x00000000253ca5b4 }, + /* x^223232 mod p(x)` << 1, x^223296 mod p(x)` << 1 */ + { 0x00000000226f417a, 0x0000000057b4b1e2 }, + /* x^222208 mod p(x)` << 1, x^222272 mod p(x)` << 1 */ + { 0x0000000045eb2eb4, 0x00000000b6bd084c }, + /* x^221184 mod p(x)` << 1, x^221248 mod p(x)` << 1 */ + { 0x000000014459d70c, 0x0000000123c2d592 }, + /* x^220160 mod p(x)` << 1, x^220224 mod p(x)` << 1 */ + { 0x00000001d406ed82, 0x00000000159dafce }, + /* x^219136 mod p(x)` << 1, x^219200 mod p(x)` << 1 */ + { 0x0000000160c8e1a8, 0x0000000127e1a64e }, + /* x^218112 mod p(x)` << 1, x^218176 mod p(x)` << 1 */ + { 0x0000000027ba8098, 0x0000000056860754 }, + /* x^217088 mod p(x)` << 1, x^217152 mod p(x)` << 1 */ + { 0x000000006d92d018, 0x00000001e661aae8 }, + /* x^216064 mod p(x)` << 1, x^216128 mod p(x)` << 1 */ + { 0x000000012ed7e3f2, 0x00000000f82c6166 }, + /* x^215040 mod p(x)` << 1, x^215104 mod p(x)` << 1 */ + { 0x000000002dc87788, 0x00000000c4f9c7ae }, + /* x^214016 mod p(x)` << 1, x^214080 mod p(x)` << 1 */ + { 0x0000000018240bb8, 0x0000000074203d20 }, + /* x^212992 mod p(x)` << 1, x^213056 mod p(x)` << 1 */ + { 0x000000001ad38158, 0x0000000198173052 }, + /* x^211968 mod p(x)` << 1, x^212032 mod p(x)` << 1 */ + { 0x00000001396b78f2, 0x00000001ce8aba54 }, + /* x^210944 mod p(x)` << 1, x^211008 mod p(x)` << 1 */ + { 0x000000011a681334, 0x00000001850d5d94 }, + /* x^209920 mod p(x)` << 1, x^209984 mod p(x)` << 1 */ + { 0x000000012104732e, 0x00000001d609239c }, + /* x^208896 mod p(x)` << 1, x^208960 mod p(x)` << 1 */ + { 0x00000000a140d90c, 0x000000001595f048 }, + /* x^207872 mod p(x)` << 1, x^207936 mod p(x)` << 1 */ + { 0x00000001b7215eda, 0x0000000042ccee08 }, + /* x^206848 mod p(x)` << 1, x^206912 mod p(x)` << 1 */ + { 0x00000001aaf1df3c, 0x000000010a389d74 }, + /* x^205824 mod p(x)` << 1, x^205888 mod p(x)` << 1 */ + { 0x0000000029d15b8a, 0x000000012a840da6 }, + /* x^204800 mod p(x)` << 1, x^204864 mod p(x)` << 1 */ + { 0x00000000f1a96922, 0x000000001d181c0c }, + /* x^203776 mod p(x)` << 1, x^203840 mod p(x)` << 1 */ + { 0x00000001ac80d03c, 0x0000000068b7d1f6 }, + /* x^202752 mod p(x)` << 1, x^202816 mod p(x)` << 1 */ + { 0x000000000f11d56a, 0x000000005b0f14fc }, + /* x^201728 mod p(x)` << 1, x^201792 mod p(x)` << 1 */ + { 0x00000001f1c022a2, 0x0000000179e9e730 }, + /* x^200704 mod p(x)` << 1, x^200768 mod p(x)` << 1 */ + { 0x0000000173d00ae2, 0x00000001ce1368d6 }, + /* x^199680 mod p(x)` << 1, x^199744 mod p(x)` << 1 */ + { 0x00000001d4ffe4ac, 0x0000000112c3a84c }, + /* x^198656 mod p(x)` << 1, x^198720 mod p(x)` << 1 */ + { 0x000000016edc5ae4, 0x00000000de940fee }, + /* x^197632 mod p(x)` << 1, x^197696 mod p(x)` << 1 */ + { 0x00000001f1a02140, 0x00000000fe896b7e }, + /* x^196608 mod p(x)` << 1, x^196672 mod p(x)` << 1 */ + { 0x00000000ca0b28a0, 0x00000001f797431c }, + /* x^195584 mod p(x)` << 1, x^195648 mod p(x)` << 1 */ + { 0x00000001928e30a2, 0x0000000053e989ba }, + /* x^194560 mod p(x)` << 1, x^194624 mod p(x)` << 1 */ + { 0x0000000097b1b002, 0x000000003920cd16 }, + /* x^193536 mod p(x)` << 1, x^193600 mod p(x)` << 1 */ + { 0x00000000b15bf906, 0x00000001e6f579b8 }, + /* x^192512 mod p(x)` << 1, x^192576 mod p(x)` << 1 */ + { 0x00000000411c5d52, 0x000000007493cb0a }, + /* x^191488 mod p(x)` << 1, x^191552 mod p(x)` << 1 */ + { 0x00000001c36f3300, 0x00000001bdd376d8 }, + /* x^190464 mod p(x)` << 1, x^190528 mod p(x)` << 1 */ + { 0x00000001119227e0, 0x000000016badfee6 }, + /* x^189440 mod p(x)` << 1, x^189504 mod p(x)` << 1 */ + { 0x00000000114d4702, 0x0000000071de5c58 }, + /* x^188416 mod p(x)` << 1, x^188480 mod p(x)` << 1 */ + { 0x00000000458b5b98, 0x00000000453f317c }, + /* x^187392 mod p(x)` << 1, x^187456 mod p(x)` << 1 */ + { 0x000000012e31fb8e, 0x0000000121675cce }, + /* x^186368 mod p(x)` << 1, x^186432 mod p(x)` << 1 */ + { 0x000000005cf619d8, 0x00000001f409ee92 }, + /* x^185344 mod p(x)` << 1, x^185408 mod p(x)` << 1 */ + { 0x0000000063f4d8b2, 0x00000000f36b9c88 }, + /* x^184320 mod p(x)` << 1, x^184384 mod p(x)` << 1 */ + { 0x000000004138dc8a, 0x0000000036b398f4 }, + /* x^183296 mod p(x)` << 1, x^183360 mod p(x)` << 1 */ + { 0x00000001d29ee8e0, 0x00000001748f9adc }, + /* x^182272 mod p(x)` << 1, x^182336 mod p(x)` << 1 */ + { 0x000000006a08ace8, 0x00000001be94ec00 }, + /* x^181248 mod p(x)` << 1, x^181312 mod p(x)` << 1 */ + { 0x0000000127d42010, 0x00000000b74370d6 }, + /* x^180224 mod p(x)` << 1, x^180288 mod p(x)` << 1 */ + { 0x0000000019d76b62, 0x00000001174d0b98 }, + /* x^179200 mod p(x)` << 1, x^179264 mod p(x)` << 1 */ + { 0x00000001b1471f6e, 0x00000000befc06a4 }, + /* x^178176 mod p(x)` << 1, x^178240 mod p(x)` << 1 */ + { 0x00000001f64c19cc, 0x00000001ae125288 }, + /* x^177152 mod p(x)` << 1, x^177216 mod p(x)` << 1 */ + { 0x00000000003c0ea0, 0x0000000095c19b34 }, + /* x^176128 mod p(x)` << 1, x^176192 mod p(x)` << 1 */ + { 0x000000014d73abf6, 0x00000001a78496f2 }, + /* x^175104 mod p(x)` << 1, x^175168 mod p(x)` << 1 */ + { 0x00000001620eb844, 0x00000001ac5390a0 }, + /* x^174080 mod p(x)` << 1, x^174144 mod p(x)` << 1 */ + { 0x0000000147655048, 0x000000002a80ed6e }, + /* x^173056 mod p(x)` << 1, x^173120 mod p(x)` << 1 */ + { 0x0000000067b5077e, 0x00000001fa9b0128 }, + /* x^172032 mod p(x)` << 1, x^172096 mod p(x)` << 1 */ + { 0x0000000010ffe206, 0x00000001ea94929e }, + /* x^171008 mod p(x)` << 1, x^171072 mod p(x)` << 1 */ + { 0x000000000fee8f1e, 0x0000000125f4305c }, + /* x^169984 mod p(x)` << 1, x^170048 mod p(x)` << 1 */ + { 0x00000001da26fbae, 0x00000001471e2002 }, + /* x^168960 mod p(x)` << 1, x^169024 mod p(x)` << 1 */ + { 0x00000001b3a8bd88, 0x0000000132d2253a }, + /* x^167936 mod p(x)` << 1, x^168000 mod p(x)` << 1 */ + { 0x00000000e8f3898e, 0x00000000f26b3592 }, + /* x^166912 mod p(x)` << 1, x^166976 mod p(x)` << 1 */ + { 0x00000000b0d0d28c, 0x00000000bc8b67b0 }, + /* x^165888 mod p(x)` << 1, x^165952 mod p(x)` << 1 */ + { 0x0000000030f2a798, 0x000000013a826ef2 }, + /* x^164864 mod p(x)` << 1, x^164928 mod p(x)` << 1 */ + { 0x000000000fba1002, 0x0000000081482c84 }, + /* x^163840 mod p(x)` << 1, x^163904 mod p(x)` << 1 */ + { 0x00000000bdb9bd72, 0x00000000e77307c2 }, + /* x^162816 mod p(x)` << 1, x^162880 mod p(x)` << 1 */ + { 0x0000000075d3bf5a, 0x00000000d4a07ec8 }, + /* x^161792 mod p(x)` << 1, x^161856 mod p(x)` << 1 */ + { 0x00000000ef1f98a0, 0x0000000017102100 }, + /* x^160768 mod p(x)` << 1, x^160832 mod p(x)` << 1 */ + { 0x00000000689c7602, 0x00000000db406486 }, + /* x^159744 mod p(x)` << 1, x^159808 mod p(x)` << 1 */ + { 0x000000016d5fa5fe, 0x0000000192db7f88 }, + /* x^158720 mod p(x)` << 1, x^158784 mod p(x)` << 1 */ + { 0x00000001d0d2b9ca, 0x000000018bf67b1e }, + /* x^157696 mod p(x)` << 1, x^157760 mod p(x)` << 1 */ + { 0x0000000041e7b470, 0x000000007c09163e }, + /* x^156672 mod p(x)` << 1, x^156736 mod p(x)` << 1 */ + { 0x00000001cbb6495e, 0x000000000adac060 }, + /* x^155648 mod p(x)` << 1, x^155712 mod p(x)` << 1 */ + { 0x000000010052a0b0, 0x00000000bd8316ae }, + /* x^154624 mod p(x)` << 1, x^154688 mod p(x)` << 1 */ + { 0x00000001d8effb5c, 0x000000019f09ab54 }, + /* x^153600 mod p(x)` << 1, x^153664 mod p(x)` << 1 */ + { 0x00000001d969853c, 0x0000000125155542 }, + /* x^152576 mod p(x)` << 1, x^152640 mod p(x)` << 1 */ + { 0x00000000523ccce2, 0x000000018fdb5882 }, + /* x^151552 mod p(x)` << 1, x^151616 mod p(x)` << 1 */ + { 0x000000001e2436bc, 0x00000000e794b3f4 }, + /* x^150528 mod p(x)` << 1, x^150592 mod p(x)` << 1 */ + { 0x00000000ddd1c3a2, 0x000000016f9bb022 }, + /* x^149504 mod p(x)` << 1, x^149568 mod p(x)` << 1 */ + { 0x0000000019fcfe38, 0x00000000290c9978 }, + /* x^148480 mod p(x)` << 1, x^148544 mod p(x)` << 1 */ + { 0x00000001ce95db64, 0x0000000083c0f350 }, + /* x^147456 mod p(x)` << 1, x^147520 mod p(x)` << 1 */ + { 0x00000000af582806, 0x0000000173ea6628 }, + /* x^146432 mod p(x)` << 1, x^146496 mod p(x)` << 1 */ + { 0x00000001006388f6, 0x00000001c8b4e00a }, + /* x^145408 mod p(x)` << 1, x^145472 mod p(x)` << 1 */ + { 0x0000000179eca00a, 0x00000000de95d6aa }, + /* x^144384 mod p(x)` << 1, x^144448 mod p(x)` << 1 */ + { 0x0000000122410a6a, 0x000000010b7f7248 }, + /* x^143360 mod p(x)` << 1, x^143424 mod p(x)` << 1 */ + { 0x000000004288e87c, 0x00000001326e3a06 }, + /* x^142336 mod p(x)` << 1, x^142400 mod p(x)` << 1 */ + { 0x000000016c5490da, 0x00000000bb62c2e6 }, + /* x^141312 mod p(x)` << 1, x^141376 mod p(x)` << 1 */ + { 0x00000000d1c71f6e, 0x0000000156a4b2c2 }, + /* x^140288 mod p(x)` << 1, x^140352 mod p(x)` << 1 */ + { 0x00000001b4ce08a6, 0x000000011dfe763a }, + /* x^139264 mod p(x)` << 1, x^139328 mod p(x)` << 1 */ + { 0x00000001466ba60c, 0x000000007bcca8e2 }, + /* x^138240 mod p(x)` << 1, x^138304 mod p(x)` << 1 */ + { 0x00000001f6c488a4, 0x0000000186118faa }, + /* x^137216 mod p(x)` << 1, x^137280 mod p(x)` << 1 */ + { 0x000000013bfb0682, 0x0000000111a65a88 }, + /* x^136192 mod p(x)` << 1, x^136256 mod p(x)` << 1 */ + { 0x00000000690e9e54, 0x000000003565e1c4 }, + /* x^135168 mod p(x)` << 1, x^135232 mod p(x)` << 1 */ + { 0x00000000281346b6, 0x000000012ed02a82 }, + /* x^134144 mod p(x)` << 1, x^134208 mod p(x)` << 1 */ + { 0x0000000156464024, 0x00000000c486ecfc }, + /* x^133120 mod p(x)` << 1, x^133184 mod p(x)` << 1 */ + { 0x000000016063a8dc, 0x0000000001b951b2 }, + /* x^132096 mod p(x)` << 1, x^132160 mod p(x)` << 1 */ + { 0x0000000116a66362, 0x0000000048143916 }, + /* x^131072 mod p(x)` << 1, x^131136 mod p(x)` << 1 */ + { 0x000000017e8aa4d2, 0x00000001dc2ae124 }, + /* x^130048 mod p(x)` << 1, x^130112 mod p(x)` << 1 */ + { 0x00000001728eb10c, 0x00000001416c58d6 }, + /* x^129024 mod p(x)` << 1, x^129088 mod p(x)` << 1 */ + { 0x00000001b08fd7fa, 0x00000000a479744a }, + /* x^128000 mod p(x)` << 1, x^128064 mod p(x)` << 1 */ + { 0x00000001092a16e8, 0x0000000096ca3a26 }, + /* x^126976 mod p(x)` << 1, x^127040 mod p(x)` << 1 */ + { 0x00000000a505637c, 0x00000000ff223d4e }, + /* x^125952 