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use num::{traits::Euclid, ToPrimitive, Zero};
use crate::{
divisible::Composite,
error::{AdicError, AdicResult},
normed::{UltraNormed, Valuation, ValuationRing},
};
/// A structure with digits that can be accessed
pub trait HasDigits {
/// Type for the digits' index,
/// e.g. `usize` for [`EAdic`](crate::EAdic) or `isize` for [`QAdic`](crate::QAdic)
type DigitIndex: ValuationRing + Euclid;
/// Number of possibilities for digits
///
/// ```
/// # use adic::{divisible::Divisible, num_adic::{MAdic, PowAdic}, traits::HasDigits, UAdic};
/// assert_eq!(7, UAdic::new(7, vec![1, 2, 3]).base().value32());
/// assert_eq!(25, PowAdic::new(UAdic::new(5, vec![3, 2, 1]), 2).base().value32());
/// assert_eq!(10, MAdic::new([
/// PowAdic::new(UAdic::new(2, vec![0, 1]), 1),
/// PowAdic::new(UAdic::new(5, vec![3, 2]), 1),
/// ]).base().value32());
/// ```
fn base(&self) -> Composite;
/// Minimum digit index, possibly zero for positive valuation numbers.
/// This is the index where the first digit of `[digits](Self::digits)` starts.
///
/// ```
/// # use adic::{normed::Valuation, traits::HasDigits, QAdic, UAdic};
/// assert_eq!(Valuation::Finite(0), UAdic::new(5, vec![2]).min_index());
/// assert_eq!(Valuation::Finite(0), UAdic::new(5, vec![0, 0, 2]).min_index());
/// assert_eq!(Valuation::Finite(0), QAdic::new(UAdic::new(5, vec![2]), 2).min_index());
/// assert_eq!(Valuation::Finite(-2), QAdic::new(UAdic::new(5, vec![2]), -2).min_index());
/// ```
fn min_index(&self) -> Valuation<Self::DigitIndex>;
/// The number of digits this number ultimately has, finite or infinite.
/// Returns `num-valuation` if `valuation` is negative and `num` if it is positive.
///
/// ```
/// # use adic::{normed::Valuation, traits::{AdicPrimitive, HasDigits}, EAdic, QAdic, UAdic};
/// assert_eq!(Valuation::Finite(3), UAdic::new(5, vec![2, 1, 3, 0]).num_digits());
/// assert_eq!(Valuation::Finite(0), UAdic::zero(5).num_digits());
/// assert_eq!(Valuation::PosInf, EAdic::new_repeating(5, vec![2, 1], vec![3, 0]).num_digits());
/// assert_eq!(Valuation::Finite(3), QAdic::new(UAdic::new(5, vec![2, 1, 3, 0]), -2).num_digits());
/// assert_eq!(Valuation::Finite(5), QAdic::new(UAdic::new(5, vec![2, 1, 3, 0]), 2).num_digits());
/// assert_eq!(Valuation::Finite(0), QAdic::new(UAdic::zero(5), 2).num_digits());
/// assert_eq!(Valuation::PosInf, QAdic::new(EAdic::new_repeating(5, vec![2, 1], vec![3, 0]), -2).num_digits());
/// ```
fn num_digits(&self) -> Valuation<usize>;
/// Test if this has a finite number of digits
///
/// ```
/// # use adic::{traits::HasDigits, EAdic, QAdic, UAdic};
/// assert!(UAdic::new(5, vec![2, 3, 1, 2, 3, 1]).has_finite_digits());
/// assert!(!EAdic::new_repeating(5, vec![2, 3, 1], vec![2, 1]).has_finite_digits());
/// assert!(QAdic::new(UAdic::new(5, vec![2, 1, 3, 0]), -2).has_finite_digits());
/// assert!(!QAdic::new(EAdic::new_repeating(5, vec![2, 1], vec![3, 0]), -2).has_finite_digits());
/// ```
fn has_finite_digits(&self) -> bool {
!matches!(self.num_digits(), Valuation::PosInf)
}
/// Gets the digit at this coefficient of p^n; error if it is beyond known digits (certainty)
///
/// ```
/// # use adic::{error::AdicError, traits::HasDigits, QAdic, UAdic, ZAdic};
/// let u = UAdic::new(5, vec![2, 1, 3]);
/// assert_eq!([Ok(2), Ok(3), Ok(0)], [u.digit(0), u.digit(2), u.digit(4)]);
/// let z = ZAdic::new_approx(5, 4, vec![2, 1, 3]);
/// assert_eq!([Ok(2), Ok(3)], [z.digit(0), z.digit(2)]);
/// assert!(matches!(z.digit(4), Err(AdicError::InappropriatePrecision(_))));
/// let u = QAdic::new(UAdic::new(5, vec![2, 1, 3]), -1);
/// assert_eq!([Ok(2), Ok(1), Ok(3), Ok(0)], [u.digit(-1), u.digit(0), u.digit(1), u.digit(2)]);
