From cdd653fd663f6550536e10f8b8b701327b2e88c7 Mon Sep 17 00:00:00 2001 From: "yenlin.lai" Date: Thu, 21 Mar 2019 16:20:57 +0800 Subject: misc: replace shopspring/decimal with our fork --- .../github.com/dexon-foundation/decimal/decimal.go | 1468 ++++++++++++++++++++ 1 file changed, 1468 insertions(+) create mode 100644 vendor/github.com/dexon-foundation/decimal/decimal.go (limited to 'vendor/github.com/dexon-foundation/decimal/decimal.go') diff --git a/vendor/github.com/dexon-foundation/decimal/decimal.go b/vendor/github.com/dexon-foundation/decimal/decimal.go new file mode 100644 index 000000000..0f5079c42 --- /dev/null +++ b/vendor/github.com/dexon-foundation/decimal/decimal.go @@ -0,0 +1,1468 @@ +// 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 + +// Common decimal constants, to make computations faster. +var ( + Zero = New(0, 0) + One = New(1, 0) + Two = New(2, 0) + Five = New(5, 0) + Ten = New(1, 1) +) + +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{}, &ErrorExponentLimit{value: value} + } + return Decimal{}, &ErrorInvalidFormat{ + reason: fmt.Sprintf( + "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 + if intString == "" && parts[1] != "" { + intString = "0" + } + expInt := -len(decimalPart) + exp += int64(expInt) + } else { + return Decimal{}, &ErrorInvalidFormat{ + reason: fmt.Sprintf( + "can't convert %s to decimal: too many .s", + value), + } + } + + dValue := new(big.Int) + _, ok := dValue.SetString(intString, 10) + if !ok { + return Decimal{}, &ErrorInvalidFormat{ + reason: fmt.Sprintf("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{}, &ErrorExponentLimit{ + value: 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) +} + +// NewFromFloat32 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+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{} + } + // 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 +func (d Decimal) Rescale(exp int32) Decimal { + return d.rescale(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 One + } + temp = d.Pow(d2.Div(Two)) + 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(Five).IsZero() { + 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 err + } + + decimal, err := NewFromString(str) + *d = decimal + if err != nil { + return 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 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 "", &ErrorInvalidType{ + reason: fmt.Sprintf( + "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 d. +func (d Decimal) Atan() Decimal { + if d.IsZero() { + return d + } + if d.IsPositive() { + return d.satan() + } + return d.Neg().satan().Neg() +} + +var _xatanP = [...]Decimal{ + NewFromFloat(-8.750608600031904122785e-01), + NewFromFloat(-1.615753718733365076637e+01), + NewFromFloat(-7.500855792314704667340e+01), + NewFromFloat(-1.228866684490136173410e+02), + NewFromFloat(-6.485021904942025371773e+01), +} + +var _xatanQ = [...]Decimal{ + NewFromFloat(2.485846490142306297962e+01), + NewFromFloat(1.650270098316988542046e+02), + NewFromFloat(4.328810604912902668951e+02), + NewFromFloat(4.853903996359136964868e+02), + NewFromFloat(1.945506571482613964425e+02), +} + +func (d Decimal) xatan() Decimal { + z := d.Mul(d) + b1 := _xatanP[0].Mul(z).Add(_xatanP[1]).Mul(z).Add(_xatanP[2]).Mul(z).Add(_xatanP[3]).Mul(z).Add(_xatanP[4]).Mul(z) + b2 := z.Add(_xatanQ[0]).Mul(z).Add(_xatanQ[1]).Mul(z).Add(_xatanQ[2]).Mul(z).Add(_xatanQ[3]).Mul(z).Add(_xatanQ[4]) + 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(New(66, -2)) { + return d.xatan() + } + if d.GreaterThan(Tan3pio8) { + return pi.Div(Two).Sub(One.Div(d).xatan()).Add(Morebits) + } + return pi.Div(New(4, 0)).Add((d.Sub(One).Div(d.Add(One))).xatan()).Add(New(5, -1).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.IsZero() { + return d + } + // make argument positive but save the sign + sign := false + if d.IsNegative() { + 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(One) + } + 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 = One.Sub(New(5, -1).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.IsNegative() { + 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(One) + } + 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 = One.Sub(New(5, -1).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.IsZero() { + return d + } + + // make argument positive but save the sign + sign := false + if d.IsNegative() { + 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(One) + } + + 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(New(1, -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 = New(-1, 0).Div(y) + } + if sign { + y = y.Neg() + } + return y +} -- cgit v1.2.3