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step.go
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step.go
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// Copyright ©2012 The bíogo 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 step implements a step vector type.
//
// A step vector can be used to represent high volume data that would be
// efficiently stored by run-length encoding.
package step
import (
"errors"
"fmt"
"github.com/biogo/store/llrb"
)
var (
ErrOutOfRange = errors.New("step: index out of range")
ErrInvertedRange = errors.New("step: inverted range")
ErrZeroLength = errors.New("step: attempt to create zero length vector")
)
type (
position struct {
pos int
val Equaler
}
lower int
query int
upper int
)
func (p *position) Compare(c llrb.Comparable) int {
return p.pos - c.(*position).pos
}
func (q lower) Compare(c llrb.Comparable) (d int) {
d = int(q) - c.(*position).pos
if d == 0 {
d = -1
}
return
}
func (q query) Compare(c llrb.Comparable) (d int) {
switch c := c.(type) {
case *position:
d = int(q) - c.pos
case query:
d = int(q) - int(c)
}
return
}
func (q upper) Compare(c llrb.Comparable) (d int) {
d = int(q) - c.(*position).pos
if d == 0 {
d = 1
}
return
}
// An Equaler is a type that can return whether it equals another Equaler.
type Equaler interface {
Equal(Equaler) bool
}
// An Int is an int type satisfying the Equaler interface.
type Int int
// Equal returns whether i equals e. Equal assumes the underlying type of e is Int.
func (i Int) Equal(e Equaler) bool {
return i == e.(Int)
}
// A Float is a float64 type satisfying the Equaler interface.
type Float float64
// Equal returns whether f equals e. For the purposes of the step package here, NaN == NaN
// evaluates to true. Equal assumes the underlying type of e is Float.
func (f Float) Equal(e Equaler) bool {
ef := e.(Float)
if f != f && ef != ef { // For our purposes NaN == NaN.
return true
}
return f == ef
}
// A Vector is type that support the storage of array type data in a run-length
// encoding format.
type Vector struct {
Zero Equaler // Ground state for the step vector.
Relaxed bool // If true, dynamic vector resize is allowed.
t llrb.Tree
min, max *position
}
// New returns a new Vector with the extent defined by start and end,
// and the ground state defined by zero. The Vector's extent is mutable
// if the Relaxed field is set to true. If a zero length vector is requested
// an error is returned.
func New(start, end int, zero Equaler) (*Vector, error) {
if start >= end {
return nil, ErrZeroLength
}
v := &Vector{
Zero: zero,
min: &position{
pos: start,
val: zero,
},
max: &position{
pos: end,
val: nil,
},
}
v.t.Insert(v.min)
v.t.Insert(v.max)
return v, nil
}
// Start returns the index of minimum position of the Vector.
func (v *Vector) Start() int { return v.min.pos }
// End returns the index of lowest position beyond the end of the Vector.
func (v *Vector) End() int { return v.max.pos }
// Len returns the length of the represented data array, that is the distance
// between the start and end of the vector.
func (v *Vector) Len() int { return v.End() - v.Start() }
// Count returns the number of steps represented in the vector.
func (v *Vector) Count() int { return v.t.Len() - 1 }
// At returns the value of the vector at position i. If i is outside the extent
// of the vector an error is returned.
func (v *Vector) At(i int) (Equaler, error) {
if i < v.Start() || i >= v.End() {
return nil, ErrOutOfRange
}
st := v.t.Floor(query(i)).(*position)
return st.val, nil
}
// StepAt returns the value and range of the step at i, where start <= i < end.
// If i is outside the extent of the vector, an error is returned.
func (v *Vector) StepAt(i int) (start, end int, e Equaler, err error) {
if i < v.Start() || i >= v.End() {
return 0, 0, nil, ErrOutOfRange
}
lo := v.t.Floor(query(i)).(*position)
hi := v.t.Ceil(upper(i)).(*position)
return lo.pos, hi.pos, lo.val, nil
}
// Set sets the value of position i to e.
