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8c337cddec
bbgo_origin/pkg/fixedpoint/dec.go
gx578007 0e2e8306b4 FEATURE: [grid2] using dnum
2023-03-20 18:00:41 +08:00

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//go:build dnum
package fixedpoint
import (
"bytes"
"database/sql/driver"
"errors"
"fmt"
"math"
"math/bits"
"strconv"
"strings"
)
type Value struct {
coef uint64
sign int8
exp int
}
const (
signPosInf = +2
signPos = +1
signZero = 0
signNeg = -1
signNegInf = -2
coefMin = 1000_0000_0000_0000
coefMax = 9999_9999_9999_9999
digitsMax = 16
shiftMax = digitsMax - 1
// to switch between scientific notion and normal presentation format
maxLeadingZeros = 19
)
// common values
var (
Zero = Value{}
One = Value{1000_0000_0000_0000, signPos, 1}
NegOne = Value{1000_0000_0000_0000, signNeg, 1}
PosInf = Value{1, signPosInf, 0}
NegInf = Value{1, signNegInf, 0}
)
var pow10f = [...]float64{
1,
10,
100,
1000,
10000,
100000,
1000000,
10000000,
100000000,
1000000000,
10000000000,
100000000000,
1000000000000,
10000000000000,
100000000000000,
1000000000000000,
10000000000000000,
100000000000000000,
1000000000000000000,
10000000000000000000,
100000000000000000000}
var pow10 = [...]uint64{
1,
10,
100,
1000,
10000,
100000,
1000000,
10000000,
100000000,
1000000000,
10000000000,
100000000000,
1000000000000,
10000000000000,
100000000000000,
1000000000000000,
10000000000000000,
100000000000000000,
1000000000000000000}
var halfpow10 = [...]uint64{
0,
5,
50,
500,
5000,
50000,
500000,
5000000,
50000000,
500000000,
5000000000,
50000000000,
500000000000,
5000000000000,
50000000000000,
500000000000000,
5000000000000000,
50000000000000000,
500000000000000000,
5000000000000000000}
func min(a int, b int) int {
if a < b {
return a
}
return b
}
func max(a int, b int) int {
if a > b {
return a
}
return b
}
func (v Value) Value() (driver.Value, error) {
return v.Float64(), nil
}
// NewFromInt returns a Value for an int
func NewFromInt(n int64) Value {
if n == 0 {
return Zero
}
// n0 := n
sign := int8(signPos)
if n < 0 {
n = -n
sign = signNeg
}
return newNoSignCheck(sign, uint64(n), digitsMax)
}
const log2of10 = 3.32192809488736234
// NewFromFloat converts a float64 to a Value
func NewFromFloat(f float64) Value {
switch {
case math.IsInf(f, +1):
return PosInf
case math.IsInf(f, -1):
return NegInf
case math.IsNaN(f):
panic("value.NewFromFloat can't convert NaN")
}
if f == 0 {
return Zero
}
sign := int8(signPos)
if f < 0 {
f = -f
sign = signNeg
}
n := uint64(f)
if float64(n) == f {
return newNoSignCheck(sign, n, digitsMax)
}
_, e := math.Frexp(f)
e = int(float32(e) / log2of10)
c := uint64(f/math.Pow10(e-16) + 0.5)
return newNoSignCheck(sign, c, e)
}
// Raw constructs a Value without normalizing - arguments must be valid.
