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dec.go
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dec.go
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package cremath
import (
"encoding/json"
"errors"
"fmt"
"math/big"
"strconv"
"strings"
sdk "github.com/cosmos/cosmos-sdk/types"
)
type BigDec struct {
i *big.Int
}
const (
// Precision is the number of decimal places
Precision = 36
// DecimalPrecisionBits is the number of bits required to represent
// the above precision
// Ceiling[Log2[10^Precision - 1]]
DecimalPrecisionBits = 120
// 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 = 256 + decimalTruncateBits
)
var (
precisionReuse = new(big.Int).Exp(big.NewInt(10), big.NewInt(Precision), nil)
sdkPrecisionReuse = new(big.Int).Exp(big.NewInt(10), big.NewInt(sdk.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 ZeroBigDec() BigDec { return BigDec{new(big.Int).Set(zeroInt)} }
func OneBigDec() BigDec { return BigDec{precisionInt()} }
// 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]
}
// NewBigDec creates a new BigDec from integer assuming whole number
func NewBigDec(i int64) BigDec {
return NewBigDecWithPrec(i, 0)
}
// NewBigDecWithPrec creates a new BigDec from integer with decimal place at prec
// CONTRACT: prec <= Precision
func NewBigDecWithPrec(i, prec int64) BigDec {
return BigDec{
new(big.Int).Mul(big.NewInt(i), precisionMultiplier(prec)),
}
}
func NewBigDecFromDec(d sdk.Dec) BigDec {
return NewBigDecFromBigIntWithPrec(d.BigInt(), sdk.Precision)
}
func (d BigDec) Dec() sdk.Dec {
// Truncate any additional decimal values that exist due to BigDec's additional precision
// This relies on big.Int's QuoMut function doing floor division
intRepresentation := new(big.Int).Quo(d.BigInt(), precisionMultiplier(sdk.Precision))
// convert int representation back to SDK Dec precision
truncatedDec := sdk.NewDecFromBigIntWithPrec(intRepresentation, sdk.Precision)
return truncatedDec
}
func (d BigDec) DecRoundUp() sdk.Dec {
return sdk.NewDecFromBigIntWithPrec(chopPrecisionAndRoundUpDec(d.i), sdk.Precision)
}
// NewBigDecFromBigInt creates a new BigDec from big integer assuming whole numbers
// CONTRACT: prec <= Precision
func NewBigDecFromBigInt(i *big.Int) BigDec {
return NewBigDecFromBigIntWithPrec(i, 0)
}
// NewBigDecFromBigIntWithPrec creates a new BigDec from big integer assuming whole numbers
// CONTRACT: prec <= Precision
func NewBigDecFromBigIntWithPrec(i *big.Int, prec int64) BigDec {
return BigDec{
new(big.Int).Mul(i, precisionMultiplier(prec)),
}
}
// NewBigDecFromInt creates a new BigDec from big integer assuming whole numbers
// CONTRACT: prec <= Precision
func NewBigDecFromInt(i sdk.Int) BigDec {
return NewBigDecFromIntWithPrec(i, 0)
}
// NewBigDecFromIntWithPrec creates a new BigDec from big integer with decimal place at prec
// CONTRACT: prec <= Precision
func NewBigDecFromIntWithPrec(i sdk.Int, prec int64) BigDec {
return BigDec{
new(big.Int).Mul(i.BigInt(), precisionMultiplier(prec)),
}
}
// NewBigDecFromStr creates 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 NewBigDecFromStr(str string) (BigDec, error) {
if len(str) == 0 {
return BigDec{}, ErrEmptyDecimalStr
}
// first extract any negative symbol
neg := false
if str[0] == '-' {
neg = true
str = str[1:]
}
if len(str) == 0 {
return BigDec{}, 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 BigDec{}, ErrInvalidDecimalLength
}
combinedStr += strs[1]
} else if len(strs) > 2 {
return BigDec{}, ErrInvalidDecimalStr
}
if lenDecs > Precision {
return BigDec{}, 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 BigDec{}, fmt.Errorf("failed to set decimal string with base 10: %s", combinedStr)
}
if combined.BitLen() > maxDecBitLen {
return BigDec{}, 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 BigDec{combined}, nil
}
func MustNewBigDecFromStr(s string) BigDec {
dec, err := NewBigDecFromStr(s)
if err != nil {
panic(err)
}
return dec
}
// Clone performs a deep copy of the receiver
// and returns the new result.
