lib/litonlylzma/litonlylzma.go

// Copyright 2022 The Wuffs Authors.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
//
// SPDX-License-Identifier: Apache-2.0 OR MIT

// ----------------

// Package litonlylzma provides a decoder and encoder for Literal Only LZMA (or
// Literal Only Xz), a subset of the LZMA (or Xz) compressed file formats.
//
// Subset means that:
//   - the Encode methods' output is a valid LZMA/Xz file and can be
//     decompressed by the tools available at https://www.7-zip.org/sdk.html or
//     https://tukaani.org/xz/ (and available as /usr/bin/lzma or /usr/bin/xz
//     on a Debian system).
//   - the Decode methods supports the Encode methods' output but they do not
//     support the full set of valid LZMA/Xz files.
//   - this codec's compression ratios are not as good as full LZMA/Xz
//     (although compression times are much faster). Moderate compression is
//     still achieved, through range coding, but there are no Lempel Ziv
//     back-references.
//
// The main benefit, compared to full LZMA/Xz, is that this implementation is
// much simpler and hence easier to study. It is around 800 lines of code,
// about a third of which are comments.
//
// Example compression numbers on a small English text file (at
// https://github.com/google/wuffs/blob/main/test/data/romeo.txt):
//   - romeo.txt             is 942 bytes (100%).
//   - romeo.txt.litonlyxz   is 708 bytes  (75%).
//   - romeo.txt.litonlylzma is 659 bytes  (70%).
//   - romeo.txt.xz          is 644 bytes  (68%).
//   - romeo.txt.lzma        is 598 bytes  (63%).
//   - romeo.txt.bz2         is 568 bytes  (60%).
//   - romeo.txt.zst         is 559 bytes  (59%).
//   - romeo.txt.gz          is 558 bytes  (59%).
//
// Example compression numbers on a large archive of source code (at
// https://cdn.kernel.org/pub/linux/kernel/v5.x/linux-5.0.1.tar.xz):
//   - linux-5.0.1.tar             is 863313920 bytes (100%).
//   - linux-5.0.1.tar.litonlyxz   is 454480932 bytes  (53%).
//   - linux-5.0.1.tar.litonlylzma is 449726070 bytes  (52%).
//   - linux-5.0.1.tar.gz          is 164575959 bytes  (19%).
//   - linux-5.0.1.tar.zst         is 156959897 bytes  (18%).
//   - linux-5.0.1.tar.bz2         is 125873134 bytes  (15%).
//   - linux-5.0.1.tar.xz          is 108233572 bytes  (13%).
//   - linux-5.0.1.tar.lzma        is 108216601 bytes  (13%).
//
// The various tools (/usr/bin/gzip, /usr/bin/xz, etc) were all ran with their
// default settings, not their "maximum compression" settings. This is why the
// linux-5.0.1.tar.xz file size above differs from what cdn.kernel.org served.
package litonlylzma

// When editing this file, consider setting "allowTestsToExecOtherPrograms =
// true" in the test code.

import (
	"errors"
	"hash/crc32"
)

var (
	// ErrUnsupportedXxxData is potentially returned by Decode.
	ErrUnsupportedLZMAData = errors.New("litonlylzma: unsupported LZMA data")
	ErrUnsupportedXzData   = errors.New("litonlylzma: unsupported Xz data")

	errInvalidLZMAData       = errors.New("litonlylzma: invalid LZMA data")
	errInvalidXzData         = errors.New("litonlylzma: invalid Xz data")
	errUnexpectedEOF         = errors.New("litonlylzma: unexpected EOF")
	errUnsupportedFileFormat = errors.New("litonlylzma: unsupported FileFormat")
)

const (
	// LZMA has a few configuration knobs but our subset-of-LZMA hard codes
	// these to LZMA's default values:
	// https://github.com/jljusten/LZMA-SDK/blob/781863cdf592da3e97420f50de5dac056ad352a5/C/LzmaEnc.h#L19-L21
	// https://github.com/jljusten/LZMA-SDK/blob/781863cdf592da3e97420f50de5dac056ad352a5/DOC/lzma-specification.txt#L43-L45
	lc = 3 // The number of Literal Context bits.
	lp = 0 // The number of Literal Position bits.
	pb = 2 // The number of Position Bits.

