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decimal.go
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decimal.go
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package types
import (
"encoding/json"
"errors"
"fmt"
"math/big"
"strconv"
"strings"
"testing"
)
var _ CustomProtobufType = (*Dec)(nil)
// NOTE: never use new(Dec) or else we will panic unmarshalling into the
// nil embedded big.Int
type Dec struct {
i *big.Int
}
const (
// number of decimal places
Precision = 18
// bits required to represent the above precision
// Ceiling[Log2[10^Precision - 1]]
DecimalPrecisionBits = 60
// decimalTruncateBits is the minimum number of bits removed
// by a truncate operation. It is equal to
// Floor[Log2[10^Precision - 1]].
decimalTruncateBits = DecimalPrecisionBits - 1
maxDecBitLen = maxBitLen + decimalTruncateBits
// max number of iterations in ApproxRoot function
maxApproxRootIterations = 100
)
var (
precisionReuse = new(big.Int).Exp(big.NewInt(10), big.NewInt(Precision), nil)
fivePrecision = new(big.Int).Quo(precisionReuse, big.NewInt(2))
precisionMultipliers []*big.Int
zeroInt = big.NewInt(0)
oneInt = big.NewInt(1)
tenInt = big.NewInt(10)
)
// Decimal errors
var (
ErrEmptyDecimalStr = errors.New("decimal string cannot be empty")
ErrInvalidDecimalLength = errors.New("invalid decimal length")
ErrInvalidDecimalStr = errors.New("invalid decimal string")
)
// Set precision multipliers
func init() {
precisionMultipliers = make([]*big.Int, Precision+1)
for i := 0; i <= Precision; i++ {
precisionMultipliers[i] = calcPrecisionMultiplier(int64(i))
}
}
func precisionInt() *big.Int {
return new(big.Int).Set(precisionReuse)
}
func ZeroDec() Dec { return Dec{new(big.Int).Set(zeroInt)} }
func OneDec() Dec { return Dec{precisionInt()} }
func SmallestDec() Dec { return Dec{new(big.Int).Set(oneInt)} }
// calculate the precision multiplier
func calcPrecisionMultiplier(prec int64) *big.Int {
if prec > Precision {
panic(fmt.Sprintf("too much precision, maximum %v, provided %v", Precision, prec))
}
zerosToAdd := Precision - prec
multiplier := new(big.Int).Exp(tenInt, big.NewInt(zerosToAdd), nil)
return multiplier
}
// get the precision multiplier, do not mutate result
func precisionMultiplier(prec int64) *big.Int {
if prec > Precision {
panic(fmt.Sprintf("too much precision, maximum %v, provided %v", Precision, prec))
}
return precisionMultipliers[prec]
}
// create a new Dec from integer assuming whole number
func NewDec(i int64) Dec {
return NewDecWithPrec(i, 0)
}
// create a new Dec from integer with decimal place at prec
// CONTRACT: prec <= Precision
func NewDecWithPrec(i, prec int64) Dec {
return Dec{
new(big.Int).Mul(big.NewInt(i), precisionMultiplier(prec)),
}
}
// create a new Dec from big integer assuming whole numbers
// CONTRACT: prec <= Precision
func NewDecFromBigInt(i *big.Int) Dec {
return NewDecFromBigIntWithPrec(i, 0)
}
// create a new Dec from big integer assuming whole numbers
// CONTRACT: prec <= Precision
func NewDecFromBigIntWithPrec(i *big.Int, prec int64) Dec {
return Dec{
new(big.Int).Mul(i, precisionMultiplier(prec)),
}
}
// create a new Dec from big integer assuming whole numbers
// CONTRACT: prec <= Precision
func NewDecFromInt(i Int) Dec {
return NewDecFromIntWithPrec(i, 0)
}
// create a new Dec from big integer with decimal place at prec
// CONTRACT: prec <= Precision
func NewDecFromIntWithPrec(i Int, prec int64) Dec {
return Dec{
new(big.Int).Mul(i.BigInt(), precisionMultiplier(prec)),
}
}
// create a decimal from an input decimal string.
