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cr50: compress array of prime deltas

Browse Source 
The array storing deltas between sequential prime numbers could be
compressed, as the vast majority of the values in the array does not
require more than 4 buts to store.

The new storage format is as follows:

 - each differential value (difference between two consecutive primes)
   is halved and stored in 4 bits, two halved values are packed per
   byte.

 - I the first one of of the two sequential halved values exceeds 0xf,
   it is stored in the array followed by a zero, stored as is (without
   halving), thus taking two bytes.

 - if the second one of the two sequential halved values exceeds 0xf,
   both values are stored in the array as is, both prepended by zeros,
   thus taking 4 bytes.

The code calculating the sequential primes parses the array according
to this format. Storing the primes in this format allows to shave from
the image size 1848 bytes.

BRANCH=cr50
BUG=b:65253310, b:65287300
TEST=verified that test_rsa test from the tpmtest suite passes.

     verified that the list of prime numbers printed out when
     PRINT_PRIMES is defined and test_rsa is ran is the same before
     and after this patch.

Change-Id: Ifdc2858a48f868ef816ccb4e351d9f60703d16e7
Signed-off-by: Vadim Bendebury <vbendeb@chromium.org>
Reviewed-on: https://chromium-review.googlesource.com/664253
Reviewed-by: Nagendra Modadugu <ngm@google.com>
This commit is contained in:
Vadim Bendebury
2017-09-12 15:07:23 -07:00
committed by chrome-bot
parent 73612726d3
commit a7d440eaec
1 changed files with 225 additions and 273 deletions
Download Patch File Download Diff File Expand all files Collapse all files

498
chip/g/dcrypto/bn.c
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@@ -815,272 +815,208 @@ int bn_modinv_vartime(struct LITE_BIGNUM *dst, const struct LITE_BIGNUM *src,
return 1;
}
#define NUM_PRIMES 4095
#define PRIME1 3
/* First NUM_PRIMES worth of primes starting with PRIME1. The entries
* are a delta / 2 encoding, i.e.:
* prime(x) = prime(x - 1) + (PRIME_DELTAS[x] * 2)
/*
* The array below is an encoding of the first 4096 primes, starting with
* PRIME1. Using 4096 of the first primes results in at least 5% improvement
* in running time over using the first 2048.
*
* Using 4096 of the first primes results in a 5-10% improvement in
* running time over using the first 2048. */
const uint8_t PRIME_DELTAS[NUM_PRIMES] = {
0, 1, 1, 2, 1, 2, 1, 2, 3, 1, 3, 2, 1, 2, 3,
3, 1, 3, 2, 1, 3, 2, 3, 4, 2, 1, 2, 1, 2, 7, 2,
3, 1, 5, 1, 3, 3, 2, 3, 3, 1, 5, 1, 2, 1, 6, 6,
2, 1, 2, 3, 1, 5, 3, 3, 3, 1, 3, 2, 1, 5, 7, 2,
1, 2, 7, 3, 5, 1, 2, 3, 4, 3, 3, 2, 3, 4, 2, 4,
5, 1, 5, 1, 3, 2, 3, 4, 2, 1, 2, 6, 4, 2, 4, 2,
3, 6, 1, 9, 3, 5, 3, 3, 1, 3, 5, 3, 3, 1, 3, 3,
2, 1, 6, 5, 1, 2, 3, 3, 1, 6, 2, 3, 4, 5, 4, 5,
4, 3, 3, 2, 4, 3, 2, 4, 2, 7, 5, 6, 1, 5, 1, 2,
1, 5, 7, 2, 1, 2, 7, 2, 1, 2, 10, 2, 4, 5, 4, 2,
3, 3, 7, 2, 3, 3, 4, 3, 6, 2, 3, 1, 5, 1, 3, 5,
1, 5, 1, 3, 9, 2, 1, 2, 3, 3, 4, 3, 3, 11, 1, 5,
4, 5, 3, 3, 4, 6, 2, 3, 3, 1, 3, 6, 5, 9, 1, 2,