mod p(x)` << 1, x^126016 mod p(x)` << 1 */ + { 0x00000000d94869b2, 0x000000010e84da42 }, + /* x^124928 mod p(x)` << 1, x^124992 mod p(x)` << 1 */ + { 0x00000001c8b203ae, 0x00000001b61ba3d0 }, + /* x^123904 mod p(x)` << 1, x^123968 mod p(x)` << 1 */ + { 0x000000005704aea0, 0x00000000680f2de8 }, + /* x^122880 mod p(x)` << 1, x^122944 mod p(x)` << 1 */ + { 0x000000012e295fa2, 0x000000008772a9a8 }, + /* x^121856 mod p(x)` << 1, x^121920 mod p(x)` << 1 */ + { 0x000000011d0908bc, 0x0000000155f295bc }, + /* x^120832 mod p(x)` << 1, x^120896 mod p(x)` << 1 */ + { 0x0000000193ed97ea, 0x00000000595f9282 }, + /* x^119808 mod p(x)` << 1, x^119872 mod p(x)` << 1 */ + { 0x000000013a0f1c52, 0x0000000164b1c25a }, + /* x^118784 mod p(x)` << 1, x^118848 mod p(x)` << 1 */ + { 0x000000010c2c40c0, 0x00000000fbd67c50 }, + /* x^117760 mod p(x)` << 1, x^117824 mod p(x)` << 1 */ + { 0x00000000ff6fac3e, 0x0000000096076268 }, + /* x^116736 mod p(x)` << 1, x^116800 mod p(x)` << 1 */ + { 0x000000017b3609c0, 0x00000001d288e4cc }, + /* x^115712 mod p(x)` << 1, x^115776 mod p(x)` << 1 */ + { 0x0000000088c8c922, 0x00000001eaac1bdc }, + /* x^114688 mod p(x)` << 1, x^114752 mod p(x)` << 1 */ + { 0x00000001751baae6, 0x00000001f1ea39e2 }, + /* x^113664 mod p(x)` << 1, x^113728 mod p(x)` << 1 */ + { 0x0000000107952972, 0x00000001eb6506fc }, + /* x^112640 mod p(x)` << 1, x^112704 mod p(x)` << 1 */ + { 0x0000000162b00abe, 0x000000010f806ffe }, + /* x^111616 mod p(x)` << 1, x^111680 mod p(x)` << 1 */ + { 0x000000000d7b404c, 0x000000010408481e }, + /* x^110592 mod p(x)` << 1, x^110656 mod p(x)` << 1 */ + { 0x00000000763b13d4, 0x0000000188260534 }, + /* x^109568 mod p(x)` << 1, x^109632 mod p(x)` << 1 */ + { 0x00000000f6dc22d8, 0x0000000058fc73e0 }, + /* x^108544 mod p(x)` << 1, x^108608 mod p(x)` << 1 */ + { 0x000000007daae060, 0x00000000391c59b8 }, + /* x^107520 mod p(x)` << 1, x^107584 mod p(x)` << 1 */ + { 0x000000013359ab7c, 0x000000018b638400 }, + /* x^106496 mod p(x)` << 1, x^106560 mod p(x)` << 1 */ + { 0x000000008add438a, 0x000000011738f5c4 }, + /* x^105472 mod p(x)` << 1, x^105536 mod p(x)` << 1 */ + { 0x00000001edbefdea, 0x000000008cf7c6da }, + /* x^104448 mod p(x)` << 1, x^104512 mod p(x)` << 1 */ + { 0x000000004104e0f8, 0x00000001ef97fb16 }, + /* x^103424 mod p(x)` << 1, x^103488 mod p(x)` << 1 */ + { 0x00000000b48a8222, 0x0000000102130e20 }, + /* x^102400 mod p(x)` << 1, x^102464 mod p(x)` << 1 */ + { 0x00000001bcb46844, 0x00000000db968898 }, + /* x^101376 mod p(x)` << 1, x^101440 mod p(x)` << 1 */ + { 0x000000013293ce0a, 0x00000000b5047b5e }, + /* x^100352 mod p(x)` << 1, x^100416 mod p(x)` << 1 */ + { 0x00000001710d0844, 0x000000010b90fdb2 }, + /* x^99328 mod p(x)` << 1, x^99392 mod p(x)` << 1 */ + { 0x0000000117907f6e, 0x000000004834a32e }, + /* x^98304 mod p(x)` << 1, x^98368 mod p(x)` << 1 */ + { 0x0000000087ddf93e, 0x0000000059c8f2b0 }, + /* x^97280 mod p(x)` << 1, x^97344 mod p(x)` << 1 */ + { 0x000000005970e9b0, 0x0000000122cec508 }, + /* x^96256 mod p(x)` << 1, x^96320 mod p(x)` << 1 */ + { 0x0000000185b2b7d0, 0x000000000a330cda }, + /* x^95232 mod p(x)` << 1, x^95296 mod p(x)` << 1 */ + { 0x00000001dcee0efc, 0x000000014a47148c }, + /* x^94208 mod p(x)` << 1, x^94272 mod p(x)` << 1 */ + { 0x0000000030da2722, 0x0000000042c61cb8 }, + /* x^93184 mod p(x)` << 1, x^93248 mod p(x)` << 1 */ + { 0x000000012f925a18, 0x0000000012fe6960 }, + /* x^92160 mod p(x)` << 1, x^92224 mod p(x)` << 1 */ + { 0x00000000dd2e357c, 0x00000000dbda2c20 }, + /* x^91136 mod p(x)` << 1, x^91200 mod p(x)` << 1 */ + { 0x00000000071c80de, 0x000000011122410c }, + /* x^90112 mod p(x)` << 1, x^90176 mod p(x)` << 1 */ + { 0x000000011513140a, 0x00000000977b2070 }, + /* x^89088 mod p(x)` << 1, x^89152 mod p(x)` << 1 */ + { 0x00000001df876e8e, 0x000000014050438e }, + /* x^88064 mod p(x)` << 1, x^88128 mod p(x)` << 1 */ + { 0x000000015f81d6ce, 0x0000000147c840e8 }, + /* x^87040 mod p(x)` << 1, x^87104 mod p(x)` << 1 */ + { 0x000000019dd94dbe, 0x00000001cc7c88ce }, + /* x^86016 mod p(x)` << 1, x^86080 mod p(x)` << 1 */ + { 0x00000001373d206e, 0x00000001476b35a4 }, + /* x^84992 mod p(x)` << 1, x^85056 mod p(x)` << 1 */ + { 0x00000000668ccade, 0x000000013d52d508 }, + /* x^83968 mod p(x)` << 1, x^84032 mod p(x)` << 1 */ + { 0x00000001b192d268, 0x000000008e4be32e }, + /* x^82944 mod p(x)` << 1, x^83008 mod p(x)` << 1 */ + { 0x00000000e30f3a78, 0x00000000024120fe }, + /* x^81920 mod p(x)` << 1, x^81984 mod p(x)` << 1 */ + { 0x000000010ef1f7bc, 0x00000000ddecddb4 }, + /* x^80896 mod p(x)` << 1, x^80960 mod p(x)` << 1 */ + { 0x00000001f5ac7380, 0x00000000d4d403bc }, + /* x^79872 mod p(x)` << 1, x^79936 mod p(x)` << 1 */ + { 0x000000011822ea70, 0x00000001734b89aa }, + /* x^78848 mod p(x)` << 1, x^78912 mod p(x)` << 1 */ + { 0x00000000c3a33848, 0x000000010e7a58d6 }, + /* x^77824 mod p(x)` << 1, x^77888 mod p(x)` << 1 */ + { 0x00000001bd151c24, 0x00000001f9f04e9c }, + /* x^76800 mod p(x)` << 1, x^76864 mod p(x)` << 1 */ + { 0x0000000056002d76, 0x00000000b692225e }, + /* x^75776 mod p(x)` << 1, x^75840 mod p(x)` << 1 */ + { 0x000000014657c4f4, 0x000000019b8d3f3e }, + /* x^74752 mod p(x)` << 1, x^74816 mod p(x)` << 1 */ + { 0x0000000113742d7c, 0x00000001a874f11e }, + /* x^73728 mod p(x)` << 1, x^73792 mod p(x)` << 1 */ + { 0x000000019c5920ba, 0x000000010d5a4254 }, + /* x^72704 mod p(x)` << 1, x^72768 mod p(x)` << 1 */ + { 0x000000005216d2d6, 0x00000000bbb2f5d6 }, + /* x^71680 mod p(x)` << 1, x^71744 mod p(x)` << 1 */ + { 0x0000000136f5ad8a, 0x0000000179cc0e36 }, + /* x^70656 mod p(x)` << 1, x^70720 mod p(x)` << 1 */ + { 0x000000018b07beb6, 0x00000001dca1da4a }, + /* x^69632 mod p(x)` << 1, x^69696 mod p(x)` << 1 */ + { 0x00000000db1e93b0, 0x00000000feb1a192 }, + /* x^68608 mod p(x)` << 1, x^68672 mod p(x)` << 1 */ + { 0x000000000b96fa3a, 0x00000000d1eeedd6 }, + /* x^67584 mod p(x)` << 1, x^67648 mod p(x)` << 1 */ + { 0x00000001d9968af0, 0x000000008fad9bb4 }, + /* x^66560 mod p(x)` << 1, x^66624 mod p(x)` << 1 */ + { 0x000000000e4a77a2, 0x00000001884938e4 }, + /* x^65536 mod p(x)` << 1, x^65600 mod p(x)` << 1 */ + { 0x00000000508c2ac8, 0x00000001bc2e9bc0 }, + /* x^64512 mod p(x)` << 1, x^64576 mod p(x)` << 1 */ + { 0x0000000021572a80, 0x00000001f9658a68 }, + /* x^63488 mod p(x)` << 1, x^63552 mod p(x)` << 1 */ + { 0x00000001b859daf2, 0x000000001b9224fc }, + /* x^62464 mod p(x)` << 1, x^62528 mod p(x)` << 1 */ + { 0x000000016f788474, 0x0000000055b2fb84 }, + /* x^61440 mod p(x)` << 1, x^61504 mod p(x)` << 1 */ + { 0x00000001b438810e, 0x000000018b090348 }, + /* x^60416 mod p(x)` << 1, x^60480 mod p(x)` << 1 */ + { 0x0000000095ddc6f2, 0x000000011ccbd5ea }, + /* x^59392 mod p(x)` << 1, x^59456 mod p(x)` << 1 */ + { 0x00000001d977c20c, 0x0000000007ae47f8 }, + /* x^58368 mod p(x)` << 1, x^58432 mod p(x)` << 1 */ + { 0x00000000ebedb99a, 0x0000000172acbec0 }, + /* x^57344 mod p(x)` << 1, x^57408 mod p(x)` << 1 */ + { 0x00000001df9e9e92, 0x00000001c6e3ff20 }, + /* x^56320 mod p(x)` << 1, x^56384 mod p(x)` << 1 */ + { 0x00000001a4a3f952, 0x00000000e1b38744 }, + /* x^55296 mod p(x)` << 1, x^55360 mod p(x)` << 1 */ + { 0x00000000e2f51220, 0x00000000791585b2 }, + /* x^54272 mod p(x)` << 1, x^54336 mod p(x)` << 1 */ + { 0x000000004aa01f3e, 0x00000000ac53b894 }, + /* x^53248 mod p(x)` << 1, x^53312 mod p(x)` << 1 */ + { 0x00000000b3e90a58, 0x00000001ed5f2cf4 }, + /* x^52224 mod p(x)` << 1, x^52288 mod p(x)` << 1 */ + { 0x000000000c9ca2aa, 0x00000001df48b2e0 }, + /* x^51200 mod p(x)` << 1, x^51264 mod p(x)` << 1 */ + { 0x0000000151682316, 0x00000000049c1c62 }, + /* x^50176 mod p(x)` << 1, x^50240 mod p(x)` << 1 */ + { 0x0000000036fce78c, 0x000000017c460c12 }, + /* x^49152 mod p(x)` << 1, x^49216 mod p(x)` << 1 */ + { 0x000000009037dc10, 0x000000015be4da7e }, + /* x^48128 mod p(x)` << 1, x^48192 mod p(x)` << 1 */ + { 0x00000000d3298582, 0x000000010f38f668 }, + /* x^47104 mod p(x)` << 1, x^47168 mod p(x)` << 1 */ + { 0x00000001b42e8ad6, 0x0000000039f40a00 }, + /* x^46080 mod p(x)` << 1, x^46144 mod p(x)` << 1 */ + { 0x00000000142a9838, 0x00000000bd4c10c4 }, + /* x^45056 mod p(x)` << 1, x^45120 mod p(x)` << 1 */ + { 0x0000000109c7f190, 0x0000000042db1d98 }, + /* x^44032 mod p(x)` << 1, x^44096 mod p(x)` << 1 */ + { 0x0000000056ff9310, 0x00000001c905bae6 }, + /* x^43008 mod p(x)` << 1, x^43072 mod p(x)` << 1 */ + { 0x00000001594513aa, 0x00000000069d40ea }, + /* x^41984 mod p(x)` << 1, x^42048 mod p(x)` << 1 */ + { 0x00000001e3b5b1e8, 0x000000008e4fbad0 }, + /* x^40960 mod p(x)` << 1, x^41024 mod p(x)` << 1 */ + { 0x000000011dd5fc08, 0x0000000047bedd46 }, + /* x^39936 mod p(x)` << 1, x^40000 mod p(x)` << 1 */ + { 0x00000001675f0cc2, 0x0000000026396bf8 }, + /* x^38912 mod p(x)` << 1, x^38976 mod p(x)` << 1 */ + { 0x00000000d1c8dd44, 0x00000000379beb92 }, + /* x^37888 mod p(x)` << 1, x^37952 mod p(x)` << 1 */ + { 0x0000000115ebd3d8, 0x000000000abae54a }, + /* x^36864 mod p(x)` << 1, x^36928 mod p(x)` << 1 */ + { 0x00000001ecbd0dac, 0x0000000007e6a128 }, + /* x^35840 mod p(x)` << 1, x^35904 mod p(x)` << 1 */ + { 0x00000000cdf67af2, 0x000000000ade29d2 }, + /* x^34816 mod p(x)` << 1, x^34880 mod p(x)` << 1 */ + { 0x000000004c01ff4c, 0x00000000f974c45c }, + /* x^33792 mod p(x)` << 1, x^33856 mod p(x)` << 1 */ + { 0x00000000f2d8657e, 0x00000000e77ac60a }, + /* x^32768 mod p(x)` << 1, x^32832 mod p(x)` << 1 */ + { 0x000000006bae74c4, 0x0000000145895816 }, + /* x^31744 mod p(x)` << 1, x^31808 mod p(x)` << 1 */ + { 0x0000000152af8aa0, 0x0000000038e362be }, + /* x^30720 mod p(x)` << 1, x^30784 mod p(x)` << 1 */ + { 0x0000000004663802, 0x000000007f991a64 }, + /* x^29696 mod p(x)` << 1, x^29760 mod p(x)` << 1 */ + { 0x00000001ab2f5afc, 0x00000000fa366d3a }, + /* x^28672 mod p(x)` << 1, x^28736 mod p(x)` << 1 */ + { 0x0000000074a4ebd4, 0x00000001a2bb34f0 }, + /* x^27648 mod p(x)` << 1, x^27712 mod p(x)` << 1 */ + { 0x00000001d7ab3a4c, 