	lpMask = (1 << lp) - 1
	pbMask = (1 << pb) - 1
)

// lzmaHeader5 is the first 5 bytes of an LZMA file using the hard-coded
// configuration for the subset-of-LZMA that this package supports.
//
// 0x5D encodes the (lc, lp, pb) triple and the next four bytes hold the u32le
// dictionary size. 0x00001000 is LZMA's minimum dictionary size, although our
// subset-of-LZMA does not use a dictionary (also called a "sliding window").
const lzmaHeader5 = "\x5D\x00\x10\x00\x00"

// xzHeader24 is the first 24 bytes of an Xz file using the hard-coded
// configuration for the subset-of-Xz that this package supports.
const xzHeader24 = "" +
	"\xFD\x37\x7A\x58\x5A\x00" + // Stream Header Magic Bytes.
	// ----
	"\x00\x01" + // Stream Flags (0x01 means CRC-32).
	"\x69\x22\xDE\x36" + // CRC-32 of the previous 2 bytes.
	// ----
	"\x02" + // Block Header Size (0x02 * 4 = 8 bytes).
	"\x00" + // Block Flags.
	"\x21" + // Filter ID (0x21 means LZMA2).
	"\x01" + // Size of Filter Properties (size of the next line).
	"\x00" + // Filter Properties (0x00 means an 0x1000 dictionary size).
	"\x00\x00\x00" + // Padding to 4-byte alignment.
	"\x37\x27\x97\xD6" // CRC-32 of the previous 8 bytes.

// rangeDecoder and rangeEncoder hold the state for range coding (also known as
// arithmetic coding, roughly speaking). "range" is a keyword in Go, so in this
// implementation, what's traditionally called the "range" fields are called
// "width" instead.
//
// Conceptually, the encoded bitstream holds a high precision number (a binary
// fraction) in the range from zero to one. High precision could mean thousands
// or millions of bits, but when decoding, only 32 of these are 'paged in' at a
// time - this is the rangeDecoder.bits field. The encoder similarly works on
// only a small, fixed number of bits.
//
// When encoding, that high precision *number* isn't fully known until the end
// of the input is reached. *During* the encoding process, what's known is a
// high precision *interval* that gets narrowed down as the input bytes are
// consumed. That interval is represented by the rangeEncoder.low and
// rangeEncoder.width fields (the width is the difference between the
// interval's upper and lower bound). Both low and width are, conceptually,
// 32-bit values - they operate at the same scale - but low is an uint64
// because of potential overflow. We'll revisit that below.
//
// Width is initialized to 0xFFFF_FFFF and shrinks every time a bit is decoded
// or encoded. Similarly, low can only increase or stay the same on each bit
// step. When width drops below (1 << 24), the rangeDecoder or rangeEncoder
// 'zooms in', left-shifting (with truncation) by 8 the bits, low and width
// fields and reading a src byte or writing a dst byte of compressed data.
//
// Writing a byte may be delayed because the encoding interval could span
// multiple possible digits. To use a decimal fraction analogy, suppose that
// our interval is [0.7138872, 0.7146055] and the low field nominally holds 4
// digits. We could emit '7' and '1' but we have to hold back on emitting
// either '3' or '4' until we can narrow down the interval further. That '3'
// digit is stashed as the pendingHead field. low is set to 8872, width is set
// to (46055 - 38872) = 7183 and we progress until the width drops below 1000,
// causing a 'zoom in' event. There are three cases:
//   - if low is less than 9000 (but starts with an '8'), we can emit the '3'
//     with confidence (and then stash '8' in the pendingHead field).
//   - if low overflows 9999, we can emit the '4' with confidence (and then
//     stash low's 'thousands digit' in the pendingHead field).
//   - if low is in 9000 ..= 9999 then we could still be unsure. Keep the '3'
//     pending but extend it so that there are two pending digits: '39'. If
//     this occurs again: '399', and so on.
//
// In all three cases, 'zooming in' causes us to shift out the most significant
// digit of the low field. This method is therefore named shiftLow here, the
// same name used in other range coding implementations, such as
// https://github.com/jljusten/LZMA-SDK/blob/781863cdf592da3e97420f50de5dac056ad352a5/C/LzmaEnc.c#L572-L602
//
// The pendingEtc fields combine to hold one or more digits ('0' ..= '9'
// decimal digits in our analogy, 0x00 ..= 0xFF bytes in our actual
// implementation). There are (1 + pendingExtra) digits in total and while the
// head digit might be any value, the extra digits must be all '9' (in the
// decimal analogy) or 0xFF (in our actual implementation).
//
// Some other implementations use the name "cache" instead of "pending", and
// store a "cacheSize" field equivalent to our (1 + pendingExtra).
//
// As above, the low field is conceptually a uint32, but it is a uint64 because
// of this potential overflow. Its high 32 bits are usually zero, rarely one
// and never anything higher. The high 32 bits essentially hold an overflow
// carry bit. If set, it flips "3999etc" to "4000etc".
//
// "Low is conceptually 4 bytes; pendingHead holds another byte" is why the
// shortest LZMA payload is 5 bytes even though the first byte is always 0x00
// and seems redundant.

