gitroast/vendor/github.com/pingcap/tidb/mysql/decimal.go

756 lines
20 KiB
Go

// The MIT License (MIT)
// Copyright (c) 2015 Spring, Inc.
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// 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.
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.
// - Based on https://github.com/oguzbilgic/fpd, which has the following license:
// """
// The MIT License (MIT)
// Copyright (c) 2013 Oguz Bilgic
// Permission is hereby granted, free of charge, to any person obtaining a copy of
// this software and associated documentation files (the "Software"), to deal in
// the Software without restriction, including without limitation the rights to
// use, copy, modify, merge, publish, distribute, sublicense, and/or sell 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.
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
// FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
// COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
// IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
// CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
// """
// Copyright 2015 PingCAP, Inc.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// See the License for the specific language governing permissions and
// limitations under the License.
package mysql
// Decimal implements an arbitrary precision fixed-point decimal.
//
// To use as part of a struct:
//
// type Struct struct {
// Number Decimal
// }
//
// The zero-value of a Decimal is 0, as you would expect.
//
// The best way to create a new Decimal is to use decimal.NewFromString, ex:
//
// n, err := decimal.NewFromString("-123.4567")
// n.String() // output: "-123.4567"
//
// NOTE: this can "only" represent numbers with a maximum of 2^31 digits
// after the decimal point.
import (
"database/sql/driver"
"fmt"
"math"
"math/big"
"strconv"
"strings"
)
// DivisionPrecision is the number of decimal places in the result when it
// doesn't divide exactly.
//
// Example:
//
// d1 := decimal.NewFromFloat(2).Div(decimal.NewFromFloat(3)
// d1.String() // output: "0.6667"
// d2 := decimal.NewFromFloat(2).Div(decimal.NewFromFloat(30000)
// d2.String() // output: "0.0001"
// d3 := decimal.NewFromFloat(20000).Div(decimal.NewFromFloat(3)
// d3.String() // output: "6666.6666666666666667"
// decimal.DivisionPrecision = 3
// d4 := decimal.NewFromFloat(2).Div(decimal.NewFromFloat(3)
// d4.String() // output: "0.6667"
//
const (
MaxFractionDigits = 30
DivIncreasePrecision = 4
)
// ZeroDecimal is zero constant, to make computations faster.
var ZeroDecimal = NewDecimalFromInt(0, 1)
var zeroInt = big.NewInt(0)
var oneInt = big.NewInt(1)
var fiveInt = big.NewInt(5)
var tenInt = big.NewInt(10)
// Decimal represents a fixed-point decimal. It is immutable.
// number = value * 10 ^ exp
type Decimal struct {
value *big.Int
// this must be an int32, because we cast it to float64 during
// calculations. If exp is 64 bit, we might lose precision.
// If we cared about being able to represent every possible decimal, we
// could make exp a *big.Int but it would hurt performance and numbers
// like that are unrealistic.
exp int32
fracDigits int32 // Number of fractional digits for string result.
}
// ConvertToDecimal converts interface to decimal.
func ConvertToDecimal(value interface{}) (Decimal, error) {
switch v := value.(type) {
case int8:
return NewDecimalFromInt(int64(v), 0), nil
case int16:
return NewDecimalFromInt(int64(v), 0), nil
case int32:
return NewDecimalFromInt(int64(v), 0), nil
case int64:
return NewDecimalFromInt(int64(v), 0), nil
case int:
return NewDecimalFromInt(int64(v), 0), nil
case uint8:
return NewDecimalFromUint(uint64(v), 0), nil
case uint16:
return NewDecimalFromUint(uint64(v), 0), nil
case uint32:
return NewDecimalFromUint(uint64(v), 0), nil
case uint64:
return NewDecimalFromUint(uint64(v), 0), nil
case uint:
return NewDecimalFromUint(uint64(v), 0), nil
case float32:
return NewDecimalFromFloat(float64(v)), nil
case float64:
return NewDecimalFromFloat(float64(v)), nil
case string:
return ParseDecimal(v)
case Decimal:
return v, nil
case Hex:
return NewDecimalFromInt(int64(v.Value), 0), nil
case Bit:
return NewDecimalFromUint(uint64(v.Value), 0), nil
case Enum:
return NewDecimalFromUint(uint64(v.Value), 0), nil
case Set:
return NewDecimalFromUint(uint64(v.Value), 0), nil
default:
return Decimal{}, fmt.Errorf("can't convert %v to decimal", value)
}
}
// NewDecimalFromInt returns a new fixed-point decimal, value * 10 ^ exp.