0x0000000028a9981e }, + /* x^26624 mod p(x)` << 1, x^26688 mod p(x)` << 1 */ + { 0x00000001a8da60c6, 0x00000001dbc672be }, + /* x^25600 mod p(x)` << 1, x^25664 mod p(x)` << 1 */ + { 0x000000013cf63820, 0x00000000b04d77f6 }, + /* x^24576 mod p(x)` << 1, x^24640 mod p(x)` << 1 */ + { 0x00000000bec12e1e, 0x0000000124400d96 }, + /* x^23552 mod p(x)` << 1, x^23616 mod p(x)` << 1 */ + { 0x00000001c6368010, 0x000000014ca4b414 }, + /* x^22528 mod p(x)` << 1, x^22592 mod p(x)` << 1 */ + { 0x00000001e6e78758, 0x000000012fe2c938 }, + /* x^21504 mod p(x)` << 1, x^21568 mod p(x)` << 1 */ + { 0x000000008d7f2b3c, 0x00000001faed01e6 }, + /* x^20480 mod p(x)` << 1, x^20544 mod p(x)` << 1 */ + { 0x000000016b4a156e, 0x000000007e80ecfe }, + /* x^19456 mod p(x)` << 1, x^19520 mod p(x)` << 1 */ + { 0x00000001c63cfeb6, 0x0000000098daee94 }, + /* x^18432 mod p(x)` << 1, x^18496 mod p(x)` << 1 */ + { 0x000000015f902670, 0x000000010a04edea }, + /* x^17408 mod p(x)` << 1, x^17472 mod p(x)` << 1 */ + { 0x00000001cd5de11e, 0x00000001c00b4524 }, + /* x^16384 mod p(x)` << 1, x^16448 mod p(x)` << 1 */ + { 0x000000001acaec54, 0x0000000170296550 }, + /* x^15360 mod p(x)` << 1, x^15424 mod p(x)` << 1 */ + { 0x000000002bd0ca78, 0x0000000181afaa48 }, + /* x^14336 mod p(x)` << 1, x^14400 mod p(x)` << 1 */ + { 0x0000000032d63d5c, 0x0000000185a31ffa }, + /* x^13312 mod p(x)` << 1, x^13376 mod p(x)` << 1 */ + { 0x000000001c6d4e4c, 0x000000002469f608 }, + /* x^12288 mod p(x)` << 1, x^12352 mod p(x)` << 1 */ + { 0x0000000106a60b92, 0x000000006980102a }, + /* x^11264 mod p(x)` << 1, x^11328 mod p(x)` << 1 */ + { 0x00000000d3855e12, 0x0000000111ea9ca8 }, + /* x^10240 mod p(x)` << 1, x^10304 mod p(x)` << 1 */ + { 0x00000000e3125636, 0x00000001bd1d29ce }, + /* x^9216 mod p(x)` << 1, x^9280 mod p(x)` << 1 */ + { 0x000000009e8f7ea4, 0x00000001b34b9580 }, + /* x^8192 mod p(x)` << 1, x^8256 mod p(x)` << 1 */ + { 0x00000001c82e562c, 0x000000003076054e }, + /* x^7168 mod p(x)` << 1, x^7232 mod p(x)` << 1 */ + { 0x00000000ca9f09ce, 0x000000012a608ea4 }, + /* x^6144 mod p(x)` << 1, x^6208 mod p(x)` << 1 */ + { 0x00000000c63764e6, 0x00000000784d05fe }, + /* x^5120 mod p(x)` << 1, x^5184 mod p(x)` << 1 */ + { 0x0000000168d2e49e, 0x000000016ef0d82a }, + /* x^4096 mod p(x)` << 1, x^4160 mod p(x)` << 1 */ + { 0x00000000e986c148, 0x0000000075bda454 }, + /* x^3072 mod p(x)` << 1, x^3136 mod p(x)` << 1 */ + { 0x00000000cfb65894, 0x000000003dc0a1c4 }, + /* x^2048 mod p(x)` << 1, x^2112 mod p(x)` << 1 */ + { 0x0000000111cadee4, 0x00000000e9a5d8be }, + /* x^1024 mod p(x)` << 1, x^1088 mod p(x)` << 1 */ + { 0x0000000171fb63ce, 0x00000001609bc4b4 } +#endif /* __LITTLE_ENDIAN__ */ + }; + +/* Reduce final 1024-2048 bits to 64 bits, shifting 32 bits to include the trailing 32 bits of zeros */ + +static const __vector unsigned long long vcrc_short_const[16] + __attribute__((aligned (16))) = { +#ifdef __LITTLE_ENDIAN__ + /* x^1952 mod p(x) , x^1984 mod p(x) , x^2016 mod p(x) , x^2048 mod p(x) */ + { 0x5cf015c388e56f72, 0x7fec2963e5bf8048 }, + /* x^1824 mod p(x) , x^1856 mod p(x) , x^1888 mod p(x) , x^1920 mod p(x) */ + { 0x963a18920246e2e6, 0x38e888d4844752a9 }, + /* x^1696 mod p(x) , x^1728 mod p(x) , x^1760 mod p(x) , x^1792 mod p(x) */ + { 0x419a441956993a31, 0x42316c00730206ad }, + /* x^1568 mod p(x) , x^1600 mod p(x) , x^1632 mod p(x) , x^1664 mod p(x) */ + { 0x924752ba2b830011, 0x543d5c543e65ddf9 }, + /* x^1440 mod p(x) , x^1472 mod p(x) , x^1504 mod p(x) , x^1536 mod p(x) */ + { 0x55bd7f9518e4a304, 0x78e87aaf56767c92 }, + /* x^1312 mod p(x) , x^1344 mod p(x) , x^1376 mod p(x) , x^1408 mod p(x) */ + { 0x6d76739fe0553f1e, 0x8f68fcec1903da7f }, + /* x^1184 mod p(x) , x^1216 mod p(x) , x^1248 mod p(x) , x^1280 mod p(x) */ + { 0xc133722b1fe0b5c3, 0x3f4840246791d588 }, + /* x^1056 mod p(x) , x^1088 mod p(x) , x^1120 mod p(x) , x^1152 mod p(x) */ + { 0x64b67ee0e55ef1f3, 0x34c96751b04de25a }, + /* x^928 mod p(x) , x^960 mod p(x) , x^992 mod p(x) , x^1024 mod p(x) */ + { 0x069db049b8fdb1e7, 0x156c8e180b4a395b }, + /* x^800 mod p(x) , x^832 mod p(x) , x^864 mod p(x) , x^896 mod p(x) */ + { 0xa11bfaf3c9e90b9e, 0xe0b99ccbe661f7be }, + /* x^672 mod p(x) , x^704 mod p(x) , x^736 mod p(x) , x^768 mod p(x) */ + { 0x817cdc5119b29a35, 0x041d37768cd75659 }, + /* x^544 mod p(x) , x^576 mod p(x) , x^608 mod p(x) , x^640 mod p(x) */ + { 0x1ce9d94b36c41f1c, 0x3a0777818cfaa965 }, + /* x^416 mod p(x) , x^448 mod p(x) , x^480 mod p(x) , x^512 mod p(x) */ + { 0x4f256efcb82be955, 0x0e148e8252377a55 }, + /* x^288 mod p(x) , x^320 mod p(x) , x^352 mod p(x) , x^384 mod p(x) */ + { 0xec1631edb2dea967, 0x9c25531d19e65dde }, + /* x^160 mod p(x) , x^192 mod p(x) , x^224 mod p(x) , x^256 mod p(x) */ + { 0x5d27e147510ac59a, 0x790606ff9957c0a6 }, + /* x^32 mod p(x) , x^64 mod p(x) , x^96 mod p(x) , x^128 mod p(x) */ + { 0xa66805eb18b8ea18, 0x82f63b786ea2d55c } +#else /* __LITTLE_ENDIAN__ */ + /* x^1952 mod p(x) , x^1984 mod p(x) , x^2016 mod p(x) , x^2048 mod p(x) */ + { 0x7fec2963e5bf8048, 0x5cf015c388e56f72 }, + /* x^1824 mod p(x) , x^1856 mod p(x) , x^1888 mod p(x) , x^1920 mod p(x) */ + { 0x38e888d4844752a9, 0x963a18920246e2e6 }, + /* x^1696 mod p(x) , x^1728 mod p(x) , x^1760 mod p(x) , x^1792 mod p(x) */ + { 0x42316c00730206ad, 0x419a441956993a31 }, + /* x^1568 mod p(x) , x^1600 mod p(x) , x^1632 mod p(x) , x^1664 mod p(x) */ + { 0x543d5c543e65ddf9, 0x924752ba2b830011 }, + /* x^1440 mod p(x) , x^1472 mod p(x) , x^1504 mod p(x) , x^1536 mod p(x) */ + { 0x78e87aaf56767c92, 0x55bd7f9518e4a304 }, + /* x^1312 mod p(x) , x^1344 mod p(x) , x^1376 mod p(x) , x^1408 mod p(x) */ + { 0x8f68fcec1903da7f, 0x6d76739fe0553f1e }, + /* x^1184 mod p(x) , x^1216 mod p(x) , x^1248 mod p(x) , x^1280 mod p(x) */ + { 0x3f4840246791d588, 0xc133722b1fe0b5c3 }, + /* x^1056 mod p(x) , x^1088 mod p(x) , x^1120 mod p(x) , x^1152 mod p(x) */ + { 0x34c96751b04de25a, 0x64b67ee0e55ef1f3 }, + /* x^928 mod p(x) , x^960 mod p(x) , x^992 mod p(x) , x^1024 mod p(x) */ + { 0x156c8e180b4a395b, 0x069db049b8fdb1e7 }, + /* x^800 mod p(x) , x^832 mod p(x) , x^864 mod p(x) , x^896 mod p(x) */ + { 0xe0b99ccbe661f7be, 0xa11bfaf3c9e90b9e }, + /* x^672 mod p(x) , x^704 mod p(x) , x^736 mod p(x) , x^768 mod p(x) */ + { 0x041d37768cd75659, 0x817cdc5119b29a35 }, + /* x^544 mod p(x) , x^576 mod p(x) , x^608 mod p(x) , x^640 mod p(x) */ + { 0x3a0777818cfaa965, 0x1ce9d94b36c41f1c }, + /* x^416 mod p(x) , x^448 mod p(x) , x^480 mod p(x) , x^512 mod p(x) */ + { 0x0e148e8252377a55, 0x4f256efcb82be955 }, + /* x^288 mod p(x) , x^320 mod p(x) , x^352 mod p(x) , x^384 mod p(x) */ + { 0x9c25531d19e65dde, 0xec1631edb2dea967 }, + /* x^160 mod p(x) , x^192 mod p(x) , x^224 mod p(x) , x^256 mod p(x) */ + { 0x790606ff9957c0a6, 0x5d27e147510ac59a }, + /* x^32 mod p(x) , x^64 mod p(x) , x^96 mod p(x) , x^128 mod p(x) */ + { 0x82f63b786ea2d55c, 0xa66805eb18b8ea18 } +#endif /* __LITTLE_ENDIAN__ */ + }; + +/* Barrett constants */ +/* 33 bit reflected Barrett constant m - (4^32)/n */ + +static const __vector unsigned long long v_Barrett_const[2] + __attribute__((aligned (16))) = { + /* x^64 div p(x) */ +#ifdef __LITTLE_ENDIAN__ + { 0x00000000dea713f1, 0x0000000000000000 }, + { 0x0000000105ec76f1, 0x0000000000000000 } +#else /* __LITTLE_ENDIAN__ */ + { 0x0000000000000000, 0x00000000dea713f1 }, + { 0x0000000000000000, 0x0000000105ec76f1 } +#endif /* __LITTLE_ENDIAN__ */ + }; +#endif /* POWER8_INTRINSICS */ + +#else /* __ASSEMBLER__ */ +.constants: + + /* Reduce 262144 kbits to 1024 bits */ + /* x^261120 mod p(x)` << 1, x^261184 mod p(x)` << 1 */ + .octa 0x00000000b6ca9e20000000009c37c408 + + /* x^260096 mod p(x)` << 1, x^260160 mod p(x)` << 1 */ + .octa 0x00000000350249a800000001b51df26c + + /* x^259072 mod p(x)` << 1, x^259136 mod p(x)` << 1 */ + .octa 0x00000001862dac54000000000724b9d0 + + /* x^258048 mod p(x)` << 1, x^258112 mod p(x)` << 1 */ + .octa 0x00000001d87fb48c00000001c00532fe + + /* x^257024 mod p(x)` << 1, x^257088 mod p(x)` << 1 */ + .octa 0x00000001f39b699e00000000f05a9362 + + /* x^256000 mod p(x)` << 1, x^256064 mod p(x)` << 1 */ + .octa 0x0000000101da11b400000001e1007970 + + /* x^254976 mod p(x)` << 1, x^255040 mod p(x)` << 1 */ + .octa 0x00000001cab571e000000000a57366ee + + /* x^253952 mod p(x)` << 1, x^254016 mod p(x)` << 1 */ + .octa 0x00000000c7020cfe0000000192011284 + + /* x^252928 mod p(x)` << 1, x^252992 mod p(x)` << 1 */ + .octa 0x00000000cdaed1ae0000000162716d9a + + /* x^251904 mod p(x)` << 1, x^251968 mod p(x)` << 1 */ + .octa 0x00000001e804effc00000000cd97ecde + + /* x^250880 mod p(x)` << 1, x^250944 mod p(x)` << 1 */ + .octa 0x0000000077c3ea3a0000000058812bc0 + + /* x^249856 mod p(x)` << 1, x^249920 mod p(x)` << 1 */ + .octa 0x0000000068df31b40000000088b8c12e + + /* x^248832 mod p(x)` << 1, x^248896 mod p(x)` << 1 */ + .octa 0x00000000b059b6c200000001230b234c + + /* x^247808 mod p(x)` << 1, x^247872 mod p(x)` << 1 */ + .octa 0x0000000145fb8ed800000001120b416e + + /* x^246784 mod p(x)` << 1, x^246848 mod p(x)` << 1 */ + .octa 0x00000000cbc0916800000001974aecb0 + + /* x^245760 mod p(x)` << 1, x^245824 mod p(x)` << 1 */ + .octa 0x000000005ceeedc2000000008ee3f226 + + /* x^244736 mod p(x)` << 1, x^244800 mod p(x)` << 1 */ + .octa 0x0000000047d74e8600000001089aba9a + + /* x^243712 mod p(x)` << 1, x^243776 mod p(x)` << 1 */ + .octa 0x00000001407e9e220000000065113872 + + /* x^242688 mod p(x)` << 1, x^242752 mod p(x)` << 1 */ + .octa 0x00000001da967bda000000005c07ec10 + + /* x^241664 mod p(x)` << 1, x^241728 mod p(x)` << 1 */ + .octa 0x000000006c8983680000000187590924 + + /* x^240640 mod p(x)` << 1, x^240704 mod p(x)` << 1 */ + .octa 0x00000000f2d14c9800000000e35da7c6 + + /* x^239616 mod p(x)` << 1, x^239680 mod p(x)` << 1 */ + .octa 0x00000001993c6ad4000000000415855a + + /* x^238592 mod p(x)` << 1, x^238656 mod p(x)` << 1 */ + .octa 0x000000014683d1ac0000000073617758 + + /* x^237568 