type rangeDecoder struct {
	src   []byte
	bits  uint32
	width uint32
}

type rangeEncoder struct {
	dst          []byte
	low          uint64
	width        uint32
	pendingHead  uint8
	pendingExtra uint64
}

// Precondition: (rEnc.width < (1 << 24)) or we are at the end of our input
// (and are flushing the rangeEncoder).
func (rEnc *rangeEncoder) shiftLow() {
	if rEnc.low < 0x0_FF00_0000 {
		rEnc.dst = append(rEnc.dst, rEnc.pendingHead+0x00)
		for ; rEnc.pendingExtra > 0; rEnc.pendingExtra-- {
			rEnc.dst = append(rEnc.dst, 0xFF)
		}
		rEnc.pendingHead = uint8(rEnc.low >> 24)
		rEnc.pendingExtra = 0
		rEnc.low = (rEnc.low << 8) & 0xFFFF_FFFF

	} else if rEnc.low < 0x1_0000_0000 {
		rEnc.pendingExtra++
		rEnc.low = (rEnc.low << 8) & 0xFFFF_FFFF

	} else {
		rEnc.dst = append(rEnc.dst, rEnc.pendingHead+0x01)
		for ; rEnc.pendingExtra > 0; rEnc.pendingExtra-- {
			rEnc.dst = append(rEnc.dst, 0x00)
		}
		rEnc.pendingHead = uint8(rEnc.low >> 24)
		rEnc.pendingExtra = 0
		rEnc.low = (rEnc.low << 8) & 0xFFFF_FFFF
	}
}

// prob is a probability (out of 100%) whose uint16 value ranges from 0 to
// (1 << 11) = 2048 inclusive. For example, prob(1024) means a 50% probability
// and prob(384) means a (384 / 2048) = 18.75% probability.
//
// Specifically, it is the probability that the next bit is 0 (instead of 1).
type prob uint16

const (
	// probBits is such that prob(1 << probBits) means a 100% probability.
	probBits = 11
	minProb  = 0
	maxProb  = 1 << probBits
)

func setProbsToOneHalf(p []prob) {
	for i := range p {
		p[i] = 1 << (probBits - 1)
	}
}

// adaptShift scales how much to adjust "the probability that the next bit is
// 0" after seeing the current bit. The probability is adaptive in that the
// current bit being 0 (or 1) increases (or decreases) the probability that the
// next bit is 0. The larger adaptShift is, the slower the adaptation.
const adaptShift = 5

func (p *prob) decodeBit(rDec *rangeDecoder) (bitValue uint32, retErr error) {
	threshold := (rDec.width >> probBits) * uint32(*p)
	if rDec.bits < threshold {
		bitValue = 0
		rDec.width = threshold
		*p += (maxProb - *p) >> adaptShift
	} else {
		bitValue = 1
		rDec.bits -= threshold
		rDec.width -= threshold
		*p -= (*p - minProb) >> adaptShift
	}

