devela/num/float/wrapper/shared.rs
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// devela::num::float::wrapper::shared
//
//! Shared methods.
//
#[allow(unused_imports)]
use super::super::shared_docs::*;
use crate::{concat as cc, iif, stringify as sfy, Float, Sign};
/// Implements methods independently of any features
///
/// $f: the floating-point type.
/// $uf: unsigned int type with the same bit-size.
/// $ie: signed int type used for integer exponentiation.
/// $ue: unsigned int type used for integer exponentiation and number of terms (u32).
/// $cap: the capability feature that enables the given implementation. E.g "_float_f32".
/// $cmp: the feature that enables some methods depending on Compare. E.g "_cmp_f32".
macro_rules! impl_float_shared {
() => {
impl_float_shared![
(f32:u32, i32, u32):"_float_f32":"_cmp_f32",
(f64:u64, i32, u32):"_float_f64":"_cmp_f64"
];
};
($( ($f:ty:$uf:ty, $ie:ty, $ue:ty) : $cap:literal : $cmp:literal ),+) => {
$( impl_float_shared![@$f:$uf, $ie, $ue, $cap:$cmp]; )+
};
(@$f:ty:$uf:ty, $ie:ty, $ue:ty, $cap:literal : $cmp:literal) => {
#[doc = crate::doc_availability!(feature = $cap)]
///
/// # *Common implementations with or without `std` or `libm`*.
#[cfg(feature = $cap )]
// #[cfg_attr(feature = "nightly_doc", doc(cfg(feature = $cap)))]
impl Float<$f> {
/// The largest integer less than or equal to itself.
/// # Formulation
#[doc = crate::FORMULA_FLOOR!()]
#[must_use]
pub const fn const_floor(self) -> Float<$f> {
let mut result = self.const_trunc().0;
if self.0.is_sign_negative() && Float(self.0 - result).abs().0 > <$f>::EPSILON {
result -= 1.0;
}
Float(result)
}
/// The smallest integer greater than or equal to itself.
/// # Formulation
#[doc = FORMULA_CEIL!()]
#[must_use]
pub const fn const_ceil(self) -> Float<$f> {
let mut result = self.const_trunc().0;
if self.0.is_sign_positive() && Float(self.0 - result).abs().0 > <$f>::EPSILON {
result += 1.0;
}
Float(result)
}
/// The nearest integer to itself, default rounding
///
/// This is the default [`round_ties_away`] implementation.
#[must_use]
pub const fn const_round(self) -> Float<$f> { self.const_round_ties_away() }
/// The nearest integer to itself, rounding ties away from `0.0`.
///
/// This is the default [`round`] implementation.
///
/// # Formulation
#[doc = FORMULA_ROUND_TIES_AWAY!()]
#[must_use]
pub const fn const_round_ties_away(self) -> Float<$f> {
Float(self.0 +
Float(0.5 - 0.25 * <$f>::EPSILON).const_copysign(self.0).0)
.const_trunc()
}
/// Returns the nearest integer to `x`, rounding ties to the nearest even integer.
/// # Formulation
#[doc = FORMULA_ROUND_TIES_EVEN!()]
#[must_use]
pub const fn const_round_ties_even(self) -> Float<$f> {
let r = self.const_round_ties_away();
if r.0 % 2.0 == 0.0 {
r
} else {
#[allow(clippy::float_cmp, reason = "IMPROVE")]
if Float(self.0 - r.0).abs().0 == 0.5 { // -0.5 < error_margin
Float(r.0 - self.const_signum().0)
} else {
r
}
}
}
/// The integral part.
/// This means that non-integer numbers are always truncated towards zero.
///
/// # Formulation
#[doc = FORMULA_TRUNC!()]
///
/// This implementation uses bitwise manipulation to remove the fractional part
/// of the floating-point number. The exponent is extracted, and a mask is
/// created to remove the fractional part. The new bits are then used to create
/// the truncated floating-point number.