mod p(x)` << 1, x^237632 mod p(x)` << 1 */ + .octa 0x00000001a7c93e6c0000000176021d28 + + /* x^236544 mod p(x)` << 1, x^236608 mod p(x)` << 1 */ + .octa 0x000000010211e90a00000001c358fd0a + + /* x^235520 mod p(x)` << 1, x^235584 mod p(x)` << 1 */ + .octa 0x000000001119403e00000001ff7a2c18 + + /* x^234496 mod p(x)` << 1, x^234560 mod p(x)` << 1 */ + .octa 0x000000001c3261aa00000000f2d9f7e4 + + /* x^233472 mod p(x)` << 1, x^233536 mod p(x)` << 1 */ + .octa 0x000000014e37a634000000016cf1f9c8 + + /* x^232448 mod p(x)` << 1, x^232512 mod p(x)` << 1 */ + .octa 0x0000000073786c0c000000010af9279a + + /* x^231424 mod p(x)` << 1, x^231488 mod p(x)` << 1 */ + .octa 0x000000011dc037f80000000004f101e8 + + /* x^230400 mod p(x)` << 1, x^230464 mod p(x)` << 1 */ + .octa 0x0000000031433dfc0000000070bcf184 + + /* x^229376 mod p(x)` << 1, x^229440 mod p(x)` << 1 */ + .octa 0x000000009cde8348000000000a8de642 + + /* x^228352 mod p(x)` << 1, x^228416 mod p(x)` << 1 */ + .octa 0x0000000038d3c2a60000000062ea130c + + /* x^227328 mod p(x)` << 1, x^227392 mod p(x)` << 1 */ + .octa 0x000000011b25f26000000001eb31cbb2 + + /* x^226304 mod p(x)` << 1, x^226368 mod p(x)` << 1 */ + .octa 0x000000001629e6f00000000170783448 + + /* x^225280 mod p(x)` << 1, x^225344 mod p(x)` << 1 */ + .octa 0x0000000160838b4c00000001a684b4c6 + + /* x^224256 mod p(x)` << 1, x^224320 mod p(x)` << 1 */ + .octa 0x000000007a44011c00000000253ca5b4 + + /* x^223232 mod p(x)` << 1, x^223296 mod p(x)` << 1 */ + .octa 0x00000000226f417a0000000057b4b1e2 + + /* x^222208 mod p(x)` << 1, x^222272 mod p(x)` << 1 */ + .octa 0x0000000045eb2eb400000000b6bd084c + + /* x^221184 mod p(x)` << 1, x^221248 mod p(x)` << 1 */ + .octa 0x000000014459d70c0000000123c2d592 + + /* x^220160 mod p(x)` << 1, x^220224 mod p(x)` << 1 */ + .octa 0x00000001d406ed8200000000159dafce + + /* x^219136 mod p(x)` << 1, x^219200 mod p(x)` << 1 */ + .octa 0x0000000160c8e1a80000000127e1a64e + + /* x^218112 mod p(x)` << 1, x^218176 mod p(x)` << 1 */ + .octa 0x0000000027ba80980000000056860754 + + /* x^217088 mod p(x)` << 1, x^217152 mod p(x)` << 1 */ + .octa 0x000000006d92d01800000001e661aae8 + + /* x^216064 mod p(x)` << 1, x^216128 mod p(x)` << 1 */ + .octa 0x000000012ed7e3f200000000f82c6166 + + /* x^215040 mod p(x)` << 1, x^215104 mod p(x)` << 1 */ + .octa 0x000000002dc8778800000000c4f9c7ae + + /* x^214016 mod p(x)` << 1, x^214080 mod p(x)` << 1 */ + .octa 0x0000000018240bb80000000074203d20 + + /* x^212992 mod p(x)` << 1, x^213056 mod p(x)` << 1 */ + .octa 0x000000001ad381580000000198173052 + + /* x^211968 mod p(x)` << 1, x^212032 mod p(x)` << 1 */ + .octa 0x00000001396b78f200000001ce8aba54 + + /* x^210944 mod p(x)` << 1, x^211008 mod p(x)` << 1 */ + .octa 0x000000011a68133400000001850d5d94 + + /* x^209920 mod p(x)` << 1, x^209984 mod p(x)` << 1 */ + .octa 0x000000012104732e00000001d609239c + + /* x^208896 mod p(x)` << 1, x^208960 mod p(x)` << 1 */ + .octa 0x00000000a140d90c000000001595f048 + + /* x^207872 mod p(x)` << 1, x^207936 mod p(x)` << 1 */ + .octa 0x00000001b7215eda0000000042ccee08 + + /* x^206848 mod p(x)` << 1, x^206912 mod p(x)` << 1 */ + .octa 0x00000001aaf1df3c000000010a389d74 + + /* x^205824 mod p(x)` << 1, x^205888 mod p(x)` << 1 */ + .octa 0x0000000029d15b8a000000012a840da6 + + /* x^204800 mod p(x)` << 1, x^204864 mod p(x)` << 1 */ + .octa 0x00000000f1a96922000000001d181c0c + + /* x^203776 mod p(x)` << 1, x^203840 mod p(x)` << 1 */ + .octa 0x00000001ac80d03c0000000068b7d1f6 + + /* x^202752 mod p(x)` << 1, x^202816 mod p(x)` << 1 */ + .octa 0x000000000f11d56a000000005b0f14fc + + /* x^201728 mod p(x)` << 1, x^201792 mod p(x)` << 1 */ + .octa 0x00000001f1c022a20000000179e9e730 + + /* x^200704 mod p(x)` << 1, x^200768 mod p(x)` << 1 */ + .octa 0x0000000173d00ae200000001ce1368d6 + + /* x^199680 mod p(x)` << 1, x^199744 mod p(x)` << 1 */ + .octa 0x00000001d4ffe4ac0000000112c3a84c + + /* x^198656 mod p(x)` << 1, x^198720 mod p(x)` << 1 */ + .octa 0x000000016edc5ae400000000de940fee + + /* x^197632 mod p(x)` << 1, x^197696 mod p(x)` << 1 */ + .octa 0x00000001f1a0214000000000fe896b7e + + /* x^196608 mod p(x)` << 1, x^196672 mod p(x)` << 1 */ + .octa 0x00000000ca0b28a000000001f797431c + + /* x^195584 mod p(x)` << 1, x^195648 mod p(x)` << 1 */ + .octa 0x00000001928e30a20000000053e989ba + + /* x^194560 mod p(x)` << 1, x^194624 mod p(x)` << 1 */ + .octa 0x0000000097b1b002000000003920cd16 + + /* x^193536 mod p(x)` << 1, x^193600 mod p(x)` << 1 */ + .octa 0x00000000b15bf90600000001e6f579b8 + + /* x^192512 mod p(x)` << 1, x^192576 mod p(x)` << 1 */ + .octa 0x00000000411c5d52000000007493cb0a + + /* x^191488 mod p(x)` << 1, x^191552 mod p(x)` << 1 */ + .octa 0x00000001c36f330000000001bdd376d8 + + /* x^190464 mod p(x)` << 1, x^190528 mod p(x)` << 1 */ + .octa 0x00000001119227e0000000016badfee6 + + /* x^189440 mod p(x)` << 1, x^189504 mod p(x)` << 1 */ + .octa 0x00000000114d47020000000071de5c58 + + /* x^188416 mod p(x)` << 1, x^188480 mod p(x)` << 1 */ + .octa 0x00000000458b5b9800000000453f317c + + /* x^187392 mod p(x)` << 1, x^187456 mod p(x)` << 1 */ + .octa 0x000000012e31fb8e0000000121675cce + + /* x^186368 mod p(x)` << 1, x^186432 mod p(x)` << 1 */ + .octa 0x000000005cf619d800000001f409ee92 + + /* x^185344 mod p(x)` << 1, x^185408 mod p(x)` << 1 */ + .octa 0x0000000063f4d8b200000000f36b9c88 + + /* x^184320 mod p(x)` << 1, x^184384 mod p(x)` << 1 */ + .octa 0x000000004138dc8a0000000036b398f4 + + /* x^183296 mod p(x)` << 1, x^183360 mod p(x)` << 1 */ + .octa 0x00000001d29ee8e000000001748f9adc + + /* x^182272 mod p(x)` << 1, x^182336 mod p(x)` << 1 */ + .octa 0x000000006a08ace800000001be94ec00 + + /* x^181248 mod p(x)` << 1, x^181312 mod p(x)` << 1 */ + .octa 0x0000000127d4201000000000b74370d6 + + /* x^180224 mod p(x)` << 1, x^180288 mod p(x)` << 1 */ + .octa 0x0000000019d76b6200000001174d0b98 + + /* x^179200 mod p(x)` << 1, x^179264 mod p(x)` << 1 */ + .octa 0x00000001b1471f6e00000000befc06a4 + + /* x^178176 mod p(x)` << 1, x^178240 mod p(x)` << 1 */ + .octa 0x00000001f64c19cc00000001ae125288 + + /* x^177152 mod p(x)` << 1, x^177216 mod p(x)` << 1 */ + .octa 0x00000000003c0ea00000000095c19b34 + + /* x^176128 mod p(x)` << 1, x^176192 mod p(x)` << 1 */ + .octa 0x000000014d73abf600000001a78496f2 + + /* x^175104 mod p(x)` << 1, x^175168 mod p(x)` << 1 */ + .octa 0x00000001620eb84400000001ac5390a0 + + /* x^174080 mod p(x)` << 1, x^174144 mod p(x)` << 1 */ + .octa 0x0000000147655048000000002a80ed6e + + /* x^173056 mod p(x)` << 1, x^173120 mod p(x)` << 1 */ + .octa 0x0000000067b5077e00000001fa9b0128 + + /* x^172032 mod p(x)` << 1, x^172096 mod p(x)` << 1 */ + .octa 0x0000000010ffe20600000001ea94929e + + /* x^171008 mod p(x)` << 1, x^171072 mod p(x)` << 1 */ + .octa 0x000000000fee8f1e0000000125f4305c + + /* x^169984 mod p(x)` << 1, x^170048 mod p(x)` << 1 */ + .octa 0x00000001da26fbae00000001471e2002 + + /* x^168960 mod p(x)` << 1, x^169024 mod p(x)` << 1 */ + .octa 0x00000001b3a8bd880000000132d2253a + + /* x^167936 mod p(x)` << 1, x^168000 mod p(x)` << 1 */ + .octa 0x00000000e8f3898e00000000f26b3592 + + /* x^166912 mod p(x)` << 1, x^166976 mod p(x)` << 1 */ + .octa 0x00000000b0d0d28c00000000bc8b67b0 + + /* x^165888 mod p(x)` << 1, x^165952 mod p(x)` << 1 */ + .octa 0x0000000030f2a798000000013a826ef2 + + /* x^164864 mod p(x)` << 1, x^164928 mod p(x)` << 1 */ + .octa 0x000000000fba10020000000081482c84 + + /* x^163840 mod p(x)` << 1, x^163904 mod p(x)` << 1 */ + .octa 0x00000000bdb9bd7200000000e77307c2 + + /* x^162816 mod p(x)` << 1, x^162880 mod p(x)` << 1 */ + .octa 0x0000000075d3bf5a00000000d4a07ec8 + + /* x^161792 mod p(x)` << 1, x^161856 mod p(x)` << 1 */ + .octa 0x00000000ef1f98a00000000017102100 + + /* x^160768 mod p(x)` << 1, x^160832 mod p(x)` << 1 */ + .octa 0x00000000689c760200000000db406486 + + /* x^159744 mod p(x)` << 1, x^159808 mod p(x)` << 1 */ + .octa 0x000000016d5fa5fe0000000192db7f88 + + /* x^158720 mod p(x)` << 1, x^158784 mod p(x)` << 1 */ + .octa 0x00000001d0d2b9ca000000018bf67b1e + + /* x^157696 mod p(x)` << 1, x^157760 mod p(x)` << 1 */ + .octa 0x0000000041e7b470000000007c09163e + + /* x^156672 mod p(x)` << 1, x^156736 mod p(x)` << 1 */ + .octa 0x00000001cbb6495e000000000adac060 + + /* x^155648 mod p(x)` << 1, x^155712 mod p(x)` << 1 */ + .octa 0x000000010052a0b000000000bd8316ae + + /* x^154624 mod p(x)` << 1, x^154688 mod p(x)` << 1 */ + .octa 0x00000001d8effb5c000000019f09ab54 + + /* x^153600 mod p(x)` << 1, x^153664 mod p(x)` << 1 */ + .octa 0x00000001d969853c0000000125155542 + + /* x^152576 mod p(x)` << 1, x^152640 mod p(x)` << 1 */ + .octa 0x00000000523ccce2000000018fdb5882 + + /* x^151552 mod p(x)` << 1, x^151616 mod p(x)` << 1 */ + .octa 0x000000001e2436bc00000000e794b3f4 + + /* x^150528 mod p(x)` << 1, x^150592 mod p(x)` << 1 */ + .octa 0x00000000ddd1c3a2000000016f9bb022 + + /* x^149504 mod p(x)` << 1, x^149568 mod p(x)` << 1 */ + .octa 0x0000000019fcfe3800000000290c9978 + + /* x^148480 mod p(x)` << 1, x^148544 mod p(x)` << 1 */ + .octa 0x00000001ce95db640000000083c0f350 + + /* x^147456 mod p(x)` << 1, x^147520 mod p(x)` << 1 */ + .octa 0x00000000af5828060000000173ea6628 + + /* x^146432 mod p(x)` << 1, x^146496 mod p(x)` << 1 */ + .octa 0x00000001006388f600000001c8b4e00a + + /* x^145408 mod p(x)` << 1, x^145472 mod p(x)` << 1 */ + .octa 0x0000000179eca00a00000000de95d6aa + + /* x^144384 mod p(x)` << 1, x^144448 mod p(x)` << 1 */ + .octa 0x0000000122410a6a000000010b7f7248 + + /* x^143360 mod p(x)` << 1, x^143424 mod p(x)` << 1 */ + .octa 0x000000004288e87c00000001326e3a06 + + /* x^142336 mod p(x)` << 1, x^142400 mod p(x)` << 1 */ + .octa 0x000000016c5490da00000000bb62c2e6 + + /* x^141312 mod p(x)` << 1, x^141376 mod p(x)` << 1 */ + .octa 0x00000000d1c71f6e0000000156a4b2c2 + + /* x^140288 mod p(x)` << 1, x^140352 mod p(x)` << 1 */ + .octa 0x00000001b4ce08a6000000011dfe763a + + /* x^139264 mod p(x)` << 