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use crate::simd::*;
use std::{
error::Error,
fmt,
hash::{Hash, Hasher},
result,
};
#[derive(Clone, Copy, Debug, Eq, PartialEq)]
pub enum IntervalErrorKind {
PossiblyUndefinedOperation,
UndefinedOperation,
}
#[derive(Clone, Debug, Eq, PartialEq)]
pub struct IntervalError {
pub(crate) kind: IntervalErrorKind,
}
impl IntervalError {
/// Returns the type of the error.
pub fn kind(&self) -> IntervalErrorKind {
self.kind
}
}
impl fmt::Display for IntervalError {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
match self.kind {
IntervalErrorKind::PossiblyUndefinedOperation => {
write!(f, "possibly undefined operation")
}
IntervalErrorKind::UndefinedOperation => write!(f, "undefined operation"),
}
}
}
impl Error for IntervalError {}
/// An alias for [`Result<T, E>`](`result::Result`) with [`E = IntervalError`](`IntervalError`).
pub type Result<T> = result::Result<T, IntervalError>;
/// An interval with [`f64`] bounds.
///
/// It is sometimes referred to as a *bare* interval in contrast to a decorated interval ([`DecInterval`]).
#[derive(Clone, Copy, Debug)]
#[repr(C)]
pub struct Interval {
// An interval is stored in a SIMD vector in the neginf-sup-nan form:
//
// - An nonempty interval [a, b] is stored as [-a; b].
// - An empty interval is stored as [NaN; NaN].
//
// Elements of SIMD vectors are separated by a semicolon to distinguish from interval bounds.
//
// Representations of zeros and NaNs are arbitrary; a zero can be either +0.0 or -0.0,
// and a NaN can be either a qNaN or a sNaN with an arbitrary payload.
//
// In Debug formatting, the value of `rep` is printed as either
// `__m128d(-a, b)` (on x86-64) or `float64x2_t(-a, b)` (on AArch64).
pub(crate) rep: F64X2,
}
unsafe impl Send for Interval {}
unsafe impl Sync for Interval {}
impl Unpin for Interval {}
impl Interval {
pub(crate) fn inf_raw(self) -> f64 {
-extract0(self.rep)
}
pub(crate) fn sup_raw(self) -> f64 {
extract1(self.rep)
}
pub(crate) fn with_infsup_raw(a: f64, b: f64) -> Self {
Self {
rep: constant(-a, b),
}
}
pub(crate) fn zero() -> Self {
Self { rep: splat(0.0) }
}
}
impl PartialEq for Interval {
fn eq(&self, rhs: &Self) -> bool {
self.both_empty(*rhs) | all(eq(self.rep, rhs.rep))
}
}
impl Eq for Interval {}
impl Hash for Interval {
fn hash<H: Hasher>(&self, state: &mut H) {
self.inf().to_bits().hash(state);
self.sup().to_bits().hash(state);
}
}
impl TryFrom<(f64, f64)> for Interval {
type Error = IntervalError;
fn try_from((a, b): (f64, f64)) -> Result<Self> {
if a <= b && a != f64::INFINITY && b != f64::NEG_INFINITY {
Ok(Self::with_infsup_raw(a, b))
} else {
Err(Self::Error {
kind: IntervalErrorKind::UndefinedOperation,
})
}
}
}
/// The decoration of a [`DecInterval`].
#[derive(Clone, Copy, Debug, Eq, Hash, Ord, PartialEq, PartialOrd)]
#[repr(u8)]
pub enum Decoration {
/// The βill-formedβ decoration.
Ill = 0,
/// The βtrivialβ decoration.
Trv = 4,
/// The βdefinedβ decoration.
Def = 8,
/// The βdefined and continuousβ decoration.
Dac = 12,
/// The βcommonβ decoration.
Com = 16,
}
/// The decorated version of [`Interval`].
