mat/io.go - third_party/github.com/gonum/gonum - Git at Google

 // Copyright ©2015 The Gonum Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.

 package mat

 import (
 	"bytes"
 	"encoding/binary"
 	"errors"
 	"fmt"
 	"io"
 	"math"
 )

 // version is the current on-disk codec version.
 const version uint32 = 0x1

 // maxLen is the biggest slice/array len one can create on a 32/64b platform.
 const maxLen = int64(int(^uint(0) >> 1))

 var (
 	headerSize  = binary.Size(storage{})
 	sizeFloat64 = binary.Size(float64(0))

 	errWrongType = errors.New("mat: wrong data type")

 	errTooBig    = errors.New("mat: resulting data slice too big")
 	errTooSmall  = errors.New("mat: input slice too small")
 	errBadBuffer = errors.New("mat: data buffer size mismatch")
 	errBadSize   = errors.New("mat: invalid dimension")
 )

 // Type encoding scheme:
 //
 // Type 		Form 	Packing 	Uplo 		Unit 		Rows 	Columns kU 	kL
 // uint8 		[GST] 	uint8 [BPF] 	uint8 [AUL] 	bool 		int64 	int64 	int64 	int64
 // General 		'G' 	'F' 		'A' 		false 		r 	c 	0 	0
 // Band 		'G' 	'B' 		'A' 		false 		r 	c 	kU 	kL
 // Symmetric 		'S' 	'F' 		ul 		false 		n 	n 	0 	0
 // SymmetricBand 	'S' 	'B' 		ul 		false 		n 	n 	k 	k
 // SymmetricPacked 	'S' 	'P' 		ul 		false 		n 	n 	0 	0
 // Triangular 		'T' 	'F' 		ul 		Diag==Unit 	n 	n 	0 	0
 // TriangularBand 	'T' 	'B' 		ul 		Diag==Unit 	n 	n 	k 	k
 // TriangularPacked 	'T' 	'P' 		ul	 	Diag==Unit 	n 	n 	0 	0
 //
 // G - general, S - symmetric, T - triangular
 // F - full, B - band, P - packed
 // A - all, U - upper, L - lower

 // MarshalBinary encodes the receiver into a binary form and returns the result.
 //
 // Dense is little-endian encoded as follows:
 //   0 -  3  Version = 1          (uint32)
 //   4       'G'                  (byte)
 //   5       'F'                  (byte)
 //   6       'A'                  (byte)
 //   7       0                    (byte)
 //   8 - 15  number of rows       (int64)
 //  16 - 23  number of columns    (int64)
 //  24 - 31  0                    (int64)
 //  32 - 39  0                    (int64)
 //  40 - ..  matrix data elements (float64)
 //           [0,0] [0,1] ... [0,ncols-1]
 //           [1,0] [1,1] ... [1,ncols-1]
 //           ...
 //           [nrows-1,0] ... [nrows-1,ncols-1]
 func (m Dense) MarshalBinary() ([]byte, error) {
 	bufLen := int64(headerSize) + int64(m.mat.Rows)*int64(m.mat.Cols)*int64(sizeFloat64)
 	if bufLen <= 0 {
 		// bufLen is too big and has wrapped around.
 		return nil, errTooBig
 	}

 	header := storage{
 		Form: 'G', Packing: 'F', Uplo: 'A',
 		Rows: int64(m.mat.Rows), Cols: int64(m.mat.Cols),
 		Version: version,
 	}
 	buf := make([]byte, bufLen)
 	n, err := header.marshalBinaryTo(bytes.NewBuffer(buf[:0]))
 	if err != nil {
 		return buf[:n], err
 	}

 	p := headerSize
 	r, c := m.Dims()
 	for i := 0; i < r; i++ {
 		for j := 0; j < c; j++ {
 			binary.LittleEndian.PutUint64(buf[p:p+sizeFloat64], math.Float64bits(m.at(i, j)))
 			p += sizeFloat64
 		}
 	}