1, x^139328 mod p(x)` << 1 */ + .octa 0x00000001466ba60c000000007bcca8e2 + + /* x^138240 mod p(x)` << 1, x^138304 mod p(x)` << 1 */ + .octa 0x00000001f6c488a40000000186118faa + + /* x^137216 mod p(x)` << 1, x^137280 mod p(x)` << 1 */ + .octa 0x000000013bfb06820000000111a65a88 + + /* x^136192 mod p(x)` << 1, x^136256 mod p(x)` << 1 */ + .octa 0x00000000690e9e54000000003565e1c4 + + /* x^135168 mod p(x)` << 1, x^135232 mod p(x)` << 1 */ + .octa 0x00000000281346b6000000012ed02a82 + + /* x^134144 mod p(x)` << 1, x^134208 mod p(x)` << 1 */ + .octa 0x000000015646402400000000c486ecfc + + /* x^133120 mod p(x)` << 1, x^133184 mod p(x)` << 1 */ + .octa 0x000000016063a8dc0000000001b951b2 + + /* x^132096 mod p(x)` << 1, x^132160 mod p(x)` << 1 */ + .octa 0x0000000116a663620000000048143916 + + /* x^131072 mod p(x)` << 1, x^131136 mod p(x)` << 1 */ + .octa 0x000000017e8aa4d200000001dc2ae124 + + /* x^130048 mod p(x)` << 1, x^130112 mod p(x)` << 1 */ + .octa 0x00000001728eb10c00000001416c58d6 + + /* x^129024 mod p(x)` << 1, x^129088 mod p(x)` << 1 */ + .octa 0x00000001b08fd7fa00000000a479744a + + /* x^128000 mod p(x)` << 1, x^128064 mod p(x)` << 1 */ + .octa 0x00000001092a16e80000000096ca3a26 + + /* x^126976 mod p(x)` << 1, x^127040 mod p(x)` << 1 */ + .octa 0x00000000a505637c00000000ff223d4e + + /* x^125952 mod p(x)` << 1, x^126016 mod p(x)` << 1 */ + .octa 0x00000000d94869b2000000010e84da42 + + /* x^124928 mod p(x)` << 1, x^124992 mod p(x)` << 1 */ + .octa 0x00000001c8b203ae00000001b61ba3d0 + + /* x^123904 mod p(x)` << 1, x^123968 mod p(x)` << 1 */ + .octa 0x000000005704aea000000000680f2de8 + + /* x^122880 mod p(x)` << 1, x^122944 mod p(x)` << 1 */ + .octa 0x000000012e295fa2000000008772a9a8 + + /* x^121856 mod p(x)` << 1, x^121920 mod p(x)` << 1 */ + .octa 0x000000011d0908bc0000000155f295bc + + /* x^120832 mod p(x)` << 1, x^120896 mod p(x)` << 1 */ + .octa 0x0000000193ed97ea00000000595f9282 + + /* x^119808 mod p(x)` << 1, x^119872 mod p(x)` << 1 */ + .octa 0x000000013a0f1c520000000164b1c25a + + /* x^118784 mod p(x)` << 1, x^118848 mod p(x)` << 1 */ + .octa 0x000000010c2c40c000000000fbd67c50 + + /* x^117760 mod p(x)` << 1, x^117824 mod p(x)` << 1 */ + .octa 0x00000000ff6fac3e0000000096076268 + + /* x^116736 mod p(x)` << 1, x^116800 mod p(x)` << 1 */ + .octa 0x000000017b3609c000000001d288e4cc + + /* x^115712 mod p(x)` << 1, x^115776 mod p(x)` << 1 */ + .octa 0x0000000088c8c92200000001eaac1bdc + + /* x^114688 mod p(x)` << 1, x^114752 mod p(x)` << 1 */ + .octa 0x00000001751baae600000001f1ea39e2 + + /* x^113664 mod p(x)` << 1, x^113728 mod p(x)` << 1 */ + .octa 0x000000010795297200000001eb6506fc + + /* x^112640 mod p(x)` << 1, x^112704 mod p(x)` << 1 */ + .octa 0x0000000162b00abe000000010f806ffe + + /* x^111616 mod p(x)` << 1, x^111680 mod p(x)` << 1 */ + .octa 0x000000000d7b404c000000010408481e + + /* x^110592 mod p(x)` << 1, x^110656 mod p(x)` << 1 */ + .octa 0x00000000763b13d40000000188260534 + + /* x^109568 mod p(x)` << 1, x^109632 mod p(x)` << 1 */ + .octa 0x00000000f6dc22d80000000058fc73e0 + + /* x^108544 mod p(x)` << 1, x^108608 mod p(x)` << 1 */ + .octa 0x000000007daae06000000000391c59b8 + + /* x^107520 mod p(x)` << 1, x^107584 mod p(x)` << 1 */ + .octa 0x000000013359ab7c000000018b638400 + + /* x^106496 mod p(x)` << 1, x^106560 mod p(x)` << 1 */ + .octa 0x000000008add438a000000011738f5c4 + + /* x^105472 mod p(x)` << 1, x^105536 mod p(x)` << 1 */ + .octa 0x00000001edbefdea000000008cf7c6da + + /* x^104448 mod p(x)` << 1, x^104512 mod p(x)` << 1 */ + .octa 0x000000004104e0f800000001ef97fb16 + + /* x^103424 mod p(x)` << 1, x^103488 mod p(x)` << 1 */ + .octa 0x00000000b48a82220000000102130e20 + + /* x^102400 mod p(x)` << 1, x^102464 mod p(x)` << 1 */ + .octa 0x00000001bcb4684400000000db968898 + + /* x^101376 mod p(x)` << 1, x^101440 mod p(x)` << 1 */ + .octa 0x000000013293ce0a00000000b5047b5e + + /* x^100352 mod p(x)` << 1, x^100416 mod p(x)` << 1 */ + .octa 0x00000001710d0844000000010b90fdb2 + + /* x^99328 mod p(x)` << 1, x^99392 mod p(x)` << 1 */ + .octa 0x0000000117907f6e000000004834a32e + + /* x^98304 mod p(x)` << 1, x^98368 mod p(x)` << 1 */ + .octa 0x0000000087ddf93e0000000059c8f2b0 + + /* x^97280 mod p(x)` << 1, x^97344 mod p(x)` << 1 */ + .octa 0x000000005970e9b00000000122cec508 + + /* x^96256 mod p(x)` << 1, x^96320 mod p(x)` << 1 */ + .octa 0x0000000185b2b7d0000000000a330cda + + /* x^95232 mod p(x)` << 1, x^95296 mod p(x)` << 1 */ + .octa 0x00000001dcee0efc000000014a47148c + + /* x^94208 mod p(x)` << 1, x^94272 mod p(x)` << 1 */ + .octa 0x0000000030da27220000000042c61cb8 + + /* x^93184 mod p(x)` << 1, x^93248 mod p(x)` << 1 */ + .octa 0x000000012f925a180000000012fe6960 + + /* x^92160 mod p(x)` << 1, x^92224 mod p(x)` << 1 */ + .octa 0x00000000dd2e357c00000000dbda2c20 + + /* x^91136 mod p(x)` << 1, x^91200 mod p(x)` << 1 */ + .octa 0x00000000071c80de000000011122410c + + /* x^90112 mod p(x)` << 1, x^90176 mod p(x)` << 1 */ + .octa 0x000000011513140a00000000977b2070 + + /* x^89088 mod p(x)` << 1, x^89152 mod p(x)` << 1 */ + .octa 0x00000001df876e8e000000014050438e + + /* x^88064 mod p(x)` << 1, x^88128 mod p(x)` << 1 */ + .octa 0x000000015f81d6ce0000000147c840e8 + + /* x^87040 mod p(x)` << 1, x^87104 mod p(x)` << 1 */ + .octa 0x000000019dd94dbe00000001cc7c88ce + + /* x^86016 mod p(x)` << 1, x^86080 mod p(x)` << 1 */ + .octa 0x00000001373d206e00000001476b35a4 + + /* x^84992 mod p(x)` << 1, x^85056 mod p(x)` << 1 */ + .octa 0x00000000668ccade000000013d52d508 + + /* x^83968 mod p(x)` << 1, x^84032 mod p(x)` << 1 */ + .octa 0x00000001b192d268000000008e4be32e + + /* x^82944 mod p(x)` << 1, x^83008 mod p(x)` << 1 */ + .octa 0x00000000e30f3a7800000000024120fe + + /* x^81920 mod p(x)` << 1, x^81984 mod p(x)` << 1 */ + .octa 0x000000010ef1f7bc00000000ddecddb4 + + /* x^80896 mod p(x)` << 1, x^80960 mod p(x)` << 1 */ + .octa 0x00000001f5ac738000000000d4d403bc + + /* x^79872 mod p(x)` << 1, x^79936 mod p(x)` << 1 */ + .octa 0x000000011822ea7000000001734b89aa + + /* x^78848 mod p(x)` << 1, x^78912 mod p(x)` << 1 */ + .octa 0x00000000c3a33848000000010e7a58d6 + + /* x^77824 mod p(x)` << 1, x^77888 mod p(x)` << 1 */ + .octa 0x00000001bd151c2400000001f9f04e9c + + /* x^76800 mod p(x)` << 1, x^76864 mod p(x)` << 1 */ + .octa 0x0000000056002d7600000000b692225e + + /* x^75776 mod p(x)` << 1, x^75840 mod p(x)` << 1 */ + .octa 0x000000014657c4f4000000019b8d3f3e + + /* x^74752 mod p(x)` << 1, x^74816 mod p(x)` << 1 */ + .octa 0x0000000113742d7c00000001a874f11e + + /* x^73728 mod p(x)` << 1, x^73792 mod p(x)` << 1 */ + .octa 0x000000019c5920ba000000010d5a4254 + + /* x^72704 mod p(x)` << 1, x^72768 mod p(x)` << 1 */ + .octa 0x000000005216d2d600000000bbb2f5d6 + + /* x^71680 mod p(x)` << 1, x^71744 mod p(x)` << 1 */ + .octa 0x0000000136f5ad8a0000000179cc0e36 + + /* x^70656 mod p(x)` << 1, x^70720 mod p(x)` << 1 */ + .octa 0x000000018b07beb600000001dca1da4a + + /* x^69632 mod p(x)` << 1, x^69696 mod p(x)` << 1 */ + .octa 0x00000000db1e93b000000000feb1a192 + + /* x^68608 mod p(x)` << 1, x^68672 mod p(x)` << 1 */ + .octa 0x000000000b96fa3a00000000d1eeedd6 + + /* x^67584 mod p(x)` << 1, x^67648 mod p(x)` << 1 */ + .octa 0x00000001d9968af0000000008fad9bb4 + + /* x^66560 mod p(x)` << 1, x^66624 mod p(x)` << 1 */ + .octa 0x000000000e4a77a200000001884938e4 + + /* x^65536 mod p(x)` << 1, x^65600 mod p(x)` << 1 */ + .octa 0x00000000508c2ac800000001bc2e9bc0 + + /* x^64512 mod p(x)` << 1, x^64576 mod p(x)` << 1 */ + .octa 0x0000000021572a8000000001f9658a68 + + /* x^63488 mod p(x)` << 1, x^63552 mod p(x)` << 1 */ + .octa 0x00000001b859daf2000000001b9224fc + + /* x^62464 mod p(x)` << 1, x^62528 mod p(x)` << 1 */ + .octa 0x000000016f7884740000000055b2fb84 + + /* x^61440 mod p(x)` << 1, x^61504 mod p(x)` << 1 */ + .octa 0x00000001b438810e000000018b090348 + + /* x^60416 mod p(x)` << 1, x^60480 mod p(x)` << 1 */ + .octa 0x0000000095ddc6f2000000011ccbd5ea + + /* x^59392 mod p(x)` << 1, x^59456 mod p(x)` << 1 */ + .octa 0x00000001d977c20c0000000007ae47f8 + + /* x^58368 mod p(x)` << 1, x^58432 mod p(x)` << 1 */ + .octa 0x00000000ebedb99a0000000172acbec0 + + /* x^57344 mod p(x)` << 1, x^57408 mod p(x)` << 1 */ + .octa 0x00000001df9e9e9200000001c6e3ff20 + + /* x^56320 mod p(x)` << 1, x^56384 mod p(x)` << 1 */ + .octa 0x00000001a4a3f95200000000e1b38744 + + /* x^55296 mod p(x)` << 1, x^55360 mod p(x)` << 1 */ + .octa 0x00000000e2f5122000000000791585b2 + + /* x^54272 mod p(x)` << 1, x^54336 mod p(x)` << 1 */ + .octa 0x000000004aa01f3e00000000ac53b894 + + /* x^53248 mod p(x)` << 1, x^53312 mod p(x)` << 1 */ + .octa 0x00000000b3e90a5800000001ed5f2cf4 + + /* x^52224 mod p(x)` << 1, x^52288 mod p(x)` << 1 */ + .octa 0x000000000c9ca2aa00000001df48b2e0 + + /* x^51200 mod p(x)` << 1, x^51264 mod p(x)` << 1 */ + .octa 0x000000015168231600000000049c1c62 + + /* x^50176 mod p(x)` << 1, x^50240 mod p(x)` << 1 */ + .octa 0x0000000036fce78c000000017c460c12 + + /* x^49152 mod p(x)` << 1, x^49216 mod p(x)` << 1 */ + .octa 0x000000009037dc10000000015be4da7e + + /* x^48128 mod p(x)` << 1, x^48192 mod p(x)` << 1 */ + .octa 0x00000000d3298582000000010f38f668 + + /* x^47104 mod p(x)` << 1, x^47168 mod p(x)` << 1 */ + .octa 0x00000001b42e8ad60000000039f40a00 + + /* x^46080 mod p(x)` << 1, x^46144 mod p(x)` << 1 */ + .octa 0x00000000142a983800000000bd4c10c4 + + /* x^45056 mod p(x)` << 1, x^45120 mod p(x)` << 1 */ + .octa 0x0000000109c7f1900000000042db1d98 + + /* x^44032 mod p(x)` << 1, x^44096 mod p(x)` << 1 */ + .octa 0x0000000056ff931000000001c905bae6 + + /* x^43008 mod p(x)` << 1, x^43072 mod p(x)` << 1 */ + .octa 0x00000001594513aa00000000069d40ea + + /* x^41984 mod p(x)` << 1, x^42048 mod p(x)` << 1 */ + .octa 0x00000001e3b5b1e8000000008e4fbad0 + + /* x^40960 mod p(x)` << 1, x^41024 mod p(x)` << 1 */ + .octa 0x000000011dd5fc080000000047bedd46 + + /* x^39936 mod p(x)` << 1, x^40000 mod p(x)` << 1 */ + .octa 