devela/num/int/wrapper/impl_core.rs
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// devela::num::int::wrapper::impl_core
//
//! Implements core methods for [`Int`].
//
// TOC
// - signed|unsigned
// - abs
// - is_even
// - is_odd
// - gcd
// - gcd_ext
// - gcd_ext_euc
// - lcm
// - scale
// - scale_wrap
// - midpoint
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;
#[cfg(feature = "cast")]
use crate::Cast;
#[allow(unused_imports)]
use crate::{cswap, iif, paste, unwrap, GcdReturn, Int, NumError::Overflow, NumResult as Result};
/// Implements core methods for [`Int`].
///
/// # Args
/// $t: the input/output type
/// $cap: the capability feature enabling the given implementation. E.g "_int_u8"
///
/// $ut: the unsigned type of the same size as $t (only for signed)
/// $ucap: the feature enabling some methods related to `$ut` (signed midpoint)
///
/// $up: the upcasted type to do the operations on (for lcm). E.g u8
///
/// $iup: the signed upcasted type for some methods (gcd_ext). E.g. i16 (only for unsigned)
/// $icap: the feature enabling some methods related to `$iup`. E.g "_int_i16" (only for unsigned)
///
/// $d: the doclink suffix for the method name
macro_rules! impl_core {
() => {
impl_core![signed
// $t :$cap :$ut :$ucap |$up |$d
i8 :"_int_i8" :u8 :"_int_u8" |i16 |"",
i16 :"_int_i16" :u16 :"_int_u16" |i32 |"-1",
i32 :"_int_i32" :u32 :"_int_u32" |i64 |"-2",
i64 :"_int_i64" :u64 :"_int_u64" |i128 |"-3",
i128 :"_int_i128" :u128 :"_int_u128" |i128 |"-4",
isize :"_int_isize" :usize :"_int_usize" |isize_up |"-5"
];
impl_core![unsigned
// $t :$cap :$up |$iup :$iucap |$d
u8 :"_int_u8" :u16 |i16 :"_int_i16" |"-6",
u16 :"_int_u16" :u32 |i32 :"_int_i32" |"-7",
u32 :"_int_u32" :u64 |i64 :"_int_i64" |"-8",
u64 :"_int_u64" :u128 |i128 :"_int_i128" |"-9",
u128 :"_int_u128" :u128 |i128 :"_int_i128" |"-10"
//usize :"_int_usize" :usize_up |isize_up :"_int_isize_up" |"-11"]; // MAYBE
];
#[cfg(target_pointer_width = "32")]
impl_core![unsigned usize :"_int_usize" :usize_up |isize_up :"_int_i64" |"-11"];
#[cfg(target_pointer_width = "64")]
impl_core![unsigned usize :"_int_usize" :usize_up |isize_up :"_int_i128" |"-11"];
};
(signed $( $t:ty : $cap:literal : $ut:ty : $ucap:literal | $up:ty |$d:literal ),+) => {
$( impl_core![@signed $t :$cap :$ut :$ucap :$up |$d]; )+
};
(unsigned $( $t:ty : $cap:literal : $up:ty | $iup:ty : $icap:literal |$d:literal ),+) => {
$( impl_core![@unsigned $t :$cap :$up |$iup :$icap |$d]; )+
};
(
// implements signed ops
@signed $t:ty : $cap:literal : $ut:ty : $ucap:literal : $up:ty |$d:literal) => { paste! {
#[doc = crate::doc_availability!(feature = $cap)]
///
#[doc = "# Integer core methods for `" $t "`\n\n"]
#[doc = "- [abs](#method.abs" $d ")"]
#[doc = "- [is_even](#method.is_even" $d ")"]
#[doc = "- [is_odd](#method.is_odd" $d ")"]
#[doc = "- [gcd](#method.gcd" $d ")"]
#[doc = "- [gcd_ext](#method.gcd_ext" $d ")"]
#[doc = "- [gcd_ext_euc](#method.gcd_ext_euc" $d ")"]
#[doc = "- [lcm](#method.lcm" $d ")"]
#[doc = "- [scale](#method.scale" $d ")"]
#[doc = "- [scale_wrap](#method.scale_wrap" $d ")"]
#[doc = "- [midpoint](#method.midpoint" $d ")"]
///
#[cfg(feature = $cap )]
impl Int<$t> {
/// Returns the absolute value of `self`.
