decimal/decimal.go

// Package decimal implements an arbitrary precision fixed-point decimal.
//
// To use as part of a struct:
//
//     type Struct struct {
//         Number Decimal
//     }
//
// The zero-value of a Decimal is 0, as you would expect.
//
// The best way to create a new Decimal is to use decimal.NewFromString, ex:
//
//     n, err := decimal.NewFromString("-123.4567")
//     n.String() // output: "-123.4567"
//
// NOTE: This can "only" represent numbers with a maximum of 2^31 digits
// after the decimal point.
package decimal

import (
	"database/sql/driver"
	"fmt"
	"math"
	"math/big"
	"strconv"
	"strings"
)

// DivisionPrecision is the number of decimal places in the result when it
// doesn't divide exactly.
//
// Example:
//
//     d1 := decimal.NewFromFloat(2).Div(decimal.NewFromFloat(3)
//     d1.String() // output: "0.6666666666666667"
//     d2 := decimal.NewFromFloat(2).Div(decimal.NewFromFloat(30000)
//     d2.String() // output: "0.0000666666666667"
//     d3 := decimal.NewFromFloat(20000).Div(decimal.NewFromFloat(3)
//     d3.String() // output: "6666.6666666666666667"
//     decimal.DivisionPrecision = 3
//     d4 := decimal.NewFromFloat(2).Div(decimal.NewFromFloat(3)
//     d4.String() // output: "0.667"
//
var DivisionPrecision = 16

// Zero constant, to make computations faster.
var Zero = New(0, 1)

var zeroInt = big.NewInt(0)
var oneInt = big.NewInt(1)
var fiveInt = big.NewInt(5)
var tenInt = big.NewInt(10)

// Decimal represents a fixed-point decimal. It is immutable.
// number = value * 10 ^ exp
type Decimal struct {
	value *big.Int

	// NOTE(vadim): this must be an int32, because we cast it to float64 during
	// calculations. If exp is 64 bit, we might lose precision.
	// If we cared about being able to represent every possible decimal, we
	// could make exp a *big.Int but it would hurt performance and numbers
	// like that are unrealistic.
	exp int32
}

// New returns a new fixed-point decimal, value * 10 ^ exp.
func New(value int64, exp int32) Decimal {
	return Decimal{
		value: big.NewInt(value),
		exp:   exp,
	}
}

// NewFromString returns a new Decimal from a string representation.
//
// Example:
//
//     d, err := NewFromString("-123.45")
//     d2, err := NewFromString(".0001")
//
func NewFromString(value string) (Decimal, error) {
	originalInput := value
	var intString string
	var exp int64

	// Check if number is using scientific notation
	eIndex := strings.IndexAny(value, "Ee")
	if eIndex != -1 {
		expInt, err := strconv.ParseInt(value[eIndex+1:], 10, 32)
		if err != nil {
			if e, ok := err.(*strconv.NumError); ok && e.Err == strconv.ErrRange {
				return Decimal{}, fmt.Errorf("can't convert %s to decimal: fractional part too long", value)
			}
			return Decimal{}, fmt.Errorf("can't convert %s to decimal: exponent is not numeric", value)
		}
		value = value[:eIndex]
		exp = expInt
	}

	parts := strings.Split(value, ".")
	if len(parts) == 1 {
		// There is no decimal point, we can just parse the original string as
		// an int
		intString = value
	} else if len(parts) == 2 {
		intString = parts[0] + parts[1]
		expInt := -len(parts[1])
		exp += int64(expInt)
	} else {
		return Decimal{}, fmt.Errorf("can't convert %s to decimal: too many .s", value)
	}

	dValue := new(big.Int)
	_, ok := dValue.SetString(intString, 10)
	if !ok {
		return Decimal{}, fmt.Errorf("can't convert %s to decimal", value)
	}

	if exp < math.MinInt32 || exp > math.MaxInt32 {
		// NOTE(vadim): I doubt a string could realistically be this long
		return Decimal{}, fmt.Errorf("can't convert %s to decimal: fractional part too long", originalInput)
	}

	return Decimal{
		value: dValue,
		exp:   int32(exp),
	}, nil
}

// NewFromFloat converts a float64 to Decimal.
//
// Example:
//
//     NewFromFloat(123.45678901234567).String() // output: "123.4567890123456"
//     NewFromFloat(.00000000000000001).String() // output: "0.00000000000000001"
//
// NOTE: this will panic on NaN, +/-inf
func NewFromFloat(value float64) Decimal {
	floor := math.Floor(value)

	// fast path, where float is an int
	if floor == value && !math.IsInf(value, 0) {
		return New(int64(value), 0)
	}

