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mirror of https://github.com/trezor/trezor-firmware.git synced 2024-11-15 20:19:23 +00:00

add more precomputation to ecdsa signing

This commit is contained in:
Pavol Rusnak 2014-05-15 17:11:26 +02:00
parent 94d4a3733e
commit 06dd166a82
4 changed files with 614 additions and 77 deletions

130
bignum.c
View File

@ -303,14 +303,20 @@ void bn_inverse(bignum256 *x, const bignum256 *prime)
void bn_inverse(bignum256 *x, const bignum256 *prime)
{
int i, j, k, len1, len2, mask;
uint32_t u[9], v[9], s[10], r[10], temp, temp2;
uint8_t buf[32];
uint32_t u[8], v[8], s[9], r[10], temp32;
uint64_t temp, temp2;
bn_fast_mod(x, prime);
bn_mod(x, prime);
for (i = 0; i < 9; i++) {
u[i] = prime->val[i];
v[i] = x->val[i];
bn_write_be(prime, buf);
for (i = 0; i < 8; i++) {
u[i] = read_be(buf + 28 - i * 4);
}
len1 = 9;
bn_write_be(x, buf);
for (i = 0; i < 8; i++) {
v[i] = read_be(buf + 28 - i * 4);
}
len1 = 8;
s[0] = 1;
r[0] = 0;
len2 = 1;
@ -327,13 +333,13 @@ void bn_inverse(bignum256 *x, const bignum256 *prime)
if (i == 0) break;
mask = (1 << i) - 1;
for (j = 0; j + 1 < len1; j++) {
u[j] = (u[j] >> i) | ((u[j + 1] & mask) << (30 - i));
u[j] = (u[j] >> i) | ((u[j + 1] & mask) << (32 - i));
}
u[j] = (u[j] >> i);
mask = (1 << (30 - i)) - 1;
s[len2] = s[len2 - 1] >> (30 - i);
mask = (1 << (32 - i)) - 1;
s[len2] = s[len2 - 1] >> (32 - i);
for (j = len2 - 1; j > 0; j--) {
s[j] = (s[j - 1] >> (30 - i)) | ((s[j] & mask) << i);
s[j] = (s[j - 1] >> (32 - i)) | ((s[j] & mask) << i);
}
s[0] = (s[0] & mask) << i;
if (s[len2]) {
@ -349,13 +355,13 @@ void bn_inverse(bignum256 *x, const bignum256 *prime)
if (i == 0) break;
mask = (1 << i) - 1;
for (j = 0; j + 1 < len1; j++) {
v[j] = (v[j] >> i) | ((v[j + 1] & mask) << (30 - i));
v[j] = (v[j] >> i) | ((v[j + 1] & mask) << (32 - i));
}
v[j] = (v[j] >> i);
mask = (1 << (30 - i)) - 1;
r[len2] = r[len2 - 1] >> (30 - i);
mask = (1 << (32 - i)) - 1;
r[len2] = r[len2 - 1] >> (32 - i);
for (j = len2 - 1; j > 0; j--) {
r[j] = (r[j - 1] >> (30 - i)) | ((r[j] & mask) << i);
r[j] = (r[j - 1] >> (32 - i)) | ((r[j] & mask) << i);
}
r[0] = (r[0] & mask) << i;
if (r[len2]) {
@ -368,23 +374,25 @@ void bn_inverse(bignum256 *x, const bignum256 *prime)
i = len1 - 1;
while (i > 0 && u[i] == v[i]) i--;
if (u[i] > v[i]) {
temp = 0x40000000u + u[0] - v[0];
u[0] = (temp >> 1) & 0x1FFFFFFF;
temp >>= 30;
temp = 0x100000000ull + u[0] - v[0];
u[0] = (temp >> 1) & 0x7FFFFFFF;
temp >>= 32;
for (i = 1; i < len1; i++) {
temp += 0x3FFFFFFFu + u[i] - v[i];
u[i - 1] += (temp & 1) << 29;
u[i] = (temp >> 1) & 0x1FFFFFFF;
temp >>= 30;
temp += 0xFFFFFFFFull + u[i] - v[i];
u[i - 1] += (temp & 1) << 31;
u[i] = (temp >> 1) & 0x7FFFFFFF;
temp >>= 32;
}
temp = temp2 = 0;
for (i = 0; i < len2; i++) {
temp += s[i] + r[i];
temp2 += s[i] << 1;
r[i] = temp & 0x3FFFFFFF;
s[i] = temp2 & 0x3FFFFFFF;
temp >>= 30;
temp2 >>= 30;
temp += s[i];
temp += r[i];
temp2 += s[i];
temp2 += s[i];
r[i] = temp;
s[i] = temp2;
temp >>= 32;
temp2 >>= 32;
}
if (temp != 0 || temp2 != 0) {
r[len2] = temp;
@ -392,23 +400,25 @@ void bn_inverse(bignum256 *x, const bignum256 *prime)
len2++;
}
} else {
temp = 0x40000000u + v[0] - u[0];
v[0] = (temp >> 1) & 0x1FFFFFFF;
temp >>= 30;
temp = 0x100000000ull + v[0] - u[0];
v[0] = (temp >> 1) & 0x7FFFFFFF;
temp >>= 32;
for (i = 1; i < len1; i++) {
temp += 0x3FFFFFFFu + v[i] - u[i];
v[i - 1] += (temp & 1) << 29;
v[i] = (temp >> 1) & 0x1FFFFFFF;
temp >>= 30;
temp += 0xFFFFFFFFull + v[i] - u[i];
v[i - 1] += (temp & 1) << 31;
v[i] = (temp >> 1) & 0x7FFFFFFF;
temp >>= 32;
}
temp = temp2 = 0;
for (i = 0; i < len2; i++) {
temp += s[i] + r[i];
temp2 += r[i] << 1;
s[i] = temp & 0x3FFFFFFF;
r[i] = temp2 & 0x3FFFFFFF;
temp >>= 30;
temp2 >>= 30;
temp += s[i];
temp += r[i];
temp2 += r[i];
temp2 += r[i];
s[i] = temp;
r[i] = temp2;
temp >>= 32;
temp2 >>= 32;
}
if (temp != 0 || temp2 != 0) {
s[len2] = temp;
@ -419,21 +429,33 @@ void bn_inverse(bignum256 *x, const bignum256 *prime)
if (u[len1 - 1] == 0 && v[len1 - 1] == 0) len1--;
k++;
}
j = r[0] >> 30;
r[0] = r[0] & 0x3FFFFFFFu;
for (i = 1; i < len2; i++) {
uint32_t q = r[i] >> (30 - 2 * i);
r[i] = ((r[i] << (2 * i)) & 0x3FFFFFFFu) + j;
j=q;
}
r[i] = j;
i++;
for (; i < 9; i++) r[i] = 0;
i = 8;
while (i > 0 && r[i] == prime->val[i]) i--;
if (r[i] >= prime->val[i]) {
temp = 1;
temp32 = 1;
for (i = 0; i < 9; i++) {
temp += 0x3FFFFFFF + r[i] - prime->val[i];
r[i] = temp & 0x3FFFFFFF;
temp >>= 30;
temp32 += 0x3FFFFFFF + r[i] - prime->val[i];
r[i] = temp32 & 0x3FFFFFFF;
temp32 >>= 30;
}
}
temp = 1;
temp32 = 1;
for (i = 0; i < 9; i++) {
temp += 0x3FFFFFFF + prime->val[i] - r[i];
r[i] = temp & 0x3FFFFFFF;
temp >>= 30;
temp32 += 0x3FFFFFFF + prime->val[i] - r[i];
r[i] = temp32 & 0x3FFFFFFF;
temp32 >>= 30;
}
int done = 0;
#if USE_PRECOMPUTED_IV
@ -449,14 +471,14 @@ void bn_inverse(bignum256 *x, const bignum256 *prime)
if (!done) {
for (j = 0; j < k; j++) {
if (r[0] & 1) {
temp = r[0] + prime->val[0];
r[0] = (temp >> 1) & 0x1FFFFFFF;
temp >>= 30;
temp32 = r[0] + prime->val[0];
r[0] = (temp32 >> 1) & 0x1FFFFFFF;
temp32 >>= 30;
for (i = 1; i < 9; i++) {
temp += r[i] + prime->val[i];