// Used by SuValue Unpack
func Raw(sign int8, coef uint64, exp int) Value {
return Value{coef, sign, int(exp)}
}
func newNoSignCheck(sign int8, coef uint64, exp int) Value {
atmax := false
for coef > coefMax {
coef = (coef + 5) / 10
exp++
atmax = true
}
if !atmax {
p := maxShift(coef)
coef *= pow10[p]
exp -= p
}
return Value{coef, sign, exp}
}
// New constructs a Value, maximizing coef and handling exp out of range
// Used to normalize results of operations
func New(sign int8, coef uint64, exp int) Value {
if sign == 0 || coef == 0 {
return Zero
} else if sign == signPosInf {
return PosInf
} else if sign == signNegInf {
return NegInf
} else {
atmax := false
for coef > coefMax {
coef = (coef + 5) / 10
exp++
atmax = true
}
if !atmax {
p := maxShift(coef)
coef *= pow10[p]
exp -= p
}
return Value{coef, sign, exp}
}
}
func maxShift(x uint64) int {
i := ilog10(x)
if i > shiftMax {
return 0
}
return shiftMax - i
}
func ilog10(x uint64) int {
// based on Hacker's Delight
if x == 0 {
return 0
}
y := (19 * (63 - bits.LeadingZeros64(x))) >> 6
if y < 18 && x >= pow10[y+1] {
y++
}
return y
}
func Inf(sign int8) Value {
switch {
case sign < 0:
return NegInf
case sign > 0:
return PosInf
default:
return Zero
}
}
func (dn Value) FormatString(prec int) string {
if dn.sign == 0 {
if prec <= 0 {
return "0"
} else {
return "0." + strings.Repeat("0", prec)
}
}
sign := ""
if dn.sign < 0 {
sign = "-"
}
if dn.IsInf() {
return sign + "inf"
}
digits := getDigits(dn.coef)
nd := len(digits)
e := int(dn.exp) - nd
if -maxLeadingZeros <= dn.exp && dn.exp <= 0 {
// decimal to the left
if prec+e+nd > 0 {
return sign + "0." + strings.Repeat("0", -e-nd) + digits[:min(prec+e+nd, nd)] + strings.Repeat("0", max(0, prec-nd+e+nd))
} else if -e-nd > 0 {
return "0." + strings.Repeat("0", -e-nd)
} else {
return "0"
}
} else if -nd < e && e <= -1 {
// decimal within
dec := nd + e
decimals := digits[dec:min(dec+prec, nd)]
return sign + digits[:dec] + "." + decimals + strings.Repeat("0", max(0, prec-len(decimals)))
} else if 0 < dn.exp && dn.exp <= digitsMax {
// decimal to the right
if prec > 0 {
return sign + digits + strings.Repeat("0", e) + "." + strings.Repeat("0", prec)
} else {
return sign + digits + strings.Repeat("0", e)
}
} else {
// scientific notation
after := ""
if nd > 1 {
after = "." + digits[1:min(1+prec, nd)] + strings.Repeat("0", max(0, min(1+prec, nd)-1-prec))
}
return sign + digits[:1] + after + "e" + strconv.Itoa(int(dn.exp-1))
}
}
// String returns a string representation of the Value
func (dn Value) String() string {
if dn.sign == 0 {
return "0"
}
sign := ""
if dn.sign < 0 {
sign = "-"
}
if dn.IsInf() {
return sign + "inf"
}
digits := getDigits(dn.coef)
nd := len(digits)
e := int(dn.exp) - nd
if -maxLeadingZeros <= dn.exp && dn.exp <= 0 {
// decimal to the left
return sign + "0." + strings.Repeat("0", -e-nd) + digits
} else if -nd < e && e <= -1 {
// decimal within
dec := nd + e
return sign + digits[:dec] + "." + digits[dec:]
} else if 0 < dn.exp && dn.exp <= digitsMax {
// decimal to the right
return sign + digits + strings.Repeat("0", e)
} else {
// scientific notation
after := ""
if nd > 1 {
after = "." + digits[1:]
}
return sign + digits[:1] + after + "e" + strconv.Itoa(int(dn.exp-1))
}
}
func (dn Value) Percentage() string {
if dn.sign == 0 {
return "0%"
}
sign := ""
if dn.sign < 0 {
sign = "-"
}
if dn.IsInf() {
return sign + "inf%"
}
digits := getDigits(dn.coef)
