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