#136: Start working on database persistence
This commit is contained in:
21
vendor/lukechampine.com/uint128/LICENSE
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21
vendor/lukechampine.com/uint128/LICENSE
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The MIT License (MIT)
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Copyright (c) 2019 Luke Champine
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Permission is hereby granted, free of charge, to any person obtaining a copy
|
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of this software and associated documentation files (the "Software"), to deal
|
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in the Software without restriction, including without limitation the rights
|
||||
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
|
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copies of the Software, and to permit persons to whom the Software is
|
||||
furnished to do so, subject to the following conditions:
|
||||
|
||||
The above copyright notice and this permission notice shall be included in
|
||||
all copies or substantial portions of the Software.
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|
||||
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
|
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
|
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THE SOFTWARE.
|
46
vendor/lukechampine.com/uint128/README.md
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46
vendor/lukechampine.com/uint128/README.md
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uint128
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-------
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[](https://godoc.org/github.com/lukechampine/uint128)
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[](https://goreportcard.com/report/github.com/lukechampine/uint128)
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```
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go get lukechampine.com/uint128
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```
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`uint128` provides a high-performance `Uint128` type that supports standard arithmetic
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operations. Unlike `math/big`, operations on `Uint128` values always produce new values
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instead of modifying a pointer receiver. A `Uint128` value is therefore immutable, just
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like `uint64` and friends.
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The name `uint128.Uint128` stutters, so I recommend either using a "dot import"
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or aliasing `uint128.Uint128` to give it a project-specific name. Embedding the type
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is not recommended, because methods will still return `uint128.Uint128`; this means that,
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if you want to extend the type with new methods, your best bet is probably to copy the
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source code wholesale and rename the identifier. ¯\\\_(ツ)\_/¯
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# Benchmarks
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Addition, multiplication, and subtraction are on par with their native 64-bit
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equivalents. Division is slower: ~20x slower when dividing a `Uint128` by a
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`uint64`, and ~100x slower when dividing by a `Uint128`. However, division is
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still faster than with `big.Int` (for the same operands), especially when
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dividing by a `uint64`.
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```
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BenchmarkArithmetic/Add-4 2000000000 0.45 ns/op 0 B/op 0 allocs/op
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BenchmarkArithmetic/Sub-4 2000000000 0.67 ns/op 0 B/op 0 allocs/op
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BenchmarkArithmetic/Mul-4 2000000000 0.42 ns/op 0 B/op 0 allocs/op
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BenchmarkArithmetic/Lsh-4 2000000000 1.06 ns/op 0 B/op 0 allocs/op
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BenchmarkArithmetic/Rsh-4 2000000000 1.06 ns/op 0 B/op 0 allocs/op
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BenchmarkDivision/native_64/64-4 2000000000 0.39 ns/op 0 B/op 0 allocs/op
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BenchmarkDivision/Div_128/64-4 2000000000 6.28 ns/op 0 B/op 0 allocs/op
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BenchmarkDivision/Div_128/128-4 30000000 45.2 ns/op 0 B/op 0 allocs/op
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BenchmarkDivision/big.Int_128/64-4 20000000 98.2 ns/op 8 B/op 1 allocs/op
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BenchmarkDivision/big.Int_128/128-4 30000000 53.4 ns/op 48 B/op 1 allocs/op
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BenchmarkString/Uint128-4 10000000 173 ns/op 48 B/op 1 allocs/op
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BenchmarkString/big.Int-4 5000000 350 ns/op 144 B/op 3 allocs/op
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```
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3
vendor/lukechampine.com/uint128/go.mod
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3
vendor/lukechampine.com/uint128/go.mod
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module lukechampine.com/uint128
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go 1.12
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417
vendor/lukechampine.com/uint128/uint128.go
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417
vendor/lukechampine.com/uint128/uint128.go
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package uint128 // import "lukechampine.com/uint128"
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import (
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"encoding/binary"
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"math"
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"math/big"
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"math/bits"
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)
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// Zero is a zero-valued uint128.