r[i - 1] += (temp & 1) << 29;
r[i] = (temp >> 1) & 0x1FFFFFFF;
temp >>= 30;
temp32 += r[i] + prime->val[i];
r[i - 1] += (temp32 & 1) << 29;
r[i] = (temp32 >> 1) & 0x1FFFFFFF;
temp32 >>= 30;
}
} else {
for (i = 0; i < 8; i++) {

31
ecdsa.c
View File

@ -122,38 +122,39 @@ void point_multiply(const bignum256 *k, const curve_point *p, curve_point *res)
// res = k * G
void scalar_multiply(const bignum256 *k, curve_point *res)
{
int i, j;
int i;
// result is zero
int is_zero = 1;
#if USE_PRECOMPUTED_CP
int exp = 0;
#else
curve_point curr;
// initial res
memcpy(&curr, &G256k1, sizeof(curve_point));
#endif
for (i = 0; i < 9; i++) {
for (j = 0; j < 30; j++) {
if (i == 8 && (k->val[i] >> j) == 0) break;
if (k->val[i] & (1u << j)) {
for (i = 0; i < 256; i++) {
if (k->val[i / 30] & (1u << (i % 30))) {
if (is_zero) {
#if USE_PRECOMPUTED_CP
memcpy(res, secp256k1_cp + exp, sizeof(curve_point));
if (i < 255 && (k->val[(i + 1) / 30] & (1u << ((i + 1) % 30)))) {
memcpy(res, secp256k1_cp2 + i, sizeof(curve_point));
i++;
} else {
memcpy(res, secp256k1_cp + i, sizeof(curve_point));
}
#else
memcpy(res, &curr, sizeof(curve_point));
#endif
is_zero = 0;
} else {
#if USE_PRECOMPUTED_CP
point_add(secp256k1_cp + exp, res);
if (i < 255 && (k->val[(i + 1) / 30] & (1u << ((i + 1) % 30)))) {
point_add(secp256k1_cp2 + i, res);
i++;
} else {
point_add(secp256k1_cp + i, res);
}
#else
point_add(&curr, res);
#endif
}
}
#if USE_PRECOMPUTED_CP
exp++;
#else
#if ! USE_PRECOMPUTED_CP
point_double(&curr);
#endif
}

View File

@ -815,4 +815,517 @@ const curve_point secp256k1_cp[256] = {
{/*.x =*/{/*.val =*/{0x3f8be384, 0x22f4c810, 0x31db6c3e, 0x3b02ab68, 0x1ef07271, 0x2b5b253f, 0x23e1b251, 0x24290af9, 0xb237}},
/*.y =*/{/*.val =*/{0x2b19880e, 0x4291cf7, 0x9ecb58d, 0x3c013d05, 0x1f94517, 0x143e22aa, 0x15edbe8d, 0x1a524675, 0xfc6b}}},
};
const curve_point secp256k1_cp2[255] = {
{/*.x =*/{/*.val =*/{0x3ce036f9, 0x1807c44e, 0x36f99b08, 0xc721160, 0x1d5229b5, 0x113e17e2, 0xc310493, 0x22806496, 0xf930}},
/*.y =*/{/*.val =*/{0x4b8e672, 0x32e7f5d6, 0xc2231b6, 0x2a664d, 0x37f35665, 0xcdf98a8, 0x1e8140fe, 0x1ec3d8cb, 0x388f}}},
{/*.x =*/{/*.val =*/{0x20297556, 0x3c15e851, 0x168a18b2, 0x3d91cbe1, 0x1235d382, 0x14e850d5, 0x2eea4204, 0x1ef55d57, 0xfff9}},
/*.y =*/{/*.val =*/{0x3075f297, 0x321c30da, 0x18fe4a03, 0x203c3d94, 0x5c560de, 0x3a5805fd, 0x3b620f3b, 0x1ddeab3e, 0xae12}}},
{/*.x =*/{/*.val =*/{0x30afe85a, 0x16c3d1c1, 0x220095bc, 0x1f3d1065, 0x33463368, 0xe3c0135, 0x3561b15c, 0x5755239, 0xd011}},
/*.y =*/{/*.val =*/{0x34062327, 0x2c146c4f, 0x1a86d526, 0x8e31776, 0x3bd81579, 0x1914df85, 0x1e0d7a8b, 0x13ff7205, 0xa9f3}}},
{/*.x =*/{/*.val =*/{0x3202e6ce, 0x140af6a2, 0x162b7940, 0xc8550e7, 0x3a8b0968, 0x2724586, 0x133d48ac, 0x310d504f, 0xfe72}},
/*.y =*/{/*.val =*/{0xf58c5bf, 0x1e3b4bef, 0x34a9d229, 0x372238da, 0x32998101, 0x2d1f8275, 0x24a68d3a, 0x37819ffc, 0x6851}}},
{/*.x =*/{/*.val =*/{0x1118e5c3, 0x2f61c2a8, 0x12bebc19, 0x15e6c9d1, 0x265b4bfc, 0x595bbd3, 0x1307db44, 0xcd76591, 0x6eca}},
/*.y =*/{/*.val =*/{0x5a08668, 0x2628bde0, 0x3f8ec344, 0x125a8e8e, 0x3875a03a, 0x3d5e41d2, 0x20710592, 0x8ed5e9e, 0xd501}}},
{/*.x =*/{/*.val =*/{0x3f8cb0e3, 0xe4ceb29, 0x1efe3a44, 0xbad4ff8, 0x2eb72ea2, 0x1938112c, 0x16d8f8fa, 0x20395d11, 0x3f0e}},
/*.y =*/{/*.val =*/{0x2a5f404f, 0x2c0a278b, 0x25b53a4c, 0x494ea9, 0x1d01b395, 0x2e702121, 0xbc91e90, 0x35f5ca5b, 0xcb66}}},
{/*.x =*/{/*.val =*/{0x33ce1752, 0x1edd43dc, 0x3cd204ec, 0x20f1e5f5, 0x1c9aeae7, 0x377d9366, 0x1c635812, 0x36963407, 0xd7a0}},
/*.y =*/{/*.val =*/{0x762cef4, 0x2f009ce0, 0x62b742b, 0x38102a30, 0x2284650b, 0xa4a0d03, 0x8032f6f, 0x1c381a00, 0x9127}}},
{/*.x =*/{/*.val =*/{0x35476085, 0x2422dc06, 0x2eb9f84a, 0x1c539de5, 0xed1afb5, 0xeab5a9e, 0xcd3e10d, 0x29c19e82, 0x3443}},
/*.y =*/{/*.val =*/{0xb8f52d8, 0x34d212f6, 0xc2b67f6, 0x2292c9f4, 0x3e1da901, 0x3a312e31, 0x36f854f6, 0x1e97e0a6, 0x661a}}},
{/*.x =*/{/*.val =*/{0x257e8dfa, 0x33f032e7, 0x3c7e184f, 0x20246468, 0x298ca009, 0x28c3e2b2, 0x19c4c0d9, 0x33cbfc1e, 0x8262}},
/*.y =*/{/*.val =*/{0x3bac376a, 0x173fe363, 0x314c4783, 0x2dbb4cca, 0x334f3457, 0x3b88bb16, 0x9e4e66f, 0x25788244, 0x83fd}}},
{/*.x =*/{/*.val =*/{0x3c70620c, 0x5f307c9, 0x3c288d9d, 0x26312faa, 0x27178049, 0x374c68ad, 0x236dc60, 0x2a29234b, 0x1653}},
/*.y =*/{/*.val =*/{0x315b32cd, 0x328ba074, 0x3d3dc526, 0xabdd237, 0x3a701c01, 0x2a651d3b, 0x37f7aeaf, 0xa424d6b, 0x338}}},
{/*.x =*/{/*.val =*/{0x271dabcd, 0x1f50ae9b, 0x1e5cb4f4, 0x34ff9262, 0x35373f54, 0x22b8c982, 0x3f43c609, 0x393edad8, 0xd49e}},
/*.y =*/{/*.val =*/{0x16603c2, 0x19aa433c, 0x2ff7031e, 0x271424c4, 0x1bf35612, 0x21fa9e98, 0x1490dd7c, 0x38e48269, 0x531}}},
{/*.x =*/{/*.val =*/{0xc8c828a, 0xfcc2ae4, 0x16ae41f5, 0xbac90b2, 0x281c7513, 0x1283605f, 0x9e750e4, 0x21472905, 0x5f94}},
/*.y =*/{/*.val =*/{0x37344d80, 0x3fac28fc, 0x3c68b04b, 0x19b7dd53, 0x2f35e8c, 0x1e5f622, 0x1fee8e5f, 0x30ee2be8, 0x26b8}}},
{/*.x =*/{/*.val =*/{0x5041216, 0x16dfe3c7, 0x2b836a6, 0x1ccd7da1, 0x2fed523f, 0x2d67bf70, 0x3acf4128, 0xc5ec87d, 0xda75}},
/*.y =*/{/*.val =*/{0x2e708572, 0x2bb4ca61, 0x37acedad, 0x2ab01eb9, 0x2d7fc6e9, 0x27886cd0, 0x2d5f0df1, 0x2811afdc, 0x73f8}}},
