mirror of
https://github.com/amadvance/snapraid.git
synced 2026-10-26 19:01:57 -04:00
Use primitive generator 3 for AES Cauchy mode
This commit is contained in:
Andrea Mazzoleni
parent
f855bf4d82
commit
b5d507fbe9
21 changed files with 7444 additions and 5791 deletions
285
raid/test.c
285
raid/test.c
|
|
@ -141,6 +141,165 @@ int raid_test_sort(void)
|
|||
return 0;
|
||||
}
|
||||
|
||||
/*
|
||||
* Tests the mathematical properties required by a Cauchy RAID mode.
|
||||
*
|
||||
* This is intentionally only a fast sanity check. It does not prove that
|
||||
* all square submatrices are nonsingular. The exhaustive verification of
|
||||
* the MDS property is performed by raid/test/invtest.
|
||||
*
|
||||
* SnapRAID uses two Extended Cauchy constructions:
|
||||
*
|
||||
* RAID_MODE_CAUCHY_RAID:
|
||||
* polynomial 0x11d
|
||||
* primitive generator g=2
|
||||
*
|
||||
* RAID_MODE_CAUCHY_AES:
|
||||
* polynomial 0x11b
|
||||
* primitive generator g=3
|
||||
*
|
||||
* The parity generation tests compare optimized implementations against
|
||||
* raid_gen_ref(), but both use the same active generator matrix. Therefore
|
||||
* they can agree even if the matrix itself is mathematically unsuitable.
|
||||
*
|
||||
* This test instead checks a few fundamental properties of the field
|
||||
* generator and of the generated Cauchy matrix.
|
||||
*/
|
||||
int raid_test_poly(unsigned mode)
|
||||
{
|
||||
int i, j;
|
||||
int p, d;
|
||||
|
||||
/*
|
||||
* This test is defined only for the two Cauchy modes.
|
||||
*
|
||||
* Vandermonde parity intentionally uses a different construction and
|
||||
* is not part of this test.
|
||||
*/
|
||||
if (mode != RAID_MODE_CAUCHY_RAID
|
||||
&& mode != RAID_MODE_CAUCHY_AES)
|
||||
return -1;
|
||||
|
||||
/*
|
||||
* Select the mode first so that:
|
||||
*
|
||||
* raid_gfexp
|
||||
* raid_gfcauchy
|
||||
* raid_gfmul
|
||||
* raid_gfinv
|
||||
*
|
||||
* all refer to the tables of the field being tested.
|
||||
*
|
||||
* This also verifies the normal raid_mode() table selection path
|
||||
* instead of accessing the *_raid or *_aes tables directly.
|
||||
*/
|
||||
raid_mode(mode);
|
||||
|
||||
/*
|
||||
* Primitive order alone is not enough to protect parity format
|
||||
* compatibility. Each Cauchy mode has a fixed reducing polynomial
|
||||
* and primitive generator, which determine the actual matrix coefficients.
|
||||
*/
|
||||
if (mode == RAID_MODE_CAUCHY_RAID) {
|
||||
if (raid_poly_byte != RAID_POLY_RAID)
|
||||
return -1;
|
||||
if (raid_gfexp[1] != 2)
|
||||
return -1;
|
||||
} else if (mode == RAID_MODE_CAUCHY_AES) {
|
||||
if (raid_poly_byte != RAID_POLY_AES)
|
||||
return -1;
|
||||
if (raid_gfexp[1] != 3)
|
||||
return -1;
|
||||
}
|
||||
|
||||
/*
|
||||
* raid_gfexp[a] contains g^a for the primitive generator associated
|
||||
* with the active Cauchy mode.
|
||||
*
|
||||
* The multiplicative group GF(2^8)* contains 255 elements:
|
||||
*
|
||||
* 255 = 3 * 5 * 17
|
||||
*
|
||||
* The order of every nonzero field element divides 255.
|
||||
*
|
||||
* To prove that g has order exactly 255, it is therefore sufficient
|
||||
* to verify:
|
||||
*
|
||||
* g^255 == 1
|
||||
*
|
||||
* and to exclude the three maximal proper divisors:
|
||||
*
|
||||
* 255 / 3 = 85
|
||||
* 255 / 5 = 51
|
||||
* 255 / 17 = 15
|
||||
*
|
||||
* Hence a primitive generator must satisfy:
|
||||
*
|
||||
* g^85 != 1
|
||||
* g^51 != 1
|
||||
* g^15 != 1
|
||||
*/
|
||||
if (raid_gfexp[0] != 1)
|
||||
return -1;
|
||||
if (raid_gfexp[255] != 1)
|
||||
return -1;
|
||||
if (raid_gfexp[85] == 1)
|
||||
return -1;
|
||||
if (raid_gfexp[51] == 1)
|
||||
return -1;
|
||||
if (raid_gfexp[15] == 1)
|
||||
return -1;
|
||||
|
||||
/*
|
||||
* The Q row of the Extended Cauchy matrix contains:
|
||||
*
|
||||
* 1, g, g^2, g^3, ...