	if rDec.width < (1 << 24) {
		if len(rDec.src) <= 0 {
			return 0, errUnexpectedEOF
		}
		rDec.bits = rDec.bits<<8 | uint32(rDec.src[0])
		rDec.width <<= 8
		rDec.src = rDec.src[1:]
	}
	return bitValue, retErr
}

func (p *prob) encodeBit(rEnc *rangeEncoder, bitValue uint32) {
	threshold := (rEnc.width >> probBits) * uint32(*p)
	if bitValue == 0 {
		rEnc.width = threshold
		*p += (maxProb - *p) >> adaptShift
	} else {
		rEnc.low += uint64(threshold)
		rEnc.width -= threshold
		*p -= (*p - minProb) >> adaptShift
	}
	if rEnc.width < (1 << 24) {
		rEnc.width <<= 8
		rEnc.shiftLow()
	}
}

// byteProbs hold probabilities for coding 8 bits (1 byte) of data. It is a 256
// element array such that:
//   - The 0th element is unused.
//   - The 1st element holds the probability that the 7th bit (the highest, most
//     significant bit) is 0.
//   - The 2nd element holds the probability that the 6th bit is 0, conditional
//     on the high bit being 0.
//   - The 3rd element holds the probability that the 6th bit is 0, conditional
//     on the high bit being 1.
//   - The 4th element holds the probability that the 5th bit is 0, conditional
//     on the high two bits being 00.
//   - The 5th element holds the probability that the 5th bit is 0, conditional
//     on the high two bits being 01.
//   - The 6th element holds the probability that the 5th bit is 0, conditional
//     on the high two bits being 10.
//   - The 7th element holds the probability that the 5th bit is 0, conditional
//     on the high two bits being 11.
//   - The 8th element holds the probability that the 4th bit is 0, conditional
//     on the high three bits being 000.
//   - etc
//   - The 255th element holds the probability that the 0th bit (the lowest,
//     least significant bit) is 0, conditional on the high seven bits being
//     1111111.
//
// Put another way, the 256 elements' value of N, as in "it's a probability for
// the Nth bit", looks like this (when arranged in 8 rows of 32 elements):
//
//	u7665555444444443333333333333333
//	22222222222222222222222222222222
//	11111111111111111111111111111111
//	11111111111111111111111111111111
//	00000000000000000000000000000000
//	00000000000000000000000000000000
//	00000000000000000000000000000000
//	00000000000000000000000000000000
//
// The 'u' means that the 0th element is unused.
type byteProbs [0x100]prob

func (p *byteProbs) decodeByte(rDec *rangeDecoder) (byteValue byte, retErr error) {
	index := uint32(1)
	for index < 0x100 {
		if bitValue, err := p[index].decodeBit(rDec); err != nil {
			return 0, err
		} else {
			index = index<<1 | bitValue
		}
	}
	return byte(index), nil
}

func (p *byteProbs) encodeByte(rEnc *rangeEncoder, byteValue byte) {
	b := uint32(byteValue)
	index := uint32(1)
	for i := 7; i >= 0; i-- {
		bitValue := (b >> uint(i)) & 1
		p[index].encodeBit(rEnc, bitValue)
		index = index<<1 | bitValue
	}
}

// FileFormat is a compressed file format, either the original LZMA format
// itself or something like Xz that builds on or varies that.
//
// Each valid FileFormatXxx value does not distinguish between the full file
// format (as spoken by numerous Xxx software tools) and the subset-of-Xxx
// implemented by this package. Specifically, FileFormatLZMA.Encode will
// produce compressed data that is valid full-LZMA (and is also valid
// subset-of-LZMA). FileFormatLZMA.Decode can decode subset-of-LZMA (but not
// full-LZMA).
type FileFormat uint32

const (
	FileFormatInvalid = FileFormat(0)
	FileFormatLZMA    = FileFormat(1)
	FileFormatXz      = FileFormat(2)
)

func (f FileFormat) String() string {
	switch f {
	case FileFormatLZMA:
		return "FileFormatLZMA"
	case FileFormatXz:
		return "FileFormatXz"
	}
	return "FileFormatInvalid"
}

