435 lines
10 KiB
Go
435 lines
10 KiB
Go
// Copyright (C) MongoDB, Inc. 2017-present.
|
|
//
|
|
// Licensed under the Apache License, Version 2.0 (the "License"); you may
|
|
// not use this file except in compliance with the License. You may obtain
|
|
// a copy of the License at http://www.apache.org/licenses/LICENSE-2.0
|
|
//
|
|
// Based on gopkg.in/mgo.v2/bson by Gustavo Niemeyer
|
|
// See THIRD-PARTY-NOTICES for original license terms.
|
|
|
|
package primitive
|
|
|
|
import (
|
|
"encoding/json"
|
|
"errors"
|
|
"fmt"
|
|
"math/big"
|
|
"regexp"
|
|
"strconv"
|
|
"strings"
|
|
)
|
|
|
|
// These constants are the maximum and minimum values for the exponent field in a decimal128 value.
|
|
const (
|
|
MaxDecimal128Exp = 6111
|
|
MinDecimal128Exp = -6176
|
|
)
|
|
|
|
// These errors are returned when an invalid value is parsed as a big.Int.
|
|
var (
|
|
ErrParseNaN = errors.New("cannot parse NaN as a *big.Int")
|
|
ErrParseInf = errors.New("cannot parse Infinity as a *big.Int")
|
|
ErrParseNegInf = errors.New("cannot parse -Infinity as a *big.Int")
|
|
)
|
|
|
|
// Decimal128 holds decimal128 BSON values.
|
|
type Decimal128 struct {
|
|
h, l uint64
|
|
}
|
|
|
|
// NewDecimal128 creates a Decimal128 using the provide high and low uint64s.
|
|
func NewDecimal128(h, l uint64) Decimal128 {
|
|
return Decimal128{h: h, l: l}
|
|
}
|
|
|
|
// GetBytes returns the underlying bytes of the BSON decimal value as two uint64 values. The first
|
|
// contains the most first 8 bytes of the value and the second contains the latter.
|
|
func (d Decimal128) GetBytes() (uint64, uint64) {
|
|
return d.h, d.l
|
|
}
|
|
|
|
// String returns a string representation of the decimal value.
|
|
func (d Decimal128) String() string {
|
|
var posSign int // positive sign
|
|
var exp int // exponent
|
|
var high, low uint64 // significand high/low
|
|
|
|
if d.h>>63&1 == 0 {
|
|
posSign = 1
|
|
}
|
|
|
|
switch d.h >> 58 & (1<<5 - 1) {
|
|
case 0x1F:
|
|
return "NaN"
|
|
case 0x1E:
|
|
return "-Infinity"[posSign:]
|
|
}
|
|
|
|
low = d.l
|
|
if d.h>>61&3 == 3 {
|
|
// Bits: 1*sign 2*ignored 14*exponent 111*significand.
|
|
// Implicit 0b100 prefix in significand.
|
|
exp = int(d.h >> 47 & (1<<14 - 1))
|
|
//high = 4<<47 | d.h&(1<<47-1)
|
|
// Spec says all of these values are out of range.
|
|
high, low = 0, 0
|
|
} else {
|
|
// Bits: 1*sign 14*exponent 113*significand
|
|
exp = int(d.h >> 49 & (1<<14 - 1))
|
|
high = d.h & (1<<49 - 1)
|
|
}
|
|
exp += MinDecimal128Exp
|
|
|
|
// Would be handled by the logic below, but that's trivial and common.
|
|
if high == 0 && low == 0 && exp == 0 {
|
|
return "-0"[posSign:]
|
|
}
|
|
|
|
var repr [48]byte // Loop 5 times over 9 digits plus dot, negative sign, and leading zero.
|
|
var last = len(repr)
|
|
var i = len(repr)
|
|
var dot = len(repr) + exp
|
|
var rem uint32
|
|
Loop:
|
|
for d9 := 0; d9 < 5; d9++ {
|
|
high, low, rem = divmod(high, low, 1e9)
|
|
for d1 := 0; d1 < 9; d1++ {
|
|
// Handle "-0.0", "0.00123400", "-1.00E-6", "1.050E+3", etc.
|
|
if i < len(repr) && (dot == i || low == 0 && high == 0 && rem > 0 && rem < 10 && (dot < i-6 || exp > 0)) {
|
|
exp += len(repr) - i
|
|
i--
|
|
repr[i] = '.'