 	return buf, nil
 }

 // MarshalBinaryTo encodes the receiver into a binary form and writes it into w.
 // MarshalBinaryTo returns the number of bytes written into w and an error, if any.
 //
 // See MarshalBinary for the on-disk layout.
 func (m Dense) MarshalBinaryTo(w io.Writer) (int, error) {
 	header := storage{
 		Form: 'G', Packing: 'F', Uplo: 'A',
 		Rows: int64(m.mat.Rows), Cols: int64(m.mat.Cols),
 		Version: version,
 	}
 	n, err := header.marshalBinaryTo(w)
 	if err != nil {
 		return n, err
 	}

 	r, c := m.Dims()
 	var b [8]byte
 	for i := 0; i < r; i++ {
 		for j := 0; j < c; j++ {
 			binary.LittleEndian.PutUint64(b[:], math.Float64bits(m.at(i, j)))
 			nn, err := w.Write(b[:])
 			n += nn
 			if err != nil {
 				return n, err
 			}
 		}
 	}

 	return n, nil
 }

 // UnmarshalBinary decodes the binary form into the receiver.
 // It panics if the receiver is a non-empty Dense matrix.
 //
 // See MarshalBinary for the on-disk layout.
 //
 // Limited checks on the validity of the binary input are performed:
 //  - matrix.ErrShape is returned if the number of rows or columns is negative,
 //  - an error is returned if the resulting Dense matrix is too
 //  big for the current architecture (e.g. a 16GB matrix written by a
 //  64b application and read back from a 32b application.)
 // UnmarshalBinary does not limit the size of the unmarshaled matrix, and so
 // it should not be used on untrusted data.
 func (m *Dense) UnmarshalBinary(data []byte) error {
 	if !m.IsEmpty() {
 		panic("mat: unmarshal into non-empty matrix")
 	}

 	if len(data) < headerSize {
 		return errTooSmall
 	}

 	var header storage
 	err := header.unmarshalBinary(data[:headerSize])
 	if err != nil {
 		return err
 	}
 	rows := header.Rows
 	cols := header.Cols
 	header.Version = 0
 	header.Rows = 0
 	header.Cols = 0
 	if (header != storage{Form: 'G', Packing: 'F', Uplo: 'A'}) {
 		return errWrongType
 	}
 	if rows < 0 || cols < 0 {
 		return errBadSize
 	}
 	size := rows * cols
 	if size == 0 {
 		return ErrZeroLength
 	}
 	if int(size) < 0 || size > maxLen {
 		return errTooBig
 	}
 	if len(data) != headerSize+int(rows*cols)*sizeFloat64 {
 		return errBadBuffer
 	}

 	p := headerSize
 	m.reuseAsNonZeroed(int(rows), int(cols))
 	for i := range m.mat.Data {
 		m.mat.Data[i] = math.Float64frombits(binary.LittleEndian.Uint64(data[p : p+sizeFloat64]))
 		p += sizeFloat64
 	}

 	return nil
 }

 // UnmarshalBinaryFrom decodes the binary form into the receiver and returns
 // the number of bytes read and an error if any.
 // It panics if the receiver is a non-empty Dense matrix.
 //
 // See MarshalBinary for the on-disk layout.
 //
 // Limited checks on the validity of the binary input are performed:
 //  - matrix.ErrShape is returned if the number of rows or columns is negative,
 //  - an error is returned if the resulting Dense matrix is too
 //  big for the current architecture (e.g. a 16GB matrix written by a
 //  64b application and read back from a 32b application.)
 // UnmarshalBinary does not limit the size of the unmarshaled matrix, and so
 // it should not be used on untrusted data.
 func (m *Dense) UnmarshalBinaryFrom(r io.Reader) (int, error) {
 	if !m.IsEmpty() {
 		panic("mat: unmarshal into non-empty matrix")
 	}

 	var header storage
 	n, err := header.unmarshalBinaryFrom(r)
 	if err != nil {
 		return n, err
 	}
 	rows := header.Rows
 	cols := header.Cols
 	header.Version = 0
 	header.Rows = 0
 	header.Cols = 0
 	if (header != storage{Form: 'G', Packing: 'F', Uplo: 'A'}) {
 		return n, errWrongType
 	}
 	if rows < 0 || cols < 0 {
 		return n, errBadSize
 	}
 	size := rows * cols
 	if size == 0 {
 		return n, ErrZeroLength
 	}
 	if int(size) < 0 || size > maxLen {
 		return n, errTooBig
 	}

