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