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