Hein
337af294f3
Fixes GO-2026-6629 (golang.org/x/text precis panic). Bumps bun and bun/dialect/pgdialect together to v1.3.0; go directive now 1.26.0.
1486 lines
42 KiB
Go
1486 lines
42 KiB
Go
// Package decimal implements an arbitrary precision fixed-point decimal.
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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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// To use Decimal as part of a struct:
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//
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// type StructName struct {
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// Number Decimal
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// }
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//
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// Note: This can "only" represent numbers with a maximum of 2^31 digits after the decimal point.
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package decimal
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import (
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"fmt"
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"math"
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"math/big"
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"math/bits"
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"regexp"
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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: "0.6666666666666667"
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// d2 := decimal.NewFromFloat(2).Div(decimal.NewFromFloat(30000))
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// d2.String() // output: "0.0000666666666667"
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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: "0.667"
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var DivisionPrecision = 16
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// PowPrecisionNegativeExponent specifies the number of digits after the decimal point in the results of
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// Pow, PowInt32 and PowBigInt for negative or non-integer exponents. A result that would round to 0 keeps
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// PowPrecisionNegativeExponent significant digits instead (at least one).
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// PowWithPrecision is not affected, it takes the precision as an argument.
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//
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// Example:
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//
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// d1, err := decimal.NewFromFloat(15.2).PowInt32(-2)
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// d1.String() // output: "0.0043282548476454"
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//
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// decimal.PowPrecisionNegativeExponent = 24
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// d2, err := decimal.NewFromFloat(15.2).PowInt32(-2)
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// d2.String() // output: "0.004328254847645429362881"
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var PowPrecisionNegativeExponent = 16
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// MarshalJSONWithoutQuotes should be set to true if you want the decimal to
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// be JSON marshaled as a number, instead of as a string.
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// WARNING: this is dangerous for decimals with many digits, since many JSON
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// unmarshallers (ex: Javascript's) will unmarshal JSON numbers to IEEE 754
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// double-precision floating point numbers, which means you can potentially
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// silently lose precision.
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var MarshalJSONWithoutQuotes = false
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// TrimTrailingZeros specifies whether trailing zeroes should be trimmed from a string representation of decimal.
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// If set to true, trailing zeroes will be truncated (2.00 -> 2, 3.11 -> 3.11, 13.000 -> 13),
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// otherwise trailing zeroes will be preserved (2.00 -> 2.00, 3.11 -> 3.11, 13.000 -> 13.000).
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// Setting this value to false can be useful for APIs where exact decimal string representation matters.
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var TrimTrailingZeros = true
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// UseScientificNotation specifies whether scientific notation should be used when a decimal is turned
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// into a string that has a "negative" precision.
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//
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// For example, 1200 rounded to the nearest 100 cannot accurately be shown as "1200" because the last two
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// digits are unknown. With this set to true, that number would be expressed as "1.2E3" instead.
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var UseScientificNotation = false
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// ExpMaxIterations specifies the maximum number of iterations needed to calculate
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// precise natural exponent value using ExpHullAbrham method.
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var ExpMaxIterations = 1000
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// MaxDecodeExponent is the largest exponent magnitude that NewFromString and UnmarshalBinary accept,
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// and so UnmarshalJSON, UnmarshalText, Scan, GobDecode, DecodeSpanner and their NullDecimal variants too.
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// Operations like String, Add and Float64 take time and memory that grow with the exponent, so without
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// this limit a short input like "1e-2000000000" can stall the process or exhaust its memory.
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// The default covers the float64 and IEEE 754 decimal128 exponent ranges.
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//
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// Values created with New, NewFromBigInt or arithmetic are not checked, so they may not decode back from
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// their own String or MarshalBinary output. The limit does not bound the cost of Pow or ExpTaylor
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// arguments or of very long inputs; validate those separately.
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//
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// Set it once at program start, before any decoding. Raise it only for trusted input.
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var MaxDecodeExponent = 10000
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// Zero constant, to make computations faster.
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// Zero should never be compared with == or != directly, please use decimal.Equal or decimal.Cmp instead.
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var Zero = Decimal{}
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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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// NOTE(vadim): 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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}
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func (d Decimal) getValue() *big.Int {
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if d.value == nil {
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return zeroInt
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}
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return d.value
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}
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// New returns a new fixed-point decimal, value * 10 ^ exp.
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func New(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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}
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}
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// NewFromInt converts an int64 to Decimal.
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//
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// Example:
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//
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// NewFromInt(123).String() // output: "123"
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// NewFromInt(-10).String() // output: "-10"
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func NewFromInt(value int64) Decimal {
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return Decimal{
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value: big.NewInt(value),
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exp: 0,
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}
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}
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// NewFromInt32 converts an int32 to Decimal.
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//
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// Example:
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//
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// NewFromInt(123).String() // output: "123"
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// NewFromInt(-10).String() // output: "-10"
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func NewFromInt32(value int32) Decimal {
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return Decimal{
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value: big.NewInt(int64(value)),
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exp: 0,
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}
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}
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// NewFromUint64 converts an uint64 to Decimal.
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//
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// Example:
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//
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// NewFromUint64(123).String() // output: "123"
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func NewFromUint64(value uint64) Decimal {
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return Decimal{
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value: new(big.Int).SetUint64(value),
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exp: 0,
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}
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}
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// NewFromBigInt returns a new Decimal from a big.Int, value * 10 ^ exp
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func NewFromBigInt(value *big.Int, exp int32) Decimal {
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return Decimal{
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value: new(big.Int).Set(value),
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exp: exp,
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}
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}
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// NewFromBigRat returns a new Decimal from a big.Rat. The numerator and
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// denominator are divided and rounded to the given precision.
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//
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// Example:
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//
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// d1 := NewFromBigRat(big.NewRat(0, 1), 0) // output: "0"
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// d2 := NewFromBigRat(big.NewRat(4, 5), 1) // output: "0.8"
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// d3 := NewFromBigRat(big.NewRat(1000, 3), 3) // output: "333.333"
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// d4 := NewFromBigRat(big.NewRat(2, 7), 4) // output: "0.2857"
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func NewFromBigRat(value *big.Rat, precision int32) Decimal {
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return Decimal{
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value: new(big.Int).Set(value.Num()),
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exp: 0,
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}.DivRound(Decimal{
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value: new(big.Int).Set(value.Denom()),
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exp: 0,
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}, precision)
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}
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// NewFromString returns a new Decimal from a string representation.
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// Trailing zeroes are not trimmed.
