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Réécrituer de number

This commit is contained in:
Benjamin VAUDOUR 2024-02-21 10:12:59 +01:00
parent 2177ea9449
commit 5b437644bd
6 changed files with 885 additions and 1186 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))
) )

481
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" tpe: Integer,
sign: signOf(sign),
} }
} }
func integerString(n *big.Int, base uint, sign int) string { // Nan retourne NaN.
out := n.Text(int(base)) func Nan() Number { return Undefined(0) }
if sign < 0 { // Inf retourne +∞.
out = fmt.Sprintf("-%s", out) 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()
} }
if base != 10 { n := Number{
out = fmt.Sprintf("(%d)%s", base, out) number: option.Some(new(big.Rat).SetInt(i)),
sign: 1,
base: formatBase(base...),
tpe: Integer,
} }
return out return n.format()
} }
func fractionString(n, d *big.Int, base uint, sign int) string { // IntOf retourne un nombre entier à partir d’un entier, et éventuellement une base.
out := fmt.Sprintf("%s/%s", n.Text(int(base)), d.Text(int(base))) func IntOf[N integer | float](i N, base ...uint) Number {
return IntOf0(new(big.Int).SetInt64(int64(i)), 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 { func pow[N integer | float, M integer | float](b N, p ...M) Number {
base := n.Base() if len(p) > 0 {
num, denom := n.num(), n.denom() return IntOf(b).pow(int64(p[0]))
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 ""
}
} }
return IntOf(b).pow(int64(FloatingPrecision))
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 { // Zero retourne le nombre 0.
base := n.Base() func Zero(base ...uint) Number { return IntOf(0, 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,
atom: pow(base, exponent),
})
} else if exponent < 0 {
num = num.Mul(Number{
base: base,
tpe: Integer,
atom: pow(base, -exponent),
})
}
if num.Lt(denom) { // One retourne le nombre 1.
exponent-- func One(base ...uint) Number { return IntOf(1, base...) }
num.Mul(Int(base, base))
} // Two retourne le nombre 2.
tmp = num.Div(denom) func Two(base ...uint) Number { return IntOf(2, base...) }
// DecOf0 retourne un nombre décimal à partir d’un rationnel.
func DecOf0(f *big.Rat, base ...uint) Number {
if f == nil {
return Nan()
} }
out := decimalString(tmp) n := Number{
number: option.Some(new(big.Rat).Set(f)),
signExponent := "" sign: 1,
if exponent > 0 { base: formatBase(base...),
signExponent = "+" tpe: Decimal,
} else if exponent < 0 {
signExponent = "-"
} }
if base == 10 { return n.format()
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. // DecOf retourne un nombre décimal à partir d’un flottant.
func (n Number) String() string { func DecOf[N integer | float](f float64, base ...uint) Number {
if nb, ok := n.get(); ok { return DecOf0(new(big.Rat).SetFloat64(float64(f)))
switch n.Type() {
case Integer:
return integerString(nb.Num(), n.Base(), n.Sign())
case Fraction:
return fractionString(nb.Num(), nb.Denom(), n.base, n.Sign())
case Scientific:
return scientificStsring(n)
default:
return decimalString(n)
}
}
return undefinedString(n.Sign())
} }
func parseBase(str string) (next string, base option.Option[uint]) { // 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 }
}

861
number/number.go
View File

File diff suppressed because it is too large Load Diff

135
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))
} }
@ -24,36 +25,33 @@ 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() }
func Abs(n Number) Number { return n.Abs() } func Abs(n Number) Number { return n.Abs() }
func Num(n Number) Number { return n.Num() } func Num(n Number) Number { return n.Num() }
func Denom(n Number) Number { return n.Denom() } func Denom(n Number) Number { return n.Denom() }
func Inc(n Number) Number { return n.Inc() } 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)
} }