From e48262b1aae6b2a11f162afc1d6a1f5003fda008 Mon Sep 17 00:00:00 2001 From: Kostiantyn Masliuk <1pkg@protonmail.com> Date: Mon, 14 Nov 2022 23:05:32 -0800 Subject: [PATCH] add readme --- README.MD | 190 ++++++++++++++++++++++++++++++++++++++++++++++++- bits.go | 12 +++- bits_test.go | 2 +- h_gopher.png | Bin 0 -> 96867 bytes h_test.go | 4 +- support.go | 2 +- varinit.go | 58 +++++++-------- varint_test.go | 92 ++++++++++++++---------- 8 files changed, 281 insertions(+), 79 deletions(-) create mode 100644 h_gopher.png diff --git a/README.MD b/README.MD index 441c37e..f1bb91b 100644 --- a/README.MD +++ b/README.MD @@ -1,11 +1,199 @@ -# VarInt: fast & memory efficient arbitrary bit length integers. +

+ varint +

+ +# VarInt: fast & memory efficient arbitrary bit width integers in Go. ## Introduction +VarInt Go library provides fast & memory efficient arbitrary bit width unsigned integer array type. + +The purpose of VarInt to provide the maximum memory compact way to use and store unsigned custom bits integers. It does so by storing all the integers adjacent to each other inside a continuous numeric byte slice. It allocates the underlying numeric bytes slice only once on creation and doesn't expect to allocate any more memory afterwards. VarInt provides all the basic arithmetic and bitwise operations. To apply any of these operations, internal bits manipulations are required which implies certain computational overhead. Thus providing a tradeoff between CPU time and memory. Overhead grows lineraly, proportionally to bit len and is comparable with overhead from big.Int operations. Unlike big.Int however, VarInt uses exact number of bits to store the integers inside. Which makes VarInt extremely memory efficient. For example, to store a slice of 100 integers 100 bit each, big.Int requires 12400 bits, while VarInt needs exactly 10000 bits. In the same fashion VarInt also provides an efficient way to store integers smaller than 64 bits. For example, to store a slice of 1000 integers 2 bit each, []uin8 requires 8000 bits, while VarInt needs exactly 2000 bits. However, note that VarInt is no way close to be optimized as well as big.Int, and provides diminishing returns as bit length grows above certain threshold. + +Currently, in a conscious decision multiple operations are implemented in favour of simplicity and not computational complexity, this includes Mul that uses standard long multiplication instead of fast multiplication algorithms like Karatsuba multiplication, and Div that uses standard slow division instead of fast division algorithms. The main rationale behind this choice is the fact that VarInt has the most efficiency when used for small and medium size integers in the range of 1 to 5000 bit width, therefore asymptotic complexity should be less significant for this library. Note that VarInt carries a small fixed overhead internaly, it allocates 2 separate uint cells at the beginning of the numeric bytes slice to store length and bit length. It also collocates extra Bits variable at the end of numeric bytes slice which is used internally for many operations as a computation temporary buffer, including: Mul, Div, Mod, Sort. Currently, for simplicity and consistency most VarInt operations apply changes in place on the provided index and require the provided Bits to have exactly the same bit len, otherwise ErrorUnequalBitLengthCardinality is returned. Currently, VarInt provides only unsigned arithmetic. + ## Examples +**Allocate 10000 integers VarInt 25 bits in width. And then fills it with its max value.** + +```go +vint, _ := varint.NewVarInt(25, 10000) +b := varint.NewBits(25, []uint{ 33554431 }) +for i := 0; i < 10000; i++ { + _ = vint.Set(i, b) +} +``` + +**Allocate 10000 integers VarInt 25 bits in width. Fills it with increasing values, and rotates it right.** + +```go +vint, _ := varint.NewVarInt(25, 10000) +for i := 0; i < 10000; i++ { + _ = vint.Set(i, varint.NewBitsBits(25, varint.NewBitsUint(uint(i)))) +} +b := varint.NewBits(25, nil) +_ = vint.Get(0, b) +for i := 1; i < 10000; i++ { + _ = vint.GetSet(i, b) +} +_ = vint.Set(0, b) +``` + +**Allocates 10000 integers VarInt 50 bits in width. Fills it with random values, then finds min and max values.