devela/num/float/wrapper/libm_std.rs
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// devela::num::float::wrapper::libm_std
//
//! Methods depending on libm, std, or their absence
//
// TOC
// - impls for libm
// - impls for std && not(libm)
// - impls for not(std) && not(libm)
// - macro helper: impl_fp!
use crate::Float;
#[cfg(feature = "dep_libm")]
mod _libm {
use super::{super::super::shared_docs::*, impl_fp, Float};
use crate::{_dep::libm::Libm, iif};
// custom implementations are commented out
impl_fp![libm:f*:
r"The largest integer less than or equal to `x`.
$$ \lfloor x \rfloor = \max \{ n \in \mathbb{Z} \,|\, n \leq x \} $$ "
floor = floor: ;
r"The smallest integer greater than or equal to `x`.
$$ \lceil x \rceil = \min \{ n \in \mathbb{Z} \,|\, n \geq x \} $$"
ceil = ceil: ;
"The nearest integer to itself, rounding ties away from `0.0`."
round = round_ties_away: ;
"The integral part."
trunc = trunc: ;
// fract
// split == modf
// abs
// signum
"A number composed of its magnitude and the `sign` of other."
copysign = copysign: sign;
"Fused multiply-add. Computes (self * mul) + add with only one rounding error."
fma = mul_add: mul, add;
// div_euclid
// rem_euclid
"Raises itself to the `p` floating point power."
pow = powf: p;
// powi
"Square root."
sqrt = sqrt: ;
"$e^x$ (the exponential function)."
exp = exp: ;
"$2^x$."
exp2 = exp2: ;
"$e^x -1$, more accurately for small values of `x`."
expm1 = exp_m1: ;
// ln = ln: x;
"The natural logarithm."
log = ln: ;
"The natural logarithm plus 1, more accurately."
log1p = ln_1p: ;
// log
"The base 2 logarithm."
log2 = log2: ;
"The base 10 logarithm."
log10 = log10: ;
"The cubic root."
cbrt = cbrt: ;
"The hypothenuse (the euclidean distance)."
hypot = hypot: other;
"The sine."
sin = sin: ;
"The cosine."
cos = cos: ;
"The tangent."
tan = tan: ;
"The arc sine."
asin = asin: ;
"The arc cosine."
acos = acos: ;
"The arc tangent."
atan = atan: ;
"The arc tangent of two variables."
atan2 = atan2: other;
// sin_cos
"The hyperbolic sine."
sinh = sinh: ;
"The hyperbolic cosine."
cosh = cosh: ;
"The hyperbolic tangent."
tanh = tanh: ;
"The inverse hyperbolic sine."
asinh = asinh: ;
"The inverse hyperbolic cosine."
acosh = acosh: ;
"The inverse hyperbolic tangent."
atanh = atanh: ;
"The minimum of two numbers, ignoring `NaN`."
fmax = max: other;
"The minimum of two numbers, ignoring `NaN`."
fmin = min: other;
/* only in libm */
"`10^x`."
exp10 = exp10: ;
"The gamma function. Generalizes the factorial function to complex numbers."
tgamma = gamma: ;
"The natural logarithm of the absolute value of the gamma function."
lgamma = lgamma: ;
"The error function."
erf = erf: ;
"The complementary error function (1 - erf)."
erfc = erfc: ;
"The bessel function of the first kind, of order 0."
j0 = j0: ;
"The bessel function of the first kind, of order 1."
j1 = j1: ;
// jn
"The bessel function of the second kind, of order 0."
y0 = y0: ;
"The bessel function of the second kind, of order 1."
y1 = y1:
// yn
];
/// $f: the floating-point type.
/// $e: the integer type for integer exponentiation.
/// $cap: the capability feature enables the given implementation. E.g "_float_f32".
macro_rules! custom_impls {
() => {
custom_impls![(f32, i32):"_float_f32", (f64, i32):"_float_f64"];
};
($( ($f:ty, $e:ty): $cap:literal ),+) => {
$( custom_impls![@$f, $e, $cap]; )+
};
(@$f:ty, $e:ty, $cap:literal) => {
#[doc = crate::doc_availability!(feature = $cap)]
///
/// # *Implementations using the `libm` feature*.
#[cfg(feature = $cap )]
// #[cfg_attr(feature = "nightly_doc", doc(cfg(feature = $cap)))]
impl Float<$f> {
/// The fractional part.
/// # Formulation
#[doc = FORMULA_FRACT!()]
#[must_use]
pub fn fract(self) -> Float<$f> { Float(self.0 - Libm::<$f>::trunc(self.0)) }
/// The integral and fractional parts.
/// # Formulation
#[doc = FORMULA_SPLIT!()]
#[must_use]
pub fn split(self) -> (Float<$f>, Float<$f>) {
let (i, f) = Libm::<$f>::modf(self.0);
(Self(i), Self(f))
}
/// A number that represents the sign of `x`, propagating `NaN`.
#[must_use]
pub fn signum(self) -> Float<$f> {
if self.0.is_nan() {
Self::NAN
} else {
Float(Libm::<$f>::copysign(1.0, self.0))
}
}
/// Returns the nearest integer to `x`, rounding ties to the nearest even integer.
