devela/num/int/wrapper/impl_root.rs
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// devela::num::int::wrapper::impl_root
//
//! Implements root related methods for [`Int`].
//
// TOC
// - signed|unsigned:
// - is_square
// - sqrt_ceil
// - sqrt_floor
// - sqrt_round
// - is_power TODO
// - root_ceil
// - root_floor
// - root_round TODO
use super::super::shared_docs::*;
#[cfg(any(feature = "_int_isize", feature = "_int_usize"))]
use crate::isize_up;
#[cfg(feature = "_int_usize")]
use crate::usize_up;
#[allow(unused_imports, reason = "various reasons")]
use crate::NumError::{self, NonNegativeRequired, NonZeroRequired, Overflow};
use crate::{iif, num::upcasted_op, paste, Int, NumResult as Result};
// helper function to be called from the cold path branch when nth == 0 in root_*.
#[cold] #[inline(never)] #[rustfmt::skip] #[cfg(_int··)]
const fn cold_err_zero<T>() -> Result<T> { Err(NonZeroRequired) }
// helper function to be called from the cold path branches with an ok result.
#[cold] #[inline(never)] #[rustfmt::skip] #[cfg(_int··)]
const fn cold_ok_int<T>(t: T) -> Result<T> { Ok(t) }
/// Implements root related methods for [`Int`].
///
/// # Args
/// $t: the input/output type. E.g. i8.
/// $up: the upcasted input/output type. E.g. i16.
/// $cap: the capability feature that enables the given implementation. E.g "_int_i8".
/// $cmp: the feature that enables the given implementation. E.g "_cmp_i8".
///
/// $d: the doclink suffix for the method name
macro_rules! impl_root {
() => {
impl_root![signed
i8 |i16 :"_int_i8" :"_cmp_i8" |"",
i16 |i32 :"_int_i16" :"_cmp_i16" |"-1",
i32 |i64 :"_int_i32" :"_cmp_i32" |"-2",
i64 |i128 :"_int_i64" :"_cmp_i64" |"-3",
i128 |i128 :"_int_i128" :"_cmp_i128" |"-4",
isize |isize_up :"_int_isize" :"_cmp_isize" |"-5"
];
impl_root![unsigned
u8 |u16 :"_int_u8" :"_cmp_u8" |"-6",
u16 |u32 :"_int_u16" :"_cmp_u16" | "-7",
u32 |u64 :"_int_u32" :"_cmp_u32" | "-8",
u64 |u128 :"_int_u64" :"_cmp_u64" | "-9",
u128 |u128 :"_int_u128" :"_cmp_u128" | "-10",
usize |usize_up :"_int_usize" /*_cmp_usize*/ | "-11" // always available
];
};
(signed $( $t:ty | $up:ty : $cap:literal $(: $cmp:literal)? | $d:literal ),+) => {
$( impl_root![@signed $t|$up:$cap $(:$cmp)? | $d]; )+
};
(unsigned $( $t:ty | $up:ty : $cap:literal $(: $cmp:literal)? | $d:literal ),+) => {
$( impl_root![@unsigned $t|$up:$cap $(:$cmp)? | $d]; )+
};
(
// implements signed ops
@signed $t:ty | $up:ty : $cap:literal $(: $cmp:literal)? | $d:literal) => { paste! {
/* sqrt (signed) */
#[doc = crate::doc_availability!(feature = $cap)]
///
#[doc = "# Integer root related methods for `" $t "`\n\n"]
#[doc = "- [is_square](#method.is_square" $d ")"]
#[doc = "- [sqrt_ceil](#method.sqrt_ceil" $d ")"]
#[doc = "- [sqrt_floor](#method.sqrt_floor" $d ")"]
#[doc = "- [sqrt_round](#method.sqrt_round" $d ")"]
#[doc = "- [root_ceil](#method.root_ceil" $d ")"]
#[doc = "- [root_floor](#method.root_floor" $d ")"]
#[cfg(feature = $cap )]
impl Int<$t> {
/// Returns `true` if it's a perfect square.
///
/// Returns `false` otherwise, which includes all negative values.