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//
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// Example:
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//
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// d, err := NewFromString("-123.45")
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// d2, err := NewFromString(".0001")
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// d3, err := NewFromString("1.47000")
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func NewFromString(value string) (Decimal, error) {
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originalInput := value
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var exp int64
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// Check if number is using scientific notation and find dots
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eIndex := -1
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pIndex := -1
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for i, r := range value {
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if r == 'E' || r == 'e' {
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if eIndex > -1 {
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return Decimal{}, fmt.Errorf("can't convert %s to decimal: multiple 'E' characters found", value)
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}
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eIndex = i
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continue
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}
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if r == '.' {
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if pIndex > -1 {
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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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pIndex = i
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}
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}
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if eIndex != -1 {
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expInt, err := strconv.ParseInt(value[eIndex+1:], 10, 32)
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if err != nil {
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if e, ok := err.(*strconv.NumError); ok && e.Err == strconv.ErrRange {
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return Decimal{}, fmt.Errorf("can't convert %s to decimal: fractional part too long", value)
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}
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return Decimal{}, fmt.Errorf("can't convert %s to decimal: exponent is not numeric", value)
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}
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value = value[:eIndex]
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exp = expInt
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}
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numLen := len(value)
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if pIndex != -1 {
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if pIndex+1 < len(value) && (value[pIndex+1] == '-' || value[pIndex+1] == '+') {
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// ParseInt and SetString would accept the sign once the point is removed, as in ".-5"
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return Decimal{}, fmt.Errorf("can't convert %s to decimal", value)
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}
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numLen--
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expInt := -len(value[pIndex+1:])
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exp += int64(expInt)
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}
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var dValue *big.Int
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// parsing in an int64 is faster than new(big.Int).SetString so this is just a shortcut for strings we know won't overflow
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if numLen <= 18 {
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parsed64, ok := parseInt64SkipIndex(value, pIndex)
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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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dValue = big.NewInt(parsed64)
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} else {
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intString := value
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if pIndex != -1 {
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intString = value[:pIndex] + value[pIndex+1:]
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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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}
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if exp < math.MinInt32 || exp > math.MaxInt32 {
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// NOTE(vadim): I doubt a string could realistically be this long
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return Decimal{}, fmt.Errorf("can't convert %s to decimal: fractional part too long", originalInput)
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}
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if exp > int64(MaxDecodeExponent) || exp < -int64(MaxDecodeExponent) {
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return Decimal{}, fmt.Errorf("can't convert %s to decimal: exponent %d exceeds MaxDecodeExponent (%d)", originalInput, exp, MaxDecodeExponent)
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}
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return Decimal{
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value: dValue,
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exp: int32(exp),
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}, nil
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}
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// parseInt64SkipIndex parses s without the byte at index skip as strconv.ParseInt(s, 10, 64) would,
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// s must have at most 18 other bytes so that the result can't overflow.
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func parseInt64SkipIndex(s string, skip int) (int64, bool) {
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i, neg := 0, false
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if len(s) > 0 && skip != 0 && (s[0] == '+' || s[0] == '-') {
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i, neg = 1, s[0] == '-'
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}
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var n int64
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digits := 0
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for ; i < len(s); i++ {
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if i == skip {
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continue
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}
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c := s[i]
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if c < '0' || c > '9' {
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return 0, false
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}
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n = n*10 + int64(c-'0')
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digits++
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}
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if neg {
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n = -n
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}
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return n, digits > 0
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}
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// NewFromFormattedString returns a new Decimal from a formatted string representation.
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// The second argument - replRegexp, is a regular expression that is used to find characters that should be
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// removed from given decimal string representation. All matched characters will be replaced with an empty string.
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//
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// Example:
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//
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// r := regexp.MustCompile("[$,]")
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// d1, err := NewFromFormattedString("$5,125.99", r)
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//
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// r2 := regexp.MustCompile("[_]")
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// d2, err := NewFromFormattedString("1_000_000", r2)
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//
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// r3 := regexp.MustCompile("[USD\\s]")
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// d3, err := NewFromFormattedString("5000 USD", r3)
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func NewFromFormattedString(value string, replRegexp *regexp.Regexp) (Decimal, error) {
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parsedValue := replRegexp.ReplaceAllString(value, "")
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d, err := NewFromString(parsedValue)
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if err != nil {
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return Decimal{}, err
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}
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return d, nil
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}
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// RequireFromString returns a new Decimal from a string representation
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// or panics if NewFromString had returned an error.
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//
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// Example:
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//
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// d := RequireFromString("-123.45")
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// d2 := RequireFromString(".0001")
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func RequireFromString(value string) Decimal {
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dec, err := NewFromString(value)
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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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// NewFromFloat converts a float64 to Decimal.
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//
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// The result is the shortest decimal that converts back to the same float64,
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// the same number that strconv.FormatFloat(value, 'f', -1, 64) prints.
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// This is typically 15 digits, but may be more in some cases.
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// See https://www.exploringbinary.com/decimal-precision-of-binary-floating-point-numbers/ for more information.
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//
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// This is not always the exact value stored in the float. Whole numbers larger
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// than 2^53 can change: float64(1<<62) is exactly 4611686018427387904, but
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// NewFromFloat returns 4611686018427388000. To convert whole numbers exactly,
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// use NewFromFloatWithExponent(value, 0).
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//
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// For slightly faster conversion, use NewFromFloatWithExponent where you can specify the precision in absolute terms.
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//
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// NOTE: this will panic on NaN, +/-inf
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func NewFromFloat(value float64) Decimal {
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if value == 0 {
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return New(0, 0)
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}
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return newFromFloat(value, math.Float64bits(value), &float64info)
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}
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// NewFromFloat32 converts a float32 to Decimal.
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//
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// The result is the shortest decimal that converts back to the same float32.
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// This is typically 6-8 digits depending on the input.
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// See https://www.exploringbinary.com/decimal-precision-of-binary-floating-point-numbers/ for more information.
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//
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// As with NewFromFloat, whole numbers larger than 2^24 can change. To convert
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// them exactly, use NewFromFloatWithExponent(float64(value), 0).
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//
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// For slightly faster conversion, use NewFromFloatWithExponent where you can specify the precision in absolute terms.