nd := len(digits)
e := int(dn.exp) - nd + 2
if -maxLeadingZeros <= dn.exp && dn.exp <= -2 {
// decimal to the left
return sign + "0." + strings.Repeat("0", -e-nd) + digits + "%"
} else if -nd < e && e <= -1 {
// decimal within
dec := nd + e
return sign + digits[:dec] + "." + digits[dec:] + "%"
} else if -2 < dn.exp && dn.exp <= digitsMax {
// decimal to the right
return sign + digits + strings.Repeat("0", e) + "%"
} else {
// scientific notation
after := ""
if nd > 1 {
after = "." + digits[1:]
}
return sign + digits[:1] + after + "e" + strconv.Itoa(int(dn.exp-1)) + "%"
}
}
func (dn Value) FormatPercentage(prec int) string {
if dn.sign == 0 {
if prec <= 0 {
return "0"
} else {
return "0." + strings.Repeat("0", prec)
}
}
sign := ""
if dn.sign < 0 {
sign = "-"
}
if dn.IsInf() {
return sign + "inf"
}
digits := getDigits(dn.coef)
nd := len(digits)
exp := dn.exp + 2
e := int(exp) - nd
if -maxLeadingZeros <= exp && exp <= 0 {
// decimal to the left
if prec+e+nd > 0 {
return sign + "0." + strings.Repeat("0", -e-nd) + digits[:min(prec+e+nd, nd)] + strings.Repeat("0", max(0, prec-nd+e+nd)) + "%"
} else if -e-nd > 0 {
return "0." + strings.Repeat("0", -e-nd) + "%"
} else {
return "0"
}
} else if -nd < e && e <= -1 {
// decimal within
dec := nd + e
decimals := digits[dec:min(dec+prec, nd)]
return sign + digits[:dec] + "." + decimals + strings.Repeat("0", max(0, prec-len(decimals))) + "%"
} else if 0 < exp && exp <= digitsMax {
// decimal to the right
if prec > 0 {
return sign + digits + strings.Repeat("0", e) + "." + strings.Repeat("0", prec) + "%"
} else {
return sign + digits + strings.Repeat("0", e) + "%"
}
} else {
// scientific notation
after := ""
if nd > 1 {
after = "." + digits[1:min(1+prec, nd)] + strings.Repeat("0", max(0, min(1+prec, nd)-1-prec))
}
return sign + digits[:1] + after + "e" + strconv.Itoa(int(exp-1)) + "%"
}
}
func (dn Value) SignedPercentage() string {
if dn.Sign() >= 0 {
return "+" + dn.Percentage()
}
return dn.Percentage()
}
// get digit length
func (a Value) NumDigits() int {
i := shiftMax
coef := a.coef
nd := 0
for coef != 0 && coef < pow10[i] {
i--
}
for coef != 0 {
coef %= pow10[i]
i--
nd++
}
return nd
}
// alias of Exp
func (a Value) NumIntDigits() int {
return a.exp
}
// get fractional digits
func (a Value) NumFractionalDigits() int {
nd := a.NumDigits()
return nd - a.exp
}
func getDigits(coef uint64) string {
var digits [digitsMax]byte
i := shiftMax
nd := 0
for coef != 0 {
digits[nd] = byte('0' + (coef / pow10[i]))
coef %= pow10[i]
nd++
i--
}
return string(digits[:nd])
}
func (v *Value) Scan(src interface{}) error {
var err error
switch d := src.(type) {
case int64:
*v = NewFromInt(d)
return nil
case float64:
*v = NewFromFloat(d)
return nil
case []byte:
*v, err = NewFromString(string(d))
if err != nil {
return err
}
return nil
default:
}
return fmt.Errorf("fixedpoint.Value scan error, type %T is not supported, value: %+v", src, src)
}
// NewFromString parses a numeric string and returns a Value representation.
func NewFromString(s string) (Value, error) {
length := len(s)
if length == 0 {
return Zero, nil
}
isPercentage := s[length-1] == '%'
if isPercentage {
s = s[:length-1]
}
r := &reader{s, 0}
sign := r.getSign()
if r.matchStrIgnoreCase("inf") {
return Inf(sign), nil
}
coef, exp := r.getCoef()
exp += r.getExp()
if r.len() != 0 { // didn't consume entire string
return Zero, errors.New("invalid number")