 	m.reuseAsNonZeroed(int(rows), int(cols))
 	var b [8]byte
 	for i := range m.mat.Data {
 		nn, err := readFull(r, b[:])
 		n += nn
 		if err != nil {
 			if err == io.EOF {
 				return n, io.ErrUnexpectedEOF
 			}
 			return n, err
 		}
 		m.mat.Data[i] = math.Float64frombits(binary.LittleEndian.Uint64(b[:]))
 	}

 	return n, nil
 }

 // MarshalBinary encodes the receiver into a binary form and returns the result.
 //
 // VecDense is little-endian encoded as follows:
 //
 //   0 -  3  Version = 1            (uint32)
 //   4       'G'                    (byte)
 //   5       'F'                    (byte)
 //   6       'A'                    (byte)
 //   7       0                      (byte)
 //   8 - 15  number of elements     (int64)
 //  16 - 23  1                      (int64)
 //  24 - 31  0                      (int64)
 //  32 - 39  0                      (int64)
 //  40 - ..  vector's data elements (float64)
 func (v VecDense) MarshalBinary() ([]byte, error) {
 	bufLen := int64(headerSize) + int64(v.mat.N)*int64(sizeFloat64)
 	if bufLen <= 0 {
 		// bufLen is too big and has wrapped around.
 		return nil, errTooBig
 	}

 	header := storage{
 		Form: 'G', Packing: 'F', Uplo: 'A',
 		Rows: int64(v.mat.N), Cols: 1,
 		Version: version,
 	}
 	buf := make([]byte, bufLen)
 	n, err := header.marshalBinaryTo(bytes.NewBuffer(buf[:0]))
 	if err != nil {
 		return buf[:n], err
 	}

 	p := headerSize
 	for i := 0; i < v.mat.N; i++ {
 		binary.LittleEndian.PutUint64(buf[p:p+sizeFloat64], math.Float64bits(v.at(i)))
 		p += sizeFloat64
 	}

 	return buf, nil
 }

 // MarshalBinaryTo encodes the receiver into a binary form, writes it to w and
 // returns the number of bytes written and an error if any.
 //
 // See MarshalBainry for the on-disk format.
 func (v VecDense) MarshalBinaryTo(w io.Writer) (int, error) {
 	header := storage{
 		Form: 'G', Packing: 'F', Uplo: 'A',
 		Rows: int64(v.mat.N), Cols: 1,
 		Version: version,
 	}
 	n, err := header.marshalBinaryTo(w)
 	if err != nil {
 		return n, err
 	}

 	var buf [8]byte
 	for i := 0; i < v.mat.N; i++ {
 		binary.LittleEndian.PutUint64(buf[:], math.Float64bits(v.at(i)))
 		nn, err := w.Write(buf[:])
 		n += nn
 		if err != nil {
 			return n, err
 		}
 	}

 	return n, nil
 }

 // UnmarshalBinary decodes the binary form into the receiver.
 // It panics if the receiver is a non-empty VecDense.
 //
 // See MarshalBinary for the on-disk layout.
 //
 // Limited checks on the validity of the binary input are performed:
 //  - matrix.ErrShape is returned if the number of rows is negative,
 //  - an error is returned if the resulting VecDense is too
 //  big for the current architecture (e.g. a 16GB vector written by a
 //  64b application and read back from a 32b application.)
 // UnmarshalBinary does not limit the size of the unmarshaled vector, and so
 // it should not be used on untrusted data.
 func (v *VecDense) UnmarshalBinary(data []byte) error {
 	if !v.IsEmpty() {
 		panic("mat: unmarshal into non-empty vector")
 	}

