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package inf
import (
"math/big"
)
// Rounder represents a method for rounding the (possibly infinite decimal)
// result of a division to a finite Dec. It is used by Dec.Round() and
// Dec.Quo().
//
// See the Example for results of using each Rounder with some sample values.
//
type Rounder rounder
// See http://speleotrove.com/decimal/damodel.html#refround for more detailed
// definitions of these rounding modes.
var (
RoundDown Rounder // towards 0
RoundUp Rounder // away from 0
RoundFloor Rounder // towards -infinity
RoundCeil Rounder // towards +infinity
RoundHalfDown Rounder // to nearest; towards 0 if same distance
RoundHalfUp Rounder // to nearest; away from 0 if same distance
RoundHalfEven Rounder // to nearest; even last digit if same distance
)
// RoundExact is to be used in the case when rounding is not necessary.
// When used with Quo or Round, it returns the result verbatim when it can be
// expressed exactly with the given precision, and it returns nil otherwise.
// QuoExact is a shorthand for using Quo with RoundExact.
var RoundExact Rounder
type rounder interface {
// When UseRemainder() returns true, the Round() method is passed the
// remainder of the division, expressed as the numerator and denominator of
// a rational.
UseRemainder() bool
// Round sets the rounded value of a quotient to z, and returns z.
// quo is rounded down (truncated towards zero) to the scale obtained from
// the Scaler in Quo().
//
// When the remainder is not used, remNum and remDen are nil.
// When used, the remainder is normalized between -1 and 1; that is:
//
// -|remDen| < remNum < |remDen|
//
// remDen has the same sign as y, and remNum is zero or has the same sign
// as x.
Round(z, quo *Dec, remNum, remDen *big.Int) *Dec
}
type rndr struct {
useRem bool
round func(z, quo *Dec, remNum, remDen *big.Int) *Dec
}
func (r rndr) UseRemainder() bool {
return r.useRem
}
func (r rndr) Round(z, quo *Dec, remNum, remDen *big.Int) *Dec {
return r.round(z, quo, remNum, remDen)
}
var intSign = []*big.Int{big.NewInt(-1), big.NewInt(0), big.NewInt(1)}
func roundHalf(f func(c int, odd uint) (roundUp bool)) func(z, q *Dec, rA, rB *big.Int) *Dec {
return func(z, q *Dec, rA, rB *big.Int) *Dec {
z.Set(q)
brA, brB := rA.BitLen(), rB.BitLen()
if brA < brB-1 {
// brA < brB-1 => |rA| < |rB/2|
return z
}
roundUp := false
srA, srB := rA.Sign(), rB.Sign()
s := srA * srB
if brA == brB-1 {
rA2 := new(big.Int).Lsh(rA, 1)
if s < 0 {
rA2.Neg(rA2)
}
roundUp = f(rA2.Cmp(rB)*srB, z.UnscaledBig().Bit(0))
} else {
// brA > brB-1 => |rA| > |rB/2|
roundUp = true
}
if roundUp {
z.UnscaledBig().Add(z.UnscaledBig(), intSign[s+1])
}
return z
}
}
func init() {
RoundExact = rndr{true,
func(z, q *Dec, rA, rB *big.Int) *Dec {
if rA.Sign() != 0 {
return nil
}
return z.Set(q)
}}
RoundDown = rndr{false,
func(z, q *Dec, rA, rB *big.Int) *Dec {
return z.Set(q)
}}
RoundUp = rndr{true,
func(z, q *Dec, rA, rB *big.Int) *Dec {
z.Set(q)
if rA.Sign() != 0 {
z.UnscaledBig().Add(z.UnscaledBig(), intSign[rA.Sign()*rB.Sign()+1])
}
return z
}}
RoundFloor = rndr{true,
func(z, q *Dec, rA, rB *big.Int) *Dec {
z.Set(q)
if rA.Sign()*rB.Sign() < 0 {
z.UnscaledBig().Add(z.UnscaledBig(), intSign[0])
}
return z
}}
RoundCeil = rndr{true,
func(z, q *Dec, rA, rB *big.Int) *Dec {
z.Set(q)
if rA.Sign()*rB.Sign() > 0 {
z.UnscaledBig().Add(z.UnscaledBig(), intSign[2])
}
return z
}}
RoundHalfDown = rndr{true, roundHalf(
func(c int, odd uint) bool {
return c > 0
})}
RoundHalfUp = rndr{true, roundHalf(
func(c int, odd uint) bool {
return c >= 0
})}
RoundHalfEven = rndr{true, roundHalf(
func(c int, odd uint) bool {
return c > 0 || c == 0 && odd == 1
})}
}
|
