func gfInverse(a gfElement) gfElement {
	if a == gfZero {
		log.Panicln("No multiplicative inverse of 0")
	}
	return gfExpTable[255-gfLogTable[a]]
}
gfInverse returns the multiplicative inverse of a, a^-1.

a * a^-1 = 1
package reedsolomon
import "log"
const (
	gfZero = gfElement(0)
	gfOne  = gfElement(1)
)
var (
	gfExpTable = [256]gfElement{
		  1, 2, 4, 8, 16, 32, 64, 128, 29, 58,
		  116, 232, 205, 135, 19, 38, 76, 152, 45, 90,
		  180, 117, 234, 201, 143, 3, 6, 12, 24, 48,
		  96, 192, 157, 39, 78, 156, 37, 74, 148, 53,
		  106, 212, 181, 119, 238, 193, 159, 35, 70, 140,
		  5, 10, 20, 40, 80, 160, 93, 186, 105, 210,
		  185, 111, 222, 161, 95, 190, 97, 194, 153, 47,
		  94, 188, 101, 202, 137, 15, 30, 60, 120, 240,
		  253, 231, 211, 187, 107, 214, 177, 127, 254, 225,
		  223, 163, 91, 182, 113, 226, 217, 175, 67, 134,
		  17, 34, 68, 136, 13, 26, 52, 104, 208, 189,
		  103, 206, 129, 31, 62, 124, 248, 237, 199, 147,
		  59, 118, 236, 197, 151, 51, 102, 204, 133, 23,
		  46, 92, 184, 109, 218, 169, 79, 158, 33, 66,
		  132, 21, 42, 84, 168, 77, 154, 41, 82, 164,
		  85, 170, 73, 146, 57, 114, 228, 213, 183, 115,
		  230, 209, 191, 99, 198, 145, 63, 126, 252, 229,
		  215, 179, 123, 246, 241, 255, 227, 219, 171, 75,
		  150, 49, 98, 196, 149, 55, 110, 220, 165, 87,
		  174, 65, 130, 25, 50, 100, 200, 141, 7, 14,
		  28, 56, 112, 224, 221, 167, 83, 166, 81, 162,
		  89, 178, 121, 242, 249, 239, 195, 155, 43, 86,
		  172, 69, 138, 9, 18, 36, 72, 144, 61, 122,
		  244, 245, 247, 243, 251, 235, 203, 139, 11, 22,
		  44, 88, 176, 125, 250, 233, 207, 131, 27, 54,
		  108, 216, 173, 71, 142, 1}
	gfLogTable = [256]int{
		  -1, 0, 1, 25, 2, 50, 26, 198, 3, 223,
		  51, 238, 27, 104, 199, 75, 4, 100, 224, 14,
		  52, 141, 239, 129, 28, 193, 105, 248, 200, 8,
		  76, 113, 5, 138, 101, 47, 225, 36, 15, 33,
		  53, 147, 142, 218, 240, 18, 130, 69, 29, 181,
		  194, 125, 106, 39, 249, 185, 201, 154, 9, 120,
		  77, 228, 114, 166, 6, 191, 139, 98, 102, 221,
		  48, 253, 226, 152, 37, 179, 16, 145, 34, 136,
		  54, 208, 148, 206, 143, 150, 219, 189, 241, 210,
		  19, 92, 131, 56, 70, 64, 30, 66, 182, 163,
		  195, 72, 126, 110, 107, 58, 40, 84, 250, 133,
		  186, 61, 202, 94, 155, 159, 10, 21, 121, 43,
		  78, 212, 229, 172, 115, 243, 167, 87, 7, 112,
		  192, 247, 140, 128, 99, 13, 103, 74, 222, 237,
		  49, 197, 254, 24, 227, 165, 153, 119, 38, 184,
		  180, 124, 17, 68, 146, 217, 35, 32, 137, 46,
		  55, 63, 209, 91, 149, 188, 207, 205, 144, 135,
		  151, 178, 220, 252, 190, 97, 242, 86, 211, 171,
		  20, 42, 93, 158, 132, 60, 57, 83, 71, 109,
		  65, 162, 31, 45, 67, 216, 183, 123, 164, 118,
		  196, 23, 73, 236, 127, 12, 111, 246, 108, 161,
		  59, 82, 41, 157, 85, 170, 251, 96, 134, 177,
		  187, 204, 62, 90, 203, 89, 95, 176, 156, 169,
		  160, 81, 11, 245, 22, 235, 122, 117, 44, 215,
		  79, 174, 213, 233, 230, 231, 173, 232, 116, 214,
		  244, 234, 168, 80, 88, 175}
)
type gfElement uint8
func newGFElement(data byte) gfElement {
	return gfElement(data)
}
func gfAdd(a, b gfElement) gfElement {
	return a ^ b
}
func gfSub(a, b gfElement) gfElement {
	return a ^ b
}
func gfMultiply(a, b gfElement) gfElement {
	if a == gfZero || b == gfZero {
		return gfZero
	}
	return gfExpTable[(gfLogTable[a]+gfLogTable[b])%255]
}
func gfDivide(a, b gfElement) gfElement {
	if a == gfZero {
		return gfZero
	} else if b == gfZero {
		log.Panicln("Divide by zero")
	}
	return gfMultiply(a, gfInverse(b))
}