** + +```go +vint, _ := varint.NewVarInt(50, 10000) +rnd := rand.New(rand.NewSource(time.Now().UnixNano())) +for i := 0; i < 10000; i++ { + _ = vint.Set(i, varint.NewBitsRand(50, rnd)) +} +bmin, bmax, b := varint.NewBits(50, nil), varint.NewBits(50, nil), varint.NewBits(50, nil) +_, _ = vint.Get(0, bmin), vint.Get(0, bmax) +for i := 1; i < 10000; i++ { + _ = vint.Get(i, b) + switch { + case varint.Compare(b, bmin) == -1: + bmin = varint.NewBitsBits(50, b) + case varint.Compare(b, bmax) == 1: + bmax = varint.NewBitsBits(50, b) + } +} +``` + +**Allocates 10000 integers VarInt 50 bits in width. Fills it from big.Int channel, then subtracts 1000 from even numbers and adds 1 to odd numbers. Finally, converts integers back to the big.Int channel.** + +```go +ch := make(chan *big.Int) +vint, _ := varint.NewVarInt(50, 10000) +for i := 0; i < 10000; i++ { + _ = vint.Set(i, varint.NewBitsBits(50, varint.NewBitsBigInt(<-ch))) +} +b1000, b1 := varint.NewBitsBits(50, varint.NewBitsUint(1000)), varint.NewBitsBits(50, varint.NewBitsUint(1)) +for i := 0; i < 10000; i++ { + if i % 2 == 0 { + _ = vint.Sub(i, b1000) + } else { + _ = vint.Add(i, b1) + } +} +for i := 0; i < 10000; i++ { + _ = vint.Get(i, b1) + ch <- b1.BigInt() +} +``` + +**Allocates 10000 integers VarInt 50 bits in width. Fills it with random values, then if bitwise negation for a number is even multiply it by 2.** + +```go +vint, _ := varint.NewVarInt(50, 10000) +rnd := rand.New(rand.NewSource(time.Now().UnixNano())) +for i := 0; i < 10000; i++ { + _ = vint.Set(i, varint.NewBitsRand(50, rnd)) +} +b, b2 := varint.NewBits(50, nil), varint.NewBitsBits(50, varint.NewBitsUint(2)) +for i := 0; i < 10000; i++ { + _ = vint.Get(i, b) + _ = vint.Not(i) + _ = vint.Mod(i, b2) + _ = vint.GetSet(i, b) + if b.Empty() { + _ = vint.Mul(i, b2) + } +} +``` + +**Allocates 10000 integers VarInt 100 bits in width. Fills it with random values, then sorts it in ascending order.** + +```go +vint, _ := varint.NewVarInt(100, 10000) +rnd := rand.New(rand.NewSource(time.Now().UnixNano())) +for i := 0; i < 10000; i++ { + _ = vint.Set(i, varint.NewBitsRand(100, rnd)) +} +sort.Sort(varint.Sortable(vint)) +``` + +**Allocates 10000 integers VarInt 100 bits in width. Fills it with random values, then flushes it to a file and reads it back.** + +```go +vint, _ := varint.NewVarInt(100, 10000) +rnd := rand.New(rand.NewSource(time.Now().UnixNano())) +for i := 0; i < 10000; i++ { + _ = vint.Set(i, varint.NewBitsRand(100, rnd)) +} +f, _ := os.Create("vint.bin") +defer os.Remove(f.Name()) +_, _ = f.ReadFrom(varint.Encode(vint)) +f, _ = os.Open(f.Name()) +_ = varint.Decode(f, vint) +``` + ## Benchmarks +**Arithmetic Operations 100000000 integers, 4 bits width** + +| | ns/op | B/op | allocs/op | allocs/MB | +| :---------: | :---: | :--: | :-------: | :-------: | +| VarInt | 103.3 | 0 | 0 | 47.69 | +| Uint8 Slice | 1.555 | 0 | 0 | 95.38 | + +**Arithmetic Operations 10000000 integers, 64 bits width** + +| | ns/op | B/op | allocs/op | allocs/MB | +| :----------: | :---: | :--: | :-------: | :-------: | +| VarInt | 99.46 | 0 | 0 | 76.30 | +| Uint64 Slice | 2.398 | 0 | 0 | 76.30 | + +**Arithmetic Operations 10000000 integers, 100 bits width** + +| | ns/op | B/op | allocs/op | allocs/MB | +| :----------: | :---: | :--: | :-------: | :-------: | +| VarInt | 169.4 | 0 | 0 | 119.2 | +| BigInt Slice | 504.9 | 120 | 3 | 495.9 | + +**Arithmetic Operations 100000 integers, 10000 bits width** + +| | ns/op | B/op | allocs/op | allocs/MB | +| :----------: | :------: | :--: | :-------: | :-------: | +| VarInt | 78451 | 0 | 0 | 119.2 | +| BigInt Slice | 657.8 .0 | 148 | 2 | 145.8 | + +**Bitwise Operations 100000000 integers, 4 bits width** + +| | ns/op | B/op | allocs/op | allocs/MB | +| :---------: | :---: | :--: | :-------: | :-------: | +| VarInt | 76.84 | 0 | 0 | 47.69 | +| Uint8 Slice | 2.42 | 0 | 0 | 95.38 | + +**Arithmetic Operations 10000000 integers, 64 bits width** + +| | ns/op | B/op | allocs/op | allocs/MB | +| :----------: | :---: | :--: | :-------: | :-------: | +| VarInt | 79.06 | 0 | 0 | 76.30 | +| Uint64 Slice | 2.451 | 0 | 0 | 76.30 | + +**Arithmetic Operations 10000000 integers, 100 bits width** + +| | ns/op | B/op | allocs/op | allocs/MB | +| :----------: | :---: | :--: | :-------: | :-------: | +| VarInt | 134.5 | 0 | 0 | 119.2 | +| BigInt Slice | 186.9 | 48 | 1 | 427.2 | + +**Arithmetic Operations 100000 integers, 10000 bits width** + +| | ns/op | B/op | allocs/op | allocs/MB | +| :----------: | :---: | :--: | :-------: | :-------: | +| VarInt | 5273 | 0 | 0 | 119.2 | +| BigInt Slice | 172.3 | 153 | 0 | 150.3 | + +The benchmarks from above are run using, see `BenchmarkVarIntOperations` for more details. + +``` +go version go1.19.3 darwin/amd64 +Intel(R) Core(TM) i5-1030NG7 CPU @ 1.10GHz +go test -run=^$ -bench ^BenchmarkVarIntOperations$ github.com/1pkg/varint -benchtime 1000000x +``` + ## Licence VarInt is licensed under the MIT License. diff --git a/bits.go b/bits.go index ef5b0cc..da026dc 100644 --- a/bits.go +++ b/bits.go @@ -27,6 +27,7 @@ type Bits []uint // doesn't fit into the provided bit length, it is truncated to fit into the provided bit len. // In case the provided bit len is negative number, actual bit len is calculated from the bytes slice. // In case the provided bit len is 0, empty Bits marker is returned. +// See Bits type for more details. func NewBits(blen int, bytes []uint) Bits { if blen == 0 { return []uint{0} @@ -70,18 +71,21 @@ func NewBits(blen int, bytes []uint) Bits { // NewBitsUint allocates and returns new Bits instance with // deduced bit length to exactly fit the provided number. +// See Bits type for more details. func NewBitsUint(n uint) Bits { return NewBits(-1, []uint{n}) } // NewBitsBits allocates, copies and returns new Bits instance -// from the provided Bits, effectively making a deep copy of it. -func NewBitsBits(bits Bits) Bits { - return NewBits(bits.BitLen(), bits.Bytes()) +// from the provided bit len and Bits, effectively making a deep copy of it. +// See Bits type for more details. +func NewBitsBits(blen int, bits Bits) Bits { + return NewBits(blen, bits.Bytes()) } // NewBitsRand allocates and returns new Bits instance filled with // random bytes from provided Rand that fits the provided bit length. +// See Bits type for more details. func NewBitsRand(blen int, rnd *rand.Rand) Bits { // Calculate number of whole words plus // one word if partial mod word is needed. @@ -97,6 +101,7 @@ func NewBitsRand(blen int, rnd *rand.Rand) Bits { // NewBitsBigInt allocates, copies and returns new Bits instance // from the provided big.Int, it deduces bit length to exactly fit // the provided number. In case nil is provided empty Bits marker is returned. +// See Bits type for more details. func NewBitsBigInt(i *big.Int) Bits { if i == nil { return NewBitsUint(0) @@ -115,6 +120,7 @@ func NewBitsBigInt(i *big.Int) Bits { // converted to 2, base values above 62 are converted to 62. Leading plus '+' sings are ignored. // Separating underscore '_' signs are allowed and also ignored. In case empty or invalid // string is provided a special nil Bits marker is returned. The implementation follows big.Int. +// See Bits type for more details. func NewBitsString(s string, base int) Bits { // Fix unsuported bases to closest supported. const minb, maxb = 2, 62 diff --git a/bits_test.go b/bits_test.go index 32b64d9..d5ee874 100644 --- a/bits_test.go +++ b/bits_test.go @@ -67,7 +67,7 @@ func TestBitsNew(t *testing.T) { test(tname, th.T, func(h h) { b := NewBits(tcase.blen, tcase.bytes) bn := NewBitsUint(tcase.n) - bb := NewBitsBits(tcase.bits) + bb := NewBitsBits(tcase.blen, tcase.bits) bbig := NewBitsBigInt(tcase.big) brnd := NewBitsRand(tcase.blen, rnd) bs := NewBitsString(tcase.s, tcase.base) diff --git a/h_gopher.png b/h_gopher.png new file mode 100644 index 0000000000000000000000000000000000000000..515187b3db202c8061afc79a3c624049bba7bd05 GIT binary patch literal 96867 zcmV(}K+wO5P)x##S&_qpd5G{~=op}jD)Ce{)U z?`|b%;QFtJ`1>~K`WbEsQ8W-~pgZ)ZoMM*0`1SZ8skvxYe% zfCbBZD!9kpHh$S#@V+N>^ZPhpUcyOh4S6ktspnD9UGq`zJ>_oheLJUizJbJi5qH{G 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