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"
	"encoding/binary"
	"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

// MarshalJSONWithoutQuotes should be set to true if you want the decimal to
// be JSON marshaled as a number, instead of as a string.
// WARNING: this is dangerous for decimals with many digits, since many JSON
// unmarshallers (ex: Javascript's) will unmarshal JSON numbers to IEEE 754
// double-precision floating point numbers, which means you can potentially
// silently lose precision.
var MarshalJSONWithoutQuotes = false

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

// fiveDec used in Cash Rounding
var fiveDec = New(5, 0)

var zeroInt = big.NewInt(0)
var oneInt = big.NewInt(1)
var twoInt = big.NewInt(2)
var fourInt = big.NewInt(4)
var fiveInt = big.NewInt(5)
var tenInt = big.NewInt(10)
var twentyInt = big.NewInt(20)

// 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,
	}
}

// NewFromBigInt returns a new Decimal from a big.Int, value * 10 ^ exp
func NewFromBigInt(value *big.Int, exp int32) Decimal {
	return Decimal{
		value: big.NewInt(0).Set(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 {
		// strip the insignificant digits for more accurate comparisons.
		decimalPart := strings.TrimRight(parts[1], "0")
		intString = parts[0] + decimalPart
		expInt := -len(decimalPart)
		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
}

// RequireFromString returns a new Decimal from a string representation
// or panics if NewFromString would have returned an error.
//
// Example:
//
//     d := RequireFromString("-123.45")
//     d2 := RequireFromString(".0001")
//
func RequireFromString(value string) Decimal {
	dec, err := NewFromString(value)
	if err != nil {
		panic(err)
	}
	return dec
}

// NewFromFloat converts a float64 to Decimal.
//
// The converted number will contain the number of significant digits that can be
// represented in a float with reliable roundtrip.
// This is typically 15 digits, but may be more in some cases.
// See https://www.exploringbinary.com/decimal-precision-of-binary-floating-point-numbers/ for more information.
//
// For slightly faster conversion, use NewFromFloatWithExponent where you can specify the precision in absolute terms.
//
// NOTE: this will panic on NaN, +/-inf
func NewFromFloat(value float64) Decimal {
	if value == 0 {
		return New(0, 0)
	}
	return newFromFloat(value, math.Float64bits(value), &float64info)
}

// NewFromFloat converts a float32 to Decimal.
//
// The converted number will contain the number of significant digits that can be
// represented in a float with reliable roundtrip.
// This is typically 6-8 digits depending on the input.
// See https://www.exploringbinary.com/decimal-precision-of-binary-floating-point-numbers/ for more information.
//
// For slightly faster conversion, use NewFromFloatWithExponent where you can specify the precision in absolute terms.
//
// NOTE: this will panic on NaN, +/-inf
func NewFromFloat32(value float32) Decimal {
	if value == 0 {
		return New(0, 0)
	}
	// XOR is workaround for https://github.com/golang/go/issues/26285
	a := math.Float32bits(value) ^ 0x80808080
	return newFromFloat(float64(value), uint64(a)^0x80808080, &float32info)
}

func newFromFloat(val float64, bits uint64, flt *floatInfo) Decimal {
	if math.IsNaN(val) || math.IsInf(val, 0) {
		panic(fmt.Sprintf("Cannot create a Decimal from %v", val))
	}
	exp := int(bits>>flt.mantbits) & (1<<flt.expbits - 1)
	mant := bits & (uint64(1)<<flt.mantbits - 1)

	switch exp {
	case 0:
		// denormalized
		exp++

	default:
		// add implicit top bit
		mant |= uint64(1) << flt.mantbits
	}
	exp += flt.bias

	var d decimal
	d.Assign(mant)
	d.Shift(exp - int(flt.mantbits))
	d.neg = bits>>(flt.expbits+flt.mantbits) != 0

	roundShortest(&d, mant, exp, flt)
	// If less than 19 digits, we can do calculation in an int64.
	if d.nd < 19 {
		tmp := int64(0)
		m := int64(1)
		for i := d.nd - 1; i >= 0; i-- {
			tmp += m * int64(d.d[i]-'0')
			m *= 10
		}
		if d.neg {
			tmp *= -1
		}
		return Decimal{value: big.NewInt(tmp), exp: int32(d.dp) - int32(d.nd)}
	}
	dValue := new(big.Int)
	dValue, ok := dValue.SetString(string(d.d[:d.nd]), 10)
	if ok {
		return Decimal{value: dValue, exp: int32(d.dp) - int32(d.nd)}
	}

