/*
Copyright 2017 Google Inc. All rights reserved.

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/

package s2

// nthDerivativeCoder provides Nth Derivative Coding.
//   (In signal processing disciplines, this is known as N-th Delta Coding.)
//
// Good for varint coding integer sequences with polynomial trends.
//
// Instead of coding a sequence of values directly, code its nth-order discrete
// derivative.  Overflow in integer addition and subtraction makes this a
// lossless transform.
//
//                                       constant     linear      quadratic
//                                        trend       trend         trend
//                                      /        \  /        \  /           \_
// input                               |0  0  0  0  1  2  3  4  9  16  25  36
// 0th derivative(identity)            |0  0  0  0  1  2  3  4  9  16  25  36
// 1st derivative(delta coding)        |   0  0  0  1  1  1  1  5   7   9  11
// 2nd derivative(linear prediction)   |      0  0  1  0  0  0  4   2   2   2
//                                      -------------------------------------
//                                      0  1  2  3  4  5  6  7  8   9  10  11
//                                                  n in sequence
//
// Higher-order codings can break even or be detrimental on other sequences.
//
//                                           random            oscillating
//                                      /               \  /                  \_
// input                               |5  9  6  1   8  8  2 -2   4  -4   6  -6
// 0th derivative(identity)            |5  9  6  1   8  8  2 -2   4  -4   6  -6
// 1st derivative(delta coding)        |   4 -3 -5   7  0 -6 -4   6  -8  10 -12
// 2nd derivative(linear prediction)   |     -7 -2  12 -7 -6  2  10 -14  18 -22
//                                      ---------------------------------------
//                                      0  1  2  3  4   5  6  7   8   9  10  11
//                                                  n in sequence
//
// Note that the nth derivative isn't available until sequence item n.  Earlier
// values are coded at lower order.  For the above table, read 5 4 -7 -2 12 ...
type nthDerivativeCoder struct {
	n, m   int
	memory [10]int32
}

// newNthDerivativeCoder returns a new coder, where n is the derivative order of the encoder (the N in NthDerivative).
// n must be within [0,10].
func newNthDerivativeCoder(n int) *nthDerivativeCoder {
	c := &nthDerivativeCoder{n: n}
	if n < 0 || n > len(c.memory) {
		panic("unsupported n. Must be within [0,10].")
	}
	return c
}

func (c *nthDerivativeCoder) encode(k int32) int32 {
	for i := 0; i < c.m; i++ {
		delta := k - c.memory[i]
		c.memory[i] = k
		k = delta
	}
	if c.m < c.n {
		c.memory[c.m] = k
		c.m++
	}
	return k
}

func (c *nthDerivativeCoder) decode(k int32) int32 {
	if c.m < c.n {
		c.m++
	}
	for i := c.m - 1; i >= 0; i-- {
		c.memory[i] += k
		k = c.memory[i]
	}
	return k
}
