// Copyright 2017 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
//go:generate stringer -type RoundingMode
package number
import (
"math"
"strconv"
)
// RoundingMode determines how a number is rounded to the desired precision.
type RoundingMode byte
const (
ToNearestEven RoundingMode = iota // towards the nearest integer, or towards an even number if equidistant.
ToNearestZero // towards the nearest integer, or towards zero if equidistant.
ToNearestAway // towards the nearest integer, or away from zero if equidistant.
ToPositiveInf // towards infinity
ToNegativeInf // towards negative infinity
ToZero // towards zero
AwayFromZero // away from zero
numModes
)
const maxIntDigits = 20
// A Decimal represents a floating point number in decimal format.
// Digits represents a number [0, 1.0), and the absolute value represented by
// Decimal is Digits * 10^Exp. Leading and trailing zeros may be omitted and Exp
// may point outside a valid position in Digits.
//
// Examples:
// Number Decimal
// 12345 Digits: [1, 2, 3, 4, 5], Exp: 5
// 12.345 Digits: [1, 2, 3, 4, 5], Exp: 2
// 12000 Digits: [1, 2], Exp: 5
// 12000.00 Digits: [1, 2], Exp: 5
// 0.00123 Digits: [1, 2, 3], Exp: -2
// 0 Digits: [], Exp: 0
type Decimal struct {
digits
buf [maxIntDigits]byte
}
type digits struct {
Digits []byte // mantissa digits, big-endian
Exp int32 // exponent
Neg bool
Inf bool // Takes precedence over Digits and Exp.
NaN bool // Takes precedence over Inf.
}
// Digits represents a floating point number represented in digits of the
// base in which a number is to be displayed. It is similar to Decimal, but
// keeps track of trailing fraction zeros and the comma placement for
// engineering notation. Digits must have at least one digit.
//
// Examples:
// Number Decimal
// decimal
// 12345 Digits: [1, 2, 3, 4, 5], Exp: 5 End: 5
// 12.345 Digits: [1, 2, 3, 4, 5], Exp: 2 End: 5
// 12000 Digits: [1, 2], Exp: 5 End: 5
// 12000.00 Digits: [1, 2], Exp: 5 End: 7
// 0.00123 Digits: [1, 2, 3], Exp: -2 End: 3
// 0 Digits: [], Exp: 0 End: 1
// scientific (actual exp is Exp - Comma)
// 0e0 Digits: [0], Exp: 1, End: 1, Comma: 1
// .0e0 Digits: [0], Exp: 0, End: 1, Comma: 0
// 0.0e0 Digits: [0], Exp: 1, End: 2, Comma: 1
// 1.23e4 Digits: [1, 2, 3], Exp: 5, End: 3, Comma: 1
// .123e5 Digits: [1, 2, 3], Exp: 5, End: 3, Comma: 0
// engineering
// 12.3e3 Digits: [1, 2, 3], Exp: 5, End: 3, Comma: 2
type Digits struct {
digits
// End indicates the end position of the number.
End int32 // For decimals Exp <= End. For scientific len(Digits) <= End.
// Comma is used for the comma position for scientific (always 0 or 1) and
// engineering notation (always 0, 1, 2, or 3).
Comma uint8
// IsScientific indicates whether this number is to be rendered as a
// scientific number.
IsScientific bool
}
func (d *Digits) NumFracDigits() int {
if d.Exp >= d.End {
return 0
}
return int(d.End - d.Exp)
}
// normalize returns a new Decimal with leading and trailing zeros removed.
func (d *Decimal) normalize() (n Decimal) {
n = *d
b := n.Digits
// Strip leading zeros. Resulting number of digits is significant digits.
for len(b) > 0 && b[0] == 0 {
b = b[1:]
n.Exp--
}
// Strip trailing zeros
for len(b) > 0 && b[len(b)-1] == 0 {
b = b[:len(b)-1]
}
if len(b) == 0 {
n.Exp = 0
}
n.Digits = b
return n
}
func (d *Decimal) clear() {
b := d.Digits
if b == nil {
b = d.buf[:0]
}
*d = Decimal{}
d.Digits = b[:0]
}
func (x *Decimal) String() string {
if x.NaN {
return "NaN"
}
var buf []byte
if x.Neg {
buf = append(buf, '-')
}
if x.Inf {
buf = append(buf, "Inf"...)
return string(buf)
}
switch {
case len(x.Digits) == 0:
buf = append(buf, '0')
case x.Exp <= 0:
// 0.00ddd
buf = append(buf, "0."...)
