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// 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 { if posSign { return new(big.Int), 0, nil } 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 $numberDecimal") } str, ok = d128.(string) if !ok { return errors.New("not an extended JSON Decimal128: expected decimal to be string") } } *d, err = ParseDecimal128(str) return err } func divmod(h, l uint64, div uint32) (qh, ql uint64, rem uint32) { div64 := uint64(div) a := h >> 32 aq := a / div64 ar := a % div64 b := ar<<32 + h&(1<<32-1) bq := b / div64 br := b % div64 c := br<<32 + l>>32 cq := c / div64 cr := c % div64 d := cr<<32 + l&(1<<32-1) dq := d / div64 dr := d % div64 return (aq<<32 | bq), (cq<<32 | dq), uint32(dr) } var dNaN = Decimal128{0x1F << 58, 0} var dPosInf = Decimal128{0x1E << 58, 0} var dNegInf = Decimal128{0x3E << 58, 0} func dErr(s string) (Decimal128, error) { return dNaN, fmt.Errorf("cannot parse %q as a decimal128", s) } // match scientific notation number, example -10.15e-18 var normalNumber = regexp.MustCompile(`^(?P[-+]?\d*)?(?:\.(?P\d*))?(?:[Ee](?P[-+]?\d+))?$`) // 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) }