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Diffstat (limited to 'vendor/github.com/shopspring/decimal/decimal.go')
| -rw-r--r-- | vendor/github.com/shopspring/decimal/decimal.go | 1904 |
1 files changed, 0 insertions, 1904 deletions
diff --git a/vendor/github.com/shopspring/decimal/decimal.go b/vendor/github.com/shopspring/decimal/decimal.go deleted file mode 100644 index 84405ec1c..000000000 --- a/vendor/github.com/shopspring/decimal/decimal.go +++ /dev/null @@ -1,1904 +0,0 @@ -// Package decimal implements an arbitrary precision fixed-point 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" -// -// To use Decimal as part of a struct: -// -// type Struct struct { -// Number Decimal -// } -// -// 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" - "regexp" - "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 - -// ExpMaxIterations specifies the maximum number of iterations needed to calculate -// precise natural exponent value using ExpHullAbrham method. -var ExpMaxIterations = 1000 - -// Zero constant, to make computations faster. -// Zero should never be compared with == or != directly, please use decimal.Equal or decimal.Cmp instead. -var Zero = New(0, 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) - -var factorials = []Decimal{New(1, 0)} - -// 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, - } -} - -// NewFromInt converts a int64 to Decimal. -// -// Example: -// -// NewFromInt(123).String() // output: "123" -// NewFromInt(-10).String() // output: "-10" -func NewFromInt(value int64) Decimal { - return Decimal{ - value: big.NewInt(value), - exp: 0, - } -} - -// NewFromInt32 converts a int32 to Decimal. -// -// Example: -// -// NewFromInt(123).String() // output: "123" -// NewFromInt(-10).String() // output: "-10" -func NewFromInt32(value int32) Decimal { - return Decimal{ - value: big.NewInt(int64(value)), - exp: 0, - } -} - -// NewFromBigInt returns a new Decimal from a big.Int, value * 10 ^ exp -func NewFromBigInt(value *big.Int, exp int32) Decimal { - return Decimal{ - value: new(big.Int).Set(value), - exp: exp, - } -} - -// NewFromString returns a new Decimal from a string representation. -// Trailing zeroes are not trimmed. -// -// Example: -// -// d, err := NewFromString("-123.45") -// d2, err := NewFromString(".0001") -// d3, err := NewFromString("1.47000") -// -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 - } - - pIndex := -1 - vLen := len(value) - for i := 0; i < vLen; i++ { - if value[i] == '.' { - if pIndex > -1 { - return Decimal{}, fmt.Errorf("can't convert %s to decimal: too many .s", value) - } - pIndex = i - } - } - - if pIndex == -1 { - // There is no decimal point, we can just parse the original string as - // an int - intString = value - } else { - if pIndex+1 < vLen { - intString = value[:pIndex] + value[pIndex+1:] - } else { - intString = value[:pIndex] - } - expInt := -len(value[pIndex+1:]) - exp += int64(expInt) - } - - var dValue *big.Int - // strconv.ParseInt is faster than new(big.Int).SetString so this is just a shortcut for strings we know won't overflow - if len(intString) <= 18 { - parsed64, err := strconv.ParseInt(intString, 10, 64) - if err != nil { - return Decimal{}, fmt.Errorf("can't convert %s to decimal", value) - } - dValue = big.NewInt(parsed64) - } else { - 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 -} - -// NewFromFormattedString returns a new Decimal from a formatted string representation. -// The second argument - replRegexp, is a regular expression that is used to find characters that should be -// removed from given decimal string representation. All matched characters will be replaced with an empty string. -// -// Example: -// -// r := regexp.MustCompile("[$,]") -// d1, err := NewFromFormattedString("$5,125.99", r) -// -// r2 := regexp.MustCompile("[_]") -// d2, err := NewFromFormattedString("1_000_000", r2) -// -// r3 := regexp.MustCompile("[USD\\s]") -// d3, err := NewFromFormattedString("5000 USD", r3) -// -func NewFromFormattedString(value string, replRegexp *regexp.Regexp) (Decimal, error) { - parsedValue := replRegexp.ReplaceAllString(value, "") - d, err := NewFromString(parsedValue) - if err != nil { - return Decimal{}, err - } - return d, 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 - 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{} - } - // 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, - } -} - -// Copy returns a copy of decimal with the same value and exponent, but a different pointer to value. -func (d Decimal) Copy() Decimal { - d.ensureInitialized() - return Decimal{ - value: &(*d.value), - exp: d.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() - - if d.exp == exp { - return Decimal{ - new(big.Int).Set(d.value), - d.exp, - } - } - - // 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 { - if !d.IsNegative() { - return d - } - 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 { - rd, rd2 := RescalePair(d, d2) - - d3Value := new(big.Int).Add(rd.value, rd2.value) - return Decimal{ - value: d3Value, - exp: rd.exp, - } -} - -// Sub returns d - d2. -func (d Decimal) Sub(d2 Decimal) Decimal { - rd, rd2 := RescalePair(d, d2) - - d3Value := new(big.Int).Sub(rd.value, rd2.value) - return Decimal{ - value: d3Value, - exp: rd.exp, - } -} - -// 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) -} - -// ExpHullAbrham calculates the natural exponent of decimal (e to the power of d) using Hull-Abraham algorithm. -// OverallPrecision argument specifies the overall precision of the result (integer part + decimal part). -// -// ExpHullAbrham is faster than ExpTaylor for small precision values, but it is much slower for large precision values. -// -// Example: -// -// NewFromFloat(26.1).ExpHullAbrham(2).String() // output: "220000000000" -// NewFromFloat(26.1).ExpHullAbrham(20).String() // output: "216314672147.05767284" -// -func (d Decimal) ExpHullAbrham(overallPrecision uint32) (Decimal, error) { - // Algorithm based on Variable precision exponential function. - // ACM Transactions on Mathematical Software by T. E. Hull & A. Abrham. - if d.IsZero() { - return Decimal{oneInt, 0}, nil - } - - currentPrecision := overallPrecision - - // Algorithm does not work if currentPrecision * 23 < |x|. - // Precision is automatically increased in such cases, so the value can be calculated precisely. - // If newly calculated precision is higher than ExpMaxIterations the currentPrecision will not be changed. - f := d.Abs().InexactFloat64() - if ncp := f / 23; ncp > float64(currentPrecision) && ncp < float64(ExpMaxIterations) { - currentPrecision = uint32(math.Ceil(ncp)) - } - - // fail if abs(d) beyond an over/underflow threshold - overflowThreshold := New(23*int64(currentPrecision), 0) - if d.Abs().Cmp(overflowThreshold) > 0 { - return Decimal{}, fmt.Errorf("over/underflow threshold, exp(x) cannot be calculated precisely") - } - - // Return 1 if abs(d) small enough; this also avoids later over/underflow - overflowThreshold2 := New(9, -int32(currentPrecision)-1) - if d.Abs().Cmp(overflowThreshold2) <= 0 { - return Decimal{oneInt, d.exp}, nil - } - - // t is the smallest integer >= 0 such that the corresponding abs(d/k) < 1 - t := d.exp + int32(d.NumDigits()) // Add d.NumDigits because the paper assumes that d.value [0.1, 1) - - if t < 0 { - t = 0 - } - - k := New(1, t) // reduction factor - r := Decimal{new(big.Int).Set(d.value), d.exp - t} // reduced argument - p := int32(currentPrecision) + t + 2 // precision for calculating the sum - - // Determine n, the number of therms for calculating sum - // use first Newton step (1.435p - 1.182) / log10(p/abs(r)) - // for