#[doc = FORMULA_IS_SQUARE!()]
/// # Examples
/// ```
/// # use devela::Int;
#[doc="assert_eq![Int(12_" $t ").is_square(), false];"]
#[doc="assert_eq![Int(13_" $t ").is_square(), false];"]
#[doc="assert_eq![Int(16_" $t ").is_square(), true];"]
#[doc="assert_eq![Int(20_" $t ").is_square(), false];"]
#[doc="assert_eq![Int(21_" $t ").is_square(), false];"]
#[doc="assert_eq![Int(-16_" $t ").is_square(), false];"]
/// ```
$(
/// # Features
#[doc = "This will only be *const* if the " $cmp " feature is enabled."]
#[cfg(feature = $cmp)]
)? // $cmp
#[must_use]
pub const fn is_square(self) -> bool {
let a = self.0;
iif![let Ok(sqrt) = self.sqrt_floor(); sqrt.0 * sqrt.0 == a; false]
}
$( // $cmp
#[cfg(not(feature = $cmp))] #[allow(missing_docs)]
pub fn is_square(self) -> bool {
let a = self.0;
iif![let Ok(sqrt) = self.sqrt_floor(); sqrt.0 * sqrt.0 == a; false]
}
)?
/// Returns the ceiled integer square root.
/// # Errors
/// Returns [`NonNegativeRequired`] if `self` is negative.
/// # Formulation
#[doc = ALGORITHM_SQRT_CEIL!()]
/// # Examples
/// ```
/// # use devela::{Int, NumError::NonNegativeRequired};
#[doc="assert_eq![Int(12_" $t ").sqrt_ceil(), Ok(Int(4))];"]
#[doc="assert_eq![Int(13_" $t ").sqrt_ceil(), Ok(Int(4))];"]
#[doc="assert_eq![Int(16_" $t ").sqrt_ceil(), Ok(Int(4))];"]
#[doc="assert_eq![Int(20_" $t ").sqrt_ceil(), Ok(Int(5))];"]
#[doc="assert_eq![Int(21_" $t ").sqrt_ceil(), Ok(Int(5))];"]
#[doc="assert_eq![Int(-4_" $t ").sqrt_ceil(), Err(NonNegativeRequired)];"]
/// ```
$(
/// # Features
#[doc = "This will only be *const* if the " $cmp " feature is enabled."]
#[cfg(feature = $cmp)]
)? // $cmp
pub const fn sqrt_ceil(self) -> Result<Int<$t>> {
let a = self.0;
if let Ok(floor) = self.sqrt_floor() {
iif![floor.0 * floor.0 == a; Ok(floor); Ok(Int(floor.0 + 1))]
} else {
Err(NonNegativeRequired)
}
}
$( // $ cmp
#[cfg(not(feature = $cmp))] #[allow(missing_docs)]
pub fn sqrt_ceil(self) -> Result<Int<$t>> {
let a = self.0;
if let Ok(floor) = self.sqrt_floor() {
iif![floor.0 * floor.0 == a; Ok(floor); Ok(Int(floor.0 + 1))]
} else {
Err(NonNegativeRequired)
}
}
)?
/// Returns the floored integer square root.
///
/// # Errors
/// Returns [`NonNegativeRequired`] if `self` is negative.
///
/// # Formulation
#[doc = ALGORITHM_SQRT_FLOOR!()]
/// # Examples
/// ```
/// # use devela::{Int, NumError::NonNegativeRequired};
#[doc="assert_eq![Int(12_" $t ").sqrt_floor(), Ok(Int(3))];"]
#[doc="assert_eq![Int(13_" $t ").sqrt_floor(), Ok(Int(3))];"]
#[doc="assert_eq![Int(16_" $t ").sqrt_floor(), Ok(Int(4))];"]
#[doc="assert_eq![Int(20_" $t ").sqrt_floor(), Ok(Int(4))];"]
#[doc="assert_eq![Int(21_" $t ").sqrt_floor(), Ok(Int(4))];"]
#[doc="assert_eq![Int(-4_" $t ").sqrt_floor(), Err(NonNegativeRequired)];"]
/// ```
$(
/// # Features
#[doc = "This will only be *const* if the " $cmp " feature is enabled."]