func NewDecimalFromInt(value int64, exp int32) Decimal {
return Decimal{
value: big.NewInt(value),
exp: exp,
fracDigits: fracDigitsDefault(exp),
}
}
// NewDecimalFromUint returns a new fixed-point decimal, value * 10 ^ exp.
func NewDecimalFromUint(value uint64, exp int32) Decimal {
return Decimal{
value: big.NewInt(0).SetUint64(value),
exp: exp,
fracDigits: fracDigitsDefault(exp),
}
}
// ParseDecimal returns a new Decimal from a string representation.
//
// Example:
//
// d, err := ParseDecimal("-123.45")
// d2, err := ParseDecimal(".0001")
//
func ParseDecimal(value string) (Decimal, error) {
var intString string
var exp = int32(0)
n := strings.IndexAny(value, "eE")
if n > 0 {
// It is scientific notation, like 3.14e10
expInt, err := strconv.Atoi(value[n+1:])
if err != nil {
return Decimal{}, fmt.Errorf("can't convert %s to decimal, incorrect exponent", value)
}
value = value[0:n]
exp = int32(expInt)
}
parts := strings.Split(value, ".")
if len(parts) == 1 {
// There is no decimal point, we can just parse the original string as
// an int.
intString = value
} else if len(parts) == 2 {
intString = parts[0] + parts[1]
expInt := -len(parts[1])
exp += int32(expInt)
} else {
return Decimal{}, fmt.Errorf("can't convert %s to decimal: too many .s", value)
}
dValue := new(big.Int)
_, ok := dValue.SetString(intString, 10)
if !ok {
return Decimal{}, fmt.Errorf("can't convert %s to decimal", value)
}
val := Decimal{
value: dValue,
exp: exp,
fracDigits: fracDigitsDefault(exp),
}
if exp < -MaxFractionDigits {
val = val.rescale(-MaxFractionDigits)
}
return val, nil
}
// NewDecimalFromFloat converts a float64 to Decimal.
//
// Example:
//
// NewDecimalFromFloat(123.45678901234567).String() // output: "123.4567890123456"
// NewDecimalFromFloat(.00000000000000001).String() // output: "0.00000000000000001"
//
// NOTE: this will panic on NaN, +/-inf.
func NewDecimalFromFloat(value float64) Decimal {
floor := math.Floor(value)
// fast path, where float is an int.
if floor == value && !math.IsInf(value, 0) {
return NewDecimalFromInt(int64(value), 0)
}
str := strconv.FormatFloat(value, 'f', -1, 64)
dec, err := ParseDecimal(str)
if err != nil {
panic(err)
}
return dec
}
// NewDecimalFromFloatWithExponent converts a float64 to Decimal, with an arbitrary
// number of fractional digits.
//
// Example:
//
// NewDecimalFromFloatWithExponent(123.456, -2).String() // output: "123.46"
//
func NewDecimalFromFloatWithExponent(value float64, exp int32) Decimal {
mul := math.Pow(10, -float64(exp))
floatValue := value * mul
if math.IsNaN(floatValue) || math.IsInf(floatValue, 0) {
panic(fmt.Sprintf("Cannot create a Decimal from %v", floatValue))
}
dValue := big.NewInt(round(floatValue))
return Decimal{
value: dValue,
exp: exp,
fracDigits: fracDigitsDefault(exp),
}
}
// rescale returns a rescaled version of the decimal. Returned
// decimal may be less precise if the given exponent is bigger
// than the initial exponent of the Decimal.
// NOTE: this will truncate, NOT round
//
// Example:
//
// d := New(12345, -4)
// d2 := d.rescale(-1)
// d3 := d2.rescale(-4)
// println(d1)
// println(d2)
// println(d3)
//
// Output:
//
// 1.2345
// 1.2
// 1.2000
//
func (d Decimal) rescale(exp int32) Decimal {
d.ensureInitialized()
if exp < -MaxFractionDigits-1 {
// Limit the number of digits but we can not call Round here because it is called by Round.