	return NewFromFloatWithExponent(val, int32(d.dp)-int32(d.nd))
}

// 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 {
	if math.IsNaN(value) || math.IsInf(value, 0) {
		panic(fmt.Sprintf("Cannot create a Decimal from %v", value))
	}

	bits := math.Float64bits(value)
	mant := bits & (1<<52 - 1)
	exp2 := int32((bits >> 52) & (1<<11 - 1))
	sign := bits >> 63

	if exp2 == 0 {
		// specials
		if mant == 0 {
			return Decimal{}
		} else {
			// subnormal
			exp2++
		}
	} else {
		// normal
		mant |= 1 << 52
	}

	exp2 -= 1023 + 52

	// normalizing base-2 values
	for mant&1 == 0 {
		mant = mant >> 1
		exp2++
	}

	// maximum number of fractional base-10 digits to represent 2^N exactly cannot be more than -N if N<0
	if exp < 0 && exp < exp2 {
		if exp2 < 0 {
			exp = exp2
		} else {
			exp = 0
		}
	}

	// representing 10^M * 2^N as 5^M * 2^(M+N)
	exp2 -= exp

	temp := big.NewInt(1)
	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,
	}
}

// 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,
	}
}

// Neg returns -d.
func (d Decimal) Neg() Decimal {
	d.ensureInitialized()
	val := new(big.Int).Neg(d.value)
	return Decimal{
		value: val,
		exp:   d.exp,
	}
}

// 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),
	}
}

// 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.
func (d Decimal) Shift(shift int32) Decimal {
	d.ensureInitialized()
	return Decimal{
		value: new(big.Int).Set(d.value),
		exp:   d.exp + shift,
	}
}

// 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
	}

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

	return q.Add(New(1, -precision))
}

// Mod returns d % d2.
func (d Decimal) Mod(d2 Decimal) Decimal {
	quo := d.Div(d2).Truncate(0)
	return d.Sub(d2.Mul(quo))
}

// Pow returns d to the power d2
func (d Decimal) Pow(d2 Decimal) Decimal {
	var temp Decimal
	if d2.IntPart() == 0 {
		return NewFromFloat(1)
	}
	temp = d.Pow(d2.Div(NewFromFloat(2)))
	if d2.IntPart()%2 == 0 {
		return temp.Mul(temp)
	}
	if d2.IntPart() > 0 {
		return temp.Mul(temp).Mul(d)
	}
	return temp.Mul(temp).Div(d)
}

// 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 {
	d.ensureInitialized()
	d2.ensureInitialized()

	if d.exp == d2.exp {
		return d.value.Cmp(d2.value)
	}

	baseExp := min(d.exp, d2.exp)
	rd := d.rescale(baseExp)
	rd2 := d2.rescale(baseExp)

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

// 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 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 {
	if d.value == nil {
		return 0
	}
	return d.value.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 big.NewInt(0).Set(d.value)
}

// 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)
	}

	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)
}

// StringFixedBank returns a banker 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: "5.4"
// 	   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) StringFixedBank(places int32) string {
	rounded := d.RoundBank(places)
	return rounded.string(false)
}

// StringFixedCash returns a Swedish/Cash rounded fixed-point string. For
// more details see the documentation at function RoundCash.
func (d Decimal) StringFixedCash(interval uint8) string {
	rounded := d.RoundCash(interval)
	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++
	if ret.value.Sign() < 0 && m.Cmp(zeroInt) != 0 {
		ret.value.Add(ret.value, oneInt)
	}

	return ret
}

// 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).Round(1).String() // output: "5.4"
// 	   NewFromFloat(545).Round(-1).String() // output: "540"
// 	   NewFromFloat(5.46).Round(1).String() // output: "5.5"
// 	   NewFromFloat(546).Round(-1).String() // output: "550"
// 	   NewFromFloat(5.55).Round(1).String() // output: "5.6"
// 	   NewFromFloat(555).Round(-1).String() // output: "560"
//
func (d Decimal) RoundBank(places int32) Decimal {

