gotosocial/vendor/github.com/golang/geo/s2/nthderivative.go
Tobi Smethurst 98263a7de6
Grand test fixup (#138)
* start fixing up tests

* fix up tests + automate with drone

* fiddle with linting

* messing about with drone.yml

* some more fiddling

* hmmm

* add cache

* add vendor directory

* verbose

* ci updates

* update some little things

* update sig
2021-08-12 21:03:24 +02:00

89 lines
3.4 KiB
Go

// 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
}