#[must_use]
pub const fn abs(self) -> Int<$t> { Int(self.0.abs()) }
/// Returns `true` if `self` is an even number.
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc = "assert![Int(2_" $t ").is_even()];"]
#[doc = "assert![Int(-2_" $t ").is_even()];"]
#[doc = "assert![!Int(3_" $t ").is_even()];"]
#[doc = "assert![Int(0_" $t ").is_even()];"]
/// ```
#[must_use]
pub const fn is_even(self) -> bool { self.0 & 1 == 0 }
/// Returns `true` if `self` is an odd number.
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc = "assert![Int(3_" $t ").is_odd()];"]
#[doc = "assert![Int(-3_" $t ").is_odd()];"]
#[doc = "assert![!Int(2_" $t ").is_odd()];"]
#[doc = "assert![!Int(0_" $t ").is_odd()];"]
/// ```
#[must_use]
pub const fn is_odd(self) -> bool { self.0 & 1 == 1 }
/* signed gcd, lcm */
/// Returns the <abbr title="Greatest Common Divisor">GCD</abbr>.
///
/// Uses Stein's algorithm which is much more efficient to compute than Euclid's.
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc = "assert_eq![Int(4), Int(64_" $t ").gcd(36)];"]
#[doc = "assert_eq![Int(4), Int(-64_" $t ").gcd(36)];"]
#[doc = "assert_eq![Int(4), Int(64_" $t ").gcd(-36)];"]
#[doc = "assert_eq![Int(4), Int(-64_" $t ").gcd(-36)];"]
#[doc = "assert_eq![Int(36), Int(0_" $t ").gcd(36)];"]
#[doc = "assert_eq![Int(64), Int(64_" $t ").gcd(0)];"]
/// ```
#[must_use]
pub const fn gcd(self, b: $t) -> Int<$t> {
let [mut a, mut b] = [self.0.abs(), b.abs()];
iif![a == 0; return Int(b)];
iif![b == 0; return Int(a)];
// Let k be the greatest power of 2 dividing both a and b:
let k = (a | b).trailing_zeros();
// Divide a and b by 2 until they become odd:
a >>= a.trailing_zeros();
b >>= b.trailing_zeros();
// Break when a == GCD of a / 2^k:
while b != 0 {
b >>= b.trailing_zeros();
// ensure b >= a before subtraction:
iif![a > b; cswap![a, b]; b -= a];
}
Int(a << k)
// Euclid's algorithm:
// while a != b { iif![a > b; a -= b; b -= a] }; a
}
/// Returns the <abbr title="Greatest Common Divisor">GCD</abbr>
/// and the Bézout coeficients.
///
/// This version uses the extended Stein's algorithm which is much more
/// efficient to compute than Euclid's. It uses only simple arithmetic
/// operations and works by dividing the inputs by 2 until they are odd,
/// and then subtracting the smaller number from the larger one.
///
/// The Bézout's coefficients are not unique, and different algorithms
/// can yield different coefficients that all satisfy Bézout's identity.
///
/// Bézout's identity states that for any two integers a and b,
/// there exist integers x and y such that $ax + by = gcd(a, b)$.