// valid must come in the form:
//
// (-) whole integers (.) decimal integers
//
// examples of acceptable input include:
//
// -123.456
// 456.7890
// 345
// -456789
//
// NOTE - An error will return if more decimal places
// are provided in the string than the constant Precision.
//
// CONTRACT - This function does not mutate the input str.
func NewDecFromStr(str string) (Dec, error) {
if len(str) == 0 {
return Dec{}, fmt.Errorf("%s: %w", str, ErrEmptyDecimalStr)
}
// first extract any negative symbol
neg := false
if str[0] == '-' {
neg = true
str = str[1:]
}
if len(str) == 0 {
return Dec{}, fmt.Errorf("%s: %w", str, ErrEmptyDecimalStr)
}
strs := strings.Split(str, ".")
lenDecs := 0
combinedStr := strs[0]
if len(strs) == 2 { // has a decimal place
lenDecs = len(strs[1])
if lenDecs == 0 || len(combinedStr) == 0 {
return Dec{}, ErrInvalidDecimalLength
}
combinedStr += strs[1]
} else if len(strs) > 2 {
return Dec{}, ErrInvalidDecimalStr
}
if lenDecs > Precision {
return Dec{}, fmt.Errorf("value '%s' exceeds max precision by %d decimal places: max precision %d", str, Precision-lenDecs, Precision)
}
// add some extra zero's to correct to the Precision factor
zerosToAdd := Precision - lenDecs
zeros := fmt.Sprintf(`%0`+strconv.Itoa(zerosToAdd)+`s`, "")
combinedStr += zeros
combined, ok := new(big.Int).SetString(combinedStr, 10) // base 10
if !ok {
return Dec{}, fmt.Errorf("failed to set decimal string with base 10: %s", combinedStr)
}
if combined.BitLen() > maxDecBitLen {
return Dec{}, fmt.Errorf("decimal '%s' out of range; bitLen: got %d, max %d", str, combined.BitLen(), maxDecBitLen)
}
if neg {
combined = new(big.Int).Neg(combined)
}
return Dec{combined}, nil
}
// Decimal from string, panic on error
func MustNewDecFromStr(s string) Dec {
dec, err := NewDecFromStr(s)
if err != nil {
panic(err)
}
return dec
}
func (d Dec) IsNil() bool { return d.i == nil } // is decimal nil
func (d Dec) IsZero() bool { return (d.i).Sign() == 0 } // is equal to zero
func (d Dec) IsNegative() bool { return (d.i).Sign() == -1 } // is negative
func (d Dec) IsPositive() bool { return (d.i).Sign() == 1 } // is positive
func (d Dec) Equal(d2 Dec) bool { return (d.i).Cmp(d2.i) == 0 } // equal decimals
func (d Dec) GT(d2 Dec) bool { return (d.i).Cmp(d2.i) > 0 } // greater than
func (d Dec) GTE(d2 Dec) bool { return (d.i).Cmp(d2.i) >= 0 } // greater than or equal
func (d Dec) LT(d2 Dec) bool { return (d.i).Cmp(d2.i) < 0 } // less than
func (d Dec) LTE(d2 Dec) bool { return (d.i).Cmp(d2.i) <= 0 } // less than or equal
func (d Dec) Neg() Dec { return Dec{new(big.Int).Neg(d.i)} } // reverse the decimal sign
func (d Dec) Abs() Dec { return Dec{new(big.Int).Abs(d.i)} } // absolute value
// BigInt returns a copy of the underlying big.Int.
