gob/number/atom.go

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
}