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use std::{cmp::Ordering, num::FpCategory};
use crate::{FloatConst, Num, Signed, UnsignedInt};
/// Flating point types.
///
/// Exposes:
/// - The `Num` trait
/// - Floating point constants
/// - Floating point functionality
///
/// See [`f32`] or [`f64`].
///
/// [`f32`]: https://doc.rust-lang.org/std/primitive.f32.html
/// [`f64`]: https://doc.rust-lang.org/std/primitive.f64.html
pub trait Float: Num + FloatConst + Signed {
/// The unsigned integer variant of the type with the same size.
///
/// This is not normally defined for floats and is only here to be the
/// return type of `.to_bits` and input for `.from_bits`.
type Bits: UnsignedInt;
/// The byte array variant of the type with the same size.
///
/// This is not normally defined for floats and is only here for the
/// to/from endian functons.
type Bytes;
/// The radix or base of the internal representation.
const RADIX: u32;
/// Number of significant digits in base 2.
const MANTISSA_DIGITS: u32;
/// Approximate number of significant digits in base 10.
const DIGITS: u32;
/// Machine epsilon value for this floating point type.
const EPSILON: Self;
/// Smallest positive normal value.
const MIN_POSITIVE: Self;
/// One greater than the minimum possible normal power of 2 exponent.
const MIN_EXP: i32;
/// One greater than the maximum possible power of 2 exponent.
const MAX_EXP: i32;
/// Minimum x for which 10^x is normal.
const MIN_10_EXP: i32;
/// Maximum x for which 10^x is normal.
const MAX_10_EXP: i32;
/// Not a Number (NaN).
const NAN: Self;
/// Infinity (∞).
const INFINITY: Self;
/// Negative infinity (−∞).
const NEG_INFINITY: Self;
/// Returns the largest integer less than or equal to `self`.
#[must_use]
fn floor(self) -> Self;
/// Returns the smallest integer greater than or equal to `self`.
#[must_use]
fn ceil(self) -> Self;
/// Returns the nearest integer to `self`.
#[must_use]
fn round(self) -> Self;
/// Returns the nearest integer to a number.
#[must_use]
fn round_ties_even(self) -> Self;
/// Returns the integer part of `self`.
#[must_use]
fn trunc(self) -> Self;
/// Returns the fractional part of `self`.
#[must_use]
fn fract(self) -> Self;
/// Fused multiply-add.
#[must_use]
fn mul_add(self, a: Self, b: Self) -> Self;
/// Calculates Euclidean division, the matching method for `rem_euclid`.
#[must_use]
fn div_euclid(self, rhs: Self) -> Self;
/// Calculates the least nonnegative remainder of `self (mod rhs)`.
#[must_use]
fn rem_euclid(self, rhs: Self) -> Self;
/// Raises a number to an integer power.
#[must_use]
fn powi(self, n: i32) -> Self;
/// Raises a number to a floating point power.
#[must_use]
fn powf(self, n: Self) -> Self;
/// Returns the square root of a number.
#[must_use]
fn sqrt(self) -> Self;
/// Returns `e^(self)`.
#[must_use]
fn exp(self) -> Self;
/// Returns `2^(self)`.
#[must_use]
fn exp2(self) -> Self;
/// Returns the natural logarithm of a number.
#[must_use]
fn ln(self) -> Self;
/// Returns the logarithm of the number with respect to an arbitrary base.
#[must_use]
fn log(self, base: Self) -> Self;
/// Returns the base 2 logarithm of the number.
#[must_use]
fn log2(self) -> Self;
/// Returns the base 10 logarithm of the number.
#[must_use]
fn log10(self) -> Self;
/// Returns the cube root of a number.
#[must_use]
fn cbrt(self) -> Self;
/// Compute the distance between the origin and a point (`x`, `y`) on the Euclidean plane.
#[must_use]
fn hypot(self, other: Self) -> Self;
/// Computes the sine of a number (in radians).
#[must_use]
fn sin(self) -> Self;
/// Computes the cosine of a number (in radians).
