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path: root/vendor/gopkg.in/inf.v0/dec.go
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diff --git a/vendor/gopkg.in/inf.v0/dec.go b/vendor/gopkg.in/inf.v0/dec.go
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+// Package inf (type inf.Dec) implements "infinite-precision" decimal
+// arithmetic.
+// "Infinite precision" describes two characteristics: practically unlimited
+// precision for decimal number representation and no support for calculating
+// with any specific fixed precision.
+// (Although there is no practical limit on precision, inf.Dec can only
+// represent finite decimals.)
+//
+// This package is currently in experimental stage and the API may change.
+//
+// This package does NOT support:
+// - rounding to specific precisions (as opposed to specific decimal positions)
+// - the notion of context (each rounding must be explicit)
+// - NaN and Inf values, and distinguishing between positive and negative zero
+// - conversions to and from float32/64 types
+//
+// Features considered for possible addition:
+// + formatting options
+// + Exp method
+// + combined operations such as AddRound/MulAdd etc
+// + exchanging data in decimal32/64/128 formats
+//
+package inf // import "gopkg.in/inf.v0"
+
+// TODO:
+// - avoid excessive deep copying (quo and rounders)
+
+import (
+ "fmt"
+ "io"
+ "math/big"
+ "strings"
+)
+
+// A Dec represents a signed arbitrary-precision decimal.
+// It is a combination of a sign, an arbitrary-precision integer coefficient
+// value, and a signed fixed-precision exponent value.
+// The sign and the coefficient value are handled together as a signed value
+// and referred to as the unscaled value.
+// (Positive and negative zero values are not distinguished.)
+// Since the exponent is most commonly non-positive, it is handled in negated
+// form and referred to as scale.
+//
+// The mathematical value of a Dec equals:
+//
+// unscaled * 10**(-scale)
+//
+// Note that different Dec representations may have equal mathematical values.
+//
+// unscaled scale String()
+// -------------------------
+// 0 0 "0"
+// 0 2 "0.00"
+// 0 -2 "0"
+// 1 0 "1"
+// 100 2 "1.00"
+// 10 0 "10"
+// 1 -1 "10"
+//
+// The zero value for a Dec represents the value 0 with scale 0.
+//
+// Operations are typically performed through the *Dec type.
+// The semantics of the assignment operation "=" for "bare" Dec values is
+// undefined and should not be relied on.
+//
+// Methods are typically of the form:
+//
+// func (z *Dec) Op(x, y *Dec) *Dec
+//
+// and implement operations z = x Op y with the result as receiver; if it
+// is one of the operands it may be overwritten (and its memory reused).
+// To enable chaining of operations, the result is also returned. Methods
+// returning a result other than *Dec take one of the operands as the receiver.
+//
+// A "bare" Quo method (quotient / division operation) is not provided, as the
+// result is not always a finite decimal and thus in general cannot be
+// represented as a Dec.
+// Instead, in the common case when rounding is (potentially) necessary,
+// QuoRound should be used with a Scale and a Rounder.
+// QuoExact or QuoRound with RoundExact can be used in the special cases when it
+// is known that the result is always a finite decimal.
+//
+type Dec struct {
+ unscaled big.Int
+ scale Scale
+}
+
+// Scale represents the type used for the scale of a Dec.
+type Scale int32
+
+const scaleSize = 4 // bytes in a Scale value
+
+// Scaler represents a method for obtaining the scale to use for the result of
+// an operation on x and y.
+type scaler interface {
+ Scale(x *Dec, y *Dec) Scale
+}
+
+var bigInt = [...]*big.Int{
+ big.NewInt(0), big.NewInt(1), big.NewInt(2), big.NewInt(3), big.NewInt(4),
+ big.NewInt(5), big.NewInt(6), big.NewInt(7), big.NewInt(8), big.NewInt(9),
+ big.NewInt(10),
+}
+
+var exp10cache [64]big.Int = func() [64]big.Int {
+ e10, e10i := [64]big.Int{}, bigInt[1]
+ for i, _ := range e10 {
+ e10[i].Set(e10i)
+ e10i = new(big.Int).Mul(e10i, bigInt[10])
+ }
+ return e10
+}()
+
+// NewDec allocates and returns a new Dec set to the given int64 unscaled value
+// and scale.