 	if len(data) < headerSize {
 		return errTooSmall
 	}

 	var header storage
 	err := header.unmarshalBinary(data[:headerSize])
 	if err != nil {
 		return err
 	}
 	if header.Cols != 1 {
 		return ErrShape
 	}
 	n := header.Rows
 	header.Version = 0
 	header.Rows = 0
 	header.Cols = 0
 	if (header != storage{Form: 'G', Packing: 'F', Uplo: 'A'}) {
 		return errWrongType
 	}
 	if n == 0 {
 		return ErrZeroLength
 	}
 	if n < 0 {
 		return errBadSize
 	}
 	if int64(maxLen) < n {
 		return errTooBig
 	}
 	if len(data) != headerSize+int(n)*sizeFloat64 {
 		return errBadBuffer
 	}

 	p := headerSize
 	v.reuseAsNonZeroed(int(n))
 	for i := range v.mat.Data {
 		v.mat.Data[i] = math.Float64frombits(binary.LittleEndian.Uint64(data[p : p+sizeFloat64]))
 		p += sizeFloat64
 	}

 	return nil
 }

 // UnmarshalBinaryFrom decodes the binary form into the receiver, from the
 // io.Reader and returns the number of bytes read and an error if any.
 // It panics if the receiver is a non-empty VecDense.
 //
 // See MarshalBinary for the on-disk layout.
 // See UnmarshalBinary for the list of sanity checks performed on the input.
 func (v *VecDense) UnmarshalBinaryFrom(r io.Reader) (int, error) {
 	if !v.IsEmpty() {
 		panic("mat: unmarshal into non-empty vector")
 	}

 	var header storage
 	n, err := header.unmarshalBinaryFrom(r)
 	if err != nil {
 		return n, err
 	}
 	if header.Cols != 1 {
 		return n, ErrShape
 	}
 	l := header.Rows
 	header.Version = 0
 	header.Rows = 0
 	header.Cols = 0
 	if (header != storage{Form: 'G', Packing: 'F', Uplo: 'A'}) {
 		return n, errWrongType
 	}
 	if l == 0 {
 		return n, ErrZeroLength
 	}
 	if l < 0 {
 		return n, errBadSize
 	}
 	if int64(maxLen) < l {
 		return n, errTooBig
 	}

 	v.reuseAsNonZeroed(int(l))
 	var b [8]byte
 	for i := range v.mat.Data {
 		nn, err := readFull(r, b[:])
 		n += nn
 		if err != nil {
 			if err == io.EOF {
 				return n, io.ErrUnexpectedEOF
 			}
 			return n, err
 		}
 		v.mat.Data[i] = math.Float64frombits(binary.LittleEndian.Uint64(b[:]))
 	}

 	return n, nil
 }

 // storage is the internal representation of the storage format of a
 // serialised matrix.
 type storage struct {
 	Version uint32 // Keep this first.
 	Form    byte   // [GST]
 	Packing byte   // [BPF]
 	Uplo    byte   // [AUL]
 	Unit    bool
 	Rows    int64
 	Cols    int64
 	KU      int64
 	KL      int64
 }

 // TODO(kortschak): Consider replacing these with calls to direct
 // encoding/decoding of fields rather than to binary.Write/binary.Read.

 func (s storage) marshalBinaryTo(w io.Writer) (int, error) {
 	buf := bytes.NewBuffer(make([]byte, 0, headerSize))
 	err := binary.Write(buf, binary.LittleEndian, s)
 	if err != nil {
 		return 0, err
 	}
 	return w.Write(buf.Bytes())
 }

 func (s *storage) unmarshalBinary(buf []byte) error {
 	err := binary.Read(bytes.NewReader(buf), binary.LittleEndian, s)
 	if err != nil {
 		return err
 	}
 	if s.Version != version {
 		return fmt.Errorf("mat: incorrect version: %d", s.Version)
 	}
 	return nil
 }

 func (s *storage) unmarshalBinaryFrom(r io.Reader) (int, error) {
 	buf := make([]byte, headerSize)
 	n, err := readFull(r, buf)
 	if err != nil {
 		return n, err
 	}
 	return n, s.unmarshalBinary(buf[:n])
 }