func (v *Vector) Set(i int, e Equaler) {
if i < v.min.pos || v.max.pos <= i {
if !v.Relaxed {
panic(ErrOutOfRange)
}
if i < v.min.pos {
if i == v.min.pos-1 {
if e.Equal(v.min.val) {
v.min.pos--
} else {
v.min = &position{pos: i, val: e}
v.t.Insert(v.min)
}
} else {
if v.min.val.Equal(v.Zero) {
v.min.pos = i + 1
} else {
v.min = &position{pos: i + 1, val: v.Zero}
v.t.Insert(v.min)
}
if e.Equal(v.Zero) {
v.min.pos--
} else {
v.min = &position{pos: i, val: e}
v.t.Insert(v.min)
}
}
} else if i >= v.max.pos {
if i == v.max.pos {
v.max.pos++
prev := v.t.Floor(query(i)).(*position)
if !e.Equal(prev.val) {
v.t.Insert(&position{pos: i, val: e})
}
} else {
mpos := v.max.pos
v.max.pos = i + 1
prev := v.t.Floor(query(i)).(*position)
if !prev.val.Equal(v.Zero) {
v.t.Insert(&position{pos: mpos, val: v.Zero})
}
if !e.Equal(v.Zero) {
v.t.Insert(&position{pos: i, val: e})
}
}
}
return
}
lo := v.t.Floor(query(i)).(*position)
if e.Equal(lo.val) {
return
}
hi := v.t.Ceil(upper(i)).(*position)
if lo.pos == i {
if hi.pos == i+1 {
if hi != v.max && e.Equal(hi.val) {
v.t.Delete(query(i))
hi.pos--
if v.min.pos == i {
v.min = hi
}
} else {
lo.val = e
}
if i > v.min.pos {
prev := v.t.Floor(query(i - 1)).(*position)
if e.Equal(prev.val) {
v.t.Delete(query(i))
}
}
} else {
lo.pos = i + 1
prev := v.t.Floor(query(i))
if prev == nil {
v.min = &position{pos: i, val: e}
v.t.Insert(v.min)
} else if !e.Equal(prev.(*position).val) {
v.t.Insert(&position{pos: i, val: e})
}
}
} else {
if hi.pos == i+1 {
if hi != v.max && e.Equal(hi.val) {
hi.pos--
} else {
v.t.Insert(&position{pos: i, val: e})
}
} else {
v.t.Insert(&position{pos: i, val: e})
v.t.Insert(&position{pos: i + 1, val: lo.val})
}
}
}
// SetRange sets the value of positions [start, end) to e.
func (v *Vector) SetRange(start, end int, e Equaler) {
switch l := end - start; {
case l == 0:
if !v.Relaxed && (start < v.min.pos || start >= v.max.pos) {
panic(ErrOutOfRange)
}
return
case l == 1:
v.Set(start, e)
return
case l < 0:
panic(ErrInvertedRange)
}
if !v.Relaxed && (start < v.min.pos || end > v.max.pos || start == v.max.pos) {
panic(ErrOutOfRange)
}
// Do fast path complete vector replacement if possible.
if start <= v.min.pos && v.max.pos <= end {
v.t = llrb.Tree{}
*v.min = position{pos: start, val: e}
v.t.Insert(v.min)
v.max.pos = end
v.t.Insert(v.max)
return
}
// Handle cases where the given range is entirely outside the vector.
switch {
case start >= v.max.pos:
oldEnd := v.max.pos
v.max.pos = end
if start != oldEnd {
prev := v.t.Floor(query(oldEnd)).(*position)
if !prev.val.Equal(v.Zero) {
v.t.Insert(&position{pos: oldEnd, val: v.Zero})
}
}
last := v.t.Floor(query(start)).(*position)
if !e.Equal(last.val) {
v.t.Insert(&position{pos: start, val: e})
}
return
case end < v.min.pos:
if v.min.val.Equal(v.Zero) {
v.min.pos = end
} else {
v.min = &position{pos: end, val: v.Zero}
v.t.Insert(v.min)
}
fallthrough
case end == v.min.pos:
if e.Equal(v.min.val) {
v.min.pos = start
} else {
v.min = &position{pos: start, val: e}
v.t.Insert(v.min)
}
return
}
// Handle cases where the given range
last := v.t.Floor(query(end)).(*position)
deleteRangeInclusive(&v.t, start, end)
switch {
// is entirely within the existing vector;
case v.min.pos < start && end <= v.max.pos:
prev := v.t.Floor(query(start)).(*position)
if !e.Equal(prev.val) {
v.t.Insert(&position{pos: start, val: e})
}
if last.val == nil {
v.t.Insert(v.max)
} else if !e.Equal(last.val) {
v.t.Insert(&position{pos: end, val: last.val})
}
// hangs over the left end and the right end is in the vector; or
case start <= v.min.pos:
lastVal := last.val
*v.min = position{pos: start, val: e}
v.t.Insert(v.min)
if !e.Equal(lastVal) {
v.t.Insert(&position{pos: end, val: lastVal})
}
// hangs over the right end and the left end is in the vector.
case end > v.max.pos:
v.max.pos = end
v.t.Insert(v.max)
prev := v.t.Floor(query(start)).(*position)
if e.Equal(prev.val) {
return
}
if last.val == nil || !e.Equal(last.val) {
v.t.Insert(&position{pos: start, val: e})
}
default:
panic("step: unexpected case")
}
}
// deleteRangeInclusive deletes all steps within the given range.
// Note that llrb.(*Tree).DoRange does not operate on the node matching the end of a range.
func deleteRangeInclusive(t *llrb.Tree, start, end int) {
var delQ []llrb.Comparable
t.DoRange(func(c llrb.Comparable) (done bool) {
delQ = append(delQ, c)
return
}, query(start), query(end+1))
for _, p := range delQ {
t.Delete(p)
}
}
// An Operation is a non-mutating function that can be applied to a vector using Do
// and DoRange.
type Operation func(start, end int, e Equaler)
// Do performs the function fn on steps stored in the Vector in ascending sort order
// of start position. fn is passed the start, end and value of the step.