// Decode converts src from the Literal Only LZMA/Xz compressed file format,
// appending the decoding to dst.
//
// It is valid to pass a nil dst, like the way it's valid to pass nil to the
// built-in append function.
//
// Decode also returns the suffix of src that was not used during decoding.
//
// It can also return partial results. The appendedDst and remainingSrc return
// values may be non-zero even if retErr is non-zero.
//
// It returns ErrUnsupportedXxxData if the source bytes look like Xxx formatted
// data that is outside the subset-of-Xxx that this package implements.
func (f FileFormat) Decode(dst []byte, src []byte) (appendedDst []byte, remainingSrc []byte, retErr error) {
	switch f {
	case FileFormatLZMA:
		return decodeLZMA(dst, src)
	case FileFormatXz:
		return decodeXz(dst, src)
	}
	return nil, nil, errUnsupportedFileFormat
}

func decodeLZMA(dst []byte, src []byte) (appendedDst []byte, remainingSrc []byte, retErr error) {
	// LZMA consists of a 13 byte header and then at least a 5 byte payload
	// (range coded data). The 13 byte header is:
	//  - 1 byte for the (lc, lp, pb) triple with max values (8, 4, 4),
	//  - 4 bytes u32le dictionary size and
	//  - 8 bytes i64le uncompressed size.
	if (len(src) < 18) || (src[0] >= (9 * 5 * 5)) {
		return dst, nil, errInvalidLZMAData
	} else if string(src[:5]) != lzmaHeader5 {
		return dst, nil, ErrUnsupportedLZMAData
	}

	size := uint64(0)
	for i := 0; i < 8; i++ {
		size |= uint64(src[5+i]) << uint(8*i)
	}
	if int64(size) < -1 {
		return dst, nil, errInvalidLZMAData
	} else if int64(size) == -1 {
		return dst, nil, ErrUnsupportedLZMAData
	}

	return decodeRaw(dst, src[13:], size, ErrUnsupportedLZMAData)
}

func decodeXz(dst []byte, src []byte) (appendedDst []byte, remainingSrc []byte, retErr error) {
	originalDstLen := len(dst)
	originalSrcLen := len(src)

	// Decode the headers.
	if (len(src) < 24) || (string(src[:6]) != xzHeader24[:6]) {
		return dst, src, errInvalidXzData
	} else if string(src[6:24]) != xzHeader24[6:24] {
		return dst, src, ErrUnsupportedXzData
	}
	src = src[24:]

	// Decode the payload as multiple chunks.
	for {
		if len(src) == 0 {
			return dst, src, errInvalidXzData

		} else if src[0] == 0x00 { // No more chunks.
			src = src[1:]
			break

		} else if src[0] == 0x01 { // Independent uncompressed chunk.
			if len(src) < 3 {
				return dst, src, errInvalidXzData
			}
			uncompressedSize := (uint32(src[1]) << 8) + (uint32(src[2]) << 0) + 1
			src = src[3:]
			if uint64(uncompressedSize) > uint64(len(src)) {
				return dst, src, errInvalidXzData
			}
			dst = append(dst, src[:uncompressedSize]...)
			src = src[uncompressedSize:]

		} else if src[0] == 0xE0 { // Independent LZMA chunk.
			if len(src) < 6 {
				return dst, src, errInvalidXzData
			} else if src[5] != 0x5D { // Like lzmaHeader5[0], this encodes lc=3, lp=0, pb=2.
				return dst, src, ErrUnsupportedXzData
			}
			uncompressedSize := (uint32(src[1]) << 8) + (uint32(src[2]) << 0) + 1
			compressedSize := (uint32(src[3]) << 8) + (uint32(src[4]) << 0) + 1
			src = src[6:]
			if uint64(compressedSize) > uint64(len(src)) {
				return dst, src, errInvalidXzData
			}
			lenSrc := len(src)
			dst, src, retErr = decodeRaw(dst, src, uint64(uncompressedSize), ErrUnsupportedXzData)
			if retErr != nil {
				return dst, src, retErr
			} else if lenSrc != (len(src) + int(compressedSize)) {
				return dst, src, errInvalidXzData
			}