	round := d.Round(places)
	remainder := d.Sub(round).Abs()

	half := New(5, -places-1)
	if remainder.Cmp(half) == 0 && round.value.Bit(0) != 0 {
		if round.value.Sign() < 0 {
			round.value.Add(round.value, oneInt)
		} else {
			round.value.Sub(round.value, 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, 15, 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)
// 	   15:  10 cent rounding 3.45 => 3.40 (5 gets rounded down)
// 	   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 15:
		if d.exp < 0 {
			// TODO: optimize and reduce allocations
			orgExp := d.exp
			dOne := New(10^-int64(orgExp), orgExp)
			d2 := d
			d2.exp = 0
			if d2.Mod(fiveDec).Equal(Zero) {
				d2.exp = orgExp
				d2 = d2.Sub(dOne)
				d = d2
			}
		}
		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, 15, 25, 50, 100", interval))
	}
	dVal := Decimal{
		value: iVal,
	}
	// TODO: optimize those calculations to reduce the high allocations (~29 allocs).
	return d.Mul(dVal).Round(0).Div(dVal).Truncate(2)
}

// Floor returns the nearest integer value less than or equal to d.
func (d Decimal) Floor() Decimal {
	d.ensureInitialized()

	if d.exp >= 0 {
		return d
	}

	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()

	if d.exp >= 0 {
		return d
	}

	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 {
	if string(decimalBytes) == "null" {
		return nil
	}

	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) {
	var str string
	if MarshalJSONWithoutQuotes {
		str = d.String()
	} else {
		str = "\"" + d.String() + "\""
	}
	return []byte(str), nil
}

// UnmarshalBinary implements the encoding.BinaryUnmarshaler interface. As a string representation
// is already used when encoding to text, this method stores that string as []byte
func (d *Decimal) UnmarshalBinary(data []byte) error {
	// Extract the exponent
	d.exp = int32(binary.BigEndian.Uint32(data[:4]))

	// Extract the value
	d.value = new(big.Int)
	return d.value.GobDecode(data[4:])
}

// MarshalBinary implements the encoding.BinaryMarshaler interface.
func (d Decimal) MarshalBinary() (data []byte, err error) {
	// Write the exponent first since it's a fixed size
	v1 := make([]byte, 4)
	binary.BigEndian.PutUint32(v1, uint32(d.exp))

	// Add the value
	var v2 []byte
	if v2, err = d.value.GobEncode(); err != nil {
		return
	}

	// Return the byte array
	data = append(v1, v2...)
	return
}

// Scan implements the sql.Scanner interface for database deserialization.
func (d *Decimal) Scan(value interface{}) error {
	// first try to see if the data is stored in database as a Numeric datatype
	switch v := value.(type) {

	case float32:
		*d = NewFromFloat(float64(v))
		return nil

	case float64:
		// numeric in sqlite3 sends us float64
		*d = NewFromFloat(v)
		return nil

	case int64:
		// at least in sqlite3 when the value is 0 in db, the data is sent
		// to us as an int64 instead of a float64 ...
		*d = New(v, 0)
		return nil

	default:
		// default is trying to interpret value stored as string
		str, err := unquoteIfQuoted(v)
		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
}

// GobEncode implements the gob.GobEncoder interface for gob serialization.
func (d Decimal) GobEncode() ([]byte, error) {
	return d.MarshalBinary()
}

// GobDecode implements the gob.GobDecoder interface for gob serialization.
func (d *Decimal) GobDecode(data []byte) error {
	return d.UnmarshalBinary(data)
}

// StringScaled first scales the decimal then calls .String() on it.
// NOTE: buggy, unintuitive, and DEPRECATED! Use StringFixed instead.
func (d Decimal) StringScaled(exp int32) string {
	return d.rescale(exp).String()
}

func (d Decimal) string(trimTrailingZeros bool) string {
	if d.exp >= 0 {
		return d.rescale(0).value.String()
	}

	abs := new(big.Int).Abs(d.value)
	str := abs.String()

	var intPart, fractionalPart string

	// 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)
	}
}

// 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 {
	total := first
	for _, item := range rest {
		total = total.Add(item)
	}

	return total
}

// 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)
}

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

func unquoteIfQuoted(value interface{}) (string, error) {
	var bytes []byte

	switch v := value.(type) {
	case string:
		bytes = []byte(v)
	case []byte:
		bytes = v
	default:
		return "", fmt.Errorf("Could not convert value '%+v' to byte array of type '%T'",
			value, 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
}