|
||||
*
|
||||
* SnapRAID supports RAID_DATA_MAX data disks, so all generator powers
|
||||
* corresponding to those columns must be distinct.
|
||||
*
|
||||
* A primitive generator of order 255 guarantees this, but checking it
|
||||
* explicitly is inexpensive and also verifies the generated
|
||||
* raid_gfexp[] table itself.
|
||||
*/
|
||||
for (i = 0; i < RAID_DATA_MAX; ++i)
|
||||
for (j = i + 1; j < RAID_DATA_MAX; ++j)
|
||||
if (raid_gfexp[i] == raid_gfexp[j])
|
||||
return -1;
|
||||
|
||||
/*
|
||||
* The second row of the Extended Cauchy matrix is exactly g^d.
|
||||
*
|
||||
* Verify that the exponent table and the actual matrix used for
|
||||
* parity generation agree for every supported data column.
|
||||
*
|
||||
* This makes sure that the primitive generator checked above is the
|
||||
* same generator actually used by the Q row.
|
||||
*/
|
||||
for (d = 0; d < RAID_DATA_MAX; ++d)
|
||||
if (raid_gfcauchy[1][d] != raid_gfexp[d])
|
||||
return -1;
|
||||
|
||||
/*
|
||||
* Every coefficient of the active 6x251 Cauchy generator matrix must
|
||||
* be nonzero.
|
||||
*
|
||||
* A single coefficient is itself a 1x1 submatrix, so a zero
|
||||
* coefficient would make that submatrix singular and immediately
|
||||
* disprove the MDS property.
|
||||
*
|
||||
* Absence of zero coefficients is only a necessary condition. It does
|
||||
* not prove that every larger square submatrix is nonsingular. That
|
||||
* exhaustive verification remains the responsibility of invtest.
|
||||
*/
|
||||
for (p = 0; p < RAID_PARITY_MAX; ++p)
|
||||
for (d = 0; d < RAID_DATA_MAX; ++d)
|
||||
if (raid_gfcauchy[p][d] == 0)
|
||||
return -1;
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
#define test_setup(i) f[i - 1][nf[i - 1]++]
|
||||
|
||||
int raid_test_rec(int mode, int nd, size_t size)
|
||||
|
|
@ -374,25 +533,49 @@ int raid_test_par(int mode, int nd, size_t size)
|
|||
/* setup all the available functions */
|
||||
test_setup(1) = raid_gen1_int32;
|
||||
test_setup(1) = raid_gen1_int64;
|
||||
test_setup(2) = raid_gen2_int32;
|
||||
test_setup(2) = raid_gen2_int64;
|
||||
test_setup(2) = raid_gen2_int8;
|
||||
if (mode == RAID_MODE_CAUCHY_AES) {
|
||||
test_setup(2) = raid_gen2_int32_aes;
|
||||
test_setup(2) = raid_gen2_int64_aes;
|
||||
} else {
|
||||
test_setup(2) = raid_gen2_int32_raid;
|
||||
test_setup(2) = raid_gen2_int64_raid;
|
||||
}
|
||||
|
||||
#ifdef CONFIG_NEON
|
||||
test_setup(1) = raid_gen1_neon;
|
||||
test_setup(2) = raid_gen2_neon;
|
||||
if (mode == RAID_MODE_CAUCHY_AES)
|
||||
test_setup(2) = raid_gen2_neon_aes;
|
||||
else
|
||||
test_setup(2) = raid_gen2_neon_raid;
|
||||
#endif
|
||||
|
||||
#ifdef CONFIG_X86
|
||||
if (raid_cpu_has_sse2()) {
|
||||
test_setup(1) = raid_gen1_sse2;
|
||||
test_setup(2) = raid_gen2_sse2;
|
||||
if (mode == RAID_MODE_CAUCHY_AES)
|
||||
test_setup(2) = raid_gen2_sse2_aes;
|
||||
else