solving appropriate equation, along with directed - // roundings and simple rational bound for log10(p/abs(r)) - rf := r.Abs().InexactFloat64() - pf := float64(p) - nf := math.Ceil((1.453*pf - 1.182) / math.Log10(pf/rf)) - if nf > float64(ExpMaxIterations) || math.IsNaN(nf) { - return Decimal{}, fmt.Errorf("exact value cannot be calculated in <=ExpMaxIterations iterations") - } - n := int64(nf) - - tmp := New(0, 0) - sum := New(1, 0) - one := New(1, 0) - for i := n - 1; i > 0; i-- { - tmp.value.SetInt64(i) - sum = sum.Mul(r.DivRound(tmp, p)) - sum = sum.Add(one) - } - - ki := k.IntPart() - res := New(1, 0) - for i := ki; i > 0; i-- { - res = res.Mul(sum) - } - - resNumDigits := int32(res.NumDigits()) - - var roundDigits int32 - if resNumDigits > abs(res.exp) { - roundDigits = int32(currentPrecision) - resNumDigits - res.exp - } else { - roundDigits = int32(currentPrecision) - } - - res = res.Round(roundDigits) - - return res, nil -} - -// ExpTaylor calculates the natural exponent of decimal (e to the power of d) using Taylor series expansion. -// Precision argument specifies how precise the result must be (number of digits after decimal point). -// Negative precision is allowed. -// -// ExpTaylor is much faster for large precision values than ExpHullAbrham. -// -// Example: -// -// d, err := NewFromFloat(26.1).ExpTaylor(2).String() -// d.String() // output: "216314672147.06" -// -// NewFromFloat(26.1).ExpTaylor(20).String() -// d.String() // output: "216314672147.05767284062928674083" -// -// NewFromFloat(26.1).ExpTaylor(-10).String() -// d.String() // output: "220000000000" -// -func (d Decimal) ExpTaylor(precision int32) (Decimal, error) { - // Note(mwoss): Implementation can be optimized by exclusively using big.Int API only - if d.IsZero() { - return Decimal{oneInt, 0}.Round(precision), nil - } - - var epsilon Decimal - var divPrecision int32 - if precision < 0 { - epsilon = New(1, -1) - divPrecision = 8 - } else { - epsilon = New(1, -precision-1) - divPrecision = precision + 1 - } - - decAbs := d.Abs() - pow := d.Abs() - factorial := New(1, 0) - - result := New(1, 0) - - for i := int64(1); ; { - step := pow.DivRound(factorial, divPrecision) - result = result.Add(step) - - // Stop Taylor series when current step is smaller than epsilon - if step.Cmp(epsilon) < 0 { - break - } - - pow = pow.Mul(decAbs) - - i++ - - // Calculate next factorial number or retrieve cached value - if len(factorials) >= int(i) && !factorials[i-1].IsZero() { - factorial = factorials[i-1] - } else { - // To avoid any race conditions, firstly the zero value is appended to a slice to create - // a spot for newly calculated factorial. After that, the zero value is replaced by calculated - // factorial using the index notation. - factorial = factorials[i-2].Mul(New(i, 0)) - factorials = append(factorials, Zero) - factorials[i-1] = factorial - } - } - - if d.Sign() < 0 { - result = New(1, 0).DivRound(result, precision+1) - } - - result = result.Round(precision) - return result, nil -} - -// NumDigits returns the number of digits of the decimal coefficient (d.Value) -// Note: Current implementation is extremely slow for large decimals and/or decimals with large fractional part -func (d Decimal) NumDigits() int { - // Note(mwoss): It can be optimized, unnecessary cast of big.Int to string - if d.IsNegative() { - return len(d.value.String()) - 1 - } - return len(d.value.String()) -} - -// IsInteger returns true when decimal can be represented as an integer value, otherwise, it returns false. -func (d Decimal) IsInteger() bool { - // The most typical case, all decimal with exponent higher or equal 0 can be represented as integer - if d.exp >= 0 { - return true - } - // When the exponent is negative we have to check every number after the decimal place - // If all of them are zeroes, we