0x00000001675f0cc20000000026396bf8 + + /* x^38912 mod p(x)` << 1, x^38976 mod p(x)` << 1 */ + .octa 0x00000000d1c8dd4400000000379beb92 + + /* x^37888 mod p(x)` << 1, x^37952 mod p(x)` << 1 */ + .octa 0x0000000115ebd3d8000000000abae54a + + /* x^36864 mod p(x)` << 1, x^36928 mod p(x)` << 1 */ + .octa 0x00000001ecbd0dac0000000007e6a128 + + /* x^35840 mod p(x)` << 1, x^35904 mod p(x)` << 1 */ + .octa 0x00000000cdf67af2000000000ade29d2 + + /* x^34816 mod p(x)` << 1, x^34880 mod p(x)` << 1 */ + .octa 0x000000004c01ff4c00000000f974c45c + + /* x^33792 mod p(x)` << 1, x^33856 mod p(x)` << 1 */ + .octa 0x00000000f2d8657e00000000e77ac60a + + /* x^32768 mod p(x)` << 1, x^32832 mod p(x)` << 1 */ + .octa 0x000000006bae74c40000000145895816 + + /* x^31744 mod p(x)` << 1, x^31808 mod p(x)` << 1 */ + .octa 0x0000000152af8aa00000000038e362be + + /* x^30720 mod p(x)` << 1, x^30784 mod p(x)` << 1 */ + .octa 0x0000000004663802000000007f991a64 + + /* x^29696 mod p(x)` << 1, x^29760 mod p(x)` << 1 */ + .octa 0x00000001ab2f5afc00000000fa366d3a + + /* x^28672 mod p(x)` << 1, x^28736 mod p(x)` << 1 */ + .octa 0x0000000074a4ebd400000001a2bb34f0 + + /* x^27648 mod p(x)` << 1, x^27712 mod p(x)` << 1 */ + .octa 0x00000001d7ab3a4c0000000028a9981e + + /* x^26624 mod p(x)` << 1, x^26688 mod p(x)` << 1 */ + .octa 0x00000001a8da60c600000001dbc672be + + /* x^25600 mod p(x)` << 1, x^25664 mod p(x)` << 1 */ + .octa 0x000000013cf6382000000000b04d77f6 + + /* x^24576 mod p(x)` << 1, x^24640 mod p(x)` << 1 */ + .octa 0x00000000bec12e1e0000000124400d96 + + /* x^23552 mod p(x)` << 1, x^23616 mod p(x)` << 1 */ + .octa 0x00000001c6368010000000014ca4b414 + + /* x^22528 mod p(x)` << 1, x^22592 mod p(x)` << 1 */ + .octa 0x00000001e6e78758000000012fe2c938 + + /* x^21504 mod p(x)` << 1, x^21568 mod p(x)` << 1 */ + .octa 0x000000008d7f2b3c00000001faed01e6 + + /* x^20480 mod p(x)` << 1, x^20544 mod p(x)` << 1 */ + .octa 0x000000016b4a156e000000007e80ecfe + + /* x^19456 mod p(x)` << 1, x^19520 mod p(x)` << 1 */ + .octa 0x00000001c63cfeb60000000098daee94 + + /* x^18432 mod p(x)` << 1, x^18496 mod p(x)` << 1 */ + .octa 0x000000015f902670000000010a04edea + + /* x^17408 mod p(x)` << 1, x^17472 mod p(x)` << 1 */ + .octa 0x00000001cd5de11e00000001c00b4524 + + /* x^16384 mod p(x)` << 1, x^16448 mod p(x)` << 1 */ + .octa 0x000000001acaec540000000170296550 + + /* x^15360 mod p(x)` << 1, x^15424 mod p(x)` << 1 */ + .octa 0x000000002bd0ca780000000181afaa48 + + /* x^14336 mod p(x)` << 1, x^14400 mod p(x)` << 1 */ + .octa 0x0000000032d63d5c0000000185a31ffa + + /* x^13312 mod p(x)` << 1, x^13376 mod p(x)` << 1 */ + .octa 0x000000001c6d4e4c000000002469f608 + + /* x^12288 mod p(x)` << 1, x^12352 mod p(x)` << 1 */ + .octa 0x0000000106a60b92000000006980102a + + /* x^11264 mod p(x)` << 1, x^11328 mod p(x)` << 1 */ + .octa 0x00000000d3855e120000000111ea9ca8 + + /* x^10240 mod p(x)` << 1, x^10304 mod p(x)` << 1 */ + .octa 0x00000000e312563600000001bd1d29ce + + /* x^9216 mod p(x)` << 1, x^9280 mod p(x)` << 1 */ + .octa 0x000000009e8f7ea400000001b34b9580 + + /* x^8192 mod p(x)` << 1, x^8256 mod p(x)` << 1 */ + .octa 0x00000001c82e562c000000003076054e + + /* x^7168 mod p(x)` << 1, x^7232 mod p(x)` << 1 */ + .octa 0x00000000ca9f09ce000000012a608ea4 + + /* x^6144 mod p(x)` << 1, x^6208 mod p(x)` << 1 */ + .octa 0x00000000c63764e600000000784d05fe + + /* x^5120 mod p(x)` << 1, x^5184 mod p(x)` << 1 */ + .octa 0x0000000168d2e49e000000016ef0d82a + + /* x^4096 mod p(x)` << 1, x^4160 mod p(x)` << 1 */ + .octa 0x00000000e986c1480000000075bda454 + + /* x^3072 mod p(x)` << 1, x^3136 mod p(x)` << 1 */ + .octa 0x00000000cfb65894000000003dc0a1c4 + + /* x^2048 mod p(x)` << 1, x^2112 mod p(x)` << 1 */ + .octa 0x0000000111cadee400000000e9a5d8be + + /* x^1024 mod p(x)` << 1, x^1088 mod p(x)` << 1 */ + .octa 0x0000000171fb63ce00000001609bc4b4 + +.short_constants: + + /* Reduce final 1024-2048 bits to 64 bits, shifting 32 bits to include the trailing 32 bits of zeros */ + /* x^1952 mod p(x)`, x^1984 mod p(x)`, x^2016 mod p(x)`, x^2048 mod p(x)` */ + .octa 0x7fec2963e5bf80485cf015c388e56f72 + + /* x^1824 mod p(x)`, x^1856 mod p(x)`, x^1888 mod p(x)`, x^1920 mod p(x)` */ + .octa 0x38e888d4844752a9963a18920246e2e6 + + /* x^1696 mod p(x)`, x^1728 mod p(x)`, x^1760 mod p(x)`, x^1792 mod p(x)` */ + .octa 0x42316c00730206ad419a441956993a31 + + /* x^1568 mod p(x)`, x^1600 mod p(x)`, x^1632 mod p(x)`, x^1664 mod p(x)` */ + .octa 0x543d5c543e65ddf9924752ba2b830011 + + /* x^1440 mod p(x)`, x^1472 mod p(x)`, x^1504 mod p(x)`, x^1536 mod p(x)` */ + .octa 0x78e87aaf56767c9255bd7f9518e4a304 + + /* x^1312 mod p(x)`, x^1344 mod p(x)`, x^1376 mod p(x)`, x^1408 mod p(x)` */ + .octa 0x8f68fcec1903da7f6d76739fe0553f1e + + /* x^1184 mod p(x)`, x^1216 mod p(x)`, x^1248 mod p(x)`, x^1280 mod p(x)` */ + .octa 0x3f4840246791d588c133722b1fe0b5c3 + + /* x^1056 mod p(x)`, x^1088 mod p(x)`, x^1120 mod p(x)`, x^1152 mod p(x)` */ + .octa 0x34c96751b04de25a64b67ee0e55ef1f3 + + /* x^928 mod p(x)`, x^960 mod p(x)`, x^992 mod p(x)`, x^1024 mod p(x)` */ + .octa 0x156c8e180b4a395b069db049b8fdb1e7 + + /* x^800 mod p(x)`, x^832 mod p(x)`, x^864 mod p(x)`, x^896 mod p(x)` */ + .octa 0xe0b99ccbe661f7bea11bfaf3c9e90b9e + + /* x^672 mod p(x)`, x^704 mod p(x)`, x^736 mod p(x)`, x^768 mod p(x)` */ + .octa 0x041d37768cd75659817cdc5119b29a35 + + /* x^544 mod p(x)`, x^576 mod p(x)`, x^608 mod p(x)`, x^640 mod p(x)` */ + .octa 0x3a0777818cfaa9651ce9d94b36c41f1c + + /* x^416 mod p(x)`, x^448 mod p(x)`, x^480 mod p(x)`, x^512 mod p(x)` */ + .octa 0x0e148e8252377a554f256efcb82be955 + + /* x^288 mod p(x)`, x^320 mod p(x)`, x^352 mod p(x)`, x^384 mod p(x)` */ + .octa 0x9c25531d19e65ddeec1631edb2dea967 + + /* x^160 mod p(x)`, x^192 mod p(x)`, x^224 mod p(x)`, x^256 mod p(x)` */ + .octa 0x790606ff9957c0a65d27e147510ac59a + + /* x^32 mod p(x)`, x^64 mod p(x)`, x^96 mod p(x)`, x^128 mod p(x)` */ + .octa 0x82f63b786ea2d55ca66805eb18b8ea18 + + +.barrett_constants: + /* 33 bit reflected Barrett constant m - (4^32)/n */ + .octa 0x000000000000000000000000dea713f1 /* x^64 div p(x)` */ + /* 33 bit reflected Barrett constant n */ + .octa 0x00000000000000000000000105ec76f1 +#endif /* __ASSEMBLER__ */ diff --git a/src/Common/HashTable/vec_crc32.c b/src/Common/HashTable/vec_crc32.c new file mode 100644 index 000000000000..db09dfd11d72 --- /dev/null +++ b/src/Common/HashTable/vec_crc32.c @@ -0,0 +1,703 @@ +/* + * Calculate the checksum of data that is 16 byte aligned and a multiple of + * 16 bytes. + * + * The first step is to reduce it to 1024 bits. We do this in 8 parallel + * chunks in order to mask the latency of the vpmsum instructions. If we + * have more than 32 kB of data to checksum we repeat this step multiple + * times, passing in the previous 1024 bits. + * + * The next step is to reduce the 1024 bits to 64 bits. This step adds + * 32 bits of 0s to the end - this matches what a CRC does. We just + * calculate constants that land the data in this 32 bits. + * + * We then use fixed point Barrett reduction to compute a mod n over GF(2) + * for n = CRC using POWER8 instructions. We use x = 32. + * + * http://en.wikipedia.org/wiki/Barrett_reduction + * + * This code uses gcc vector builtins instead using assembly directly. + * + * Copyright (C) 2017 Rogerio Alves , IBM + * + * This program is free software; you can redistribute it and/or + * modify it under the terms of either: + * + * a) the GNU General Public License as published by the Free Software + * Foundation; either version 2 of the License, or (at your option) + * any later version, or + * b) the Apache License, Version 2.0 + */ +#pragma clang diagnostic push +#pragma clang diagnostic ignored "-Wreserved-identifier" +#pragma clang diagnostic ignored "-Wcast-qual" +#pragma clang diagnostic ignored "-Wreserved-identifier" +#pragma clang diagnostic ignored "-Wcast-qual" +#pragma clang diagnostic ignored "-Wlanguage-extension-token" +#pragma clang diagnostic ignored "-Wdeclaration-after-statement" +#pragma clang diagnostic ignored "-Wold-style-cast" +#pragma clang diagnostic ignored "-Wdeprecate-lax-vec-conv-all" +#pragma clang diagnostic ignored "-Wshorten-64-to-32" + +#include +#include +#include +#include +#define POWER8_INTRINSICS +#define CRC_TABLE + +#ifdef CRC32_CONSTANTS_HEADER +#include CRC32_CONSTANTS_HEADER +#else +#include "crc32_constants.h" +#endif +#define VMX_ALIGN 16 +#define VMX_ALIGN_MASK (VMX_ALIGN-1) + +#ifdef REFLECT +static unsigned int crc32_align(unsigned int crc, const unsigned char *p, + unsigned long len) +{ + while (len--) + crc = crc_table[(crc ^ *p++) & 0xff] ^ (crc >> 8); + return crc; +} +#else +static unsigned int crc32_align(unsigned int crc, const unsigned char *p, + unsigned long len) +{ + while (len--) + crc = crc_table[((crc >> 24) ^ *p++) & 0xff] ^ (crc << 8); + return crc; +} +#endif + +static unsigned int __attribute__ ((aligned (32))) +__crc32_vpmsum(unsigned int crc, const void* p, unsigned long len); + +#ifndef CRC32_FUNCTION +#define CRC32_FUNCTION crc32_vpmsum +#endif + +unsigned int CRC32_FUNCTION(unsigned int crc, const unsigned char *p, + unsigned long len) +{ + unsigned int prealign; + unsigned int tail; + +#ifdef CRC_XOR + crc ^= 0xffffffff; +#endif + + if (len < VMX_ALIGN + VMX_ALIGN_MASK) { + crc = crc32_align(crc, p, len); + goto out; + } + + if ((unsigned long)p & VMX_ALIGN_MASK) { + prealign = VMX_ALIGN - ((unsigned long)p & VMX_ALIGN_MASK); + crc = crc32_align(crc, p, prealign); + len -= prealign; + p += prealign; + } + + crc = __crc32_vpmsum(crc, p, len & ~VMX_ALIGN_MASK); + + tail = len & VMX_ALIGN_MASK; + if (tail) { + p += len & ~VMX_ALIGN_MASK; + crc = crc32_align(crc, p, tail); + } + +out: +#ifdef CRC_XOR + crc ^= 0xffffffff; +#endif + + return crc; +} + +/* This wrapper function works around the fact that crc32_vpmsum + * does not gracefully handle the case where the data