{/*.x =*/{/*.val =*/{0x3c62bac0, 0x1414c93c, 0x1f0ab069, 0x54377d4, 0x28b70e19, 0x12df4b0f, 0x3469c136, 0x3c3e408f, 0x9530}},
/*.y =*/{/*.val =*/{0x3618e309, 0x1e2af6a5, 0x31fdc684, 0x16cca14b, 0x3333e0e2, 0x34bdfd66, 0x321e234d, 0xc16a3e7, 0x8f3c}}},
{/*.x =*/{/*.val =*/{0x1c3c9c8f, 0x19c10e17, 0x24367b20, 0x205bfb8f, 0x2332b0f2, 0x27fd0eaa, 0x298fd6f0, 0xb72f90, 0x67be}},
/*.y =*/{/*.val =*/{0x193652d9, 0x14e12661, 0x388c2be5, 0x264efd82, 0x291693cd, 0x2516d820, 0x1ef84a2c, 0x1569cf93, 0x7a9b}}},
{/*.x =*/{/*.val =*/{0x10aaa33a, 0x7e6f2f8, 0x17b9ca51, 0x24b74a70, 0x1718368c, 0x1a404ef1, 0x3876adf5, 0x924bd3b, 0x893b}},
/*.y =*/{/*.val =*/{0x11af3445, 0x1ee02e2b, 0x3ceeb426, 0xe7a2884, 0x107f32a4, 0xe801d99, 0x1c89ef41, 0x14ad9cb4, 0xcdb1}}},
{/*.x =*/{/*.val =*/{0x36e55dc8, 0x2e24485b, 0x2ca04394, 0x3e56adba, 0x1094426f, 0x12910301, 0x1ffb2ba8, 0x1011e431, 0x4431}},
/*.y =*/{/*.val =*/{0x1be323b3, 0x76512bb, 0x2aa2e503, 0x1a8a6de7, 0x2fed7a6, 0x260dfd59, 0x366f8fe9, 0x3050b994, 0x96b0}}},
{/*.x =*/{/*.val =*/{0x33f0e9aa, 0x3ad78658, 0x11bd34b3, 0x449ddac, 0x138d268, 0x92b8356, 0x326adb79, 0x3fa15d7, 0xe538}},
/*.y =*/{/*.val =*/{0x82720f, 0x12e904d9, 0x68318ec, 0x2e53977d, 0xc8e016f, 0x244d8e49, 0x3b41d5b6, 0x361ce421, 0xb97f}}},
{/*.x =*/{/*.val =*/{0x2ebc61d6, 0x2bb4d86f, 0x1ff42de1, 0x23f4e9f6, 0x2b1f518a, 0x17c34575, 0x19af0c39, 0x3cf928fb, 0x939f}},
/*.y =*/{/*.val =*/{0x23f5cb70, 0x1d7a919a, 0x38c7f82e, 0x2fc9bad, 0x16c0498, 0x1bf13bbc, 0x3a90e9d4, 0xef3c22d, 0xdeab}}},
{/*.x =*/{/*.val =*/{0x497e0df, 0x5b84d37, 0xf76f530, 0xeed0dbb, 0x2029a04c, 0x161e17f9, 0x3293078, 0xf94ab8e, 0xfdc6}},
/*.y =*/{/*.val =*/{0x1b9eb19f, 0x1811127, 0x335d9d5f, 0x2fac8bef, 0x22e8b87b, 0x3dc50a2b, 0x3bb52e3d, 0x2b59eb3a, 0x292d}}},
{/*.x =*/{/*.val =*/{0x355812dd, 0x28a960b, 0x12d30e2a, 0x1119c8d5, 0x18f78e3d, 0x2afb5b01, 0x3352f0b6, 0x2f5ea4bf, 0x7029}},
/*.y =*/{/*.val =*/{0x1a2d2927, 0x87319ac, 0x3b2c73c7, 0x36ba1090, 0x683ac47, 0x19512b8c, 0xb3d27dd, 0x3eb6bf7a, 0xb0ee}}},
{/*.x =*/{/*.val =*/{0x3181fdc2, 0x336affe6, 0xc62364d, 0xbd8aed7, 0x234e7edd, 0x992e062, 0x26e474aa, 0x40abd1f, 0xf42c}},
/*.y =*/{/*.val =*/{0x2485d7fd, 0x7c0024e, 0x22acf268, 0x5540b66, 0x2fe22a4c, 0x2b4172e1, 0x2806c78f, 0xead1b3f, 0x5750}}},
{/*.x =*/{/*.val =*/{0x2edd7dd6, 0x219b51f7, 0x1e1968c3, 0xddbf899, 0x3cfdec49, 0x29e103b9, 0x3524bca5, 0x33da8931, 0x32cf}},
/*.y =*/{/*.val =*/{0x3e08e330, 0x17f512bb, 0x349a08b2, 0x3633480, 0x1f561e7a, 0x2025a902, 0x27748620, 0x1a8d25da, 0x2184}}},
{/*.x =*/{/*.val =*/{0x21231d11, 0x399d20c4, 0x2aaad7c, 0x2acdb18f, 0x37c39822, 0x455731d, 0x388e433d, 0x3507a2e4, 0x3514}},
/*.y =*/{/*.val =*/{0x23855df5, 0xf5bed03, 0x2f79ebe5, 0x213cc742, 0x39eff93, 0x1344795a, 0x17eb8ef4, 0xc940580, 0x89a8}}},
{/*.x =*/{/*.val =*/{0x633cb1, 0x159f827a, 0x1d021132, 0x168892da, 0x181fcb57, 0x189cc848, 0x2cad400c, 0x273cc5ea, 0x6dde}},
/*.y =*/{/*.val =*/{0x27ce6b34, 0x1f7526a9, 0x3859ef35, 0x2c9ff6b3, 0x3a66a880, 0x27be1a86, 0x3e41d5c9, 0x3ef9e9c1, 0x9188}}},
{/*.x =*/{/*.val =*/{0x4e5467d, 0x342f5da9, 0x1bbface4, 0x2422ae06, 0x970e940, 0x7d8b83b, 0x1a1222c2, 0x193c3f1a, 0x97d0}},
/*.y =*/{/*.val =*/{0x1e9cb3fa, 0x25cc03f4, 0xf17ccd7, 0x17ecee15, 0x10861fda, 0x1f19bea1, 0x2cc03f, 0x13cbb4cd, 0x8997}}},
{/*.x =*/{/*.val =*/{0x13613bec, 0x32a072e4, 0x1cfe67c, 0x2d7f2744, 0xf972a8b, 0x6ccf71d, 0x137bdedf, 0x32ae324e, 0x2dcf}},
/*.y =*/{/*.val =*/{0x1a039215, 0x39cc2492, 0x33f5f383, 0xcb3eeb4, 0x36c6f437, 0x222df5b, 0xa41265f, 0x3137651d, 0x46db}}},
{/*.x =*/{/*.val =*/{0x7fb9e1a, 0x1f345c21, 0x22a32961, 0x39d2dd37, 0x2b0e767f, 0xaf26ee, 0x2c5a8f1a, 0x1052a923, 0x1bec}},
/*.y =*/{/*.val =*/{0x349c0443, 0x1fdb845d, 0xc9796e5, 0x4e176ba, 0x54b0f68, 0x26f15cc3, 0x266678a7, 0x19c11c04, 0xe358}}},
{/*.x =*/{/*.val =*/{0x3b7ceceb, 0xfd9e3fe, 0x97faf0f, 0x2967e4e2, 0x2e681473, 0x3ee049bd, 0x2d45036f, 0x2188109d, 0x437a}},
/*.y =*/{/*.val =*/{0x16c181e1, 0xd8ef30d, 0x8f97827, 0x883f3f7, 0x1297ff87, 0x23fada67, 0x2c32f69b, 0x1ae84fba, 0xb91}}},
{/*.x =*/{/*.val =*/{0x1cbf00eb, 0x3276761f, 0x18d02274, 0x2d3a62f0, 0x230bc241, 0x385bda86, 0x2d4dc49b, 0x1c2ba5ba, 0xb890}},
/*.y =*/{/*.val =*/{0x1b0e664e, 0x2dfc6f34, 0x2b96a671, 0x362c1ad, 0x4a766cb, 0xa539307, 0x2d88f472, 0x3230b228, 0x6f24}}},
{/*.x =*/{/*.val =*/{0x36fbe7b2, 0x275bfe6a, 0x18d65a3b, 0x2b7b7051, 0x2884605e, 0x1aeec6ca, 0x41f8f33, 0x21d9a72d, 0x2648}},
/*.y =*/{/*.val =*/{0x21bc2a34, 0xca9e2f0, 0x20eb6039, 0xe36605a, 0x2ddf1856, 0x3cb72b40, 0x144988f2, 0x36ad2c80, 0x9e15}}},
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/*.y =*/{/*.val =*/{0x2e25fc0a, 0x26800fe6, 0xb63338f, 0x2fed4cb6, 0x130d6f3f, 0x15c3d894, 0x25edb63d, 0x1761ea8d, 0xa0e7}}},
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/*.y =*/{/*.val =*/{0x18aa258d, 0x13af9825, 0x2bb6a883, 0x296258c0, 0x2d1f754c, 0x1ea3185a, 0x1e0424d5, 0xdc0e035, 0xc68a}}},
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/*.y =*/{/*.val =*/{0x1ce0a03, 0x1b340441, 0x2e16eeb, 0x2684acc2, 0x2536d49c, 0x3888fbbd, 0x1b61ea54, 0xb8535b3, 0xfae6}}},
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/*.y =*/{/*.val =*/{0x3bb25302, 0x42a9346, 0xde59b1a, 0x1020ae59, 0x8a96d0, 0x33865be7, 0x1e5c9bfc, 0x38515254, 0xf65b}}},