buf = appendZeros(buf, -int(x.Exp))
buf = appendDigits(buf, x.Digits)
case /* 0 < */ int(x.Exp) < len(x.Digits):
// dd.ddd
buf = appendDigits(buf, x.Digits[:x.Exp])
buf = append(buf, '.')
buf = appendDigits(buf, x.Digits[x.Exp:])
default: // len(x.Digits) <= x.Exp
// ddd00
buf = appendDigits(buf, x.Digits)
buf = appendZeros(buf, int(x.Exp)-len(x.Digits))
}
return string(buf)
}
func appendDigits(buf []byte, digits []byte) []byte {
for _, c := range digits {
buf = append(buf, c+'0')
}
return buf
}
// appendZeros appends n 0 digits to buf and returns buf.
func appendZeros(buf []byte, n int) []byte {
for ; n > 0; n-- {
buf = append(buf, '0')
}
return buf
}
func (d *digits) round(mode RoundingMode, n int) {
if n >= len(d.Digits) {
return
}
// Make rounding decision: The result mantissa is truncated ("rounded down")
// by default. Decide if we need to increment, or "round up", the (unsigned)
// mantissa.
inc := false
switch mode {
case ToNegativeInf:
inc = d.Neg
case ToPositiveInf:
inc = !d.Neg
case ToZero:
// nothing to do
case AwayFromZero:
inc = true
case ToNearestEven:
inc = d.Digits[n] > 5 || d.Digits[n] == 5 &&
(len(d.Digits) > n+1 || n == 0 || d.Digits[n-1]&1 != 0)
case ToNearestAway:
inc = d.Digits[n] >= 5
case ToNearestZero:
inc = d.Digits[n] > 5 || d.Digits[n] == 5 && len(d.Digits) > n+1
default:
panic("unreachable")
}
if inc {
d.roundUp(n)
} else {
d.roundDown(n)
}
}
// roundFloat rounds a floating point number.
func (r RoundingMode) roundFloat(x float64) float64 {
// Make rounding decision: The result mantissa is truncated ("rounded down")
// by default. Decide if we need to increment, or "round up", the (unsigned)
// mantissa.
abs := x
if x < 0 {
abs = -x
}
i, f := math.Modf(abs)
if f == 0.0 {
return x
}
inc := false
switch r {
case ToNegativeInf:
inc = x < 0
case ToPositiveInf:
inc = x >= 0
case ToZero:
// nothing to do
case AwayFromZero:
inc = true
case ToNearestEven:
// TODO: check overflow
inc = f > 0.5 || f == 0.5 && int64(i)&1 != 0
case ToNearestAway:
inc = f >= 0.5
case ToNearestZero:
inc = f > 0.5
default:
panic("unreachable")
}
if inc {
i += 1
}
if abs != x {
i = -i
}
return i
}
func (x *digits) roundUp(n int) {
if n < 0 || n >= len(x.Digits) {
return // nothing to do
}
// find first digit < 9
for n > 0 && x.Digits[n-1] >= 9 {
n--
}
if n == 0 {
// all digits are 9s => round up to 1 and update exponent
x.Digits[0] = 1 // ok since len(x.Digits) > n
x.Digits = x.Digits[:1]
x.Exp++
return
}
x.Digits[n-1]++
x.Digits = x.Digits[:n]
// x already trimmed
}
func (x *digits) roundDown(n int) {
if n < 0 || n >= len(x.Digits) {
return // nothing to do
}
x.Digits = x.Digits[:n]
trim(x)
}
// trim cuts off any trailing zeros from x's mantissa;
// they are meaningless for the value of x.
func trim(x *digits) {
i := len(x.Digits)
for i > 0 && x.Digits[i-1] == 0 {
i--
}
x.Digits = x.Digits[:i]
if i == 0 {
x.Exp = 0
}
}
// A Converter converts a number into decimals according to the given rounding
// criteria.
type Converter interface {
Convert(d *Decimal, r RoundingContext)
}
const (
signed = true
unsigned = false
)
// Convert converts the given number to the decimal representation using the
// supplied RoundingContext.
func (d *Decimal) Convert(r RoundingContext, number interface{}) {
switch f := number.(type) {
case Converter:
d.clear()
f.Convert(d, r)
case float32:
d.ConvertFloat(r, float64(f), 32)
case float64:
d.ConvertFloat(r, f, 64)
case int:
d.ConvertInt(r, signed, uint64(f))
case int8:
d.ConvertInt(r, signed, uint64(f))
case int16:
d.ConvertInt(r, signed, uint64(f))
case int32:
d.ConvertInt(r, signed, uint64(f))
case int64:
d.ConvertInt(r, signed, uint64(f))
case uint:
d.ConvertInt(r, unsigned, uint64(f))
case uint8:
d.ConvertInt(r, unsigned, uint64(f))
case uint16:
d.ConvertInt(r, unsigned, uint64(f))
case uint32:
d.ConvertInt(r, unsigned, uint64(f))
case uint64:
d.ConvertInt(r, unsigned, f)
default:
d.NaN = true
// TODO:
// case string: if produced by strconv, allows for easy arbitrary pos.