 // readFull reads from r into buf until it has read len(buf).
 // It returns the number of bytes copied and an error if fewer bytes were read.
 // If an EOF happens after reading fewer than len(buf) bytes, io.ErrUnexpectedEOF is returned.
 func readFull(r io.Reader, buf []byte) (int, error) {
 	var n int
 	var err error
 	for n < len(buf) && err == nil {
 		var nn int
 		nn, err = r.Read(buf[n:])
 		n += nn
 	}
 	if n == len(buf) {
 		return n, nil
 	}
 	if err == io.EOF {
 		return n, io.ErrUnexpectedEOF
 	}
 	return n, err
 }
	// Copyright ©2015 The Gonum Authors. All rights reserved.
	// Use of this source code is governed by a BSD-style
	// license that can be found in the LICENSE file.

	package mat

	import (
	"bytes"
	"encoding/binary"
	"errors"
	"fmt"
	"io"
	"math"
	)

	// version is the current on-disk codec version.
	const version uint32 = 0x1

	// maxLen is the biggest slice/array len one can create on a 32/64b platform.
	const maxLen = int64(int(^uint(0) >> 1))

	var (
	headerSize = binary.Size(storage{})
	sizeFloat64 = binary.Size(float64(0))

	errWrongType = errors.New("mat: wrong data type")

	errTooBig = errors.New("mat: resulting data slice too big")
	errTooSmall = errors.New("mat: input slice too small")
	errBadBuffer = errors.New("mat: data buffer size mismatch")
	errBadSize = errors.New("mat: invalid dimension")
	)

	// Type encoding scheme:
	//
	// Type Form Packing Uplo Unit Rows Columns kU kL
	// uint8 [GST] uint8 [BPF] uint8 [AUL] bool int64 int64 int64 int64
	// General 'G' 'F' 'A' false r c 0 0
	// Band 'G' 'B' 'A' false r c kU kL
	// Symmetric 'S' 'F' ul false n n 0 0
	// SymmetricBand 'S' 'B' ul false n n k k
	// SymmetricPacked 'S' 'P' ul false n n 0 0
	// Triangular 'T' 'F' ul Diag==Unit n n 0 0
	// TriangularBand 'T' 'B' ul Diag==Unit n n k k
	// TriangularPacked 'T' 'P' ul Diag==Unit n n 0 0
	//
	// G - general, S - symmetric, T - triangular
	// F - full, B - band, P - packed
	// A - all, U - upper, L - lower

	// MarshalBinary encodes the receiver into a binary form and returns the result.
	//
	// Dense is little-endian encoded as follows:
	// 0 - 3 Version = 1 (uint32)
	// 4 'G' (byte)
	// 5 'F' (byte)
	// 6 'A' (byte)
	// 7 0 (byte)
	// 8 - 15 number of rows (int64)
	// 16 - 23 number of columns (int64)
	// 24 - 31 0 (int64)
	// 32 - 39 0 (int64)
	// 40 - .. matrix data elements (float64)
	// [0,0] [0,1] ... [0,ncols-1]
	// [1,0] [1,1] ... [1,ncols-1]
	// ...
	// [nrows-1,0] ... [nrows-1,ncols-1]
	func (m Dense) MarshalBinary() ([]byte, error) {
	bufLen := int64(headerSize) + int64(m.mat.Rows)int64(m.mat.Cols)int64(sizeFloat64)
	if bufLen <= 0 {
	// bufLen is too big and has wrapped around.
	return nil, errTooBig
	}

	header := storage{
	Form: 'G', Packing: 'F', Uplo: 'A',
	Rows: int64(m.mat.Rows), Cols: int64(m.mat.Cols),
	Version: version,
	}
	buf := make([]byte, bufLen)
	n, err := header.marshalBinaryTo(bytes.NewBuffer(buf[:0]))
	if err != nil {
	return buf[:n], err
	}

	p := headerSize
	r, c := m.Dims()
	for i := 0; i < r; i++ {
	for j := 0; j < c; j++ {
	binary.LittleEndian.PutUint64(buf[p:p+sizeFloat64], math.Float64bits(m.at(i, j)))
	p += sizeFloat64
	}
	}