// Limit it to MaxFractionDigits + 1 to make sure the final result is correct.
exp = -MaxFractionDigits - 1
}
// Must convert exps to float64 before - to prevent overflow.
diff := math.Abs(float64(exp) - float64(d.exp))
value := new(big.Int).Set(d.value)
expScale := new(big.Int).Exp(tenInt, big.NewInt(int64(diff)), nil)
if exp > d.exp {
value = value.Quo(value, expScale)
} else if exp < d.exp {
value = value.Mul(value, expScale)
}
return Decimal{
value: value,
exp: exp,
fracDigits: d.fracDigits,
}
}
// Abs returns the absolute value of the decimal.
func (d Decimal) Abs() Decimal {
d.ensureInitialized()
d2Value := new(big.Int).Abs(d.value)
return Decimal{
value: d2Value,
exp: d.exp,
fracDigits: d.fracDigits,
}
}
// Add returns d + d2.
func (d Decimal) Add(d2 Decimal) Decimal {
baseExp := min(d.exp, d2.exp)
rd := d.rescale(baseExp)
rd2 := d2.rescale(baseExp)
d3Value := new(big.Int).Add(rd.value, rd2.value)
return Decimal{
value: d3Value,
exp: baseExp,
fracDigits: fracDigitsPlus(d.fracDigits, d2.fracDigits),
}
}
// Sub returns d - d2.
func (d Decimal) Sub(d2 Decimal) Decimal {
baseExp := min(d.exp, d2.exp)
rd := d.rescale(baseExp)
rd2 := d2.rescale(baseExp)
d3Value := new(big.Int).Sub(rd.value, rd2.value)
return Decimal{
value: d3Value,
exp: baseExp,
fracDigits: fracDigitsPlus(d.fracDigits, d2.fracDigits),
}
}
// Mul returns d * d2.
func (d Decimal) Mul(d2 Decimal) Decimal {
d.ensureInitialized()
d2.ensureInitialized()
expInt64 := int64(d.exp) + int64(d2.exp)
if expInt64 > math.MaxInt32 || expInt64 < math.MinInt32 {
// It is better to panic than to give incorrect results, as
// decimals are usually used for money.
panic(fmt.Sprintf("exponent %v overflows an int32!", expInt64))
}
d3Value := new(big.Int).Mul(d.value, d2.value)
val := Decimal{
value: d3Value,
exp: int32(expInt64),
fracDigits: fracDigitsMul(d.fracDigits, d2.fracDigits),
}
if val.exp < -(MaxFractionDigits) {
val = val.Round(MaxFractionDigits)
}
return val
}
// Div returns d / d2. If it doesn't divide exactly, the result will have
// DivisionPrecision digits after the decimal point.
func (d Decimal) Div(d2 Decimal) Decimal {
// Division is hard, use Rat to do it.
ratNum := d.Rat()
ratDenom := d2.Rat()
quoRat := big.NewRat(0, 1).Quo(ratNum, ratDenom)
// Converting from Rat to Decimal inefficiently for now.
ret, err := ParseDecimal(quoRat.FloatString(MaxFractionDigits + 1))
if err != nil {
panic(err) // This should never happen.
}
// To pass test "2 / 3 * 3 < 2" -> "1".
ret = ret.Truncate(MaxFractionDigits)
ret.fracDigits = fracDigitsDiv(d.fracDigits)
return ret
}
// Cmp compares the numbers represented by d and d2, and returns:
//
// -1 if d < d2
// 0 if d == d2
// +1 if d > d2
//
func (d Decimal) Cmp(d2 Decimal) int {
baseExp := min(d.exp, d2.exp)
rd := d.rescale(baseExp)
rd2 := d2.rescale(baseExp)
return rd.value.Cmp(rd2.value)
}
// Equals returns whether the numbers represented by d and d2 are equal.
func (d Decimal) Equals(d2 Decimal) bool {
return d.Cmp(d2) == 0
}
// Exponent returns the exponent, or scale component of the decimal.
func (d Decimal) Exponent() int32 {
return d.exp
}
// FracDigits returns the number of fractional digits of the decimal.
func (d Decimal) FracDigits() int32 {
return d.fracDigits
}
// IntPart returns the integer component of the decimal.