} else if coef == 0 || exp < math.MinInt8 {
return Zero, nil
} else if exp > math.MaxInt8 {
return Inf(sign), nil
}
if isPercentage {
exp -= 2
}
atmax := false
for coef > coefMax {
coef = (coef + 5) / 10
exp++
atmax = true
}
if !atmax {
p := maxShift(coef)
coef *= pow10[p]
exp -= p
}
// check(coefMin <= coef && coef <= coefMax)
return Value{coef, sign, exp}, nil
}
func MustNewFromString(input string) Value {
v, err := NewFromString(input)
if err != nil {
panic(fmt.Errorf("cannot parse %s into fixedpoint, error: %s", input, err.Error()))
}
return v
}
func NewFromBytes(s []byte) (Value, error) {
length := len(s)
if length == 0 {
return Zero, nil
}
isPercentage := s[length-1] == '%'
if isPercentage {
s = s[:length-1]
}
r := &readerBytes{s, 0}
sign := r.getSign()
if r.matchStrIgnoreCase("inf") {
return Inf(sign), nil
}
coef, exp := r.getCoef()
exp += r.getExp()
if r.len() != 0 { // didn't consume entire string
return Zero, errors.New("invalid number")
} else if coef == 0 || exp < math.MinInt8 {
return Zero, nil
} else if exp > math.MaxInt8 {
return Inf(sign), nil
}
if isPercentage {
exp -= 2
}
atmax := false
for coef > coefMax {
coef = (coef + 5) / 10
exp++
atmax = true
}
if !atmax {
p := maxShift(coef)
coef *= pow10[p]
exp -= p
}
// check(coefMin <= coef && coef <= coefMax)
return Value{coef, sign, exp}, nil
}
func MustNewFromBytes(input []byte) Value {
v, err := NewFromBytes(input)
if err != nil {
panic(fmt.Errorf("cannot parse %s into fixedpoint, error: %s", input, err.Error()))
}
return v
}
// TODO: refactor by interface
type readerBytes struct {
s []byte
i int
}
func (r *readerBytes) cur() byte {
if r.i >= len(r.s) {
return 0
}
return byte(r.s[r.i])
}
func (r *readerBytes) prev() byte {
if r.i == 0 {
return 0
}
return byte(r.s[r.i-1])
}
func (r *readerBytes) len() int {
return len(r.s) - r.i
}
func (r *readerBytes) match(c byte) bool {
if r.cur() == c {
r.i++
return true
}
return false
}
func (r *readerBytes) matchDigit() bool {
c := r.cur()
if '0' <= c && c <= '9' {
r.i++
return true
}
return false
}
func (r *readerBytes) matchStrIgnoreCase(pre string) bool {
pre = strings.ToLower(pre)
boundary := r.i + len(pre)
if boundary > len(r.s) {
return false
}
for i, c := range bytes.ToLower(r.s[r.i:boundary]) {
if pre[i] != c {
return false
}
}
r.i = boundary
return true
}
func (r *readerBytes) getSign() int8 {
if r.match('-') {
return int8(signNeg)
}
r.match('+')
return int8(signPos)
}
func (r *readerBytes) getCoef() (uint64, int) {
digits := false
beforeDecimal := true
for r.match('0') {
digits = true
}
if r.cur() == '.' && r.len() > 1 {
digits = false
}
n := uint64(0)
exp := 0
p := shiftMax
for {
c := r.cur()
if r.matchDigit() {
digits = true
// ignore extra decimal places
if c != '0' && p >= 0 {
n += uint64(c-'0') * pow10[p]
}
p--
} else if beforeDecimal {
// decimal point or end
exp = shiftMax - p
if !r.match('.') {
break
}
beforeDecimal = false
if !digits {
for r.match('0') {
digits = true
exp--
}
}
} else {
break
}
}
if !digits {
panic("numbers require at least one digit")
}
return n, exp
}
func (r *readerBytes) getExp() int {
e := 0
if r.match('e') || r.match('E') {
esign := r.getSign()
for r.matchDigit() {
e = e*10 + int(r.prev()-'0')
}
e *= int(esign)
}
return e
}
type reader struct {
s string
i int
}
func (r *reader) cur() byte {
if r.i >= len(r.s) {
return 0
}
return byte(r.s[r.i])
}
func (r *reader) prev() byte {
if r.i == 0 {
return 0
