Merge pull request #503 from penglei0/perf/optimize-gf-inversion-calculate

[=]: optimize the gf inversion calculation

Author: cherylsy

src/transport/fec_schemes/xqc_galois_calculation.c

@@ -68,16 +68,7 @@ xqc_galois_divide(unsigned char a, unsigned char b, unsigned char *res)
 unsigned char
 xqc_galois_inversion(unsigned char a)
 {
-    int i = 0;
-    if (a == 0) {
-        return 0;
-    }
-    for (i = 1; i < 256; i++) {
-        if (xqc_galois_multiply(a, i) == 1) {
-            return i;
-        }
-    }
-    return 0;
+    return xqc_galois_inv_table[a];
 }
 
 

src/transport/fec_schemes/xqc_galois_calculation.h

@@ -15,7 +15,7 @@
 
 /**
  * The following table stands for log_a(x) and exp_a(x),
- * where a is the polynomial(here we use 29, (2^8 +) 2^4 + 2^3 + 2^2 + 1) used to generate a Galois field of 256 elements.
+ * where a is the polynomial(here we use 285 (0x11D), 2^8 + 2^4 + 2^3 + 2^2 + 1) used to generate a Galois field of 256 elements.
  * and x is in [0, 255].
  */
 static const unsigned char xqc_rs_log_table[256] = {
@@ -122,6 +122,30 @@ static const unsigned char xqc_rs_exp_table[510] = {
     27, 54, 108, -40, -83, 71, -114
 };
 
+/**
+ * inversion table based on irreducible polynomial 285 (0x11D) where F(x) = x^8
+ * + x^4 + x^3 + x^2 + 1, minimum primitive element α = x = 2.
+ */
+static const unsigned char xqc_galois_inv_table[256] = {
+    0,   1,   142, 244, 71,  167, 122, 186, 173, 157, 221, 152, 61,  170, 93,
+    150, 216, 114, 192, 88,  224, 62,  76,  102, 144, 222, 85,  128, 160, 131,
+    75,  42,  108, 237, 57,  81,  96,  86,  44,  138, 112, 208, 31,  74,  38,
+    139, 51,  110, 72,  137, 111, 46,  164, 195, 64,  94,  80,  34,  207, 169,
+    171, 12,  21,  225, 54,  95,  248, 213, 146, 78,  166, 4,   48,  136, 43,
+    30,  22,  103, 69,  147, 56,  35,  104, 140, 129, 26,  37,  97,  19,  193,
+    203, 99,  151, 14,  55,  65,  36,  87,  202, 91,  185, 196, 23,  77,  82,
+    141, 239, 179, 32,  236, 47,  50,  40,  209, 17,  217, 233, 251, 218, 121,
+    219, 119, 6,   187, 132, 205, 254, 252, 27,  84,  161, 29,  124, 204, 228,
+    176, 73,  49,  39,  45,  83,  105, 2,   245, 24,  223, 68,  79,  155, 188,
+    15,  92,  11,  220, 189, 148, 172, 9,   199, 162, 28,  130, 159, 198, 52,
+    194, 70,  5,   206, 59,  13,  60,  156, 8,   190, 183, 135, 229, 238, 107,
+    235, 242, 191, 175, 197, 100, 7,   123, 149, 154, 174, 182, 18,  89,  165,
+    53,  101, 184, 163, 158, 210, 247, 98,  90,  133, 125, 168, 58,  41,  113,
+    200, 246, 249, 67,  215, 214, 16,  115, 118, 120, 153, 10,  25,  145, 20,
+    63,  230, 240, 134, 177, 226, 241, 250, 116, 243, 180, 109, 33,  178, 106,
+    227, 231, 181, 234, 3,   143, 211, 201, 66,  212, 232, 117, 127, 255, 126,
+    253};
+
 unsigned char xqc_galois_multiply(unsigned char a, unsigned char b);
 unsigned char xqc_galois_exp(unsigned char a, unsigned char n);