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3 Commits
c4029042e0 ... 5b437644bd

Author SHA1 Message Date
Benjamin VAUDOUR 5b437644bd Réécrituer de number 2024-02-21 10:12:59 +01:00
Benjamin VAUDOUR 2177ea9449 Corrections shell/console/atom 2024-02-21 10:12:23 +01:00
Benjamin VAUDOUR 46731e79d8 Ajout d’un stringer sur option.Result (à des fins de debug) 2024-02-21 10:10:49 +01:00
8 changed files with 906 additions and 1199 deletions
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502
number/atom.go
View File

@ -1,502 +0,0 @@
package number
import (
"math/big"
"gitea.zaclys.com/bvaudour/gob/option"
)
type atom struct {
number option.Option[*big.Rat]
sign int
}
func undefined[S integer | float](sign S) atom {
out := atom{
sign: signOf(sign),
}
return out.format()
}
func rational[S integer | float](rat *big.Rat, sign ...S) atom {
s := 1
if len(sign) > 0 {
s = signOf(sign[0])
}
out := atom{
number: option.Some(rat),
sign: s,
}
return out.format()
}
func frac0[S integer | float](num, denom *big.Int, sign ...S) atom {
if denom.IsInt64() && denom.Int64() == 0 {
s := num.Sign()
if len(sign) > 0 {
s *= signOf(sign[0])
}
return undefined(s)
}
rat := new(big.Rat).SetFrac(num, denom)
return rational(rat, sign...)
}
func frac[N integer | float, S integer | float](num, denom N, sign ...S) atom {
if denom == 0 {
s := signOf(num)
if len(sign) > 0 {
s *= signOf(sign[0])
}
return undefined(s)
}
rat := new(big.Rat).SetFrac64(int64(num), int64(denom))
return rational(rat, sign...)
}
func entire0[S integer | float](n *big.Int, sign ...S) atom {
rat := new(big.Rat).SetInt(n)
return rational(rat, sign...)
}
func entire[N integer | float, S integer | float](n N, sign ...S) atom {
rat := new(big.Rat).SetInt64(int64(n))
return rational(rat, sign...)
}
func decimal[N integer | float, S integer | float](n N, sign ...S) atom {
rat := new(big.Rat).SetFloat64(float64(n))
return rational(rat, sign...)
}
func pow[B integer | float, P integer | float](base B, precision ...P) atom {
p := FloatingPrecision
if len(precision) > 0 {
p = uint64(precision[0])
}
a := entire(formatBase(base), 1)
return a.pow(p)
}
func (a atom) get() (*big.Rat, bool) {
return a.number.Get()
}
func (a *atom) format() atom {
if nb, ok := a.get(); ok {
a.sign *= nb.Sign()
nb.Abs(nb)
}
a.sign = signOf(a.sign)
return *a
}
func (a atom) clone(format ...bool) atom {
out := atom{
sign: a.sign,
}
if nb, ok := a.get(); ok {
out.number = option.Some(new(big.Rat).Set(nb))
}
if len(format) > 0 && format[0] {
return out.format()
}
return out
}
func (a atom) rat() (nb *big.Rat, ok bool) {
if nb, ok = a.get(); ok {
nb = new(big.Rat).Set(nb)
if a.sign < 0 {
nb.Neg(nb)
} else if a.sign == 0 {
nb.SetInt64(0)
}
}
return
}
func (a atom) Sign() int {
return a.sign
}
func (a atom) IsNeg() bool {
return a.Sign() < 0
}
func (a atom) IsPos() bool {
return !a.IsNeg()
}
func (a atom) IsZero() bool {
return a.Is(0)
}
func (a atom) neg() atom {
out := a.clone()
out.sign = -out.sign
return out.format()
}
func (a atom) abs() atom {
out := a.clone()
if out.sign < 0 {
out.sign = -out.sign
}
return out.format()
}
func (a atom) IsDefined() bool {
return a.number.IsDefined()
}
func (a atom) IsInf() bool {
return !a.IsDefined() && a.Sign() > 0
}
func (a atom) IsNegInf() bool {
return !a.IsDefined() && a.Sign() < 0
}
func (a atom) IsNan() bool {
return !a.IsDefined() && a.Sign() == 0
}
func (a atom) Is(i int64) bool {
if nb, ok := a.get(); ok {
return nb.IsInt() && nb.Num().Int64()*int64(a.Sign()) == i
}
return false
}
func (a atom) IsFloat(f float64) bool {
if nb, ok := a.get(); ok {
e, ok := nb.Float64()
return ok && e*float64(a.Sign()) == f
}
return false
}
func (a atom) isInt() bool {
if nb, ok := a.get(); ok {
return nb.IsInt()
}
return false
}
func (a atom) isInt64() bool {
if nb, ok := a.get(); ok {
return nb.IsInt() && nb.Num().IsInt64()
}
return false
}
func (a atom) toInt64() (n int64, ok bool) {
var nb *big.Rat
if nb, ok = a.get(); ok {
if nb.IsInt() {
if num := nb.Num(); num.IsInt64() {
n = num.Int64()
}
}
}
return
}
func (a *atom) setInt() atom {
if nb, ok := a.get(); ok {
nb.SetInt(new(big.Int).Quo(nb.Num(), nb.Denom()))
}
return a.format()
}
func (a atom) num() atom {
if a.Sign() == 0 {
return entire(0, 0)
} else if nb, ok := a.get(); ok {
return entire0(nb.Num(), a.Sign())
}
return entire(a.Sign(), 1)
}
func (a atom) denom() atom {
if nb, ok := a.get(); ok {
return entire0(nb.Denom(), 1)
}
return entire(0, 0)
}
func (a1 atom) cmp(a2 atom) int {
if a1.IsNan() {
if a2.IsNan() {
return 0
}
return -2
} else if a2.IsNan() {
return 2
} else if nb1, ok := a1.rat(); ok {
if nb2, ok := a2.rat(); ok {
return nb1.Cmp(nb2)
}
return -a2.Sign()
} else if a2.IsDefined() {
return a1.Sign()
}
return compare(a1.Sign(), a2.Sign())
}
func (a1 atom) add(a2 atom) atom {
if r1, ok := a1.rat(); ok {
if r2, ok := a2.rat(); ok {
return rational(new(big.Rat).Add(r1, r2), 1)
}
return a2.clone()
} else if a2.IsDefined() || a1.Sign() == a2.Sign() {
return undefined(a1.Sign())
}
return undefined(0)
}
func (a1 atom) sub(a2 atom) atom {
return a1.add(a2.neg())
}
func (a atom) inc() atom {
return a.add(entire(1, 1))
}
func (a atom) dec() atom {
return a.sub(entire(1, 1))
}
func (a1 atom) mul(a2 atom) atom {
s := a1.Sign() * a2.Sign()
if nb1, ok := a1.get(); ok {
if nb2, ok := a2.get(); ok {
return rational(new(big.Rat).Mul(nb1, nb2), s)
}
}
return undefined(s)
}
func (a1 atom) div(a2 atom) atom {
if nb1, ok := a1.get(); ok {
if nb2, ok := a2.get(); ok {
if nb2.IsInt() && nb2.Num().IsInt64() && nb2.Num().Int64() == 0 {
return undefined(0)
}
return rational(new(big.Rat).Quo(nb1, nb2), a1.Sign()*a2.Sign())
}
return undefined(a1.Sign() * a2.Sign())
} else if a2.IsDefined() {
return undefined(a1.Sign() * a2.Sign())
}
return undefined(0)
}
func (a1 atom) quo(a2 atom) atom {
if nb1, ok := a1.get(); ok {
if nb2, ok := a2.get(); ok {
if nb2.IsInt() && nb2.Num().IsInt64() && nb2.Num().Int64() == 0 {
return undefined(0)
}
n := new(big.Int).Mul(nb1.Num(), nb2.Num())
d := new(big.Int).Mul(nb1.Denom(), nb2.Denom())
return entire0(new(big.Int).Quo(n, d), a1.Sign()*a2.Sign())
}
return undefined(a1.Sign() * a2.Sign())
} else if a2.IsDefined() {
return undefined(a1.Sign() * a2.Sign())
}
return undefined(0)
}
func (a1 atom) quoRem(a2 atom) (q, r atom) {
q = a1.quo(a2)
r = a1.sub(a2.mul(q))
return
}
func (a1 atom) rem(a2 atom) atom {
_, r := a1.quoRem(a2)
return r
}
func (a atom) inv() atom {
if nb, ok := a.get(); ok {
n, d := nb.Num(), nb.Denom()
return frac0(d, n, a.Sign())
}
if a.Sign() == 0 {
return undefined(0)
}
return entire(0, 0)
}
func (a atom) pow(p uint64) atom {
switch {
case p == 0:
if a.IsNan() {
return undefined(0)
}
return entire(0, 0)
case p == 1:
return a.clone(true)
case p == 2:
return a.mul(a)
case p&1 == 0:
return a.mul(a).pow(p >> 1)
default:
return a.mul(a).pow(p >> 1).mul(a)
}
}
func (a atom) optimize(precision atom) atom {
if a.isInt() || !a.IsDefined() {
return a
}
n1, d1 := a.num().abs(), a.denom()
t := n1.mul(precision).quo(d1)
an := t.div(precision)
n2, d2 := an.num(), an.denom()
if n2.cmp(n1) < 0 || d2.cmp(d1) < 0 {
t.sign = a.sign
return t.format()
}
return a
}
func (a atom) heron(n uint64, tmp atom) atom {
n0 := entire(int64(n), 1)
n1 := n0.dec()
return ((tmp.mul(n1)).add(a.div(tmp.pow(n - 1)))).div(n0)
}
func (a atom) sqrtn(n uint64, base uint) atom {
switch {
case a.IsNan() || n < 2 || (a.IsNeg() && n&1 == 0):
return undefined(0)
case a.IsZero() || a.Is(1) || !a.IsDefined():
return a.clone(true)
default:
precision := pow(base, FloatingPrecision)
pi := precision.inv()
out := a.heron(n, a).optimize(precision)
for {
t := a.heron(n, out).optimize(precision)
if out.cmp(t) == 0 {
break
} else if out.sub(t).abs().cmp(pi) < 0 {
out = t
break
}
}
return out
}
}
func (a atom) IsEven() bool {
if nb, ok := a.get(); ok {
return nb.IsInt() && nb.Num().Bit(0) == 0
}
return false
}
func (a atom) IsOdd() bool {
if nb, ok := a.get(); ok {
return nb.IsInt() && nb.Num().Bit(0) != 0
}
return false
}
func (a atom) lsh(n uint) atom {
if nb, ok := a.get(); ok {
if nb.IsInt() {
num, denom := new(big.Int).Lsh(nb.Num(), n), nb.Denom()
return frac0(num, denom, a.Sign())
}
return a.mul(pow(2, n))
}
return undefined(a.Sign())
}
func (a atom) rsh(n uint) atom {
if nb, ok := a.get(); ok {
if nb.IsInt() {
num, denom := new(big.Int).Rsh(nb.Num(), n), nb.Denom()
return frac0(num, denom, a.Sign())
}
return a.div(pow(2, n))
}
return undefined(a.Sign())
}
func (a atom) len(base uint) int {
if nb, ok := a.get(); ok {
if !nb.IsInt() {
return -1
}
num := nb.Num()
if num.IsInt64() && num.Int64() == 0 {
return 1
}
s := num.Text(int(base))
return len(s)
}
return -1
}
func (a atom) bit(n uint64, base uint) int {
if !a.isInt() {
return -1
}
out := a
if n > 0 {
out = a.quo(pow(base, n))
}
out = out.rem(entire(base, 1))
if nb, ok := out.get(); ok {
return int(nb.Num().Int64())
}
return -1
}