// NullDecimal represents a nullable decimal with compatibility for
// scanning null values from the database.
type NullDecimal struct {
	Decimal Decimal
	Valid   bool
}

// Scan implements the sql.Scanner interface for database deserialization.
func (d *NullDecimal) Scan(value interface{}) error {
	if value == nil {
		d.Valid = false
		return nil
	}
	d.Valid = true
	return d.Decimal.Scan(value)
}

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

// UnmarshalJSON implements the json.Unmarshaler interface.
func (d *NullDecimal) UnmarshalJSON(decimalBytes []byte) error {
	if string(decimalBytes) == "null" {
		d.Valid = false
		return nil
	}
	d.Valid = true
	return d.Decimal.UnmarshalJSON(decimalBytes)
}

// MarshalJSON implements the json.Marshaler interface.
func (d NullDecimal) MarshalJSON() ([]byte, error) {
	if !d.Valid {
		return []byte("null"), nil
	}
	return d.Decimal.MarshalJSON()
}

// Trig functions

// Atan returns the arctangent, in radians, of x.
func (x Decimal) Atan() Decimal {
	if x.Equal(NewFromFloat(0.0)) {
		return x
	}
	if x.GreaterThan(NewFromFloat(0.0)) {
		return x.satan()
	}
	return x.Neg().satan().Neg()
}

func (d Decimal) xatan() Decimal {
	P0 := NewFromFloat(-8.750608600031904122785e-01)
	P1 := NewFromFloat(-1.615753718733365076637e+01)
	P2 := NewFromFloat(-7.500855792314704667340e+01)
	P3 := NewFromFloat(-1.228866684490136173410e+02)
	P4 := NewFromFloat(-6.485021904942025371773e+01)
	Q0 := NewFromFloat(2.485846490142306297962e+01)
	Q1 := NewFromFloat(1.650270098316988542046e+02)
	Q2 := NewFromFloat(4.328810604912902668951e+02)
	Q3 := NewFromFloat(4.853903996359136964868e+02)
	Q4 := NewFromFloat(1.945506571482613964425e+02)
	z := d.Mul(d)
	b1 := P0.Mul(z).Add(P1).Mul(z).Add(P2).Mul(z).Add(P3).Mul(z).Add(P4).Mul(z)
	b2 := z.Add(Q0).Mul(z).Add(Q1).Mul(z).Add(Q2).Mul(z).Add(Q3).Mul(z).Add(Q4)
	z = b1.Div(b2)
	z = d.Mul(z).Add(d)
	return z
}

// satan reduces its argument (known to be positive)
// to the range [0, 0.66] and calls xatan.
func (d Decimal) satan() Decimal {
	Morebits := NewFromFloat(6.123233995736765886130e-17) // pi/2 = PIO2 + Morebits
	Tan3pio8 := NewFromFloat(2.41421356237309504880)      // tan(3*pi/8)
	pi := NewFromFloat(3.14159265358979323846264338327950288419716939937510582097494459)

	if d.LessThanOrEqual(NewFromFloat(0.66)) {
		return d.xatan()
	}
	if d.GreaterThan(Tan3pio8) {
		return pi.Div(NewFromFloat(2.0)).Sub(NewFromFloat(1.0).Div(d).xatan()).Add(Morebits)
	}
	return pi.Div(NewFromFloat(4.0)).Add((d.Sub(NewFromFloat(1.0)).Div(d.Add(NewFromFloat(1.0)))).xatan()).Add(NewFromFloat(0.5).Mul(Morebits))
}

// sin coefficients
  var _sin = [...]Decimal{
  	NewFromFloat(1.58962301576546568060E-10), // 0x3de5d8fd1fd19ccd
  	NewFromFloat(-2.50507477628578072866E-8), // 0xbe5ae5e5a9291f5d
  	NewFromFloat(2.75573136213857245213E-6),  // 0x3ec71de3567d48a1
  	NewFromFloat(-1.98412698295895385996E-4), // 0xbf2a01a019bfdf03
  	NewFromFloat(8.33333333332211858878E-3),  // 0x3f8111111110f7d0
  	NewFromFloat(-1.66666666666666307295E-1), // 0xbfc5555555555548
  }