/// let z = QAdic::new(ZAdic::new_approx(5, 3, vec![2, 1, 3]), -1);
/// assert_eq!([Ok(2), Ok(1), Ok(3)], [z.digit(-1), z.digit(0), z.digit(1)]);
/// assert!(matches!(z.digit(2), Err(AdicError::InappropriatePrecision(_))));
/// ```
fn digit(&self, n: Self::DigitIndex) -> AdicResult<u32>;
/// Returns the digit in the zeroth position or Err if it is beyond known digits (certainty)
///
/// ```
/// # use adic::{error::AdicError, traits::HasDigits, QAdic, UAdic, ZAdic};
/// assert_eq!(Ok(2), UAdic::new(5, vec![2, 3, 1]).digit0());
/// assert!(matches!(ZAdic::empty(5).digit0(), Err(AdicError::InappropriatePrecision(_))));
/// assert_eq!(Ok(3), QAdic::new(UAdic::new(5, vec![2, 3, 1]), -1).digit0());
/// assert_eq!(Ok(0), QAdic::new(UAdic::new(5, vec![2, 3, 1]), -4).digit0());
/// assert!(matches!(
/// QAdic::new(ZAdic::new_approx(5, 2, vec![1, 2]), -3).digit0(),
/// Err(AdicError::InappropriatePrecision(_))
/// ));
/// ```
fn digit0(&self) -> AdicResult<u32> {
self.digit(Self::DigitIndex::zero())
}
/// Digits iterator for this object, starting from [`min_index`](Self::min_index)
///
/// ```
/// # use adic::{traits::HasDigits, EAdic, QAdic, UAdic};
/// let u = UAdic::new(5, vec![2, 1, 3]);
/// assert_eq!(vec![2, 1, 3], u.digits().collect::<Vec<_>>());
/// let r = EAdic::new_repeating(5, vec![2, 1], vec![3]);
/// assert_eq!(vec![2, 1, 3, 3, 3, 3], r.digits().take(6).collect::<Vec<_>>());
/// let q = QAdic::new(UAdic::new(5, vec![2, 1, 3]), -1);
/// assert_eq!(vec![2, 1, 3], q.digits().collect::<Vec<_>>());
/// let q = QAdic::new(UAdic::new(5, vec![2, 1, 3]), 1);
/// assert_eq!(vec![0, 2, 1, 3], q.digits().collect::<Vec<_>>());
/// ```
fn digits(&self) -> impl Iterator<Item=u32>;
/// Flips the digit indices from positive to negative and returns the corresponding `f64`.
/// E.g. if this is an adic number, it flips the digits around its decimal point and
/// returns the value as a real number.
///
/// ```
/// # use assertables::assert_approx_eq;
/// # use adic::{traits::HasDigits, EAdic, QAdic};
/// // 10._5 => 0.01_5 => 0.04
/// assert_approx_eq!(EAdic::new(5, vec![0, 1]).real_projection().unwrap(), 0.04);
/// // ...444444.4_5 => 4.44444...._5 => 5
/// assert_approx_eq!(QAdic::new(EAdic::new_repeating(5, vec![], vec![4]), -1).real_projection().unwrap(), 5.0);
/// // 0._5 => 0
/// assert_approx_eq!(EAdic::new(5, vec![]).real_projection().unwrap(), 0.0);
/// ```
fn real_projection(&self) -> AdicResult<f64> {
let zero = Self::DigitIndex::zero();
let input_offset = match self.min_index() {
Valuation::Finite(v) if v < zero => (zero - v).try_into_usize()?,
Valuation::Finite(_) => 0,
Valuation::PosInf => panic!("Valuation cannot be infinite for the input"),
};
// Add 1 so we flip around the decimal point instead of the digit
let input_offset = -isize::try_from(input_offset)? + 1;
let inverse_base = 1.0 / f64::from(u32::from(self.base()));
let offset_power = inverse_base.powf(f64::from(i32::try_from(input_offset)?));
// epsilon > base.powf(-i)
// i > -log_base(epsilon)
let log_eps = f64::EPSILON.log(f64::from(u32::from(self.base())));
let num_terms = (-log_eps).ceil().to_usize().ok_or(AdicError::BadConversion)?;
let projected: f64 = self.digits()
.take(num_terms)
.enumerate()
.map(|(i, d)| Ok(f64::from(d)*inverse_base.powf(f64::from(u32::try_from(i)?))))
.collect::<AdicResult<Vec<_>>>()?
.into_iter()
.sum();
Ok(projected * offset_power)
}
}
/// A structure that has digits with a concept of certain and uncertain digits
pub trait HasApproximateDigits: HasDigits {
/// The index of the first unknown digit for this number: `v(...0021.30_5) = 4`
///
/// Returns a [`Valuation`].
/// Returns `PosInf` for an exact numbers and `Finite(v)` for an approximate number with digits to the `v-th` valuation.