pointer is NULL. There + * may be room for performance improvement here. + */ +uint32_t crc32_ppc(uint32_t crc, unsigned char const *data, size_t len) { + unsigned char *buf2; + + if (!data) { + buf2 = (unsigned char *)malloc(len); + bzero(buf2, len); + crc = crc32_vpmsum(crc, buf2, len); + free(buf2); + } else { + crc = crc32_vpmsum(crc, data, (unsigned long)len); + } + return crc; +} + +#if defined (__clang__) +#include "clang_workaround.h" +#else +#define __builtin_pack_vector(a, b) __builtin_pack_vector_int128 ((a), (b)) +#define __builtin_unpack_vector_0(a) __builtin_unpack_vector_int128 ((vector __int128_t)(a), 0) +#define __builtin_unpack_vector_1(a) __builtin_unpack_vector_int128 ((vector __int128_t)(a), 1) +#endif + +/* When we have a load-store in a single-dispatch group and address overlap + * such that foward is not allowed (load-hit-store) the group must be flushed. + * A group ending NOP prevents the flush. + */ +#define GROUP_ENDING_NOP asm("ori 2,2,0" ::: "memory") + +#if defined(__BIG_ENDIAN__) && defined (REFLECT) +#define BYTESWAP_DATA +#elif defined(__LITTLE_ENDIAN__) && !defined(REFLECT) +#define BYTESWAP_DATA +#endif + +#ifdef BYTESWAP_DATA +#define VEC_PERM(vr, va, vb, vc) vr = vec_perm(va, vb,\ + (__vector unsigned char) vc) +#if defined(__LITTLE_ENDIAN__) +/* Byte reverse permute constant LE. */ +static const __vector unsigned long long vperm_const + __attribute__ ((aligned(16))) = { 0x08090A0B0C0D0E0FUL, + 0x0001020304050607UL }; +#else +static const __vector unsigned long long vperm_const + __attribute__ ((aligned(16))) = { 0x0F0E0D0C0B0A0908UL, + 0X0706050403020100UL }; +#endif +#else +#define VEC_PERM(vr, va, vb, vc) +#endif + +static unsigned int __attribute__ ((aligned (32))) +__crc32_vpmsum(unsigned int crc, const void* p, unsigned long len) { + + const __vector unsigned long long vzero = {0,0}; + const __vector unsigned long long vones = {0xffffffffffffffffUL, + 0xffffffffffffffffUL}; + +#ifdef REFLECT + const __vector unsigned long long vmask_32bit = + (__vector unsigned long long)vec_sld((__vector unsigned char)vzero, + (__vector unsigned char)vones, 4); +#endif + + const __vector unsigned long long vmask_64bit = + (__vector unsigned long long)vec_sld((__vector unsigned char)vzero, + (__vector unsigned char)vones, 8); + + __vector unsigned long long vcrc; + + __vector unsigned long long vconst1, vconst2; + + /* vdata0-vdata7 will contain our data (p). */ + __vector unsigned long long vdata0, vdata1, vdata2, vdata3, vdata4, + vdata5, vdata6, vdata7; + + /* v0-v7 will contain our checksums */ + __vector unsigned long long v0 = {0,0}; + __vector unsigned long long v1 = {0,0}; + __vector unsigned long long v2 = {0,0}; + __vector unsigned long long v3 = {0,0}; + __vector unsigned long long v4 = {0,0}; + __vector unsigned long long v5 = {0,0}; + __vector unsigned long long v6 = {0,0}; + __vector unsigned long long v7 = {0,0}; + + + /* Vector auxiliary variables. */ + __vector unsigned long long va0, va1, va2, va3, va4, va5, va6, va7; + + unsigned int result = 0; + unsigned int offset; /* Constant table offset. */ + + unsigned long i; /* Counter. */ + unsigned long chunks; + + unsigned long block_size; + int next_block = 0; + + /* Align by 128 bits. The last 128 bit block will be processed at end. */ + unsigned long length = len & 0xFFFFFFFFFFFFFF80UL; + +#ifdef REFLECT + vcrc = (__vector unsigned long long)__builtin_pack_vector(0UL, crc); +#else + vcrc = (__vector unsigned long long)__builtin_pack_vector(crc, 0UL); + + /* Shift into top 32 bits */ + vcrc = (__vector unsigned long long)vec_sld((__vector unsigned char)vcrc, + (__vector unsigned char)vzero, 4); +#endif + + /* Short version. */ + if (len < 256) { + /* Calculate where in the constant table we need to start. */ + offset = 256 - len; + + vconst1 = vec_ld(offset, vcrc_short_const); + vdata0 = vec_ld(0, (__vector unsigned long long*) p); + VEC_PERM(vdata0, vdata0, vconst1, vperm_const); + + /* xor initial value*/ + vdata0 = vec_xor(vdata0, vcrc); + + vdata0 = (__vector unsigned long long) __builtin_crypto_vpmsumw + ((__vector unsigned int)vdata0, (__vector unsigned int)vconst1); + v0 = vec_xor(v0, vdata0); + + for (i = 16; i < len; i += 16) { + vconst1 = vec_ld(offset + i, vcrc_short_const); + vdata0 = vec_ld(i, (__vector unsigned long long*) p); + VEC_PERM(vdata0, vdata0, vconst1, vperm_const); + vdata0 = (__vector unsigned long long) __builtin_crypto_vpmsumw + ((__vector unsigned int)vdata0, (__vector unsigned int)vconst1); + v0 = vec_xor(v0, vdata0); + } + } else { + + /* Load initial values. */ + vdata0 = vec_ld(0, (__vector unsigned long long*) p); + vdata1 = vec_ld(16, (__vector unsigned long long*) p); + + VEC_PERM(vdata0, vdata0, vdata0, vperm_const); + VEC_PERM(vdata1, vdata1, vdata1, vperm_const); + + vdata2 = vec_ld(32, (__vector unsigned long long*) p); + vdata3 = vec_ld(48, (__vector unsigned long long*) p); + + VEC_PERM(vdata2, vdata2, vdata2, vperm_const); + VEC_PERM(vdata3, vdata3, vdata3, vperm_const); + + vdata4 = vec_ld(64, (__vector unsigned long long*) p); + vdata5 = vec_ld(80, (__vector unsigned long long*) p); + + VEC_PERM(vdata4, vdata4, vdata4, vperm_const); + VEC_PERM(vdata5, vdata5, vdata5, vperm_const); + + vdata6 = vec_ld(96, (__vector unsigned long long*) p); + vdata7 = vec_ld(112, (__vector unsigned long long*) p); + + VEC_PERM(vdata6, vdata6, vdata6, vperm_const); + VEC_PERM(vdata7, vdata7, vdata7, vperm_const); + + /* xor in initial value */ + vdata0 = vec_xor(vdata0, vcrc); + + p = (char *)p + 128; + + do { + /* Checksum in blocks of MAX_SIZE_VALUE. */ + block_size = length; + if (block_size > MAX_SIZE_VALUE) { + block_size = MAX_SIZE_VALUE; + } + + length = length - block_size; + + /* + * Work out the offset into the constants table to start at. Each + * constant is 16 bytes, and it is used against 128 bytes of input + * data - 128 / 16 = 8 + */ + offset = (MAX_SIZE_VALUE/8) - (block_size/8); + /* We reduce our final 128 bytes in a separate step */ + chunks = (block_size/128)-1; + + vconst1 = vec_ld(offset, vcrc_const); + + va0 = __builtin_crypto_vpmsumd ((__vector unsigned long long)vdata0, + (__vector unsigned long long)vconst1); + va1 = __builtin_crypto_vpmsumd ((__vector unsigned long long)vdata1, + (__vector unsigned long long)vconst1); + va2 = __builtin_crypto_vpmsumd ((__vector unsigned long long)vdata2, + (__vector unsigned long long)vconst1); + va3 = __builtin_crypto_vpmsumd ((__vector unsigned long long)vdata3, + (__vector unsigned long long)vconst1); + va4 = __builtin_crypto_vpmsumd ((__vector unsigned long long)vdata4, + (__vector unsigned long long)vconst1); + va5 = __builtin_crypto_vpmsumd ((__vector unsigned long long)vdata5, + (__vector unsigned long long)vconst1); + va6 = __builtin_crypto_vpmsumd ((__vector unsigned long long)vdata6, + (__vector unsigned long long)vconst1); + va7 = __builtin_crypto_vpmsumd ((__vector unsigned long long)vdata7, + (__vector unsigned long long)vconst1); + + if (chunks > 1) { + offset += 16; + vconst2 = vec_ld(offset, vcrc_const); + GROUP_ENDING_NOP; + + vdata0 = vec_ld(0, (__vector unsigned long long*) p); + VEC_PERM(vdata0, vdata0, vdata0, vperm_const); + + vdata1 = vec_ld(16, (__vector unsigned long long*) p); + VEC_PERM(vdata1, vdata1, vdata1, vperm_const); + + vdata2 = vec_ld(32, (__vector unsigned long long*) p); + VEC_PERM(vdata2, vdata2, vdata2, vperm_const); + + vdata3 = vec_ld(48, (__vector unsigned long long*) p); + VEC_PERM(vdata3, vdata3, vdata3, vperm_const); + + vdata4 = vec_ld(64, (__vector unsigned long long*) p); + VEC_PERM(vdata4, vdata4, vdata4, vperm_const); + + vdata5 = vec_ld(80, (__vector unsigned long long*) p); + VEC_PERM(vdata5, vdata5, vdata5, vperm_const); + + vdata6 = vec_ld(96, (__vector unsigned long long*) p); + VEC_PERM(vdata6, vdata6, vdata6, vperm_const); + + vdata7 = vec_ld(112, (__vector unsigned long long*) p); + VEC_PERM(vdata7, vdata7, vdata7, vperm_const); + + p = (char *)p + 128; + + /* + * main loop. We modulo schedule it such that it takes three + * iterations to complete - first iteration load, second + * iteration vpmsum, third iteration xor. + */ + for (i = 0; i < chunks-2; i++) { + vconst1 = vec_ld(offset, vcrc_const); + offset += 16; + GROUP_ENDING_NOP; + + v0 = vec_xor(v0, va0); + va0 = __builtin_crypto_vpmsumd ((__vector unsigned long + long)vdata0, (__vector unsigned long long)vconst2); + vdata0 = vec_ld(0, (__vector unsigned long long*) p); + VEC_PERM(vdata0, vdata0, vdata0, vperm_const); + GROUP_ENDING_NOP; + + v1 = vec_xor(v1, va1); + va1 = __builtin_crypto_vpmsumd ((__vector unsigned long + long)vdata1, (__vector unsigned long long)vconst2); + vdata1 = vec_ld(16, (__vector unsigned long long*) p); + VEC_PERM(vdata1, vdata1, vdata1, vperm_const); + GROUP_ENDING_NOP; + + v2 = vec_xor(v2, va2); + va2 = __builtin_crypto_vpmsumd ((__vector unsigned long + long)vdata2, (__vector unsigned long long)vconst2); + vdata2 = vec_ld(32, (__vector unsigned long long*) p); + VEC_PERM(vdata2, vdata2, vdata2, vperm_const); + GROUP_ENDING_NOP; + + v3 = vec_xor(v3, va3); + va3 = __builtin_crypto_vpmsumd ((__vector unsigned long + long)vdata3, (__vector unsigned long long)vconst2); + vdata3 = vec_ld(48, (__vector unsigned long long*) p); + VEC_PERM(vdata3, vdata3, vdata3, vperm_const); + + vconst2 = vec_ld(offset, vcrc_const); + GROUP_ENDING_NOP; + + v4 = vec_xor(v4, va4); + va4 = __builtin_crypto_vpmsumd ((__vector unsigned long + long)vdata4, (__vector unsigned long long)vconst1); + vdata4 = vec_ld(64, (__vector unsigned long long*) p); + VEC_PERM(vdata4, vdata4, vdata4, vperm_const); + GROUP_ENDING_NOP; + + v5 = vec_xor(v5, va5); + va5 = __builtin_crypto_vpmsumd ((__vector unsigned long + long)vdata5, (__vector unsigned long long)vconst1); + vdata5 = vec_ld(80, (__vector unsigned long