// FFT returns the fourier transform of v.
func FFT(v Poly) Poly {
y := make(Poly, len(v))
n := int64(len(v))
w := number.ModularPower(omega, (modular-1)/n, modular)
fft(v, y, modular, w, 1)
return y
}
// IFFT returns the inverted fourier transform of v.
func IFFT(v Poly) Poly {
y := make(Poly, len(v))
n := int64(len(v))
w := number.ModularPower(omega, (modular-1)/n, modular)
w1 := number.ModularInvert(w, modular)
fft(v, y, modular, w1, 1)
n1 := number.ModularInvert(n, modular)
for i := range y {
y[i] = y[i] * n1 % modular
}
return y
}
// MillerRabinK test if n is a prime, testing for k times.
func MillerRabinK(n int64, k int) bool {
if n <= 3 {
return n > 1
}
if n%2 == 0 {
return false
}
d := n - 1
s := 0
for d%2 == 0 {
d /= 2
s++
}
for ; k > 0; k-- {
x := number.ModularPower(rand.Int63n(n-3)+2, d, n)
if x == 1 || x == n-1 {
continue
}
r := 1
for ; r < s; r++ {
x = number.ModularMultiply(x, x, n)
if x == 1 {
return false
}
if x == n-1 {
break
}
}
if r == s {
return false
}
}
return true
}