|
|
last = i - 1
|
|
dot = len(repr) // Unmark.
|
|
}
|
|
c := '0' + byte(rem%10)
|
|
rem /= 10
|
|
i--
|
|
repr[i] = c
|
|
// Handle "0E+3", "1E+3", etc.
|
|
if low == 0 && high == 0 && rem == 0 && i == len(repr)-1 && (dot < i-5 || exp > 0) {
|
|
last = i
|
|
break Loop
|
|
}
|
|
if c != '0' {
|
|
last = i
|
|
}
|
|
// Break early. Works without it, but why.
|
|
if dot > i && low == 0 && high == 0 && rem == 0 {
|
|
break Loop
|
|
}
|
|
}
|
|
}
|
|
repr[last-1] = '-'
|
|
last--
|
|
|
|
if exp > 0 {
|
|
return string(repr[last+posSign:]) + "E+" + strconv.Itoa(exp)
|
|
}
|
|
if exp < 0 {
|
|
return string(repr[last+posSign:]) + "E" + strconv.Itoa(exp)
|
|
}
|
|
return string(repr[last+posSign:])
|
|
}
|
|
|
|
// BigInt returns significand as big.Int and exponent, bi * 10 ^ exp.
|
|
func (d Decimal128) BigInt() (*big.Int, int, error) {
|
|
high, low := d.GetBytes()
|
|
posSign := high>>63&1 == 0 // positive sign
|
|
|
|
switch high >> 58 & (1<<5 - 1) {
|
|
case 0x1F:
|
|
return nil, 0, ErrParseNaN
|
|
case 0x1E:
|
|
if posSign {
|
|
return nil, 0, ErrParseInf
|
|
}
|
|
return nil, 0, ErrParseNegInf
|
|
}
|
|
|
|
var exp int
|
|
if high>>61&3 == 3 {
|
|
// Bits: 1*sign 2*ignored 14*exponent 111*significand.
|
|
// Implicit 0b100 prefix in significand.
|
|
exp = int(high >> 47 & (1<<14 - 1))
|
|
//high = 4<<47 | d.h&(1<<47-1)
|
|
// Spec says all of these values are out of range.
|
|
high, low = 0, 0
|
|
} else {
|
|
// Bits: 1*sign 14*exponent 113*significand
|
|
exp = int(high >> 49 & (1<<14 - 1))
|
|
high = high & (1<<49 - 1)
|
|
}
|
|
exp += MinDecimal128Exp
|
|
|
|
// Would be handled by the logic below, but that's trivial and common.
|
|
if high == 0 && low == 0 && exp == 0 {
|
|
return new(big.Int), 0, nil
|
|
}
|
|
|
|
bi := big.NewInt(0)
|
|
const host32bit = ^uint(0)>>32 == 0
|
|
if host32bit {
|
|
bi.SetBits([]big.Word{big.Word(low), big.Word(low >> 32), big.Word(high), big.Word(high >> 32)})
|
|
} else {
|
|
bi.SetBits([]big.Word{big.Word(low), big.Word(high)})
|
|
}
|
|
|
|
if !posSign {
|
|
return bi.Neg(bi), exp, nil
|
|
}
|
|
return bi, exp, nil
|
|
}
|
|
|
|
// IsNaN returns whether d is NaN.
|
|
func (d Decimal128) IsNaN() bool {
|
|
return d.h>>58&(1<<5-1) == 0x1F
|
|
}
|
|
|
|
// IsInf returns:
|
|
//
|
|
// +1 d == Infinity
|
|
// 0 other case
|
|
// -1 d == -Infinity
|
|
func (d Decimal128) IsInf() int {
|
|
if d.h>>58&(1<<5-1) != 0x1E {
|
|
return 0
|
|
}
|
|
|
|
if d.h>>63&1 == 0 {
|
|
return 1
|
|
}
|
|
return -1
|
|
}
|
|
|
|
// IsZero returns true if d is the empty Decimal128.
|
|
func (d Decimal128) IsZero() bool {
|
|
return d.h == 0 && d.l == 0
|
|
}
|
|
|
|
// MarshalJSON returns Decimal128 as a string.