		} else {
			return dst, src, ErrUnsupportedXzData
		}
	}
	unpaddedSizeWant := uint64((originalSrcLen - 12) - len(src) + 4)
	for i := unpaddedSizeWant & 3; (i & 3) != 0; i++ {
		if (len(src) == 0) || (src[0] != 0x00) {
			return dst, src, errInvalidXzData
		}
		src = src[1:]
	}
	if len(src) < 4 {
		return dst, src, errInvalidXzData
	}
	checksum := crc32.ChecksumIEEE(dst[originalDstLen:])
	if (src[0] != uint8(checksum>>0)) ||
		(src[1] != uint8(checksum>>8)) ||
		(src[2] != uint8(checksum>>16)) ||
		(src[3] != uint8(checksum>>24)) {
		return dst, src, errInvalidXzData
	}
	src = src[4:]

	// Decode the index.
	srcCheckpoint1 := src
	if (len(src) < 2) || (src[0] != 0x00) || (src[1] != 0x01) {
		return dst, src, errInvalidXzData
	}
	src = src[2:]
	src, unpaddedSizeHave, ok := decodeUvarint(src)
	if !ok || (unpaddedSizeHave != unpaddedSizeWant) {
		return dst, src, errInvalidXzData
	}
	src, uncompressedSize, ok := decodeUvarint(src)
	if !ok || (uncompressedSize != uint64(len(dst)-originalDstLen)) {
		return dst, src, errInvalidXzData
	}
	for i := (len(srcCheckpoint1) - len(src)) & 3; (i & 3) != 0; i++ {
		if (len(src) == 0) || (src[0] != 0x00) {
			return dst, src, errInvalidXzData
		}
		src = src[1:]
	}
	backwardSize := (len(srcCheckpoint1) - len(src)) >> 2
	if len(src) < 4 {
		return dst, src, errInvalidXzData
	}
	checksum = crc32.ChecksumIEEE(srcCheckpoint1[:len(srcCheckpoint1)-len(src)])
	if (src[0] != uint8(checksum>>0)) ||
		(src[1] != uint8(checksum>>8)) ||
		(src[2] != uint8(checksum>>16)) ||
		(src[3] != uint8(checksum>>24)) {
		return dst, src, errInvalidXzData
	}
	src = src[4:]

	// Decode the footer.
	if len(src) < 12 {
		return dst, src, errInvalidXzData
	}
	checksum = crc32.ChecksumIEEE(src[4:10])
	if (src[0] != uint8(checksum>>0)) || // Checksum.
		(src[1] != uint8(checksum>>8)) ||
		(src[2] != uint8(checksum>>16)) ||
		(src[3] != uint8(checksum>>24)) ||
		(src[4] != uint8(backwardSize>>0)) || // Backward Size.
		(src[5] != uint8(backwardSize>>8)) ||
		(src[6] != uint8(backwardSize>>16)) ||
		(src[7] != uint8(backwardSize>>24)) ||
		(src[8] != xzHeader24[6]) || // Stream Flags again.
		(src[9] != xzHeader24[7]) ||
		(src[10] != 0x59) || // Stream Footer Magic Bytes.
		(src[11] != 0x5A) {
		return dst, src, errInvalidXzData
	}
	return dst, src[12:], nil
}

func decodeRaw(dst []byte, src []byte, size uint64, errUnsupported error) (appendedDst []byte, remainingSrc []byte, retErr error) {
	if (len(src) < 5) || (src[0] != 0x00) {
		return dst, src, errUnsupported
	}

	rDec := rangeDecoder{
		src: src[5:],
		bits: (uint32(src[1]) << 24) |
			(uint32(src[2]) << 16) |
			(uint32(src[3]) << 8) |
			(uint32(src[4]) << 0),
		width: 0xFFFF_FFFF,
	}

	posProbs := [1 << pb]prob{}
	setProbsToOneHalf(posProbs[:])

	litProbs := [1 << (lc + lp)]byteProbs{}
	for ij := range litProbs {
		setProbsToOneHalf(litProbs[ij][:])
	}