}
return byte(r.s[r.i-1])
}
func (r *reader) len() int {
return len(r.s) - r.i
}
func (r *reader) match(c byte) bool {
if r.cur() == c {
r.i++
return true
}
return false
}
func (r *reader) matchDigit() bool {
c := r.cur()
if '0' <= c && c <= '9' {
r.i++
return true
}
return false
}
func (r *reader) matchStrIgnoreCase(pre string) bool {
boundary := r.i + len(pre)
if boundary > len(r.s) {
return false
}
data := strings.ToLower(r.s[r.i:boundary])
pre = strings.ToLower(pre)
if data == pre {
r.i = boundary
return true
}
return false
}
func (r *reader) getSign() int8 {
if r.match('-') {
return int8(signNeg)
}
r.match('+')
return int8(signPos)
}
func (r *reader) getCoef() (uint64, int) {
digits := false
beforeDecimal := true
for r.match('0') {
digits = true
}
if r.cur() == '.' && r.len() > 1 {
digits = false
}
n := uint64(0)
exp := 0
p := shiftMax
for {
c := r.cur()
if r.matchDigit() {
digits = true
// ignore extra decimal places
if c != '0' && p >= 0 {
n += uint64(c-'0') * pow10[p]
}
p--
} else if beforeDecimal {
// decimal point or end
exp = shiftMax - p
if !r.match('.') {
break
}
beforeDecimal = false
if !digits {
for r.match('0') {
digits = true
exp--
}
}
} else {
break
}
}
if !digits {
panic("numbers require at least one digit")
}
return n, exp
}
func (r *reader) getExp() int {
e := 0
if r.match('e') || r.match('E') {
esign := r.getSign()
for r.matchDigit() {
e = e*10 + int(r.prev()-'0')
}
e *= int(esign)
}
return e
}
// end of FromStr ---------------------------------------------------
// IsInf returns true if a Value is positive or negative infinite
func (dn Value) IsInf() bool {
return dn.sign == signPosInf || dn.sign == signNegInf
}
// IsZero returns true if a Value is zero
func (dn Value) IsZero() bool {
return dn.sign == signZero
}
// Float64 converts a Value to float64
func (dn Value) Float64() float64 {
if dn.IsInf() {
return math.Inf(int(dn.sign))
}
g := float64(dn.coef)
if dn.sign == signNeg {
g = -g
}
i := int(dn.exp) - digitsMax
return g * math.Pow(10, float64(i))
}
// Int64 converts a Value to an int64, returning whether it was convertible
func (dn Value) Int64() int64 {
if dn.sign == 0 {
return 0
}
if dn.sign != signNegInf && dn.sign != signPosInf {
if 0 < dn.exp && dn.exp < digitsMax {
return int64(dn.sign) * int64(dn.coef/pow10[digitsMax-dn.exp])
} else if dn.exp <= 0 && dn.coef != 0 {
result := math.Log10(float64(dn.coef)) - float64(digitsMax) + float64(dn.exp)
return int64(dn.sign) * int64(math.Pow(10, result))
}
if dn.exp == digitsMax {
return int64(dn.sign) * int64(dn.coef)
}
if dn.exp == digitsMax+1 {
return int64(dn.sign) * (int64(dn.coef) * 10)
}
if dn.exp == digitsMax+2 {
return int64(dn.sign) * (int64(dn.coef) * 100)
}
if dn.exp == digitsMax+3 && dn.coef < math.MaxInt64/1000 {
return int64(dn.sign) * (int64(dn.coef) * 1000)
}
}
panic("unable to convert Value to int64")
}
func (dn Value) Int() int {
// if int is int64, this is a nop
n := dn.Int64()
if int64(int(n)) != n {
panic("unable to convert Value to int32")
}
return int(n)
}
// Sign returns -1 for negative, 0 for zero, and +1 for positive
func (dn Value) Sign() int {
return int(dn.sign)
}
// Coef returns the coefficient
func (dn Value) Coef() uint64 {
return dn.coef
}
// Exp returns the exponent
func (dn Value) Exp() int {
return int(dn.exp)
}
// Frac returns the fractional portion, i.e. x - x.Int()
func (dn Value) Frac() Value {