	return buf, nil
	}

	// MarshalBinaryTo encodes the receiver into a binary form and writes it into w.
	// MarshalBinaryTo returns the number of bytes written into w and an error, if any.
	//
	// See MarshalBinary for the on-disk layout.
	func (m Dense) MarshalBinaryTo(w io.Writer) (int, error) {
	header := storage{
	Form: 'G', Packing: 'F', Uplo: 'A',
	Rows: int64(m.mat.Rows), Cols: int64(m.mat.Cols),
	Version: version,
	}
	n, err := header.marshalBinaryTo(w)
	if err != nil {
	return n, err
	}

	r, c := m.Dims()
	var b [8]byte
	for i := 0; i < r; i++ {
	for j := 0; j < c; j++ {
	binary.LittleEndian.PutUint64(b[:], math.Float64bits(m.at(i, j)))
	nn, err := w.Write(b[:])
	n += nn
	if err != nil {
	return n, err
	}
	}
	}

	return n, nil
	}

	// UnmarshalBinary decodes the binary form into the receiver.
	// It panics if the receiver is a non-empty Dense matrix.
	//
	// See MarshalBinary for the on-disk layout.
	//
	// Limited checks on the validity of the binary input are performed:
	// - matrix.ErrShape is returned if the number of rows or columns is negative,
	// - an error is returned if the resulting Dense matrix is too
	// big for the current architecture (e.g. a 16GB matrix written by a
	// 64b application and read back from a 32b application.)
	// UnmarshalBinary does not limit the size of the unmarshaled matrix, and so
	// it should not be used on untrusted data.
	func (m *Dense) UnmarshalBinary(data []byte) error {
	if !m.IsEmpty() {
	panic("mat: unmarshal into non-empty matrix")
	}

	if len(data) < headerSize {
	return errTooSmall
	}

	var header storage
	err := header.unmarshalBinary(data[:headerSize])
	if err != nil {
	return err
	}
	rows := header.Rows
	cols := header.Cols
	header.Version = 0
	header.Rows = 0
	header.Cols = 0
	if (header != storage{Form: 'G', Packing: 'F', Uplo: 'A'}) {
	return errWrongType
	}
	if rows < 0 \|\| cols < 0 {
	return errBadSize
	}
	size := rows * cols
	if size == 0 {
	return ErrZeroLength
	}
	if int(size) < 0 \|\| size > maxLen {
	return errTooBig
	}
	if len(data) != headerSize+int(rowscols)sizeFloat64 {
	return errBadBuffer
	}

	p := headerSize
	m.reuseAsNonZeroed(int(rows), int(cols))
	for i := range m.mat.Data {
	m.mat.Data[i] = math.Float64frombits(binary.LittleEndian.Uint64(data[p : p+sizeFloat64]))
	p += sizeFloat64
	}

	return nil
	}

	// UnmarshalBinaryFrom decodes the binary form into the receiver and returns
	// the number of bytes read and an error if any.
	// It panics if the receiver is a non-empty Dense matrix.
	//
	// See MarshalBinary for the on-disk layout.
	//
	// Limited checks on the validity of the binary input are performed:
	// - matrix.ErrShape is returned if the number of rows or columns is negative,
	// - an error is returned if the resulting Dense matrix is too
	// big for the current architecture (e.g. a 16GB matrix written by a
	// 64b application and read back from a 32b application.)
	// UnmarshalBinary does not limit the size of the unmarshaled matrix, and so
	// it should not be used on untrusted data.
	func (m *Dense) UnmarshalBinaryFrom(r io.Reader) (int, error) {
	if !m.IsEmpty() {
	panic("mat: unmarshal into non-empty matrix")
	}

	var header storage
	n, err := header.unmarshalBinaryFrom(r)
	if err != nil {
	return n, err
	}
	rows := header.Rows
	cols := header.Cols
	header.Version = 0
	header.Rows = 0
	header.Cols = 0
	if (header != storage{Form: 'G', Packing: 'F', Uplo: 'A'}) {
	return n, errWrongType
	}
	if rows < 0 \|\| cols < 0 {
	return n, errBadSize
	}
	size := rows * cols
	if size == 0 {
	return n, ErrZeroLength
	}
	if int(size) < 0 \|\| size > maxLen {
	return n, errTooBig
	}