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc = "let (gcd, x, y) = Int(32_" $t ").gcd_ext(36).as_tuple();"]
/// assert_eq!(gcd.0, 4);
/// assert_eq!(x.0 * 32 + y.0 * 36, gcd.0);
/// ```
pub const fn gcd_ext(self, b: $t) -> GcdReturn<Int<$t>, Int<$t>> {
let [mut a, mut b] = [self.0.abs(), b.abs()];
if a == 0 { return GcdReturn::new(Int(b), Int(0), Int(1)); }
if b == 0 { return GcdReturn::new(Int(a), Int(1), Int(0)); }
let mut k = 0;
while ((a | b) & 1) == 0 {
a >>= 1;
b >>= 1;
k += 1;
}
let (a0, b0, mut sa, mut sb, mut ta, mut tb) = (a, b, 1, 0, 0, 1);
while (a & 1) == 0 {
if (sa & 1) != 0 || (sb & 1) != 0 {
sa -= b0;
sb += a0;
}
a >>= 1;
sa >>= 1;
sb >>= 1;
}
while b != 0 {
while (b & 1) == 0 {
if (ta & 1) != 0 || (tb & 1) != 0 {
ta -= b0;
tb += a0;
}
b >>= 1;
ta >>= 1;
tb >>= 1;
}
if a > b {
cswap![a, b];
cswap![sa, ta];
cswap![sb, tb];
}
b -= a;
ta -= sa;
tb -= sb;
}
GcdReturn::new(Int(a << k), Int(sa), Int(sb))
}
/// Returns the <abbr title="Greatest Common Divisor">GCD</abbr>
/// and the Bézout coeficients.
///
/// This version uses the extended Euclids's algorithm, which uses a
/// series of euclidean divisions and works by subtracting multiples
/// of the smaller number from the larger one.
///
/// The Bézout's coefficients are not unique, and different algorithms
/// can yield different coefficients that all satisfy Bézout's identity.
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc = "let (gcd, x, y) = Int(32_" $t ").gcd_ext_euc(36).as_tuple();"]
/// assert_eq!(gcd.0, 4);
/// assert_eq!(x.0 * 32 + y.0 * 36, gcd.0);
/// ```
pub const fn gcd_ext_euc(self, b: $t) -> GcdReturn<Int<$t>, Int<$t>> {
let a = self.0;
if a == 0 {
GcdReturn::new(Int(b), Int(0), Int(1))
} else {
let (g, x, y) = Int(b % a).gcd_ext_euc(a).as_tuple_copy();
GcdReturn::new(g, Int(y.0 - (b / a) * x.0), x)
}
}
/// Returns the <abbr title="Least Common Multiple">LCM</abbr>.
///
#[doc = "Performs operations internally as [`" $up "`] for the inner operations."]
///
/// # Errors
/// Can [`Overflow`].
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc = "assert_eq![Int(12_" $t ").lcm(15), Ok(Int(60))];"]
#[doc = "assert_eq![Int(-12_" $t ").lcm(15), Ok(Int(60))];"]
#[doc = "assert_eq![Int(12_" $t ").lcm(-15), Ok(Int(60))];"]
/// ```
pub const fn lcm(self, b: $t) -> Result<Int<$t>> {
let (aup, bup) = (self.0 as $up, b as $up);
let res = (aup * bup).abs() / self.gcd(b).0 as $up;
iif![res <= $t::MAX as $up; Ok(Int(res as $t)); Err(Overflow(None))]
}
/// Returns a scaled value between `[min..=max]` to a new range `[a..=b]`.
///
#[doc = "Performs operations internally as [`" $up "`] for the checked operations."]
///
/// If the value lies outside of `[min..=max]` it will result in extrapolation.