|
||||
test_setup(2) = raid_gen2_sse2_raid;
|
||||
#ifdef CONFIG_X86_64
|
||||
test_setup(2) = raid_gen2_sse2ext;
|
||||
if (mode == RAID_MODE_CAUCHY_AES)
|
||||
test_setup(2) = raid_gen2_sse2ext_aes;
|
||||
else
|
||||
test_setup(2) = raid_gen2_sse2ext_raid;
|
||||
#endif
|
||||
}
|
||||
if (raid_cpu_has_avx2()) {
|
||||
test_setup(1) = raid_gen1_avx2;
|
||||
test_setup(2) = raid_gen2_avx2;
|
||||
if (mode == RAID_MODE_CAUCHY_AES)
|
||||
test_setup(2) = raid_gen2_avx2_aes;
|
||||
else
|
||||
test_setup(2) = raid_gen2_avx2_raid;
|
||||
#ifdef CONFIG_X86_64
|
||||
if (mode == RAID_MODE_CAUCHY_AES)
|
||||
test_setup(2) = raid_gen2_avx2ext_aes;
|
||||
else
|
||||
test_setup(2) = raid_gen2_avx2ext_raid;
|
||||
#endif
|
||||
}
|
||||
#ifdef CONFIG_X86_64
|
||||
if (raid_cpu_has_avx512bw()) {
|
||||
|
|
@ -401,10 +584,10 @@ int raid_test_par(int mode, int nd, size_t size)
|
|||
}
|
||||
if (mode == RAID_MODE_CAUCHY_AES) {
|
||||
if (raid_cpu_has_avx2gfni()) {
|
||||
test_setup(2) = raid_gen2_avx2gfni;
|
||||
test_setup(2) = raid_gen2_avx2gfni_aes;
|
||||
}
|
||||
if (raid_cpu_has_avx512gfni()) {
|
||||
test_setup(2) = raid_gen2_avx512gfni;
|
||||
test_setup(2) = raid_gen2_avx512gfni_aes;
|
||||
}
|
||||
}
|
||||
#endif
|
||||
|
|
@ -417,31 +600,57 @@ int raid_test_par(int mode, int nd, size_t size)
|
|||
test_setup(6) = raid_gen6_int8;
|
||||
|
||||
#ifdef CONFIG_NEON
|
||||
test_setup(3) = raid_gen3_neon;
|
||||
test_setup(4) = raid_gen4_neon;
|
||||
test_setup(5) = raid_gen5_neon;
|
||||
test_setup(6) = raid_gen6_neon;
|
||||
if (mode == RAID_MODE_CAUCHY_AES) {
|
||||
test_setup(3) = raid_gen3_neon_aes;
|
||||
test_setup(4) = raid_gen4_neon_aes;
|
||||
test_setup(5) = raid_gen5_neon_aes;
|
||||
test_setup(6) = raid_gen6_neon_aes;
|
||||
} else {
|
||||
test_setup(3) = raid_gen3_neon_raid;
|
||||
test_setup(4) = raid_gen4_neon_raid;
|
||||
test_setup(5) = raid_gen5_neon_raid;
|
||||
test_setup(6) = raid_gen6_neon_raid;
|
||||
}
|
||||
#endif
|
||||
|
||||
#ifdef CONFIG_X86
|
||||
if (raid_cpu_has_ssse3()) {
|
||||
test_setup(3) = raid_gen3_ssse3;
|
||||
test_setup(4) = raid_gen4_ssse3;
|
||||
test_setup(5) = raid_gen5_ssse3;
|
||||
test_setup(6) = raid_gen6_ssse3;
|
||||
if (mode == RAID_MODE_CAUCHY_AES) {
|
||||
test_setup(3) = raid_gen3_ssse3_aes;
|
||||
test_setup(4) = raid_gen4_ssse3_aes;
|
||||
} else {
|
||||
test_setup(3) = raid_gen3_ssse3_raid;
|
||||
test_setup(4) = raid_gen4_ssse3_raid;
|
||||
test_setup(5) = raid_gen5_ssse3_raid;
|
||||
test_setup(6) = raid_gen6_ssse3_raid;
|
||||
}
|
||||
#ifdef CONFIG_X86_64
|
||||
test_setup(3) = raid_gen3_ssse3ext;
|
||||
test_setup(4) = raid_gen4_ssse3ext;
|
||||
test_setup(5) = raid_gen5_ssse3ext;
|
||||
test_setup(6) = raid_gen6_ssse3ext;
|
||||
if (mode == RAID_MODE_CAUCHY_AES) {
|
||||
test_setup(3) = raid_gen3_ssse3ext_aes;
|
||||
test_setup(4) = raid_gen4_ssse3ext_aes;
|
||||
test_setup(5) = raid_gen5_ssse3ext_aes;