func (d Dec) BigInt() *big.Int {
if d.IsNil() {
return nil
}
cp := new(big.Int)
return cp.Set(d.i)
}
// addition
func (d Dec) Add(d2 Dec) Dec {
res := new(big.Int).Add(d.i, d2.i)
if res.BitLen() > maxDecBitLen {
panic("Int overflow")
}
return Dec{res}
}
// subtraction
func (d Dec) Sub(d2 Dec) Dec {
res := new(big.Int).Sub(d.i, d2.i)
if res.BitLen() > maxDecBitLen {
panic("Int overflow")
}
return Dec{res}
}
// multiplication
func (d Dec) Mul(d2 Dec) Dec {
mul := new(big.Int).Mul(d.i, d2.i)
chopped := chopPrecisionAndRound(mul)
if chopped.BitLen() > maxDecBitLen {
panic("Int overflow")
}
return Dec{chopped}
}
// multiplication truncate
func (d Dec) MulTruncate(d2 Dec) Dec {
mul := new(big.Int).Mul(d.i, d2.i)
chopped := chopPrecisionAndTruncate(mul)
if chopped.BitLen() > maxDecBitLen {
panic("Int overflow")
}
return Dec{chopped}
}
// multiplication
func (d Dec) MulInt(i Int) Dec {
mul := new(big.Int).Mul(d.i, i.i)
if mul.BitLen() > maxDecBitLen {
panic("Int overflow")
}
return Dec{mul}
}
// MulInt64 - multiplication with int64
func (d Dec) MulInt64(i int64) Dec {
mul := new(big.Int).Mul(d.i, big.NewInt(i))
if mul.BitLen() > maxDecBitLen {
panic("Int overflow")
}
return Dec{mul}
}
// quotient
func (d Dec) Quo(d2 Dec) Dec {
// multiply precision twice
mul := new(big.Int).Mul(d.i, precisionReuse)
mul.Mul(mul, precisionReuse)
quo := new(big.Int).Quo(mul, d2.i)
chopped := chopPrecisionAndRound(quo)
if chopped.BitLen() > maxDecBitLen {
panic("Int overflow")
}
return Dec{chopped}
}
// quotient truncate
func (d Dec) QuoTruncate(d2 Dec) Dec {
// multiply precision twice
mul := new(big.Int).Mul(d.i, precisionReuse)
mul.Mul(mul, precisionReuse)
quo := mul.Quo(mul, d2.i)
chopped := chopPrecisionAndTruncate(quo)
if chopped.BitLen() > maxDecBitLen {
panic("Int overflow")
}
return Dec{chopped}
}
// quotient, round up
func (d Dec) QuoRoundUp(d2 Dec) Dec {
// multiply precision twice
mul := new(big.Int).Mul(d.i, precisionReuse)
mul.Mul(mul, precisionReuse)
quo := new(big.Int).Quo(mul, d2.i)
chopped := chopPrecisionAndRoundUp(quo)
if chopped.BitLen() > maxDecBitLen {
panic("Int overflow")
}
return Dec{chopped}
}
// quotient
func (d Dec) QuoInt(i Int) Dec {
mul := new(big.Int).Quo(d.i, i.i)
return Dec{mul}
}
// QuoInt64 - quotient with int64
func (d Dec) QuoInt64(i int64) Dec {
mul := new(big.Int).Quo(d.i, big.NewInt(i))
return Dec{mul}
}
// ApproxRoot returns an approximate estimation of a Dec's positive real nth root
// using Newton's method (where n is positive). The algorithm starts with some guess and
// computes the sequence of improved guesses until an answer converges to an
// approximate answer. It returns `|d|.ApproxRoot() * -1` if input is negative.
// A maximum number of 100 iterations is used a backup boundary condition for
// cases where the answer never converges enough to satisfy the main condition.