func (d Decimal) IntPart() int64 {
scaledD := d.rescale(0)
return scaledD.value.Int64()
}
// Rat returns a rational number representation of the decimal.
func (d Decimal) Rat() *big.Rat {
d.ensureInitialized()
if d.exp <= 0 {
// It must negate after casting to prevent int32 overflow.
denom := new(big.Int).Exp(tenInt, big.NewInt(-int64(d.exp)), nil)
return new(big.Rat).SetFrac(d.value, denom)
}
mul := new(big.Int).Exp(tenInt, big.NewInt(int64(d.exp)), nil)
num := new(big.Int).Mul(d.value, mul)
return new(big.Rat).SetFrac(num, oneInt)
}
// Float64 returns the nearest float64 value for d and a bool indicating
// whether f represents d exactly.
// For more details, see the documentation for big.Rat.Float64.
func (d Decimal) Float64() (f float64, exact bool) {
return d.Rat().Float64()
}
// String returns the string representation of the decimal
// with the fixed point.
//
// Example:
//
// d := New(-12345, -3)
// println(d.String())
//
// Output:
//
// -12.345
//
func (d Decimal) String() string {
return d.StringFixed(d.fracDigits)
}
// StringFixed returns a rounded fixed-point string with places digits after
// the decimal point.
//
// Example:
//
// NewFromFloat(0).StringFixed(2) // output: "0.00"
// NewFromFloat(0).StringFixed(0) // output: "0"
// NewFromFloat(5.45).StringFixed(0) // output: "5"
// NewFromFloat(5.45).StringFixed(1) // output: "5.5"
// NewFromFloat(5.45).StringFixed(2) // output: "5.45"
// NewFromFloat(5.45).StringFixed(3) // output: "5.450"
// NewFromFloat(545).StringFixed(-1) // output: "550"
//
func (d Decimal) StringFixed(places int32) string {
rounded := d.Round(places)
return rounded.string(false)
}
// Round rounds the decimal to places decimal places.
// If places < 0, it will round the integer part to the nearest 10^(-places).
//
// Example:
//
// NewFromFloat(5.45).Round(1).String() // output: "5.5"
// NewFromFloat(545).Round(-1).String() // output: "550"
//
func (d Decimal) Round(places int32) Decimal {
// Truncate to places + 1.
ret := d.rescale(-places - 1)
// Add sign(d) * 0.5.
if ret.value.Sign() < 0 {
ret.value.Sub(ret.value, fiveInt)
} else {
ret.value.Add(ret.value, fiveInt)
}
// Floor for positive numbers, Ceil for negative numbers.
_, m := ret.value.DivMod(ret.value, tenInt, new(big.Int))
ret.exp++
if ret.value.Sign() < 0 && m.Cmp(zeroInt) != 0 {
ret.value.Add(ret.value, oneInt)
}
ret.fracDigits = places
return ret
}
// Floor returns the nearest integer value less than or equal to d.
func (d Decimal) Floor() Decimal {
d.ensureInitialized()
exp := big.NewInt(10)
// It must negate after casting to prevent int32 overflow.
exp.Exp(exp, big.NewInt(-int64(d.exp)), nil)
z := new(big.Int).Div(d.value, exp)
return Decimal{value: z, exp: 0}
}
// Ceil returns the nearest integer value greater than or equal to d.
func (d Decimal) Ceil() Decimal {
d.ensureInitialized()
exp := big.NewInt(10)
// It must negate after casting to prevent int32 overflow.
exp.Exp(exp, big.NewInt(-int64(d.exp)), nil)
z, m := new(big.Int).DivMod(d.value, exp, new(big.Int))
if m.Cmp(zeroInt) != 0 {
z.Add(z, oneInt)
}
return Decimal{value: z, exp: 0}
}
// Truncate truncates off digits from the number, without rounding.
//
// NOTE: precision is the last digit that will not be truncated (must be >= 0).