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var Zero Uint128
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// Max is the largest possible uint128 value.
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var Max = New(math.MaxUint64, math.MaxUint64)
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// A Uint128 is an unsigned 128-bit number.
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type Uint128 struct {
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Lo, Hi uint64
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}
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// IsZero returns true if u == 0.
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func (u Uint128) IsZero() bool {
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// NOTE: we do not compare against Zero, because that is a global variable
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// that could be modified.
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return u == Uint128{}
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}
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// Equals returns true if u == v.
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//
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// Uint128 values can be compared directly with ==, but use of the Equals method
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// is preferred for consistency.
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func (u Uint128) Equals(v Uint128) bool {
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return u == v
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}
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// Equals64 returns true if u == v.
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func (u Uint128) Equals64(v uint64) bool {
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return u.Lo == v && u.Hi == 0
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}
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// Cmp compares u and v and returns:
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//
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// -1 if u < v
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// 0 if u == v
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// +1 if u > v
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//
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func (u Uint128) Cmp(v Uint128) int {
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if u == v {
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return 0
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} else if u.Hi < v.Hi || (u.Hi == v.Hi && u.Lo < v.Lo) {
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return -1
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} else {
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return 1
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}
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}
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// Cmp64 compares u and v and returns:
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//
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// -1 if u < v
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// 0 if u == v
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// +1 if u > v
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//
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func (u Uint128) Cmp64(v uint64) int {
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if u.Hi == 0 && u.Lo == v {
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return 0
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} else if u.Hi == 0 && u.Lo < v {
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return -1
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} else {
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return 1
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}
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}
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// And returns u&v.
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func (u Uint128) And(v Uint128) Uint128 {
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return Uint128{u.Lo & v.Lo, u.Hi & v.Hi}
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}
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// And64 returns u&v.
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func (u Uint128) And64(v uint64) Uint128 {
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return Uint128{u.Lo & v, u.Hi & 0}
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}
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// Or returns u|v.
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func (u Uint128) Or(v Uint128) Uint128 {
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return Uint128{u.Lo | v.Lo, u.Hi | v.Hi}
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}
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// Or64 returns u|v.
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func (u Uint128) Or64(v uint64) Uint128 {
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return Uint128{u.Lo | v, u.Hi | 0}
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}
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// Xor returns u^v.
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func (u Uint128) Xor(v Uint128) Uint128 {
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return Uint128{u.Lo ^ v.Lo, u.Hi ^ v.Hi}
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}
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// Xor64 returns u^v.
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func (u Uint128) Xor64(v uint64) Uint128 {
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return Uint128{u.Lo ^ v, u.Hi ^ 0}
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}
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// Add returns u+v.
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func (u Uint128) Add(v Uint128) Uint128 {
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lo, carry := bits.Add64(u.Lo, v.Lo, 0)
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hi, carry := bits.Add64(u.Hi, v.Hi, carry)
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if carry != 0 {
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panic("overflow")
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}
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return Uint128{lo, hi}
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}
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// AddWrap returns u+v with wraparound semantics; for example,
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// Max.AddWrap(From64(1)) == Zero.
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func (u Uint128) AddWrap(v Uint128) Uint128 {
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lo, carry := bits.Add64(u.Lo, v.Lo, 0)
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hi, _ := bits.Add64(u.Hi, v.Hi, carry)
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return Uint128{lo, hi}
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}
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// Add64 returns u+v.
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func (u Uint128) Add64(v uint64) Uint128 {
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lo, carry := bits.Add64(u.Lo, v, 0)
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hi, carry := bits.Add64(u.Hi, 0, carry)
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if carry != 0 {
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panic("overflow")
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}
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return Uint128{lo, hi}
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}
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// AddWrap64 returns u+v with wraparound semantics; for example,
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// Max.AddWrap64(1) == Zero.
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func (u Uint128) AddWrap64(v uint64) Uint128 {
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lo, carry := bits.Add64(u.Lo, v, 0)
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hi := u.Hi + carry
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return Uint128{lo, hi}
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}
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// Sub returns u-v.