	m.reuseAsNonZeroed(int(rows), int(cols))
	var b [8]byte
	for i := range m.mat.Data {
	nn, err := readFull(r, b[:])
	n += nn
	if err != nil {
	if err == io.EOF {
	return n, io.ErrUnexpectedEOF
	}
	return n, err
	}
	m.mat.Data[i] = math.Float64frombits(binary.LittleEndian.Uint64(b[:]))
	}

	return n, nil
	}

	// MarshalBinary encodes the receiver into a binary form and returns the result.
	//
	// VecDense is little-endian encoded as follows:
	//
	// 0 - 3 Version = 1 (uint32)
	// 4 'G' (byte)
	// 5 'F' (byte)
	// 6 'A' (byte)
	// 7 0 (byte)
	// 8 - 15 number of elements (int64)
	// 16 - 23 1 (int64)
	// 24 - 31 0 (int64)
	// 32 - 39 0 (int64)
	// 40 - .. vector's data elements (float64)
	func (v VecDense) MarshalBinary() ([]byte, error) {
	bufLen := int64(headerSize) + int64(v.mat.N)*int64(sizeFloat64)
	if bufLen <= 0 {
	// bufLen is too big and has wrapped around.
	return nil, errTooBig
	}

	header := storage{
	Form: 'G', Packing: 'F', Uplo: 'A',
	Rows: int64(v.mat.N), Cols: 1,
	Version: version,
	}
	buf := make([]byte, bufLen)
	n, err := header.marshalBinaryTo(bytes.NewBuffer(buf[:0]))
	if err != nil {
	return buf[:n], err
	}

	p := headerSize
	for i := 0; i < v.mat.N; i++ {
	binary.LittleEndian.PutUint64(buf[p:p+sizeFloat64], math.Float64bits(v.at(i)))
	p += sizeFloat64
	}

	return buf, nil
	}

	// MarshalBinaryTo encodes the receiver into a binary form, writes it to w and
	// returns the number of bytes written and an error if any.
	//
	// See MarshalBainry for the on-disk format.
	func (v VecDense) MarshalBinaryTo(w io.Writer) (int, error) {
	header := storage{
	Form: 'G', Packing: 'F', Uplo: 'A',
	Rows: int64(v.mat.N), Cols: 1,
	Version: version,
	}
	n, err := header.marshalBinaryTo(w)
	if err != nil {
	return n, err
	}

	var buf [8]byte
	for i := 0; i < v.mat.N; i++ {
	binary.LittleEndian.PutUint64(buf[:], math.Float64bits(v.at(i)))
	nn, err := w.Write(buf[:])
	n += nn
	if err != nil {
	return n, err
	}
	}

	return n, nil
	}

	// UnmarshalBinary decodes the binary form into the receiver.
	// It panics if the receiver is a non-empty VecDense.
	//
	// See MarshalBinary for the on-disk layout.
	//
	// Limited checks on the validity of the binary input are performed:
	// - matrix.ErrShape is returned if the number of rows is negative,
	// - an error is returned if the resulting VecDense is too
	// big for the current architecture (e.g. a 16GB vector written by a
	// 64b application and read back from a 32b application.)
	// UnmarshalBinary does not limit the size of the unmarshaled vector, and so
	// it should not be used on untrusted data.
	func (v *VecDense) UnmarshalBinary(data []byte) error {
	if !v.IsEmpty() {
	panic("mat: unmarshal into non-empty vector")
	}

	if len(data) < headerSize {
	return errTooSmall
	}

	var header storage
	err := header.unmarshalBinary(data[:headerSize])
	if err != nil {
	return err
	}
	if header.Cols != 1 {
	return ErrShape
	}
	n := header.Rows
	header.Version = 0
	header.Rows = 0
	header.Cols = 0
	if (header != storage{Form: 'G', Packing: 'F', Uplo: 'A'}) {
	return errWrongType
	}
	if n == 0 {
	return ErrZeroLength
	}
	if n < 0 {
	return errBadSize
	}
	if int64(maxLen) < n {
	return errTooBig
	}
	if len(data) != headerSize+int(n)*sizeFloat64 {
	return errBadBuffer
	}