	// slow path: float is a decimal
	// HACK(vadim): do this the slow hacky way for now because the logic to
	// convert a base-2 float to base-10 properly is not trivial
	str := strconv.FormatFloat(value, 'f', -1, 64)
	dec, err := NewFromString(str)
	if err != nil {
		panic(err)
	}
	return dec
}

// NewFromFloatWithExponent converts a float64 to Decimal, with an arbitrary
// number of fractional digits.
//
// Example:
//
//     NewFromFloatWithExponent(123.456, -2).String() // output: "123.46"
//
func NewFromFloatWithExponent(value float64, exp int32) Decimal {
	mul := math.Pow(10, -float64(exp))
	floatValue := value * mul
	if math.IsNaN(floatValue) || math.IsInf(floatValue, 0) {
		panic(fmt.Sprintf("Cannot create a Decimal from %v", floatValue))
	}
	dValue := big.NewInt(round(floatValue))

	return Decimal{
		value: dValue,
		exp:   exp,
	}
}

// rescale returns a rescaled version of the decimal. Returned
// decimal may be less precise if the given exponent is bigger
// than the initial exponent of the Decimal.
// NOTE: this will truncate, NOT round
//
// Example:
//
// 	d := New(12345, -4)
//	d2 := d.rescale(-1)
//	d3 := d2.rescale(-4)
//	println(d1)
//	println(d2)
//	println(d3)
//
// Output:
//
//	1.2345
//	1.2
//	1.2000
//
func (d Decimal) rescale(exp int32) Decimal {
	d.ensureInitialized()
	// NOTE(vadim): must convert exps to float64 before - to prevent overflow
	diff := math.Abs(float64(exp) - float64(d.exp))
	value := new(big.Int).Set(d.value)

	expScale := new(big.Int).Exp(tenInt, big.NewInt(int64(diff)), nil)
	if exp > d.exp {
		value = value.Quo(value, expScale)
	} else if exp < d.exp {
		value = value.Mul(value, expScale)
	}

	return Decimal{
		value: value,
		exp:   exp,
	}
}

// Abs returns the absolute value of the decimal.
func (d Decimal) Abs() Decimal {
	d.ensureInitialized()
	d2Value := new(big.Int).Abs(d.value)
	return Decimal{
		value: d2Value,
		exp:   d.exp,
	}
}

// Add returns d + d2.
func (d Decimal) Add(d2 Decimal) Decimal {
	baseScale := min(d.exp, d2.exp)
	rd := d.rescale(baseScale)
	rd2 := d2.rescale(baseScale)

	d3Value := new(big.Int).Add(rd.value, rd2.value)
	return Decimal{
		value: d3Value,
		exp:   baseScale,
	}
}

// Sub returns d - d2.
func (d Decimal) Sub(d2 Decimal) Decimal {
	baseScale := min(d.exp, d2.exp)
	rd := d.rescale(baseScale)
	rd2 := d2.rescale(baseScale)

	d3Value := new(big.Int).Sub(rd.value, rd2.value)
	return Decimal{
		value: d3Value,
		exp:   baseScale,
	}
}

// Mul returns d * d2.
func (d Decimal) Mul(d2 Decimal) Decimal {
	d.ensureInitialized()
	d2.ensureInitialized()

	expInt64 := int64(d.exp) + int64(d2.exp)
	if expInt64 > math.MaxInt32 || expInt64 < math.MinInt32 {
		// 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.value, d2.value)
	return Decimal{
		value: d3Value,
		exp:   int32(expInt64),
	}
}

// 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 divsion 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) {
	d.ensureInitialized()
	d2.ensureInitialized()
	if (d2.value.Sign()==0) {
		panic("decimal division by 0")
	}
	scale := -precision
	e := int64(d.exp - d2.exp - scale)
	if e > math.MaxInt32 || e < math.MinInt32 {
		panic("overflow in decimal QuoRem")
	}
	var aa, bb, expo big.Int
	var scalerest int32
	// d = a 10^ea
	// d2 = b 10^eb
	if e < 0 {
		aa = *d.value
		expo.SetInt64(-e)
		bb.Exp(tenInt, &expo, nil)
		bb.Mul(d2.value, &bb)
		scalerest = d.exp
		// now aa = a
		//     bb = b 10^(scale + eb - ea)
	} else {
		expo.SetInt64(e)
		aa.Exp(tenInt, &expo, nil)
		aa.Mul(d.value, &aa)
		bb = *d2.value
		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
	q, r := d.QuoRem(d2, precision)
	// the actual rounding decision is based on comparing r*10^precision and d2/2
	// instead compare 2 r 10 ^precision and d2
	var rv2 big.Int
	rv2.Abs(r.value)
	rv2.Lsh(&rv2, 1)
	// now rv2 = abs(r.value) * 2
	r2 := Decimal{value: &rv2, exp: r.exp + precision}
	// r2 is now 2 * r * 10 ^ precision
	var c = r2.Cmp(d2.Abs())

	if c < 0 {
		return q
	} else {
		if d.value.Sign()*d2.value.Sign() < 0 {
			return q.Sub(New(1, -precision))
		} else {
			return q.Add(New(1, -precision))
		}
	}
}