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func (u Uint128) Sub(v Uint128) Uint128 {
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lo, borrow := bits.Sub64(u.Lo, v.Lo, 0)
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hi, borrow := bits.Sub64(u.Hi, v.Hi, borrow)
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if borrow != 0 {
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panic("underflow")
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}
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return Uint128{lo, hi}
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}
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// SubWrap returns u-v with wraparound semantics; for example,
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// Zero.SubWrap(From64(1)) == Max.
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func (u Uint128) SubWrap(v Uint128) Uint128 {
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lo, borrow := bits.Sub64(u.Lo, v.Lo, 0)
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hi, _ := bits.Sub64(u.Hi, v.Hi, borrow)
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return Uint128{lo, hi}
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}
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// Sub64 returns u-v.
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func (u Uint128) Sub64(v uint64) Uint128 {
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lo, borrow := bits.Sub64(u.Lo, v, 0)
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hi, borrow := bits.Sub64(u.Hi, 0, borrow)
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if borrow != 0 {
|
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panic("underflow")
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}
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return Uint128{lo, hi}
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}
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// SubWrap64 returns u-v with wraparound semantics; for example,
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// Zero.SubWrap64(1) == Max.
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func (u Uint128) SubWrap64(v uint64) Uint128 {
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lo, borrow := bits.Sub64(u.Lo, v, 0)
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hi := u.Hi - borrow
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return Uint128{lo, hi}
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}
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|
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// Mul returns u*v, panicking on overflow.
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func (u Uint128) Mul(v Uint128) Uint128 {
|
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hi, lo := bits.Mul64(u.Lo, v.Lo)
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p0, p1 := bits.Mul64(u.Hi, v.Lo)
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p2, p3 := bits.Mul64(u.Lo, v.Hi)
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hi, c0 := bits.Add64(hi, p1, 0)
|
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hi, c1 := bits.Add64(hi, p3, c0)
|
||||
if (u.Hi != 0 && v.Hi != 0) || p0 != 0 || p2 != 0 || c1 != 0 {
|
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panic("overflow")
|
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}
|
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return Uint128{lo, hi}
|
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}
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// MulWrap returns u*v with wraparound semantics; for example,
|
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// Max.MulWrap(Max) == 1.
|
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func (u Uint128) MulWrap(v Uint128) Uint128 {
|
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hi, lo := bits.Mul64(u.Lo, v.Lo)
|
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hi += u.Hi*v.Lo + u.Lo*v.Hi
|
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return Uint128{lo, hi}
|
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}
|
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|
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// Mul64 returns u*v, panicking on overflow.
|
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func (u Uint128) Mul64(v uint64) Uint128 {
|
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hi, lo := bits.Mul64(u.Lo, v)
|
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p0, p1 := bits.Mul64(u.Hi, v)
|
||||
hi, c0 := bits.Add64(hi, p1, 0)
|
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if p0 != 0 || c0 != 0 {
|
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panic("overflow")
|
||||
}
|
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return Uint128{lo, hi}
|
||||
}
|
||||
|
||||
// MulWrap64 returns u*v with wraparound semantics; for example,
|
||||
// Max.MulWrap64(2) == Max.Sub64(1).
|
||||
func (u Uint128) MulWrap64(v uint64) Uint128 {
|
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hi, lo := bits.Mul64(u.Lo, v)
|
||||
hi += u.Hi * v
|
||||
return Uint128{lo, hi}
|
||||
}
|
||||
|
||||
// Div returns u/v.
|
||||
func (u Uint128) Div(v Uint128) Uint128 {
|
||||
q, _ := u.QuoRem(v)
|
||||
return q
|
||||
}
|
||||
|
||||
// Div64 returns u/v.
|
||||
func (u Uint128) Div64(v uint64) Uint128 {
|
||||
q, _ := u.QuoRem64(v)
|
||||
return q
|
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}
|
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|
||||
// QuoRem returns q = u/v and r = u%v.