	pos := uint32(0)
	prev := byte(0)
	curr := byte(0)
	for ; size > 0; size-- {
		if bitValue, err := posProbs[pos&pbMask].decodeBit(&rDec); err != nil {
			return dst, rDec.src, err
		} else if bitValue != 0 {
			// A full-LZMA decoder would implement Lempel Ziv matches (or the
			// End of Stream marker) here. Our simpler subset-of-LZMA decoder
			// only uses literals.
			return dst, rDec.src, errUnsupported
		}

		i := (pos & lpMask) << lc
		j := uint32(prev) >> (8 - lc)
		if curr, retErr = litProbs[i|j].decodeByte(&rDec); retErr != nil {
			return dst, rDec.src, retErr
		}
		dst = append(dst, curr)
		pos++
		prev = curr
	}

	return dst, rDec.src, nil
}

func decodeUvarint(src []byte) (remainingSrc []byte, x uint64, ok bool) {
	for i := uint32(0); (i < 63) && (len(src) > 0); i += 7 {
		s := src[0]
		src = src[1:]
		x |= uint64(s&0x7F) << i
		if (s & 0x80) == 0 {
			return src, x, true
		}
	}
	return src, 0, false
}

// Encode converts src to the Literal Only LZMA compressed file format,
// appending the encoding to dst.
//
// It is valid to pass a nil dst, like the way it's valid to pass nil to the
// built-in append function.
func (f FileFormat) Encode(dst []byte, src []byte) (appendedDst []byte, retErr error) {
	switch f {
	case FileFormatLZMA:
		return encodeLZMA(dst, src)
	case FileFormatXz:
		return encodeXz(dst, src)
	}
	return nil, errUnsupportedFileFormat
}

func encodeLZMA(dst []byte, src []byte) (appendedDst []byte, retErr error) {
	dst = append(dst, lzmaHeader5...)
	size := len(src)
	for i := 0; i < 8; i++ {
		dst = append(dst, byte(size))
		size >>= 8
	}
	return encodeRaw(dst, src), nil
}

func encodeXz(dst []byte, src []byte) (appendedDst []byte, retErr error) {
	// Encode the headers (12 byte stream header then 12 byte block header).
	// The block's unpaddedSize calculation ignores the stream header.
	dstLen0 := len(dst) + 12
	dst = append(dst, xzHeader24...)

	// Encode the payload as multiple chunks.
	//
	// Later XZ chunks can depend on earlier ones (and doing so can help
	// compression ratios) but for simplicity, this encoder emits independent
	// chunks. Each chunk's maximum compressed and uncompressed size are both
	// equal to 0x10000 = 65536 bytes, roughly speaking. The encoder partitions
	// the src into 65536 byte sub-slices. If a sub-slice's LZMA-compressed
	// form would be longer, the encoder emits an uncompressed chunk instead.
	rawLZMA := []byte(nil)
	for remaining := src; len(remaining) > 0; {
		srcChunk := []byte(nil)
		if len(remaining) > 0x10000 {
			srcChunk, remaining = remaining[:0x10000], remaining[0x10000:]
		} else {
			srcChunk, remaining = remaining, nil
		}