#[must_use]
pub const fn const_trunc(self) -> Float<$f> {
let bits = self.0.to_bits();
const BIAS: $ie = Float::<$f>::BIAS as $ie;
const SIG_BITS: $ie = Float::<$f>::SIGNIFICAND_BITS as $ie;
const EXP_MASK: $uf = (1 << Float::<$f>::EXPONENT_BITS) - 1;
#[allow(clippy::cast_possible_wrap)]
let exponent = (((bits >> SIG_BITS) & EXP_MASK) as $ie) - BIAS;
if exponent < 0 {
iif![self.0.is_sign_positive(); Float(0.0); Float(-0.0)]
} else if exponent < SIG_BITS {
let mask = !(((1 as $uf) << (SIG_BITS - exponent)) - 1);
let new_bits = bits & mask;
Float(<$f>::from_bits(new_bits))
} else {
self
}
}
/// Returns the nearest integer, rounding ties to the nearest odd integer.
/// # Formulation
#[doc = FORMULA_ROUND_TIES_ODD!()]
#[must_use]
pub fn const_round_ties_odd(self) -> Float<$f> {
let r = self.const_round_ties_away();
iif![r.0 % 2.0 != 0.0; r ;
iif![(self - r).abs() == 0.5; r + self.const_signum(); r]]
}
/// Returns the nearest integer, rounding ties to the nearest odd integer.
/// # Formulation
#[doc = FORMULA_ROUND_TIES_ODD!()]
#[must_use]
pub fn round_ties_odd(self) -> Float<$f> {
let r = self.round_ties_away();
iif![r.0 % 2.0 != 0.0; r ;
iif![(self - r).abs() == 0.5; r + self.signum(); r]]
}
/// The fractional part.
/// # Formulation
#[doc = FORMULA_FRACT!()]
#[must_use]
pub const fn const_fract(self) -> Float<$f> {
Float(self.0 - self.const_trunc().0)
}
/// The integral and fractional parts.
/// # Formulation
#[doc = FORMULA_SPLIT!()]
#[must_use]
pub const fn const_split(self) -> (Float<$f>, Float<$f>) {
let trunc = self.const_trunc();
(trunc, Float(self.0 - trunc.0))
}
/// A number that represents its sign, propagating `NaN`.
#[must_use]
pub const fn const_signum(self) -> Float<$f> {
if self.0.is_nan() { Float(<$f>::NAN) } else { Self::ONE.const_copysign(self.0) }
}
/// A number composed of the magnitude of itself and the `sign` of other.
#[must_use]
pub const fn const_copysign(self, sign: $f) -> Float<$f> {
const SIGN_MASK: $uf = <$uf>::MAX / 2 + 1;
const VALUE_MASK: $uf = <$uf>::MAX / 2;
let sign_bit = sign.to_bits() & SIGN_MASK;
let value_bits = self.0.to_bits() & VALUE_MASK;
Float(<$f>::from_bits(value_bits | sign_bit))
}
/// Returns the [`Sign`].
#[must_use]
pub const fn sign(self) -> Sign {
if self.is_sign_positive() { Sign::Positive } else { Sign::Negative }
}
/// Returns the [`Sign`], returning [`None`][Sign::None] for zero
#[must_use]
pub const fn sign_nonzero(self) -> Sign {
if self.is_zero() {
Sign::None
} else if self.is_sign_positive() {
Sign::Positive
} else {
Sign::Negative
}
}
/// Returns `true` if `self` has a positive sign.
#[must_use]
pub const fn is_sign_positive(self) -> bool { self.0.is_sign_positive() }
/// Returns `true` if `self` has a negative sign.
#[must_use]
pub const fn is_sign_negative(self) -> bool { self.0.is_sign_negative() }
/// Returns `true` if `self` is 0.0 or -0.0.
#[must_use]
pub const fn is_zero(self) -> bool {
let non_sign_bits_mask = !(<$uf>::MAX / 2 + 1);
(self.0.to_bits() & non_sign_bits_mask) == 0
}
/// Returns `true` if `self` has a positive sign and is not zero.
#[must_use]
pub const fn is_sign_positive_nonzero(self) -> bool {
!self.is_zero() && self.is_sign_positive()
}
/// Returns `true` if `self` has a negative sign and is not zero.
#[must_use]
pub const fn is_sign_negative_nonzero(self) -> bool {
!self.is_zero() && self.is_sign_negative()
}
/// Computes `(x * mul + add)` normally.