func (d Dec) ApproxRoot(root uint64) (guess Dec, err error) {
defer func() {
if r := recover(); r != nil {
var ok bool
err, ok = r.(error)
if !ok {
err = errors.New("out of bounds")
}
}
}()
if d.IsNegative() {
absRoot, err := d.MulInt64(-1).ApproxRoot(root)
return absRoot.MulInt64(-1), err
}
if root == 1 || d.IsZero() || d.Equal(OneDec()) {
return d, nil
}
if root == 0 {
return OneDec(), nil
}
rootInt := NewIntFromUint64(root)
guess, delta := OneDec(), OneDec()
for iter := 0; delta.Abs().GT(SmallestDec()) && iter < maxApproxRootIterations; iter++ {
prev := guess.Power(root - 1)
if prev.IsZero() {
prev = SmallestDec()
}
delta = d.Quo(prev)
delta = delta.Sub(guess)
delta = delta.QuoInt(rootInt)
guess = guess.Add(delta)
}
return guess, nil
}
// Power returns a the result of raising to a positive integer power
func (d Dec) Power(power uint64) Dec {
if power == 0 {
return OneDec()
}
tmp := OneDec()
for i := power; i > 1; {
if i%2 != 0 {
tmp = tmp.Mul(d)
}
i /= 2
d = d.Mul(d)
}
return d.Mul(tmp)
}
// ApproxSqrt is a wrapper around ApproxRoot for the common special case
// of finding the square root of a number. It returns -(sqrt(abs(d)) if input is negative.
func (d Dec) ApproxSqrt() (Dec, error) {
return d.ApproxRoot(2)
}
// is integer, e.g. decimals are zero
func (d Dec) IsInteger() bool {
return new(big.Int).Rem(d.i, precisionReuse).Sign() == 0
}
// format decimal state
func (d Dec) Format(s fmt.State, verb rune) {
_, err := s.Write([]byte(d.String()))
if err != nil {
panic(err)
}
}
func (d Dec) String() string {
if d.i == nil {
return d.i.String()
}
isNeg := d.IsNegative()
if isNeg {
d = d.Neg()
}
bzInt, err := d.i.MarshalText()
if err != nil {
return ""
}
inputSize := len(bzInt)
var bzStr []byte
// TODO: Remove trailing zeros
// case 1, purely decimal
if inputSize <= Precision {
bzStr = make([]byte, Precision+2)
// 0. prefix
bzStr[0] = byte('0')
bzStr[1] = byte('.')
// set relevant digits to 0
for i := 0; i < Precision-inputSize; i++ {
bzStr[i+2] = byte('0')
}
// set final digits
copy(bzStr[2+(Precision-inputSize):], bzInt)
} else {
// inputSize + 1 to account for the decimal point that is being added
bzStr = make([]byte, inputSize+1)
decPointPlace := inputSize - Precision
copy(bzStr, bzInt[:decPointPlace]) // pre-decimal digits
bzStr[decPointPlace] = byte('.') // decimal point
copy(bzStr[decPointPlace+1:], bzInt[decPointPlace:]) // post-decimal digits
}
if isNeg {
return "-" + string(bzStr)
}
return string(bzStr)
}
// Float64 returns the float64 representation of a Dec.
// Will return the error if the conversion failed.
func (d Dec) Float64() (float64, error) {
return strconv.ParseFloat(d.String(), 64)
}
// MustFloat64 returns the float64 representation of a Dec.
// Would panic if the conversion failed.
func (d Dec) MustFloat64() float64 {
if value, err := strconv.ParseFloat(d.String(), 64); err != nil {
panic(err)
} else {
return value
}
}
// ____
// __| |__ "chop 'em
// ` \ round!"
// ___|| ~ _ -bankers
// | | __
// | | | __|__|__
// |_____: / | $$$ |
// |________|
// Remove a Precision amount of rightmost digits and perform bankers rounding
// on the remainder (gaussian rounding) on the digits which have been removed.
//
// Mutates the input. Use the non-mutative version if that is undesired
func chopPrecisionAndRound(d *big.Int) *big.Int {
// remove the negative and add it back when returning
if d.Sign() == -1 {
// make d positive, compute chopped value, and then un-mutate d
d = d.Neg(d)
d = chopPrecisionAndRound(d)
d = d.Neg(d)
return d
}
// get the truncated quotient and remainder
quo, rem := d, big.NewInt(0)
quo, rem = quo.QuoRem(d, precisionReuse, rem)
if rem.Sign() == 0 { // remainder is zero
return quo
}
switch rem.Cmp(fivePrecision) {
case -1:
return quo
case 1:
return quo.Add(quo, oneInt)
default: // bankers rounding must take place
// always round to an even number
if quo.Bit(0) == 0 {
return quo
}
return quo.Add(quo, oneInt)
}
}
func chopPrecisionAndRoundUp(d *big.Int) *big.Int {
// remove the negative and add it back when returning
if d.Sign() == -1 {
// make d positive, compute chopped value, and then un-mutate d
d = d.Neg(d)
// truncate since d is negative...