|
|
func (d Decimal128) MarshalJSON() ([]byte, error) {
|
|
return json.Marshal(d.String())
|
|
}
|
|
|
|
// UnmarshalJSON creates a primitive.Decimal128 from a JSON string, an extended JSON $numberDecimal value, or the string
|
|
// "null". If b is a JSON string or extended JSON value, d will have the value of that string, and if b is "null", d will
|
|
// be unchanged.
|
|
func (d *Decimal128) UnmarshalJSON(b []byte) error {
|
|
// Ignore "null" to keep parity with the standard library. Decoding a JSON null into a non-pointer Decimal128 field
|
|
// will leave the field unchanged. For pointer values, encoding/json will set the pointer to nil and will not
|
|
// enter the UnmarshalJSON hook.
|
|
if string(b) == "null" {
|
|
return nil
|
|
}
|
|
|
|
var res interface{}
|
|
err := json.Unmarshal(b, &res)
|
|
if err != nil {
|
|
return err
|
|
}
|
|
str, ok := res.(string)
|
|
|
|
// Extended JSON
|
|
if !ok {
|
|
m, ok := res.(map[string]interface{})
|
|
if !ok {
|
|
return errors.New("not an extended JSON Decimal128: expected document")
|
|
}
|
|
d128, ok := m["$numberDecimal"]
|
|
if !ok {
|
|
return errors.New("not an extended JSON Decimal128: expected key $numberDecimal")
|
|
}
|
|
str, ok = d128.(string)
|
|
if !ok {
|
|
return errors.New("not an extended JSON Decimal128: expected decimal to be string")
|
|
}
|
|
}
|
|
|
|
*d, err = ParseDecimal128(str)
|
|
return err
|
|
}
|
|
|
|
func divmod(h, l uint64, div uint32) (qh, ql uint64, rem uint32) {
|
|
div64 := uint64(div)
|
|
a := h >> 32
|
|
aq := a / div64
|
|
ar := a % div64
|
|
b := ar<<32 + h&(1<<32-1)
|
|
bq := b / div64
|
|
br := b % div64
|
|
c := br<<32 + l>>32
|
|
cq := c / div64
|
|
cr := c % div64
|
|
d := cr<<32 + l&(1<<32-1)
|
|
dq := d / div64
|
|
dr := d % div64
|
|
return (aq<<32 | bq), (cq<<32 | dq), uint32(dr)
|
|
}
|
|
|
|
var dNaN = Decimal128{0x1F << 58, 0}
|
|
var dPosInf = Decimal128{0x1E << 58, 0}
|
|
var dNegInf = Decimal128{0x3E << 58, 0}
|
|
|
|
func dErr(s string) (Decimal128, error) {
|
|
return dNaN, fmt.Errorf("cannot parse %q as a decimal128", s)
|
|
}
|
|
|
|
// match scientific notation number, example -10.15e-18
|
|
var normalNumber = regexp.MustCompile(`^(?P<int>[-+]?\d*)?(?:\.(?P<dec>\d*))?(?:[Ee](?P<exp>[-+]?\d+))?$`)
|
|
|
|
// ParseDecimal128 takes the given string and attempts to parse it into a valid
|
|
// Decimal128 value.
|
|
func ParseDecimal128(s string) (Decimal128, error) {
|
|
if s == "" {
|
|
return dErr(s)
|
|
}
|
|
|
|
matches := normalNumber.FindStringSubmatch(s)
|
|
if len(matches) == 0 {
|
|
orig := s
|
|
neg := s[0] == '-'
|
|
if neg || s[0] == '+' {
|
|
s = s[1:]
|
|
}
|
|
|
|
if s == "NaN" || s == "nan" || strings.EqualFold(s, "nan") {
|
|
return dNaN, nil
|
|
}
|
|
if s == "Inf" || s == "inf" || strings.EqualFold(s, "inf") || strings.EqualFold(s, "infinity") {
|
|
if neg {
|
|
return dNegInf, nil
|
|
}
|
|
return dPosInf, nil
|
|
}
|
|
return dErr(orig)
|
|
}
|
|
|
|
intPart := matches[1]
|
|
decPart := matches[2]
|
|
expPart := matches[3]
|
|
|
|
var err error
|
|
exp := 0
|
|
if expPart != "" {
|
|
exp, err = strconv.Atoi(expPart)
|
|
if err != nil {
|
|
return dErr(s)
|
|
}
|
|
}
|
|
if decPart != "" {
|
|
exp -= len(decPart)
|
|
}
|
|
|
|
if len(strings.Trim(intPart+decPart, "-0")) > 35 {
|
|
return dErr(s)
|
|
}
|
|
|
|
// Parse the significand (i.e. the non-exponent part) as a big.Int.