///
/// # Errors
/// Can [`Overflow`] for extrapolated values that can't fit the type,
/// and for overflowing arithmetic operations in the following formula:
///
/// # Formula
#[doc = FORMULA_SCALE!()]
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc = "assert_eq![Ok(Int(40)), Int(60_" $t ").scale(0, 120, 30, 50)]; // interpolate"]
#[doc = "assert_eq![Ok(Int(112)), Int(100_" $t ").scale(0, 80, 0, 90)]; // extrapolate"]
/// # #[cfg(feature = "_int_i8")]
/// assert![Int(100_i8).scale(0, 50, 0, 90).is_err()]; // extrapolate and overflow
/// ```
#[cfg(feature = "cast")]
#[cfg_attr(feature = "nightly_doc", doc(cfg(feature = "cast")))]
pub const fn scale(self, min: $t, max: $t, a: $t, b: $t) -> Result<Int<$t>> {
let v = self.0 as $up;
let (min, max, a, b) = (min as $up, max as $up, a as $up, b as $up);
let b_a = iif![let Some(n) = b.checked_sub(a); n; return Err(Overflow(None))];
let v_min = iif![let Some(n) = v.checked_sub(min); n; return Err(Overflow(None))];
let mul = iif![let Some(n) = b_a.checked_mul(v_min); n; return Err(Overflow(None))];
let max_min = iif![let Some(n) = max.checked_sub(min); n; return Err(Overflow(None))];
let div = iif![let Some(n) = mul.checked_div(max_min); n; return Err(Overflow(None))];
let sum = iif![let Some(n) = div.checked_add(a); n; return Err(Overflow(None))];
match Cast(sum).[<checked_cast_to_ $t>]() {
Ok(n) => Ok(Int(n)),
Err(e) => Err(e),
}
}
/// Returns a scaled value between `[min..=max]` to a new range `[a..=b]`.
///
#[doc = "Performs operations internally as [`" $up "`]."]
///
/// If the value lies outside of `[min..=max]` it will result in extrapolation, and
/// if the value doesn't fit in the type it will wrap around its boundaries.
///
/// # Panics
/// Could panic for large values of `i128` or `u128`.
///
/// # Formula
#[doc = FORMULA_SCALE!()]
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc = "assert_eq![Int(40), Int(60_" $t ").scale_wrap(0, 120, 30, 50)]; // interpolate"]
#[doc = "assert_eq![Int(112), Int(100_" $t ").scale_wrap(0, 80, 0, 90)]; // extrapolate"]
/// # #[cfg(feature = "_int_i8")]
/// assert_eq![Int(-76), Int(100_i8).scale_wrap(0, 50, 0, 90)]; // extrapolate and wrap
/// ```
pub const fn scale_wrap(self, min: $t, max: $t, a: $t, b: $t) -> Int<$t> {
let v = self.0 as $up;
let (min, max, a, b) = (min as $up, max as $up, a as $up, b as $up);
Int(((b - a) * (v - min) / (max - min) + a) as $t)
}
// MAYBE: scale_saturate
/// Calculates the middle point of `self` and `other`.
///
/// The result is always rounded towards negative infinity.
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc = concat!("assert_eq![Int(0_", stringify!($t), ").midpoint(4), 2];")]
#[doc = concat!("assert_eq![Int(0_", stringify!($t), ").midpoint(-1), -1];")]
#[doc = concat!("assert_eq![Int(-1_", stringify!($t), ").midpoint(0), -1];")]
/// ```
// WAIT: [num_midpoint](https://github.com/rust-lang/rust/issues/110840)
// NOTE: based on Rust's std implementation.
#[cfg(feature = $ucap )]
#[cfg_attr(feature = "nightly_doc", doc(cfg(feature = $ucap)))]
pub const fn midpoint(self, other: $t) -> Int<$t> {
const U: $ut = <$t>::MIN.unsigned_abs();
// Map a $t to a $ut
// ex: i8 [-128; 127] to [0; 255]
const fn map(a: $t) -> $ut { (a as $ut) ^ U }
// Map a $ut to a $t
// ex: u8 [0; 255] to [-128; 127]
const fn demap(a: $ut) -> $t { (a ^ U) as $t }
Int(demap(Int(map(self.0)).midpoint(map(other)).0))
}
}
}};
(
// implements unsigned ops
@unsigned $t:ty : $cap:literal : $up:ty | $iup:ty : $icap:literal |$d:literal) => { paste! {
#[doc = crate::doc_availability!(feature = $cap)]
///
#[doc = "# Integer core methods for `" $t "`\n\n"]
#[doc = "- [abs](#method.abs" $d ")"]
#[doc = "- [is_even](#method.is_even" $d ")"]
#[doc = "- [is_odd](#method.is_odd" $d ")"]
#[doc = "- [gcd](#method.gcd" $d ")"]
#[doc = "- [gcd_ext](#method.gcd_ext" $d ")"]
#[doc = "- [gcd_ext_euc](#method.gcd_ext_euc" $d ")"]
#[doc = "- [lcm](#method.lcm" $d ")"]
#[doc = "- [scale](#method.scale" $d ")"]
#[doc = "- [scale_wrap](#method.scale_wrap" $d ")"]
#[doc = "- [midpoint](#method.midpoint" $d ")"]
///
#[cfg(feature = $cap )]
impl Int<$t> {
/// Returns the absolute value of `self` (no-op).