if dn.sign == 0 || dn.sign == signNegInf || dn.sign == signPosInf ||
dn.exp >= digitsMax {
return Zero
}
if dn.exp <= 0 {
return dn
}
frac := dn.coef % pow10[digitsMax-dn.exp]
if frac == dn.coef {
return dn
}
return New(dn.sign, frac, int(dn.exp))
}
type RoundingMode int
const (
Up RoundingMode = iota
Down
HalfUp
)
// Trunc returns the integer portion (truncating any fractional part)
func (dn Value) Trunc() Value {
return dn.integer(Down)
}
func (dn Value) integer(mode RoundingMode) Value {
if dn.sign == 0 || dn.sign == signNegInf || dn.sign == signPosInf ||
dn.exp >= digitsMax {
return dn
}
if dn.exp <= 0 {
if mode == Up ||
(mode == HalfUp && dn.exp == 0 && dn.coef >= One.coef*5) {
return New(dn.sign, One.coef, int(dn.exp)+1)
}
return Zero
}
e := digitsMax - dn.exp
frac := dn.coef % pow10[e]
if frac == 0 {
return dn
}
i := dn.coef - frac
if (mode == Up && frac > 0) || (mode == HalfUp && frac >= halfpow10[e]) {
return New(dn.sign, i+pow10[e], int(dn.exp)) // normalize
}
return Value{i, dn.sign, dn.exp}
}
func (dn Value) Floor() Value {
return dn.Round(0, Down)
}
func (dn Value) Round(r int, mode RoundingMode) Value {
if dn.sign == 0 || dn.sign == signNegInf || dn.sign == signPosInf ||
r >= digitsMax {
return dn
}
if r <= -digitsMax {
return Zero
}
n := New(dn.sign, dn.coef, int(dn.exp)+r) // multiply by 10^r
n = n.integer(mode)
if n.sign == signPos || n.sign == signNeg { // i.e. not zero or inf
return New(n.sign, n.coef, int(n.exp)-r)
}
return n
}
// arithmetic operations -------------------------------------------------------
// Neg returns the Value negated i.e. sign reversed
func (dn Value) Neg() Value {
return Value{dn.coef, -dn.sign, dn.exp}
}
// Abs returns the Value with a positive sign
func (dn Value) Abs() Value {
if dn.sign < 0 {
return Value{dn.coef, -dn.sign, dn.exp}
}
return dn
}
// Equal returns true if two Value's are equal
func Equal(x, y Value) bool {
return x.sign == y.sign && x.exp == y.exp && x.coef == y.coef
}
func (x Value) Eq(y Value) bool {
return Equal(x, y)
}
func Max(x, y Value) Value {
if Compare(x, y) > 0 {
return x
}
return y
}
func Min(x, y Value) Value {
if Compare(x, y) < 0 {
return x
}
return y
}
// Compare compares two Value's returning -1 for <, 0 for ==, +1 for >
func Compare(x, y Value) int {
switch {
case x.sign < y.sign:
return -1
case x.sign > y.sign:
return 1
case x == y:
return 0
}
sign := int(x.sign)
switch {
case sign == 0 || sign == signNegInf || sign == signPosInf:
return 0
case x.exp < y.exp:
return -sign
case x.exp > y.exp:
return +sign
case x.coef < y.coef:
return -sign
case x.coef > y.coef:
return +sign
default:
return 0
}
}
func (x Value) Compare(y Value) int {
return Compare(x, y)
}
func (v Value) MarshalYAML() (interface{}, error) {
return v.FormatString(8), nil
}
func (v *Value) UnmarshalYAML(unmarshal func(a interface{}) error) (err error) {
var f float64
if err = unmarshal(&f); err == nil {
*v = NewFromFloat(f)
return
}
var i int64
if err = unmarshal(&i); err == nil {
*v = NewFromInt(i)
return
}
var s string
if err = unmarshal(&s); err == nil {
nv, err2 := NewFromString(s)
if err2 == nil {
*v = nv
return
}
}
return err
}
// FIXME: should we limit to 8 prec?
func (v Value) MarshalJSON() ([]byte, error) {
if v.IsInf() {
return []byte("\"" + v.String() + "\""), nil
}
return []byte(v.FormatString(8)), nil
}
func (v *Value) UnmarshalJSON(data []byte) error {
// FIXME: do we need to compare {}, [], "", or "null"?