	p := headerSize
	v.reuseAsNonZeroed(int(n))
	for i := range v.mat.Data {
	v.mat.Data[i] = math.Float64frombits(binary.LittleEndian.Uint64(data[p : p+sizeFloat64]))
	p += sizeFloat64
	}

	return nil
	}

	// UnmarshalBinaryFrom decodes the binary form into the receiver, from the
	// io.Reader and returns the number of bytes read and an error if any.
	// It panics if the receiver is a non-empty VecDense.
	//
	// See MarshalBinary for the on-disk layout.
	// See UnmarshalBinary for the list of sanity checks performed on the input.
	func (v *VecDense) UnmarshalBinaryFrom(r io.Reader) (int, error) {
	if !v.IsEmpty() {
	panic("mat: unmarshal into non-empty vector")
	}

	var header storage
	n, err := header.unmarshalBinaryFrom(r)
	if err != nil {
	return n, err
	}
	if header.Cols != 1 {
	return n, ErrShape
	}
	l := header.Rows
	header.Version = 0
	header.Rows = 0
	header.Cols = 0
	if (header != storage{Form: 'G', Packing: 'F', Uplo: 'A'}) {
	return n, errWrongType
	}
	if l == 0 {
	return n, ErrZeroLength
	}
	if l < 0 {
	return n, errBadSize
	}
	if int64(maxLen) < l {
	return n, errTooBig
	}

	v.reuseAsNonZeroed(int(l))
	var b [8]byte
	for i := range v.mat.Data {
	nn, err := readFull(r, b[:])
	n += nn
	if err != nil {
	if err == io.EOF {
	return n, io.ErrUnexpectedEOF
	}
	return n, err
	}
	v.mat.Data[i] = math.Float64frombits(binary.LittleEndian.Uint64(b[:]))
	}

	return n, nil
	}

	// storage is the internal representation of the storage format of a
	// serialised matrix.
	type storage struct {
	Version uint32 // Keep this first.
	Form byte // [GST]
	Packing byte // [BPF]
	Uplo byte // [AUL]
	Unit bool
	Rows int64
	Cols int64
	KU int64
	KL int64
	}

	// TODO(kortschak): Consider replacing these with calls to direct
	// encoding/decoding of fields rather than to binary.Write/binary.Read.

	func (s storage) marshalBinaryTo(w io.Writer) (int, error) {
	buf := bytes.NewBuffer(make([]byte, 0, headerSize))
	err := binary.Write(buf, binary.LittleEndian, s)
	if err != nil {
	return 0, err
	}
	return w.Write(buf.Bytes())
	}

	func (s *storage) unmarshalBinary(buf []byte) error {
	err := binary.Read(bytes.NewReader(buf), binary.LittleEndian, s)
	if err != nil {
	return err
	}
	if s.Version != version {
	return fmt.Errorf("mat: incorrect version: %d", s.Version)
	}
	return nil
	}

	func (s *storage) unmarshalBinaryFrom(r io.Reader) (int, error) {
	buf := make([]byte, headerSize)
	n, err := readFull(r, buf)
	if err != nil {
	return n, err
	}
	return n, s.unmarshalBinary(buf[:n])
	}

	// readFull reads from r into buf until it has read len(buf).
	// It returns the number of bytes copied and an error if fewer bytes were read.
	// If an EOF happens after reading fewer than len(buf) bytes, io.ErrUnexpectedEOF is returned.
	func readFull(r io.Reader, buf []byte) (int, error) {
	var n int
	var err error
	for n < len(buf) && err == nil {
	var nn int
	nn, err = r.Read(buf[n:])
	n += nn
	}
	if n == len(buf) {
	return n, nil
	}
	if err == io.EOF {
	return n, io.ErrUnexpectedEOF
	}
	return n, err
	}