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/*.y =*/{/*.val =*/{0x2716c458, 0x25cacb78, 0x2e449345, 0x2a08f96c, 0x6725494, 0x16d3cd09, 0x1eeeaee7, 0x2259faec, 0xb631}}},
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/*.y =*/{/*.val =*/{0x19d0bed1, 0x1900e4ae, 0x30539199, 0x28e249d2, 0x4804b47, 0x271cddc1, 0x362d5cfd, 0x54beff8, 0x6205}}},
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/*.y =*/{/*.val =*/{0x129138df, 0x1a3e7f86, 0xc417dcd, 0x216d86b, 0x11bf1e6, 0x8aec13a, 0x2c4acda6, 0x8f9c892, 0x3804}}},
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/*.y =*/{/*.val =*/{0x1b679d58, 0xec9fabd, 0x39f9d42d, 0x2b88c712, 0x36d3bb3b, 0x159430bc, 0xc508cd, 0x7e7eb98, 0x6533}}},
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/*.y =*/{/*.val =*/{0x11470e89, 0x39e7a5fe, 0x91f5606, 0x2dbd581a, 0x2927475d, 0x2a9b2154, 0xd31619, 0x18c68766, 0x34a9}}},
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/*.y =*/{/*.val =*/{0x134a8f6b, 0x1494113a, 0x2a4a468e, 0x2db1eccf, 0x1ba31f9a, 0x143e4863, 0x23fa1c6, 0x16a0b8dc, 0xdcea}}},
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/*.y =*/{/*.val =*/{0x6c1006f, 0x3e053999, 0x3cecad9d, 0x12e6c1d0, 0x3b0f63ef, 0xa9f90fd, 0x2be9ac3f, 0x4f0118d, 0x3de9}}},
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/*.y =*/{/*.val =*/{0x2a0e5888, 0x33c042f, 0x245a9c44, 0x1dbfcb72, 0x32c1a284, 0x7e54a27, 0x488520f, 0xcd459b4, 0x5403}}},
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/*.y =*/{/*.val =*/{0x3ee097fd, 0x20748c63, 0x11251996, 0x18cbbba3, 0x2082e91, 0x2a1383b6, 0x2c0afafc, 0x3736f6c1, 0xad4b}}},
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/*.y =*/{/*.val =*/{0x3108cd25, 0x1f2b8146, 0x25bad0df, 0x166b1d89, 0x1d034f89, 0x30491ebc, 0x1a064e77, 0x2f7d0a0f, 0xd901}}},
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/*.y =*/{/*.val =*/{0x3e1e77d9, 0x2d09b03c, 0x317d099f, 0x21db71, 0x2bf5acc3, 0x322ceb96, 0x176aa401, 0x3754d41c, 0xd719}}},
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/*.y =*/{/*.val =*/{0xe98c4d1, 0x3ff50365, 0x269e2f31, 0x225b657b, 0x1cd86b4b, 0xf7de042, 0x10613b82, 0x21516b0e, 0x5e6a}}},
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/*.y =*/{/*.val =*/{0x2f10cf0a, 0x368f1f65, 0x366e9fa4, 0x178d435f, 0x117f9308, 0xb77a250, 0x1c069b86, 0x3a48c228, 0xaa65}}},
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/*.y =*/{/*.val =*/{0x4fad9e0, 0x386d89e7, 0x157a7ee8, 0x19430908, 0x32a306af, 0x23439013, 0x2c6680b3, 0x3839aa7, 0xe5d3}}},
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/*.y =*/{/*.val =*/{0x1ae78402, 0x6c374b3, 0x1a8c2145, 0x24ed0935, 0x1c0681ba, 0x19f114d7, 0x2ed713f, 0x31fb8a58, 0xc39d}}},
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/*.y =*/{/*.val =*/{0x9df8052, 0x3855dbc6, 0x3918eac6, 0x28c8d510, 0xec8d7d3, 0x34d25302, 0x326f4fef, 0x5302c, 0x3b21}}},
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/*.y =*/{/*.val =*/{0x29aea3b0, 0x1b650e85, 0x2dacdfa9, 0xbde88fb, 0x28eff528, 0x36d13fec, 0x3282d607, 0x3b6092c3, 0x3eef}}},
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/*.y =*/{/*.val =*/{0x2878fee0, 0xfdb4ecc, 0x19ae68d5, 0x1e1760e5, 0xaf14548, 0x1092e11e, 0x1b0447aa, 0x1d1ec649, 0x4aa8}}},
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/*.y =*/{/*.val =*/{0x1ac1683, 0x34361004, 0x2c7bf300, 0x16b4239, 0x367acb0e, 0x26e8b6c0, 0x1d9db9c1, 0x39526a8, 0x10e8}}},
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/*.y =*/{/*.val =*/{0x274504ad, 0x1c2702ae, 0xec98f6f, 0x274c6013, 0x10d4b7fc, 0x7b4bf9c, 0x3d26f710, 0x26ef0094, 0x52d}}},
{/*.x =*/{/*.val =*/{0x1136602, 0x2c2e9195, 0x19e3a5bb, 0x311bd203, 0x333b3d38, 0x1624dfc8, 0x2dfc33d0, 0x9ca0120, 0x87d1}},
/*.y =*/{/*.val =*/{0x18af6aac, 0x3da0f107, 0x3d3bf7c4, 0x2a211d1b, 0x27745387, 0x289db3fd, 0x203de926, 0x921c296, 0x71ce}}},
{/*.x =*/{/*.val =*/{0x30e74459, 0x1d28d722, 0x3ddb6dd6, 0x3c8dd8e1, 0x3c8a91fe, 0x3d1961c4, 0x5680590, 0x1e0753b0, 0x28df}},
/*.y =*/{/*.val =*/{0x2f5e656f, 0x3781f303, 0x1ae6f0a8, 0x1e56e940, 0x322794a3, 0x36c5e243, 0x30f17cb0, 0x27a99a84, 0xf149}}},
{/*.x =*/{/*.val =*/{0x29c71143, 0x11b67714, 0xf057ea3, 0x1fab6b11, 0x23fa352e, 0x1f33e400, 0x3ea103ca, 0x17e588ae, 0xeb4}},
/*.y =*/{/*.val =*/{0xb70b136, 0x22a33688, 0x22b1bf4c, 0x165a7a9a, 0x1e2857d6, 0x1807d640, 0xbd0f573, 0xbd6160e, 0x52c4}}},
{/*.x =*/{/*.val =*/{0x1507a7e6, 0x37cdaf22, 0x305f129b, 0x25896ebd, 0x310c41c0, 0xa1458cd, 0x1ad0d5f4, 0x142c15d1, 0x232d}},
/*.y =*/{/*.val =*/{0x152b5892, 0x1c202084, 0x6459ccb, 0x18303bed, 0x2257f712, 0xe22b7c1, 0x33f6b086, 0xeb14d79, 0x780f}}},
{/*.x =*/{/*.val =*/{0x177e7775, 0x222a29b8, 0xed95f63, 0x385564e2, 0x1291aeb5, 0x150eeb3d, 0x233cee58, 0x1a8ebfe5, 0x9d89}},
/*.y =*/{/*.val =*/{0x3a056691, 0x3f3db4ea, 0x299253be, 0x26735fb8, 0x10927de8, 0x2593b5c9, 0x1bf0b94e, 0x2a790fd2, 0xdd91}}},
{/*.x =*/{/*.val =*/{0xc904ed3, 0x1655fc7a, 0x5857841, 0xa9d1624, 0x272384df, 0x3e3990c4, 0x18dff97, 0x230b4b6e, 0xcf}},
/*.y =*/{/*.val =*/{0x396f77c1, 0x2658ed, 0x32f6827b, 0x26475e74, 0x1bd81122, 0x35706f54, 0x1d44119d, 0x3a9e0, 0xaaad}}},