func (v *Vector) Do(fn Operation) {
var (
la *position
min = v.min.pos
)
v.t.Do(func(c llrb.Comparable) (done bool) {
p := c.(*position)
if p.pos != min {
fn(la.pos, p.pos, la.val)
}
la = p
return
})
}
// Do performs the function fn on steps stored in the Vector over the range [from, to)
// in ascending sort order of start position. fn is passed the start, end and value of
// the step.
func (v *Vector) DoRange(from, to int, fn Operation) error {
if to < from {
return ErrInvertedRange
}
var (
la *position
min = v.min.pos
max = v.max.pos
)
if to <= min || from >= max {
return ErrOutOfRange
}
_, end, e, _ := v.StepAt(from)
if end > to {
end = to
}
fn(from, end, e)
if end == to {
return nil
}
v.t.DoRange(func(c llrb.Comparable) (done bool) {
p := c.(*position)
if p.pos != end {
fn(la.pos, p.pos, la.val)
}
la = p
return
}, query(end), query(to))
if to > la.pos {
fn(la.pos, to, la.val)
}
return nil
}
// A Mutator is a function that is used by Apply and ApplyRange to alter values within
// a Vector.
type Mutator func(Equaler) Equaler
// Convenience mutator functions. Mutator functions are used by Apply and ApplyRange
// to alter step values in a value-dependent manner. These mutators assume the stored
// type matches the function and will panic is this is not true.
var (
IncInt Mutator = incInt // Increment an int value.
DecInt Mutator = decInt // Decrement an int value.
IncFloat Mutator = incFloat // Increment a float64 value.
DecFloat Mutator = decFloat // Decrement a float64 value.
)
func incInt(e Equaler) Equaler { return e.(Int) + 1 }
func decInt(e Equaler) Equaler { return e.(Int) - 1 }
func incFloat(e Equaler) Equaler { return e.(Float) + 1 }
func decFloat(e Equaler) Equaler { return e.(Float) - 1 }
// Apply applies the mutator function m to steps stored in the Vector in ascending sort order
// of start position. Redundant steps resulting from changes in step values are erased.
func (v *Vector) Apply(m Mutator) {
var (
la Equaler
min = v.min.pos
max = v.max.pos
delQ []query
)
v.t.Do(func(c llrb.Comparable) (done bool) {
p := c.(*position)
if p.pos == max {
return true
}
p.val = m(p.val)
if p.pos != min && p.pos != max && p.val.Equal(la) {
delQ = append(delQ, query(p.pos))
}
la = p.val
return
})
for _, d := range delQ {
v.t.Delete(d)
}
}
// Apply applies the mutator function m to steps stored in the Vector in over the range
// [from, to) in ascending sort order of start position. Redundant steps resulting from
// changes in step values are erased.
func (v *Vector) ApplyRange(from, to int, m Mutator) error {
if to < from {
return ErrInvertedRange
}
if from == to {
return nil
}
var (
la Equaler
old position
min = v.min.pos
max = v.max.pos
delQ []query
)
if !v.Relaxed && (to <= min || from >= max) {
return ErrOutOfRange
}
if v.Relaxed {
if from < min {
v.SetRange(from, min, v.Zero)
}
if max < to {
v.SetRange(max, to, v.Zero)
}
}
var end int
old.pos, end, old.val, _ = v.StepAt(from)
la = old.val
la = m(la)
if to <= end {
v.SetRange(from, to, la)
return nil
}
if !la.Equal(old.val) {
switch {
case from > min:
if !la.Equal(v.t.Floor(lower(from)).(*position).val) {
v.t.Insert(&position{from, la})
} else {
v.t.Delete(query(from))
}
case from < min:
v.SetRange(from, min, la)
default:
*v.min = position{from, la}
}
}
var tail *position
v.t.DoRange(func(c llrb.Comparable) (done bool) {
p := c.(*position)
if p.pos == max {
// We should be at v.t.Max(), but don't stop
// just in case there is more. We want to fail
// noisily if max < v.t.Max().
return
}
if p.pos == to {
tail = p
return
}
old = *p // Needed for fix-up of last step if to is not at a step boundary.
p.val = m(p.val)
if p.pos != min && p.val.Equal(la) {
delQ = append(delQ, query(p.pos))
}
la = p.val
return
}, query(end), upper(to))
for _, d := range delQ {
v.t.Delete(d)
}
if to < max {
if tail == nil {
prev := v.t.Floor(lower(to)).(*position)
if old.pos != from && !old.val.Equal(prev.val) {
v.t.Insert(&position{to, old.val})
}
} else {
prev := v.t.Floor(lower(tail.pos)).(*position)
if tail.val != nil && tail.val.Equal(prev.val) {
v.t.Delete(query(tail.pos))
}
}
return nil
}
if v.Relaxed && to > max {
v.SetRange(max, to, m(v.Zero))
}
return nil
}
// String returns a string representation a Vector, displaying step start
// positions and values. The last step indicates the end of the vector and
// always has an associated value of nil.
func (v *Vector) String() string {
sb := make([]string, 0, v.t.Len())
v.t.Do(func(c llrb.Comparable) (done bool) {
p := c.(*position)
sb = append(sb, fmt.Sprintf("%d:%v", p.pos, p.val))
return
})
return fmt.Sprintf("%v", sb)
}