d = chopPrecisionAndTruncate(d)
d = d.Neg(d)
return d
}
// get the truncated quotient and remainder
quo, rem := d, big.NewInt(0)
quo, rem = quo.QuoRem(d, precisionReuse, rem)
if rem.Sign() == 0 { // remainder is zero
return quo
}
return quo.Add(quo, oneInt)
}
func chopPrecisionAndRoundNonMutative(d *big.Int) *big.Int {
tmp := new(big.Int).Set(d)
return chopPrecisionAndRound(tmp)
}
// RoundInt64 rounds the decimal using bankers rounding
func (d Dec) RoundInt64() int64 {
chopped := chopPrecisionAndRoundNonMutative(d.i)
if !chopped.IsInt64() {
panic("Int64() out of bound")
}
return chopped.Int64()
}
// RoundInt round the decimal using bankers rounding
func (d Dec) RoundInt() Int {
return NewIntFromBigInt(chopPrecisionAndRoundNonMutative(d.i))
}
// chopPrecisionAndTruncate is similar to chopPrecisionAndRound,
// but always rounds down. It does not mutate the input.
func chopPrecisionAndTruncate(d *big.Int) *big.Int {
return new(big.Int).Quo(d, precisionReuse)
}
// TruncateInt64 truncates the decimals from the number and returns an int64
func (d Dec) TruncateInt64() int64 {
chopped := chopPrecisionAndTruncate(d.i)
if !chopped.IsInt64() {
panic("Int64() out of bound")
}
return chopped.Int64()
}
// TruncateInt truncates the decimals from the number and returns an Int
func (d Dec) TruncateInt() Int {
return NewIntFromBigInt(chopPrecisionAndTruncate(d.i))
}
// TruncateDec truncates the decimals from the number and returns a Dec
func (d Dec) TruncateDec() Dec {
return NewDecFromBigInt(chopPrecisionAndTruncate(d.i))
}
// Ceil returns the smallest interger value (as a decimal) that is greater than
// or equal to the given decimal.
func (d Dec) Ceil() Dec {
tmp := new(big.Int).Set(d.i)
quo, rem := tmp, big.NewInt(0)
quo, rem = quo.QuoRem(tmp, precisionReuse, rem)
// no need to round with a zero remainder regardless of sign
if rem.Cmp(zeroInt) == 0 {
return NewDecFromBigInt(quo)
}
if rem.Sign() == -1 {
return NewDecFromBigInt(quo)
}
return NewDecFromBigInt(quo.Add(quo, oneInt))
}
// MaxSortableDec is the largest Dec that can be passed into SortableDecBytes()
// Its negative form is the least Dec that can be passed in.
var MaxSortableDec = OneDec().Quo(SmallestDec())
// ValidSortableDec ensures that a Dec is within the sortable bounds,
// a Dec can't have a precision of less than 10^-18.
// Max sortable decimal was set to the reciprocal of SmallestDec.
func ValidSortableDec(dec Dec) bool {
return dec.Abs().LTE(MaxSortableDec)
}
// SortableDecBytes returns a byte slice representation of a Dec that can be sorted.
// Left and right pads with 0s so there are 18 digits to left and right of the decimal point.