3, 1, 3, 2, 1, 2, 6, 1, 3, 17, 3, 3, 4, 9, 5, 7,
2, 1, 2, 3, 4, 2, 1, 3, 6, 5, 1, 2, 1, 2, 3, 6,
6, 4, 6, 3, 2, 3, 4, 2, 4, 2, 7, 2, 3, 1, 2, 3,
1, 3, 5, 10, 3, 2, 1, 12, 2, 1, 5, 6, 1, 5, 4, 3,
3, 3, 9, 3, 2, 1, 6, 5, 6, 4, 8, 7, 3, 2, 1, 2,
1, 5, 6, 3, 3, 9, 1, 8, 1, 11, 3, 4, 3, 2, 1, 2,
4, 3, 5, 1, 5, 7, 5, 3, 6, 1, 2, 1, 5, 6, 1, 8,
1, 3, 2, 1, 5, 4, 9, 12, 2, 3, 4, 8, 1, 2, 4, 8,
1, 2, 4, 3, 3, 2, 6, 1, 11, 3, 1, 3, 2, 3, 7, 3,
2, 1, 3, 2, 3, 6, 3, 3, 7, 2, 3, 6, 4, 3, 2, 13,
9, 5, 4, 2, 3, 1, 3, 11, 6, 1, 8, 4, 2, 6, 7, 5,
1, 2, 4, 3, 3, 2, 1, 2, 3, 4, 2, 1, 3, 5, 1, 5,
4, 2, 7, 5, 6, 1, 3, 2, 1, 8, 7, 2, 3, 4, 3, 2,
9, 4, 5, 3, 3, 4, 5, 6, 7, 2, 3, 3, 1, 14, 1, 5,
4, 2, 7, 2, 4, 6, 3, 6, 2, 3, 10, 5, 1, 8, 13, 2,
1, 6, 3, 2, 6, 3, 4, 2, 4, 11, 1, 2, 1, 6, 14, 1,
3, 3, 3, 2, 3, 1, 6, 2, 6, 1, 5, 1, 8, 1, 8, 3,
10, 8, 4, 2, 1, 2, 1, 11, 4, 6, 3, 5, 1, 2, 3, 1,
3, 5, 1, 6, 5, 1, 5, 7, 3, 2, 3, 4, 3, 3, 8, 6,
1, 2, 7, 3, 2, 4, 5, 4, 3, 3, 11, 3, 1, 5, 7, 2,
3, 9, 1, 5, 7, 2, 1, 5, 7, 2, 4, 9, 2, 3, 1, 2,
3, 1, 6, 2, 10, 11, 6, 1, 2, 3, 3, 1, 3, 11, 1, 3,
8, 3, 6, 1, 3, 6, 8, 1, 2, 3, 7, 2, 1, 9, 12, 5,
3, 1, 5, 1, 5, 1, 5, 3, 1, 5, 1, 5, 3, 4, 15, 5,
1, 5, 4, 3, 5, 9, 3, 6, 6, 1, 9, 3, 2, 3, 3, 9,
1, 5, 7, 3, 2, 1, 2, 12, 1, 6, 3, 8, 4, 3, 3, 9,
8, 1, 2, 3, 1, 3, 3, 5, 3, 6, 6, 9, 1, 3, 2, 9,
4, 12, 2, 1, 2, 3, 1, 6, 2, 7, 15, 5, 3, 6, 7, 3,
5, 6, 1, 2, 3, 4, 3, 5, 1, 2, 7, 3, 3, 2, 3, 1,
5, 1, 8, 6, 4, 9, 2, 3, 6, 1, 3, 3, 3, 14, 3, 7,
2, 4, 5, 4, 6, 9, 2, 1, 2, 12, 6, 3, 1, 8, 3, 3,
7, 5, 7, 2, 15, 3, 3, 3, 4, 3, 2, 1, 6, 3, 2, 1,
3, 11, 3, 1, 2, 9, 1, 2, 6, 1, 3, 2, 13, 3, 3, 2,
4, 5, 16, 8, 1, 3, 2, 1, 2, 1, 5, 7, 3, 2, 4, 5,
3, 10, 2, 1, 3, 15, 2, 4, 5, 3, 3, 4, 3, 6, 2, 3,
1, 3, 2, 3, 1, 5, 1, 8, 3, 10, 2, 6, 7, 14, 3, 10,
2, 9, 4, 3, 2, 3, 7, 3, 3, 5, 1, 5, 6, 4, 5, 1,
5, 4, 6, 5, 12, 1, 2, 4, 3, 2, 4, 9, 5, 3, 3, 1,
3, 5, 6, 1, 5, 3, 3, 3, 4, 3, 5, 3, 1, 3, 3, 3,
5, 4, 12, 3, 11, 1, 9, 2, 4, 5, 15, 4, 9, 2, 1, 5,
3, 1, 3, 2, 9, 4, 6, 9, 8, 3, 1, 6, 3, 5, 1, 5,
1, 3, 5, 7, 2, 12, 1, 8, 1, 5, 1, 5, 10, 2, 1, 2,
4, 8, 3, 3, 1, 6, 8, 4, 2, 3, 15, 1, 5, 1, 3, 2,
3, 3, 4, 3, 2, 6, 3, 4, 6, 2, 7, 6, 5, 12, 3, 6,
3, 1, 11, 4, 9, 5, 3, 7, 2, 1, 3, 5, 4, 3, 2, 3,
15, 7, 5, 1, 6, 5, 1, 8, 1, 9, 12, 9, 3, 8, 9, 3,
1, 9, 2, 3, 1, 5, 4, 5, 3, 3, 4, 2, 3, 1, 5, 1,
6, 2, 3, 3, 1, 6, 2, 7, 9, 2, 3, 10, 2, 4, 3, 2,
4, 2, 7, 3, 2, 7, 6, 2, 1, 15, 2, 12, 3, 3, 6, 6,
7, 3, 2, 1, 2, 9, 3, 6, 4, 3, 2, 6, 1, 6, 15, 8,
1, 3, 11, 7, 3, 5, 6, 3, 1, 2, 4, 5, 3, 3, 12, 7,
3, 2, 4, 6, 9, 5, 1, 5, 1, 2, 3, 10, 3, 2, 7, 2,
1, 2, 7, 3, 6, 12, 5, 3, 4, 5, 1, 15, 2, 3, 1, 6,
2, 7, 3, 17, 6, 4, 3, 5, 1, 2, 10, 5, 4, 8, 1, 5,
7, 2, 1, 6, 3, 8, 3, 4, 2, 4, 2, 3, 4, 3, 3, 6,
3, 2, 3, 3, 4, 9, 2, 10, 2, 6, 1, 5, 3, 1, 5, 6,
1, 2, 10, 3, 15, 3, 2, 4, 5, 6, 3, 1, 14, 1, 3, 2,
1, 8, 6, 1, 3, 5, 4, 12, 6, 3, 9, 3, 2, 7, 3, 2,
6, 4, 3, 6, 2, 3, 6, 3, 6, 1, 8, 10, 2, 1, 5, 9,
4, 2, 7, 2, 1, 3, 11, 3, 7, 3, 3, 5, 3, 1, 5, 1,
2, 1, 11, 1, 2, 3, 3, 6, 3, 7, 5, 6, 3, 4, 2, 18,
7, 6, 3, 2, 3, 1, 6, 3, 6, 8, 1, 5, 4, 11, 1, 6,