// Sin returns the sine of the radian argument x.
  func (d Decimal) Sin() Decimal {
		PI4A := NewFromFloat(7.85398125648498535156E-1)                             // 0x3fe921fb40000000, Pi/4 split into three parts
		PI4B := NewFromFloat(3.77489470793079817668E-8)                             // 0x3e64442d00000000,
		PI4C := NewFromFloat(2.69515142907905952645E-15)                            // 0x3ce8469898cc5170,
		M4PI := NewFromFloat(1.273239544735162542821171882678754627704620361328125) // 4/pi

  	if d.Equal(NewFromFloat(0.0)) {
			return d
		}
  	// make argument positive but save the sign
  	sign := false
  	if d.LessThan(NewFromFloat(0.0)) {
  		d = d.Neg()
  		sign = true
  	}

		j := d.Mul(M4PI).IntPart()    // integer part of x/(Pi/4), as integer for tests on the phase angle
  	y := NewFromFloat(float64(j)) // integer part of x/(Pi/4), as float

  	// map zeros to origin
  	if j&1 == 1 {
  		j++
  		y = y.Add(NewFromFloat(1.0))
  	}
  	j &= 7 // octant modulo 2Pi radians (360 degrees)
  	// reflect in x axis
  	if j > 3 {
  		sign = !sign
  		j -= 4
  	}
		z := d.Sub(y.Mul(PI4A)).Sub(y.Mul(PI4B)).Sub(y.Mul(PI4C)) // Extended precision modular arithmetic
  	zz := z.Mul(z)

  	if j == 1 || j == 2 {
			w := zz.Mul(zz).Mul(_cos[0].Mul(zz).Add(_cos[1]).Mul(zz).Add(_cos[2]).Mul(zz).Add(_cos[3]).Mul(zz).Add(_cos[4]).Mul(zz).Add(_cos[5]))
			y = NewFromFloat(1.0).Sub(NewFromFloat(0.5).Mul(zz)).Add(w)
  	} else {
			y = z.Add(z.Mul(zz).Mul(_sin[0].Mul(zz).Add(_sin[1]).Mul(zz).Add(_sin[2]).Mul(zz).Add(_sin[3]).Mul(zz).Add(_sin[4]).Mul(zz).Add(_sin[5])))
  	}
  	if sign {
  		y = y.Neg()
  	}
  	return y
  }

	// cos coefficients
  var _cos = [...]Decimal{
  	NewFromFloat(-1.13585365213876817300E-11), // 0xbda8fa49a0861a9b
  	NewFromFloat(2.08757008419747316778E-9),   // 0x3e21ee9d7b4e3f05
  	NewFromFloat(-2.75573141792967388112E-7),  // 0xbe927e4f7eac4bc6
  	NewFromFloat(2.48015872888517045348E-5),   // 0x3efa01a019c844f5
  	NewFromFloat(-1.38888888888730564116E-3),  // 0xbf56c16c16c14f91
  	NewFromFloat(4.16666666666665929218E-2),   // 0x3fa555555555554b
  }

	// Cos returns the cosine of the radian argument x.
  func (d Decimal) Cos() Decimal {

		PI4A := NewFromFloat(7.85398125648498535156E-1)                             // 0x3fe921fb40000000, Pi/4 split into three parts
		PI4B := NewFromFloat(3.77489470793079817668E-8)                             // 0x3e64442d00000000,
		PI4C := NewFromFloat(2.69515142907905952645E-15)                            // 0x3ce8469898cc5170,
		M4PI := NewFromFloat(1.273239544735162542821171882678754627704620361328125) // 4/pi

  	// make argument positive
		sign := false
  	if d.LessThan(NewFromFloat(0.0)) {
  		d = d.Neg()
  	}

		j := d.Mul(M4PI).IntPart()    // integer part of x/(Pi/4), as integer for tests on the phase angle
  	y := NewFromFloat(float64(j)) // integer part of x/(Pi/4), as float