func (d BigDec) Clone() BigDec {
return BigDec{new(big.Int).Set(d.i)}
}
func (d BigDec) IsNil() bool { return d.i == nil } // is decimal nil
func (d BigDec) IsZero() bool { return (d.i).Sign() == 0 } // is equal to zero
func (d BigDec) IsNegative() bool { return (d.i).Sign() == -1 } // is negative
func (d BigDec) IsPositive() bool { return (d.i).Sign() == 1 } // is positive
func (d BigDec) Equal(d2 BigDec) bool { return (d.i).Cmp(d2.i) == 0 } // equal decimals
func (d BigDec) GT(d2 BigDec) bool { return (d.i).Cmp(d2.i) > 0 } // greater than
func (d BigDec) GTE(d2 BigDec) bool { return (d.i).Cmp(d2.i) >= 0 } // greater than or equal
func (d BigDec) LT(d2 BigDec) bool { return (d.i).Cmp(d2.i) < 0 } // less than
func (d BigDec) LTE(d2 BigDec) bool { return (d.i).Cmp(d2.i) <= 0 } // less than or equal
func (d BigDec) Neg() BigDec { return BigDec{new(big.Int).Neg(d.i)} } // reverse the decimal sign
func (d BigDec) Abs() BigDec { return BigDec{new(big.Int).Abs(d.i)} } // absolute value
// BigInt returns a copy of the underlying big.Int.
func (d BigDec) BigInt() *big.Int {
if d.i == nil {
return nil
}
return new(big.Int).Set(d.i)
}
func (d BigDec) Add(d2 BigDec) BigDec {
return d.Clone().AddMut(d2)
}
// AddMut sets d to the sum d+d2 and returns d.
func (d BigDec) AddMut(d2 BigDec) BigDec {
d.i.Add(d.i, d2.i)
if d.i.BitLen() > maxDecBitLen {
panic("Int overflow")
}
return d
}
func (d BigDec) Sub(d2 BigDec) BigDec {
return d.Clone().SubMut(d2)
}
// SubMut sets d to the difference d-d2 and returns d.
func (d BigDec) SubMut(d2 BigDec) BigDec {
d.i.Sub(d.i, d2.i)
if d.i.BitLen() > maxDecBitLen {
panic("Int overflow")
}
return d
}
func (d BigDec) Mul(d2 BigDec) BigDec {
return d.Clone().MulMut(d2)
}
// MulMut sets d to the product d*d2 and returns d.
func (d BigDec) MulMut(d2 BigDec) BigDec {
d.i.Mul(d.i, d2.i)
d.i = chopPrecisionAndRound(d.i)
if d.i.BitLen() > maxDecBitLen {
panic("Int overflow")
}
return d
}
func (d BigDec) MulTruncate(d2 BigDec) BigDec {
return d.Clone().MulTruncateMut(d2)
}
func (d BigDec) MulTruncateMut(d2 BigDec) BigDec {
d.i.Mul(d.i, d2.i)
d.i = chopPrecisionAndTruncateMut(d.i)
if d.i.BitLen() > maxDecBitLen {
panic("Int overflow")
}
return d
}
func (d BigDec) MulRoundUp(d2 BigDec) BigDec {
return d.Clone().MulRoundUpMut(d2)
}
func (d BigDec) MulRoundUpMut(d2 BigDec) BigDec {
d.i.Mul(d.i, d2.i)
d.i = chopPrecisionAndRoundUpBigDec(d.i)
if d.i.BitLen() > maxDecBitLen {
panic("Int overflow")
}
return d
}
func (d BigDec) MulInt(i sdk.Int) BigDec {
return d.Clone().MulIntMut(i)
}
func (d BigDec) MulIntMut(i sdk.Int) BigDec {
d.i.Mul(d.i, i.BigInt()) // XXX
if d.i.BitLen() > maxDecBitLen {
panic("Int overflow")
}
return d
}
func (d BigDec) MulInt64(i int64) BigDec {
return d.Clone().MulInt64Mut(i)
}
// MulInt64Mut - multiplication with int64
func (d BigDec) MulInt64Mut(i int64) BigDec {
d.i.Mul(d.i, big.NewInt(i))
if d.i.BitLen() > maxDecBitLen {
panic("Int overflow")
}
return d
}
func (d BigDec) Quo(d2 BigDec) BigDec {
return d.Clone().QuoMut(d2)
}
// QuoMut sets d to the quotient d/d2 and returns z.