3, 2, 3, 9, 1, 6, 3, 2, 6, 4, 3, 6, 2, 3, 6, 3,
1, 6, 6, 2, 7, 3, 8, 3, 1, 5, 4, 9, 3, 17, 1, 14,
1, 11, 3, 1, 5, 6, 1, 3, 2, 4, 11, 3, 1, 5, 4, 2,
3, 4, 2, 6, 9, 6, 10, 2, 3, 3, 4, 2, 1, 8, 6, 1,
5, 4, 5, 1, 2, 3, 7, 6, 11, 4, 14, 1, 2, 10, 2, 1,
2, 7, 5, 6, 1, 6, 8, 1, 14, 4, 11, 4, 2, 3, 3, 7,
2, 4, 6, 3, 3, 2, 10, 2, 9, 1, 6, 3, 2, 3, 7, 9,
5, 4, 5, 16, 3, 5, 3, 3, 1, 3, 8, 3, 1, 6, 3, 14,
1, 5, 4, 8, 3, 4, 3, 5, 12, 10, 5, 1, 5, 1, 6, 2,
3, 10, 2, 1, 6, 9, 5, 1, 5, 1, 2, 10, 8, 13, 2, 4,
3, 2, 6, 3, 4, 6, 6, 3, 2, 4, 11, 1, 8, 7, 5, 3,
6, 6, 7, 3, 2, 10, 2, 6, 3, 1, 3, 3, 8, 4, 11, 1,
14, 4, 3, 2, 10, 2, 6, 12, 10, 2, 4, 5, 1, 8, 1, 6,
6, 17, 1, 2, 3, 6, 3, 3, 4, 3, 2, 1, 3, 12, 2, 10,
5, 3, 3, 7, 2, 3, 3, 1, 6, 3, 5, 1, 5, 3, 10, 2,
13, 2, 1, 3, 11, 1, 12, 2, 3, 1, 2, 3, 12, 3, 4, 2,
1, 17, 3, 4, 8, 6, 1, 5, 1, 5, 3, 4, 2, 4, 6, 11,
3, 7, 2, 13, 2, 1, 6, 5, 4, 2, 4, 6, 2, 7, 3, 8,
3, 4, 2, 3, 3, 4, 3, 5, 6, 1, 3, 3, 8, 4, 3, 3,
6, 5, 1, 3, 9, 2, 3, 3, 3, 6, 9, 4, 3, 5, 4, 9,
2, 7, 3, 9, 5, 4, 5, 6, 1, 3, 6, 6, 18, 2, 3, 4,
2, 3, 1, 2, 9, 6, 3, 4, 3, 3, 2, 9, 1, 2, 1, 12,
2, 3, 3, 7, 15, 3, 2, 3, 6, 3, 10, 2, 4, 2, 4, 3,
3, 2, 15, 1, 5, 6, 4, 5, 4, 12, 3, 6, 2, 7, 2, 3,
1, 14, 7, 8, 1, 6, 3, 2, 10, 5, 3, 3, 3, 4, 5, 6,
7, 5, 7, 8, 7, 5, 7, 3, 8, 3, 4, 3, 8, 10, 5, 1,
3, 2, 1, 2, 6, 1, 5, 1, 3, 11, 3, 1, 2, 9, 4, 5,
4, 11, 1, 5, 9, 7, 2, 1, 2, 9, 1, 2, 3, 4, 5, 1,
15, 2, 15, 1, 5, 1, 9, 2, 9, 3, 7, 5, 1, 2, 10, 18,
3, 2, 3, 7, 2, 10, 5, 7, 11, 3, 1, 15, 6, 5, 9, 1,
2, 7, 3, 11, 9, 1, 6, 3, 2, 4, 2, 4, 3, 5, 1, 6,
9, 5, 7, 8, 7, 2, 3, 3, 1, 3, 2, 1, 14, 1, 14, 3,
1, 2, 3, 7, 2, 6, 7, 8, 7, 2, 3, 4, 3, 2, 3, 3,
3, 4, 2, 4, 2, 7, 8, 4, 3, 2, 6, 4, 8, 1, 5, 4,
2, 3, 13, 3, 5, 4, 2, 3, 6, 7, 15, 2, 7, 11, 4, 6,
2, 3, 4, 5, 3, 7, 5, 3, 1, 5, 6, 6, 7, 3, 3, 9,
5, 3, 4, 9, 2, 3, 1, 3, 5, 1, 5, 4, 3, 3, 5, 1,
9, 5, 1, 6, 2, 3, 4, 5, 6, 7, 6, 2, 4, 5, 3, 3,
10, 2, 7, 8, 7, 5, 4, 5, 6, 1, 9, 3, 6, 5, 6, 1,
2, 1, 6, 3, 2, 4, 2, 22, 2, 1, 2, 1, 5, 6, 3, 3,
7, 2, 3, 3, 3, 4, 3, 18, 9, 2, 3, 1, 6, 3, 3, 3,
2, 7, 11, 6, 1, 9, 5, 3, 13, 12, 2, 1, 2, 1, 2, 7,
2, 3, 3, 4, 8, 6, 1, 21, 2, 1, 2, 12, 3, 3, 1, 9,
2, 7, 3, 14, 9, 7, 3, 5, 6, 1, 3, 6, 15, 3, 2, 3,
3, 7, 2, 1, 12, 2, 3, 3, 13, 5, 9, 3, 4, 3, 3, 15,
2, 6, 6, 1, 8, 1, 3, 2, 6, 9, 1, 3, 2, 13, 6, 3,
6, 2, 12, 12, 6, 3, 1, 6, 14, 4, 2, 3, 6, 1, 9, 3,
2, 3, 3, 10, 8, 1, 3, 3, 9, 5, 3, 1, 2, 4, 3, 3,
12, 8, 3, 4, 5, 3, 7, 11, 4, 8, 3, 1, 6, 2, 1, 11,
4, 9, 17, 1, 3, 9, 2, 3, 3, 4, 5, 4, 9, 3, 2, 1,
2, 4, 8, 1, 6, 6, 3, 9, 2, 3, 3, 3, 1, 3, 6, 5,
10, 6, 9, 2, 3, 1, 8, 1, 5, 7, 2, 15, 1, 5, 6, 1,
12, 3, 8, 4, 5, 1, 6, 11, 3, 1, 8, 10, 5, 1, 6, 6,
9, 5, 6, 3, 1, 5, 1, 3, 5, 9, 1, 6, 3, 2, 3, 1,
12, 14, 1, 2, 1, 5, 1, 8, 6, 4, 11, 1, 3, 2, 1, 5,
3, 10, 6, 5, 4, 6, 3, 3, 3, 2, 9, 1, 2, 6, 9, 1,
6, 3, 2, 1, 8, 6, 6, 7, 2, 4, 9, 2, 6, 7, 3, 3,
2, 4, 3, 2, 10, 6, 5, 7, 2, 1, 8, 1, 6, 15, 2, 3,
12, 10, 12, 5, 4, 6, 5, 6, 3, 6, 6, 3, 4, 8, 7, 3,
2, 3, 18, 10, 5, 15, 6, 1, 2, 1, 14, 6, 7, 3, 11, 4,
2, 9, 3, 7, 9, 2, 3, 1, 3, 17, 9, 1, 8, 3, 9, 1,
12, 2, 1, 3, 6, 3, 6, 5, 4, 3, 8, 6, 4, 5, 7, 20,