#[cfg(feature = $cmp)]
)? // $cmp
pub const fn sqrt_floor(self) -> Result<Int<$t>> {
let a = crate::Compare(self.0).min(<$t>::MAX - 1); // avoid overflow on MAX
if a.is_negative() {
Err(NonNegativeRequired)
} else if a < 2 {
Ok(self)
} else {
let (mut x, mut y) = (a, (a + a / a) / 2);
while y < x {
x = y;
y = (x + a / x) / 2;
}
Ok(Int(x))
}
}
$( // $cmp
#[cfg(not(feature = $cmp))] #[allow(missing_docs)]
pub fn sqrt_floor(self) -> Result<Int<$t>> {
let a = self.0.min(<$t>::MAX - 1); // avoid overflow on MAX
if a.is_negative() {
Err(NonNegativeRequired)
} else if a < 2 {
Ok(self)
} else {
let (mut x, mut y) = (a, (a + a / a) / 2);
while y < x {
x = y;
y = (x + a / x) / 2;
}
Ok(Int(x))
}
}
)?
/// Returns the rounded integer square root.
///
#[doc = "Performs operations internally as [`" $up "`]."]
///
/// # Features
/// Uses `unsafe_hint` for performance optimizations with upcasted arithmetic.
///
/// # Errors
/// Returns [`NonNegativeRequired`] if `self` is negative, or possibly [`Overflow`]
/// if there's no larger type to upcast and the value is close to its maximum.
/// # Formulation
#[doc = ALGORITHM_SQRT_ROUND!()]
/// # Examples
/// ```
/// # use devela::{Int, NumError::NonNegativeRequired};
#[doc="assert_eq![Int(12_" $t ").sqrt_round(), Ok(Int(3))];"]
#[doc="assert_eq![Int(13_" $t ").sqrt_round(), Ok(Int(4))];"]
#[doc="assert_eq![Int(16_" $t ").sqrt_round(), Ok(Int(4))];"]
#[doc="assert_eq![Int(20_" $t ").sqrt_round(), Ok(Int(4))];"]
#[doc="assert_eq![Int(21_" $t ").sqrt_round(), Ok(Int(5))];"]
#[doc="assert_eq![Int(-4_" $t ").sqrt_round(), Err(NonNegativeRequired)];"]
/// ```
pub const fn sqrt_round(self) -> Result<Int<$t>> {
let a = self.0 as $up;
if a.is_negative() {
Err(NonNegativeRequired)
} else if a < 2 {
Ok(self)
} else {
// sqrt_floor
let sum = upcasted_op![add_err(a, a / a) $t => $up];
let (mut x, mut y) = (a, sum / 2);
while y < x {
x = y;
let sum = upcasted_op![add_err(x, a / x) $t => $up];
y = sum / 2;
}
// do we have to round up?
let mul = upcasted_op![mul_err(x, x) $t => $up];
iif![a - mul >= (x + 1) * (x + 1) - a; Ok(Int(x as $t + 1)); Ok(Int(x as $t))]
}
}
/* root (signed) */
/// Returns the ceiled integer `nth` root.
///
#[doc = FORMULA_ROOT_CEIL_SIGNED!()]
///
/// # Errors
/// Returns [`NonZeroRequired`] if `nth` is 0, or
/// [`NonNegativeRequired`] if `self` is negative and `nth` is even.
///
/// # Examples
/// ```
/// # use devela::{Int, NumError::NonNegativeRequired};
#[doc="assert_eq![Int(48_" $t ").root_ceil(4), Ok(Int(3))];"]
#[doc="assert_eq![Int(70_" $t ").root_ceil(4), Ok(Int(3))];"]
#[doc="assert_eq![Int(81_" $t ").root_ceil(4), Ok(Int(3))];"]
#[doc="assert_eq![Int(88_" $t ").root_ceil(4), Ok(Int(4))];"]
#[doc="assert_eq![Int(114_" $t ").root_ceil(4), Ok(Int(4))];"]
#[doc="assert_eq![Int(-81" $t ").root_ceil(4), Err(NonNegativeRequired)];"]
#[doc="assert_eq![Int(" $t "::MAX).root_ceil(1), Ok(Int(" $t "::MAX))];"]
/// ```
/// # Formulation
/// ## Piece-wise
#[doc = PIECEWISE_ROOT_CEIL_SIGNED!()]
/// ## Algorithm
#[doc = ALGORITHM_ROOT_CEIL_SIGNED!()]
pub const fn root_ceil(self, nth: u32) -> Result<Int<$t>> {
if nth == 0 {
cold_err_zero()
} else if nth == 1 {
cold_ok_int(self)
} else if self.0 == 0 {
cold_ok_int(Int(0))
} else if self.0 < 0 && nth % 2 == 0 {
Err(NonNegativeRequired)
} else {
let mut x = 1 as $t;
let positive_base = self.0.abs();
while let Some(val) = x.checked_pow(nth) {
if val > positive_base { break; }
x += 1;
}
let floor_root = x - 1;
let ceil_root = if floor_root.pow(nth) == positive_base {
floor_root
} else {
floor_root + 1
};
Ok(Int(ceil_root * self.0.signum()))
}
}
/// Returns the floored integer `nth` root.