#[must_use]
fn cos(self) -> Self;
/// Computes the tangent of a number (in radians).
#[must_use]
fn tan(self) -> Self;
/// Computes the arcsine of a number.
#[must_use]
fn asin(self) -> Self;
/// Computes the arccosine of a number.
#[must_use]
fn acos(self) -> Self;
/// Computes the arctangent of a number.
#[must_use]
fn atan(self) -> Self;
/// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).
#[must_use]
fn atan2(self, other: Self) -> Self;
/// Simultaneously computes the sine and cosine of the number, `x`.
#[must_use]
fn sin_cos(self) -> (Self, Self);
/// Returns `e^(self) - 1` in a way that is accurate even if the number is close to zero.
#[must_use]
fn exp_m1(self) -> Self;
/// Returns `ln(1+n)` (natural logarithm) more accurately than if the operations were performed separately.
#[must_use]
fn ln_1p(self) -> Self;
/// Hyperbolic sine function.
#[must_use]
fn sinh(self) -> Self;
/// Hyperbolic cosine function.
#[must_use]
fn cosh(self) -> Self;
/// Hyperbolic tangent function.
#[must_use]
fn tanh(self) -> Self;
/// Inverse hyperbolic sine function.
#[must_use]
fn asinh(self) -> Self;
/// Inverse hyperbolic cosine function.
#[must_use]
fn acosh(self) -> Self;
/// Inverse hyperbolic tangent function.
#[must_use]
fn atanh(self) -> Self;
/// Returns `true` if this value is NaN.
#[must_use]
fn is_nan(self) -> bool;
/// Returns `true` if this value is positive or negative infinity.
#[must_use]
fn is_infinite(self) -> bool;
/// Returns `true` if this number is neither infinite nor NaN.
#[must_use]
fn is_finite(self) -> bool;
/// Returns `true` if the number is subnormal.
#[must_use]
fn is_subnormal(self) -> bool;
/// Returns `true` if the number is neither zero, infinite, subnormal, or NaN.
#[must_use]
fn is_normal(self) -> bool;
/// Returns the floating point category of the number.
#[must_use]
fn classify(self) -> FpCategory;
/// Returns `true` if `self` has a positive sign.
#[must_use]
fn is_sign_positive(self) -> bool;
/// Returns `true` if `self` has a negative sign.
#[must_use]
fn is_sign_negative(self) -> bool;
/// Returns the least number greater than `self`.
#[must_use]
fn next_up(self) -> Self;
/// Returns the greatest number less than `self`.
#[must_use]
fn next_down(self) -> Self;
/// Takes the reciprocal (inverse) of a number, `1/x`.
#[must_use]
fn recip(self) -> Self;
/// Converts radians to degrees.
#[must_use]
fn to_degrees(self) -> Self;
/// Converts degrees to radians.
#[must_use]
fn to_radians(self) -> Self;
/// Returns the maximum of the two numbers, ignoring NaN.
#[deprecated = "Use `NumOrd::max` instead"]
#[must_use]
fn max(self, other: Self) -> Self;
/// Returns the minimum of the two numbers, ignoring NaN.
#[deprecated = "Use `NumOrd::min` instead"]
#[must_use]
fn min(self, other: Self) -> Self;
/// Calculates the midpoint (average) between `self` and `rhs`.
#[must_use]
fn midpoint(self, other: Self) -> Self;
/// Raw transmutation to `u32`.
#[must_use]
fn to_bits(self) -> Self::Bits;
/// Raw transmutation from `u32`.
#[must_use]
fn from_bits(v: Self::Bits) -> Self;
/// Returns the memory representation as a big-endian byte array.
#[must_use]
fn to_be_bytes(self) -> Self::Bytes;
/// Returns the memory representation as a little-endian byte array.
#[must_use]
fn to_le_bytes(self) -> Self::Bytes;
/// Returns the memory representation as a native-endian byte array.
#[must_use]
fn to_ne_bytes(self) -> Self::Bytes;
/// Creates a float from a big-endian byte array.