func (d BigDec) QuoMut(d2 BigDec) BigDec {
// multiply precision twice
d.i.Mul(d.i, precisionReuse)
d.i.Mul(d.i, precisionReuse)
d.i.Quo(d.i, d2.i)
d.i = chopPrecisionAndRound(d.i)
if d.i.BitLen() > maxDecBitLen {
panic("Int overflow")
}
return d
}
func (d BigDec) QuoTruncate(d2 BigDec) BigDec {
return d.Clone().QuoTruncateMut(d2)
}
func (d BigDec) QuoTruncateMut(d2 BigDec) BigDec {
// multiply precision twice
d.i.Mul(d.i, precisionReuse)
d.i.Mul(d.i, precisionReuse)
d.i.Quo(d.i, d2.i)
d.i = chopPrecisionAndTruncateMut(d.i)
if d.i.BitLen() > maxDecBitLen {
panic("Int overflow")
}
return d
}
func (d BigDec) QuoRoundUp(d2 BigDec) BigDec {
return d.Clone().QuoRoundUpMut(d2)
}
func (d BigDec) QuoRoundUpMut(d2 BigDec) BigDec {
// multiply precision twice
d.i.Mul(d.i, precisionReuse)
d.i.Mul(d.i, precisionReuse)
d.i.Quo(d.i, d2.i)
d.i = chopPrecisionAndRoundUpMut(d.i, precisionReuse)
if d.i.BitLen() > maxDecBitLen {
panic("Int overflow")
}
return d
}
func (d BigDec) QuoInt(i sdk.Int) BigDec {
return d.Clone().QuoIntMut(i)
}
func (d BigDec) QuoIntMut(i sdk.Int) BigDec {
d.i.Quo(d.i, i.BigInt()) // XXX
return d
}
func (d BigDec) QuoInt64(i int64) BigDec {
return d.Clone().QuoInt64Mut(i)
}
// QuoInt64Mut - quotient with int64
func (d BigDec) QuoInt64Mut(i int64) BigDec {
d.i.Quo(d.i, big.NewInt(i))
return d
}
func (d BigDec) Power(power uint64) BigDec {
return d.Clone().PowerMut(power)
}
// PowerMut returns the result of raising to a positive integer power
func (d BigDec) PowerMut(power uint64) BigDec {
if power == 0 {
return OneBigDec()
}
tmp := OneBigDec()
for i := power; i > 1; {
if i%2 != 0 {
tmp.MulMut(d)
}
i /= 2
d.MulMut(d)
}
return d.MulMut(tmp)
}
// is integer, e.g. decimals are zero
func (d BigDec) IsInteger() bool {
return new(big.Int).Rem(d.i, precisionReuse).Sign() == 0
}
// format decimal state
func (d BigDec) Format(s fmt.State, verb rune) {
_, err := s.Write([]byte(d.String()))
if err != nil {
panic(err)
}
}
func (d BigDec) 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)
}
// ____
// __| |__ "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)
}
}
// chopPrecisionAndRoundUpBigDec removes a Precision amount of rightmost digits and rounds up.