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//
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// NOTE: this will panic on NaN, +/-inf
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func NewFromFloat32(value float32) Decimal {
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if value == 0 {
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return New(0, 0)
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}
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// XOR is workaround for https://github.com/golang/go/issues/26285
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a := math.Float32bits(value) ^ 0x80808080
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return newFromFloat(float64(value), uint64(a)^0x80808080, &float32info)
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}
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func newFromFloat(val float64, bits uint64, flt *floatInfo) Decimal {
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if math.IsNaN(val) || math.IsInf(val, 0) {
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panic(fmt.Sprintf("Cannot create a Decimal from %v", val))
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}
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exp := int(bits>>flt.mantbits) & (1<<flt.expbits - 1)
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mant := bits & (uint64(1)<<flt.mantbits - 1)
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switch exp {
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case 0:
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// denormalized
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exp++
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default:
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// add implicit top bit
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mant |= uint64(1) << flt.mantbits
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}
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exp += flt.bias
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var d decimal
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d.Assign(mant)
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d.Shift(exp - int(flt.mantbits))
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d.neg = bits>>(flt.expbits+flt.mantbits) != 0
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roundShortest(&d, mant, exp, flt)
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// If less than 19 digits, we can do calculation in an int64.
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if d.nd < 19 {
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tmp := int64(0)
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m := int64(1)
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for i := d.nd - 1; i >= 0; i-- {
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tmp += m * int64(d.d[i]-'0')
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m *= 10
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}
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if d.neg {
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tmp *= -1
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}
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return Decimal{value: big.NewInt(tmp), exp: int32(d.dp) - int32(d.nd)}
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}
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dValue := new(big.Int)
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dValue, ok := dValue.SetString(string(d.d[:d.nd]), 10)
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if ok {
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return Decimal{value: dValue, exp: int32(d.dp) - int32(d.nd)}
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}
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return NewFromFloatWithExponent(val, int32(d.dp)-int32(d.nd))
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}
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// NewFromFloatWithExponent 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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|
// NewFromFloatWithExponent(123.456, -2).String() // output: "123.46"
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func NewFromFloatWithExponent(value float64, exp int32) Decimal {
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if math.IsNaN(value) || math.IsInf(value, 0) {
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panic(fmt.Sprintf("Cannot create a Decimal from %v", value))
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}
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bits := math.Float64bits(value)
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mant := bits & (1<<52 - 1)
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exp2 := int32((bits >> 52) & (1<<11 - 1))
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sign := bits >> 63
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if exp2 == 0 {
|
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// specials
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if mant == 0 {
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return Decimal{}
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}
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// subnormal
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exp2++
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} else {
|
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// normal
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mant |= 1 << 52
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}
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exp2 -= 1023 + 52
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|
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// normalizing base-2 values
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|
for mant&1 == 0 {
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mant = mant >> 1
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exp2++
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}
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|
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// maximum number of fractional base-10 digits to represent 2^N exactly cannot be more than -N if N<0
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if exp < 0 && exp < exp2 {
|
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if exp2 < 0 {
|
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exp = exp2
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} else {
|
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exp = 0
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}
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}
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|
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// representing 10^M * 2^N as 5^M * 2^(M+N)
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exp2 -= exp
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temp := big.NewInt(1)
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|
dMant := big.NewInt(int64(mant))
|
|
|
|
// applying 5^M
|
|
if exp > 0 {
|
|
temp = temp.SetInt64(int64(exp))
|
|
temp = temp.Exp(fiveInt, temp, nil)
|
|
} else if exp < 0 {
|
|
temp = temp.SetInt64(-int64(exp))
|
|
temp = temp.Exp(fiveInt, temp, nil)
|
|
dMant = dMant.Mul(dMant, temp)
|
|
temp = temp.SetUint64(1)
|
|
}
|
|
|
|
// applying 2^(M+N)
|
|
if exp2 > 0 {
|
|
dMant = dMant.Lsh(dMant, uint(exp2))
|
|
} else if exp2 < 0 {
|
|
temp = temp.Lsh(temp, uint(-exp2))
|
|
}
|
|
|
|
// rounding and downscaling
|
|
if exp > 0 || exp2 < 0 {
|
|
halfDown := new(big.Int).Rsh(temp, 1)
|
|
dMant = dMant.Add(dMant, halfDown)
|
|
dMant = dMant.Quo(dMant, temp)
|
|
}
|
|
|
|
if sign == 1 {
|
|
dMant = dMant.Neg(dMant)
|
|
}
|
|
|
|
return Decimal{
|
|
value: dMant,
|
|
exp: exp,
|
|
}
|
|
}
|
|
|
|
// Copy returns a copy of decimal with the same value and exponent, but a different pointer to value.
|
|
func (d Decimal) Copy() Decimal {
|
|
return Decimal{
|
|
value: new(big.Int).Set(d.getValue()),
|
|
exp: d.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 {
|
|
if d.exp == exp {
|
|
return Decimal{
|
|
new(big.Int).Set(d.getValue()),
|
|
d.exp,
|
|
}
|
|
}
|
|
|
|
// NOTE(vadim): must convert exps to float64 before - to prevent overflow
|
|
diff := math.Abs(float64(exp) - float64(d.exp))
|
|
value := new(big.Int)
|
|
if exp > d.exp {
|
|
value.Quo(d.getValue(), pow10(int64(diff)))
|
|
if value.Sign() == 0 && d.getValue().Sign() != 0 {
|
|
// reflect.DeepEqual tells an empty word slice from nil, keep the empty one that
|
|
// dividing a copy of d.value in place used to leave
|
|
value.SetBits([]big.Word{})
|
|
}
|
|
} else {
|
|
value.Mul(d.getValue(), pow10(int64(diff)))
|
|
}
|
|
|
|
return Decimal{
|
|
value: value,
|
|
exp: exp,
|
|
}
|
|
}
|
|
|
|
// Abs returns the absolute value of the decimal.
|
|
func (d Decimal) Abs() Decimal {
|
|
if !d.IsNegative() {
|
|
return d
|
|
}
|
|
d2Value := new(big.Int).Abs(d.getValue())
|
|
return Decimal{
|
|
value: d2Value,
|
|
exp: d.exp,
|
|
}
|
|
}
|
|
|
|
// Add returns d + d2.
|
|
func (d Decimal) Add(d2 Decimal) Decimal {
|
|
// rescale returns a new value, so the sum can be stored in it
|
|
if d.exp < d2.exp {
|
|
r := d2.rescale(d.exp)
|
|
r.value.Add(d.getValue(), r.value)
|
|
return r
|
|
} else if d.exp > d2.exp {
|
|
r := d.rescale(d2.exp)
|
|
r.value.Add(r.value, d2.getValue())
|
|
return r
|
|
}
|
|
|
|
d3Value := new(big.Int).Add(d.getValue(), d2.getValue())
|
|
return Decimal{
|
|
value: d3Value,
|
|
exp: d.exp,
|
|
}
|
|
}
|
|
|
|
// Sub returns d - d2.