#[must_use]
pub const fn abs(self) -> Int<$t> { self }
/// Returns `true` if `self` is an even number.
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc = "assert![Int(2_" $t ").is_even()];"]
#[doc = "assert![!Int(3_" $t ").is_even()];"]
#[doc = "assert![Int(0_" $t ").is_even()];"]
/// ```
#[must_use]
pub const fn is_even(self) -> bool { self.0 & 1 == 0 }
/// Returns `true` if `self` is an odd number.
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc = "assert![Int(3_" $t ").is_odd()];"]
#[doc = "assert![!Int(2_" $t ").is_odd()];"]
#[doc = "assert![!Int(0_" $t ").is_odd()];"]
/// ```
#[must_use]
pub const fn is_odd(self) -> bool { self.0 & 1 == 1 }
/* unsigned gcd, lcm */
/// Returns the <abbr title="Greatest Common Divisor">GCD</abbr>.
///
/// Uses Stein's algorithm which is much more efficient to compute than Euclid's.
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc = "assert_eq![Int(4), Int(64_" $t ").gcd(36)];"]
#[doc = "assert_eq![Int(36), Int(0_" $t ").gcd(36)];"]
#[doc = "assert_eq![Int(64), Int(64_" $t ").gcd(0)];"]
/// ```
#[must_use]
pub const fn gcd(self, mut b: $t) -> Int<$t> {
let mut a = self.0;
iif![a == 0; return Int(b)];
iif![b == 0; return self];
// Let k be the greatest power of 2 dividing both a and b:
let k = (a | b).trailing_zeros();
// Divide a and b by 2 until they become odd:
a >>= a.trailing_zeros();
b >>= b.trailing_zeros();
// Break when a == GCD of a / 2^k:
while b != 0 {
b >>= b.trailing_zeros();
// ensure b >= a before subtraction:
iif![a > b; cswap![a, b]; b -= a];
}
Int(a << k)
// Euclid's algorithm:
// while a != b { iif![a > b; a -= b; b -= a] }; a
}
/// Returns the <abbr title="Greatest Common Divisor">GCD</abbr>
/// and the Bézout coeficients.
///
#[doc = "Performs inner operations and returns coefficients as [`" $iup "`]."]
///
/// This version uses the extended Stein's algorithm which is much more
/// efficient to compute than Euclid's. It uses only simple arithmetic
/// operations and works by dividing the inputs by 2 until they are odd,
/// and then subtracting the smaller number from the larger one.
///
/// The Bézout's coefficients are not unique, and different algorithms
/// can yield different coefficients that all satisfy Bézout's identity.
///
/// Bézout's identity states that for any two integers a and b,
/// there exist integers x and y such that $ax + by = gcd(a, b)$.
///
/// # Errors
/// Can return [`Overflow`] for `u128`.