3, 1, 3, 2, 6, 7, 2, 1, 2, 1, 2, 4, 3, 5, 3, 3,
1, 3, 3, 3, 6, 3, 12, 5, 1, 5, 3, 6, 3, 3, 7, 3,
3, 26, 10, 3, 5, 1, 5, 4, 5, 6, 6, 1, 3, 2, 7, 8,
4, 6, 3, 11, 1, 5, 4, 3, 11, 1, 11, 3, 4, 5, 6, 6,
1, 5, 3, 6, 1, 2, 7, 5, 1, 3, 9, 2, 6, 4, 9, 6,
3, 3, 2, 3, 3, 7, 2, 1, 6, 6, 2, 3, 9, 9, 6, 1,
8, 6, 4, 9, 5, 13, 2, 3, 4, 3, 3, 2, 1, 5, 10, 2,
3, 4, 2, 10, 5, 1, 17, 1, 2, 12, 1, 6, 6, 5, 3, 1,
6, 15, 3, 6, 8, 6, 1, 11, 9, 6, 7, 5, 1, 6, 6, 2,
1, 2, 3, 6, 1, 8, 9, 1, 20, 4, 8, 3, 4, 5, 1, 2,
9, 4, 5, 4, 6, 2, 9, 1, 9, 5, 1, 2, 1, 2, 4, 14,
1, 3, 11, 6, 3, 7, 9, 2, 3, 4, 3, 3, 5, 4, 2, 1,
9, 5, 3, 10, 11, 4, 3, 15, 2, 1, 2, 9, 3, 15, 1, 2,
4, 3, 2, 3, 6, 7, 17, 7, 3, 2, 1, 3, 2, 7, 2, 1,
3, 14, 1, 2, 3, 4, 5, 1, 5, 1, 5, 1, 2, 15, 1, 6,
6, 5, 9, 6, 7, 5, 1, 6, 3, 5, 3, 7, 6, 2, 7, 2,
9, 1, 5, 4, 2, 4, 5, 6, 9, 9, 4, 3, 9, 8, 7, 3,
3, 5, 7, 2, 3, 1, 6, 6, 2, 3, 3, 6, 1, 8, 1, 6,
3, 2, 7, 3, 2, 1, 6, 9, 2, 18, 9, 6, 6, 1, 2, 1,
2, 4, 6, 2, 18, 3, 9, 1, 6, 5, 3, 6, 12, 4, 3, 3,
8, 6, 1, 9, 5, 10, 5, 1, 3, 9, 2, 1, 20, 3, 1, 8,
1, 2, 4, 9, 5, 6, 3, 1, 5, 4, 2, 3, 6, 1, 5, 9,
4, 3, 2, 10, 2, 3, 18, 3, 1, 5, 3, 12, 3, 7, 8, 3,
9, 1, 5, 10, 5, 4, 3, 2, 3, 1, 5, 1, 6, 2, 1, 2,
4, 5, 3, 6, 9, 7, 6, 8, 4, 3, 8, 4, 2, 1, 3, 9,
12, 9, 5, 6, 1, 2, 7, 5, 3, 3, 3, 9, 6, 1, 14, 9,
7, 8, 6, 7, 12, 6, 11, 3, 1, 5, 4, 2, 1, 2, 7, 6,
3, 2, 3, 7, 2, 1, 2, 15, 3, 1, 3, 5, 1, 15, 11, 1,
2, 3, 4, 3, 3, 8, 6, 6, 3, 4, 2, 1, 12, 6, 2, 3,
4, 3, 3, 5, 1, 3, 6, 14, 7, 3, 2, 6, 4, 3, 6, 2,
3, 7, 3, 6, 5, 3, 3, 4, 3, 3, 2, 1, 2, 4, 6, 2,
7, 9, 5, 1, 8, 3, 10, 3, 5, 4, 2, 15, 18, 6, 4, 11,
6, 1, 3, 6, 8, 3, 3, 1, 9, 2, 13, 2, 4, 9, 5, 4,
5, 3, 7, 2, 10, 11, 9, 6, 4, 14, 6, 3, 3, 4, 3, 6,
12, 8, 7, 2, 7, 6, 3, 5, 6, 10, 3, 2, 4, 9, 6, 9,
5, 1, 2, 10, 5, 7, 2, 3, 1, 5, 12, 9, 1, 2, 10, 8,
7, 5, 7, 3, 2, 3, 10, 3, 5, 3, 1, 6, 3, 15, 5, 4,
3, 2, 3, 4, 20, 1, 2, 1, 6, 9, 2, 3, 4, 5, 3, 9,
9, 1, 6, 8, 4, 3, 2, 3, 3, 1, 26, 7, 2, 10, 8, 1,
2, 3, 6, 1, 3, 6, 6, 3, 2, 7, 5, 3, 3, 7, 5, 7,
8, 4, 3, 6, 2, 4, 11, 3, 1, 9, 11, 3, 1, 9, 3, 8,
7, 5, 3, 6, 1, 3, 2, 4, 9, 6, 8, 1, 2, 7, 2, 4,
6, 6, 15, 8, 4, 2, 1, 3, 11, 6, 4, 5, 3, 3, 3, 7,
3, 9, 5, 6, 1, 5, 1, 2, 13, 2, 6, 4, 2, 9, 4, 5,
7, 8, 3, 3, 4, 5, 3, 4, 3, 6, 5, 10, 5, 4, 2, 6,
13, 9, 2, 6, 9, 3, 15, 3, 4, 3, 11, 6, 1, 2, 3, 3,
1, 5, 1, 2, 3, 3, 1, 3, 11, 9, 3, 9, 6, 4, 6, 3,
5, 6, 1, 8, 1, 5, 1, 5, 9, 3, 10, 2, 1, 3, 11, 3,
3, 9, 3, 7, 6, 8, 1, 3, 3, 2, 7, 6, 2, 1, 9, 8,
18, 6, 3, 7, 14, 1, 6, 3, 6, 3, 2, 1, 8, 15, 4, 12,
3, 15, 5, 1, 9, 2, 3, 6, 4, 11, 1, 3, 11, 9, 1, 5,
1, 5, 15, 1, 14, 3, 7, 8, 3, 10, 8, 1, 3, 2, 16, 2,
1, 2, 3, 1, 6, 2, 3, 3, 6, 1, 3, 2, 3, 4, 3, 2,
10, 2, 16, 5, 4, 8, 1, 11, 1, 2, 3, 4, 3, 8, 7, 2,
9, 4, 2, 10, 3, 6, 6, 3, 5, 1, 5, 1, 6, 14, 6, 9,
1, 9, 5, 4, 5, 24, 1, 2, 3, 4, 5, 1, 5, 15, 1, 18,
3, 5, 3, 1, 9, 2, 3, 4, 8, 7, 8, 3, 7, 2, 10, 2,
3, 1, 5, 6, 1, 3, 6, 3, 3, 2, 6, 1, 3, 2, 6, 3,
4, 2, 1, 3, 9, 5, 3, 4, 6, 3, 11, 1, 3, 6, 9, 2,
7, 3, 2, 10, 3, 8, 4, 2, 4, 11, 4, 6, 3, 3, 8, 6,
9, 15, 4, 2, 1, 2, 3, 13, 2, 7, 12, 11, 3, 1, 3, 5,
3, 7, 3, 3, 6, 5, 3, 1, 6, 5, 6, 4, 9, 9, 5, 3,