|
|
bi, ok := new(big.Int).SetString(intPart+decPart, 10)
|
|
if !ok {
|
|
return dErr(s)
|
|
}
|
|
|
|
d, ok := ParseDecimal128FromBigInt(bi, exp)
|
|
if !ok {
|
|
return dErr(s)
|
|
}
|
|
|
|
if bi.Sign() == 0 && s[0] == '-' {
|
|
d.h |= 1 << 63
|
|
}
|
|
|
|
return d, nil
|
|
}
|
|
|
|
var (
|
|
ten = big.NewInt(10)
|
|
zero = new(big.Int)
|
|
|
|
maxS, _ = new(big.Int).SetString("9999999999999999999999999999999999", 10)
|
|
)
|
|
|
|
// ParseDecimal128FromBigInt attempts to parse the given significand and exponent into a valid Decimal128 value.
|
|
func ParseDecimal128FromBigInt(bi *big.Int, exp int) (Decimal128, bool) {
|
|
//copy
|
|
bi = new(big.Int).Set(bi)
|
|
|
|
q := new(big.Int)
|
|
r := new(big.Int)
|
|
|
|
// If the significand is zero, the logical value will always be zero, independent of the
|
|
// exponent. However, the loops for handling out-of-range exponent values below may be extremely
|
|
// slow for zero values because the significand never changes. Limit the exponent value to the
|
|
// supported range here to prevent entering the loops below.
|
|
if bi.Cmp(zero) == 0 {
|
|
if exp > MaxDecimal128Exp {
|
|
exp = MaxDecimal128Exp
|
|
}
|
|
if exp < MinDecimal128Exp {
|
|
exp = MinDecimal128Exp
|
|
}
|
|
}
|
|
|
|
for bigIntCmpAbs(bi, maxS) == 1 {
|
|
bi, _ = q.QuoRem(bi, ten, r)
|
|
if r.Cmp(zero) != 0 {
|
|
return Decimal128{}, false
|
|
}
|
|
exp++
|
|
if exp > MaxDecimal128Exp {
|
|
return Decimal128{}, false
|
|
}
|
|
}
|
|
|
|
for exp < MinDecimal128Exp {
|
|
// Subnormal.
|
|
bi, _ = q.QuoRem(bi, ten, r)
|
|
if r.Cmp(zero) != 0 {
|
|
return Decimal128{}, false
|
|
}
|
|
exp++
|
|
}
|
|
for exp > MaxDecimal128Exp {
|
|
// Clamped.
|
|
bi.Mul(bi, ten)
|
|
if bigIntCmpAbs(bi, maxS) == 1 {
|
|
return Decimal128{}, false
|
|
}
|
|
exp--
|
|
}
|
|
|
|
b := bi.Bytes()
|
|
var h, l uint64
|
|
for i := 0; i < len(b); i++ {
|
|
if i < len(b)-8 {
|
|
h = h<<8 | uint64(b[i])
|
|
continue
|
|
}
|
|
l = l<<8 | uint64(b[i])
|
|
}
|
|
|
|
h |= uint64(exp-MinDecimal128Exp) & uint64(1<<14-1) << 49
|
|
if bi.Sign() == -1 {
|
|
h |= 1 << 63
|
|
}
|
|
|
|
return Decimal128{h: h, l: l}, true
|
|
}
|
|
|
|
// bigIntCmpAbs computes big.Int.Cmp(absoluteValue(x), absoluteValue(y)).
|
|
func bigIntCmpAbs(x, y *big.Int) int {
|
|
xAbs := bigIntAbsValue(x)
|
|
yAbs := bigIntAbsValue(y)
|
|
return xAbs.Cmp(yAbs)
|
|
}
|
|
|
|
// bigIntAbsValue returns a big.Int containing the absolute value of b.
|
|
// If b is already a non-negative number, it is returned without any changes or copies.
|
|
func bigIntAbsValue(b *big.Int) *big.Int {
|
|
if b.Sign() >= 0 {
|
|
return b // already positive
|
|
}
|
|
return new(big.Int).Abs(b)
|
|
}
|