// IsFundamentalDiscriminant returns true if the given discriminant is
// fundamental.
func IsFundamentalDiscriminant(D *mathx.Int) bool {
d := D.Int64()
absd := d
if d < 0 {
absd = -absd
}
if d == 1 {
return true
}
if PosMod(d, 4) == 1 && IsSquareFree64(absd) {
return true
}
if PosMod(d, 4) == 0 {
if IsSquareFree64(absd / 4) {
return PosMod(d/4, 4) == 2 || PosMod(d/4, 4) == 3
}
}
return false
}
// String returns a kind messy decimal string version of this.
// It is utterly precise, and will use as many decimal digits
// as are necessary to completely represent this number.
func (f Float) String() string {
sign := "+"
if !f.sign {
sign = "-"
}
var whole *mathx.Int
var fraction *mathx.Int
if f.exp <= 0 {
whole = f.mantissa.Rsh(uint(-f.exp))
fraction = f.mantissa.Sub(whole.Lsh(uint(-f.exp)))
} else {
whole = mathx.NewInt(0)
fraction = f.mantissa
}
whole = f.mantissa.Rsh(uint(-f.exp))
fraction = f.mantissa.Sub(whole.Lsh(uint(-f.exp)))
digits := ""
for fraction.Sign() != 0 {
fraction = fraction.Mul64(10)
digit := fraction.Rsh(uint(-f.exp))
fraction = fraction.Sub(digit.Lsh(uint(-f.exp)))
digits += digit.String()
}
if digits == "" {
digits = "0"
}
return fmt.Sprintf("%s%s.%s", sign, whole.String(), digits)
}