// Non-mutative.
func chopPrecisionAndRoundUpBigDec(d *big.Int) *big.Int {
return chopPrecisionAndRoundUpMut(d, precisionReuse)
}
// chopPrecisionAndRoundUpDec removes DecPrecision amount of rightmost digits and rounds up.
// Non-mutative.
func chopPrecisionAndRoundUpDec(d *big.Int) *big.Int {
copy := new(big.Int).Set(d)
return chopPrecisionAndRoundUpMut(copy, sdkPrecisionReuse)
}
// chopPrecisionAndRoundUp removes a Precision amount of rightmost digits and rounds up.
// Mutates input d.
// Mutations occur:
// - By calling chopPrecisionAndTruncateMut.
// - Using input d directly in QuoRem.
func chopPrecisionAndRoundUpMut(d *big.Int, precisionReuse *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 = chopPrecisionAndTruncateMut(d)
d = d.Neg(d)
return d
}
// get the truncated quotient and remainder
_, rem := d.QuoRem(d, precisionReuse, big.NewInt(0))
if rem.Sign() == 0 { // remainder is zero
return d
}
return d.Add(d, oneInt)
}
// 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)
}
// chopPrecisionAndTruncate is similar to chopPrecisionAndRound,
// but always rounds down. It mutates the input.
func chopPrecisionAndTruncateMut(d *big.Int) *big.Int {
return d.Quo(d, precisionReuse)
}
// TruncateInt truncates the decimals from the number and returns an Int
func (d BigDec) TruncateInt() sdk.Int {
return sdk.NewIntFromBigInt(chopPrecisionAndTruncate(d.i))
}
// Truncate truncates the decimals from the number and returns a BigDec
func (d BigDec) Truncate() BigDec {
return NewBigDecFromBigInt(chopPrecisionAndTruncate(d.i))
}
// Ceil returns the smallest interger value (as a decimal) that is greater than
// or equal to the given decimal.
func (d BigDec) Ceil() BigDec {
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 NewBigDecFromBigInt(quo)
}
if rem.Sign() == -1 {
return NewBigDecFromBigInt(quo)
}
return NewBigDecFromBigInt(quo.Add(quo, oneInt))
}
// 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 BigDec) MarshalJSON() ([]byte, error) {
if d.i == nil {
return nilJSON, nil
}
return json.Marshal(d.String())
}
// UnmarshalJSON defines custom decoding scheme
func (d *BigDec) 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
}
newDec, err := NewBigDecFromStr(text)
if err != nil {
return err
}
d.i = newDec.i
return nil
}
// MarshalYAML returns the YAML representation.
func (d BigDec) MarshalYAML() (interface{}, error) {
return d.String(), nil
}
// Marshal implements the gogo proto custom type interface.
func (d BigDec) 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 BigDec) MarshalTo(data []byte) (n int, err error) {
if d.i == nil {
d.i = new(big.Int)
}
if d.i.Sign() == 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 *BigDec) Unmarshal(data []byte) error {
if len(data) == 0 {
d.i = 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 BigDec) Size() int {
bz, _ := d.Marshal()
return len(bz)
}
// Override Amino binary serialization by proxying to protobuf.
func (d BigDec) MarshalAmino() ([]byte, error) { return d.Marshal() }
func (d *BigDec) UnmarshalAmino(bz []byte) error { return d.Unmarshal(bz) }
// MinBigDec returns minimum decimal between two.
func MinBigDec(d1, d2 BigDec) BigDec {
if d1.LT(d2) {
return d1
}
return d2
}
// MaxBigDec returns maximum decimal between two.
func MaxBigDec(d1, d2 BigDec) BigDec {
if d1.LT(d2) {
return d2
}
return d1
}
func (d BigDec) Sqrt() BigDec {
return d.Clone().SqrtMut()
}
func (d BigDec) SqrtMut() BigDec {
if d.IsNegative() {
panic("square root of negative number")
}
d.i.Mul(d.i, precisionReuse)
r := new(big.Int).Sqrt(d.i)
c := new(big.Int).Mul(r, r)
if c.Cmp(d.i) == -1 {
r.Add(r, oneInt)
}
return BigDec{r}
}