|
|
func (d Decimal) Sub(d2 Decimal) Decimal {
|
|
// rescale returns a new value, so the difference can be stored in it
|
|
if d.exp < d2.exp {
|
|
r := d2.rescale(d.exp)
|
|
r.value.Sub(d.getValue(), r.value)
|
|
return r
|
|
} else if d.exp > d2.exp {
|
|
r := d.rescale(d2.exp)
|
|
r.value.Sub(r.value, d2.getValue())
|
|
return r
|
|
}
|
|
|
|
d3Value := new(big.Int).Sub(d.getValue(), d2.getValue())
|
|
return Decimal{
|
|
value: d3Value,
|
|
exp: d.exp,
|
|
}
|
|
}
|
|
|
|
// Neg returns -d.
|
|
func (d Decimal) Neg() Decimal {
|
|
val := new(big.Int).Neg(d.getValue())
|
|
return Decimal{
|
|
value: val,
|
|
exp: d.exp,
|
|
}
|
|
}
|
|
|
|
// Mul returns d * d2.
|
|
func (d Decimal) Mul(d2 Decimal) Decimal {
|
|
expInt64 := int64(d.exp) + int64(d2.exp)
|
|
if expInt64 > math.MaxInt32 || expInt64 < math.MinInt32 {
|
|
// NOTE(vadim): better to panic than 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.getValue(), d2.getValue())
|
|
return Decimal{
|
|
value: d3Value,
|
|
exp: int32(expInt64),
|
|
}
|
|
}
|
|
|
|
// Shift shifts the decimal in base 10.
|
|
// It shifts left when shift is positive and right if shift is negative.
|
|
// In simpler terms, the given value for shift is added to the exponent
|
|
// of the decimal.
|
|
// Shift panics if the resulting exponent does not fit in an int32.
|
|
func (d Decimal) Shift(shift int32) Decimal {
|
|
exp := int64(d.exp) + int64(shift)
|
|
if exp > math.MaxInt32 || exp < math.MinInt32 {
|
|
panic(fmt.Sprintf("exponent %v overflows an int32!", exp))
|
|
}
|
|
value := d.getValue()
|
|
if value.Sign() == 0 {
|
|
// a copy of zero has a nil word slice, which reflect.DeepEqual tells from an empty one
|
|
value = zeroInt
|
|
}
|
|
return Decimal{
|
|
value: value,
|
|
exp: int32(exp),
|
|
}
|
|
}
|
|
|
|
// 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 {
|
|
return d.DivRound(d2, int32(DivisionPrecision))
|
|
}
|
|
|
|
// QuoRem does division with remainder
|
|
// d.QuoRem(d2,precision) returns quotient q and remainder r such that
|
|
//
|
|
// d = d2 * q + r, q an integer multiple of 10^(-precision)
|
|
// 0 <= r < abs(d2) * 10 ^(-precision) if d>=0
|
|
// 0 >= r > -abs(d2) * 10 ^(-precision) if d<0
|
|
//
|
|
// Note that precision<0 is allowed as input.
|
|
func (d Decimal) QuoRem(d2 Decimal, precision int32) (Decimal, Decimal) {
|
|
return d.quoRem(d2, precision, nil)
|
|
}
|
|
|
|
// quoRem is QuoRem that also sets bb, if not nil, to the divisor in the units of the remainder.
|
|
func (d Decimal) quoRem(d2 Decimal, precision int32, bb *big.Int) (Decimal, Decimal) {
|
|
if d2.getValue().Sign() == 0 {
|
|
panic("decimal division by 0")
|
|
}
|
|
scale := -precision
|
|
e := int64(d.exp) - int64(d2.exp) - int64(scale)
|
|
if e > math.MaxInt32 || e < math.MinInt32 {
|
|
panic("overflow in decimal QuoRem")
|
|
}
|
|
if bb == nil {
|
|
bb = new(big.Int)
|
|
}
|
|
var aa big.Int
|
|
var scalerest int32
|
|
// d = a 10^ea
|
|
// d2 = b 10^eb
|
|
if e < 0 {
|
|
aa = *d.getValue()
|
|
bb.Mul(d2.getValue(), pow10(-e))
|
|
scalerest = d.exp
|
|
// now aa = a
|
|
// bb = b 10^(scale + eb - ea)
|
|
} else {
|
|
aa.Mul(d.getValue(), pow10(e))
|
|
*bb = *d2.getValue()
|
|
scalerest = scale + d2.exp
|
|
// now aa = a ^ (ea - eb - scale)
|
|
// bb = b
|
|
}
|
|
var q, r big.Int
|
|
q.QuoRem(&aa, bb, &r)
|
|
dq := Decimal{value: &q, exp: scale}
|
|
dr := Decimal{value: &r, exp: scalerest}
|
|
return dq, dr
|
|
}
|
|
|
|
// DivRound divides and rounds to a given precision
|
|
// i.e. to an integer multiple of 10^(-precision)
|
|
//
|
|
// for a positive quotient digit 5 is rounded up, away from 0
|
|
// if the quotient is negative then digit 5 is rounded down, away from 0
|
|
//
|
|
// Note that precision<0 is allowed as input.
|
|
func (d Decimal) DivRound(d2 Decimal, precision int32) Decimal {
|
|
// quoRem already checks initialization
|
|
var bb big.Int
|
|
q, r := d.quoRem(d2, precision, &bb)
|
|
// the actual rounding decision is based on comparing r*10^precision and d2/2,
|
|
// which is comparing 2*|r.value| and |bb|
|
|
var rv2 big.Int
|
|
rv2.Abs(r.getValue())
|
|
rv2.Lsh(&rv2, 1)
|
|
if rv2.CmpAbs(&bb) < 0 {
|
|
return q
|
|
}
|
|
|
|
if d.getValue().Sign()*d2.getValue().Sign() < 0 {
|
|
q.value.Sub(q.value, oneInt)
|
|
} else {
|
|
q.value.Add(q.value, oneInt)
|
|
}
|
|
return q
|
|
}
|
|
|
|
// Mod returns d % d2.
|
|
func (d Decimal) Mod(d2 Decimal) Decimal {
|
|
_, r := d.QuoRem(d2, 0)
|
|
return r
|
|
}
|
|
|
|
// NumDigits returns the number of digits of the decimal coefficient (d.Value)
|
|
func (d Decimal) NumDigits() int {
|
|
v := d.getValue()
|
|
if v.IsInt64() {
|
|
u := uint64(v.Int64())
|
|
if u == 0 {
|
|
return 1
|
|
}
|
|
if v.Sign() < 0 {
|
|
u = -u
|
|
}
|
|
// Not math.Log10, which rounds an exact 1eN like 1e15 down (see #420).
|
|
// bits.Len64(u)*1233>>12 is floor(log10(2^bits)), the digit count or one less.