///
/// ## Notes on equality comparison
///
/// By definition, a NaI is *not* equal to itself:
///
/// ```
/// use inari::*;
/// assert_ne!(DecInterval::NAI, DecInterval::NAI);
/// ```
///
/// For this reason, the traits [`Eq`] and [`Hash`] are not implemented for the type.
#[derive(Clone, Copy, Debug)]
#[repr(C)]
pub struct DecInterval {
pub(crate) x: Interval,
pub(crate) d: Decoration,
}
unsafe impl Send for DecInterval {}
unsafe impl Sync for DecInterval {}
impl Unpin for DecInterval {}
impl DecInterval {
/// Creates a [`DecInterval`] from the given interval and the decoration below:
///
/// | Interval | Decoration |
/// | -------------------- | ------------------- |
/// | Nonempty and bounded | [`Decoration::Com`] |
/// | Unbounded | [`Decoration::Dac`] |
/// | Empty | [`Decoration::Trv`] |
pub fn new(x: Interval) -> Self {
use Decoration::*;
let d = if x.is_empty() {
Trv
} else if !x.is_common_interval() {
Dac
} else {
Com
};
Self::new_unchecked(x, d)
}
/// Creates a [`DecInterval`] from the given interval and decoration.
/// If the decoration is invalid for the interval, the first one in the list is used:
///
/// | Interval | Valid decorations |
/// | -------------------- | ------------------------------------------------------------------------------------------------------- |
/// | Nonempty and bounded | [`Decoration::Com`], [`Decoration::Dac`], [`Decoration::Def`], [`Decoration::Trv`], [`Decoration::Ill`] |
/// | Unbounded | [`Decoration::Dac`], [`Decoration::Def`], [`Decoration::Trv`], [`Decoration::Ill`] |
/// | Empty | [`Decoration::Trv`], [`Decoration::Ill`] |
pub fn set_dec(x: Interval, d: Decoration) -> Self {
use Decoration::*;
if d == Ill {
Self::NAI
} else if x.is_empty() {
Self::EMPTY
} else if d == Com && !x.is_common_interval() {
Self::new_unchecked(x, Dac)
} else {
Self::new_unchecked(x, d)
}
}
/// Returns the interval part of `self` if it is not NaI; otherwise, [`None`].
pub fn interval(self) -> Option<Interval> {
if self.is_nai() {
return None;
}
Some(self.x)
}
/// Returns the decoration part `self`.
pub fn decoration(self) -> Decoration {
self.d
}
pub(crate) const fn new_unchecked(x: Interval, d: Decoration) -> Self {
Self { x, d }
}
}
impl PartialEq for DecInterval {
fn eq(&self, rhs: &Self) -> bool {
if self.is_nai() || rhs.is_nai() {
return false;
}
self.x == rhs.x
}
}
impl TryFrom<(f64, f64)> for DecInterval {
type Error = IntervalError;
fn try_from(x: (f64, f64)) -> Result<Self> {
match Interval::try_from(x) {
Ok(x) => Ok(Self::new(x)),
_ => Err(Self::Error {
kind: IntervalErrorKind::UndefinedOperation,
}),
}
}
}
#[doc(hidden)]
#[macro_export]
macro_rules! _interval {
($a:expr, $b:expr) => {{
use ::std::{convert::TryFrom, primitive::*};
fn is_f64(_: f64) {}
is_f64($a);
is_f64($b);
$crate::Interval::try_from(($a, $b))
}};
}
#[cfg(not(feature = "gmp"))]
#[macro_export]
macro_rules! interval {
($a:expr, $b:expr) => {
$crate::_interval!($a, $b)
};
}
/// Creates an [`Interval`] from [`f64`] bounds or from a bare interval literal.
///
/// There are two variants of the macro:
///
/// - `interval!(a, b)`
///
/// Creates an interval $\[a, b\]$.
/// The condition $a β€ b β§ a < +β β§ b > -β$ must be held.
///
/// `a` and `b` must be [`f64`] values.
///
/// - `interval!(s)`
///
/// Creates an interval from a bare interval literal. `s` must be a string slice ([`&str`]).
///
/// The result is a [`Result<Interval>`].