// Cmp compares the numbers represented by d and d2 and returns:
//
//     -1 if d <  d2
//      0 if d == d2
//     +1 if d >  d2
//
func (d Decimal) Cmp(d2 Decimal) int {
	baseExp := min(d.exp, d2.exp)
	rd := d.rescale(baseExp)
	rd2 := d2.rescale(baseExp)

	return rd.value.Cmp(rd2.value)
}

// Equals returns whether the numbers represented by d and d2 are equal.
func (d Decimal) Equals(d2 Decimal) bool {
	return d.Cmp(d2) == 0
}

// Exponent returns the exponent, or scale component of the decimal.
func (d Decimal) Exponent() int32 {
	return d.exp
}

// IntPart returns the integer component of the decimal.
func (d Decimal) IntPart() int64 {
	scaledD := d.rescale(0)
	return scaledD.value.Int64()
}

// Rat returns a rational number representation of the decimal.
func (d Decimal) Rat() *big.Rat {
	d.ensureInitialized()
	if d.exp <= 0 {
		// NOTE(vadim): must negate after casting to prevent int32 overflow
		denom := new(big.Int).Exp(tenInt, big.NewInt(-int64(d.exp)), nil)
		return new(big.Rat).SetFrac(d.value, denom)
	} else {
		mul := new(big.Int).Exp(tenInt, big.NewInt(int64(d.exp)), nil)
		num := new(big.Int).Mul(d.value, mul)
		return new(big.Rat).SetFrac(num, oneInt)
	}
}

// Float64 returns the nearest float64 value for d and a bool indicating
// whether f represents d exactly.
// For more details, see the documentation for big.Rat.Float64
func (d Decimal) Float64() (f float64, exact bool) {
	return d.Rat().Float64()
}

// String returns the string representation of the decimal
// with the fixed point.
//
// Example:
//
//     d := New(-12345, -3)
//     println(d.String())
//
// Output:
//
//     -12.345
//
func (d Decimal) String() string {
	return d.string(true)
}

// StringFixed returns a rounded fixed-point string with places digits after
// the decimal point.
//
// Example:
//
// 	   NewFromFloat(0).StringFixed(2) // output: "0.00"
// 	   NewFromFloat(0).StringFixed(0) // output: "0"
// 	   NewFromFloat(5.45).StringFixed(0) // output: "5"
// 	   NewFromFloat(5.45).StringFixed(1) // output: "5.5"
// 	   NewFromFloat(5.45).StringFixed(2) // output: "5.45"
// 	   NewFromFloat(5.45).StringFixed(3) // output: "5.450"
// 	   NewFromFloat(545).StringFixed(-1) // output: "550"
//
func (d Decimal) StringFixed(places int32) string {
	rounded := d.Round(places)
	return rounded.string(false)
}

// Round rounds the decimal to places decimal places.
// If places < 0, it will round the integer part to the nearest 10^(-places).
//
// Example:
//
// 	   NewFromFloat(5.45).Round(1).String() // output: "5.5"
// 	   NewFromFloat(545).Round(-1).String() // output: "550"
//
func (d Decimal) Round(places int32) Decimal {
	// truncate to places + 1
	ret := d.rescale(-places - 1)

	// add sign(d) * 0.5
	if ret.value.Sign() < 0 {
		ret.value.Sub(ret.value, fiveInt)
	} else {
		ret.value.Add(ret.value, fiveInt)
	}

	// floor for positive numbers, ceil for negative numbers
	_, m := ret.value.DivMod(ret.value, tenInt, new(big.Int))
	ret.exp += 1
	if ret.value.Sign() < 0 && m.Cmp(zeroInt) != 0 {
		ret.value.Add(ret.value, oneInt)
	}

	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)

	// NOTE(vadim): 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)

	// NOTE(vadim): 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 {
		return d.rescale(-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 := NewFromString(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 = NewFromString(str)

	return err
}

// Value implements the driver.Valuer interface for database serialization.
func (d Decimal) Value() (driver.Value, error) {
	return d.String(), nil
}

// UnmarshalText implements the encoding.TextUnmarshaler interface for XML
// deserialization.
func (d *Decimal) UnmarshalText(text []byte) error {
	str := string(text)

	dec, err := NewFromString(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
}

// NOTE: buggy, unintuitive, and DEPRECATED! Use StringFixed instead.
// StringScaled first scales the decimal then calls .String() on it.
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

	// 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)
		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)
	}
}

// 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
}

// 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
}

func min(x, y int32) int32 {
	if x >= y {
		return y
	}
	return x
}

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
}