4, 8, 3, 3, 4, 8, 10, 2, 1, 5, 1, 5, 6, 3, 4, 3,
5, 10, 5, 9, 13, 2, 3, 15, 1, 2, 4, 3, 6, 6, 9, 2,
4, 11, 3, 1, 6, 17, 3, 9, 6, 3, 1, 14, 7, 8, 7, 2,
7, 6, 2, 3, 3, 1, 18, 2, 3, 10, 6, 12, 3, 11, 1, 8,
9, 6, 6, 9, 1, 3, 3, 3, 2, 3, 7, 2, 1, 11, 4, 6,
3, 5, 3, 4, 6, 9, 6, 3, 5, 1, 11, 7, 3, 3, 2, 9,
3, 10, 11, 1, 6, 12, 2, 9, 9, 1, 11, 1, 2, 6, 4, 6,
5, 7, 2, 1, 9, 8, 19, 3, 3, 3, 6, 5, 3, 6, 4, 3,
2, 3, 7, 15, 3, 5, 4, 11, 3, 4, 6, 5, 1, 5, 1, 3,
5, 1, 5, 6, 9, 10, 3, 2, 4, 11, 3, 3, 15, 3, 7, 3,
6, 6, 3, 5, 1, 5, 15, 1, 8, 4, 2, 1, 3, 9, 2, 1,
3, 2, 13, 2, 4, 3, 5, 1, 2, 3, 4, 2, 3, 15, 6, 1,
3, 3, 2, 10, 11, 4, 2, 1, 2, 36, 4, 2, 4, 11, 1, 2,
7, 5, 1, 2, 10, 3, 5, 9, 3, 10, 8, 3, 4, 3, 2, 10,
6, 11, 1, 2, 1, 6, 5, 9, 1, 11, 3, 9, 15, 1, 5, 7,
5, 4, 8, 25, 3, 5, 4, 5, 6, 3, 9, 1, 11, 3, 1, 2,
3, 4, 3, 3, 5, 9, 1, 11, 1, 8, 7, 5, 3, 1, 6, 5,
10, 2, 7, 3, 2, 18, 1, 2, 3, 6, 1, 2, 7, 6, 3, 2,
3, 1, 3, 2, 10, 5, 1, 5, 3, 6, 1, 12, 6, 6, 3, 3,
2, 12, 1, 2, 12, 1, 3, 2, 3, 4, 8, 3, 1, 5, 6, 7,
3, 17, 3, 7, 3, 2, 1, 15, 11, 4, 2, 3, 4, 2, 1, 14,
1, 3, 2, 13, 9, 11, 1, 3, 8, 3, 1, 8, 6, 1, 6, 2,
3, 3, 7, 5, 3, 4, 6, 2, 9, 1, 5, 4, 8, 3, 3, 15,
1, 5, 9, 1, 5, 4, 2, 4, 6, 12, 20, 1, 6, 5, 3, 6,
1, 6, 2, 1, 2, 3, 9, 7, 6, 3, 2, 7, 15, 2, 4, 5,
4, 3, 5, 9, 4, 2, 7, 8, 3, 4, 2, 3, 1, 5, 1, 6,
2, 1, 2, 3, 4, 2, 3, 16, 12, 5, 4, 9, 5, 1, 3, 5,
1, 2, 9, 3, 6, 1, 8, 1, 11, 3, 3, 4, 9, 2, 9, 6,
4, 3, 2, 10, 3, 15, 11, 6, 1, 3, 9, 2, 31, 2, 1, 6,
3, 5, 1, 6, 6, 14, 1, 2, 7, 11, 3, 1, 3, 3, 5, 7,
2, 1, 5, 3, 4, 5, 7, 5, 3, 1, 6, 11, 9, 4, 5, 9,
6, 1, 6, 2, 6, 1, 5, 1, 3, 9, 3, 3, 17, 3, 1, 6,
2, 3, 9, 9, 1, 8, 3, 3, 4, 3, 5, 9, 4, 5, 4, 5,
1, 2, 9, 13, 6, 11, 1, 2, 1, 11, 3, 3, 7, 8, 3, 10,
5, 6, 1, 9, 21, 2, 12, 1, 3, 5, 6, 1, 3, 5, 4, 2,
3, 6, 6, 4, 2, 3, 6, 15, 10, 3, 12, 3, 5, 6, 1, 5,
10, 3, 3, 2, 6, 7, 5, 9, 6, 4, 3, 6, 2, 7, 5, 1,
6, 15, 8, 1, 6, 3, 2, 1, 2, 3, 13, 2, 9, 1, 2, 3,
7, 27, 3, 26, 1, 8, 3, 3, 6, 13, 2, 1, 3, 11, 3, 1,
6, 6, 3, 5, 9, 1, 6, 6, 5, 9, 6, 3, 4, 3, 5, 3,
4, 2, 1, 2, 10, 12, 3, 3, 5, 7, 5, 1, 11, 3, 7, 5,
13, 2, 9, 4, 6, 6, 5, 6, 3, 4, 8, 3, 4, 3, 3, 11,
1, 5, 10, 5, 3, 22, 9, 3, 5, 1, 2, 3, 7, 2, 13, 2,
1, 6, 5, 4, 2, 4, 6, 2, 6, 4, 11, 4, 3, 5, 9, 3,
3, 4, 3, 6, 2, 4, 9, 5, 6, 3, 6, 1, 3, 2, 1, 8,
6, 6, 7, 5, 7, 3, 5, 6, 1, 6, 3, 2, 3, 1, 6, 2,
13, 3, 9, 3, 5, 3, 1, 9, 5, 4, 2, 13, 5, 10, 3, 8,
10, 6, 5, 4, 5, 1, 8, 3, 10, 5, 10, 2, 15, 1, 2, 4,
8, 1, 9, 2, 1, 3, 5, 9, 6, 7, 9, 3, 8, 10, 3, 2,
4, 3, 2, 3, 6, 4, 5, 1, 6, 3, 2, 1, 3, 5, 1, 8,
6, 7, 5, 3, 4, 3, 14, 1, 3, 9, 15, 17, 1, 8, 6, 1,
9, 8, 3, 4, 5, 4, 5, 4, 5, 22, 3, 3, 2, 10, 2, 1,
2, 7, 14, 4, 3, 8, 7, 15, 3, 15, 2, 7, 5, 3, 3, 4,
2, 9, 6, 3, 1, 11, 6, 4, 3, 6, 2, 7, 2, 3, 1, 2,
9, 10, 3, 8, 19, 8, 1, 2, 3, 1, 20, 21, 7, 2, 3, 1,
12, 5, 3, 1, 9, 5, 6, 1, 8, 1, 3, 8, 3, 4, 2, 1,
5, 3, 4, 5, 1, 9, 8, 4, 6, 9, 6, 3, 6, 5, 3, 3
* Most byte entries in the array contain two sequential differentials between
* two adjacent prime numbers, each differential halved (as the difference is
* always even) and packed into 4 bits.
