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//! # traits::realfloat
//!
//! Types that implement this trait can be considered as real floating-point numbers.
use crate::number::{
instances::{int::Int, integer::Integer},
traits::{floating::Floating, integral::Integral, one::One, realfrac::RealFrac, zero::Zero},
utils::{clamp, from_integral, integral_power, non_negative_integral_power},
};
/// Concepts of RealFloat.
pub trait RealFloat: RealFrac + Floating {
/// The base of the numerical system.
///
/// The base, also known as "radix" in standards,
/// is typically `2`, which represents binary representation.
/// However, for decimal numbers, the base may be `10`.
const FLOAT_RADIX: Int = Int::of(2);
/// Number of digits in the radix used, including any implicit digit, but not counting the sign bit.
const FLOAT_DIGITS: Int;
/// In the standard representation of floating-point numbers,
/// the range of the exponent is defined as `[-m + 2, m + 1)`
/// if the maximum value of the floating-point exponent is `m`.
const FLOAT_RANGE: (Int, Int);
/// Decode a real floating-point number into its significand and exponent.
///
/// **NEED FIX**
///
/// ```rust,ignore
/// let rfp : F;
/// let (significand, exponent) = rfp.decode_float();
/// let radix = F::FLOAT_RADIX;
/// assert_eq!(significand * integral_power(radix, exponent), rfp);
/// ```
fn decode_float(self) -> (Integer, Int) {
let range = Self::FLOAT_RANGE.1 + Int::one();
let exponent = self
.absolute_value()
.logarithmic_base(from_integral(Self::FLOAT_RADIX))
.ceiling::<Int>();
let modified_exponent = if self.is_zero() {
Int::zero()
} else if exponent.is_zero() {
range - Self::FLOAT_DIGITS
} else {
exponent.clone() - Self::FLOAT_DIGITS
};
let significand =
integral_power(from_integral(Self::FLOAT_RADIX), modified_exponent.clone())
.map(|p| self.clone() / p)
.map(|p| p.to_rational().numerator)
.expect(
"Error[RealFloat::decode_float]: Should be able to produce the correct result.",
);
let significand_range =
non_negative_integral_power(Self::FLOAT_RADIX, Self::FLOAT_DIGITS + Int::one())
.expect(
"Error[RealFloat::decode_float]: Should be able to produce the correct result.",
)
.to_integer();
let modified_significand = if modified_exponent.is_zero() {
significand.modulus(
if self > Self::zero() {
significand_range
} else {
-significand_range
} - Integer::one(),
)
} else {
significand
};
(modified_significand, modified_exponent)
}
/// Encode the given significand and exponent into a floating-point number.
fn encode_float(significand: Integer, exponent: Int) -> Self {
integral_power(from_integral(Self::FLOAT_RADIX), exponent)
.map(|p: Self| p * Self::from_integer(significand))
.expect("Error[RealFloat::encode_float]: Should be able to produce the correct result.")
}
/// Return the actual exponent in the floating-point representation.
///
/// In Haskell, it defines like:
///
/// ```haskell
/// exponent 0 = 0
/// exponent x = snd (decodeFloat x) + floatDigits x
/// ```
fn exponent(self) -> Int {
if self.is_zero() {
Int::zero()
} else {
self.decode_float().1 + Self::FLOAT_DIGITS
}
}
/// Return the actual significand in the floating-point representation.
fn significand(self) -> Self {
Self::encode_float(self.decode_float().0, -Self::FLOAT_DIGITS)
}
/// Multiplies a real floating-point number by an integer power of the radix.
///
/// **NEED FIX**
fn scale_float(self, factor: Int) -> Self {
if self.is_zero() || self.is_not_a_number() || self.is_infinite_number() {
self
} else {
let (significand, exponent) = self.decode_float();
let (lower_boundary, upper_boundary) = Self::FLOAT_RANGE;
let factor_p = upper_boundary - lower_boundary + Int::of(4) * Self::FLOAT_DIGITS;
Self::encode_float(significand, exponent + clamp(factor_p, factor))
}
}
/// Validate whether a given real floating-point number is NaN.
fn is_not_a_number(&self) -> bool;
/// Validate whether a given real floating-point number is Inf.
fn is_infinite_number(&self) -> bool;
/// Validate whether a given real floating-point number is in a denormalized form.
fn is_denormalized(&self) -> bool;
/// Validate whether a given real floating-point number is "negative zero".
fn is_negative_zero(&self) -> bool;
/// The two-parameter arctangent function, atan2(y, x).
fn arc_tangent_2(y: Self, x: Self) -> Self {
if x > Self::zero() {
(y / x).arc_tangent()
} else if x.is_zero() && y > Self::zero() {
Self::PI * Self::half()
} else if x < Self::zero() && y > Self::zero() {
Self::PI + (y / x).arc_tangent()
} else if (x <= Self::zero() && y < Self::zero())
|| (x < Self::zero() && y.is_negative_zero())
|| (x.is_negative_zero() && y.is_negative_zero())
{
-Self::arc_tangent_2(-y, x)
} else if y.is_zero() && (x < Self::zero() || x.is_negative_zero()) {
Self::PI
} else if x.is_zero() && y.is_zero() {
y
} else {
x + y
}
}
}