{/*.x =*/{/*.val =*/{0xcf8cffd, 0x2cad6622, 0x3a45ae61, 0xb9ac56d, 0x1bdd8943, 0x2bee23de, 0x38c1bd45, 0x26dfc7f9, 0x80}},
/*.y =*/{/*.val =*/{0xdb5f32f, 0x24751686, 0x12b9f93d, 0x28d03eb6, 0x12fdc912, 0x2320db79, 0x1a863028, 0x3808afd0, 0xf817}}},
{/*.x =*/{/*.val =*/{0x2dc7a626, 0x11f741e6, 0x33cdcc02, 0x1772ade, 0x46b0734, 0x32bc48c9, 0x806bce4, 0x1b28b13e, 0x2f45}},
/*.y =*/{/*.val =*/{0x25279532, 0x2b3ac002, 0x16eaea9e, 0x13236f70, 0x9f5302, 0x47ed991, 0x50544d2, 0x1c69e919, 0xf8cf}}},
{/*.x =*/{/*.val =*/{0x1a328d6a, 0x2eaa0623, 0x1adc18bd, 0x135dcea5, 0x308fa7b2, 0x1a264616, 0x34e00a34, 0x3016e988, 0xc663}},
/*.y =*/{/*.val =*/{0x3ec9b8c0, 0xec2edaa, 0x12bf9cc2, 0x21547a94, 0x171317dd, 0x2bf73c9d, 0x21c38d39, 0x3a6357dc, 0x3331}}},
{/*.x =*/{/*.val =*/{0x22143fb0, 0x370d6995, 0x3c205dd6, 0x3ee4a0c2, 0x399597a9, 0x2bfcce51, 0x383790cf, 0x37070ceb, 0x292a}},
/*.y =*/{/*.val =*/{0x236ad01c, 0x2a76d8f3, 0x35e9d4d8, 0xf998b5c, 0x4ecf6d8, 0x65a2833, 0xb647f3f, 0x1986f3b8, 0xa072}}},
{/*.x =*/{/*.val =*/{0x30b90e0b, 0x27b079b0, 0x3094a458, 0x3fc74e7e, 0x675b3d6, 0x32012967, 0x67d3fed, 0x1fe6b55, 0xa435}},
/*.y =*/{/*.val =*/{0x3a1fdc20, 0x3c002e64, 0x3599b5a3, 0xa880d94, 0xbe8c0dc, 0x341f32d0, 0x3d71a142, 0xb72530f, 0x7c8f}}},
{/*.x =*/{/*.val =*/{0x188f4d82, 0x2e7474ad, 0x159204ac, 0x9937676, 0x21d6fcaf, 0x170c09b0, 0x1c515b0e, 0x1665c1b9, 0x6dd5}},
/*.y =*/{/*.val =*/{0x14132ad3, 0x287aadab, 0x15927be5, 0x3db9c11b, 0x2d0f9478, 0x3346376d, 0x1233dd46, 0x109ff54d, 0xbc92}}},
{/*.x =*/{/*.val =*/{0x1e05dccc, 0xcb60046, 0x19a93e5, 0xfe8fb53, 0x13d172ae, 0x1b825ae5, 0x1a030954, 0x3db85d4f, 0xb8ce}},
/*.y =*/{/*.val =*/{0xc6d5750, 0x52833f, 0x26b68133, 0x1d5ff0da, 0x12bd99df, 0x3529d393, 0x9bbf6a4, 0x229829b3, 0x302b}}},
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/*.y =*/{/*.val =*/{0x2859679b, 0x8562ca3, 0x3781a11d, 0x2abe07ae, 0x30a0dde0, 0x3cffcb95, 0x1f32f516, 0xe1ced66, 0x85e1}}},
{/*.x =*/{/*.val =*/{0x388f7e09, 0xaa8ad9f, 0x27d92cde, 0x280dde6e, 0x1dc0beb3, 0x384b9691, 0x5fcbbd8, 0x218f53c8, 0x5e6a}},
/*.y =*/{/*.val =*/{0x8dfca97, 0x2f58a19d, 0x3b4cfe3b, 0x23940dc8, 0x140234a6, 0x12a347da, 0x8edfc44, 0x681e28e, 0xc257}}},
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/*.y =*/{/*.val =*/{0x3f480c26, 0x3407b39, 0x3de01414, 0x8104f71, 0x1e8fb495, 0x2f3a351a, 0x27a6598, 0xe575ec3, 0x7b2c}}},
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/*.y =*/{/*.val =*/{0x269da7e, 0x306b92e4, 0x23ac8bbc, 0x1c01b7a4, 0x2d0eebad, 0x30acf0ac, 0x3e30d07e, 0x34282a88, 0x9619}}},
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/*.y =*/{/*.val =*/{0x328625e0, 0xd24c39c, 0x3fc97539, 0x1e943695, 0x219da1a8, 0x335c269c, 0x1a01e186, 0xf93d350, 0xdd6e}}},
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/*.y =*/{/*.val =*/{0x2faed097, 0xf32697f, 0x5769df4, 0x39964bfc, 0x39ad0f29, 0x244e7f96, 0x30d49d58, 0x263ee658, 0x15c6}}},
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/*.y =*/{/*.val =*/{0x248d28ac, 0x1f7884ad, 0xcb6ad56, 0x33c28fe9, 0x11ab13fc, 0x28440e45, 0x303053f2, 0x35451759, 0x3d53}}},
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/*.y =*/{/*.val =*/{0x3ca6b774, 0x17896781, 0x84fa5e2, 0x1cb6cc52, 0x2e34719, 0x3313c526, 0x3e97c3c7, 0x250982bc, 0xc028}}},
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/*.y =*/{/*.val =*/{0x2774299e, 0x36a1ccd2, 0x3716284a, 0x253c8efb, 0x2434597d, 0x3d58d185, 0x21ef428b, 0x29a5dbc9, 0xf9d8}}},
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/*.y =*/{/*.val =*/{0x2dd92db5, 0x11ba631e, 0x3e09e433, 0x3fde6936, 0x215e28e2, 0x1996ca1c, 0x288915a8, 0x31b3ff90, 0xc735}}},
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/*.y =*/{/*.val =*/{0x2da63e86, 0x265fd370, 0x22ed9de, 0xfbdf3e5, 0x3e6df412, 0x5cbb9d5, 0x88d72d6, 0x25e612ad, 0x852e}}},
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/*.y =*/{/*.val =*/{0x10100fa5, 0xfa93f55, 0x47e417d, 0x3cffb334, 0x1324c5eb, 0x2a9986a6, 0x383f391e, 0x1b100296, 0x985f}}},
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/*.y =*/{/*.val =*/{0x3cb01f48, 0x25796108, 0x2266162f, 0x2e8d9083, 0x2c315598, 0x3fcc6bdc, 0x12cda13d, 0x3a4e46e0, 0x2eef}}},
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/*.y =*/{/*.val =*/{0x2f97b82e, 0x1c80a5f8, 0x1100d1ec, 0x3e8a0cd2, 0x35046e47, 0x2e865b4c, 0x105ca520, 0x30028c67, 0xf194}}},
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/*.y =*/{/*.val =*/{0x3f172571, 0x1547dd2a, 0x17cdcca6, 0xea9b68b, 0x134daf4e, 0x26a0b4db, 0x1b911145, 0x37c225bf, 0x99ae}}},
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/*.y =*/{/*.val =*/{0x20d7c9ed, 0x9362df4, 0x2edcaa18, 0x3503fe4c, 0xb685241, 0x31e59377, 0x39ec2f33, 0x1ab2d0b1, 0x38d4}}},
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/*.y =*/{/*.val =*/{0x13f48c51, 0x114e89be, 0x1bba2862, 0x2f548ad5, 0x2288f426, 0x4a93333, 0x1f900789, 0x3bea33b2, 0xe7cc}}},
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/*.y =*/{/*.val =*/{0x44a7569, 0xb6393bc, 0x117da7f2, 0x8a28a35, 0x290e9aaa, 0x35abfd7a, 0x2fcd1b2a, 0x1d6038d5, 0xb446}}},
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/*.y =*/{/*.val =*/{0x17226c13, 0x2ed62953, 0xc6026e7, 0x3da24e65, 0x6442aa4, 0x176caf42, 0x3de26da8, 0x38f8242f, 0xb863}}},
