gf256.c File Reference

GF(2^8) arithmetic with SIMD-accelerated region multiply. More...

#include <stddef.h>
#include <stdint.h>
#include <string.h>
#include "gf256.h"
#include "aaruformat/simd.h"

Go to the source code of this file.

Functions
static void	gf256_init_tables (void)
	Initialize log/antilog tables for GF(2^8) with polynomial 0x11D.
uint8_t	gf256_mul (uint8_t a, uint8_t b)
	Multiply two elements in GF(2^8) with polynomial 0x11D.
uint8_t	gf256_div (uint8_t a, uint8_t b)
	Divide two elements in GF(2^8).
uint8_t	gf256_inv (uint8_t a)
	Compute multiplicative inverse in GF(2^8).
static void	gf256_build_mul_tables (uint8_t coeff, uint8_t low_tbl[16], uint8_t hi_tbl[16])
	Build the two 16-byte nibble lookup tables for a given coefficient.
static void	gf256_mul_region_scalar (uint8_t *dst, const uint8_t *src, uint8_t coeff, size_t len)
static void	gf256_xor_region_scalar (uint8_t *dst, const uint8_t *src, size_t len)
void	gf256_mul_region (uint8_t *dst, const uint8_t *src, uint8_t coeff, size_t len)
	Multiply-accumulate a region: dst[i] ^= GF_mul(src[i], coeff) for all i.
void	gf256_xor_region (uint8_t *dst, const uint8_t *src, size_t len)
	XOR a region: dst[i] ^= src[i] for all i.

Variables
static uint8_t	gf256_log_table [256]
	Log table: gf256_log[x] = discrete log base 2 of x in GF(2^8).
static uint8_t	gf256_exp_table [512]
	Anti-log (exp) table: gf256_exp[i] = 2^i mod P.
static int	gf256_tables_initialized = 0
	Flag to ensure tables are initialized exactly once.

Detailed Description

GF(2^8) arithmetic with SIMD-accelerated region multiply.

Galois Field GF(2^8) with irreducible polynomial x^8 + x^4 + x^3 + x^2 + 1 (0x11D). Uses log/antilog tables for scalar operations and 4-bit nibble split tables with SIMD shuffle for vectorized region multiply-accumulate.

Definition in file gf256.c.

Function Documentation

gf256_build_mul_tables()

void gf256_build_mul_tables ( uint8_t coeff, uint8_t low_tbl[16], uint8_t hi_tbl[16] )

static

Build the two 16-byte nibble lookup tables for a given coefficient.

Definition at line 114 of file gf256.c.

References gf256_build_mul_tables(), gf256_init_tables(), and gf256_mul().

Referenced by gf256_build_mul_tables(), and gf256_mul_region_scalar().

gf256_div()

uint8_t gf256_div	(	uint8_t	a,
		uint8_t	b )

Divide two elements in GF(2^8).

Parameters

a	Dividend.
b	Divisor (must be non-zero).

Returns

Quotient a/b in GF(2^8).

Definition at line 84 of file gf256.c.

References gf256_div(), gf256_exp_table, gf256_init_tables(), and gf256_log_table.

Referenced by gf256_div().

gf256_init_tables()

void gf256_init_tables ( void )

static

Initialize log/antilog tables for GF(2^8) with polynomial 0x11D.

Definition at line 51 of file gf256.c.

References gf256_exp_table, gf256_init_tables(), gf256_log_table, and gf256_tables_initialized.

Referenced by gf256_build_mul_tables(), gf256_div(), gf256_init_tables(), gf256_inv(), gf256_mul(), and gf256_mul_region().

gf256_inv()

uint8_t gf256_inv

(

uint8_t

a

)

Compute multiplicative inverse in GF(2^8).

Parameters

a	Element (must be non-zero).

Returns

Inverse a^(-1) in GF(2^8).

Definition at line 92 of file gf256.c.

References gf256_exp_table, gf256_init_tables(), gf256_inv(), and gf256_log_table.

Referenced by gf256_inv(), and invert_matrix().

gf256_mul()

uint8_t gf256_mul	(	uint8_t	a,
		uint8_t	b )

Multiply two elements in GF(2^8) with polynomial 0x11D.

Parameters

a	First operand.
b	Second operand.

Returns

Product a*b in GF(2^8).

Definition at line 77 of file gf256.c.

References gf256_exp_table, gf256_init_tables(), gf256_log_table, and gf256_mul().

Referenced by build_vandermonde(), gf256_build_mul_tables(), gf256_mul(), invert_matrix(), rs_create(), and rs_decode().

gf256_mul_region()

void gf256_mul_region	(	uint8_t *	dst,
		const uint8_t *	src,
		uint8_t	coeff,
		size_t	len )

Multiply-accumulate a region: dst[i] ^= GF_mul(src[i], coeff) for all i.

Uses SIMD acceleration when available (AVX2 > SSSE3 > NEON > scalar). If coeff is 0, this is a no-op. If coeff is 1, this is XOR.

Parameters

dst	Destination buffer (read-modify-write).
src	Source buffer (read-only).
coeff	GF(2^8) coefficient.
len	Number of bytes to process.

Definition at line 350 of file gf256.c.

References gf256_init_tables(), gf256_mul_region(), gf256_mul_region_scalar(), and gf256_xor_region().

Referenced by gf256_mul_region(), rs_decode(), and rs_encode_incremental().

gf256_mul_region_scalar()

void gf256_mul_region_scalar ( uint8_t * dst, const uint8_t * src, uint8_t coeff, size_t len )

static

Definition at line 126 of file gf256.c.

References gf256_build_mul_tables(), and gf256_mul_region_scalar().

Referenced by gf256_mul_region(), and gf256_mul_region_scalar().

gf256_xor_region()

void gf256_xor_region	(	uint8_t *	dst,
		const uint8_t *	src,
		size_t	len )

XOR a region: dst[i] ^= src[i] for all i.

Uses SIMD acceleration when available.

Parameters

dst	Destination buffer (read-modify-write).
src	Source buffer (read-only).
len	Number of bytes to process.

Definition at line 370 of file gf256.c.

References gf256_xor_region(), and gf256_xor_region_scalar().

Referenced by gf256_mul_region(), and gf256_xor_region().

gf256_xor_region_scalar()

void gf256_xor_region_scalar ( uint8_t * dst, const uint8_t * src, size_t len )

static

Definition at line 135 of file gf256.c.

References gf256_xor_region_scalar().

Referenced by gf256_xor_region(), and gf256_xor_region_scalar().

Variable Documentation

gf256_exp_table

uint8_t gf256_exp_table[512]

static

Anti-log (exp) table: gf256_exp[i] = 2^i mod P.

Extended to 512 entries to avoid modular reduction.

Definition at line 43 of file gf256.c.

Referenced by gf256_div(), gf256_init_tables(), gf256_inv(), and gf256_mul().

gf256_log_table

uint8_t gf256_log_table[256]

static

Log table: gf256_log[x] = discrete log base 2 of x in GF(2^8).

gf256_log[0] is undefined.

Definition at line 41 of file gf256.c.

Referenced by gf256_div(), gf256_init_tables(), gf256_inv(), and gf256_mul().

gf256_tables_initialized

int gf256_tables_initialized = 0

static

Flag to ensure tables are initialized exactly once.

Definition at line 46 of file gf256.c.

Referenced by gf256_init_tables().