///
#[doc = FORMULA_ROOT_FLOOR_SIGNED!()]
///
/// # Errors
/// Returns [`NonZeroRequired`] if `nth` is 0, or
/// [`NonNegativeRequired`] if `self` is negative and `nth` is even.
///
/// # Examples
/// ```
/// # use devela::{Int, NumError::NonNegativeRequired};
#[doc="assert_eq![Int(48_" $t ").root_floor(4), Ok(Int(2))];"]
#[doc="assert_eq![Int(70_" $t ").root_floor(4), Ok(Int(2))];"]
#[doc="assert_eq![Int(81_" $t ").root_floor(4), Ok(Int(3))];"]
#[doc="assert_eq![Int(88_" $t ").root_floor(4), Ok(Int(3))];"]
#[doc="assert_eq![Int(114_" $t ").root_floor(4), Ok(Int(3))];"]
#[doc="assert_eq![Int(-81_" $t ").root_floor(4), Err(NonNegativeRequired)];"]
#[doc="assert_eq![Int(" $t "::MAX).root_floor(1), Ok(Int(" $t "::MAX))];"]
/// ```
/// # Formulations
/// ## Piece-wise
#[doc = PIECEWISE_ROOT_FLOOR_SIGNED!()]
/// ## Algorithm
#[doc = ALGORITHM_ROOT_FLOOR_SIGNED!()]
pub const fn root_floor(self, nth: u32) -> Result<Int<$t>> {
if nth == 0 {
cold_err_zero()
} else if nth == 1 {
cold_ok_int(self)
} else if self.0 == 0 {
cold_ok_int(Int(0))
} else if self.0 < 0 && nth % 2 == 0 {
Err(NonNegativeRequired)
} else {
let mut x = 1 as $t;
let positive_base = self.0.abs();
while let Some(val) = x.checked_pow(nth) {
if val > positive_base { break; }
x += 1;
}
Ok(Int((x - 1) * self.0.signum()))
}
}
// TODO: root_round
}
}};
(
// implements unsigned ops
@unsigned $t:ty | $up:ty : $cap:literal $(: $cmp:literal)? | $d:literal) => { paste! {
#[doc = crate::doc_availability!(feature = $cap)]
///
#[doc = "# Integer root related methods for `" $t "`\n\n"]
#[doc = "- [is_square](#method.is_square" $d ")"]
#[doc = "- [sqrt_ceil](#method.sqrt_ceil" $d ")"]
#[doc = "- [sqrt_floor](#method.sqrt_floor" $d ")"]
#[doc = "- [sqrt_round](#method.sqrt_round" $d ")"]
#[doc = "- [root_ceil](#method.root_ceil" $d ")"]
#[doc = "- [root_floor](#method.root_floor" $d ")"]
#[cfg(feature = $cap )]
impl Int<$t> {
/* sqrt (unsigned) */
/// Returns `true` if it's a perfect square, false otherwise.
/// # Formulation
#[doc = FORMULA_IS_SQUARE!()]
/// # Examples
/// ```
/// # use devela::Int;
#[doc="assert_eq![Int(12_" $t ").is_square(), false];"]
#[doc="assert_eq![Int(13_" $t ").is_square(), false];"]
#[doc="assert_eq![Int(16_" $t ").is_square(), true];"]
#[doc="assert_eq![Int(20_" $t ").is_square(), false];"]
#[doc="assert_eq![Int(21_" $t ").is_square(), false];"]
/// ```
$(
/// # Features
#[doc = "This will only be *const* if the " $cmp " feature is enabled."]
#[cfg(feature = $cmp)]
)? // $cmp
#[must_use]
pub const fn is_square(self) -> bool {
let a = self.0;
let sqrt = self.sqrt_floor();
sqrt.0 * sqrt.0 == a
}
$( // $cmp
#[cfg(not(feature = $cmp))] #[allow(missing_docs)]
pub fn is_square(self) -> bool {
let a = self.0;
let sqrt = self.sqrt_floor();
sqrt.0 * sqrt.0 == a
}
)?
/// Returns the ceiled integer square root.
///
/// # Formulation
#[doc = ALGORITHM_SQRT_CEIL!()]
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc="assert_eq![Int(12_" $t ").sqrt_ceil(), Int(4)];"]
#[doc="assert_eq![Int(13_" $t ").sqrt_ceil(), Int(4)];"]
#[doc="assert_eq![Int(16_" $t ").sqrt_ceil(), Int(4)];"]
#[doc="assert_eq![Int(20_" $t ").sqrt_ceil(), Int(5)];"]
#[doc="assert_eq![Int(21_" $t ").sqrt_ceil(), Int(5)];"]
/// ```
$(
/// # Features
#[doc = "This will only be *const* if the " $cmp " feature is enabled."]
#[cfg(feature = $cmp)]
)? // $cmp
#[must_use]
pub const fn sqrt_ceil(self) -> Int<$t> {
let a = self.0; let floor = self.sqrt_floor();
iif![floor.0 * floor.0 == a; floor; Int(floor.0 + 1)]
}
$( // $cmp
#[cfg(not(feature = $cmp))] #[allow(missing_docs)]
pub fn sqrt_ceil(self) -> Int<$t> {
let a = self.0; let floor = self.sqrt_floor();
iif![floor.0 * floor.0 == a; floor; Int(floor.0 + 1)]
}
)?
/// Returns the floored integer square root.
///
/// # Formulation
#[doc = ALGORITHM_SQRT_FLOOR!()]
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc="assert_eq![Int(12_" $t ").sqrt_floor(), Int(3)];"]
#[doc="assert_eq![Int(13_" $t ").sqrt_floor(), Int(3)];"]
#[doc="assert_eq![Int(16_" $t ").sqrt_floor(), Int(4)];"]
#[doc="assert_eq![Int(20_" $t ").sqrt_floor(), Int(4)];"]
#[doc="assert_eq![Int(21_" $t ").sqrt_floor(), Int(4)];"]
/// ```
$(
/// # Features
#[doc = "This will only be *const* if the " $cmp " feature is enabled."]
#[cfg(feature = $cmp)]
)? // $cmp
#[must_use]
pub const fn sqrt_floor(self) -> Int<$t> {
let a = crate::Compare(self.0).min(<$t>::MAX - 1); // avoid overflow on MAX
if a < 2 {
self
} else {
let (mut x, mut y) = (a, (a + a / a) / 2);
while y < x {
x = y;
y = (x + a / x) / 2;
}
Int(x)
}
}
$( // $cmp
#[cfg(not(feature = $cmp))] #[allow(missing_docs)]
pub fn sqrt_floor(self) -> Int<$t> {
let a = self.0.min(<$t>::MAX - 1); // avoid overflow on MAX
if a < 2 {
self
} else {
let (mut x, mut y) = (a, (a + a / a) / 2);
while y < x {
x = y;
y = (x + a / x) / 2;
}
Int(x)
}
}
)?
/// Returns the rounded integer square root.
///
#[doc = "Performs operations internally as [`" $up "`]."]
///
/// # Features
/// Uses `unsafe_hint` for performance optimizations with upcasted arithmetic.
///
/// # Errors
/// Can returns [`Overflow`] if there's no larger type to upcast and the value
/// is close to its maximum.
///
/// # Formulation
#[doc = ALGORITHM_SQRT_ROUND!()]
/// # Examples
/// ```
/// # use devela::Int;
#[doc="assert_eq![Int(12_" $t ").sqrt_round(), Ok(Int(3))];"]
#[doc="assert_eq![Int(13_" $t ").sqrt_round(), Ok(Int(4))];"]
#[doc="assert_eq![Int(16_" $t ").sqrt_round(), Ok(Int(4))];"]
#[doc="assert_eq![Int(20_" $t ").sqrt_round(), Ok(Int(4))];"]
#[doc="assert_eq![Int(21_" $t ").sqrt_round(), Ok(Int(5))];"]
/// ```
pub const fn sqrt_round(self) -> Result<Int<$t>> {
let a = self.0 as $up;
if a < 2 {
Ok(self)
} else {
// sqrt_floor
let sum = upcasted_op![add_err(a, a / a) $t => $up];
let (mut x, mut y) = (a, sum / 2);
while y < x {
x = y;
let sum = upcasted_op![add_err(x, a / x) $t => $up];
y = sum / 2;
}
// do we have to round up?
let mul = upcasted_op![mul_err(x, x) $t => $up];
iif![a - mul >= (x + 1) * (x + 1) - a; Ok(Int(x as $t + 1)); Ok(Int(x as $t))]
}
}
/* root (unsigned) */
/// Returns the ceiled integer `nth` root.
///
#[doc = FORMULA_ROOT_CEIL_UNSIGNED!()]
///
/// # Errors
/// Returns [`NonZeroRequired`] if `nth` is 0.
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc="assert_eq![Int(48_" $t ").root_ceil(4), Ok(Int(3))];"]
#[doc="assert_eq![Int(70_" $t ").root_ceil(4), Ok(Int(3))];"]
#[doc="assert_eq![Int(81_" $t ").root_ceil(4), Ok(Int(3))];"]
#[doc="assert_eq![Int(88_" $t ").root_ceil(4), Ok(Int(4))];"]
#[doc="assert_eq![Int(114_" $t ").root_ceil(4), Ok(Int(4))];"]
#[doc="assert_eq![Int(" $t "::MAX).root_ceil(1), Ok(Int(" $t "::MAX))];"]
/// ```
/// # Formulation
/// ## Piece-wise
#[doc = PIECEWISE_ROOT_CEIL_UNSIGNED!()]
/// ## Algorithm
#[doc = ALGORITHM_ROOT_CEIL_UNSIGNED!()]
pub const fn root_ceil(self, nth: u32) -> Result<Int<$t>> {
match self.root_floor(nth) {
Ok(floor_root) => {
if floor_root.0.pow(nth) == self.0 {
Ok(floor_root)
} else {
Ok(Int(floor_root.0 + 1))
}
},
Err(e) => Err(e),
}
}
/// Returns the floored integer `nth` root.
///
#[doc = FORMULA_ROOT_FLOOR_UNSIGNED!()]
///
/// # Errors
/// Returns [`NonZeroRequired`] if `nth` is 0.
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc="assert_eq![Int(48_" $t ").root_floor(4), Ok(Int(2))];"]
#[doc="assert_eq![Int(70_" $t ").root_floor(4), Ok(Int(2))];"]
#[doc="assert_eq![Int(81_" $t ").root_floor(4), Ok(Int(3))];"]
#[doc="assert_eq![Int(88_" $t ").root_floor(4), Ok(Int(3))];"]
#[doc="assert_eq![Int(114_" $t ").root_floor(4), Ok(Int(3))];"]
#[doc="assert_eq![Int(" $t "::MAX).root_floor(1), Ok(Int(" $t "::MAX))];"]
/// ```
/// # Formulations
/// ## Piece-wise
#[doc = PIECEWISE_ROOT_FLOOR_UNSIGNED!()]
/// ## Algorithm
#[doc = ALGORITHM_ROOT_FLOOR_UNSIGNED!()]
pub const fn root_floor(self, nth: u32) -> Result<Int<$t>> {
if nth == 0 {
cold_err_zero()
} else if nth == 1 {
cold_ok_int(self)
} else if self.0 == 0 {
cold_ok_int(Int(0))
} else {
let mut x = 1 as $t;
while let Some(val) = x.checked_pow(nth) {
iif![val > self.0; break];
x += 1;
}
Ok(Int(x - 1))
}
}
// TODO: root_round
}
}};
}
impl_root!();