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/*.y =*/{/*.val =*/{0x1b110258, 0x3ccb7025, 0x249a9bd3, 0x12b2eb3e, 0x1c85b69e, 0x3d98364c, 0x38404431, 0x26ee44c0, 0xe27f}}},
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/*.y =*/{/*.val =*/{0x5116b26, 0x30e411fe, 0x3d65fdc4, 0x3ed293f6, 0xb4dcf6d, 0x39301ab7, 0x584e8e6, 0x25ad3a55, 0x4151}}},
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/*.y =*/{/*.val =*/{0x3d9c4777, 0x31fcb8a5, 0x256ebb09, 0xbd1ec15, 0x2b2906b2, 0x1d086400, 0x21566287, 0x12e620e9, 0x90b2}}},
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/*.y =*/{/*.val =*/{0x2f5183a7, 0x19b9743a, 0x11151742, 0xa9ef36b, 0xcd6950e, 0x1c43e89a, 0x245eb58f, 0x337e271b, 0xa92}}},
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/*.y =*/{/*.val =*/{0x1f15fa2a, 0x3d473ead, 0x1d176ed6, 0x8379f7, 0x3267839a, 0x1525c8a5, 0x1a28901c, 0x2b290244, 0xd670}}},
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/*.y =*/{/*.val =*/{0x171dfea, 0x1a98d611, 0x36854f06, 0xcccf8b0, 0x10f9f7eb, 0x211d7b4, 0x1d7cfdf7, 0xe7e3cf1, 0xc91a}}},
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/*.y =*/{/*.val =*/{0x36b01c43, 0x3ac98e19, 0x18800b01, 0xfa7944d, 0x1dc3ac25, 0x9d40507, 0x1ddd7416, 0x1479107b, 0x75b0}}},
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/*.y =*/{/*.val =*/{0x3f15ab7d, 0x2b2da7e8, 0x1c51f9a6, 0x2be456ba, 0x1ac30426, 0x4b6c807, 0xf204c1a, 0x2062f709, 0xc147}}},
{/*.x =*/{/*.val =*/{0x195b6f7e, 0x25527d71, 0x38b2021f, 0x2ccad4f4, 0x1876cdbe, 0x14eab42, 0x1a30c83a, 0x1f474133, 0xa5ac}},
/*.y =*/{/*.val =*/{0xab19c84, 0x236edcc2, 0x1818a484, 0x38e4583d, 0x19ee1b99, 0x30f2491f, 0xf55b36c, 0x2282ad50, 0xdf0b}}},
{/*.x =*/{/*.val =*/{0xe81c1bc, 0x24e92b93, 0x2bb5b33b, 0x14d97962, 0xce767d2, 0x2056e35a, 0x4635ad, 0x3c15197, 0x336}},
/*.y =*/{/*.val =*/{0x166cbedd, 0x1b74a259, 0x8115017, 0x5ca3ad7, 0x30675323, 0x1a710944, 0x350014ff, 0x2d7e4315, 0x7e48}}},
{/*.x =*/{/*.val =*/{0x14bc0324, 0x2a208b00, 0x24d2cfc5, 0x21fc0a35, 0x2f119155, 0x198968d9, 0xe7c338e, 0x299908fa, 0xb96b}},
/*.y =*/{/*.val =*/{0x36c2ee15, 0x2d3afff6, 0x25ba8374, 0x33948a51, 0x1876b383, 0x3119268a, 0x285dfbea, 0xb336cee, 0xe83c}}},
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/*.y =*/{/*.val =*/{0x38d91fc1, 0x1e81dbcb, 0x9535dca, 0x1dc8951, 0x37e67e11, 0x3f209702, 0x3bd84aa7, 0x18392601, 0xc0d4}}},
{/*.x =*/{/*.val =*/{0xbb9dc8f, 0x23226e1, 0x1edd333d, 0x2a7a4fbd, 0x2787d1ab, 0x3dc0d4d4, 0x26864248, 0x1073b870, 0xfd99}},
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/*.y =*/{/*.val =*/{0x8be2dd, 0x2fe21d3c, 0x47be4ed, 0xc140ac0, 0x20d7e6a3, 0xf2d1009, 0xb6fb18a, 0x34c4086c, 0xd552}}},
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/*.y =*/{/*.val =*/{0x33fc22c4, 0xa0c4fec, 0x26c04c9c, 0x2645849f, 0x3f0cd508, 0x21bb065a, 0x1e98b29f, 0x496553f, 0x449a}}},
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/*.y =*/{/*.val =*/{0x27eed395, 0x8a09a41, 0xa8dfa80, 0x22709c24, 0x1a2138dd, 0x3db76d2a, 0xe3aeb15, 0x773265b, 0x603}}},
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/*.y =*/{/*.val =*/{0x300d358b, 0x394ab4ef, 0x4efb15d, 0x2614d60f, 0xb2439d6, 0x31c8115c, 0x1f0f5f95, 0x3e7a3a2c, 0x6c31}}},
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/*.y =*/{/*.val =*/{0x2451553f, 0x2837c990, 0x382a3120, 0x1549d580, 0x3e3b61b2, 0x2fb05054, 0x1cacf4c1, 0x20b9a3d9, 0xe01e}}},
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/*.y =*/{/*.val =*/{0x3c0259be, 0x8c33a7f, 0x14567d1e, 0x1d602413, 0x178bd1a8, 0x3b3793fa, 0x6fc2a5c, 0x3db716d2, 0x1237}}},
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/*.y =*/{/*.val =*/{0x10a2b918, 0x1a5e4b00, 0x1c3f5f1e, 0x23875cf8, 0x2911644b, 0xc5225e2, 0x36fbfa21, 0x1a90475d, 0x74eb}}},
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/*.y =*/{/*.val =*/{0x31f15109, 0x1e86cb5, 0x373af55e, 0x35c8c34f, 0x230bd6d, 0x1b53c6e, 0x2a2f61b8, 0x212b172d, 0x4a9}}},
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/*.y =*/{/*.val =*/{0x1b32b3bc, 0x26083b0c, 0x35e5f9f3, 0x3948efcf, 0x59d2f2c, 0x3e5e242, 0x3be7a03c, 0x34ffe08a, 0xf97e}}},
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/*.y =*/{/*.val =*/{0x38fafeee, 0x3b1baf9b, 0x1cb494ad, 0x16fd37c9, 0xd7c8c26, 0x35650e88, 0x19f28c46, 0x260e04bf, 0x71a8}}},
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/*.y =*/{/*.val =*/{0x24f59de0, 0x10fced68, 0x20328258, 0x2962763d, 0x2143c678, 0x38d2d621, 0x2d1ac5f, 0x3b49af55, 0xcdf4}}},
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/*.y =*/{/*.val =*/{0x2eb3d8a7, 0x32a7875c, 0x15fe035, 0x398b696, 0x3ff204be, 0x6555e5f, 0x32e11ae7, 0xb7e8107, 0x5f38}}},
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/*.y =*/{/*.val =*/{0x12b856f0, 0x3031db27, 0x23d9a7bf, 0xaa13292, 0x222e3bca, 0x1890c835, 0x3b7b6f86, 0x315e0940, 0xac5f}}},
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/*.y =*/{/*.val =*/{0x33f39758, 0xd4cafba, 0x3d54f320, 0x23bab9da, 0xbb8f48b, 0x32489c59, 0x355552a1, 0x35a4c2f7, 0x4774}}},
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/*.y =*/{/*.val =*/{0x3c0594ba, 0x3073959, 0x1ab5b8da, 0x39717c3f, 0x198f667d, 0x3d981d5c, 0x7f42c44, 0x3858f7fc, 0xd13a}}},