// For this reason, there is a maximum and minimum value for this, enforced by ValidSortableDec.
func SortableDecBytes(dec Dec) []byte {
if !ValidSortableDec(dec) {
panic("dec must be within bounds")
}
// Instead of adding an extra byte to all sortable decs in order to handle max sortable, we just
// makes its bytes be "max" which comes after all numbers in ASCIIbetical order
if dec.Equal(MaxSortableDec) {
return []byte("max")
}
// For the same reason, we make the bytes of minimum sortable dec be --, which comes before all numbers.
if dec.Equal(MaxSortableDec.Neg()) {
return []byte("--")
}
// We move the negative sign to the front of all the left padded 0s, to make negative numbers come before positive numbers
if dec.IsNegative() {
return append([]byte("-"), []byte(fmt.Sprintf(fmt.Sprintf("%%0%ds", Precision*2+1), dec.Abs().String()))...)
}
return []byte(fmt.Sprintf(fmt.Sprintf("%%0%ds", Precision*2+1), dec.String()))
}
// reuse nil values
var nilJSON []byte
func init() {
empty := new(big.Int)
bz, _ := empty.MarshalText()
nilJSON, _ = json.Marshal(string(bz))
}
// MarshalJSON marshals the decimal
func (d Dec) MarshalJSON() ([]byte, error) {
if d.i == nil {
return nilJSON, nil
}
return json.Marshal(d.String())
}
// UnmarshalJSON defines custom decoding scheme
func (d *Dec) UnmarshalJSON(bz []byte) error {
if d.i == nil {
d.i = new(big.Int)
}
var text string
err := json.Unmarshal(bz, &text)
if err != nil {
return err
}
// TODO: Reuse dec allocation
newDec, err := NewDecFromStr(text)
if err != nil {
return err
}
d.i = newDec.i
return nil
}
// MarshalYAML returns the YAML representation.
func (d Dec) MarshalYAML() (interface{}, error) {
return d.String(), nil
}
// Marshal implements the gogo proto custom type interface.
func (d Dec) Marshal() ([]byte, error) {
if d.i == nil {
d.i = new(big.Int)
}
return d.i.MarshalText()
}
// MarshalTo implements the gogo proto custom type interface.
func (d *Dec) MarshalTo(data []byte) (n int, err error) {
if d.i == nil {
d.i = new(big.Int)
}
if d.i.Cmp(zeroInt) == 0 {
copy(data, []byte{0x30})
return 1, nil
}
bz, err := d.Marshal()
if err != nil {
return 0, err
}
copy(data, bz)
return len(bz), nil
}
// Unmarshal implements the gogo proto custom type interface.
func (d *Dec) Unmarshal(data []byte) error {
if len(data) == 0 {
d = nil
return nil
}
if d.i == nil {
d.i = new(big.Int)
}
if err := d.i.UnmarshalText(data); err != nil {
return err
}
if d.i.BitLen() > maxDecBitLen {
return fmt.Errorf("decimal out of range; got: %d, max: %d", d.i.BitLen(), maxDecBitLen)
}
return nil
}
// Size implements the gogo proto custom type interface.
func (d *Dec) Size() int {
bz, _ := d.Marshal()
return len(bz)
}
// Override Amino binary serialization by proxying to protobuf.
func (d Dec) MarshalAmino() ([]byte, error) { return d.Marshal() }
func (d *Dec) UnmarshalAmino(bz []byte) error { return d.Unmarshal(bz) }
func (dp DecProto) String() string {
return dp.Dec.String()
}
// helpers
// test if two decimal arrays are equal
func DecsEqual(d1s, d2s []Dec) bool {
if len(d1s) != len(d2s) {
return false
}
for i, d1 := range d1s {
if !d1.Equal(d2s[i]) {
return false
}
}
return true
}
// minimum decimal between two
func MinDec(d1, d2 Dec) Dec {
if d1.LT(d2) {
return d1
}
return d2
}
// maximum decimal between two
func MaxDec(d1, d2 Dec) Dec {
if d1.LT(d2) {
return d2
}
return d1
}
// intended to be used with require/assert: require.True(DecEq(...))
func DecEq(t *testing.T, exp, got Dec) (*testing.T, bool, string, string, string) {
return t, exp.Equal(got), "expected:\t%v\ngot:\t\t%v", exp.String(), got.String()
}