// Package provides a shifted, reversed fibonacci encoding of bytes
//
// http://en.wikipedia.org/wiki/Fibonacci_coding maps positive integers as
// 1 - 11, 2 - 011, 3 - 0011, 4 - 1011, 5 - 00011
//
// Incrementing input bytes by one to allow for zero gives
// 0 - 11, 1 - 011, 2 - 0011, 3 - 1011, 4 - 00011
//
// The codes are then reversed so that they are easily stored in uints
// 0 - 11, 1 - 110, 2 - 1100, 3 - 1101, 4 - 11000
package fibonacci

type Numbers []uint64

// Returns the n-th fibonacci number
// The result is stored after calculation
func (f Numbers) Nth(index int) uint64 {
	switch {
	case index <= 1:
		return 1
	case f[index] > 0:
		break
	default:
		f[index] = f.Nth(index-1) + f.Nth(index-2)
	}
	return f[index]
}

// Returns a fibonacci code for an integer as specified in the package doc.
func (f Numbers) Code(value uint64) (result uint64) {
	// Increment to encode zero as one
	value++

	// Find the nearest fibonacci number
	i := 0
	for f.Nth(i+1) <= value {
		i++
	}

	// Leading bit that signals the start of a fibonacci-encoded integer
	result |= 1

	// Find the Zeckendorf's representation by raising a bit for each
	// fibonacci number that is less or equal to the difference
	// between the value and the previous such number
	for ; i >= 1; i-- {
		result <<= 1
		if f.Nth(i) <= value {
			result |= 1
			value -= f.Nth(i)
		}
	}
	return
}

// Returns an integer from a fibonacci code as specified in the package doc.
func (f Numbers) Decode(value uint64) (result uint64) {
	i := 1
	for (value & 3) != 3 {
		if (value & 1) == 1 {
			result += f.Nth(i)
		}
		value >>= 1
		i++
	}
	result += f.Nth(i) - 1
	return
}