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/*.y =*/{/*.val =*/{0x9eeb5e9, 0x390732fe, 0x1ad82484, 0x11fb1151, 0x2d39a60a, 0x106ad8b, 0x20927573, 0xca20d9b, 0x72ea}}},
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/*.y =*/{/*.val =*/{0x3e2dbc57, 0x30c25f88, 0xe01e841, 0x284e7b2a, 0xba853a7, 0x1e3d7c58, 0x5b1d7ed, 0x2687d98e, 0xa5ba}}},
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/*.y =*/{/*.val =*/{0x252d0566, 0x1f1e5ac8, 0x351ba73b, 0x10c28ce5, 0x34c6f01f, 0x13b5b68a, 0x1ca43bfb, 0x316f346e, 0xd6e3}}},
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/*.y =*/{/*.val =*/{0x2d7a27f2, 0x214f3c9e, 0x49fd3f5, 0x6d622e4, 0x3ef5c641, 0xaecd847, 0xb1eabd1, 0x1e18b4f0, 0xfa92}}},
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/*.y =*/{/*.val =*/{0x450fa6f, 0x23cf359a, 0x3d4f8896, 0x2a1edf4d, 0x2d7060fc, 0x3249148e, 0x39f71ad4, 0x3f944301, 0xea91}}},
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/*.y =*/{/*.val =*/{0x2a9e3eae, 0x4edca90, 0x205bb69b, 0xe154bf2, 0x12255a1c, 0x3f8cf6da, 0x81c72c5, 0x1ca611c1, 0xb8b5}}},
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/*.y =*/{/*.val =*/{0x3e3ca504, 0x5fd151b, 0x33245cb1, 0x2cabbc7, 0x1c9a03d3, 0x36d5c01f, 0x1ecd55e, 0x215a9e3, 0x247e}}},
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/*.y =*/{/*.val =*/{0x26f06930, 0x758c2a, 0x236934f9, 0x32544bb0, 0x6d2ae5c, 0x3b130b2f, 0x22ebfd7f, 0x15cf49df, 0x3766}}},
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/*.y =*/{/*.val =*/{0x11ce85ca, 0x14ca6a76, 0x1e5ffa44, 0x1aaa7bcf, 0x2a4b7a79, 0x2407c55c, 0x15e05c2c, 0x3e32691e, 0xae8a}}},
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/*.y =*/{/*.val =*/{0x4ea66fe, 0x12b1ea27, 0xa7f9411, 0x1cb1804c, 0x1767ed5f, 0x29babb20, 0x5f222cd, 0x135010ee, 0x639f}}},
{/*.x =*/{/*.val =*/{0x24b84b48, 0xc3d15c7, 0x1e817ea8, 0x2b7d31e6, 0x17f7091, 0x43d5df5, 0x1a4f5419, 0x37c39f51, 0x5fb1}},
/*.y =*/{/*.val =*/{0x37be8eb8, 0x1fb7a9a8, 0x33f21ad7, 0xa70e421, 0x2d258206, 0x3d191bf9, 0x4d49fbc, 0x3eef2f0f, 0x2152}}},
{/*.x =*/{/*.val =*/{0x2aa2a748, 0x15d87054, 0x378c403d, 0x2c99f85, 0x2835d8c9, 0x337e7d1a, 0x141486c5, 0x27edac70, 0x135a}},
/*.y =*/{/*.val =*/{0x38a6cf84, 0xc41675b, 0x3f91ab2d, 0x19b84fa2, 0x9453a65, 0x18b97f9c, 0x15938e7, 0x778b2a8, 0xa869}}},
{/*.x =*/{/*.val =*/{0xfd69985, 0x2717764, 0x1df72aea, 0xc2732db, 0xccf149f, 0x3da437ef, 0x32f7e788, 0x1d9d73ad, 0xae9}},
/*.y =*/{/*.val =*/{0x1409a003, 0x2723ad04, 0x2ee1aff8, 0x2e67505e, 0x1a54c5d0, 0x237fb814, 0x8d14e9b, 0x265cfdb9, 0x9121}}},
{/*.x =*/{/*.val =*/{0x2078afb0, 0x39d6b9e5, 0x1261974, 0x3fc4b1b1, 0x2d170714, 0x3511a319, 0x163b5248, 0x1af35d98, 0x209d}},
/*.y =*/{/*.val =*/{0x2740b310, 0x1746ddd6, 0x1f4e3e38, 0x3b6de4ce, 0x98a5b01, 0x196eaea6, 0x33280a09, 0x4d0a79e, 0x1a2f}}},
{/*.x =*/{/*.val =*/{0x1f55a9bf, 0x2f2c0a63, 0x1ea5bf8e, 0x2c057bca, 0x17c578f6, 0xc1fd807, 0x23181810, 0x263ae71b, 0x7262}},
/*.y =*/{/*.val =*/{0x3c3accae, 0x45be2c2, 0x673b4e, 0x1e5ef2f0, 0x1099e0be, 0xd68bbcf, 0x29bfda98, 0x22006a77, 0x38d4}}},
{/*.x =*/{/*.val =*/{0x3dbb04fa, 0x5c195a8, 0x118911f9, 0x29c145ac, 0x26b5e114, 0x2e090979, 0x26ed4d7c, 0xb7eecd1, 0x7fe4}},
/*.y =*/{/*.val =*/{0x21908c89, 0x359d2447, 0x2c1b9c55, 0x3a28a234, 0x334cf0aa, 0x1b22c1e5, 0x5f4330f, 0x1e82d3d7, 0x2eec}}},
{/*.x =*/{/*.val =*/{0x2e4b3ba0, 0x2167d8d7, 0x18bf1f17, 0xaafbd7c, 0x3f245f5c, 0x385c3cc6, 0x3fb73bef, 0x4414887, 0x4108}},
/*.y =*/{/*.val =*/{0x17525595, 0x21a58770, 0x1a064554, 0xd926159, 0x2b849813, 0x2996b875, 0x35668f2c, 0x3cda5dbf, 0xdc37}}},
{/*.x =*/{/*.val =*/{0xe5485, 0x22799a8, 0x1da5df02, 0x4c1a2fd, 0x320f1245, 0x31c2189c, 0x2bdff8e2, 0x1db5e4e8, 0x1cd2}},
/*.y =*/{/*.val =*/{0x85fbd7f, 0x2973c146, 0x209a4ecc, 0x34389c2c, 0x2e977f99, 0x2cd35154, 0x2af738d4, 0x2f7462cb, 0x6615}}},
{/*.x =*/{/*.val =*/{0x290bc03e, 0x31d4f566, 0x1e015e33, 0x2c3ce4d4, 0x50f8084, 0x2a497dd1, 0x2072e9e5, 0x363b4b20, 0x2cee}},
/*.y =*/{/*.val =*/{0x3ab82adc, 0x32dcae2d, 0xd53cd01, 0x77e73c8, 0x7daeb4a, 0x143adebf, 0x1de3ecd8, 0x1ae03a6e, 0xa427}}},
{/*.x =*/{/*.val =*/{0x3009ee3e, 0x2e71352e, 0x729ead5, 0x9a8799e, 0x272de237, 0x273af1, 0x22ac92b7, 0x216c0cba, 0xb17a}},
/*.y =*/{/*.val =*/{0x296b911d, 0x18f947b, 0x446fa38, 0x85b29f2, 0x26eda65, 0x63f703, 0x29a65f5c, 0x9a749ac, 0x966e}}},
{/*.x =*/{/*.val =*/{0xe103dd6, 0x37dc51c8, 0x4859a, 0x1181301f, 0x12a17ac3, 0x84f3f16, 0x203f836a, 0x1ef55690, 0xbc47}},
/*.y =*/{/*.val =*/{0x16f7c343, 0xe420b63, 0x23b44ac6, 0xa4d5cb1, 0x1ea6395d, 0x2b154b1b, 0xdd526cb, 0x7890a6a, 0xe31e}}},
{/*.x =*/{/*.val =*/{0x36695f94, 0xb602c60, 0x1627fa59, 0x285a71a4, 0x39a9cf62, 0x32e1a0eb, 0x18f5fd0c, 0x17546d15, 0xb1d2}},
/*.y =*/{/*.val =*/{0x1ee32736, 0x16dfae69, 0x3863edca, 0x3dbc636a, 0x2ba81760, 0x3a82b066, 0x290b1f7b, 0x369c80c3, 0x706d}}},
{/*.x =*/{/*.val =*/{0x36f83231, 0x265c4062, 0x20425e34, 0x30c3639d, 0x33fdd0b7, 0x5609d96, 0x2ba26a8d, 0x23314d40, 0x850f}},
/*.y =*/{/*.val =*/{0x1f2e8373, 0x280c6a75, 0x322d77f4, 0x216fe85d, 0x2cc7890a, 0x3dc21ae0, 0x39053d0b, 0x276f80a9, 0xbc4a}}},
{/*.x =*/{/*.val =*/{0x39343959, 0xb882f6f, 0x2c9ce78a, 0x28673cbe, 0x1bc1f617, 0x2bfa4c24, 0x651465d, 0x6e01743, 0x2d38}},