+func NewDec(unscaled int64, scale Scale) *Dec {
+ return new(Dec).SetUnscaled(unscaled).SetScale(scale)
+}
+
+// NewDecBig allocates and returns a new Dec set to the given *big.Int unscaled
+// value and scale.
+func NewDecBig(unscaled *big.Int, scale Scale) *Dec {
+ return new(Dec).SetUnscaledBig(unscaled).SetScale(scale)
+}
+
+// Scale returns the scale of x.
+func (x *Dec) Scale() Scale {
+ return x.scale
+}
+
+// Unscaled returns the unscaled value of x for u and true for ok when the
+// unscaled value can be represented as int64; otherwise it returns an undefined
+// int64 value for u and false for ok. Use x.UnscaledBig().Int64() to avoid
+// checking the validity of the value when the check is known to be redundant.
+func (x *Dec) Unscaled() (u int64, ok bool) {
+ u = x.unscaled.Int64()
+ var i big.Int
+ ok = i.SetInt64(u).Cmp(&x.unscaled) == 0
+ return
+}
+
+// UnscaledBig returns the unscaled value of x as *big.Int.
+func (x *Dec) UnscaledBig() *big.Int {
+ return &x.unscaled
+}
+
+// SetScale sets the scale of z, with the unscaled value unchanged, and returns
+// z.
+// The mathematical value of the Dec changes as if it was multiplied by
+// 10**(oldscale-scale).
+func (z *Dec) SetScale(scale Scale) *Dec {
+ z.scale = scale
+ return z
+}
+
+// SetUnscaled sets the unscaled value of z, with the scale unchanged, and
+// returns z.
+func (z *Dec) SetUnscaled(unscaled int64) *Dec {
+ z.unscaled.SetInt64(unscaled)
+ return z
+}
+
+// SetUnscaledBig sets the unscaled value of z, with the scale unchanged, and
+// returns z.
+func (z *Dec) SetUnscaledBig(unscaled *big.Int) *Dec {
+ z.unscaled.Set(unscaled)
+ return z
+}
+
+// Set sets z to the value of x and returns z.
+// It does nothing if z == x.
+func (z *Dec) Set(x *Dec) *Dec {
+ if z != x {
+ z.SetUnscaledBig(x.UnscaledBig())
+ z.SetScale(x.Scale())
+ }
+ return z
+}
+
+// Sign returns:
+//
+// -1 if x < 0
+// 0 if x == 0
+// +1 if x > 0
+//
+func (x *Dec) Sign() int {
+ return x.UnscaledBig().Sign()
+}
+
+// Neg sets z to -x and returns z.
+func (z *Dec) Neg(x *Dec) *Dec {
+ z.SetScale(x.Scale())
+ z.UnscaledBig().Neg(x.UnscaledBig())
+ return z
+}
+
+// Cmp compares x and y and returns:
+//
+// -1 if x < y
+// 0 if x == y
+// +1 if x > y
+//
+func (x *Dec) Cmp(y *Dec) int {
+ xx, yy := upscale(x, y)
+ return xx.UnscaledBig().Cmp(yy.UnscaledBig())
+}
+
+// Abs sets z to |x| (the absolute value of x) and returns z.
+func (z *Dec) Abs(x *Dec) *Dec {
+ z.SetScale(x.Scale())
+ z.UnscaledBig().Abs(x.UnscaledBig())
+ return z
+}
+
+// Add sets z to the sum x+y and returns z.
+// The scale of z is the greater of the scales of x and y.
+func (z *Dec) Add(x, y *Dec) *Dec {
+ xx, yy := upscale(x, y)
+ z.SetScale(xx.Scale())
+ z.UnscaledBig().Add(xx.UnscaledBig(), yy.UnscaledBig())
+ return z
+}
+
+// Sub sets z to the difference x-y and returns z.
+// The scale of z is the greater of the scales of x and y.
+func (z *Dec) Sub(x, y *Dec) *Dec {
+ xx, yy := upscale(x, y)
+ z.SetScale(xx.Scale())
+ z.UnscaledBig().Sub(xx.UnscaledBig(), yy.UnscaledBig())
+ return z
+}
+
+// Mul sets z to the product x*y and returns z.
+// The scale of z is the sum of the scales of x and y.
+func (z *Dec) Mul(x, y *Dec) *Dec {
+ z.SetScale(x.Scale() + y.Scale())
+ z.UnscaledBig().Mul(x.UnscaledBig(), y.UnscaledBig())
+ return z
+}
+
+// Round sets z to the value of x rounded to Scale s using Rounder r, and
+// returns z.