*
* If a halved differential value exceeds 0xf (and as such does not fit into 4
* bits), a zero is placed in the array followed by the value literal (no
* halving).
*
* If out of two consecutive differencials only the second one exceeds 0xf,
* the first one still is put into the array in its own byte prepended by a
* zero.
*/
const uint8_t PRIME_DELTAS[] = {
1, 18, 18, 18, 49, 50, 18, 51, 19, 33, 50, 52,
33, 33, 39, 35, 21, 19, 50, 51, 21, 18, 22, 98,
18, 49, 83, 51, 19, 33, 87, 33, 39, 53, 18, 52,
51, 35, 66, 69, 21, 19, 35, 66, 18, 100, 36, 35,
97, 147, 83, 49, 53, 51, 19, 50, 22, 81, 35, 49,
98, 52, 84, 84, 51, 36, 50, 66, 117, 97, 81, 33,
87, 33, 39, 33, 42, 36, 84, 35, 55, 35, 52, 54,
35, 21, 19, 81, 81, 57, 33, 35, 52, 51, 177, 84,
83, 52, 98, 51, 19, 101, 145, 35, 19, 33, 38, 19,
0, 34, 51, 73, 87, 33, 35, 66, 19, 101, 18, 18,
54, 100, 99, 35, 66, 66, 114, 49, 35, 19, 90, 50,
28, 33, 86, 21, 67, 51, 147, 33, 101, 100, 135, 50,
18, 21, 99, 57, 24, 27, 52, 50, 18, 67, 81, 87,
83, 97, 33, 86, 24, 19, 33, 84, 156, 35, 72, 18,
72, 18, 67, 50, 97, 179, 19, 35, 115, 33, 50, 54,
51, 114, 54, 67, 45, 149, 66, 49, 59, 97, 132, 38,
117, 18, 67, 50, 18, 52, 33, 53, 21, 66, 117, 97,
50, 24, 114, 52, 50, 148, 83, 52, 86, 114, 51, 30,
21, 66, 114, 70, 54, 35, 165, 24, 210, 22, 50, 99,
66, 75, 18, 22, 225, 51, 50, 49, 98, 97, 81, 129,
131, 168, 66, 18, 27, 70, 53, 18, 49, 53, 22, 81,
87, 50, 52, 51, 134, 18, 115, 36, 84, 51, 179, 21,
114, 57, 21, 114, 21, 114, 73, 35, 18, 49, 98, 171,
97, 35, 49, 59, 19, 131, 97, 54, 129, 35, 114, 25,
197, 49, 81, 81, 83, 21, 21, 52, 245, 21, 67, 89,
54, 97, 147, 35, 57, 21, 115, 33, 44, 22, 56, 67,
57, 129, 35, 19, 53, 54, 105, 19, 41, 76, 33, 35,
22, 39, 245, 54, 115, 86, 18, 52, 53, 18, 115, 50,
49, 81, 134, 73, 35, 97, 51, 62, 55, 36, 84, 105,
33, 44, 99, 24, 51, 117, 114, 243, 51, 67, 33, 99,
33, 59, 49, 41, 18, 97, 50, 211, 50, 69, 0, 32,
129, 50, 18, 21, 115, 36, 83, 162, 19, 242, 69, 51,
67, 98, 49, 50, 49, 81, 131, 162, 103, 227, 162, 148,
50, 55, 51, 81, 86, 69, 21, 70, 92, 18, 67, 36,
149, 51, 19, 86, 21, 51, 52, 53, 49, 51, 53, 76,
59, 25, 36, 95, 73, 33, 83, 19, 41, 70, 152, 49,
99, 81, 81, 53, 114, 193, 129, 81, 90, 33, 36, 131,
49, 104, 66, 63, 21, 19, 35, 52, 50, 99, 70, 39,
101, 195, 99, 27, 73, 83, 114, 19, 84, 50, 63, 117,
22, 81, 129, 156, 147, 137, 49, 146, 49, 84, 83, 52,
35, 21, 22, 35, 49, 98, 121, 35, 162, 67, 36, 39,
50, 118, 33, 242, 195, 54, 103, 50, 18, 147, 100, 50,
97, 111, 129, 59, 115, 86, 49, 36, 83, 60, 115, 36,
105, 81, 81, 35, 163, 39, 33, 39, 54, 197, 52, 81,
242, 49, 98, 115, 0, 34, 100, 53, 18, 165, 72, 21,
114, 22, 56, 52, 36, 35, 67, 54, 50, 51, 73, 42,
38, 21, 49, 86, 18, 163, 243, 36, 86, 49, 225, 50,
24, 97, 53, 76, 99, 147, 39, 50, 100, 54, 35, 99,
97, 138, 33, 89, 66, 114, 19, 179, 115, 53, 49, 81,
33, 177, 35, 54, 55, 86, 52, 0, 4, 0, 36, 118,
50, 49, 99, 104, 21, 75, 22, 50, 57, 22, 50, 100,
54, 35, 99, 22, 98, 115, 131, 21, 73, 0, 6, 0,
34, 30, 27, 49, 86, 19, 36, 179, 21, 66, 52, 38,
150, 162, 51, 66, 24, 97, 84, 81, 35, 118, 180, 225,
42, 33, 39, 86, 22, 129, 228, 180, 35, 55, 36, 99,
50, 162, 145, 99, 35, 121, 84, 0, 10, 0, 32, 53,
51, 19, 131, 22, 62, 21, 72, 52, 53, 202, 81, 81,
98, 58, 33, 105, 81, 81, 42, 141, 36, 50, 99, 70,
99, 36, 177, 135, 83, 102, 115, 42, 38, 49, 51, 132,
177, 228, 50, 162, 108, 162, 69, 24, 22, 0, 12, 0,
34, 18, 54, 51, 67, 33, 60, 42, 83, 55, 35, 49,
99, 81, 83, 162, 210, 19, 177, 194, 49, 35, 195, 66,
0, 2, 0, 34, 52, 134, 21, 21, 52, 36, 107, 55,
45, 33, 101, 66, 70, 39, 56, 52, 35, 52, 53, 97,