76
number/const.go
View File

@ -7,42 +7,56 @@ import (
var ( var (
FloatingPrecision uint64 = 10 // Nombre de chiffres après la virgule pour un nombre décimal ou un nombre scientifique FloatingPrecision uint64 = 10 // Nombre de chiffres après la virgule pour un nombre décimal ou un nombre scientifique
FixedPrecision = false // Si vrai le nombre chiffre après la virgule est fixe. FixedPrecision = false // Si vrai le nombre de chiffres après la virgule est fixe.
) )
const ( const (
regSign = `\+|-` rSign = `(\+|-)`
regBSign = `0|1` rBSign = `(0|1)`
regBase = `\(\d+\)` rNb2 = `(0|1)`
regBase2 = `B|b` rNb8 = `[0-7]`
regBase8 = `O|o` rNb10 = `\d`
regBase16 = `X|x` rNb16 = `[0-9a-fA-F]`
regNb = `[0-9a-zA-Z]` rNbN = `[0-9a-zA-Z]`
regNb2 = `0|1` rBase2 = `(B|b)`
regNb8 = `[0-7]` rBase8 = `(O|o)`
regNb10 = `\d` rBase16 = `(X|x)`
regNb16 = `[0-9a-fA-F]` rExp10 = `E|e`
regExp = `×\d+\^` rExpN = `×\d+\^`
regExp10 = `E|e`
) )
var ( var (
regInt = regexp.MustCompile(fmt.Sprintf(`%s(%s)?%s+`, regBase, regSign, regNb)) rInt2 = fmt.Sprintf(`(%s)%s+`, rBase2, rNb2)
regInt2 = regexp.MustCompile(fmt.Sprintf(`(%s)(%s)(%s)+`, regBSign, regBase2, regNb2)) rInt8 = fmt.Sprintf(`(%s)%s+`, rBase8, rNb8)
regInt8 = regexp.MustCompile(fmt.Sprintf(`(%s)(%s)(%s)+`, regBSign, regBase8, regNb8)) rInt10 = fmt.Sprintf(`(%s)%s+`, rSign, rNb10)
regInt10 = regexp.MustCompile(fmt.Sprintf(`(%s)?%s+`, regSign, regNb10)) rInt16 = fmt.Sprintf(`(%s)%s+`, rBase8, rNb8)
regInt16 = regexp.MustCompile(fmt.Sprintf(`(%s)(%s)(%s)+`, regBSign, regBase16, regNb16)) rIntN = fmt.Sprintf(`\(%s+\)%s?%s+`, rNb10, rSign, rNbN)
rIntB = fmt.Sprintf(`%s(%s|%s|%s)`, rBSign, rInt2, rInt8, rInt16)
rInt = fmt.Sprintf(`(%s|%s|%s)`, rInt10, rIntN, rIntB)
regDec = regexp.MustCompile(fmt.Sprintf(`%s(%s)?(%s*\.%s+|%s+\.)`, regBase, regSign, regNb, regNb, regNb)) rDec2 = fmt.Sprintf(`(%s)(%s+\.%s*|\.%s+)`, rBase2, rNb2, rNb2, rNb2)
regDec2 = regexp.MustCompile(fmt.Sprintf(`(%s)(%s)((%s)*\.(%s)+|(%s)+\.)`, regBSign, regBase2, regNb2, regNb2, regNb2)) rDec8 = fmt.Sprintf(`(%s)(%s+\.%s*|\.%s+)`, rBase8, rNb8, rNb8, rNb8)
regDec8 = regexp.MustCompile(fmt.Sprintf(`(%s)(%s)((%s)*\.(%s)+|(%s)+\.)`, regBSign, regBase8, regNb8, regNb8, regNb8)) rDec10 = fmt.Sprintf(`%s?(%s+\.%s*|\.%s+)`, rSign, rNb10, rNb10, rNb10)
regDec10 = regexp.MustCompile(fmt.Sprintf(`(%s)?(%s*\.%s+|%s+\.)`, regSign, regNb10, regNb10, regNb10)) rDec16 = fmt.Sprintf(`(%s)(%s+\.%s*|\.%s+)`, rBase16, rNb16, rNb16, rNb16)
regDec16 = regexp.MustCompile(fmt.Sprintf(`(%s)(%s)((%s)*\.(%s)+|(%s)+\.)`, regBSign, regBase16, regNb16, regNb16, regNb16)) rDecN = fmt.Sprintf(`\(%s+\)%s?(%s+\.%s*|\.%s+)`, rNb10, rSign, rNbN, rNbN, rNbN)
rDecB = fmt.Sprintf(`%s(%s|%s|%s)`, rBSign, rDec2, rDec8, rDec16)
regFrac = regexp.MustCompile(fmt.Sprintf(`%s(%s)?%s+/(%s)?%s+`, regBase, regSign, regNb, regSign, regNb)) rDec = fmt.Sprintf(`(%s|%s|%s)`, rDec10, rDecN, rDecB)
regFrac10 = regexp.MustCompile(fmt.Sprintf(`(%s)?%s+/(%s)?%s+`, regSign, regNb10, regSign, regNb10)) rExponent10 = fmt.Sprintf(`(%s|%s)(%s)%s?%s+`, rInt10, rDec10, rExp10, rSign, rNb10)
rExponentN = fmt.Sprintf(`(%s|%s)%s%s?%s+`, rInt, rDec, rExpN, rSign, rNb10)
regSci = regexp.MustCompile(fmt.Sprintf(`%s(%s)?(%s*\.%s+|%s+\.?)%s(%s)?(%s)+`, regBase, regSign, regNb, regNb, regNb, regExp, regSign, regNb10)) rAll10 = fmt.Sprintf(`(%s|%s)((%s)%s?%s+)?`, rInt10, rDec10, regExp10, rSign, rNb10)
regSci10Simple = regexp.MustCompile(fmt.Sprintf(`%s(%s)?(%s*\.%s+|%s+\.?)`, regSign, regNb10, regNb10, regNb10, regExp, regSign, regNb10)) rAllN = fmt.Sprintf(`(%s|%s)(%s%s?%s+)?`, rInt, rDec, rExpN, rSign, rNb10)
regSci10 = regexp.MustCompile(fmt.Sprintf(`%s(%s)?(%s*\.%s+|%s+\.?)`, regSign, regNb10, regNb10, regNb10, regExp10, regSign, regNb10)) rAll = fmt.Sprintf(`(%s|%s)`, rAll10, rAllN)
)
var (
regInt10 = regexp.MustCompile(fmt.Sprintf(`^%s$`, rInt10))
regIntN = regexp.MustCompile(fmt.Sprintf(`^%s$`, rIntN))
regIntB = regexp.MustCompile(fmt.Sprintf(`^%s$`, rIntB))
regDec = regexp.MustCompile(fmt.Sprintf(`^%s$`, rDec))
regExp10 = regexp.MustCompile(fmt.Sprintf(`^%s$`, rExponent10))
regExpN = regexp.MustCompile(fmt.Sprintf(`^%s$`, rExpN))
regFrac = regexp.MustCompile(fmt.Sprintf(`^%s/%s$`, rAll, rAll))
) )