///
/// If the construction is invalid,
/// an [`Err`] value with [`IntervalErrorKind::UndefinedOperation`] is returned.
/// If it fails to determine whether the construction is valid or not,
/// [`IntervalErrorKind::PossiblyUndefinedOperation`] is returned.
///
/// For creating a constant, the macro [`const_interval!`] should be preferred over this one.
///
/// [`const_interval!`]: crate::const_interval
#[cfg(feature = "gmp")]
#[macro_export]
macro_rules! interval {
($s:expr) => {{
use ::std::primitive::*;
fn is_str(_: &str) {}
is_str($s);
$s.parse::<$crate::Interval>()
}};
($a:expr, $b:expr) => {
$crate::_interval!($a, $b)
};
}
/// Creates an [`Interval`] from a bare interval literal, only if the conversion is exact.
///
/// `s` must be a string slice ([`&str`]). THe result is a [`Result<Interval>`].
///
/// If the construction is invalid or inexact,
/// an [`Err`] value with [`IntervalErrorKind::UndefinedOperation`] is returned.
/// If it fails to determine whether the construction is valid or not,
/// [`IntervalErrorKind::PossiblyUndefinedOperation`] is returned.
///
/// Bare interval literals obtained by `format!("{:x}", x)` should always be converted back.
///
/// ## Examples
///
/// ### Exact construction
///
/// ```
/// use inari::*;
/// assert_eq!(interval_exact!("[1.25]"), Ok(const_interval!(1.25, 1.25)));
/// ```
///
/// ```
/// use inari::*;
/// let s = format!("{:x}", Interval::PI);
/// assert_eq!(s, "[0x3.243f6a8885a3p+0,0x3.243f6a8885a32p+0]");
/// assert_eq!(interval_exact!(&s), Ok(Interval::PI));
/// ```
///
/// ### Inexact construction
///
/// ```
/// use inari::*;
/// let result = interval_exact!("[0.1]");
/// assert!(result.is_err());
/// assert_eq!(result.unwrap_err().kind(), IntervalErrorKind::UndefinedOperation);
/// ```
#[cfg(feature = "gmp")]
#[macro_export]
macro_rules! interval_exact {
($s:expr) => {{
use ::std::primitive::*;
fn is_str(_: &str) {}
is_str($s);
$crate::Interval::_try_from_str_exact($s)
}};
}
#[doc(hidden)]
#[macro_export]
macro_rules! _dec_interval {
($a:expr, $b:expr) => {{
use ::std::{convert::TryFrom, primitive::*};
fn is_f64(_: f64) {}
is_f64($a);
is_f64($b);
$crate::DecInterval::try_from(($a, $b))
}};
}
#[cfg(not(feature = "gmp"))]
#[macro_export]
macro_rules! dec_interval {
($a:expr, $b:expr) => {
$crate::_dec_interval!($a, $b)
};
}
/// Creates a [`DecInterval`] from [`f64`] bounds or from a decorated interval literal.
///
/// There are two variants of the macro:
///
/// - `dec_interval!(a, b)`
///
/// Creates a decorated interval $\[a, b\]$ with the strongest decoration.
/// The condition $a β€ b β§ a < +β β§ b > -β$ must be held.
///
/// `a` and `b` must be [`f64`] values.
///
/// - `dec_interval!(s)`
///
/// Creates a decorated interval from a decorated interval literal.
/// `s` must be a string slice ([`&str`]).
///
/// The result is a [`Result<DecInterval>`].
///
/// If the construction is invalid,
/// an [`Err`] value with [`IntervalErrorKind::UndefinedOperation`] is returned.
/// If it fails to determine whether the construction is valid or not,
/// [`IntervalErrorKind::PossiblyUndefinedOperation`] is returned.
///
/// For creating a constant, the macro [`const_dec_interval!`] should be preferred over this one.
///
/// [`const_dec_interval!`]: crate::const_dec_interval
#[cfg(feature = "gmp")]
#[macro_export]
macro_rules! dec_interval {
($s:expr) => {{
use ::std::primitive::*;
fn is_str(_: &str) {}
is_str($s);
$s.parse::<$crate::DecInterval>()
}};
($a:expr, $b:expr) => {
$crate::_dec_interval!($a, $b)
};
}
/// Creates an [`Interval`] from [`f64`] bounds.
///
/// `a` and `b` must be constant `f64` values. The result is an [`Interval`].
///
/// The macro can be used in [constant expressions](https://doc.rust-lang.org/reference/const_eval.html#constant-expressions).
///
/// The usage is almost the same as the macro [`interval!(a, b)`](`interval!`)
/// except that this macro returns an [`Interval`] directly,
/// or results in a compilation error if the construction is invalid.
#[macro_export]
macro_rules! const_interval {
($a:expr, $b:expr) => {{
use ::std::{mem::transmute, primitive::*};
const _: () = assert!($a <= $b && $a != f64::INFINITY && $b != f64::NEG_INFINITY);
#[allow(unused_unsafe)]
unsafe {
// Parentheses are used to avoid `clippy::double_neg`.
transmute::<[f64; 2], $crate::Interval>([-($a), $b])
}
}};
}
/// Creates a [`DecInterval`] from [`f64`] bounds.
///
/// `a` and `b` must be constant `f64` values. The result is a [`DecInterval`].
///
/// The macro can be used in [constant expressions](https://doc.rust-lang.org/reference/const_eval.html#constant-expressions).
///
/// The usage is almost the same as the macro [`dec_interval!(a, b)`](`dec_interval!`)
/// except that this macro returns a [`DecInterval`] directly,
/// or results in a compilation error if the construction is invalid.
#[macro_export]
macro_rules! const_dec_interval {
($a:expr, $b:expr) => {{
use ::std::{mem::transmute, primitive::*};
#[repr(C)]
struct _DecInterval {
x: $crate::Interval,
d: $crate::Decoration,
}
#[allow(unused_unsafe)]
unsafe {
transmute::<_DecInterval, $crate::DecInterval>(_DecInterval {
x: $crate::const_interval!($a, $b),
d: if $a == f64::NEG_INFINITY || $b == f64::INFINITY {
$crate::Decoration::Dac
} else {
$crate::Decoration::Com
},
})
}
}};
}
#[cfg(test)]
mod tests {
use crate::*;
#[test]
fn decoration_order() {
use Decoration::*;
assert!(Ill < Trv);
assert!(Trv < Def);
assert!(Def < Dac);
assert!(Dac < Com);
}
#[test]
fn macros() {
// Check that these macros are usable for constants.
const _I: Interval = const_interval!(1.0, 2.0);
const _DI: DecInterval = const_dec_interval!(1.0, 2.0);
// Check that type inference works.
let _i = const_interval!(1.0, 2.0);
let _di = const_dec_interval!(1.0, 2.0);
assert_eq!(interval!(1.0, 1.0).unwrap(), const_interval!(1.0, 1.0));
assert_eq!(interval!(1.0, 2.0).unwrap(), const_interval!(1.0, 2.0));
assert_eq!(
interval!(f64::NEG_INFINITY, 1.0).unwrap(),
const_interval!(f64::NEG_INFINITY, 1.0)
);
assert_eq!(
interval!(1.0, f64::INFINITY).unwrap(),
const_interval!(1.0, f64::INFINITY)
);
assert_eq!(
dec_interval!(1.0, 1.0).unwrap(),
const_dec_interval!(1.0, 1.0)
);
assert_eq!(
dec_interval!(1.0, 2.0).unwrap(),
const_dec_interval!(1.0, 2.0)
);
assert_eq!(
dec_interval!(f64::NEG_INFINITY, 1.0).unwrap(),
const_dec_interval!(f64::NEG_INFINITY, 1.0)
);
assert_eq!(
dec_interval!(1.0, f64::INFINITY).unwrap(),
const_dec_interval!(1.0, f64::INFINITY)
);
}
}