51, 132, 51, 101, 19, 146, 51, 54, 148, 53, 73, 39,
57, 84, 86, 19, 102, 0, 36, 35, 66, 49, 41, 99,
67, 50, 145, 33, 194, 51, 127, 50, 54, 58, 36, 36,
51, 47, 21, 100, 84, 195, 98, 114, 49, 231, 129, 99,
42, 83, 51, 69, 103, 87, 135, 87, 56, 52, 56, 165,
19, 33, 38, 21, 19, 179, 18, 148, 84, 177, 89, 114,
18, 145, 35, 69, 31, 47, 21, 25, 41, 55, 81, 42,
0, 36, 50, 55, 42, 87, 179, 31, 101, 145, 39, 59,
145, 99, 36, 36, 53, 22, 149, 120, 114, 51, 19, 33,
225, 227, 18, 55, 38, 120, 114, 52, 50, 51, 52, 36,
39, 132, 50, 100, 129, 84, 35, 211, 84, 35, 103, 242,
123, 70, 35, 69, 55, 83, 21, 102, 115, 57, 83, 73,
35, 19, 81, 84, 51, 81, 149, 22, 35, 69, 103, 98,
69, 51, 162, 120, 117, 69, 97, 147, 101, 97, 33, 99,
36, 0, 4, 0, 44, 33, 33, 86, 51, 114, 51, 52,
0, 6, 0, 36, 146, 49, 99, 51, 39, 182, 25, 83,
220, 33, 33, 39, 35, 52, 134, 0, 2, 0, 42, 33,
44, 51, 25, 39, 62, 151, 53, 97, 54, 243, 35, 55,
33, 194, 51, 213, 147, 67, 63, 38, 97, 129, 50, 105,
19, 45, 99, 98, 204, 99, 22, 228, 35, 97, 147, 35,
58, 129, 51, 149, 49, 36, 51, 200, 52, 83, 123, 72,
49, 98, 27, 73, 0, 34, 19, 146, 51, 69, 73, 50,
18, 72, 22, 99, 146, 51, 49, 54, 90, 105, 35, 24,
21, 114, 241, 86, 28, 56, 69, 22, 179, 24, 165, 22,
105, 86, 49, 81, 53, 145, 99, 35, 28, 225, 33, 81,
134, 75, 19, 33, 83, 166, 84, 99, 51, 41, 18, 105,
22, 50, 24, 102, 114, 73, 38, 115, 50, 67, 42, 101,
114, 24, 22, 242, 60, 172, 84, 101, 99, 102, 52, 135,
50, 0, 6, 0, 36, 165, 246, 18, 30, 103, 59, 66,
147, 121, 35, 19, 0, 34, 145, 131, 145, 194, 19, 99,
101, 67, 134, 69, 0, 14, 0, 40, 49, 50, 103, 33,
33, 36, 53, 51, 19, 51, 99, 197, 21, 54, 51, 115,
0, 6, 0, 52, 163, 81, 84, 86, 97, 50, 120, 70,
59, 21, 67, 177, 179, 69, 102, 21, 54, 18, 117, 19,
146, 100, 150, 51, 35, 55, 33, 102, 35, 153, 97, 134,
73, 93, 35, 67, 50, 21, 162, 52, 42, 81, 0, 34,
18, 193, 102, 83, 22, 243, 104, 97, 185, 103, 81, 102,
33, 35, 97, 137, 0, 2, 0, 40, 72, 52, 81, 41,
69, 70, 41, 25, 81, 33, 36, 225, 59, 99, 121, 35,
67, 53, 66, 25, 83, 171, 67, 242, 18, 147, 241, 36,
50, 54, 0, 14, 0, 34, 115, 33, 50, 114, 19, 225,
35, 69, 21, 21, 18, 241, 102, 89, 103, 81, 99, 83,
118, 39, 41, 21, 66, 69, 105, 148, 57, 135, 51, 87,
35, 22, 98, 51, 97, 129, 99, 39, 50, 22, 146, 0,
36, 150, 97, 33, 36, 98, 0, 36, 57, 22, 83, 108,
67, 56, 97, 149, 165, 19, 146, 0, 2, 0, 40, 49,
129, 36, 149, 99, 21, 66, 54, 21, 148, 50, 162, 0,
6, 0, 36, 49, 83, 195, 120, 57, 21, 165, 67, 35,
21, 22, 33, 36, 83, 105, 118, 132, 56, 66, 19, 156,
149, 97, 39, 83, 51, 150, 30, 151, 134, 124, 107, 49,
84, 33, 39, 99, 35, 114, 18, 243, 19, 81, 251, 18,
52, 51, 134, 99, 66, 28, 98, 52, 51, 81, 54, 231,
50, 100, 54, 35, 115, 101, 51, 67, 50, 18, 70, 39,
149, 24, 58, 53, 66, 0, 30, 0, 36, 100, 182, 19,
104, 51, 25, 45, 36, 149, 69, 55, 42, 185, 100, 230,
51, 67, 108, 135, 39, 99, 86, 163, 36, 150, 149, 18,
165, 114, 49, 92, 145, 42, 135, 87, 50, 58, 53, 49,
99, 245, 67, 35, 0, 8, 0, 40, 18, 22, 146, 52,
83, 153, 22, 132, 50, 51, 0, 2, 0, 52, 114, 168,
18, 54, 19, 102, 50, 117, 51, 117, 120, 67, 98, 75,
49, 155, 49, 147, 135, 83, 97, 50, 73, 104, 18, 114,
70, 111, 132, 33, 59, 100, 83, 51, 115, 149, 97, 81,
45, 38, 66, 148, 87, 131, 52, 83, 67, 101, 165, 66,
109, 146, 105, 63, 52, 59, 97, 35, 49, 81, 35, 49,
59, 147, 150, 70, 53, 97, 129, 81, 89, 58, 33, 59,
51, 147, 118, 129, 51, 39, 98, 25, 0, 16, 0, 36,
99, 126, 22, 54, 50, 24, 244, 195, 245, 25, 35, 100,
177, 59, 145, 81, 95, 30, 55, 131, 168, 19, 0, 4,
0, 32, 33, 35, 22, 35, 54, 19, 35, 67, 42, 0,
4, 0, 32, 84, 129, 177, 35, 67, 135, 41, 66, 163,
102, 53, 21, 22, 230, 145, 149, 69, 0, 48, 18, 52,
