89 lines
1.8 KiB
Go
89 lines
1.8 KiB
Go
package reedsolomon
|
|
|
|
// generator polynomial
|
|
// (x-a^1) * (x - a^2) * .... * (x -a^numECWords-1)
|
|
func rsGenPoly(numECWords int) []byte {
|
|
var generator = []byte{1}
|
|
for i := 0; i < numECWords; i++ {
|
|
generator = polyMul(generator, []byte{1, gfExp[i]})
|
|
}
|
|
return generator
|
|
}
|
|
|
|
// 将一个多项式和一个标量相乘
|
|
func polyScale(poly []byte, x byte) []byte {
|
|
result := make([]byte, len(poly))
|
|
for i := 0; i < len(poly); i++ {
|
|
result[i] = gfMul(poly[i], x)
|
|
}
|
|
return result
|
|
}
|
|
|
|
func polyAdd(poly1, poly2 []byte) []byte {
|
|
size1 := len(poly1)
|
|
size2 := len(poly2)
|
|
size := size1
|
|
|
|
if size2 > size1 {
|
|
size = size2
|
|
}
|
|
result := make([]byte, size)
|
|
|
|
for i := 0; i < size1; i++ {
|
|
result[i] = byte(poly1[i])
|
|
}
|
|
|
|
for i := 0; i < size2; i++ {
|
|
result[i] ^= byte(poly2[i])
|
|
}
|
|
return result
|
|
}
|
|
|
|
// mul polynomial
|
|
func polyMul(poly1, poly2 []byte) []byte {
|
|
result := make([]byte, len(poly1)+len(poly2)-1)
|
|
for i := 0; i < len(poly1); i++ {
|
|
for j := 0; j < len(poly2); j++ {
|
|
result[i+j] ^= gfMul(poly1[i], poly2[j])
|
|
}
|
|
}
|
|
return result
|
|
}
|
|
|
|
// func polyEval(poly []byte, x byte) byte {
|
|
// y := poly[0]
|
|
// for i := 1; i < len(poly); i++ {
|
|
// y = gfMul(y, x) ^ poly[i]
|
|
// }
|
|
|
|
// return y
|
|
// }
|
|
|
|
// ref to: https://www.thonky.com/qr-code-tutorial/show-division-steps?msg_coeff=12%2C34%2C56%2C23&num_ecc_blocks=3
|
|
func polyDiv(dividend, divisor []byte) []byte {
|
|
if len(dividend) == 0 {
|
|
panic("could not div with 0 length dividend")
|
|
}
|
|
|
|
var (
|
|
leadTerm = dividend[0]
|
|
reminder, a, b []byte
|
|
)
|
|
|
|
reminder = dividend
|
|
|
|
for i := 0; i < len(dividend); i++ {
|
|
// step a: generator * leadTerm
|
|
a = polyScale(divisor, leadTerm)
|
|
|
|
// step b, xor operation
|
|
b = polyAdd(reminder, a)
|
|
|
|
// discard lead term of b
|
|
reminder = b[1:]
|
|
leadTerm = reminder[0]
|
|
}
|
|
|
|
return reminder
|
|
}
|