#[must_use]
pub const fn mul_add_fallback(self, mul: $f, add: $f) -> Float<$f> {
Float(self.0 * mul + add)
}
/// The euclidean division.
// NOTE: [incorrect computations](https://github.com/rust-lang/rust/issues/107904)
#[must_use]
pub fn div_euclid(self, other: $f) -> Float<$f> {
let q = Float(self.0 / other).trunc().0;
if self.0 % other < 0.0 {
iif![other > 0.0; Float(q - 1.0); Float(q + 1.0)]
} else {
Float(q)
}
}
/// The least non-negative remainder of `self` % `other`.
// NOTE: [yield inconsistent results](https://github.com/rust-lang/rust/issues/111405)
// WAIT:1.85 [const_float_methods](https://github.com/rust-lang/rust/pull/133389)
#[must_use]
pub const fn rem_euclid(self, other: $f) -> Float<$f> {
let r = self.0 % other;
iif![r < 0.0; Float(r + Float(other).abs().0); Float(r)]
}
/// Returns `self` between `[min..=max]` scaled to a new range `[u..=v]`.
///
/// Values of `self` outside of `[min..=max]` are not clamped
/// and will result in extrapolation.
///
/// # Formulation
#[doc = FORMULA_SCALE!()]
/// # Examples
/// ```
/// # use devela::Float;
#[doc = cc!["assert_eq![Float(45_", sfy![$f], ").scale(0., 360., 0., 1.), 0.125];"]]
#[doc = cc!["assert_eq![Float(45_", sfy![$f], ").scale(0., 360., -1., 1.), -0.75];"]]
#[doc = cc!["assert_eq![Float(0.125_", sfy![$f], ").scale(0., 1., 0., 360.), 45.];"]]
#[doc = cc!["assert_eq![Float(-0.75_", sfy![$f], ").scale(-1., 1., 0., 360.), 45.];"]]
/// ```
#[must_use]
pub const fn scale(self, min: $f, max: $f, u: $f, v: $f) -> Float<$f> {
Float((v - u) * (self.0 - min) / (max - min) + u)
}
/// Calculates a linearly interpolated value between `u..=v`
/// based on `self` as a percentage between `[0..=1]`.
///
/// Values of `self` outside `[0..=1]` are not clamped
/// and will result in extrapolation.
///
/// # Formulation
#[doc = FORMULA_LERP!()]
/// # Example
/// ```
/// # use devela::Float;
#[doc = cc!["assert_eq![Float(0.5_", sfy![$f], ").lerp(40., 80.), 60.];"]]
// TODO more examples extrapolated
/// ```
#[must_use]
pub const fn lerp(self, u: $f, v: $f) -> Float<$f> {
Float((1.0 - self.0) * u + self.0 * v)
}
/// $ 1 / \sqrt{x} $ the
/// [fast inverse square root algorithm](https://en.wikipedia.org/wiki/Fast_inverse_square_root).
#[must_use]
pub const fn fisr(self) -> Float<$f> {
let (mut i, three_halfs, x2) = (self.0.to_bits(), 1.5, self.0 * 0.5);
i = Self::FISR_MAGIC - (i >> 1);
let y = <$f>::from_bits(i);
Float(y * (three_halfs - (x2 * y * y)))
}
/// $ \sqrt{x} $ The square root calculated using the
/// [Newton-Raphson method](https://en.wikipedia.org/wiki/Newton%27s_method).
#[must_use]
pub const fn sqrt_nr(self) -> Float<$f> {
if self.0 < 0.0 {
Self::NAN
} else if self.0 == 0.0 {
Self::ZERO
} else {
let mut guess = self.0;
let mut guess_next = 0.5 * (guess + self.0 / guess);
while Self(guess - guess_next).abs().0 > Self::NR_TOLERANCE {
guess = guess_next;
guess_next = 0.5 * (guess + self.0 / guess);
}
Float(guess_next)
}
}
/// $ \sqrt{x} $ the square root calculated using the
/// [fast inverse square root algorithm](https://en.wikipedia.org/wiki/Fast_inverse_square_root).
#[must_use]
pub const fn sqrt_fisr(self) -> Float<$f> { Float(1.0 / self.fisr().0) }
/// The hypothenuse (the euclidean distance) using the
/// [fast inverse square root algorithm](https://en.wikipedia.org/wiki/Fast_inverse_square_root).