+func (z *Dec) Round(x *Dec, s Scale, r Rounder) *Dec {
+ return z.QuoRound(x, NewDec(1, 0), s, r)
+}
+
+// QuoRound sets z to the quotient x/y, rounded using the given Rounder to the
+// specified scale.
+//
+// If the rounder is RoundExact but the result can not be expressed exactly at
+// the specified scale, QuoRound returns nil, and the value of z is undefined.
+//
+// There is no corresponding Div method; the equivalent can be achieved through
+// the choice of Rounder used.
+//
+func (z *Dec) QuoRound(x, y *Dec, s Scale, r Rounder) *Dec {
+ return z.quo(x, y, sclr{s}, r)
+}
+
+func (z *Dec) quo(x, y *Dec, s scaler, r Rounder) *Dec {
+ scl := s.Scale(x, y)
+ var zzz *Dec
+ if r.UseRemainder() {
+ zz, rA, rB := new(Dec).quoRem(x, y, scl, true, new(big.Int), new(big.Int))
+ zzz = r.Round(new(Dec), zz, rA, rB)
+ } else {
+ zz, _, _ := new(Dec).quoRem(x, y, scl, false, nil, nil)
+ zzz = r.Round(new(Dec), zz, nil, nil)
+ }
+ if zzz == nil {
+ return nil
+ }
+ return z.Set(zzz)
+}
+
+// QuoExact sets z to the quotient x/y and returns z when x/y is a finite
+// decimal. Otherwise it returns nil and the value of z is undefined.
+//
+// The scale of a non-nil result is "x.Scale() - y.Scale()" or greater; it is
+// calculated so that the remainder will be zero whenever x/y is a finite
+// decimal.
+func (z *Dec) QuoExact(x, y *Dec) *Dec {
+ return z.quo(x, y, scaleQuoExact{}, RoundExact)
+}
+
+// quoRem sets z to the quotient x/y with the scale s, and if useRem is true,
+// it sets remNum and remDen to the numerator and denominator of the remainder.
+// It returns z, remNum and remDen.
+//
+// The remainder is normalized to the range -1 < r < 1 to simplify rounding;
+// that is, the results satisfy the following equation:
+//
+// x / y = z + (remNum/remDen) * 10**(-z.Scale())
+//
+// See Rounder for more details about rounding.
+//
+func (z *Dec) quoRem(x, y *Dec, s Scale, useRem bool,
+ remNum, remDen *big.Int) (*Dec, *big.Int, *big.Int) {
+ // difference (required adjustment) compared to "canonical" result scale
+ shift := s - (x.Scale() - y.Scale())
+ // pointers to adjusted unscaled dividend and divisor
+ var ix, iy *big.Int
+ switch {
+ case shift > 0:
+ // increased scale: decimal-shift dividend left
+ ix = new(big.Int).Mul(x.UnscaledBig(), exp10(shift))
+ iy = y.UnscaledBig()
+ case shift < 0:
+ // decreased scale: decimal-shift divisor left
+ ix = x.UnscaledBig()
+ iy = new(big.Int).Mul(y.UnscaledBig(), exp10(-shift))
+ default:
+ ix = x.UnscaledBig()
+ iy = y.UnscaledBig()
+ }
+ // save a copy of iy in case it to be overwritten with the result
+ iy2 := iy
+ if iy == z.UnscaledBig() {
+ iy2 = new(big.Int).Set(iy)
+ }
+ // set scale
+ z.SetScale(s)
+ // set unscaled
+ if useRem {
+ // Int division
+ _, intr := z.UnscaledBig().QuoRem(ix, iy, new(big.Int))
+ // set remainder
+ remNum.Set(intr)