///
/// # Examples
/// ```
/// # use devela::{Int, isize_up};
#[doc = "let (gcd, x, y) = Int(32_" $t ").gcd_ext(36).unwrap().as_tuple();"]
/// assert_eq!(gcd.0, 4);
#[doc = "assert_eq![x.0 * 32 + y.0 * 36, gcd.0 as " $iup "];"]
/// ```
#[cfg(all(feature = $icap, feature = "cast"))]
#[cfg_attr(feature = "nightly_doc", doc(cfg(all(feature = $icap, feature = "cast"))))]
pub const fn gcd_ext(self, b: $t) -> Result<GcdReturn<Int<$t>, Int<$iup>>> {
if self.0 == 0 { return Ok(GcdReturn::new(Int(b), Int(0), Int(1))); }
if b == 0 { return Ok(GcdReturn::new(self, Int(1), Int(0))); }
let mut a = unwrap![ok? Cast(self.0).[<checked_cast_to_ $iup>]()];
let mut b = unwrap![ok? Cast(b).[<checked_cast_to_ $iup>]()];
let mut k = 0;
while ((a | b) & 1) == 0 {
a >>= 1;
b >>= 1;
k += 1;
}
let (a0, b0, mut sa, mut sb, mut ta, mut tb) = (a, b, 1, 0, 0, 1);
while (a & 1) == 0 {
if (sa & 1) != 0 || (sb & 1) != 0 {
sa -= b0;
sb += a0;
}
a >>= 1;
sa >>= 1;
sb >>= 1;
}
while b != 0 {
while (b & 1) == 0 {
if (ta & 1) != 0 || (tb & 1) != 0 {
ta -= b0;
tb += a0;
}
b >>= 1;
ta >>= 1;
tb >>= 1;
}
if a > b {
cswap![a, b];
cswap![sa, ta];
cswap![sb, tb];
}
b -= a;
ta -= sa;
tb -= sb;
}
Ok(GcdReturn::new(Int((a << k) as $t), Int(sa), Int(sb)))
}
/// Returns the <abbr title="Greatest Common Divisor">GCD</abbr>
/// and the Bézout coeficients.
///
#[doc = "Performs inner operations and returns coefficients as [`" $iup "`]."]
///
/// This version uses the extended Euclids's algorithm, which uses a
/// series of euclidean divisions and works by subtracting multiples
/// of the smaller number from the larger one.
///
/// The Bézout's coefficients are not unique, and different algorithms
/// can yield different coefficients that all satisfy Bézout's identity.
///
/// # Errors
/// Can return [`Overflow`] for `u128`.
///
/// # Examples
/// ```
/// # use devela::{Int, isize_up};
#[doc = "let (gcd, x, y) = Int(32_" $t ").gcd_ext_euc(36).unwrap().as_tuple();"]
/// assert_eq!(gcd.0, 4);
#[doc = "assert_eq![x.0 * 32 + y.0 * 36, gcd.0 as " $iup "];"]
/// ```
#[cfg(all(feature = $icap, feature = "cast"))]
#[cfg_attr(feature = "nightly_doc", doc(cfg(all(feature = $icap, feature = "cast"))))]
pub const fn gcd_ext_euc(self, b: $t) -> Result<GcdReturn<Int<$t>, Int<$iup>>> {
let a = unwrap![ok? Cast(self.0).[<checked_cast_to_ $iup>]()];
let b = unwrap![ok? Cast(b).[<checked_cast_to_ $iup>]()];
if a == 0 {
Ok(GcdReturn::new(Int(b as $t), Int(0), Int(1)))
} else {
let (g, x, y) = Int(b % a).gcd_ext_euc(a).as_tuple_copy();
Ok(GcdReturn::new(Int(g.0 as $t), Int(y.0 - (b / a) * x.0), x))
}
}
/// Returns the <abbr title="Least Common Multiple">LCM</abbr>.
///
#[doc = "Performs operations internally as [`" $up "`] for the inner operations."]
///
/// # Errors
/// Can [`Overflow`].
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc = "assert_eq![Int(12_" $t ").lcm(15), Ok(Int(60))];"]
/// ```
pub const fn lcm(self, b: $t) -> Result<Int<$t>> {
let (aup, bup) = (self.0 as $up, b as $up);
let res = aup * bup / self.gcd(b).0 as $up;
iif![res <= $t::MAX as $up; Ok(Int(res as $t)); Err(Overflow(None))]
}
/// Returns a scaled value between `[min..=max]` to a new range `[a..=b]`.
///
#[doc = "Performs operations internally as [`" $up "`] for the checked operations."]