|
||||
func (u Uint128) QuoRem(v Uint128) (q, r Uint128) {
|
||||
if v.Hi == 0 {
|
||||
var r64 uint64
|
||||
q, r64 = u.QuoRem64(v.Lo)
|
||||
r = From64(r64)
|
||||
} else {
|
||||
// generate a "trial quotient," guaranteed to be within 1 of the actual
|
||||
// quotient, then adjust.
|
||||
n := uint(bits.LeadingZeros64(v.Hi))
|
||||
v1 := v.Lsh(n)
|
||||
u1 := u.Rsh(1)
|
||||
tq, _ := bits.Div64(u1.Hi, u1.Lo, v1.Hi)
|
||||
tq >>= 63 - n
|
||||
if tq != 0 {
|
||||
tq--
|
||||
}
|
||||
q = From64(tq)
|
||||
// calculate remainder using trial quotient, then adjust if remainder is
|
||||
// greater than divisor
|
||||
r = u.Sub(v.Mul64(tq))
|
||||
if r.Cmp(v) >= 0 {
|
||||
q = q.Add64(1)
|
||||
r = r.Sub(v)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// QuoRem64 returns q = u/v and r = u%v.
|
||||
func (u Uint128) QuoRem64(v uint64) (q Uint128, r uint64) {
|
||||
if u.Hi < v {
|
||||
q.Lo, r = bits.Div64(u.Hi, u.Lo, v)
|
||||
} else {
|
||||
q.Hi, r = bits.Div64(0, u.Hi, v)
|
||||
q.Lo, r = bits.Div64(r, u.Lo, v)
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// Mod returns r = u%v.
|
||||
func (u Uint128) Mod(v Uint128) (r Uint128) {
|
||||
_, r = u.QuoRem(v)
|
||||
return
|
||||
}
|
||||
|
||||
// Mod64 returns r = u%v.
|
||||
func (u Uint128) Mod64(v uint64) (r uint64) {
|
||||
_, r = u.QuoRem64(v)
|
||||
return
|
||||
}
|
||||
|
||||
// Lsh returns u<<n.
|
||||
func (u Uint128) Lsh(n uint) (s Uint128) {
|
||||
if n > 64 {
|
||||
s.Lo = 0
|
||||
s.Hi = u.Lo << (n - 64)
|
||||
} else {
|
||||
s.Lo = u.Lo << n
|
||||
s.Hi = u.Hi<<n | u.Lo>>(64-n)
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// Rsh returns u>>n.
|
||||
func (u Uint128) Rsh(n uint) (s Uint128) {
|
||||
if n > 64 {
|
||||
s.Lo = u.Hi >> (n - 64)
|
||||
s.Hi = 0
|
||||
} else {
|
||||
s.Lo = u.Lo>>n | u.Hi<<(64-n)
|
||||
s.Hi = u.Hi >> n
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// LeadingZeros returns the number of leading zero bits in u; the result is 128
|
||||
// for u == 0.
|
||||
func (u Uint128) LeadingZeros() int {
|
||||
if u.Hi > 0 {
|
||||
return bits.LeadingZeros64(u.Hi)
|
||||
}
|
||||
return 64 + bits.LeadingZeros64(u.Lo)
|
||||
}
|
||||
|
||||
// TrailingZeros returns the number of trailing zero bits in u; the result is
|
||||
// 128 for u == 0.
|
||||
func (u Uint128) TrailingZeros() int {
|
||||
if u.Lo > 0 {
|
||||
return bits.TrailingZeros64(u.Lo)
|
||||
}
|
||||
return 64 + bits.TrailingZeros64(u.Hi)
|
||||
}
|
||||
|
||||
// OnesCount returns the number of one bits ("population count") in u.
|
||||
func (u Uint128) OnesCount() int {
|
||||
return bits.OnesCount64(u.Hi) + bits.OnesCount64(u.Lo)
|
||||
}
|
||||
|
||||
// RotateLeft returns the value of u rotated left by (k mod 128) bits.