+ remDen.Set(iy2)
+ } else {
+ z.UnscaledBig().Quo(ix, iy)
+ }
+ return z, remNum, remDen
+}
+
+type sclr struct{ s Scale }
+
+func (s sclr) Scale(x, y *Dec) Scale {
+ return s.s
+}
+
+type scaleQuoExact struct{}
+
+func (sqe scaleQuoExact) Scale(x, y *Dec) Scale {
+ rem := new(big.Rat).SetFrac(x.UnscaledBig(), y.UnscaledBig())
+ f2, f5 := factor2(rem.Denom()), factor(rem.Denom(), bigInt[5])
+ var f10 Scale
+ if f2 > f5 {
+ f10 = Scale(f2)
+ } else {
+ f10 = Scale(f5)
+ }
+ return x.Scale() - y.Scale() + f10
+}
+
+func factor(n *big.Int, p *big.Int) int {
+ // could be improved for large factors
+ d, f := n, 0
+ for {
+ dd, dm := new(big.Int).DivMod(d, p, new(big.Int))
+ if dm.Sign() == 0 {
+ f++
+ d = dd
+ } else {
+ break
+ }
+ }
+ return f
+}
+
+func factor2(n *big.Int) int {
+ // could be improved for large factors
+ f := 0
+ for ; n.Bit(f) == 0; f++ {
+ }
+ return f
+}
+
+func upscale(a, b *Dec) (*Dec, *Dec) {
+ if a.Scale() == b.Scale() {
+ return a, b
+ }
+ if a.Scale() > b.Scale() {
+ bb := b.rescale(a.Scale())
+ return a, bb
+ }
+ aa := a.rescale(b.Scale())
+ return aa, b
+}
+
+func exp10(x Scale) *big.Int {
+ if int(x) < len(exp10cache) {
+ return &exp10cache[int(x)]
+ }
+ return new(big.Int).Exp(bigInt[10], big.NewInt(int64(x)), nil)
+}
+
+func (x *Dec) rescale(newScale Scale) *Dec {
+ shift := newScale - x.Scale()
+ switch {
+ case shift < 0:
+ e := exp10(-shift)
+ return NewDecBig(new(big.Int).Quo(x.UnscaledBig(), e), newScale)
+ case shift > 0:
+ e := exp10(shift)
+ return NewDecBig(new(big.Int).Mul(x.UnscaledBig(), e), newScale)
+ }
+ return x
+}
+
+var zeros = []byte("00000000000000000000000000000000" +
+ "00000000000000000000000000000000")
+var lzeros = Scale(len(zeros))
+
+func appendZeros(s []byte, n Scale) []byte {
+ for i := Scale(0); i < n; i += lzeros {
+ if n > i+lzeros {
+ s = append(s, zeros...)
+ } else {
+ s = append(s, zeros[0:n-i]...)
+ }
+ }
+ return s
+}
+
+func (x *Dec) String() string {
+ if x == nil {
+ return "<nil>"
+ }
+ scale := x.Scale()
+ s := []byte(x.UnscaledBig().String())
+ if scale <= 0 {
+ if scale != 0 && x.unscaled.Sign() != 0 {
+ s = appendZeros(s, -scale)
+ }
+ return string(s)
+ }
+ negbit := Scale(-((x.Sign() - 1) / 2))
+ // scale > 0
+ lens := Scale(len(s))
+ if lens-negbit <= scale {
+ ss := make([]byte, 0, scale+2)
+ if negbit == 1 {
+ ss = append(ss, '-')
+ }
+ ss = append(ss, '0', '.')
+ ss = appendZeros(ss, scale-lens+negbit)
+ ss = append(ss, s[negbit:]...)
+ return string(ss)
+ }
+ // lens > scale
+ ss := make([]byte, 0, lens+1)
+ ss = append(ss, s[:lens-scale]...)
+ ss = append(ss, '.')
+ ss = append(ss, s[lens-scale:]...)
+ return string(ss)
+}
+
+// Format is a support routine for fmt.Formatter. It accepts the decimal
+// formats 'd' and 'f', and handles both equivalently.
+// Width, precision, flags and bases 2, 8, 16 are not supported.
+func (x *Dec) Format(s fmt.State, ch rune) {
+ if ch != 'd' && ch != 'f' && ch != 'v' && ch != 's' {
+ fmt.Fprintf(s, "%%!%c(dec.Dec=%s)", ch, x.String())
+ return
+ }
+ fmt.Fprintf(s, x.String())
+}
+
+func (z *Dec) scan(r io.RuneScanner) (*Dec, error) {
+ unscaled := make([]byte, 0, 256) // collects chars of unscaled as bytes
+ dp, dg := -1, -1 // indexes of decimal point, first digit
+loop:
+ for {
+ ch, _, err := r.ReadRune()
+ if err == io.EOF {
+ break loop
+ }
+ if err != nil {
+ return nil, err
+ }
+ switch {
+ case ch == '+' || ch == '-':
+ if len(unscaled) > 0 || dp >= 0 { // must be first character
+ r.UnreadRune()
+ break loop
+ }
+ case ch == '.':
+ if dp >= 0 {
+ r.UnreadRune()
+ break loop
+ }
+ dp = len(unscaled)
+ continue // don't add to unscaled
+ case ch >= '0' && ch <= '9':
+ if dg == -1 {
+ dg = len(unscaled)
+ }
+ default:
+ r.UnreadRune()
+ break loop
+ }
+ unscaled = append(unscaled, byte(ch))
+ }
+ if dg == -1 {
+ return nil, fmt.Errorf("no digits read")
+ }
+ if dp >= 0 {
+ z.SetScale(Scale(len(unscaled) - dp))
+ } else {
+ z.SetScale(0)
+ }
+ _, ok := z.UnscaledBig().SetString(string(unscaled), 10)
+ if !ok {
+ return nil, fmt.Errorf("invalid decimal: %s", string(unscaled))
+ }
+ return z, nil
+}
+
+// SetString sets z to the value of s, interpreted as a decimal (base 10),
+// and returns z and a boolean indicating success. The scale of z is the
+// number of digits after the decimal point (including any trailing 0s),
+// or 0 if there is no decimal point. If SetString fails, the value of z
+// is undefined but the returned value is nil.
+func (z *Dec) SetString(s string) (*Dec, bool) {
+ r := strings.NewReader(s)
+ _, err := z.scan(r)
+ if err != nil {
+ return nil, false
+ }
+ _, _, err = r.ReadRune()
+ if err != io.EOF {
+ return nil, false
+ }
+ // err == io.EOF => scan consumed all of s
+ return z, true
+}
+
+// Scan is a support routine for fmt.Scanner; it sets z to the value of
+// the scanned number. It accepts the decimal formats 'd' and 'f', and
+// handles both equivalently. Bases 2, 8, 16 are not supported.
+// The scale of z is the number of digits after the decimal point
+// (including any trailing 0s), or 0 if there is no decimal point.
+func (z *Dec) Scan(s fmt.ScanState, ch rune) error {
+ if ch != 'd' && ch != 'f' && ch != 's' && ch != 'v' {
+ return fmt.Errorf("Dec.Scan: invalid verb '%c'", ch)
+ }
+ s.SkipSpace()
+ _, err := z.scan(s)
+ return err
+}
+
+// Gob encoding version
+const decGobVersion byte = 1
+
+func scaleBytes(s Scale) []byte {
+ buf := make([]byte, scaleSize)
+ i := scaleSize
+ for j := 0; j < scaleSize; j++ {
+ i--
+ buf[i] = byte(s)
+ s >>= 8
+ }
+ return buf
+}
+
+func scale(b []byte) (s Scale) {
+ for j := 0; j < scaleSize; j++ {
+ s <<= 8
+ s |= Scale(b[j])
+ }
+ return
+}
+
+// GobEncode implements the gob.GobEncoder interface.
+func (x *Dec) GobEncode() ([]byte, error) {
+ buf, err := x.UnscaledBig().GobEncode()
+ if err != nil {
+ return nil, err
+ }
+ buf = append(append(buf, scaleBytes(x.Scale())...), decGobVersion)
+ return buf, nil
+}
+
+// GobDecode implements the gob.GobDecoder interface.
+func (z *Dec) GobDecode(buf []byte) error {
+ if len(buf) == 0 {
+ return fmt.Errorf("Dec.GobDecode: no data")
+ }
+ b := buf[len(buf)-1]
+ if b != decGobVersion {
+ return fmt.Errorf("Dec.GobDecode: encoding version %d not supported", b)
+ }
+ l := len(buf) - scaleSize - 1
+ err := z.UnscaledBig().GobDecode(buf[:l])
+ if err != nil {
+ return err
+ }
+ z.SetScale(scale(buf[l : l+scaleSize]))
+ return nil
+}
+
+// MarshalText implements the encoding.TextMarshaler interface.
+func (x *Dec) MarshalText() ([]byte, error) {
+ return []byte(x.String()), nil
+}
+
+// UnmarshalText implements the encoding.TextUnmarshaler interface.
+func (z *Dec) UnmarshalText(data []byte) error {
+ _, ok := z.SetString(string(data))
+ if !ok {
+ return fmt.Errorf("invalid inf.Dec")
+ }
+ return nil
+}
generated by cgit v1.2.3-54-g00ecf (git 2.39.0) at 2024-11-15 23:12:38 +0000