  	// map zeros to origin
  	if j&1 == 1 {
  		j++
  		y = y.Add(NewFromFloat(1.0))
  	}
  	j &= 7 // octant modulo 2Pi radians (360 degrees)
  	// reflect in x axis
  	if j > 3 {
  		sign = !sign
  		j -= 4
  	}
		if j > 1 {
  		sign = !sign
  	}

		z := d.Sub(y.Mul(PI4A)).Sub(y.Mul(PI4B)).Sub(y.Mul(PI4C)) // Extended precision modular arithmetic
  	zz := z.Mul(z)

  	if j == 1 || j == 2 {
			y = z.Add(z.Mul(zz).Mul(_sin[0].Mul(zz).Add(_sin[1]).Mul(zz).Add(_sin[2]).Mul(zz).Add(_sin[3]).Mul(zz).Add(_sin[4]).Mul(zz).Add(_sin[5])))
  	} else {
			w := zz.Mul(zz).Mul(_cos[0].Mul(zz).Add(_cos[1]).Mul(zz).Add(_cos[2]).Mul(zz).Add(_cos[3]).Mul(zz).Add(_cos[4]).Mul(zz).Add(_cos[5]))
			y = NewFromFloat(1.0).Sub(NewFromFloat(0.5).Mul(zz)).Add(w)
  	}
  	if sign {
  		y = y.Neg()
  	}
  	return y
  }

	var _tanP = [...]Decimal{
  	NewFromFloat(-1.30936939181383777646E+4), // 0xc0c992d8d24f3f38
  	NewFromFloat(1.15351664838587416140E+6),  // 0x413199eca5fc9ddd
  	NewFromFloat(-1.79565251976484877988E+7), // 0xc1711fead3299176
  }
  var _tanQ = [...]Decimal{
  	NewFromFloat(1.00000000000000000000E+0),
  	NewFromFloat(1.36812963470692954678E+4),  //0x40cab8a5eeb36572
  	NewFromFloat(-1.32089234440210967447E+6), //0xc13427bc582abc96
  	NewFromFloat(2.50083801823357915839E+7),  //0x4177d98fc2ead8ef
  	NewFromFloat(-5.38695755929454629881E+7), //0xc189afe03cbe5a31
  }

  // Tan returns the tangent of the radian argument x.
  func (d Decimal) Tan() Decimal {

		PI4A := NewFromFloat(7.85398125648498535156E-1)                             // 0x3fe921fb40000000, Pi/4 split into three parts
		PI4B := NewFromFloat(3.77489470793079817668E-8)                             // 0x3e64442d00000000,
		PI4C := NewFromFloat(2.69515142907905952645E-15)                            // 0x3ce8469898cc5170,
		M4PI := NewFromFloat(1.273239544735162542821171882678754627704620361328125) // 4/pi

		if d.Equal(NewFromFloat(0.0)) {
			return d
		}

  	// make argument positive but save the sign
  	sign := false
  	if d.LessThan(NewFromFloat(0.0)) {
  		d = d.Neg()
  		sign = true
  	}

		j := d.Mul(M4PI).IntPart()    // integer part of x/(Pi/4), as integer for tests on the phase angle
  	y := NewFromFloat(float64(j)) // integer part of x/(Pi/4), as float

  	// map zeros to origin
  	if j&1 == 1 {
  		j++
  		y = y.Add(NewFromFloat(1.0))
  	}

		z := d.Sub(y.Mul(PI4A)).Sub(y.Mul(PI4B)).Sub(y.Mul(PI4C)) // Extended precision modular arithmetic
  	zz := z.Mul(z)

  	if zz.GreaterThan(NewFromFloat(1e-14)) {
			w := zz.Mul(_tanP[0].Mul(zz).Add(_tanP[1]).Mul(zz).Add(_tanP[2]))
			x := zz.Add(_tanQ[1]).Mul(zz).Add(_tanQ[2]).Mul(zz).Add(_tanQ[3]).Mul(zz).Add(_tanQ[4])
			y = z.Add(z.Mul(w.Div(x)))
  	} else {
  		y = z
  	}
  	if j&2 == 2 {
			y = NewFromFloat(-1.0).Div(y)
  	}
  	if sign {
  		y = y.Neg()
  	}
  	return y
  }