#[must_use]
pub fn round_ties_even(self) -> Float<$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]]
}
/// Returns itself clamped between `min` and `max`, ignoring `NaN`.
#[must_use]
pub fn clamp(self, min: $f, max: $f) -> Float<$f> {
self.max(min).min(max)
}
/// Raises `x` to the `p` integer power.
#[must_use]
pub fn powi(self, p: $e) -> Float<$f> { self.powf(p as $f) }
/// The logarithm of the number with respect to an arbitrary base.
#[must_use]
pub fn log(self, base: $f) -> Float<$f> {
// Float(Self::ln(base).0 / Self::ln(self).0)
Float(Float(base).ln().0 / self.ln().0)
}
/// The sine and cosine.
#[must_use]
pub fn sin_cos(self) -> (Float<$f>, Float<$f>) {
let (sin, cos) = Libm::<$f>::sincos(self.0);
(Float(sin), Float(cos))
}
// NOTE: implemented manually in `shared.rs`
//
// /// The clamped `x` value, propagating `NaN`.
// #[must_use]
// pub fn clamp_nan(x: $f, min: $f, max: $f) -> $f {
// Self::min_nan(Self::max_nan(x, min), max)
// }
// /// The maximum of two numbers, propagating `NaN`.
// #[must_use]
// pub fn max_nan(x: $f, y: $f) -> $f {
// iif![x.is_nan() || y.is_nan(); <$f>::NAN; Libm::<$f>::fmax(x, y)]
// }
// /// The minimum of two numbers, propagating `NaN`.
// #[must_use]
// pub fn min_nan(x: $f, y: $f) -> $f {
// iif![x.is_nan() || y.is_nan(); <$f>::NAN; Libm::<$f>::fmin(x, y)]
// }
/* only in libm */
/// The natural logarithm of the absolute value of the gamma function,
/// plus its sign.
#[must_use]
pub fn lgamma_r(self) -> (Float<$f>, $e) {
let (f, sign) = Libm::<$f>::lgamma_r(self.0);
(Float(f), sign)
}
/// Bessel function of the first kind, of order `n`.
#[must_use]
pub fn jn(self, n: $e) -> Float<$f> { Float(Libm::<$f>::jn(n, self.0)) }
/// Bessel function of the second kind, of order `n`.
#[must_use]
pub fn yn(self, n: $e) -> Float<$f> { Float(Libm::<$f>::yn(n, self.0)) }
}
};
}
custom_impls!();
}
#[cfg(all(not(feature = "dep_libm"), feature = "std"))]
mod _std {
use super::{super::super::shared_docs::*, impl_fp, Float};
// custom implementations are commented out:
impl_fp
// WAIT: (gamma, ln_gamma) [float_gamma](https://github.com/rust-lang/rust/issues/99842)
];
/// $f: the floating-point type.
/// $e: the integer type for integer exponentiation.
/// $cap: the capability feature that enables the given implementation. E.g "_float_f32".
macro_rules! custom_impls {
() => {
custom_impls![(f32, i32):"_float_f32", (f64, i32):"_float_f64"];
};
($( ($f:ty, $e:ty): $cap:literal ),+) => {
$( custom_impls![@$f, $e, $cap]; )+
};
(@$f:ty, $e:ty, $cap:literal) => {
#[doc = crate::doc_availability!(feature = $cap)]
///
/// # *Implementations using the `std` feature*.
#[cfg(feature = $cap )]
// #[cfg_attr(feature = "nightly_doc", doc(cfg(feature = $cap)))]
impl Float<$f> {
/// Raises itself to the `p` integer power.
#[must_use]
pub fn powi(self, p: $e) -> Float<$f> { Float(<$f>::powi(self.0, p)) }
/// Both the sine and cosine.
#[must_use]
pub fn sin_cos(self) -> (Float<$f>, Float<$f>) {
let (sin, cos) = <$f>::sin_cos(self.0);
(Float(sin), Float(cos))
}
/// The integral and fractional parts of `x`.
/// # Formulation
#[doc = FORMULA_SPLIT!()]
#[must_use]
pub fn split(self) -> (Float<$f>, Float<$f>) {
let trunc = self.trunc();
(trunc, Float(self.0 - trunc.0))
}
}
};
}
custom_impls!();
}
#[cfg(all(not(feature = "dep_libm"), not(feature = "std")))]
mod _no_std_no_libm {
use super::{super::super::shared_docs::*, Float};
/// $f: the floating-point type.
/// $uf: unsigned int type with the same bit-size.
/// $ie: the integer type for integer exponentiation.
/// $cap: the capability feature that enables the given implementation. E.g "_float_f32".
macro_rules! custom_impls {
() => {
custom_impls![(f32, u32, i32):"_float_f32", (f64, u64, i32):"_float_f64"];
};
($( ($f:ty, $uf:ty, $ie:ty) : $cap:literal ),+) => {
$( custom_impls![@$f, $uf, $ie, $cap]; )+
};
(@$f:ty, $uf:ty, $ie:ty, $cap:literal) => {
#[doc = crate::doc_availability!(feature = $cap)]
///
/// # *Implementations 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 floor(self) -> Float<$f> { self.const_floor() }
/// The smallest integer greater than or equal to itself.