|
|
n := bits.Len64(u) * 1233 >> 12
|
|
if u >= pow10Uint64[n] {
|
|
n++
|
|
}
|
|
return n
|
|
}
|
|
|
|
estimatedNumDigits := int(float64(v.BitLen()) / math.Log2(10))
|
|
|
|
// estimatedNumDigits (lg10) may be off by 1, need to verify
|
|
if v.CmpAbs(pow10(int64(estimatedNumDigits))) >= 0 {
|
|
return estimatedNumDigits + 1
|
|
}
|
|
|
|
return estimatedNumDigits
|
|
}
|
|
|
|
// IsInteger returns true when decimal can be represented as an integer value, otherwise, it returns false.
|
|
func (d Decimal) IsInteger() bool {
|
|
// The most typical case, all decimal with exponent higher or equal 0 can be represented as integer
|
|
if d.exp >= 0 {
|
|
return true
|
|
}
|
|
v := d.getValue()
|
|
if v.Sign() == 0 {
|
|
return true
|
|
}
|
|
if d.exp >= -18 && v.IsInt64() {
|
|
return v.Int64()%int64(pow10Uint64[-d.exp]) == 0
|
|
}
|
|
// When the exponent is negative we have to check every number after the decimal place
|
|
// If all of them are zeroes, we are sure that given decimal can be represented as an integer
|
|
var r big.Int
|
|
q := new(big.Int).Set(v)
|
|
for z := abs(d.exp); z > 0; z-- {
|
|
q.QuoRem(q, tenInt, &r)
|
|
if r.Cmp(zeroInt) != 0 {
|
|
return false
|
|
}
|
|
}
|
|
return true
|
|
}
|
|
|
|
// Abs calculates absolute value of any int32. Used for calculating absolute value of decimal's exponent.
|
|
func abs(n int32) int32 {
|
|
if n < 0 {
|
|
return -n
|
|
}
|
|
return n
|
|
}
|
|
|
|
// 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 {
|
|
if d.exp == d2.exp {
|
|
return d.getValue().Cmp(d2.getValue())
|
|
}
|
|
if s, s2 := d.Sign(), d2.Sign(); s != s2 {
|
|
if s > s2 {
|
|
return 1
|
|
}
|
|
return -1
|
|
} else if s == 0 {
|
|
return 0
|
|
}
|
|
|
|
var scaled big.Int
|
|
if d.exp < d2.exp {
|
|
return d.getValue().Cmp(scaled.Mul(d2.getValue(), pow10(int64(d2.exp)-int64(d.exp))))
|
|
}
|
|
return scaled.Mul(d.getValue(), pow10(int64(d.exp)-int64(d2.exp))).Cmp(d2.getValue())
|
|
}
|
|
|
|
// Compare 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) Compare(d2 Decimal) int {
|
|
return d.Cmp(d2)
|
|
}
|
|
|
|
// Equal returns whether the numbers represented by d and d2 are equal.
|
|
func (d Decimal) Equal(d2 Decimal) bool {
|
|
return d.Cmp(d2) == 0
|
|
}
|
|
|
|
// Equals returns whether the numbers represented by d and d2 are equal.
|
|
//
|
|
// Deprecated: Equals is deprecated, please use Equal method instead.
|
|
func (d Decimal) Equals(d2 Decimal) bool {
|
|
return d.Equal(d2)
|
|
}
|
|
|
|
// GreaterThan (GT) returns true when d is greater than d2.
|
|
func (d Decimal) GreaterThan(d2 Decimal) bool {
|
|
return d.Cmp(d2) == 1
|
|
}
|
|
|
|
// GreaterThanOrEqual (GTE) returns true when d is greater than or equal to d2.
|
|
func (d Decimal) GreaterThanOrEqual(d2 Decimal) bool {
|
|
cmp := d.Cmp(d2)
|
|
return cmp == 1 || cmp == 0
|
|
}
|
|
|
|
// LessThan (LT) returns true when d is less than d2.
|
|
func (d Decimal) LessThan(d2 Decimal) bool {
|
|
return d.Cmp(d2) == -1
|
|
}
|
|
|
|
// LessThanOrEqual (LTE) returns true when d is less than or equal to d2.
|
|
func (d Decimal) LessThanOrEqual(d2 Decimal) bool {
|
|
cmp := d.Cmp(d2)
|
|
return cmp == -1 || cmp == 0
|
|
}
|
|
|
|
// Sign returns:
|
|
//
|
|
// -1 if d < 0
|
|
// 0 if d == 0
|
|
// +1 if d > 0
|
|
func (d Decimal) Sign() int {
|
|
return d.getValue().Sign()
|
|
}
|
|
|
|
// IsPositive return
|
|
//
|
|
// true if d > 0
|
|
// false if d == 0
|
|
// false if d < 0
|
|
func (d Decimal) IsPositive() bool {
|
|
return d.Sign() == 1
|
|
}
|
|
|
|
// IsNegative return
|
|
//
|
|
// true if d < 0
|
|
// false if d == 0
|
|
// false if d > 0
|
|
func (d Decimal) IsNegative() bool {
|
|
return d.Sign() == -1
|
|
}
|
|
|
|
// IsZero return
|
|
//
|
|
// true if d == 0
|
|
// false if d > 0
|
|
// false if d < 0
|
|
func (d Decimal) IsZero() bool {
|
|
return d.Sign() == 0
|
|
}
|
|
|
|
// Exponent returns the exponent, or scale component of the decimal.
|
|
func (d Decimal) Exponent() int32 {
|
|
return d.exp
|
|
}
|
|
|
|
// Coefficient returns the coefficient of the decimal. It is scaled by 10^Exponent()
|
|
func (d Decimal) Coefficient() *big.Int {
|
|
// we copy the coefficient so that mutating the result does not mutate the Decimal.
|
|
return new(big.Int).Set(d.getValue())
|
|
}
|
|
|
|
// CoefficientInt64 returns the coefficient of the decimal as int64. It is scaled by 10^Exponent()
|
|
// If coefficient cannot be represented in an int64, the result will be undefined.
|
|
func (d Decimal) CoefficientInt64() int64 {
|
|
return d.getValue().Int64()
|
|
}
|
|
|
|
// IntPart returns the integer component of the decimal.
|
|
func (d Decimal) IntPart() int64 {
|
|
if v := d.getValue(); d.exp <= 0 && d.exp >= -18 && v.IsInt64() {
|
|
return v.Int64() / int64(pow10Uint64[-d.exp])
|
|
}
|
|
scaledD := d.rescale(0)
|
|
return scaledD.getValue().Int64()
|
|
}
|
|
|
|
// BigInt returns integer component of the decimal as a BigInt.