long*) p); + VEC_PERM(vdata5, vdata5, vdata5, vperm_const); + GROUP_ENDING_NOP; + + v6 = vec_xor(v6, va6); + va6 = __builtin_crypto_vpmsumd ((__vector unsigned long + long)vdata6, (__vector unsigned long long)vconst1); + vdata6 = vec_ld(96, (__vector unsigned long long*) p); + VEC_PERM(vdata6, vdata6, vdata6, vperm_const); + GROUP_ENDING_NOP; + + v7 = vec_xor(v7, va7); + va7 = __builtin_crypto_vpmsumd ((__vector unsigned long + long)vdata7, (__vector unsigned long long)vconst1); + vdata7 = vec_ld(112, (__vector unsigned long long*) p); + VEC_PERM(vdata7, vdata7, vdata7, vperm_const); + + p = (char *)p + 128; + } + + /* First cool down*/ + vconst1 = vec_ld(offset, vcrc_const); + offset += 16; + + v0 = vec_xor(v0, va0); + va0 = __builtin_crypto_vpmsumd ((__vector unsigned long + long)vdata0, (__vector unsigned long long)vconst1); + GROUP_ENDING_NOP; + + v1 = vec_xor(v1, va1); + va1 = __builtin_crypto_vpmsumd ((__vector unsigned long + long)vdata1, (__vector unsigned long long)vconst1); + GROUP_ENDING_NOP; + + v2 = vec_xor(v2, va2); + va2 = __builtin_crypto_vpmsumd ((__vector unsigned long + long)vdata2, (__vector unsigned long long)vconst1); + GROUP_ENDING_NOP; + + v3 = vec_xor(v3, va3); + va3 = __builtin_crypto_vpmsumd ((__vector unsigned long + long)vdata3, (__vector unsigned long long)vconst1); + GROUP_ENDING_NOP; + + v4 = vec_xor(v4, va4); + va4 = __builtin_crypto_vpmsumd ((__vector unsigned long + long)vdata4, (__vector unsigned long long)vconst1); + GROUP_ENDING_NOP; + + v5 = vec_xor(v5, va5); + va5 = __builtin_crypto_vpmsumd ((__vector unsigned long + long)vdata5, (__vector unsigned long long)vconst1); + GROUP_ENDING_NOP; + + v6 = vec_xor(v6, va6); + va6 = __builtin_crypto_vpmsumd ((__vector unsigned long + long)vdata6, (__vector unsigned long long)vconst1); + GROUP_ENDING_NOP; + + v7 = vec_xor(v7, va7); + va7 = __builtin_crypto_vpmsumd ((__vector unsigned long + long)vdata7, (__vector unsigned long long)vconst1); + }/* else */ + + /* Second cool down. */ + v0 = vec_xor(v0, va0); + v1 = vec_xor(v1, va1); + v2 = vec_xor(v2, va2); + v3 = vec_xor(v3, va3); + v4 = vec_xor(v4, va4); + v5 = vec_xor(v5, va5); + v6 = vec_xor(v6, va6); + v7 = vec_xor(v7, va7); + +#ifdef REFLECT + /* + * vpmsumd produces a 96 bit result in the least significant bits + * of the register. Since we are bit reflected we have to shift it + * left 32 bits so it occupies the least significant bits in the + * bit reflected domain. + */ + v0 = (__vector unsigned long long)vec_sld((__vector unsigned char)v0, + (__vector unsigned char)vzero, 4); + v1 = (__vector unsigned long long)vec_sld((__vector unsigned char)v1, + (__vector unsigned char)vzero, 4); + v2 = (__vector unsigned long long)vec_sld((__vector unsigned char)v2, + (__vector unsigned char)vzero, 4); + v3 = (__vector unsigned long long)vec_sld((__vector unsigned char)v3, + (__vector unsigned char)vzero, 4); + v4 = (__vector unsigned long long)vec_sld((__vector unsigned char)v4, + (__vector unsigned char)vzero, 4); + v5 = (__vector unsigned long long)vec_sld((__vector unsigned char)v5, + (__vector unsigned char)vzero, 4); + v6 = (__vector unsigned long long)vec_sld((__vector unsigned char)v6, + (__vector unsigned char)vzero, 4); + v7 = (__vector unsigned long long)vec_sld((__vector unsigned char)v7, + (__vector unsigned char)vzero, 4); +#endif + + /* xor with the last 1024 bits. */ + va0 = vec_ld(0, (__vector unsigned long long*) p); + VEC_PERM(va0, va0, va0, vperm_const); + + va1 = vec_ld(16, (__vector unsigned long long*) p); + VEC_PERM(va1, va1, va1, vperm_const); + + va2 = vec_ld(32, (__vector unsigned long long*) p); + VEC_PERM(va2, va2, va2, vperm_const); + + va3 = vec_ld(48, (__vector unsigned long long*) p); + VEC_PERM(va3, va3, va3, vperm_const); + + va4 = vec_ld(64, (__vector unsigned long long*) p); + VEC_PERM(va4, va4, va4, vperm_const); + + va5 = vec_ld(80, (__vector unsigned long long*) p); + VEC_PERM(va5, va5, va5, vperm_const); + + va6 = vec_ld(96, (__vector unsigned long long*) p); + VEC_PERM(va6, va6, va6, vperm_const); + + va7 = vec_ld(112, (__vector unsigned long long*) p); + VEC_PERM(va7, va7, va7, vperm_const); + + p = (char *)p + 128; + + vdata0 = vec_xor(v0, va0); + vdata1 = vec_xor(v1, va1); + vdata2 = vec_xor(v2, va2); + vdata3 = vec_xor(v3, va3); + vdata4 = vec_xor(v4, va4); + vdata5 = vec_xor(v5, va5); + vdata6 = vec_xor(v6, va6); + vdata7 = vec_xor(v7, va7); + + /* Check if we have more blocks to process */ + next_block = 0; + if (length != 0) { + next_block = 1; + + /* zero v0-v7 */ + v0 = vec_xor(v0, v0); + v1 = vec_xor(v1, v1); + v2 = vec_xor(v2, v2); + v3 = vec_xor(v3, v3); + v4 = vec_xor(v4, v4); + v5 = vec_xor(v5, v5); + v6 = vec_xor(v6, v6); + v7 = vec_xor(v7, v7); + } + length = length + 128; + + } while (next_block); + + /* Calculate how many bytes we have left. */ + length = (len & 127); + + /* Calculate where in (short) constant table we need to start. */ + offset = 128 - length; + + v0 = vec_ld(offset, vcrc_short_const); + v1 = vec_ld(offset + 16, vcrc_short_const); + v2 = vec_ld(offset + 32, vcrc_short_const); + v3 = vec_ld(offset + 48, vcrc_short_const); + v4 = vec_ld(offset + 64, vcrc_short_const); + v5 = vec_ld(offset + 80, vcrc_short_const); + v6 = vec_ld(offset + 96, vcrc_short_const); + v7 = vec_ld(offset + 112, vcrc_short_const); + + offset += 128; + + v0 = (__vector unsigned long long)__builtin_crypto_vpmsumw ( + (__vector unsigned int)vdata0,(__vector unsigned int)v0); + v1 = (__vector unsigned long long)__builtin_crypto_vpmsumw ( + (__vector unsigned int)vdata1,(__vector unsigned int)v1); + v2 = (__vector unsigned long long)__builtin_crypto_vpmsumw ( + (__vector unsigned int)vdata2,(__vector unsigned int)v2); + v3 = (__vector unsigned long long)__builtin_crypto_vpmsumw ( + (__vector unsigned int)vdata3,(__vector unsigned int)v3); + v4 = (__vector unsigned long long)__builtin_crypto_vpmsumw ( + (__vector unsigned int)vdata4,(__vector unsigned int)v4); + v5 = (__vector unsigned long long)__builtin_crypto_vpmsumw ( + (__vector unsigned int)vdata5,(__vector unsigned int)v5); + v6 = (__vector unsigned long long)__builtin_crypto_vpmsumw ( + (__vector unsigned int)vdata6,(__vector unsigned int)v6); + v7 = (__vector unsigned long long)__builtin_crypto_vpmsumw ( + (__vector unsigned int)vdata7,(__vector unsigned int)v7); + + /* Now reduce the tail (0-112 bytes). */ + for (i = 0; i < length; i+=16) { + vdata0 = vec_ld(i,(__vector unsigned long long*)p); + VEC_PERM(vdata0, vdata0, vdata0, vperm_const); + va0 = vec_ld(offset + i,vcrc_short_const); + va0 = (__vector unsigned long long)__builtin_crypto_vpmsumw ( + (__vector unsigned int)vdata0,(__vector unsigned int)va0); + v0 = vec_xor(v0, va0); + } + + /* xor all parallel chunks together. */ + v0 = vec_xor(v0, v1); + v2 = vec_xor(v2, v3); + v4 = vec_xor(v4, v5); + v6 = vec_xor(v6, v7); + + v0 = vec_xor(v0, v2); + v4 = vec_xor(v4, v6); + + v0 = vec_xor(v0, v4); + } + + /* Barrett Reduction */ + vconst1 = vec_ld(0, v_Barrett_const); + vconst2 = vec_ld(16, v_Barrett_const); + + v1 = (__vector unsigned long long)vec_sld((__vector unsigned char)v0, + (__vector unsigned char)v0, 8); + v0 = vec_xor(v1,v0); + +#ifdef REFLECT + /* shift left one bit */ + __vector unsigned char vsht_splat = vec_splat_u8 (1); + v0 = (__vector unsigned long long)vec_sll ((__vector unsigned char)v0, + vsht_splat); +#endif + + v0 = vec_and(v0, vmask_64bit); + +#ifndef REFLECT + + /* + * Now for the actual algorithm. The idea is to calculate q, + * the multiple of our polynomial that we need to subtract. By + * doing the computation 2x bits higher (ie 64 bits) and shifting the + * result back down 2x bits, we round down to the nearest multiple. + */ + + /* ma */ + v1 = __builtin_crypto_vpmsumd ((__vector unsigned long long)v0, + (__vector unsigned long long)vconst1); + /* q = floor(ma/(2^64)) */ + v1 = (__vector unsigned long long)vec_sld ((__vector unsigned char)vzero, + (__vector unsigned char)v1, 8); + /* qn */ + v1 = __builtin_crypto_vpmsumd ((__vector unsigned long long)v1, + (__vector unsigned long long)vconst2); + /* a - qn, subtraction is xor in GF(2) */ + v0 = vec_xor (v0, v1); + /* + * Get the result into r3. We need to shift it left 8 bytes: + * V0 [ 0 1 2 X ] + * V0 [ 0 X 2 3 ] + */ + result = __builtin_unpack_vector_1 (v0); +#else + + /* + * The reflected version of Barrett reduction. Instead of bit + * reflecting our data (which is expensive to do), we bit reflect our + * constants and our algorithm, which means the intermediate data in + * our vector registers goes from 0-63 instead of 63-0. We can reflect + * the algorithm because we don't carry in mod 2 arithmetic. + */ + + /* bottom 32 bits of a */ + v1 = vec_and(v0, vmask_32bit); + + /* ma */ + v1 = __builtin_crypto_vpmsumd ((__vector unsigned long long)v1, + (__vector unsigned long long)vconst1); + + /* bottom 32bits of ma */ + v1 = vec_and(v1, vmask_32bit); + /* qn */ + v1 = __builtin_crypto_vpmsumd ((__vector unsigned long long)v1, + (__vector unsigned long long)vconst2); + /* a - qn, subtraction is xor in GF(2) */ + v0 = vec_xor (v0, v1); + + /* + * Since we are bit reflected, the result (ie the low 32 bits) is in + * the high 32 bits. We just need to shift it left 4 bytes + * V0 [ 0 1 X 3 ] + * V0 [ 0 X 2 3 ] + */ + + /* shift result into top 64 bits of */ + v0 = (__vector unsigned long long)vec_sld((__vector unsigned char)v0, + (__vector unsigned char)vzero, 4); + + result = __builtin_unpack_vector_0 (v0); +#endif + + return result; +} diff --git a/src/Common/HashTable/vec_crc32.h b/src/Common/HashTable/vec_crc32.h new file mode 100644 index 000000000000..87f0e2d9f567 --- /dev/null +++ b/src/Common/HashTable/vec_crc32.h @@ -0,0 +1,12 @@ +#pragma once + +#ifdef __cplusplus +extern "C" { +#endif + +extern uint32_t crc32_ppc(uint64_t crc, unsigned char const *buffer, + size_t len); + +#ifdef __cplusplus +} +#endif