are sure that given decimal can be represented as an integer - var r big.Int - q := new(big.Int).Set(d.value) - for z := abs(d.exp); z > 0; z-- { - q.QuoRem(q, tenInt, &r) - if r.Cmp(zeroInt) != 0 { - return false - } - } - return true -} - -// Abs calculates absolute value of any int32. Used for calculating absolute value of decimal's exponent. -func abs(n int32) int32 { - if n < 0 { - return -n - } - return n -} - -// 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) - } - - rd, rd2 := RescalePair(d, d2) - - 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 { - d.ensureInitialized() - // we copy the coefficient so that mutating the result does not mutate the Decimal. - return new(big.Int).Set(d.value) -} - -// CoefficientInt64 returns the coefficient of the decimal as int64. It is scaled by 10^Exponent() -// If coefficient cannot be represented in an int64, the result will be undefined. -func (d Decimal) CoefficientInt64() int64 { - d.ensureInitialized() - return d.value.Int64() -} - -// IntPart returns the integer component of the decimal. -func (d Decimal) IntPart() int64 { - scaledD := d.rescale(0) - return scaledD.value.Int64() -} - -// BigInt returns integer component of the decimal as a BigInt. -func (d Decimal) BigInt() *big.Int { - scaledD := d.rescale(0) - i := &big.Int{} - i.SetString(scaledD.String(), 10) - return i -} - -// BigFloat returns decimal as BigFloat. -// Be aware that casting decimal to BigFloat might cause a loss of precision. -func (d Decimal) BigFloat() *big.Float { - f := &big.Float{} - f.SetString(d.String()) - return f -} - -// 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() -} - -// InexactFloat64 returns the nearest float64 value for d. -// It doesn't indicate if the returned value represents d exactly. -func (d Decimal) InexactFloat64() float64 { - f, _ := d.Float64() - return f -} - -// 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).StringFixedBank(2) // output: "0.00" -// NewFromFloat(0).StringFixedBank(0) // output: "0" -// NewFromFloat(5.45).StringFixedBank(0) // output: "5" -// NewFromFloat(5.45).StringFixedBank(1) // output: "5.4" -// NewFromFloat(5.45).StringFixedBank(2) // output: "5.45" -// NewFromFloat(5.45).StringFixedBank(3) // output: "5.450" -// NewFromFloat(545).StringFixedBank(-1) // output: "540" -// -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 { - if d.exp == -places { - return d - } - // 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 -} - -// RoundCeil rounds the decimal towards +infinity. -// -// Example: -// -// NewFromFloat(545).RoundCeil(-2).String() // output: "600" -// NewFromFloat(500).RoundCeil(-2).String() // output: "500" -// NewFromFloat(1.1001).RoundCeil(2).String() // output: "1.11" -// NewFromFloat(-1.454).RoundCeil(1).String() // output: "-1.5" -// -func (d Decimal) RoundCeil(places int32) Decimal { - if d.exp >= -places { - return d - } - - rescaled := d.rescale(-places) - if d.Equal(rescaled) { - return d - } - - if d.value.Sign() > 0 { - rescaled.value.Add(rescaled.value, oneInt) - } - - return rescaled -} - -// RoundFloor rounds the decimal towards -infinity. -// -// Example: -// -// NewFromFloat(545).RoundFloor(-2).String() // output: "500" -// NewFromFloat(-500).RoundFloor(-2).String() // output: "-500" -// NewFromFloat(1.1001).RoundFloor(2).String() // output: "1.1" -// NewFromFloat(-1.454).RoundFloor(1).String() // output: "-1.4" -// -func (d Decimal) RoundFloor(places int32) Decimal { - if d.exp >= -places { - return d - } - - rescaled := d.rescale(-places) - if d.Equal(rescaled) { - return d - } - - if d.value.Sign() < 0 { - rescaled.value.Sub(rescaled.value, oneInt) - } - - return rescaled -} - -// RoundUp rounds the decimal away from zero. -// -// Example: -// -// NewFromFloat(545).RoundUp(-2).String() // output: "600" -// NewFromFloat(500).RoundUp(-2).String() // output: "500" -// NewFromFloat(1.1001).RoundUp(2).String() // output: "1.11" -// NewFromFloat(-1.454).RoundUp(1).String() // output: "-1.4" -// -func (d Decimal) RoundUp(places int32) Decimal { - if d.exp >= -places { - return d - } - - rescaled := d.rescale(-places) - if d.Equal(rescaled) { - return d - } - - if d.value.Sign() > 0 { - rescaled.value.Add(rescaled.value, oneInt) - } else if d.value.Sign() < 0 { - rescaled.value.Sub(rescaled.value, oneInt) - } - - return rescaled -} - -// RoundDown rounds the decimal towards zero. -// -// Example: -// -// NewFromFloat(545).RoundDown(-2).String() // output: "500" -// NewFromFloat(-500).RoundDown(-2).String() // output: "-500" -// NewFromFloat(1.1001).RoundDown(2).String() // output: "1.1" -// NewFromFloat(-1.454).RoundDown(1).String() // output: "-1.5" -// -func (d Decimal) RoundDown(places int32) Decimal { - if d.exp >= -places { - return d - } - - rescaled := d.rescale(-places) - if d.Equal(rescaled) { - return d - } - return rescaled -} - -// 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).RoundBank(1).String() // output: "5.4" -// NewFromFloat(545).RoundBank(-1).String() // output: "540" -// NewFromFloat(5.46).RoundBank(1).String() // output: "5.5" -// NewFromFloat(546).RoundBank(-1).String() // output: "550" -// NewFromFloat(5.55).RoundBank(1).String() // output: "5.6" -// NewFromFloat(555).RoundBank(-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, 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) -// 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 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, 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 { - // Verify we have at least 4 bytes for the exponent. The GOB encoded value - // may be empty. - if len(data) < 4 { - return fmt.Errorf("error decoding binary %v: expected at least 4 bytes, got %d", data, len(data)) - } - - // Extract the exponent - d.exp = int32(binary.BigEndian.Uint32(data[:4])) - - // Extract the value - d.value = new(big.Int) - if err := d.value.GobDecode(data[4:]); err != nil { - return fmt.Errorf("error decoding binary %v: %s", data, err) - } - - return nil -} - -// 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) -} - -// RescalePair rescales two decimals to common exponential value (minimal exp of both decimals) -func RescalePair(d1 Decimal, d2 Decimal) (Decimal, Decimal) { - d1.ensureInitialized() - d2.ensureInitialized() - - if d1.exp == d2.exp { - return d1, d2 - } - - baseScale := min(d1.exp, d2.exp) - if baseScale != d1.exp { - return d1.rescale(baseScale), d2 - } - return d1, d2.rescale(baseScale) -} - -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 -} - -func NewNullDecimal(d Decimal) NullDecimal { - return NullDecimal{ - Decimal: d, - Valid: true, - } -} - -// 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() -} - -// UnmarshalText implements the encoding.TextUnmarshaler interface for XML -// deserialization -func (d *NullDecimal) UnmarshalText(text []byte) error { - str := string(text) - - // check for empty XML or XML without body e.g., <tag></tag> - if str == "" { - d.Valid = false - return nil - } - if err := d.Decimal.UnmarshalText(text); err != nil { - d.Valid = false - return err - } - d.Valid = true - return nil -} - -// MarshalText implements the encoding.TextMarshaler interface for XML -// serialization. -func (d NullDecimal) MarshalText() (text []byte, err error) { - if !d.Valid { - return []byte{}, nil - } - return d.Decimal.MarshalText() -} - -// Trig functions - -// Atan returns the arctangent, in radians, of x. -func (d Decimal) Atan() Decimal { - if d.Equal(NewFromFloat(0.0)) { - return d - } - if d.GreaterThan(NewFromFloat(0.0)) { - return d.satan() - } - return d.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 -} |