/// # Formulation
#[doc = FORMULA_CEIL!()]
#[must_use]
pub const fn ceil(self) -> Float<$f> { self.const_ceil() }
/// The nearest integer to itself, default rounding
///
/// This is the default [`round_ties_away`] implementation.
#[must_use]
pub const fn round(self) -> Float<$f> { self.const_round() }
/// The nearest integer to itself, rounding ties away from `0.0`.
///
/// This is the default [`round`] implementation.
///
/// # Formulation
#[doc = FORMULA_ROUND_TIES_AWAY!()]
#[must_use]
pub const fn round_ties_away(self) -> Float<$f> {self.const_round_ties_away() }
/// Returns the nearest integer to `x`, rounding ties to the nearest even integer.
/// # Formulation
#[doc = FORMULA_ROUND_TIES_EVEN!()]
#[must_use]
pub const fn round_ties_even(self) -> Float<$f> { self.const_round_ties_even() }
/// The integral part.
/// This means that non-integer numbers are always truncated towards zero.
///
/// # Formulation
#[doc = FORMULA_TRUNC!()]
///
/// This implementation uses bitwise manipulation to remove the fractional part
/// of the floating-point number. The exponent is extracted, and a mask is
/// created to remove the fractional part. The new bits are then used to create
/// the truncated floating-point number.
#[must_use]
pub const fn trunc(self) -> Float<$f> { self.const_trunc() }
/// The fractional part.
/// # Formulation
#[doc = FORMULA_FRACT!()]
#[must_use]
pub const fn fract(self) -> Float<$f> { self.const_fract() }
/// The integral and fractional parts.
/// # Formulation
#[doc = FORMULA_SPLIT!()]
#[must_use]
pub const fn split(self) -> (Float<$f>, Float<$f>) { self.const_split() }
/// A number that represents its sign, propagating `NaN`.
#[must_use]
pub const fn signum(self) -> Float<$f> { self.const_signum() }
/// A number composed of the magnitude of itself and the `sign` of other.
#[must_use]
pub const fn copysign(self, sign: $f) -> Float<$f> { self.const_copysign(sign) }
/// Returns itself clamped between `min` and `max`, ignoring `NaN`.
// WAIT:1.85 [const_float_methods](https://github.com/rust-lang/rust/pull/133389)
#[must_use]
pub const fn clamp(self, min: $f, max: $f) -> Float<$f> {
self.const_clamp(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 max(self, other: $f) -> Float<$f> { self.const_max(other) }
/// 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 min(self, other: $f) -> Float<$f> { self.const_min(other) }
/// Raises itself to the `p` integer power.
#[must_use]
pub const fn powi(self, p: $ie) -> Float<$f> { self.const_powi(p) }
}
};
}
custom_impls!();
}
/// macro helper for implementing methods for `Float`, from either `libm` or `std`.
///
/// $lib: the library to use.
/// $f: the floating-point type to support.
/// $doc: an optional documentation string.
/// $opfn: the original operation function name.
/// $op: the new operation function name in Float.
#[cfg(any(feature = "dep_libm", feature = "std"))]
macro_rules! impl_fp {
(
// Matches a wildcard floating-point type (f*).
// Expands to specific floating-point types (f32, f64).
$lib:ident : f* : $($ops:tt)*) => {
impl_fp![$lib : f32 : $($ops)*];
impl_fp![$lib : f64 : $($ops)*];
};
(
// Matches a specific floating-point type and any number of operations.
// Generates the impl block for Float<$f> and calls the matching implementation.
$lib:ident : $f:ty : $($ops:tt)*) => { $crate::paste! {
#[doc = "# *This implementation block leverages the `" $lib "` feature.*"]
impl Float<$f> {
impl_fp![@$lib : $f : $($ops)*];
}
}};
(
// Matches multiple operations and uses recursion to process each one.
@$lib:ident : $f:ty : $($doc:literal)? $opfn:ident = $op:ident : $($arg:ident),*
; $($rest:tt)*) => {
impl_fp![@$lib : $f : $($doc)? $opfn = $op : $($arg),*];
impl_fp![@$lib : $f : $($rest)*];
};
(
// Matches a single operation and implements it using the `libm` library.
@libm : $f:ty : $($doc:literal)? $opfn:ident = $op:ident : $($arg:ident),*) => {
$(#[doc = $doc])?
#[must_use]
pub fn $op(self, $($arg: $f),*) -> Float<$f> {
Float($crate::_dep::libm::Libm::<$f>::$opfn(self.0, $($arg),*))
}
};
(
// Matches a single operation and implements it using the `std` library.
@std : $f:ty : $($doc:literal)? $opfn:ident = $op:ident : $($arg:ident),*) => {
$(#[doc = $doc])?
#[must_use]
pub fn $op(self, $($arg: $f),*) -> Float<$f> {
Float(<$f>::$opfn(self.0, $($arg),*))
}
};
}
#[cfg(any(feature = "dep_libm", feature = "std"))]
use impl_fp;