///
/// # Formulation
#[doc = FORMULA_HYPOT_FISR!()]
#[must_use]
pub const fn hypot_fisr(self, y: $f) -> Float<$f> {
Float(self.0 * self.0 + y * y).sqrt_fisr()
}
/// The hypothenuse (the euclidean distance) using the
/// [Newton-Raphson method](https://en.wikipedia.org/wiki/Newton%27s_method).
///
/// # Formulation
#[doc = FORMULA_HYPOT_NR!()]
#[must_use]
pub const fn hypot_nr(self, y: $f) -> Float<$f> {
Float(self.0 * self.0 + y * y).sqrt_nr()
}
/// $ \sqrt\[3\]{x} $ The cubic root calculated using the
/// [Newton-Raphson method](https://en.wikipedia.org/wiki/Newton%27s_method).
#[must_use]
pub const fn cbrt_nr(self) -> Float<$f> {
iif![self.0 == 0.0; return self];
let mut guess = self.0;
loop {
let next_guess = (2.0 * guess + self.0 / (guess * guess)) / 3.0;
if Float(next_guess - guess).abs().0 < Self::NR_TOLERANCE {
break Float(next_guess);
}
guess = next_guess;
}
}
/// The factorial of the integer value `x`.
///
/// The maximum values with a representable result are:
/// 34 for `f32` and 170 for `f64`.
///
/// Note that precision is poor for large values.
#[must_use]
pub const fn factorial(x: $ue) -> Float<$f> {
let mut result = Self::ONE.0;
// for i in 1..=x { result *= i as $f; }
let mut i = 1;
while i <= x {
result *= i as $f;
i += 1;
}
Float(result)
}
/// The absolute value of `self`.
// WAIT:1.85 [const_float_methods](https://github.com/rust-lang/rust/pull/133389)
#[must_use]
pub const fn abs(self) -> Float<$f> {
let mask = <$uf>::MAX / 2;
Float(<$f>::from_bits(self.0.to_bits() & mask))
}
/// The negative absolute value of `self` (sets its sign to be negative).
#[must_use]
pub const fn neg_abs(self) -> Float<$f> {
if self.is_sign_negative() { self } else { self.flip_sign() }
}
/// Flips its sign.
#[must_use]
pub const fn flip_sign(self) -> Float<$f> {
let sign_bit_mask = <$uf>::MAX / 2 + 1;
Float(<$f>::from_bits(self.0.to_bits() ^ sign_bit_mask))
}
/// Returns itself clamped between `min` and `max`, ignoring `NaN`.
///
/// # Example
/// ```
/// # use devela::Float;
#[doc = cc!["assert_eq![Float(50.0_", sfy![$f], ").clamp(40., 80.), 50.];"]]
#[doc = cc!["assert_eq![Float(100.0_", sfy![$f], ").clamp(40., 80.), 80.];"]]
#[doc = cc!["assert_eq![Float(10.0_", sfy![$f], ").clamp(40., 80.), 40.];"]]
/// ```
/// See also: [`clamp_nan`][Self::clamp_nan], [`clamp_total`][Self::clamp_total].
// WAIT:1.85 [const_float_methods](https://github.com/rust-lang/rust/pull/133389)
#[must_use]
pub const fn const_clamp(self, min: $f, max: $f) -> Float<$f> {
self.const_max(min).const_min(max)
}
/// The maximum between itself and `other`, ignoring `NaN`.
// WAIT:1.85 [const_float_methods](https://github.com/rust-lang/rust/pull/133389)
#[must_use]
pub const fn const_max(self, other: $f) -> Float<$f> {
if self.0.is_nan() || self.0 < other { Float(other) } else { self }
}
/// The minimum between itself and other, ignoring `NaN`.
// WAIT:1.85 [const_float_methods](https://github.com/rust-lang/rust/pull/133389)
#[must_use]
pub const fn const_min(self, other: $f) -> Float<$f> {
if other.is_nan() || self.0 < other { self } else { Float(other) }
}
/// Returns itself clamped between `min` and `max`, using total order.
