gob/number/operations.go

package number

import (
	"sort"
)

type Op1Func func(Number) Number
type Op2Func func(Number, Number) Number
type Op1To2Func func(Number) (Number, Number)
type Op2To2Func func(Number, Number) (Number, Number)
type ReduceFunc func(...Number) Number
type MapFunc func(...Number) []Number

// ToBase convertit n selon la base donnée.
func ToBase[N integer](n Number, base N) Number {
	return n.ToBase(formatBase(base))
}

func toType[N integer](n Number, t NumberType, base ...N) Number {
	n = n.ToType(t)
	if len(base) > 0 {
		n = ToBase(n, base[0])
	}

	return n
}

// ToInteger convertit n en entier.
func ToInteger[N integer](n Number, base ...N) Number { return toType(n, Integer, base...) }

// ToDecimal convertit n en décimal.
func ToDecimal[N integer](n Number, base ...N) Number { return toType(n, Decimal, base...) }

// ToFraction convertit n en fraction.
func ToFraction[N integer](n Number, base ...N) Number { return toType(n, Fraction, base...) }

// ToScientific convertit n en nombre scientifique.
func ToScientific[N integer](n Number, base ...N) Number { return toType(n, Scientific, base...) }

// Fonctions de type f(n) → n
func Neg(n Number) Number    { return n.Neg() }
func Abs(n Number) Number    { return n.Abs() }
func Num(n Number) Number    { return n.Num() }
func Denom(n Number) Number  { return n.Denom() }
func Inc(n Number) Number    { return n.Inc() }
func Dec(n Number) Number    { return n.Dec() }
func Inv(n Number) Number    { return n.Inv() }
func Fact(n Number) Number   { return n.Fact() }
func Len(n Number) Number    { return IntOf(n.Len()) }
func Sqrt(n Number) Number   { return n.Sqrt() }
func Square(n Number) Number { return n.Square() }

// Fonctions de type f(n, n) → n
func Cmp(n1, n2 Number) Number   { return IntOf(n1.Cmp(n2)) }
func Eq(n1, n2 Number) Number    { return ParseBool(n1.Eq(n2)) }
func Ne(n1, n2 Number) Number    { return ParseBool(n1.Ne(n2)) }
func Gt(n1, n2 Number) Number    { return ParseBool(n1.Gt(n2)) }
func Lt(n1, n2 Number) Number    { return ParseBool(n1.Lt(n2)) }
func Ge(n1, n2 Number) Number    { return ParseBool(n1.Ge(n2)) }
func Le(n1, n2 Number) Number    { return ParseBool(n1.Le(n2)) }
func Add(n1, n2 Number) Number   { return n1.Add(n2) }
func Sub(n1, n2 Number) Number   { return n1.Sub(n2) }
func Mul(n1, n2 Number) Number   { return n1.Mul(n2) }
func Div(n1, n2 Number) Number   { return n1.Div(n2) }
func Quo(n1, n2 Number) Number   { return n1.Quo(n2) }
func Rem(n1, n2 Number) Number   { return n1.Rem(n2) }
func Lsh(n1, n2 Number) Number   { return n1.Lsh(n2) }
func Rsh(n1, n2 Number) Number   { return n1.Rsh(n2) }
func Bit(n1, n2 Number) Number   { return IntOf(n1.Bit(n2)) }
func Pow(n1, n2 Number) Number   { return n1.Pow(n2) }
func Sqrtn(n1, n2 Number) Number { return n1.Sqrtn(n2) }

// Fonctions de type f(n) → (n, n)
func NumDenom(n Number) (Number, Number) { return n.NumDenom() }

// Fonctions de type f(n, n) → (n, n)
func QuoRem(n1, n2 Number) (Number, Number) { return n1.QuoRem(n2) }

// Autre
func Map(callback Op1Func) MapFunc {
	return func(numbers ...Number) []Number {
		out := make([]Number, len(numbers))
		for i, n := range numbers {
			out[i] = callback(n)
		}

		return out
	}
}

func Reduce(callback Op2Func) ReduceFunc {
	return func(numbers ...Number) Number {
		var acc Number
		for i, n := range numbers {
			if i == 0 {
				acc = n
			} else {
				acc = callback(acc, n)
			}
		}

		return acc
	}
}

// Max retourne le nombre le plus grand de la liste.
func Max(numbers ...Number) (n Number) {
	return Reduce(func(n1, n2 Number) Number {
		if n2.Gt(n1) {
			return n2
		}
		return n1
	})(numbers...)
}

// Min retourne le nombre le plus petit de la liste.
func Min(numbers ...Number) (n Number) {
	return Reduce(func(n1, n2 Number) Number {
		if n2.Lt(n1) {
			return n2
		}
		return n1
	})(numbers...)
}

// Sum retourne la somme des nombres.
func Sum(numbers ...Number) (n Number) { return Reduce(Add)(numbers...) }

// Mean retourne la moyenne des nombres.
func Mean(numbers ...Number) (n Number) {
	l := len(numbers)
	if l == 0 {
		return Nan()
	}

	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 {
	if !n.IsDefined() || n.Type() == Integer {
		return n
	}

	b := n.Base()
	if len(base) > 0 {
		b = formatBase(base...)
	}

	p := pow(b, precision)
	num, denom := n.Num().Mul(p), n.Denom()

	return num.Quo(denom).Div(p).ToType(n.Type())
}

// Reverse inverse l’ordre de la liste des nombres.
func Reverse(numbers ...Number) []Number {
	l := len(numbers)
	for i := 0; i < l>>1; i++ {
		j := l - 1 - i
		numbers[i], numbers[j] = numbers[j], numbers[i]
	}

	return numbers
}

// Sort trie les nombres par ordre croissant.
func Sort(numbers ...Number) []Number {
	sort.Slice(numbers, func(i, j int) bool {
		return numbers[i].Lt(numbers[j])
	})

	return numbers
}

// SortDesc trie les nombres par ordre décroissant.
func SortDesc(numbers ...Number) []Number {
	sort.Slice(numbers, func(i, j int) bool {
		return numbers[i].Gt(numbers[j])
	})

	return numbers
}