499
number/convert.go
View File

@ -9,160 +9,109 @@ import (
"gitea.zaclys.com/bvaudour/gob/option" "gitea.zaclys.com/bvaudour/gob/option"
) )
func undefinedString(sign int) string { // Undefined retourne un nombre indéfini, signé :
switch sign { // - si sign < 0, retourne -∞
case -1: // - si sign > 0, retourne +∞
return "-∞" // - sinon, retourne NaN
case +1: func Undefined[N integer | float](sign N) Number {
return "+∞" return Number{
default: base: 10,
return "NaN"
}
}
func integerString(n *big.Int, base uint, sign int) string {
out := n.Text(int(base))
if sign < 0 {
out = fmt.Sprintf("-%s", out)
}
if base != 10 {
out = fmt.Sprintf("(%d)%s", base, out)
}
return out
}
func fractionString(n, d *big.Int, base uint, sign int) string {
out := fmt.Sprintf("%s/%s", n.Text(int(base)), d.Text(int(base)))
if sign < 0 {
out = fmt.Sprintf("-%s", out)
}
if base != 10 {
out = fmt.Sprintf("(%d)%s", base, out)
}
return out
}
func decimalString(n Number) string {
base := n.Base()
num, denom := n.num(), n.denom()
p := pow(base, FloatingPrecision)
num = num.mul(p)
q := num.quo(denom)
out := "0"
if num.cmp(denom) >= 0 {
if qn, ok := q.get(); ok {
out = qn.Num().Text(int(base))
} else {
return ""
}
}
precision := int(FloatingPrecision)
if len(out) < precision {
out = fmt.Sprintf("%s%s", strings.Repeat("0", precision), out)
}
deltaPrecision := len(out) - precision
out = fmt.Sprintf("%s.%s", out[:deltaPrecision], out[deltaPrecision:])
if !FixedPrecision {
l := len(out) - 1
for out[l] == '0' {
out, l = out[:l], l-1
}
if out == "." {
out = "0."
}
}
if n.IsNeg() {
out = fmt.Sprintf("-%s", out)
} else if q.IsZero() && !n.IsZero() {
out = fmt.Sprintf("+%s", out)
}
if base != 10 {
out = fmt.Sprintf("(%d)%s", base, out)
}
return out
}
func scientificStsring(n Number) string {
base := n.Base()
var exponent int
tmp := n
if n.IsZero() {
num, denom := n.Abs().NumDenom()
nl, dl := num.Len(), denom.Len()
exponent := nl - dl
if exponent > 0 {
denom = denom.Mul(Number{
base: base,
tpe: Integer, tpe: Integer,
atom: pow(base, exponent), sign: signOf(sign),
}) }
} else if exponent < 0 { }
num = num.Mul(Number{
base: base, // Nan retourne NaN.
func Nan() Number { return Undefined(0) }
// Inf retourne +∞.
func Inf() Number { return Undefined(1) }
// NegInf retourne -∞.
func NegInf() Number { return Undefined(-1) }
// IntOf0 retourne un nombre entier à partir d’un entier, et éventuellement une base.
func IntOf0(i *big.Int, base ...uint) Number {
if i == nil {
return Nan()
}
n := Number{
number: option.Some(new(big.Rat).SetInt(i)),
sign: 1,
base: formatBase(base...),
tpe: Integer, tpe: Integer,
atom: pow(base, -exponent),
})
} }
if num.Lt(denom) { return n.format()
exponent--
num.Mul(Int(base, base))
}
tmp = num.Div(denom)
} }
out := decimalString(tmp) // IntOf retourne un nombre entier à partir d’un entier, et éventuellement une base.
func IntOf[N integer | float](i N, base ...uint) Number {
signExponent := "" return IntOf0(new(big.Int).SetInt64(int64(i)), base...)
if exponent > 0 {
signExponent = "+"
} else if exponent < 0 {
signExponent = "-"
} }
if base == 10 { func pow[N integer | float, M integer | float](b N, p ...M) Number {
return fmt.Sprintf("%sE%s%d", out, signExponent, exponent) if len(p) > 0 {
return IntOf(b).pow(int64(p[0]))
} }
return fmt.Sprintf("%s×%d^%s%d", out, base, signExponent, exponent) return IntOf(b).pow(int64(FloatingPrecision))
} }
// String retourne la représentation du nombre sous forme de chaîne de caractères. // Zero retourne le nombre 0.
func (n Number) String() string { func Zero(base ...uint) Number { return IntOf(0, base...) }
if nb, ok := n.get(); ok {
switch n.Type() { // One retourne le nombre 1.
case Integer: func One(base ...uint) Number { return IntOf(1, base...) }
return integerString(nb.Num(), n.Base(), n.Sign())
case Fraction: // Two retourne le nombre 2.
return fractionString(nb.Num(), nb.Denom(), n.base, n.Sign()) func Two(base ...uint) Number { return IntOf(2, base...) }
case Scientific:
return scientificStsring(n) // DecOf0 retourne un nombre décimal à partir d’un rationnel.
default: func DecOf0(f *big.Rat, base ...uint) Number {
return decimalString(n) if f == nil {
} return Nan()
} }
return undefinedString(n.Sign()) n := Number{
number: option.Some(new(big.Rat).Set(f)),
sign: 1,
base: formatBase(base...),
tpe: Decimal,
} }
func parseBase(str string) (next string, base option.Option[uint]) { return n.format()
}
// DecOf retourne un nombre décimal à partir d’un flottant.
func DecOf[N integer | float](f float64, base ...uint) Number {
return DecOf0(new(big.Rat).SetFloat64(float64(f)))
}
// FracOf0 retourne une fraction à partir d’un numérateur et d’un dénominateur entiers.
func FracOf0(num, denom *big.Int, base ...uint) Number {
if num == nil || denom == nil {
return Nan()
}
n := Number{
number: option.Some(new(big.Rat).SetFrac(num, denom)),
sign: 1,
base: formatBase(base...),
tpe: Fraction,
}
return n.format()
}
// FracOf retourne une fraction à partir d’un numérateur et d’un dénominateur entiers.
func FracOf[N integer | float](num, denom N, base ...uint) Number {
return FracOf0(new(big.Int).SetInt64(int64(num)), new(big.Int).SetInt64(int64(denom)), base...)
}
func parseBaseN(str string) (next string, base option.Option[uint]) {
begin := strings.Index(str, "(") begin := strings.Index(str, "(")
end := strings.Index(str, ")") end := strings.Index(str, ")")
if begin > end || begin < 0 || end < 0 {
return
}
next = str[end+1:] next = str[end+1:]
if b, err := strconv.ParseUint(str[begin+1:end], 10, 64); err == nil && isBaseValid(b) { if b, err := strconv.ParseUint(str[begin+1:end], 10, 64); err == nil && isBaseValid(b) {
@ -171,7 +120,7 @@ func parseBase(str string) (next string, base option.Option[uint]) {
return return
} }
func parseBaseN(str string) (next string, base uint) { func parseBaseB(str string) (next string, base uint) {
next = str[1:] next = str[1:]
switch str[0] { switch str[0] {
case 'B', 'b': case 'B', 'b':
@ -185,7 +134,7 @@ func parseBaseN(str string) (next string, base uint) {
return return
} }
func parseSign(str string) (next string, sign int) { func parseSignN(str string) (next string, sign int) {
switch str[0] { switch str[0] {
case '-': case '-':
next, sign = str[1:], -1 next, sign = str[1:], -1
@ -198,7 +147,7 @@ func parseSign(str string) (next string, sign int) {
return return
} }
func parseSignN(str string) (next string, sign int) { func parseSignB(str string) (next string, sign int) {
next, sign = str[1:], 1 next, sign = str[1:], 1
if str[0] == '1' { if str[0] == '1' {
sign = -1 sign = -1
@ -217,226 +166,40 @@ func parseNumber(str string, base uint) (n option.Option[*big.Int]) {
func setInt(str string, base uint, sign int) (n option.Option[Number]) { func setInt(str string, base uint, sign int) (n option.Option[Number]) {
if nb, ok := parseNumber(str, base).Get(); ok { if nb, ok := parseNumber(str, base).Get(); ok {
nn := Number{ if sign < 0 {
base: base, nb.Neg(nb)
tpe: Integer,
atom: entire0(nb, sign),
} }
n = option.Some(nn.format()) n = option.Some(IntOf0(nb, base))
}
return
}
func parseInt(str string) (n option.Option[Number]) {
next, base := parseBase(str)
if b, ok := base.Get(); ok {
next, sign := parseSign(next)
n = setInt(next, b, sign)
} }
return return
} }
func parseInt10(str string) (n option.Option[Number]) { func parseInt10(str string) (n option.Option[Number]) {
next, sign := parseSign(str) next, sign := parseSignN(str)
return setInt(next, 10, sign) return setInt(next, 10, sign)
} }
func parseIntN(str string) (n option.Option[Number]) { func parseIntB(str string) (n option.Option[Number]) {
next, sign := parseSignN(str) next, sign := parseSignB(str)
next, base := parseBaseN(next) next, base := parseBaseB(next)
return setInt(next, base, sign) return setInt(next, base, sign)
} }
func setFrac(str string, base uint, sign int) (n option.Option[Number]) { func parseIntN(str string) (n option.Option[Number]) {
i := strings.Index(str, "/") next, base := parseBaseN(str)
if i < 0 {
return
}
sNum, sDenom := str[:i], str[i:]
if num, ok := parseNumber(sNum, base).Get(); ok {
if denom, ok := parseNumber(sDenom, base).Get(); ok {
nn := Number{
base: base,
tpe: Fraction,
atom: frac0(num, denom, sign),
}
n = option.Some(nn.format())
}
}
return
}
func parseFrac(str string) (n option.Option[Number]) {
next, base := parseBase(str)
if b, ok := base.Get(); ok { if b, ok := base.Get(); ok {
next, sign := parseSign(next) next, sign := parseSignN(next)
n = setFrac(next, b, sign) n = setInt(next, b, sign)
}
return
}
func parseFrac10(str string) (n option.Option[Number]) {
next, sign := parseSign(str)
return setFrac(next, 10, sign)
}
func parseDot(str string) (next string, dot int) {
i := strings.Index(str, ".")
if i >= 0 {
next = str[:i] + str[:i]
dot = len(next) - i
}
return
}
func setDec(str string, base uint, sign int) (n option.Option[Number]) {
next, dot := parseDot(str)
if num, ok := parseNumber(next, base).Get(); ok {
denom := pow(base, dot)
nn := Number{
base: base,
tpe: Decimal,
atom: entire0(num, sign).div(denom),
}
n = option.Some(nn.format())
}
return
}
func parseDec(str string) (n option.Option[Number]) {
next, base := parseBase(str)
if b, ok := base.Get(); ok {
next, sign := parseSign(next)
n = setDec(next, b, sign)
}
return
}
func parseDec10(str string) (n option.Option[Number]) {
next, sign := parseSign(str)
return setDec(next, 10, sign)
}
func parseDecN(str string) (n option.Option[Number]) {
next, sign := parseSignN(str)
next, base := parseBaseN(next)
return setDec(next, base, sign)
}
func parseExp(str string) (next string, baseExponent option.Option[int], exponent option.Option[int]) {
begin := strings.Index(str, "x")
end := strings.Index(str, "^")
if begin > end || begin < 0 || end < 0 {
return
}
sBase, sExponent := str[begin+1:end], str[end+1:]
if b, err := strconv.Atoi(sBase); err == nil && isBaseValid(b) {
if e, err := strconv.Atoi(sExponent); err == nil {
next, baseExponent, exponent = str[:begin], option.Some(b), option.Some(e)
}
}
return
}
func parseExp10(str string) (next string, exponent option.Option[int]) {
i := strings.Index(strings.ToLower(str), "e")
if i < 0 {
return
}
sExponent := str[i+1:]
if e, err := strconv.Atoi(sExponent); err == nil {
next, exponent = str[:i], option.Some(e)
}
return
}
func setSci(str string, base uint, sign, baseExponent, exponent int) (n option.Option[Number]) {
next, dot := parseDot(str)
if num, ok := parseNumber(next, base).Get(); ok {
denom := pow(base, dot)
nn := Number{
base: base,
tpe: Scientific,
atom: entire0(num, sign).div(denom),
}
if exponent > 0 {
nn.atom = nn.atom.mul(pow(baseExponent, exponent))
} else if exponent < 0 {
nn.atom = nn.atom.div(pow(baseExponent, -exponent))
}
n = option.Some(nn.format())
}
return
}
func parseSci(str string) (n option.Option[Number]) {
next, base := parseBase(str)
if b, ok := base.Get(); ok {
next, sign := parseSign(next)
next, be, e := parseExp(next)
if baseExponent, ok := be.Get(); ok {
if exponent, ok := e.Get(); ok {
n = setSci(next, b, sign, baseExponent, exponent)
}
}
}
return
}
func parseSci10(str string) (n option.Option[Number]) {
next, sign := parseSign(str)
next, be, e := parseExp(next)
if baseExponent, ok := be.Get(); ok {
if exponent, ok := e.Get(); ok {
n = setSci(next, 10, sign, baseExponent, exponent)
}
}
return
}
func parseSci10Simple(str string) (n option.Option[Number]) {
next, sign := parseSign(str)
next, e := parseExp10(next)
if exponent, ok := e.Get(); ok {
n = setSci(next, 10, sign, 10, exponent)
} }
return return
} }
// Parse retourne un nombre à partir d’une chaîne de caractères. // Parse retourne un nombre à partir d’une chaîne de caractères.
func Parse(str string) option.Option[Number] { func Parse(str string) (out option.Option[Number]) {
switch str { switch str {
case "+∞", "<inf>", "<+inf>": case "+∞", "<inf>", "<+inf>":
return option.Some(Inf()) return option.Some(Inf())
@ -447,33 +210,50 @@ func Parse(str string) option.Option[Number] {
} }
switch { switch {
case regInt.MatchString(str):
return parseInt(str)
case regInt10.MatchString(str): case regInt10.MatchString(str):
return parseInt10(str) return parseInt10(str)
case regInt2.MatchString(str), regInt8.MatchString(str), regInt16.MatchString(str): case regIntB.MatchString(str):
return parseIntB(str)
case regIntN.MatchString(str):
return parseIntN(str) return parseIntN(str)
case regFrac.MatchString(str):
return parseFrac(str)
case regFrac10.MatchString(str):
return parseFrac10(str)
case regDec.MatchString(str): case regDec.MatchString(str):
return parseInt(str) l := len(str)
case regDec10.MatchString(str): i := strings.Index(str, ".")
return parseInt10(str) dot := l - 1 - i
case regDec2.MatchString(str), regDec8.MatchString(str), regDec16.MatchString(str): str = fmt.Sprintf("%s%s", str[:i], str[i+1:])
return parseIntN(str) if n, ok := Parse(str).Get(); ok {
case regSci.MatchString(str): out = option.Some(n.Div(pow(n.Base(), dot)).ToType(Decimal))
return parseSci(str) }
case regSci10.MatchString(str): case regExp10.MatchString(str):
return parseSci10(str) i := strings.Index(strings.ToLower(str), "e")
case regSci10Simple.MatchString(str): if exponent, err := strconv.Atoi(str[i+1:]); err == nil {
return parseSci10Simple(str) if n, ok := Parse(str[:i]).Get(); ok {
out = option.Some(n.Mul(pow(10, exponent)).ToType(Scientific))
}
}
case regExpN.MatchString(str):
i, j := strings.Index(str, "×"), strings.Index(str, "^")
if expBase, err := strconv.ParseUint(str[i+1:j], 10, 64); err == nil && isBaseValid(expBase) {
if exponent, err := strconv.Atoi(str[j+1:]); err == nil {
if n, ok := Parse(str[:i]).Get(); ok {
out = option.Some(n.Mul(pow(expBase, exponent)).ToType(Scientific))
}
}
}
case regFrac.MatchString(str):
i := strings.Index(str, "/")
num, denom := Parse(str[:i]), Parse(str[i:])
if n, ok := num.Get(); ok {
if d, ok := denom.Get(); ok {
out = option.Some(n.Div(d).ToType(Fraction))
}
}
} }
return option.None[Number]() return
} }
// ParseBool retourne 1 si vrai, et 0 sinon.
func ParseBool(b bool) Number { func ParseBool(b bool) Number {
if b { if b {
return One() return One()
@ -481,6 +261,5 @@ func ParseBool(b bool) Number {
return Zero() return Zero()
} }
func ToBool(n Number) bool { // ToBool retourne vrai si le nombre n’est ni NaN ni 0.
return !n.IsZero() && !n.IsNan() func ToBool(n Number) bool { return n.Sign() != 0 }
}

837
number/number.go
View File

@ -1,5 +1,13 @@
package number package number
import (
"fmt"
"math/big"
"strings"
"gitea.zaclys.com/bvaudour/gob/option"
)
// NumberType représente le type d’un nombre. // NumberType représente le type d’un nombre.
type NumberType uint type NumberType uint
@ -12,299 +20,585 @@ const (
// Number représente un nombre. // Number représente un nombre.
type Number struct { type Number struct {
atom number rat
sign int
tpe NumberType tpe NumberType
base uint base uint
} }
// Undefined retourne un nombre indéfini, signé : func (n *Number) get() (r *big.Rat, ok bool) {
// - si sign < 0, retourne -∞ return n.number.Get()
// - si sign > 0, retourne +∞ }
// - sinon, retourne NaN
func Undefined(sign int) Number { func (n *Number) rat() (r *big.Rat, ok bool) {
return Number{ if r, ok := n.get(); ok {
base: 10, r = new(big.Rat).Set(r)
tpe: Integer, if n.Sign() < 0 {
atom: undefined(sign), r = r.Neg(r)
} }
} }
// Nan retourne NaN. return
func Nan() Number { return Undefined(0) }
// Inf retourne +∞.
func Inf() Number { return Undefined(1) }
// NegInf retourne -∞.
func NegInf() Number { return Undefined(-1) }
// Int retourne un nombre à partir d’un entier, et éventuellement une base.
func Int[N integer](n N, base ...uint) Number {
return Number{
base: formatBase(base...),
tpe: Integer,
atom: entire(n, 1),
}
} }
// Zero retourne le nombre 0. func (n *Number) format() Number {
func Zero(base ...uint) Number { return Int(0, base...) } n.base, n.sign, n.tpe = formatBase(n.base), signOf(n.sign), min(n.tpe, Fraction)
// One retourne le nombre 1. if nb, ok := n.get(); ok {
func One(base ...uint) Number { return Int(1, base...) } n.sign *= nb.Sign()
if n.tpe == Integer && !nb.IsInt() {
// Two retourne le nombre 2. num, denom := nb.Num(), nb.Denom()
func Two(base ...uint) Number { return Int(2, base...) } nb.SetInt(num.Quo(num, denom))
// Float retourne un nombre à partir d’un flottant, et éventuellement, une base.
func Float[N ~float32 | ~float64](n N, base ...uint) Number {
return Number{
base: formatBase(base...),
tpe: Decimal,
atom: decimal(n, 1),
} }
} nb.Abs(nb)
} else {
// Frac retourne un nombre à partir du numérateur, du dénominateur, et éventuellement, une base.
func Frac[N integer](num N, denom N, base ...uint) Number {
return Number{
base: formatBase(base...),
tpe: Fraction,
atom: frac(num, denom, 1),
}
}
func (n Number) set(a atom, format ...bool) Number {
out := Number{
atom: a,
tpe: n.tpe,
base: n.base,
}
return out.format(format...)
}
func (n *Number) format(formatAtom ...bool) Number {
if len(formatAtom) > 0 && formatAtom[0] {
n.atom.format()
}
n.base = formatBase(n.base)
if !n.IsDefined() {
n.base = 10
n.tpe = Integer n.tpe = Integer
} else if n.tpe == Integer && !n.isInt() {
n.setInt()
} }
return *n return *n
} }
func (n Number) clone(format ...bool) Number { func (n Number) set(r *big.Rat, tpe NumberType, sign ...int) Number {
s := 1
if len(sign) > 0 {
s = sign[0]
}
out := Number{ out := Number{
atom: n.atom.clone(format...), base: n.Base(),
tpe: tpe,
sign: s,
number: option.Some(r),
}
return out.format()
}
// Clone crée une copie profonde du nombre.
func (n Number) Clone() Number {
out := Number{
sign: n.sign,
tpe: n.tpe, tpe: n.tpe,
base: n.base, base: n.base,
} }
if len(format) > 0 && format[0] { if nb, ok := n.get(); ok {
return out.format() out.number = option.Some(new(big.Rat).Set(nb))
} }
return out return out
} }
// Type retourne le type de nombre. // Base retourne la base utilisée pour l’affichage du nombre.
func (n Number) Type() NumberType { func (n Number) Base() uint { return n.base }
return n.tpe
}
// ToType convertit le nombre au type donné. // Type retourne le type de nombre (entier, décimal, fraction ou scientifique).
func (n Number) ToType(t NumberType) Number { func (n Number) Type() NumberType { return n.tpe }
out := n.clone()
switch t {
case Integer, Decimal, Fraction, Scientific:
out.tpe = t
default:
out.tpe = Decimal
}
return out.format(true) // Sign retourne :
} // - 0 si n = 0 ou NaN
// - 1 si n > 0
// Base retourne la base du nombre. // - -1 si n < 0
func (n Number) Base() uint { func (n Number) Sign() int { return n.sign }
return n.base
}
// ToBase convertit le nombre dans la base donnée. // ToBase convertit le nombre dans la base donnée.
func (n Number) ToBase(base uint) Number { func (n Number) ToBase(base uint) Number {
out := n.clone(true) out := n.Clone()
out.base = formatBase(base) out.base = formatBase(base)
return out return out
} }
// Neg retourne -n. // ToType convertit le nombre dans le type donné. La base est conservée, sauf si une base est fournie.
func (n Number) Neg() Number { func (n Number) ToType(tpe NumberType, base ...uint) Number {
return n.set(n.neg()) out := n.Clone()
out.tpe = tpe
out = out.format()
if len(base) > 0 {
return out.ToBase(base[0])
}
return out
} }
// Abs retourne |n|. // IsDefined retourne vrai si le nombre est défini.
func (n Number) Abs() Number { func (n Number) IsDefined() bool { return n.number.IsDefined() }
return n.set(n.abs())
}
// IsInt retourne vrai si le nombre est entier. // IsInt retourne vrai si le nombre est entier.
func (n Number) IsInt() bool { func (n Number) IsInt() bool {
return n.isInt() nb, ok := n.get()
return ok && nb.IsInt()
}
// IsInt64 retourne vrai si le nombre est convertible en int64.
func (n Number) IsInt64() bool {
nb, ok := n.get()
return ok && nb.IsInt() && nb.Num().IsInt64()
}
// IsUint64 retourne vrai si le nombre est convertible en uint64.
func (n Number) IsUint64() bool {
nb, ok := n.get()
return ok && nb.IsInt() && nb.Num().IsUint64()
}
// Is retourne vrai si n = i.
func (n Number) Is(i int64) bool {
if nb, ok := n.get(); ok && nb.IsInt() {
num := nb.Num()
return num.IsInt64() && num.Int64() == i
}
return false
}
// IsUint retourne vrai si n = u.
func (n Number) IsUint(u uint64) bool {
if nb, ok := n.get(); ok && nb.IsInt() {
num := nb.Num()
return num.IsUint64() && num.Uint64() == u
}
return false
}
// IsFloat retourne vrai si n = f.
func (n Number) IsFloat(f float64) bool {
if nb, ok := n.get(); ok {
nf, ok := nb.Float64()
return nf == f && ok
}
return false
}
// IsNeg retourne vrai si n < 0.
func (n Number) IsNeg() bool { return n.Sign() < 0 }
// IsPos retourne vrai si n > 0.
func (n Number) IsPos() bool { return !n.IsNeg() }
// IsZero retourne vrai si n = 0.
func (n Number) IsZero() bool { return n.IsDefined() && n.Sign() == 0 }
// IsInf retourne vrai si n = +∞.
func (n Number) IsInf() bool { return !n.IsDefined() && n.Sign() > 0 }
// IsNegInf retourne vrai si n = -∞.
func (n Number) IsNegInf() bool { return !n.IsDefined() && n.Sign() < 0 }
// IsNan retourne vrai si n = NaN.
func (n Number) IsNan() bool { return !n.IsDefined() && n.Sign() == 0 }
// ToInt64 retourne le nombre converti en int64, et vrai si la conversion a réussi.
func (n Number) ToInt64() (i int64, ok bool) {
var nb *big.Rat
if nb, ok = n.get(); ok {
if ok = nb.IsInt(); ok {
num := nb.Num()
if ok = num.IsInt64(); ok {
i = num.Int64()
}
}
}
return
}
// ToUint64 retourne le nombre converti en uint64, et vrai si la conversion a réussi.
func (n Number) ToUint64() (u uint64, ok bool) {
var nb *big.Rat
if nb, ok = n.get(); ok {
if ok = nb.IsInt(); ok {
num := nb.Num()
if ok = num.IsUint64(); ok {
u = num.Uint64()
}
}
}
return
}
// IsEven retourne vrai si n est entier et pair.
func (n Number) IsEven() bool {
if nb, ok := n.get(); ok {
return nb.IsInt() && nb.Num().Bit(0) == 0
}
return false
}
// IsOdd retourne vrai si n est entier et impair.
func (n Number) IsOdd() bool {
if nb, ok := n.get(); ok {
return nb.IsInt() && nb.Num().Bit(0) != 0
}
return false
} }
// Num retourne le numérateur. // Num retourne le numérateur.
func (n Number) Num() Number { func (n Number) Num() Number {
out := Number{ if n.Sign() == 0 {
atom: n.num(), return IntOf(0, n.Base())
base: n.base, } else if nb, ok := n.rat(); ok {
tpe: Integer, return IntOf0(nb.Num(), n.Base())
} }
return out.format() return IntOf(n.Sign(), n.Base())
} }
// Denom retourne le dénominateur. // Denom retourne le dénominateur.
func (n Number) Denom() Number { func (n Number) Denom() Number {
out := Number{ if nb, ok := n.get(); ok {
atom: n.denom(), return IntOf0(nb.Denom(), n.Base())
base: n.base,
tpe: Integer,
} }
return out.format() return IntOf(0, n.Base())
} }
// Num retourne le numérateur et le dénominateur. // NumDenom retourne le numérateur et le dénominateur.
func (n Number) NumDenom() (Number, Number) { func (n Number) NumDenom() (Number, Number) { return n.Num(), n.Denom() }
return n.Num(), n.Denom()
// Neg retourne -n.
func (n Number) Neg() Number {
out := n.Clone()
out.sign = -out.sign
return out
}
// Abs retourne |n|.
func (n Number) Abs() Number {
out := n.Clone()
out.sign = abs(out.sign)
return out
} }
// Cmp retourne : // Cmp retourne :
// - 1 si n1 > n2
// - -1 si n1 < n2 // - -1 si n1 < n2
// - +1 si n1 > n2 // - 0 si n1 = n2
// - 0 sinon. // - 2 ou -2 si les nombres ne sont pas comparables (ie. n1 = NaN ou n2 = NaN)
func (n1 Number) Cmp(n2 Number) int { func (n1 Number) Cmp(n2 Number) int {
return n1.cmp(n2.atom) if n1.IsNan() {
if n2.IsNan() {
return 0
}
return -2
} else if n2.IsNan() {
return 2
} else if nb1, ok := n1.rat(); ok {
if nb2, ok := n2.rat(); ok {
return nb1.Cmp(nb2)
}
return -n2.Sign()
} else if n2.IsDefined() {
return n1.Sign()
} }
return compare(n1.Sign(), n2.Sign())
}
// Eq retourne vrai si n1 = n2.
func (n1 Number) Eq(n2 Number) bool { return n1.Cmp(n2) == 0 } func (n1 Number) Eq(n2 Number) bool { return n1.Cmp(n2) == 0 }
// Ne retourne vrai si n1 ≠ n2.
func (n1 Number) Ne(n2 Number) bool { return n1.Cmp(n2) != 0 } func (n1 Number) Ne(n2 Number) bool { return n1.Cmp(n2) != 0 }
// Gt retourne vrai si n1 > n2.
func (n1 Number) Gt(n2 Number) bool { return n1.Cmp(n2) > 0 } func (n1 Number) Gt(n2 Number) bool { return n1.Cmp(n2) > 0 }
// Lt retourne vrai si n1 < n2.
func (n1 Number) Lt(n2 Number) bool { return n1.Cmp(n2) < 0 } func (n1 Number) Lt(n2 Number) bool { return n1.Cmp(n2) < 0 }
// Ge retourne vrai si n1 ≥ n2.
func (n1 Number) Ge(n2 Number) bool { return n1.Cmp(n2) >= 0 } func (n1 Number) Ge(n2 Number) bool { return n1.Cmp(n2) >= 0 }
// Le retourne vrai si n1 ≤ n2.
func (n1 Number) Le(n2 Number) bool { return n1.Cmp(n2) <= 0 } func (n1 Number) Le(n2 Number) bool { return n1.Cmp(n2) <= 0 }
// Add retourne n1 + n2. // Add retourne n1 + n2.
func (n1 Number) Add(n2 Number) Number { func (n1 Number) Add(n2 Number) Number {
out := Number{ if r1, ok := n1.rat(); ok {
base: n1.base, if r2, ok := n2.rat(); ok {
tpe: max(n1.tpe, n2.tpe), return n1.set(new(big.Rat).Add(r1, r2), max(n1.Type(), n2.Type()))
atom: n1.add(n2.atom), }
return n2.Clone()
} else if n2.IsDefined() || n1.Sign() == n2.Sign() {
return Undefined(n1.Sign())
} }
return out.format() return Nan()
} }
// Sub retourne n1 - n2. // Sub retourne n1 − n2.
func (n1 Number) Sub(n2 Number) Number { func (n1 Number) Sub(n2 Number) Number { return n1.Add(n2.Neg()) }
out := Number{
base: n1.base,
tpe: max(n1.tpe, n2.tpe),
atom: n1.sub(n2.atom),
}
return out.format()
}
// Inc retourne n + 1. // Inc retourne n + 1.
func (n Number) Inc() Number { func (n Number) Inc() Number { return n.Add(One()) }
return n.Add(One())
}
// Dec retourne n − 1. // Dec retourne n − 1.
func (n Number) Dec() Number { func (n Number) Dec() Number { return n.Sub(One()) }
return n.Sub(One())
}
// Mul retourne n1 × n2. // Mul retourne n1 × n2.
func (n1 Number) Mul(n2 Number) Number { func (n1 Number) Mul(n2 Number) Number {
out := Number{ s := n1.Sign() * n2.Sign()
base: n1.base, if nb1, ok := n1.get(); ok {
tpe: max(n1.tpe, n2.tpe), if nb2, ok := n2.get(); ok {
atom: n1.mul(n2.atom), return n1.set(new(big.Rat).Mul(nb1, nb2), max(n1.Type(), n2.Type()), s)
}
} }
return out.format() return Undefined(s)
} }
// Div retourne n1 ÷ n2 (division exacte). // Div retourne n1 / n2 (division exacte).
func (n1 Number) Div(n2 Number) Number { func (n1 Number) Div(n2 Number) Number {
out := Number{ s := n1.Sign() * n2.Sign()
base: n1.base, if nb1, ok := n1.get(); ok {
tpe: max(n1.tpe, n2.tpe), if nb2, ok := n2.get(); ok {
atom: n1.div(n2.atom), if nb2.IsInt() && nb2.Num().IsInt64() && nb2.Num().Int64() == 0 {
return Nan()
} }
return out.format() t := max(n1.Type(), n2.Type())
result := new(big.Rat).Quo(nb1, nb2)
if t == Integer && !result.IsInt() {
t = Decimal
} }
return n1.set(result, t, s)
}
return Undefined(s)
} else if n2.IsDefined() {
return Undefined(s)
}
return Nan()
}
// inv retourne 1/n.
func (n Number) Inv() Number { return IntOf(1, n.Base()).Div(n) }
// Quo retourne n1 ÷ n2 (division entière). // Quo retourne n1 ÷ n2 (division entière).
func (n1 Number) Quo(n2 Number) Number { func (n1 Number) Quo(n2 Number) Number {
out := Number{ if nb1, ok := n1.rat(); ok {
base: n1.base, if nb2, ok := n2.rat(); ok {
tpe: Integer, if nb2.IsInt() && nb2.Num().IsInt64() && nb2.Num().Int64() == 0 {
atom: n1.quo(n2.atom), return Nan()
} }
return out.format() q := new(big.Rat).Quo(nb1, nb2)
return IntOf0(new(big.Int).Quo(q.Num(), q.Denom()), n1.Base())
}
return Undefined(n1.Sign() * n2.Sign())
} else if n2.IsDefined() {
return Undefined(n1.Sign() * n2.Sign())
}
return Nan()
}
// QuoRem retourne q et r tels que n1 = q×n2 + r où q est entier.
func (n1 Number) QuoRem(n2 Number) (q, r Number) {
q = n1.Quo(n2)
r = n1.Sub(n2.Mul(q))
return
} }
// Rem retourne n1 % n2. // Rem retourne n1 % n2.
func (n1 Number) Rem(n2 Number) Number { func (n1 Number) Rem(n2 Number) Number {
out := Number{ _, r := n1.QuoRem(n2)
base: n1.base,
tpe: max(n1.tpe, n2.tpe), return r
atom: n1.rem(n2.atom),
} }
return out.format() func (n Number) pow(p int64) (out Number) {
inv := p < 0
p = abs(p)
switch {
case p == 0:
if n.IsNan() {
return Nan()
}
return IntOf(1, n.Base())
case p == 1:
out = n.Clone()
case p == 2:
out = n.Square()
case p&1 == 0:
out = n.Square().pow(p >> 1)
default:
out = n.Square().pow(p >> 1).Mul(n)
} }
// QuoRem retourne la division entière et le reste. if inv {
func (n1 Number) QuoRem(n2 Number) (q, r Number) { out = out.Inv()
q.base, r.base = n1.base, n1.base }
q.tpe, r.tpe = Integer, max(n1.tpe, n2.tpe) return
q.atom, r.atom = n1.quoRem(n2.atom) }
func (n Number) optimize(precision Number) (out Number) {
return q.format(), r.format() out = n
if n.Denom().Gt(precision) {
out = n.Num().Mul(precision).Quo(n.Denom()).Div(precision).ToType(n.Type())
} }
// Inv retourne 1 ÷ n. return
func (n Number) Inv() Number { }
t := n.tpe func (n Number) sqrt(s uint64) (out Number) {
if n.IsNan() || s < 2 || (s&1 == 0 && n.IsNeg()) {
return Nan()
} else if !n.IsDefined() {
return n.Clone()
}
s0 := IntOf(s)
s1 := s0.Dec()
precision := pow[uint, uint](n.Base())
deltaMax := precision.Inv()
heron := func(partial Number) Number {
return ((partial.Mul(s1)).Add(n.Div(partial.pow(int64(s - 1))))).Div(s0).optimize(precision)
}
out = n
for {
tmp := heron(out)
if out.Eq(tmp) {
break
} else if (tmp.Sub(out)).Abs().Lt(deltaMax) {
out = tmp
break
}
out = tmp
}
if n.Type() == Integer && out.IsInt() {
out = out.ToType(Integer)
}
return
}
// Pow retourne n1 ^ n2.
func (n1 Number) Pow(n2 Number) Number {
if !n2.IsDefined() {
return Nan()
}
p2, s2 := n2.NumDenom()
p, pok := p2.ToInt64()
s, sok := s2.ToUint64()
if !pok || !sok {
return Nan()
}
out := n1.pow(p)
if s > 1 {
out = out.sqrt(s)
}
return out
}
// Square retourne n².
func (n Number) Square() Number { return n.Mul(n) }
// Sqrtn retourne la racine n2ième de n1.
func (n1 Number) Sqrtn(n2 Number) Number {
s, ok := n2.ToUint64()
if !ok {
return Nan()
}
return n1.sqrt(s)
}
// Sqrt retourne la racine carrée de n.
func (n Number) Sqrt() Number { return n.Sqrtn(Two()) }
func (n Number) lsh(s uint64) Number {
if nb, ok := n.rat(); ok {
num, denom := nb.Num(), nb.Denom()
return FracOf0(new(big.Int).Lsh(num, uint(s)), denom, n.Base()).ToType(n.Type())
}
return n.Clone()
}
func (n Number) rsh(s uint64) Number {
if nb, ok := n.rat(); ok {
t := n.Type()
if t == Integer { if t == Integer {
t = Fraction return IntOf0(new(big.Int).Rsh(nb.Num(), uint(s)), n.Base())
}
return FracOf0(nb.Num(), new(big.Int).Lsh(nb.Denom(), uint(s)), n.Base()).ToType(t)
} }
out := Number{ return n.Clone()
tpe: t,
base: n.base,
atom: n.inv(),
} }
if n.tpe == Integer && out.IsInt() { // Lsh retourne n1 << n2.
out.tpe = Integer func (n1 Number) Lsh(n2 Number) Number {
if s, ok := n2.ToUint64(); ok {
return n1.lsh(s)
} }
return out.format() return Nan()
}
// Rsh retourne n1 >> n2.
func (n1 Number) Rsh(n2 Number) Number {
if s, ok := n2.ToUint64(); ok {
return n1.rsh(s)
}
return Nan()
}
// Len retourne le nombre de chiffre de n si n est entier ou -1 sinon.
func (n Number) Len() int {
if nb, ok := n.get(); ok {
if !nb.IsInt() {
return -1
}
num := nb.Num()
if num.IsInt64() && num.Int64() == 0 {
return 1
}
s := num.Text(int(n.Base()))
return len(s)
}
return -1
}
// Bit retourne le n2ième chiffre de n1 si n est entier, ou -1 sinon.
// Le n° de bit commence à 0 à partir de la droite.
func (n1 Number) Bit(n2 Number) int {
b, ok := n2.ToUint64()
if !ok || !n1.IsInt() {
return -1
}
out := n1
if b > 0 {
out = n1.Quo(pow(n1.Base(), b))
}
out = out.Rem(IntOf(n1.Base()))
if result, ok := out.ToInt64(); ok {
return int(result)
}
return -1
} }
// Fact retourne n!. // Fact retourne n!.
@ -315,7 +609,7 @@ func (n Number) Fact() Number {
case !n.IsInt() || n.IsNeg(): case !n.IsInt() || n.IsNeg():
return Nan() return Nan()
default: default:
out := One(n.base) out := One(n.Base())
for e := Two(); e.Le(n); e = e.Inc() { for e := Two(); e.Le(n); e = e.Inc() {
out.Mul(e) out.Mul(e)
} }
@ -323,104 +617,135 @@ func (n Number) Fact() Number {
} }
} }
// Lsh retourne n1 << n2. func (n Number) text() string {
func (n1 Number) Lsh(n2 Number) Number { if nb, ok := n.get(); ok {
if n2.IsNeg() { return nb.Num().Text(int(n.Base()))
return n1.Rsh(n2.Abs()) }
return ""
}
func (n Number) undefinedString() string {
switch n.Sign() {
case -1:
return "-∞"
case +1:
return "+∞"
default:
return "NaN"
}
}
func (n Number) intString() (out string) {
out = n.text()
if n.Sign() < 0 {
out = fmt.Sprintf("-%s", out)
} }
if n, ok := n2.toInt64(); ok && n >= 0 { if base := n.Base(); base != 10 {
return n1.set(n1.lsh(uint(n)), true) out = fmt.Sprintf("(%d)%s", base, out)
}
return Nan()
} }
// Rsh retourne n1 << n2. return
func (n1 Number) Rsh(n2 Number) Number { }
if n2.IsNeg() { func (n Number) fracString() string {
return n1.Lsh(n2.Abs()) num, denom := n.NumDenom()
return fmt.Sprintf("%s/%s", num.intString(), denom.intString())
}
func (n Number) decString() (out string) {
base, sign := n.Base(), n.Sign()
num, denom := n.NumDenom()
precision := pow[uint, uint](base)
num = num.Abs().Mul(precision)
q := num.Quo(denom)
out = "0"
if num.Ge(denom) {
out = q.text()
} }
if n, ok := n2.toInt64(); ok && n >= 0 { p := int(FloatingPrecision)
return n1.set(n1.rsh(uint(n)), true) if len(out) < p {
} out = fmt.Sprintf("%s%s", strings.Repeat("0", p), out)
return Nan()
} }
// Len retourne le nombre de chiffre d’un nombre entier (ou -1 s’il n’est pas entier) dot := len(out) - p
func (n Number) Len() int { out = fmt.Sprintf("%s.%s", out[:dot], out[dot:])
return n.len(n.base)
}
// Bit retourne le chiffre à la position n2 (en partant de 0) if !FixedPrecision {
// d’un nombre entier (ou -1 si n1 ou n2 n’est pas entier). l := len(out) - 1
func (n1 Number) Bit(n2 Number) int { for out[l] == '0' {
if n, ok := n2.toInt64(); ok && n >= 0 { out, l = out[:l], l-1
return n1.bit(uint64(n), n1.base)
} }
if out == "." {
return -1 out = "0."
}
// Pow retourne n1 ^ n2.
func (n1 Number) Pow(n2 Number) Number {
if !n2.IsDefined() {
return Nan()
}
p, s := n2.NumDenom()
if !p.isInt64() || !s.isInt64() {
n2 = n2.set(n2.optimize(pow(n2.base, FloatingPrecision)))
p, s = n2.NumDenom()
if !p.isInt64() || !s.isInt64() {
return Nan()
} }
} }
if p0, ok := p.toInt64(); ok { if sign < 0 {
if s0, ok := s.toInt64(); ok && s0 > 0 { out = fmt.Sprintf("-%s", out)
inv := p0 < 0 } else if q.IsZero() && sign > 0 {
if inv { out = fmt.Sprintf("+%s", out)
p0 = -p0
}
out := Number{
tpe: n1.tpe,
base: n1.base,
atom: n1.pow(uint64(p0)).sqrtn(uint64(s0), n1.base),
}
if inv {
out.atom = out.atom.inv()
}
if n1.tpe == Integer && !out.isInt() {
out.tpe = Decimal
} }
return out.format() if base != 10 {
} out = fmt.Sprintf("(%d)%s", base, out)
} }
return Nan() return
}
func (n Number) sciString() (out string) {
base, sign := n.Base(), n.Sign()
var exponent int
tmp := n
if !n.IsZero() {
num, denom := n.Abs().NumDenom()
nl, dl := num.Len(), denom.Len()
exponent = nl - dl
nBase := IntOf(base)
if exponent > 0 {
denom = denom.Mul(nBase.pow(int64(exponent)))
} else if exponent < 0 {
num = num.Mul(nBase.pow(int64(-exponent)))
} }
// Sqrtn retourne la racine n2ième de n1. if num.Lt(denom) {
func (n1 Number) Sqrtn(n2 Number) Number { exponent--
if n, ok := n2.toInt64(); ok && n > 0 { num = num.Mul(nBase)
out := Number{
tpe: n1.tpe,
base: n1.base,
atom: n1.sqrtn(uint64(n), n1.base),
} }
if n1.tpe == Integer && !out.isInt() { tmp = num.Div(denom)
out.tpe = Decimal
} }
return out.format() if sign < 0 {
tmp = tmp.Neg()
} }
return Nan() signExponent := ""
if exponent > 0 {
signExponent = "+"
} }
// Sqrt retourne la racine carrée de n. out = tmp.decString()
func (n Number) Sqrt() Number { if base == 10 {
return n.Sqrtn(Int(2)) return fmt.Sprintf("%sE%s%d", out, signExponent, exponent)
}
return fmt.Sprintf("%s×%d^%s%d", out, base, signExponent, exponent)
}
// String retourne la représentation du nombre sous forme de chaîne de caractères.
func (n Number) String() string {
if !n.IsDefined() {
return n.undefinedString()
}
switch n.Type() {
case Integer:
return n.intString()
case Fraction:
return n.fracString()
case Scientific:
return n.sciString()
default:
return n.decString()
}
} }

117
number/operations.go
View File

@ -11,6 +11,7 @@ type Op2To2Func func(Number, Number) (Number, Number)
type ReduceFunc func(...Number) Number type ReduceFunc func(...Number) Number
type MapFunc func(...Number) []Number type MapFunc func(...Number) []Number
// ToBase convertit n selon la base donnée.
func ToBase[N integer](n Number, base N) Number { func ToBase[N integer](n Number, base N) Number {
return n.ToBase(formatBase(base)) return n.ToBase(formatBase(base))
} }
@ -24,21 +25,17 @@ func toType[N integer](n Number, t NumberType, base ...N) Number {
return n return n
} }
func ToInteger[N integer](n Number, base ...N) Number { // ToInteger convertit n en entier.
return toType(n, Integer, base...) func ToInteger[N integer](n Number, base ...N) Number { return toType(n, Integer, base...) }
}
func ToDecimal[N integer](n Number, base ...N) Number { // ToDecimal convertit n en décimal.
return toType(n, Decimal, base...) func ToDecimal[N integer](n Number, base ...N) Number { return toType(n, Decimal, base...) }
}
func ToFraction[N integer](n Number, base ...N) Number { // ToFraction convertit n en fraction.
return toType(n, Fraction, base...) func ToFraction[N integer](n Number, base ...N) Number { return toType(n, Fraction, base...) }
}
func ToScientific[N integer](n Number, base ...N) Number { // ToScientific convertit n en nombre scientifique.
return toType(n, Scientific, base...) func ToScientific[N integer](n Number, base ...N) Number { return toType(n, Scientific, base...) }
}
// Fonctions de type f(n) → n // Fonctions de type f(n) → n
func Neg(n Number) Number { return n.Neg() } func Neg(n Number) Number { return n.Neg() }
@ -49,11 +46,12 @@ func Inc(n Number) Number { return n.Inc() }
func Dec(n Number) Number { return n.Dec() } func Dec(n Number) Number { return n.Dec() }
func Inv(n Number) Number { return n.Inv() } func Inv(n Number) Number { return n.Inv() }
func Fact(n Number) Number { return n.Fact() } func Fact(n Number) Number { return n.Fact() }
func Len(n Number) Number { return Int(n.Len()) } func Len(n Number) Number { return IntOf(n.Len()) }
func Sqrt(n Number) Number { return n.Sqrt() } func Sqrt(n Number) Number { return n.Sqrt() }
func Square(n Number) Number { return n.Square() }
// Fonctions de type f(n, n) → n // Fonctions de type f(n, n) → n
func Cmp(n1, n2 Number) Number { return Int(n1.Cmp(n2)) } func Cmp(n1, n2 Number) Number { return IntOf(n1.Cmp(n2)) }
func Eq(n1, n2 Number) Number { return ParseBool(n1.Eq(n2)) } func Eq(n1, n2 Number) Number { return ParseBool(n1.Eq(n2)) }
func Ne(n1, n2 Number) Number { return ParseBool(n1.Ne(n2)) } func Ne(n1, n2 Number) Number { return ParseBool(n1.Ne(n2)) }
func Gt(n1, n2 Number) Number { return ParseBool(n1.Gt(n2)) } func Gt(n1, n2 Number) Number { return ParseBool(n1.Gt(n2)) }
@ -68,7 +66,7 @@ func Quo(n1, n2 Number) Number { return n1.Quo(n2) }
func Rem(n1, n2 Number) Number { return n1.Rem(n2) } func Rem(n1, n2 Number) Number { return n1.Rem(n2) }
func Lsh(n1, n2 Number) Number { return n1.Lsh(n2) } func Lsh(n1, n2 Number) Number { return n1.Lsh(n2) }
func Rsh(n1, n2 Number) Number { return n1.Rsh(n2) } func Rsh(n1, n2 Number) Number { return n1.Rsh(n2) }
func Bit(n1, n2 Number) Number { return Int(n1.Bit(n2)) } func Bit(n1, n2 Number) Number { return IntOf(n1.Bit(n2)) }
func Pow(n1, n2 Number) Number { return n1.Pow(n2) } func Pow(n1, n2 Number) Number { return n1.Pow(n2) }
func Sqrtn(n1, n2 Number) Number { return n1.Sqrtn(n2) } func Sqrtn(n1, n2 Number) Number { return n1.Sqrtn(n2) }
@ -105,6 +103,7 @@ func Reduce(callback Op2Func) ReduceFunc {
} }
} }
// Max retourne le nombre le plus grand de la liste.
func Max(numbers ...Number) (n Number) { func Max(numbers ...Number) (n Number) {
return Reduce(func(n1, n2 Number) Number { return Reduce(func(n1, n2 Number) Number {
if n2.Gt(n1) { if n2.Gt(n1) {
@ -114,6 +113,7 @@ func Max(numbers ...Number) (n Number) {
})(numbers...) })(numbers...)
} }
// Min retourne le nombre le plus petit de la liste.
func Min(numbers ...Number) (n Number) { func Min(numbers ...Number) (n Number) {
return Reduce(func(n1, n2 Number) Number { return Reduce(func(n1, n2 Number) Number {
if n2.Lt(n1) { if n2.Lt(n1) {
@ -123,35 +123,100 @@ func Min(numbers ...Number) (n Number) {
})(numbers...) })(numbers...)
} }
func Sum(numbers ...Number) (n Number) { // Sum retourne la somme des nombres.
return Reduce(Add)(numbers...) func Sum(numbers ...Number) (n Number) { return Reduce(Add)(numbers...) }
}
// Mean retourne la moyenne des nombres.
func Mean(numbers ...Number) (n Number) { func Mean(numbers ...Number) (n Number) {
l := len(numbers) l := len(numbers)
if l == 0 { if l == 0 {
return Nan() return Nan()
} }
return Sum(numbers...).Div(Int(l)) return Sum(numbers...).Div(IntOf(l))
} }
// Median retourne la médiane des nombres.
func Median(numbers ...Number) Number {
l := len(numbers)
if l == 0 {
return Nan()
}
numbers = Sort(numbers...)
if l&1 == 0 {
i := l >> 1
return numbers[i].Add(numbers[i-1]).Div(Two())
}
return numbers[l>>1]
}
// Mode retourne retourne le mode des nombres (ie. le nombre le plus fréquent).
func Mode(numbers ...Number) Number {
l := len(numbers)
if l == 0 {
return Nan()
}
m := make(map[Number]int)
loop:
for _, n := range numbers {
for k := range m {
if k.Eq(n) {
m[k]++
continue loop
}
}
m[n] = 1
}
i := 0
var n Number
for k, j := range m {
if j > i {
n, i = k, j
}
}
return n
}
// Variance retourne la variance des nombres.
func Variance(numbers ...Number) Number {
m := Mean(numbers...)
if m.IsNan() {
return m
}
numbers = Map(func(n Number) Number {
return n.Sub(m).Square()
})(numbers...)
return Mean(numbers...)
}
// StdDeviation retourne l’écart-type des nombres.
func StdDeviation(numbers ...Number) Number { return Variance(numbers...).Sqrt() }
// Round arrondit le n selon la précision et la base données.
func Round(n Number, precision uint64, base ...uint) Number { func Round(n Number, precision uint64, base ...uint) Number {
if !n.IsDefined() || n.Type() == Integer { if !n.IsDefined() || n.Type() == Integer {
return n return n
} }
p := Number{ b := n.Base()
base: n.Base(), if len(base) > 0 {
tpe: n.Type(), b = formatBase(base...)
atom: pow(formatBase(base...), precision),
} }
p.format()
p := pow(b, precision)
num, denom := n.Num().Mul(p), n.Denom() num, denom := n.Num().Mul(p), n.Denom()
return num.Quo(denom).Div(p) return num.Quo(denom).Div(p).ToType(n.Type())
} }
// Reverse inverse l’ordre de la liste des nombres.
func Reverse(numbers ...Number) []Number { func Reverse(numbers ...Number) []Number {
l := len(numbers) l := len(numbers)
for i := 0; i < l>>1; i++ { for i := 0; i < l>>1; i++ {
@ -162,6 +227,7 @@ func Reverse(numbers ...Number) []Number {
return numbers return numbers
} }
// Sort trie les nombres par ordre croissant.
func Sort(numbers ...Number) []Number { func Sort(numbers ...Number) []Number {
sort.Slice(numbers, func(i, j int) bool { sort.Slice(numbers, func(i, j int) bool {
return numbers[i].Lt(numbers[j]) return numbers[i].Lt(numbers[j])
@ -170,6 +236,7 @@ func Sort(numbers ...Number) []Number {
return numbers return numbers
} }
// SortDesc trie les nombres par ordre décroissant.
func SortDesc(numbers ...Number) []Number { func SortDesc(numbers ...Number) []Number {
sort.Slice(numbers, func(i, j int) bool { sort.Slice(numbers, func(i, j int) bool {
return numbers[i].Gt(numbers[j]) return numbers[i].Gt(numbers[j])

16
number/util.go
View File

@ -1,5 +1,11 @@
package number package number
import (
"math/big"
"gitea.zaclys.com/bvaudour/gob/option"
)
type integer interface { type integer interface {
~int | ~int8 | ~int16 | ~int32 | ~int64 | ~uint | ~uint8 | ~uint16 | ~uint32 | ~uint64 ~int | ~int8 | ~int16 | ~int32 | ~int64 | ~uint | ~uint8 | ~uint16 | ~uint32 | ~uint64
} }
@ -8,6 +14,8 @@ type float interface {
~float32 | ~float64 ~float32 | ~float64
} }
type rat = option.Option[*big.Rat]
func signOf[N integer | float](n N) int { func signOf[N integer | float](n N) int {
switch { switch {
case n < 0: case n < 0:
@ -19,6 +27,14 @@ func signOf[N integer | float](n N) int {
} }
} }
func abs[N integer | float](n N) N {
if n < 0 {
return -n
}
return n
}
func compare[N integer | float](n1, n2 N) int { func compare[N integer | float](n1, n2 N) int {
return signOf(n1 - n2) return signOf(n1 - n2)
} }

12
option/result.go
View File

@ -1,5 +1,9 @@
package option package option
import (
"fmt"
)
// Result stocke un résultat : // Result stocke un résultat :
// - soit le résultat est valide, et une valeur est stockée, // - soit le résultat est valide, et une valeur est stockée,
// - soit le résultat est invalide, et une erreur est stockée. // - soit le résultat est invalide, et une erreur est stockée.
@ -41,3 +45,11 @@ func (r Result[T]) Err() (err error, ok bool) {
func (r Result[T]) IsOk() bool { func (r Result[T]) IsOk() bool {
return r.ok return r.ok
} }
func (r Result[T]) String() string {
return fmt.Sprintf(`{
value: %v,
error: %s,
ok: %v,
}`, r.v, r.err, r.ok)
}

20
shell/console/atom/input.go
View File

@ -56,11 +56,8 @@ func (in *input) restart() {
n := in.readRune() n := in.readRune()
next <- n next <- n
needClose := !n.IsOk()
if !needClose {
r, ok := n.Ok() r, ok := n.Ok()
needClose = ok && (r == Lf || r == Cr || r == C_C || r == C_D) needClose := !ok || r == Lf || r == Cr || r == C_C || r == C_D
}
if needClose { if needClose {
close(next) close(next)
@ -317,22 +314,21 @@ func (in *input) nextChar() (key nkey) {
return return
} }
var s Sequence
switch r { switch r {
case Bs: case Bs:
s = A_Bs key = nk(keyS(A_Bs))
case 'O': case 'O':
return in.escO() key = in.escO()
case '[': case '[':
return in.escBracket() key = in.escBracket()
case 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', case 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z',
'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z': 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z':
s = Sequence(r << 16) key = nk(keyS(Sequence(r << 16)))
default: //default:
return // return
} }
in.clear() in.clear()
return nk(keyS(s)) return
} }