#[must_use]
fn from_be_bytes(bytes: Self::Bytes) -> Self;
/// Creates a float from a little-endian byte array.
#[must_use]
fn from_le_bytes(bytes: Self::Bytes) -> Self;
/// Creates a float from a native-endian byte array.
#[must_use]
fn from_ne_bytes(bytes: Self::Bytes) -> Self;
/// Returns the ordering between `self` and `other` according to total order.
#[must_use]
fn total_cmp(&self, other: &Self) -> Ordering;
/// Restrict a value to a certain interval unless it is NaN.
#[deprecated = "Use `NumOrd::clamp` instead"]
#[must_use]
fn clamp(self, min: Self, max: Self) -> Self;
/// Returns a number that represents the sign of `self`.
#[must_use]
fn signum(self) -> Self;
/// Returns a number composed of the magnitude of `self` and the sign of `sign`.
#[must_use]
fn copysign(self, sign: Self) -> Self;
}
macro_rules! impl_float {
($($t:ty, $b:ty);* $(;)*) => {
$(
impl Float for $t {
type Bits = $b;
type Bytes = [u8; std::mem::size_of::<Self>()];
const RADIX: u32 = Self::RADIX;
const MANTISSA_DIGITS: u32 = Self::MANTISSA_DIGITS;
const DIGITS: u32 = Self::DIGITS;
const EPSILON: Self = Self::EPSILON;
const MIN_POSITIVE: Self = Self::MIN_POSITIVE;
const MIN_EXP: i32 = Self::MIN_EXP;
const MAX_EXP: i32 = Self::MAX_EXP;
const MIN_10_EXP: i32 = Self::MIN_10_EXP;
const MAX_10_EXP: i32 = Self::MAX_10_EXP;
const NAN: Self = Self::NAN;
const INFINITY: Self = Self::INFINITY;
const NEG_INFINITY: Self = Self::NEG_INFINITY;
#[inline(always)]
fn floor(self) -> Self { Self::floor(self) }
#[inline(always)]
fn ceil(self) -> Self { Self::ceil(self) }
#[inline(always)]
fn round(self) -> Self { Self::round(self) }
#[inline(always)]
fn round_ties_even(self) -> Self { Self::round_ties_even(self) }
#[inline(always)]
fn trunc(self) -> Self { Self::trunc(self) }
#[inline(always)]
fn fract(self) -> Self { Self::fract(self) }
#[inline(always)]
fn mul_add(self, a: Self, b: Self) -> Self { Self::mul_add(self, a, b) }
#[inline(always)]
fn div_euclid(self, rhs: Self) -> Self { Self::div_euclid(self, rhs) }
#[inline(always)]
fn rem_euclid(self, rhs: Self) -> Self { Self::rem_euclid(self, rhs) }
#[inline(always)]
fn powi(self, n: i32) -> Self { Self::powi(self, n) }
#[inline(always)]
fn powf(self, n: Self) -> Self { Self::powf(self, n) }
#[inline(always)]
fn sqrt(self) -> Self { Self::sqrt(self) }
#[inline(always)]
fn exp(self) -> Self { Self::exp(self) }
#[inline(always)]
fn exp2(self) -> Self { Self::exp2(self) }
#[inline(always)]
fn ln(self) -> Self { Self::ln(self) }
#[inline(always)]
fn log(self, base: Self) -> Self { Self::log(self, base) }
#[inline(always)]
fn log2(self) -> Self { Self::log2(self) }
#[inline(always)]
fn log10(self) -> Self { Self::log10(self) }
#[inline(always)]
fn cbrt(self) -> Self { Self::cbrt(self) }
#[inline(always)]
fn hypot(self, other: Self) -> Self { Self::hypot(self, other) }
#[inline(always)]
fn sin(self) -> Self { Self::sin(self) }
#[inline(always)]
fn cos(self) -> Self { Self::cos(self) }
#[inline(always)]
fn tan(self) -> Self { Self::tan(self) }
#[inline(always)]
fn asin(self) -> Self { Self::asin(self) }