|
||||
test_setup(6) = raid_gen6_ssse3ext_aes;
|
||||
} else {
|
||||
test_setup(3) = raid_gen3_ssse3ext_raid;
|
||||
test_setup(4) = raid_gen4_ssse3ext_raid;
|
||||
test_setup(5) = raid_gen5_ssse3ext_raid;
|
||||
test_setup(6) = raid_gen6_ssse3ext_raid;
|
||||
}
|
||||
#endif
|
||||
}
|
||||
#ifdef CONFIG_X86_64
|
||||
if (raid_cpu_has_avx2()) {
|
||||
test_setup(3) = raid_gen3_avx2ext;
|
||||
test_setup(4) = raid_gen4_avx2ext;
|
||||
test_setup(5) = raid_gen5_avx2ext;
|
||||
test_setup(6) = raid_gen6_avx2ext;
|
||||
if (mode == RAID_MODE_CAUCHY_AES) {
|
||||
test_setup(3) = raid_gen3_avx2ext_aes;
|
||||
test_setup(4) = raid_gen4_avx2ext_aes;
|
||||
test_setup(5) = raid_gen5_avx2ext_aes;
|
||||
test_setup(6) = raid_gen6_avx2ext_aes;
|
||||
} else {
|
||||
test_setup(3) = raid_gen3_avx2ext_raid;
|
||||
test_setup(4) = raid_gen4_avx2ext_raid;
|
||||
test_setup(5) = raid_gen5_avx2ext_raid;
|
||||
test_setup(6) = raid_gen6_avx2ext_raid;
|
||||
}
|
||||
}
|
||||
if (raid_cpu_has_avx512bw()) {
|
||||
test_setup(3) = raid_gen3_avx512bw;
|
||||
|
|
@ -451,38 +660,38 @@ int raid_test_par(int mode, int nd, size_t size)
|
|||
}
|
||||
if (mode == RAID_MODE_CAUCHY_AES) {
|
||||
if (raid_cpu_has_avx2gfni()) {
|
||||
test_setup(3) = raid_gen3_avx2gfni;
|
||||
test_setup(4) = raid_gen4_avx2gfni;
|
||||
test_setup(5) = raid_gen5_avx2gfni;
|
||||
test_setup(6) = raid_gen6_avx2gfni;
|
||||
test_setup(3) = raid_gen3_avx2gfni_aes;
|
||||
test_setup(4) = raid_gen4_avx2gfni_aes;
|
||||
test_setup(5) = raid_gen5_avx2gfni_aes;
|
||||
test_setup(6) = raid_gen6_avx2gfni_aes;
|
||||
}
|
||||
if (raid_cpu_has_avx512gfni()) {
|
||||
test_setup(3) = raid_gen3_avx512gfni;
|
||||
test_setup(4) = raid_gen4_avx512gfni;
|
||||
test_setup(5) = raid_gen5_avx512gfni;
|
||||
test_setup(6) = raid_gen6_avx512gfni;
|
||||
test_setup(3) = raid_gen3_avx512gfni_aes;
|
||||
test_setup(4) = raid_gen4_avx512gfni_aes;
|
||||
test_setup(5) = raid_gen5_avx512gfni_aes;
|
||||
test_setup(6) = raid_gen6_avx512gfni_aes;
|
||||
}
|
||||
}
|
||||
#endif
|
||||
#endif
|
||||
} else {
|
||||
test_setup(3) = raid_genz_int32;
|
||||
test_setup(3) = raid_genz_int64;
|
||||
test_setup(3) = raid_genz_int32_raid;
|
||||
test_setup(3) = raid_genz_int64_raid;
|
||||
|
||||
#ifdef CONFIG_NEON
|
||||
test_setup(3) = raid_genz_neon;
|
||||
test_setup(3) = raid_genz_neon_raid;
|
||||
#endif
|
||||
|
||||
#ifdef CONFIG_X86
|
||||
if (raid_cpu_has_sse2()) {
|
||||
test_setup(3) = raid_genz_sse2;
|
||||
test_setup(3) = raid_genz_sse2_raid;
|
||||
#ifdef CONFIG_X86_64
|
||||
test_setup(3) = raid_genz_sse2ext;
|
||||
test_setup(3) = raid_genz_sse2ext_raid;
|
||||
#endif
|
||||
}
|
||||
#ifdef CONFIG_X86_64
|
||||
if (raid_cpu_has_avx2())
|
||||
test_setup(3) = raid_genz_avx2ext;
|
||||
test_setup(3) = raid_genz_avx2ext_raid;
|
||||
#endif
|
||||
#endif
|
||||
}
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue