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dec.go
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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
}