|
|
func (d Decimal) BigInt() *big.Int {
|
|
scaledD := d.rescale(0)
|
|
return scaledD.getValue()
|
|
}
|
|
|
|
// BigFloat returns decimal as BigFloat.
|
|
// Be aware that casting decimal to BigFloat might cause a loss of precision.
|
|
func (d Decimal) BigFloat() *big.Float {
|
|
f := &big.Float{}
|
|
f.SetString(d.String())
|
|
return f
|
|
}
|
|
|
|
// Rat returns a rational number representation of the decimal.
|
|
func (d Decimal) Rat() *big.Rat {
|
|
if d.exp <= 0 {
|
|
// NOTE(vadim): must negate after casting to prevent int32 overflow
|
|
return new(big.Rat).SetFrac(d.getValue(), pow10(-int64(d.exp)))
|
|
}
|
|
|
|
num := new(big.Int).Mul(d.getValue(), pow10(int64(d.exp)))
|
|
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) {
|
|
// Rat() materializes 10^|exp|, which takes forever for huge exponents.
|
|
// Values that far outside the float64 range don't need it: they always
|
|
// round to zero or overflow to infinity.
|
|
sign := d.Sign()
|
|
if sign == 0 {
|
|
return 0, true
|
|
}
|
|
// Both operands are exact here, so the division is correctly rounded like Rat().Float64(),
|
|
// and the result is exact when the 5^k part of 10^k divides the coefficient.
|
|
if v := d.getValue(); d.exp <= 0 && d.exp >= -22 && v.IsInt64() {
|
|
if i := v.Int64(); i >= -1<<53 && i <= 1<<53 {
|
|
return float64(i) / float64Pow10[-d.exp], i%pow5Int64[-d.exp] == 0
|
|
}
|
|
}
|
|
// |d| lies in [10^(magnitude-1), 10^magnitude). float64 spans roughly
|
|
// 1e-324..1e308, so ±400 is safely outside it with margin to spare.
|
|
magnitude := int64(d.NumDigits()) + int64(d.exp)
|
|
if magnitude < -400 {
|
|
return math.Copysign(0, float64(sign)), false
|
|
}
|
|
if magnitude > 400 {
|
|
return math.Inf(sign), false
|
|
}
|
|
|
|
return d.Rat().Float64()
|
|
}
|
|
|
|
// InexactFloat64 returns the nearest float64 value for d.
|
|
// It doesn't indicate if the returned value represents d exactly.
|
|
func (d Decimal) InexactFloat64() float64 {
|
|
f, _ := d.Float64()
|
|
return f
|
|
}
|
|
|
|
// 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.string(TrimTrailingZeros, UseScientificNotation)
|
|
}
|
|
|
|
// 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: "540"
|
|
//
|
|
// Regardless of the UseScientificNotation option, the returned string will never be in scientific notation.
|
|
func (d Decimal) StringFixed(places int32) string {
|
|
rounded := d.Round(places)
|
|
return rounded.string(false, false)
|
|
}
|
|
|
|
// StringFixedBank returns a banker rounded fixed-point string with places digits
|
|
// after the decimal point.
|
|
//
|
|
// Example:
|
|
//
|
|
// NewFromFloat(0).StringFixedBank(2) // output: "0.00"
|
|
// NewFromFloat(0).StringFixedBank(0) // output: "0"
|
|
// NewFromFloat(5.45).StringFixedBank(0) // output: "5"
|
|
// NewFromFloat(5.45).StringFixedBank(1) // output: "5.4"
|
|
// NewFromFloat(5.45).StringFixedBank(2) // output: "5.45"
|
|
// NewFromFloat(5.45).StringFixedBank(3) // output: "5.450"
|
|
// NewFromFloat(545).StringFixedBank(-1) // output: "540"
|
|
//
|
|
// Regardless of the UseScientificNotation option, the returned string will never be in scientific notation.
|
|
func (d Decimal) StringFixedBank(places int32) string {
|
|
rounded := d.RoundBank(places)
|
|
return rounded.string(false, false)
|
|
}
|
|
|
|
// StringFixedCash returns a Swedish/Cash rounded fixed-point string. For
|
|
// more details see the documentation at function RoundCash.
|
|
//
|
|
// Regardless of the UseScientificNotation option, the returned string will never be in scientific notation.
|
|
func (d Decimal) StringFixedCash(interval uint8) string {
|
|
rounded := d.RoundCash(interval)
|
|
return rounded.string(false, 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" (with UseScientificNotation false, "5.5E2" if true)
|
|
func (d Decimal) Round(places int32) Decimal {
|
|
if d.exp == -places {
|
|
return d
|
|
}
|
|
// 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)
|
|
}
|
|
|
|
// truncate towards zero
|
|
ret.value.Quo(ret.value, tenInt)
|
|
ret.exp++
|
|
|
|
return ret
|
|
}
|
|
|
|
// RoundCeil rounds the decimal towards +infinity.
|
|
//
|
|
// Example:
|
|
//
|
|
// NewFromFloat(545).RoundCeil(-2).String() // output: "600"
|
|
// NewFromFloat(500).RoundCeil(-2).String() // output: "500"
|
|
// NewFromFloat(1.1001).RoundCeil(2).String() // output: "1.11"
|
|
// NewFromFloat(-1.454).RoundCeil(1).String() // output: "-1.4"
|
|
func (d Decimal) RoundCeil(places int32) Decimal {
|
|
if d.exp >= -places {
|
|
return d.rescale(-places)
|
|
}
|
|
|
|
// q is d truncated to places, r is not 0 when digits were dropped and has the sign of d
|
|
var r big.Int
|
|
q := new(big.Int)
|
|
q.QuoRem(d.getValue(), pow10(-int64(places)-int64(d.exp)), &r)
|
|
if r.Sign() > 0 {
|
|
q.Add(q, oneInt)
|
|
} else if q.Sign() == 0 && r.Sign() != 0 {
|
|
// reflect.DeepEqual tells an empty word slice from nil, keep the empty one that
|
|
// rounding a nonzero value to zero used to leave
|
|
q.SetBits([]big.Word{})
|
|
}
|
|
|
|
return Decimal{value: q, exp: -places}
|
|
}
|
|
|
|
// RoundFloor rounds the decimal towards -infinity.