// case reflect.Value:
// case big.Float
// case big.Int
// case big.Rat?
// catch underlyings using reflect or will this already be done by the
// message package?
}
}
// ConvertInt converts an integer to decimals.
func (d *Decimal) ConvertInt(r RoundingContext, signed bool, x uint64) {
if r.Increment > 0 {
// TODO: if uint64 is too large, fall back to float64
if signed {
d.ConvertFloat(r, float64(int64(x)), 64)
} else {
d.ConvertFloat(r, float64(x), 64)
}
return
}
d.clear()
if signed && int64(x) < 0 {
x = uint64(-int64(x))
d.Neg = true
}
d.fillIntDigits(x)
d.Exp = int32(len(d.Digits))
}
// ConvertFloat converts a floating point number to decimals.
func (d *Decimal) ConvertFloat(r RoundingContext, x float64, size int) {
d.clear()
if math.IsNaN(x) {
d.NaN = true
return
}
// Simple case: decimal notation
if r.Increment > 0 {
scale := int(r.IncrementScale)
mult := 1.0
if scale > len(scales) {
mult = math.Pow(10, float64(scale))
} else {
mult = scales[scale]
}
// We multiply x instead of dividing inc as it gives less rounding
// issues.
x *= mult
x /= float64(r.Increment)
x = r.Mode.roundFloat(x)
x *= float64(r.Increment)
x /= mult
}
abs := x
if x < 0 {
d.Neg = true
abs = -x
}
if math.IsInf(abs, 1) {
d.Inf = true
return
}
// By default we get the exact decimal representation.
verb := byte('g')
prec := -1
// As the strconv API does not return the rounding accuracy, we can only
// round using ToNearestEven.
if r.Mode == ToNearestEven {
if n := r.RoundSignificantDigits(); n >= 0 {
prec = n
} else if n = r.RoundFractionDigits(); n >= 0 {
prec = n
verb = 'f'
}
} else {
// TODO: At this point strconv's rounding is imprecise to the point that
// it is not useable for this purpose.
// See https://github.com/golang/go/issues/21714
// If rounding is requested, we ask for a large number of digits and
// round from there to simulate rounding only once.
// Ideally we would have strconv export an AppendDigits that would take
// a rounding mode and/or return an accuracy. Something like this would
// work:
// AppendDigits(dst []byte, x float64, base, size, prec int) (digits []byte, exp, accuracy int)
hasPrec := r.RoundSignificantDigits() >= 0
hasScale := r.RoundFractionDigits() >= 0
if hasPrec || hasScale {
// prec is the number of mantissa bits plus some extra for safety.
// We need at least the number of mantissa bits as decimals to
// accurately represent the floating point without rounding, as each
// bit requires one more decimal to represent: 0.5, 0.25, 0.125, ...
prec = 60
}
}
b := strconv.AppendFloat(d.Digits[:0], abs, verb, prec, size)
i := 0
k := 0
beforeDot := 1
for i < len(b) {
if c := b[i]; '0' <= c && c <= '9' {
b[k] = c - '0'
k++
d.Exp += int32(beforeDot)
} else if c == '.' {
beforeDot = 0
d.Exp = int32(k)
} else {
break
}
i++
}
d.Digits = b[:k]
if i != len(b) {
i += len("e")
pSign := i
exp := 0
for i++; i < len(b); i++ {
exp *= 10
exp += int(b[i] - '0')
}
if b[pSign] == '-' {
exp = -exp
}
d.Exp = int32(exp) + 1
}
}
func (d *Decimal) fillIntDigits(x uint64) {
if cap(d.Digits) < maxIntDigits {
d.Digits = d.buf[:]
} else {
d.Digits = d.buf[:maxIntDigits]
}
i := 0
for ; x > 0; x /= 10 {
d.Digits[i] = byte(x % 10)
i++
}
d.Digits = d.Digits[:i]
for p := 0; p < i; p++ {
i--
d.Digits[p], d.Digits[i] = d.Digits[i], d.Digits[p]
}
}
var scales [70]float64
func init() {
x := 1.0
for i := range scales {
scales[i] = x
x *= 10
}
}