///
/// If the value lies outside of `[min..=max]` it will result in extrapolation.
///
/// # Errors
/// Can [`Overflow`] for extrapolated values that can't fit the type,
/// and for overflowing arithmetic operations in the following formula:
///
/// # Formula
#[doc = FORMULA_SCALE!()]
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc ="assert_eq![Ok(Int(40)), Int(60_" $t ").scale(0, 120, 30, 50)]; // interpolate"]
#[doc ="assert_eq![Ok(Int(112)), Int(100_" $t ").scale(0, 80, 0, 90)]; // extrapolate"]
/// # #[cfg(feature = "_int_u8")]
/// assert![Int(200_u8).scale(0, 50, 0, 90).is_err()]; // extrapolate and overflow
/// ```
#[cfg(feature = "cast")]
#[cfg_attr(feature = "nightly_doc", doc(cfg(feature = "cast")))]
pub const fn scale(self, min: $t, max: $t, a: $t, b: $t) -> Result<Int<$t>> {
let v = self.0 as $up;
let (min, max, a, b) = (min as $up, max as $up, a as $up, b as $up);
let b_a = iif![let Some(n) = b.checked_sub(a); n; return Err(Overflow(None))];
let v_min = iif![let Some(n) = v.checked_sub(min); n; return Err(Overflow(None))];
let mul = iif![let Some(n) = b_a.checked_mul(v_min); n; return Err(Overflow(None))];
let max_min = iif![let Some(n) = max.checked_sub(min); n; return Err(Overflow(None))];
let div = iif![let Some(n) = mul.checked_div(max_min); n; return Err(Overflow(None))];
let sum = iif![let Some(n) = div.checked_add(a); n; return Err(Overflow(None))];
match Cast(sum).[<checked_cast_to_ $t>]() {
Ok(n) => Ok(Int(n)),
Err(e) => Err(e),
}
}
/// Returns a scaled value between `[min..=max]` to a new range `[a..=b]`.
///
#[doc = "Performs operations internally as [`" $up "`]."]
///
/// If the value lies outside of `[min..=max]` it will result in extrapolation, and
/// if the value doesn't fit in the type it will wrap around its boundaries.
///
/// # Panics
/// Could panic for large values of `i128` or `u128`.
///
/// # Formula
#[doc = FORMULA_SCALE!()]
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc = "assert_eq![Int(40), Int(60_" $t ").scale_wrap(0, 120, 30, 50)]; // interpolate"]
#[doc = "assert_eq![Int(112), Int(100_" $t ").scale_wrap(0, 80, 0, 90)]; // extrapolate"]
/// # #[cfg(feature = "_int_u8")]
/// assert_eq![Int(104), Int(200_u8).scale_wrap(0, 50, 0, 90)]; // extrapolate and wrap
/// ```
pub const fn scale_wrap(self, min: $t, max: $t, a: $t, b: $t) -> Int<$t> {
let v = self.0 as $up;
let (min, max, a, b) = (min as $up, max as $up, a as $up, b as $up);
Int(((b - a) * (v - min) / (max - min) + a) as $t)
}
// MAYBE: scale_saturate
/// Calculates the middle point of `self` and `other`.
///
/// The result is always rounded towards negative infinity.
///
/// # Examples
/// ```
/// # use devela::Int;
#[doc = concat!("assert_eq![Int(0_", stringify!($t), ").midpoint(4), 2];")]
#[doc = concat!("assert_eq![Int(1_", stringify!($t), ").midpoint(4), 2];")]
/// ```
// WAIT: [num_midpoint](https://github.com/rust-lang/rust/pull/131784)
// NOTE: based on Rust's std implementation.
pub const fn midpoint(self, other: $t) -> Int<$t> {
// Use the well known branchless algorithm from Hacker's Delight to compute
// `(a + b) / 2` without overflowing: `((a ^ b) >> 1) + (a & b)`.
Int(((self.0 ^ other) >> 1) + (self.0 & other))
}
}
}};
}
impl_core!();