///
/// # Example
/// ```
/// # use devela::Float;
#[doc = cc!["assert_eq![Float(50.0_", sfy![$f], ").clamp_total(40., 80.), 50.];"]]
#[doc = cc!["assert_eq![Float(100.0_", sfy![$f], ").clamp_total(40., 80.), 80.];"]]
#[doc = cc!["assert_eq![Float(10.0_", sfy![$f], ").clamp_total(40., 80.), 40.];"]]
/// ```
/// See also: [`clamp`][Self::clamp], [`clamp_nan`][Self::clamp_nan].
#[must_use]
#[cfg(feature = $cmp)]
#[cfg_attr(feature = "nightly_doc", doc(cfg(feature = $cmp)))]
pub const fn clamp_total(self, min: $f, max: $f) -> Float<$f> {
Float(crate::Compare(self.0).clamp(min, max))
}
/// Returns the maximum between itself and `other`, using total order.
///
/// See also: [`max_nan`][Self::max_nan].
#[must_use]
#[cfg(feature = $cmp)]
#[cfg_attr(feature = "nightly_doc", doc(cfg(feature = $cmp)))]
pub const fn max_total(self, other: $f) -> Float<$f> {
Float(crate::Compare(self.0).max(other))
}
/// Returns the minimum between itself and `other`, using total order.
///
/// See also: [`min_nan`][Self::min_nan].
#[must_use]
#[cfg(feature = $cmp)]
#[cfg_attr(feature = "nightly_doc", doc(cfg(feature = $cmp)))]
pub fn min_total(self, other: $f) -> Float<$f> {
Float(crate::Compare(self.0).min(other))
}
/// Returns itself clamped between `min` and `max`, propagating `NaN`.
///
/// # Example
/// ```
/// # use devela::Float;
#[doc = cc!["assert_eq![Float(50.0_", sfy![$f], ").clamp_nan(40., 80.), 50.];"]]
#[doc = cc!["assert_eq![Float(100.0_", sfy![$f], ").clamp_nan(40., 80.), 80.];"]]
#[doc = cc!["assert_eq![Float(10.0_", sfy![$f], ").clamp_nan(40., 80.), 40.];"]]
/// ```
/// See also: [`clamp`][Self::clamp], [`clamp_total`][Self::clamp_total].
#[must_use]
pub const fn clamp_nan(self, min: $f, max: $f) -> Float<$f> {
self.max_nan(min).min_nan(max)
}
/// Returns the maximum between itself and `other`, propagating `Nan`.
///
/// # Example
/// ```
/// # use devela::Float;
#[doc = cc!["assert_eq![Float(50.0_", sfy![$f], ").max_nan(80.), 80.];"]]
#[doc = cc!["assert_eq![Float(100.0_", sfy![$f], ").max_nan(80.), 100.];"]]
/// ```
/// See also: [`max_total`][Self::max_total].
// WAIT: [float_minimum_maximum](https://github.com/rust-lang/rust/issues/91079)
#[must_use]
#[expect(clippy::float_cmp, reason = "TODO:CHECK:IMPROVE?")]
pub const fn max_nan(self, other: $f) -> Float<$f> {
if self.0 > other {
self
} else if self.0 < other {
Float(other)
} else if self.0 == other {
iif![self.is_sign_positive() && other.is_sign_negative(); self; Float(other)]
} else {
// At least one input is NaN. Use `+` to perform NaN propagation and quieting.
Float(self.0 + other)
}
}
/// Returns the minimum between itself and `other`, propagating `Nan`.
///
/// # Example
/// ```
/// # use devela::Float;
#[doc = cc!["assert_eq![Float(50.0_", sfy![$f], ").min_nan(80.), 50.];"]]
#[doc = cc!["assert_eq![Float(100.0_", sfy![$f], ").min_nan(80.), 80.];"]]
/// ```
/// See also: [`min_total`][Self::min_total].
// WAIT: [float_minimum_maximum](https://github.com/rust-lang/rust/issues/91079)
#[must_use]
#[expect(clippy::float_cmp, reason = "TODO:CHECK:IMPROVE?")]
pub const fn min_nan(self, other: $f) -> Float<$f> {
if self.0 < other {
self
} else if self.0 > other {
Float(other)
} else if self.0 == other {
iif![self.is_sign_negative() && other.is_sign_positive(); self; Float(other)]
} else {
// At least one input is NaN. Use `+` to perform NaN propagation and quieting.