		// Emit 3 or 6 bytes of LZMA2 header. The LZMA2 file format also allows
		// for chunks to depend on previous chunks. But, as said above, we
		// produce independent chunks (favoring simplicity over maximizing
		// compression ratio). We emit one of:
		//
		//  00000001 U U  -  Uncompressed, reset dic, need reset state and set new prop
		//  111uuuuu U U P P S  -  LZMA, reset state + set new prop, reset dic
		//
		// "U U" or "uuuuu U U" is a 16-bit or 21-bit (unpacked_size - 1), "P
		// P" is a uint16_t (packed_size - 1) and S holds the LZMA properties.
		//
		// https://github.com/jljusten/LZMA-SDK/blob/781863cdf592da3e97420f50de5dac056ad352a5/C/Lzma2Dec.c#L17-L23
		rawLZMA = encodeRaw(rawLZMA[:0], srcChunk)
		if (len(srcChunk) + 3) <= (len(rawLZMA) + 6) {
			dst = append(dst,
				0x01, // Independent uncompressed chunk.
				uint8((len(srcChunk)-1)>>8),
				uint8((len(srcChunk)-1)>>0),
			)
			dst = append(dst, srcChunk...)
		} else {
			dst = append(dst,
				0xE0, // Independent LZMA chunk.
				uint8((len(srcChunk)-1)>>8),
				uint8((len(srcChunk)-1)>>0),
				uint8((len(rawLZMA)-1)>>8),
				uint8((len(rawLZMA)-1)>>0),
				0x5D, // Like lzmaHeader5[0], this encodes lc=3, lp=0, pb=2.
			)
			dst = append(dst, rawLZMA...)
		}
	}
	dst = append(dst, 0x00)                      // No more chunks.
	unpaddedSize := uint64(len(dst)-dstLen0) + 4 // +4 for the upcoming checksum.
	for 0 != 3&(len(dst)-dstLen0) {
		dst = append(dst, 0x00) // Padding
	}
	checksum := crc32.ChecksumIEEE(src)
	dst = append(dst,
		uint8(checksum>>0),
		uint8(checksum>>8),
		uint8(checksum>>16),
		uint8(checksum>>24),
	)

	// Encode the index.
	dstLen1 := len(dst)
	dst = append(dst,
		0x00, // Index Indicator.
		0x01, // Number of Records.
	)
	dst = encodeUvarint(dst, unpaddedSize)
	dst = encodeUvarint(dst, uint64(len(src)))
	for 0 != 3&(len(dst)-dstLen1) {
		dst = append(dst, 0x00) // Padding
	}
	backwardSize := (len(dst) - dstLen1) >> 2
	checksum = crc32.ChecksumIEEE(dst[dstLen1:])
	dst = append(dst,
		uint8(checksum>>0),
		uint8(checksum>>8),
		uint8(checksum>>16),
		uint8(checksum>>24),
	)

	// Encode the footer.
	dstLen2 := len(dst)
	dst = append(dst,
		0, 0, 0, 0, // Space for the checksum.
		uint8(backwardSize>>0), // Backward Size.
		uint8(backwardSize>>8),
		uint8(backwardSize>>16),
		uint8(backwardSize>>24),
		xzHeader24[6], // Stream Flags again.
		xzHeader24[7],
		0x59, // Stream Footer Magic Bytes.
		0x5A,
	)
	checksum = crc32.ChecksumIEEE(dst[dstLen2+4 : dstLen2+10])
	dst[dstLen2+0] = uint8(checksum >> 0)
	dst[dstLen2+1] = uint8(checksum >> 8)
	dst[dstLen2+2] = uint8(checksum >> 16)
	dst[dstLen2+3] = uint8(checksum >> 24)
	return dst, nil
}

func encodeRaw(dst []byte, src []byte) (appendedDst []byte) {
	rEnc := rangeEncoder{
		dst:   dst,
		width: 0xFFFF_FFFF,
	}

	posProbs := [1 << pb]prob{}
	setProbsToOneHalf(posProbs[:])

	litProbs := [1 << (lc + lp)]byteProbs{}
	for ij := range litProbs {
		setProbsToOneHalf(litProbs[ij][:])
	}

	pos := uint32(0)
	prev := byte(0)
	for _, curr := range src {
		// A full-LZMA encoder would choose between Lempel Ziv literals and
		// matches. Our simpler subset-of-LZMA encoder only uses literals, and
		// it is not a streaming encoder (it does not need to emit an End of
		// Stream marker), so we always encode a 0 bit here.
		posProbs[pos&pbMask].encodeBit(&rEnc, 0)

		i := (pos & lpMask) << lc
		j := uint32(prev) >> (8 - lc)
		litProbs[i|j].encodeByte(&rEnc, curr)
		pos++
		prev = curr
	}

	// Flush the rangeEncoder.
	for i := 0; i < 5; i++ {
		rEnc.shiftLow()
	}

	return rEnc.dst
}

func encodeUvarint(dst []byte, x uint64) []byte {
	for ; x >= 0x80; x >>= 7 {
		dst = append(dst, byte(x)|0x80)
	}
	return append(dst, byte(x))
}