|
||||
func (u Uint128) RotateLeft(k int) Uint128 {
|
||||
const n = 128
|
||||
s := uint(k) & (n - 1)
|
||||
return u.Lsh(s).Or(u.Rsh(n - s))
|
||||
}
|
||||
|
||||
// RotateRight returns the value of u rotated left by (k mod 128) bits.
|
||||
func (u Uint128) RotateRight(k int) Uint128 {
|
||||
return u.RotateLeft(-k)
|
||||
}
|
||||
|
||||
// Reverse returns the value of u with its bits in reversed order.
|
||||
func (u Uint128) Reverse() Uint128 {
|
||||
return Uint128{bits.Reverse64(u.Hi), bits.Reverse64(u.Lo)}
|
||||
}
|
||||
|
||||
// ReverseBytes returns the value of u with its bytes in reversed order.
|
||||
func (u Uint128) ReverseBytes() Uint128 {
|
||||
return Uint128{bits.ReverseBytes64(u.Hi), bits.ReverseBytes64(u.Lo)}
|
||||
}
|
||||
|
||||
// Len returns the minimum number of bits required to represent u; the result is
|
||||
// 0 for u == 0.
|
||||
func (u Uint128) Len() int {
|
||||
return 128 - u.LeadingZeros()
|
||||
}
|
||||
|
||||
// String returns the base-10 representation of u as a string.
|
||||
func (u Uint128) String() string {
|
||||
if u.IsZero() {
|
||||
return "0"
|
||||
}
|
||||
buf := []byte("0000000000000000000000000000000000000000") // log10(2^128) < 40
|
||||
for i := len(buf); ; i -= 19 {
|
||||
q, r := u.QuoRem64(1e19) // largest power of 10 that fits in a uint64
|
||||
var n int
|
||||
for ; r != 0; r /= 10 {
|
||||
n++
|
||||
buf[i-n] += byte(r % 10)
|
||||
}
|
||||
if q.IsZero() {
|
||||
return string(buf[i-n:])
|
||||
}
|
||||
u = q
|
||||
}
|
||||
}
|
||||
|
||||
// PutBytes stores u in b in little-endian order. It panics if len(b) < 16.
|
||||
func (u Uint128) PutBytes(b []byte) {
|
||||
binary.LittleEndian.PutUint64(b[:8], u.Lo)
|
||||
binary.LittleEndian.PutUint64(b[8:], u.Hi)
|
||||
}
|
||||
|
||||
// Big returns u as a *big.Int.
|
||||
func (u Uint128) Big() *big.Int {
|
||||
i := new(big.Int).SetUint64(u.Hi)
|
||||
i = i.Lsh(i, 64)
|
||||
i = i.Xor(i, new(big.Int).SetUint64(u.Lo))
|
||||
return i
|
||||
}
|
||||
|
||||
// New returns the Uint128 value (lo,hi).
|
||||
func New(lo, hi uint64) Uint128 {
|
||||
return Uint128{lo, hi}
|
||||
}
|
||||
|
||||
// From64 converts v to a Uint128 value.
|
||||
func From64(v uint64) Uint128 {
|
||||
return New(v, 0)
|
||||
}
|
||||
|
||||
// FromBytes converts b to a Uint128 value.
|
||||
func FromBytes(b []byte) Uint128 {
|
||||
return New(
|
||||
binary.LittleEndian.Uint64(b[:8]),
|
||||
binary.LittleEndian.Uint64(b[8:]),
|
||||
)
|
||||
}
|
||||
|
||||
// FromBig converts i to a Uint128 value. It panics if i is negative or
|
||||
// overflows 128 bits.
|
||||
func FromBig(i *big.Int) (u Uint128) {
|
||||
if i.Sign() < 0 {
|
||||
panic("value cannot be negative")
|
||||
} else if i.BitLen() > 128 {
|
||||
panic("value overflows Uint128")
|
||||
}
|
||||
u.Lo = i.Uint64()
|
||||
u.Hi = new(big.Int).Rsh(i, 64).Uint64()
|
||||
return u
|
||||
}
|
Reference in New Issue
Block a user