89 lines
3.4 KiB
Go
89 lines
3.4 KiB
Go
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// Copyright 2017 Google Inc. All rights reserved.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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package s2
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// nthDerivativeCoder provides Nth Derivative Coding.
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// (In signal processing disciplines, this is known as N-th Delta Coding.)
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//
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// Good for varint coding integer sequences with polynomial trends.
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//
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// Instead of coding a sequence of values directly, code its nth-order discrete
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// derivative. Overflow in integer addition and subtraction makes this a
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// lossless transform.
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//
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// constant linear quadratic
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// trend trend trend
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// / \ / \ / \_
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// input |0 0 0 0 1 2 3 4 9 16 25 36
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// 0th derivative(identity) |0 0 0 0 1 2 3 4 9 16 25 36
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// 1st derivative(delta coding) | 0 0 0 1 1 1 1 5 7 9 11
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// 2nd derivative(linear prediction) | 0 0 1 0 0 0 4 2 2 2
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// -------------------------------------
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// 0 1 2 3 4 5 6 7 8 9 10 11
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// n in sequence
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//
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// Higher-order codings can break even or be detrimental on other sequences.
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//
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// random oscillating
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// / \ / \_
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// input |5 9 6 1 8 8 2 -2 4 -4 6 -6
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// 0th derivative(identity) |5 9 6 1 8 8 2 -2 4 -4 6 -6
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// 1st derivative(delta coding) | 4 -3 -5 7 0 -6 -4 6 -8 10 -12
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// 2nd derivative(linear prediction) | -7 -2 12 -7 -6 2 10 -14 18 -22
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// ---------------------------------------
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// 0 1 2 3 4 5 6 7 8 9 10 11
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// n in sequence
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//
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// Note that the nth derivative isn't available until sequence item n. Earlier
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// values are coded at lower order. For the above table, read 5 4 -7 -2 12 ...
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type nthDerivativeCoder struct {
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n, m int
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memory [10]int32
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}
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// newNthDerivativeCoder returns a new coder, where n is the derivative order of the encoder (the N in NthDerivative).
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// n must be within [0,10].
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func newNthDerivativeCoder(n int) *nthDerivativeCoder {
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c := &nthDerivativeCoder{n: n}
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if n < 0 || n > len(c.memory) {
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panic("unsupported n. Must be within [0,10].")
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}
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return c
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}
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func (c *nthDerivativeCoder) encode(k int32) int32 {
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for i := 0; i < c.m; i++ {
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delta := k - c.memory[i]
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c.memory[i] = k
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k = delta
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}
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if c.m < c.n {
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c.memory[c.m] = k
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c.m++
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}
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return k
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}
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func (c *nthDerivativeCoder) decode(k int32) int32 {
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if c.m < c.n {
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c.m++
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}
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for i := c.m - 1; i >= 0; i-- {
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c.memory[i] += k
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k = c.memory[i]
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}
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return k
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}
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