/*.y =*/{/*.val =*/{0x1442fb00, 0x1c432ba8, 0x31e45a43, 0x14b57589, 0x31025f43, 0x2bcbce90, 0x361bf59a, 0x3782534a, 0x5451}}},
{/*.x =*/{/*.val =*/{0x152da17d, 0x18283e90, 0xd0646b1, 0x3704f6c2, 0x200bc811, 0x139ac17f, 0x18c5f089, 0x3b4783d4, 0x3bea}},
/*.y =*/{/*.val =*/{0x2cc768d2, 0x39c12617, 0x1fec416c, 0x3379dee3, 0xe1b554, 0x12a2fafa, 0x37acdfef, 0x35fd56bf, 0xc3b0}}},
{/*.x =*/{/*.val =*/{0x1063e1be, 0x6e6b413, 0x3e39a75c, 0x90a68bd, 0x3cf027a9, 0x185494f6, 0x2b14722, 0x10744758, 0x1316}},
/*.y =*/{/*.val =*/{0x21fec890, 0x3747fcf8, 0x1745b77f, 0x3ebb03e, 0x3d2bebbd, 0xb8c3f36, 0x39f06a4, 0x36985e58, 0x4c3b}}},
{/*.x =*/{/*.val =*/{0x3c46e079, 0x4a80d49, 0x1e9c78dd, 0x19a4c2e1, 0x2ba374ab, 0x3dd6b6c0, 0x3ac530fe, 0x30ab4ab3, 0xab86}},
/*.y =*/{/*.val =*/{0x3636ffe1, 0x310a2f05, 0x50d7c0e, 0x1dca3a12, 0x3200c9ce, 0x311b535c, 0x329abcf5, 0x30a18067, 0x1209}}},
{/*.x =*/{/*.val =*/{0x17d37248, 0x227c6075, 0x117ceae4, 0x20d6d947, 0x2b2787bc, 0x1bac891a, 0x36d5aa4d, 0x946f0fb, 0xadc4}},
/*.y =*/{/*.val =*/{0x2adcbc1b, 0x1811f2b3, 0x50bebc8, 0x37156ec5, 0x16f70b9, 0x18f8d8a4, 0x1e7eb5d0, 0x2dd8b8f1, 0xb0f3}}},
{/*.x =*/{/*.val =*/{0xeca5f51, 0x85ac826, 0xfc9aebf, 0x3a85c6e5, 0x5b5cfdd, 0x3b5acafc, 0x2e6962c6, 0x35453767, 0xdde9}},
/*.y =*/{/*.val =*/{0x10c638f7, 0x2b5a69cf, 0x289571f9, 0x3fbafa37, 0x3f8f0950, 0x7cd2c29, 0x28111d89, 0x1a44cf38, 0xb84e}}},
{/*.x =*/{/*.val =*/{0x209b0cca, 0x3331a956, 0xa4d6f01, 0x115d6249, 0x28da59a3, 0x1153da28, 0xf4c8d5c, 0x232c76ec, 0xd53}},
/*.y =*/{/*.val =*/{0xc929e05, 0xc6c51f8, 0x9134c97, 0xd336676, 0x2ed7cf85, 0x2a357103, 0x2c110cb0, 0x1aeb1e8f, 0xc819}}},
{/*.x =*/{/*.val =*/{0x2dd7e577, 0x2b8c0f3b, 0x136c4d56, 0x283c95a1, 0x2a2107d3, 0x1811c9c3, 0xf7b25ac, 0x3543e20a, 0xc352}},
/*.y =*/{/*.val =*/{0x38d9b570, 0x3293fe23, 0x21217063, 0x2a2aecad, 0xe79fb00, 0x354c516f, 0x2b9b96ab, 0xa0e2e9d, 0xbe77}}},
{/*.x =*/{/*.val =*/{0x23868246, 0x22fcdeb0, 0x6dd2ded, 0x27db62bd, 0x2248ba8, 0x17641f4b, 0x11d600b5, 0x1f82acce, 0xfb9d}},
/*.y =*/{/*.val =*/{0x2969605a, 0x2760f82b, 0x2a2606d2, 0x34ab4c16, 0x1475f4a6, 0x2a2e05a8, 0x3680cff2, 0x26f807d2, 0xb038}}},
{/*.x =*/{/*.val =*/{0x3712be3c, 0x1a8b8cb, 0x2146a66b, 0x257c63b6, 0x153472, 0x1c976eac, 0x1b378d3c, 0xd2764cc, 0x39d7}},
/*.y =*/{/*.val =*/{0x1c6ff65c, 0x30c067d0, 0xa41644c, 0x17bde97b, 0x2812e8ef, 0x9d55319, 0x33bf7fb1, 0x26d3d5bb, 0x8f92}}},
{/*.x =*/{/*.val =*/{0x37829372, 0x3b02a929, 0xba4553d, 0x26cc0322, 0x5796bc4, 0x189ab94e, 0x20d3b313, 0x273243cf, 0xb431}},
/*.y =*/{/*.val =*/{0xadd5427, 0x1ca73300, 0x23e11bb7, 0x1ec48572, 0x21c5a270, 0x1ebf8270, 0x3502bffb, 0x3512669b, 0x4707}}},
{/*.x =*/{/*.val =*/{0xdcbcb9e, 0x12fc449b, 0xd83c3df, 0x3e95a277, 0x143761d6, 0x30c911ff, 0x1337a9ec, 0x4b5c467, 0xcdcb}},
/*.y =*/{/*.val =*/{0x961cfd1, 0x229616b, 0x18df340a, 0x266bc90d, 0x1e9949a1, 0x3efa825b, 0x1f11fbfe, 0x38b85eee, 0xe699}}},
{/*.x =*/{/*.val =*/{0xe90bc26, 0x1e074991, 0x364d3aa0, 0x22880f84, 0xacd88a9, 0xf195b1d, 0x27275f3d, 0x385bd96d, 0x5e4d}},
/*.y =*/{/*.val =*/{0x252f79e, 0x5f546a, 0x1127f9c7, 0x194f732b, 0x3ad55207, 0xebea5e0, 0x1432904e, 0x3cb90d4f, 0x5ac5}}},
{/*.x =*/{/*.val =*/{0x754dd40, 0x18fa1c55, 0x3466cf8, 0x10898c7f, 0x32f6e9a2, 0x12107f35, 0xdfcf45b, 0x91c0cb0, 0x9729}},
/*.y =*/{/*.val =*/{0x2aa36143, 0x212d24bc, 0x1acaf493, 0x36ba1495, 0x14df3690, 0x171d772f, 0x3ea1dcd1, 0x28910997, 0x91d1}}},
{/*.x =*/{/*.val =*/{0xc7a89ee, 0x15f0d4cc, 0x2b6d4f80, 0x36f1671e, 0x18658a4b, 0x182e23f2, 0x179e1128, 0x29389a90, 0x71ef}},
/*.y =*/{/*.val =*/{0x1366a2e, 0x3d224ca7, 0x25e9a0b4, 0x2abeae23, 0x3294a22a, 0x2cb0cac5, 0x224ae9ef, 0x2a07e2ed, 0x145f}}},
{/*.x =*/{/*.val =*/{0xde0545f, 0x32c08d26, 0x106c74f5, 0x39897688, 0x3508ac80, 0x17a8012c, 0x7124a37, 0x16f31638, 0x5204}},
/*.y =*/{/*.val =*/{0x106c3d91, 0x1ba8d301, 0x28fdaf23, 0xee743ca, 0xe312b79, 0x3b67083, 0x3123ad43, 0xc7f3af8, 0x1b3f}}},
{/*.x =*/{/*.val =*/{0x3ddaa5d5, 0x1873f311, 0x14d4b7ab, 0x27a034e9, 0x16607331, 0x3bf9159a, 0x28c4e4e8, 0x2646e4be, 0x4e9}},
/*.y =*/{/*.val =*/{0x2cba1c91, 0x35f800ff, 0x255f570d, 0x3827db86, 0x957303c, 0x1ab47630, 0x327f1d9e, 0x577778a, 0x62fc}}},
{/*.x =*/{/*.val =*/{0x26a06f5e, 0x6902d65, 0x2a083702, 0x1064945b, 0x23b716a3, 0x2c350849, 0x253ac37, 0x93efa85, 0x383b}},
/*.y =*/{/*.val =*/{0x13c6e772, 0x227d1e1b, 0x38c2b040, 0x3dab9d2e, 0x2a5a19e8, 0x3d59b553, 0x1ba2044c, 0x1c1ab13b, 0x54cf}}},
{/*.x =*/{/*.val =*/{0x1bcf2dce, 0x4e6d023, 0x1dc6c02, 0x4528417, 0x3f998068, 0x2793264b, 0x6218bd4, 0xb50a4b9, 0x95e6}},
/*.y =*/{/*.val =*/{0x18c86594, 0xaf77f7d, 0x304d20e6, 0x1ecc180d, 0x28d52e5e, 0x289b8ad0, 0x2875183, 0x20610a5b, 0x6b6}}},
{/*.x =*/{/*.val =*/{0x17a6257f, 0x20149916, 0x27a6c40b, 0x1cf0ec68, 0x7e78918, 0x909d2ac, 0x14f25a64, 0xd72387d, 0x71e9}},
/*.y =*/{/*.val =*/{0x11b1e582, 0x2c85d187, 0xf70f7a5, 0x948d503, 0x2e2a52ef, 0x361ae91e, 0x22513de, 0xf967d1f, 0x78d9}}},
};
#endif

View File

@ -54,6 +54,7 @@ extern const bignum256 secp256k1_iv[256];
#if USE_PRECOMPUTED_CP
extern const curve_point secp256k1_cp[256];
extern const curve_point secp256k1_cp2[255];
#endif
#endif