//
// Example:
//
// decimal.NewFromString("123.456").Truncate(2).String() // "123.45"
//
func (d Decimal) Truncate(precision int32) Decimal {
d.ensureInitialized()
if precision >= 0 && -precision > d.exp {
d = d.rescale(-precision)
}
d.fracDigits = precision
return d
}
// UnmarshalJSON implements the json.Unmarshaler interface.
func (d *Decimal) UnmarshalJSON(decimalBytes []byte) error {
str, err := unquoteIfQuoted(decimalBytes)
if err != nil {
return fmt.Errorf("Error decoding string '%s': %s", decimalBytes, err)
}
decimal, err := ParseDecimal(str)
*d = decimal
if err != nil {
return fmt.Errorf("Error decoding string '%s': %s", str, err)
}
return nil
}
// MarshalJSON implements the json.Marshaler interface.
func (d Decimal) MarshalJSON() ([]byte, error) {
str := "\"" + d.String() + "\""
return []byte(str), nil
}
// Scan implements the sql.Scanner interface for database deserialization.
func (d *Decimal) Scan(value interface{}) error {
str, err := unquoteIfQuoted(value)
if err != nil {
return err
}
*d, err = ParseDecimal(str)
return err
}
// Value implements the driver.Valuer interface for database serialization.
func (d Decimal) Value() (driver.Value, error) {
return d.String(), nil
}
// BigIntValue returns the *bit.Int value member of decimal.
func (d Decimal) BigIntValue() *big.Int {
return d.value
}
// UnmarshalText implements the encoding.TextUnmarshaler interface for XML
// deserialization.
func (d *Decimal) UnmarshalText(text []byte) error {
str := string(text)
dec, err := ParseDecimal(str)
*d = dec
if err != nil {
return fmt.Errorf("Error decoding string '%s': %s", str, err)
}
return nil
}
// MarshalText implements the encoding.TextMarshaler interface for XML
// serialization.
func (d Decimal) MarshalText() (text []byte, err error) {
return []byte(d.String()), nil
}
// StringScaled first scales the decimal then calls .String() on it.
// NOTE: buggy, unintuitive, and DEPRECATED! Use StringFixed instead.
func (d Decimal) StringScaled(exp int32) string {
return d.rescale(exp).String()
}
func (d Decimal) string(trimTrailingZeros bool) string {
if d.exp >= 0 {
return d.rescale(0).value.String()
}
abs := new(big.Int).Abs(d.value)
str := abs.String()
var intPart, fractionalPart string
// this cast to int will cause bugs if d.exp == INT_MIN
// and you are on a 32-bit machine. Won't fix this super-edge case.
dExpInt := int(d.exp)
if len(str) > -dExpInt {
intPart = str[:len(str)+dExpInt]
fractionalPart = str[len(str)+dExpInt:]
} else {
intPart = "0"
num0s := -dExpInt - len(str)
fractionalPart = strings.Repeat("0", num0s) + str
}
if trimTrailingZeros {
i := len(fractionalPart) - 1
for ; i >= 0; i-- {
if fractionalPart[i] != '0' {
break
}
}
fractionalPart = fractionalPart[:i+1]
}
number := intPart
if len(fractionalPart) > 0 {
number += "." + fractionalPart
}
if d.value.Sign() < 0 {
return "-" + number
}
return number
}
func (d *Decimal) ensureInitialized() {
if d.value == nil {
d.value = new(big.Int)
}
}
func min(x, y int32) int32 {
if x >= y {
return y
}
return x
}
func max(x, y int32) int32 {
if x >= y {
return x
}
return y
}
func round(n float64) int64 {
if n < 0 {
return int64(n - 0.5)
}
return int64(n + 0.5)
}
func unquoteIfQuoted(value interface{}) (string, error) {
bytes, ok := value.([]byte)
if !ok {
return "", fmt.Errorf("Could not convert value '%+v' to byte array",
value)
}
// If the amount is quoted, strip the quotes.
if len(bytes) > 2 && bytes[0] == '"' && bytes[len(bytes)-1] == '"' {
bytes = bytes[1 : len(bytes)-1]
}
return string(bytes), nil
}
func fracDigitsDefault(exp int32) int32 {
if exp < 0 {
return min(MaxFractionDigits, -exp)
}
return 0
}
func fracDigitsPlus(x, y int32) int32 {
return max(x, y)
}
func fracDigitsDiv(x int32) int32 {
return min(x+DivIncreasePrecision, MaxFractionDigits)
}
func fracDigitsMul(a, b int32) int32 {
return min(MaxFractionDigits, a+b)
}