misc: replace shopspring/decimal with our fork

1 files changed, 1468 insertions, 0 deletions

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 - 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,
+	}
+}
+
+// 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
+}