if bytes.Compare(data, []byte{'n', 'u', 'l', 'l'}) == 0 {
*v = Zero
return nil
}
if len(data) == 0 {
*v = Zero
return nil
}
var err error
if data[0] == '"' {
data = data[1 : len(data)-1]
}
if *v, err = NewFromBytes(data); err != nil {
return err
}
return nil
}
func Must(v Value, err error) Value {
if err != nil {
panic(err)
}
return v
}
// v * 10^(exp)
func (v Value) MulExp(exp int) Value {
return Value{v.coef, v.sign, v.exp + exp}
}
// Sub returns the difference of two Value's
func Sub(x, y Value) Value {
return Add(x, y.Neg())
}
func (x Value) Sub(y Value) Value {
return Sub(x, y)
}
// Add returns the sum of two Value's
func Add(x, y Value) Value {
switch {
case x.sign == signZero:
return y
case y.sign == signZero:
return x
case x.IsInf():
if y.sign == -x.sign {
return Zero
}
return x
case y.IsInf():
return y
}
if !align(&x, &y) {
return x
}
if x.sign != y.sign {
return usub(x, y)
}
return uadd(x, y)
}
func (x Value) Add(y Value) Value {
return Add(x, y)
}
func uadd(x, y Value) Value {
return New(x.sign, x.coef+y.coef, int(x.exp))
}
func usub(x, y Value) Value {
if x.coef < y.coef {
return New(-x.sign, y.coef-x.coef, int(x.exp))
}
return New(x.sign, x.coef-y.coef, int(x.exp))
}
func align(x, y *Value) bool {
if x.exp == y.exp {
return true
}
if x.exp < y.exp {
*x, *y = *y, *x // swap
}
yshift := ilog10(y.coef)
e := int(x.exp - y.exp)
if e > yshift {
return false
}
yshift = e
// check(0 <= yshift && yshift <= 20)
//y.coef = (y.coef + halfpow10[yshift]) / pow10[yshift]
y.coef = (y.coef) / pow10[yshift]
// check(int(y.exp)+yshift == int(x.exp))
return true
}
const e7 = 10000000
// Mul returns the product of two Value's
func Mul(x, y Value) Value {
sign := x.sign * y.sign
switch {
case sign == signZero:
return Zero
case x.IsInf() || y.IsInf():
return Inf(sign)
}
e := int(x.exp) + int(y.exp)
// split unevenly to use full 64 bit range to get more precision
// and avoid needing xlo * ylo
xhi := x.coef / e7 // 9 digits
xlo := x.coef % e7 // 7 digits
yhi := y.coef / e7 // 9 digits
ylo := y.coef % e7 // 7 digits
c := xhi * yhi
if (xlo | ylo) != 0 {
c += (xlo*yhi + ylo*xhi) / e7
}
return New(sign, c, e-2)
}
func (x Value) Mul(y Value) Value {
return Mul(x, y)
}
// Div returns the quotient of two Value's
func Div(x, y Value) Value {
sign := x.sign * y.sign
switch {
case x.sign == signZero:
return x
case y.sign == signZero:
return Inf(x.sign)
case x.IsInf():
if y.IsInf() {
if sign < 0 {
return NegOne
}
return One
}
return Inf(sign)
case y.IsInf():
return Zero
}
coef := div128(x.coef, y.coef)
return New(sign, coef, int(x.exp)-int(y.exp))
}
func (x Value) Div(y Value) Value {
return Div(x, y)
}
// Hash returns a hash value for a Value
func (dn Value) Hash() uint32 {
return uint32(dn.coef>>32) ^ uint32(dn.coef) ^
uint32(dn.sign)<<16 ^ uint32(dn.exp)<<8
}
// Format converts a number to a string with a specified format
func (dn Value) Format(mask string) string {
if dn.IsInf() {
return "#"
}
n := dn
before := 0
after := 0
intpart := true
for _, mc := range mask {
switch mc {
case '.':
intpart = false
case '#':
if intpart {
before++
} else {
after++
}
}
}
if before+after == 0 || n.Exp() > before {
return "#" // too big to fit in mask
}
n = n.Round(after, HalfUp)
e := n.Exp()
var digits []byte
if n.IsZero() && after == 0 {
digits = []byte("0")
e = 1
} else {
digits = strconv.AppendUint(make([]byte, 0, digitsMax), n.Coef(), 10)
digits = bytes.TrimRight(digits, "0")
}
nd := len(digits)
di := e - before
// check(di <= 0)
var buf strings.Builder
sign := n.Sign()
signok := (sign >= 0)
frac := false
for _, mc := range []byte(mask) {
switch mc {
case '#':
if 0 <= di && di < nd {
buf.WriteByte(digits[di])
} else if frac || di >= 0 {
buf.WriteByte('0')
}
di++
case ',':
if di > 0 {
buf.WriteByte(',')
}
case '-', '(':
signok = true
if sign < 0 {
buf.WriteByte(mc)
}
case ')':
if sign < 0 {
buf.WriteByte(mc)
} else {
buf.WriteByte(' ')
}
case '.':
frac = true
fallthrough
default:
buf.WriteByte(mc)
}
}
if !signok {
return "-" // negative not handled by mask
}
return buf.String()
}
func Clamp(x, min, max Value) Value {
if x.Compare(min) < 0 {
return min
}
if x.Compare(max) > 0 {
return max
}
return x
}
func (x Value) Clamp(min, max Value) Value {
if x.Compare(min) < 0 {
return min
}
if x.Compare(max) > 0 {
return max
}
return x
}
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