81, 95, 0, 2, 0, 36, 53, 49, 146, 52, 135, 131,
114, 162, 49, 86, 19, 99, 50, 97, 50, 99, 66, 19,
149, 52, 99, 177, 54, 146, 115, 42, 56, 66, 75, 70,
51, 134, 159, 66, 18, 61, 39, 203, 49, 53, 55, 51,
101, 49, 101, 100, 153, 83, 72, 51, 72, 162, 21, 21,
99, 67, 90, 89, 210, 63, 18, 67, 102, 146, 75, 49,
0, 12, 0, 34, 57, 99, 30, 120, 114, 118, 35, 49,
0, 36, 35, 166, 195, 177, 137, 102, 145, 51, 50, 55,
33, 180, 99, 83, 70, 150, 53, 27, 115, 50, 147, 171,
22, 194, 153, 27, 18, 100, 101, 114, 25, 0, 16, 0,
38, 51, 54, 83, 100, 50, 55, 243, 84, 179, 70, 81,
81, 53, 21, 105, 163, 36, 179, 63, 55, 54, 99, 81,
95, 24, 66, 19, 146, 19, 45, 36, 53, 18, 52, 35,
246, 19, 50, 171, 66, 18, 0, 72, 66, 75, 18, 117,
18, 163, 89, 58, 131, 67, 42, 107, 18, 22, 89, 27,
57, 241, 87, 84, 0, 16, 0, 50, 53, 69, 99, 145,
179, 18, 52, 51, 89, 27, 24, 117, 49, 101, 162, 115,
0, 4, 0, 36, 18, 54, 18, 118, 50, 49, 50, 165,
21, 54, 28, 102, 51, 44, 18, 193, 50, 52, 131, 21,
103, 0, 6, 0, 34, 55, 50, 31, 180, 35, 66, 30,
19, 45, 155, 19, 131, 24, 97, 98, 51, 117, 52, 98,
145, 84, 131, 63, 21, 145, 84, 36, 108, 0, 40, 22,
83, 97, 98, 18, 57, 118, 50, 127, 36, 84, 53, 148,
39, 131, 66, 49, 81, 98, 18, 52, 35, 0, 32, 197,
73, 81, 53, 18, 147, 97, 129, 179, 52, 146, 150, 67,
42, 63, 182, 19, 146, 0, 62, 33, 99, 81, 102, 225,
39, 179, 19, 53, 114, 21, 52, 87, 83, 22, 185, 69,
150, 22, 38, 21, 19, 147, 0, 6, 0, 34, 49, 98,
57, 145, 131, 52, 53, 148, 84, 81, 41, 214, 177, 33,
179, 55, 131, 165, 97, 0, 18, 0, 42, 44, 19, 86,
19, 84, 35, 102, 66, 54, 250, 60, 53, 97, 90, 51,
38, 117, 150, 67, 98, 117, 22, 248, 22, 50, 18, 61,
41, 18, 55, 0, 54, 0, 6, 0, 52, 24, 51, 109,
33, 59, 49, 102, 53, 145, 102, 89, 99, 67, 83, 66,
18, 172, 51, 87, 81, 179, 117, 210, 148, 102, 86, 52,
131, 67, 59, 21, 165, 0, 6, 0, 44, 147, 81, 35,
114, 210, 22, 84, 36, 98, 100, 180, 53, 147, 52, 54,
36, 149, 99, 97, 50, 24, 102, 117, 115, 86, 22, 50,
49, 98, 211, 147, 83, 25, 84, 45, 90, 56, 166, 84,
81, 131, 165, 162, 241, 36, 129, 146, 19, 89, 103, 147,
138, 50, 67, 35, 100, 81, 99, 33, 53, 24, 103, 83,
67, 225, 57, 0, 30, 0, 34, 24, 97, 152, 52, 84,
84, 0, 10, 0, 44, 51, 42, 33, 39, 228, 56, 127,
63, 39, 83, 52, 41, 99, 27, 100, 54, 39, 35, 18,
154, 56, 0, 38, 129, 35, 0, 2, 0, 40, 0, 42,
114, 49, 197, 49, 149, 97, 129, 56, 52, 33, 83, 69,
25, 132, 105, 99, 101, 51,
};
static uint32_t bn_mod_word16(const struct LITE_BIGNUM *p, uint16_t word)
@@ -1253,18 +1189,34 @@ int DCRYPTO_bn_generate_prime(struct LITE_BIGNUM *p)
/* Save on trial division by marking known composites. */
bn_init(&composites, composites_buf, sizeof(composites_buf));
for (i = 0; i < sizeof(PRIME_DELTAS) / sizeof(PRIME_DELTAS[0]); i++) {
for (i = 0; i < ARRAY_SIZE(PRIME_DELTAS); i++) {
uint16_t rem;
uint8_t unpacked_deltas[2];
uint8_t packed_deltas = PRIME_DELTAS[i];
int k;
int m;
prime += (PRIME_DELTAS[i] << 1);
print_primes(prime);
rem = bn_mod_word16(p, prime);
/* Skip marking odd offsets (i.e. even candidates). */
for (j = (rem == 0) ? 0 : prime - rem;
j < bn_bits(&composites) << 1;
j += prime) {
if ((j & 1) == 0)
bn_set_bit(&composites, j >> 1);
if (packed_deltas) {
unpacked_deltas[0] = (packed_deltas >> 4) << 1;
unpacked_deltas[1] = (packed_deltas & 0xf) << 1;
m = 2;
} else {
i += 1;
unpacked_deltas[0] = PRIME_DELTAS[i];
m = 1;
}
for (k = 0; k < m; k++) {
prime += unpacked_deltas[k];
print_primes(prime);
rem = bn_mod_word16(p, prime);
/* Skip marking odd offsets (i.e. even candidates). */
for (j = (rem == 0) ? 0 : prime - rem;
j < bn_bits(&composites) << 1;
j += prime) {
if ((j & 1) == 0)
bn_set_bit(&composites, j >> 1);
}
}
}