|
|
//
|
|
// Example:
|
|
//
|
|
// NewFromFloat(545).RoundFloor(-2).String() // output: "500"
|
|
// NewFromFloat(-500).RoundFloor(-2).String() // output: "-500"
|
|
// NewFromFloat(1.1001).RoundFloor(2).String() // output: "1.1"
|
|
// NewFromFloat(-1.454).RoundFloor(1).String() // output: "-1.5"
|
|
func (d Decimal) RoundFloor(places int32) Decimal {
|
|
if d.exp >= -places {
|
|
return d.rescale(-places)
|
|
}
|
|
|
|
// q is d truncated to places, r is not 0 when digits were dropped and has the sign of d
|
|
var r big.Int
|
|
q := new(big.Int)
|
|
q.QuoRem(d.getValue(), pow10(-int64(places)-int64(d.exp)), &r)
|
|
if r.Sign() < 0 {
|
|
q.Sub(q, oneInt)
|
|
} else if q.Sign() == 0 && r.Sign() != 0 {
|
|
// reflect.DeepEqual tells an empty word slice from nil, keep the empty one that
|
|
// rounding a nonzero value to zero used to leave
|
|
q.SetBits([]big.Word{})
|
|
}
|
|
|
|
return Decimal{value: q, exp: -places}
|
|
}
|
|
|
|
// RoundUp rounds the decimal away from zero.
|
|
//
|
|
// Example:
|
|
//
|
|
// NewFromFloat(545).RoundUp(-2).String() // output: "600"
|
|
// NewFromFloat(500).RoundUp(-2).String() // output: "500"
|
|
// NewFromFloat(1.1001).RoundUp(2).String() // output: "1.11"
|
|
// NewFromFloat(-1.454).RoundUp(1).String() // output: "-1.5"
|
|
func (d Decimal) RoundUp(places int32) Decimal {
|
|
if d.exp >= -places {
|
|
return d.rescale(-places)
|
|
}
|
|
|
|
// q is d truncated to places, r is not 0 when digits were dropped and has the sign of d
|
|
var r big.Int
|
|
q := new(big.Int)
|
|
q.QuoRem(d.getValue(), pow10(-int64(places)-int64(d.exp)), &r)
|
|
if r.Sign() > 0 {
|
|
q.Add(q, oneInt)
|
|
} else if r.Sign() < 0 {
|
|
q.Sub(q, oneInt)
|
|
}
|
|
|
|
return Decimal{value: q, exp: -places}
|
|
}
|
|
|
|
// RoundDown rounds the decimal towards zero.
|
|
//
|
|
// Example:
|
|
//
|
|
// NewFromFloat(545).RoundDown(-2).String() // output: "500"
|
|
// NewFromFloat(-500).RoundDown(-2).String() // output: "-500"
|
|
// NewFromFloat(1.1001).RoundDown(2).String() // output: "1.1"
|
|
// NewFromFloat(-1.454).RoundDown(1).String() // output: "-1.4"
|
|
func (d Decimal) RoundDown(places int32) Decimal {
|
|
return d.rescale(-places)
|
|
}
|
|
|
|
// RoundBank rounds the decimal to places decimal places.
|
|
// If the final digit to round is equidistant from the nearest two integers the
|
|
// rounded value is taken as the even number
|
|
//
|
|
// If places < 0, it will round the integer part to the nearest 10^(-places).
|
|
//
|
|
// Examples:
|
|
//
|
|
// NewFromFloat(5.45).RoundBank(1).String() // output: "5.4"
|
|
// NewFromFloat(545).RoundBank(-1).String() // output: "540"
|
|
// NewFromFloat(5.46).RoundBank(1).String() // output: "5.5"
|
|
// NewFromFloat(546).RoundBank(-1).String() // output: "550"
|
|
// NewFromFloat(5.55).RoundBank(1).String() // output: "5.6"
|
|
// NewFromFloat(555).RoundBank(-1).String() // output: "560"
|
|
func (d Decimal) RoundBank(places int32) Decimal {
|
|
|
|
round := d.Round(places)
|
|
|
|
// it is a tie when twice the k dropped digits equal 10^k
|
|
if k := -int64(places) - int64(d.exp); k > 0 && round.getValue().Bit(0) != 0 {
|
|
var dropped big.Int
|
|
dropped.Rem(d.getValue(), pow10(k))
|
|
if dropped.Abs(&dropped).Lsh(&dropped, 1).Cmp(pow10(k)) == 0 {
|
|
if round.getValue().Sign() < 0 {
|
|
round.value = new(big.Int).Add(round.getValue(), oneInt)
|
|
} else {
|
|
round.value = new(big.Int).Sub(round.getValue(), oneInt)
|
|
}
|
|
}
|
|
}
|
|
|
|
return round
|
|
}
|
|
|
|
// RoundCash aka Cash/Penny/öre rounding rounds decimal to a specific
|
|
// interval. The amount payable for a cash transaction is rounded to the nearest
|
|
// multiple of the minimum currency unit available. The following intervals are
|
|
// available: 5, 10, 25, 50 and 100; any other number throws a panic.
|
|
//
|
|
// 5: 5 cent rounding 3.43 => 3.45
|
|
// 10: 10 cent rounding 3.45 => 3.50 (5 gets rounded up)
|
|
// 25: 25 cent rounding 3.41 => 3.50
|
|
// 50: 50 cent rounding 3.75 => 4.00
|
|
// 100: 100 cent rounding 3.50 => 4.00
|
|
//
|
|
// For more details: https://en.wikipedia.org/wiki/Cash_rounding
|
|
func (d Decimal) RoundCash(interval uint8) Decimal {
|
|
var iVal *big.Int
|
|
switch interval {
|
|
case 5:
|
|
iVal = twentyInt
|
|
case 10:
|
|
iVal = tenInt
|
|
case 25:
|
|
iVal = fourInt
|
|
case 50:
|
|
iVal = twoInt
|
|
case 100:
|
|
iVal = oneInt
|
|
default:
|
|
panic(fmt.Sprintf("Decimal does not support this Cash rounding interval `%d`. Supported: 5, 10, 25, 50, 100", interval))
|
|
}
|
|
dVal := Decimal{
|
|
value: iVal,
|
|
}
|
|
|
|
return d.Mul(dVal).Round(0).DivRound(dVal, 2)
|
|
}
|
|
|
|
// Floor returns the nearest integer value less than or equal to d.
|
|
func (d Decimal) Floor() Decimal {
|
|
if d.exp >= 0 {
|
|
return d
|
|
}
|
|
|
|
// NOTE(vadim): must negate after casting to prevent int32 overflow
|
|
z := new(big.Int).Div(d.getValue(), pow10(-int64(d.exp)))
|
|
return Decimal{value: z, exp: 0}
|
|
}
|
|
|
|
// Ceil returns the nearest integer value greater than or equal to d.
|
|
func (d Decimal) Ceil() Decimal {
|
|
if d.exp >= 0 {
|
|
return d
|
|
}
|
|
|
|
// NOTE(vadim): must negate after casting to prevent int32 overflow
|
|
z, m := new(big.Int).DivMod(d.getValue(), pow10(-int64(d.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.