#[inline(always)]
fn acos(self) -> Self { Self::acos(self) }
#[inline(always)]
fn atan(self) -> Self { Self::atan(self) }
#[inline(always)]
fn atan2(self, other: Self) -> Self { Self::atan2(self, other) }
#[inline(always)]
fn sin_cos(self) -> (Self, Self) { Self::sin_cos(self) }
#[inline(always)]
fn exp_m1(self) -> Self { Self::exp_m1(self) }
#[inline(always)]
fn ln_1p(self) -> Self { Self::ln_1p(self) }
#[inline(always)]
fn sinh(self) -> Self { Self::sinh(self) }
#[inline(always)]
fn cosh(self) -> Self { Self::cosh(self) }
#[inline(always)]
fn tanh(self) -> Self { Self::tanh(self) }
#[inline(always)]
fn asinh(self) -> Self { Self::asinh(self) }
#[inline(always)]
fn acosh(self) -> Self { Self::acosh(self) }
#[inline(always)]
fn atanh(self) -> Self { Self::atanh(self) }
#[inline(always)]
fn is_nan(self) -> bool { Self::is_nan(self) }
#[inline(always)]
fn is_infinite(self) -> bool { Self::is_infinite(self) }
#[inline(always)]
fn is_finite(self) -> bool { Self::is_finite(self) }
#[inline(always)]
fn is_subnormal(self) -> bool { Self::is_subnormal(self) }
#[inline(always)]
fn is_normal(self) -> bool { Self::is_normal(self) }
#[inline(always)]
fn classify(self) -> FpCategory { Self::classify(self) }
#[inline(always)]
fn is_sign_positive(self) -> bool { Self::is_sign_positive(self) }
#[inline(always)]
fn is_sign_negative(self) -> bool { Self::is_sign_negative(self) }
#[inline(always)]
fn next_up(self) -> Self { Self::next_up(self) }
#[inline(always)]
fn next_down(self) -> Self { Self::next_down(self) }
#[inline(always)]
fn recip(self) -> Self { Self::recip(self) }
#[inline(always)]
fn to_degrees(self) -> Self { Self::to_degrees(self) }
#[inline(always)]
fn to_radians(self) -> Self { Self::to_radians(self) }
#[inline(always)]
fn max(self, other: Self) -> Self { Self::max(self, other) }
#[inline(always)]
fn min(self, other: Self) -> Self { Self::min(self, other) }
#[inline(always)]
fn midpoint(self, other: Self) -> Self { Self::midpoint(self, other) }
#[inline(always)]
fn to_bits(self) -> Self::Bits { Self::to_bits(self) }
#[inline(always)]
fn from_bits(v: Self::Bits) -> Self { Self::from_bits(v) }
#[inline(always)]
fn to_be_bytes(self) -> Self::Bytes { Self::to_be_bytes(self) }
#[inline(always)]
fn to_le_bytes(self) -> Self::Bytes { Self::to_le_bytes(self) }
#[inline(always)]
fn to_ne_bytes(self) -> Self::Bytes { Self::to_ne_bytes(self) }
#[inline(always)]
fn from_be_bytes(bytes: Self::Bytes) -> Self { Self::from_be_bytes(bytes) }
#[inline(always)]
fn from_le_bytes(bytes: Self::Bytes) -> Self { Self::from_le_bytes(bytes) }
#[inline(always)]
fn from_ne_bytes(bytes: Self::Bytes) -> Self { Self::from_ne_bytes(bytes) }
#[inline(always)]
fn total_cmp(&self, other: &Self) -> Ordering { Self::total_cmp(self, other) }
#[inline(always)]
fn clamp(self, min: Self, max: Self) -> Self { Self::clamp(self, min, max) }
#[inline(always)]
fn signum(self) -> Self { Self::signum(self) }
#[inline(always)]
fn copysign(self, sign: Self) -> Self { Self::copysign(self, sign) }
}
)*
};
}
impl_float!(
f32, u32;
f64, u64;
);