///
/// ```
/// # use adic::{normed::Valuation, traits::HasApproximateDigits, QAdic, UAdic, ZAdic};
/// assert_eq!(Valuation::Finite(6), ZAdic::new_approx(5, 6, vec![0, 3, 1, 2]).certainty());
/// assert_eq!(Valuation::PosInf, UAdic::new(5, vec![0, 3, 1, 2]).certainty());
/// assert_eq!(Valuation::Finite(4), QAdic::new(ZAdic::new_approx(5, 6, vec![0, 3, 1, 2]), -2).certainty());
/// assert_eq!(Valuation::Finite(-2), QAdic::new(ZAdic::new_approx(5, 2, vec![0, 3]), -4).certainty());
/// assert_eq!(Valuation::PosInf, QAdic::new(UAdic::new(5, vec![0, 3, 1, 2]), -2).certainty());
/// ```
fn certainty(&self) -> Valuation<Self::DigitIndex>;
/// The number is completely uncertain, has no known digits
///
/// ```
/// # use adic::{traits::{AdicPrimitive, HasApproximateDigits}, QAdic, ZAdic};
/// assert!(!ZAdic::new_approx(5, 6, vec![0, 3, 1, 2]).has_no_certainty());
/// assert!(!ZAdic::new_approx(5, 1, vec![3]).has_no_certainty());
/// assert!(ZAdic::empty(5).has_no_certainty());
/// assert!(!QAdic::new(ZAdic::new_approx(5, 6, vec![0, 3, 1, 2]), -2).has_no_certainty());
/// assert!(!QAdic::new(ZAdic::new_approx(5, 1, vec![3]), -2).has_no_certainty());
/// assert!(QAdic::new(ZAdic::empty(5), -2).has_no_certainty());
/// assert!(!QAdic::new(ZAdic::zero(5), 0).has_no_certainty());
/// ```
fn has_no_certainty(&self) -> bool {
if let (Valuation::Finite(v), Valuation::Finite(c)) = (self.min_index(), self.certainty()) {
v >= c
} else {
false
}
}
/// The number is completely certain, has no unknown digits
///
/// ```
/// # use adic::{traits::HasApproximateDigits, UAdic, QAdic, ZAdic};
/// assert!(UAdic::new(5, vec![2, 3, 1, 2, 3, 1]).is_certain());
/// assert!(!ZAdic::new_approx(5, 6, vec![2, 3, 1, 2, 3, 1]).is_certain());
/// assert!(QAdic::new(UAdic::new(5, vec![2, 3, 1, 2, 3, 1]), -2).is_certain());
/// assert!(!QAdic::new(ZAdic::new_approx(5, 6, vec![2, 3, 1, 2, 3, 1]), -2).is_certain());
/// ```
fn is_certain(&self) -> bool {
matches!(self.certainty(), Valuation::PosInf)
}
/// The digital distance between minimum index and maximum (certainty).
///
/// Returns a [`Valuation`].
/// Returns `Finite(0)` for zero (i.e. for `infinity-infinity`).
///
/// ```
/// # use adic::{normed::Valuation, traits::HasApproximateDigits, QAdic, UAdic, ZAdic};
/// assert_eq!(Valuation::PosInf, UAdic::new(5, vec![1]).significance());
/// assert_eq!(Valuation::PosInf, UAdic::new(5, vec![0, 0, 1]).significance());
/// assert_eq!(Valuation::Finite(0), UAdic::new(5, vec![0]).significance());
/// assert_eq!(Valuation::Finite(4), ZAdic::new_approx(5, 4, vec![1, 0, 0, 0]).significance());
/// assert_eq!(Valuation::Finite(2), ZAdic::new_approx(5, 4, vec![0, 0, 1, 0]).significance());
/// assert_eq!(Valuation::Finite(0), ZAdic::new_approx(5, 4, vec![0, 0, 0, 0]).significance());
/// assert_eq!(Valuation::PosInf, QAdic::new(UAdic::new(5, vec![0, 0, 1]), -1).significance());
/// assert_eq!(Valuation::Finite(4), QAdic::new(ZAdic::new_approx(5, 4, vec![1, 0, 0, 0]), -8).significance());
/// assert_eq!(Valuation::Finite(2), QAdic::new(ZAdic::new_approx(5, 4, vec![0, 0, 1, 0]), 4).significance());
/// assert_eq!(Valuation::Finite(0), QAdic::new(ZAdic::new_approx(5, 4, vec![0, 0, 0, 0]), 4).significance());
/// ```
fn significance(&self) -> Valuation<Self::ValuationRing>
where
Self: UltraNormed<ValuationRing = Self::DigitIndex>,
Self::ValuationRing: std::ops::Sub<Output=Self::ValuationRing> {
match (self.certainty(), self.valuation()) {
(_, Valuation::PosInf) => Valuation::zero(),
(Valuation::PosInf, Valuation::Finite(_)) => Valuation::PosInf,
(Valuation::Finite(c), Valuation::Finite(v)) => {
let s = (c - v);
Valuation::Finite(s)
},
}
}
}