Float(self.0 + other)
}
}
/// Raises itself to the `p` integer power.
#[must_use]
pub const fn const_powi(self, p: $ie) -> Float<$f> {
match p {
0 => Self::ONE,
1.. => {
let mut result = self.0;
let mut i = 1;
while i < p {
result *= self.0;
i += 1;
}
Float(result)
}
_ => {
let mut result = self.0;
let mut i = 1;
let abs_p = p.abs();
while i < abs_p {
result /= self.0;
i += 1;
}
Float(result)
}
}
}
/// Evaluates a polynomial at the `self` point value, using [Horner's method].
///
/// Expects a slice of `coefficients` $[a_n, a_{n-1}, ..., a_1, a_0]$
/// representing the polynomial $ a_n * x^n + a_{n-1} * x^{(n-1)} + ... + a_1 * x + a_0 $.
///
/// # Examples
/// ```
/// # use devela::Float;
/// let coefficients = [2.0, -6.0, 2.0, -1.0];
#[doc = cc!["assert_eq![Float(3.0_", sfy![$f], ").eval_poly(&coefficients), 5.0];"]]
#[doc = cc!["assert_eq![Float(3.0_", sfy![$f], ").eval_poly(&[]), 0.0];"]]
/// ```
///
/// [Horner's method]: https://en.wikipedia.org/wiki/Horner%27s_method#Polynomial_evaluation_and_long_division
// WAIT: [for-loops in constants](https://github.com/rust-lang/rust/issues/87575)
#[must_use]
pub const fn eval_poly(self, coefficients: &[$f]) -> Float<$f> {
let coef = coefficients;
match coef.len() {
0 => Float(0.0),
1 => Float(coef[0]),
_ => {
let mut result = coef[0];
// non-const version:
// for &c in &coef[1..] {
// result = result * self.0 + c;
// }
// const version:
let mut i = 1;
while i < coef.len() {
result = result * self.0 + coef[i];
i += 1;
}
Float(result)
}
}
}
/// Approximates the derivative of the 1D function `f` at `x` point using step size `h`.
///
/// Uses the [finite difference method].
///
/// # Formulation
#[doc = FORMULA_DERIVATIVE!()]
///
/// See also the [`autodiff`] attr macro, enabled with the `nightly_autodiff` feature.
///
/// [finite difference method]: https://en.wikipedia.org/wiki/Finite_difference_method
/// [`autodiff`]: crate::autodiff
pub fn derivative<F>(f: F, x: $f, h: $f) -> Float<$f>
where
F: Fn($f) -> $f,
{
Float((f(x + h) - f(x)) / h)
}
/// Approximates the integral of the 1D function `f` over the range `[x, y]`
/// using `n` subdivisions.
///
/// Uses the [Riemann Sum](https://en.wikipedia.org/wiki/Riemann_sum).
///
/// # Formulation
#[doc = FORMULA_INTEGRATE!()]
pub fn integrate<F>(f: F, x: $f, y: $f, n: usize) -> Float<$f>
where
F: Fn($f) -> $f,
{
let dx = (y - x) / n as $f;
Float(
(0..n)
.map(|i| { let x = x + i as $f * dx; f(x) * dx })
.sum()
)
}
/// Approximates the partial derivative of the 2D function `f` at point (`x`, `y`)
/// with step size `h`, differentiating over `x`.
///
/// # Formulation
#[doc = FORMULA_PARTIAL_DERIVATIVE_X!()]
pub fn partial_derivative_x<F>(f: F, x: $f, y: $f, h: $f) -> Float<$f>
where
F: Fn($f, $f) -> $f,
{
Float((f(x + h, y) - f(x, y)) / h)
}
/// Approximates the partial derivative of the 2D function `f` at point (`x`, `y`)
/// with step size `h`, differentiating over `x`.
///
/// # Formulation
#[doc = FORMULA_PARTIAL_DERIVATIVE_Y!()]
pub fn partial_derivative_y<F>(f: F, x: $f, y: $f, h: $f) -> Float<$f>
where
F: Fn($f, $f) -> $f,
{
Float((f(x, y + h) - f(x, y)) / h)
}
}
};
}
impl_float_shared!();