|
|
//
|
|
// If precision >= 0, it specifies the number of decimal places to keep.
|
|
// If precision < 0, it truncates the integer part to the nearest 10^(-precision)
|
|
// towards zero.
|
|
//
|
|
// Example:
|
|
//
|
|
// decimal.NewFromString("123.456").Truncate(2).String() // "123.45"
|
|
// decimal.NewFromString("5432").Truncate(-2).String() // "5400"
|
|
// decimal.NewFromString("-5432").Truncate(-2).String() // "-5400"
|
|
func (d Decimal) Truncate(precision int32) Decimal {
|
|
if -precision > d.exp {
|
|
return d.rescale(-precision)
|
|
}
|
|
return d
|
|
}
|
|
|
|
// StringScaled first scales the decimal then calls .String() on it.
|
|
//
|
|
// Deprecated: buggy and unintuitive. Use StringFixed instead.
|
|
func (d Decimal) StringScaled(exp int32) string {
|
|
return d.rescale(exp).String()
|
|
}
|
|
|
|
func (d Decimal) string(trimTrailingZeros, useScientificNotation bool) string {
|
|
if d.exp == 0 {
|
|
return d.getValue().String()
|
|
}
|
|
if d.exp >= 0 {
|
|
if useScientificNotation {
|
|
return d.ScientificNotationString()
|
|
}
|
|
return d.rescale(0).value.String()
|
|
}
|
|
|
|
str := d.getValue().String()
|
|
sign := ""
|
|
if str[0] == '-' {
|
|
sign, str = "-", str[1:]
|
|
}
|
|
|
|
var intPart, leadingZeros, fractionalPart string
|
|
|
|
// NOTE(vadim): 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)
|
|
if num0s <= len(zeros) {
|
|
leadingZeros = zeros[:num0s]
|
|
} else {
|
|
leadingZeros = strings.Repeat("0", num0s)
|
|
}
|
|
fractionalPart = str
|
|
}
|
|
|
|
if trimTrailingZeros {
|
|
i := len(fractionalPart) - 1
|
|
for ; i >= 0; i-- {
|
|
if fractionalPart[i] != '0' {
|
|
break
|
|
}
|
|
}
|
|
fractionalPart = fractionalPart[:i+1]
|
|
if fractionalPart == "" {
|
|
leadingZeros = ""
|
|
}
|
|
}
|
|
|
|
if len(leadingZeros)+len(fractionalPart) > 0 {
|
|
return sign + intPart + "." + leadingZeros + fractionalPart
|
|
}
|
|
return sign + intPart
|
|
}
|
|
|
|
// ScientificNotationString serializes the decimal into standard scientific notation.
|
|
//
|
|
// The notation is normalized to have one non-zero digit followed by a decimal point and
|
|
// the remaining significant digits followed by "E" and the base-10 exponent.
|
|
//
|
|
// A zero, which has no significant digits, is simply serialized to "0".
|
|
func (d Decimal) ScientificNotationString() string {
|
|
exp := int(d.exp)
|
|
intStr := new(big.Int).Abs(d.getValue()).String()
|
|
if intStr == "0" {
|
|
return intStr
|
|
}
|
|
first := intStr[0]
|
|
var remaining string
|
|
if len(intStr) > 1 {
|
|
remaining = "." + intStr[1:]
|
|
exp = exp + len(intStr) - 1
|
|
}
|
|
number := string(first) + remaining + "E" + strconv.Itoa(exp)
|
|
if d.value.Sign() < 0 {
|
|
return "-" + number
|
|
}
|
|
return number
|
|
}
|
|
|
|
// Min returns the smallest Decimal that was passed in the arguments.
|
|
//
|
|
// To call this function with an array, you must do:
|
|
//
|
|
// Min(arr[0], arr[1:]...)
|
|
//
|
|
// This makes it harder to accidentally call Min with 0 arguments.
|
|
func Min(first Decimal, rest ...Decimal) Decimal {
|
|
ans := first
|
|
for _, item := range rest {
|
|
if item.Cmp(ans) < 0 {
|
|
ans = item
|
|
}
|
|
}
|
|
return ans
|
|
}
|
|
|
|
// Max returns the largest Decimal that was passed in the arguments.
|
|
//
|
|
// To call this function with an array, you must do:
|
|
//
|
|
// Max(arr[0], arr[1:]...)
|
|
//
|
|
// This makes it harder to accidentally call Max with 0 arguments.
|
|
func Max(first Decimal, rest ...Decimal) Decimal {
|
|
ans := first
|
|
for _, item := range rest {
|
|
if item.Cmp(ans) > 0 {
|
|
ans = item
|
|
}
|
|
}
|
|
return ans
|
|
}
|
|
|
|
// Sum returns the combined total of the provided first and rest Decimals
|
|
func Sum(first Decimal, rest ...Decimal) Decimal {
|
|
if len(rest) == 0 {
|
|
return first
|
|
}
|
|
|
|
// Add returns a new value, so the following items can be added to it in place
|
|
total := first.Add(rest[0])
|
|
last := len(rest) - 1
|
|
if last == 0 {
|
|
return total
|
|
}
|
|
var scaled big.Int
|
|
for _, item := range rest[1:last] {
|
|
switch {
|
|
case item.exp < total.exp:
|
|
total = total.rescale(item.exp)
|
|
total.value.Add(total.value, item.getValue())
|
|
case item.exp > total.exp:
|
|
total.value.Add(total.value, scaled.Mul(item.getValue(), pow10(int64(item.exp)-int64(total.exp))))
|
|
default:
|
|
total.value.Add(total.value, item.getValue())
|
|
}
|
|
}
|
|
|
|
// the last Add builds the result the same way as adding one item at a time does
|
|
return total.Add(rest[last])
|
|
}
|
|
|
|
// Avg returns the average value of the provided first and rest Decimals
|
|
func Avg(first Decimal, rest ...Decimal) Decimal {
|
|
count := New(int64(len(rest)+1), 0)
|
|
sum := Sum(first, rest...)
|
|
return sum.Div(count)
|
|
}
|
|
|
|
// RescalePair rescales two decimals to common exponential value (minimal exp of both decimals)
|
|
func RescalePair(d1 Decimal, d2 Decimal) (Decimal, Decimal) {
|
|
if d1.exp < d2.exp {
|
|
return d1, d2.rescale(d1.exp)
|
|
} else if d1.exp > d2.exp {
|
|
return d1.rescale(d2.exp), d2
|
|
}
|
|
|
|
return d1, d2
|
|
}
|