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use malachite_base::num::arithmetic::traits::DivRound;
use malachite_base::num::basic::floats::PrimitiveFloat;
use malachite_base::num::conversion::traits::{
ExactFrom, IntegerMantissaAndExponent, SciMantissaAndExponent, WrappingFrom,
};
use malachite_base::num::logic::traits::{BitAccess, SignificantBits};
use malachite_base::rounding_modes::RoundingMode;
use std::cmp::Ordering;
use Rational;
impl Rational {
/// Returns a [`Rational`]'s scientific mantissa and exponent, taking the [`Rational`] by
/// value.
///
/// When $x$ is positive, we can write $x = 2^{e_s}m_s$, where $e_s$ is an integer and $m_s$ is
/// a rational number with $1 \leq m_s < 2$. We represent the rational mantissa as a float. The
/// conversion might not be exact, so we round to the nearest float using the provided rounding
/// mode. If the rounding mode is `Exact` but the conversion is not exact, `None` is returned.
/// $$
/// f(x, r) \approx \left (\frac{x}{2^{\lfloor \log_2 x \rfloor}},
/// \lfloor \log_2 x \rfloor\right ).
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::Pow;
/// use malachite_base::num::conversion::traits::SciMantissaAndExponent;
/// use malachite_base::num::float::NiceFloat;
/// use malachite_base::rounding_modes::RoundingMode;
/// use malachite_q::Rational;
///
/// let test = |n: Rational, rm: RoundingMode, out: Option<(f32, i64)>| {
/// assert_eq!(
/// n.sci_mantissa_and_exponent_with_rounding(rm)
/// .map(|(m, e)| (NiceFloat(m), e)),
/// out.map(|(m, e)| (NiceFloat(m), e))
/// );
/// };
/// test(Rational::from(3u32), RoundingMode::Down, Some((1.5, 1)));
/// test(Rational::from(3u32), RoundingMode::Ceiling, Some((1.5, 1)));
/// test(Rational::from(3u32), RoundingMode::Up, Some((1.5, 1)));
/// test(Rational::from(3u32), RoundingMode::Nearest, Some((1.5, 1)));
/// test(Rational::from(3u32), RoundingMode::Exact, Some((1.5, 1)));
///
/// test(Rational::from_signeds(1, 3), RoundingMode::Floor, Some((1.3333333, -2)));
/// test(Rational::from_signeds(1, 3), RoundingMode::Down, Some((1.3333333, -2)));
/// test(Rational::from_signeds(1, 3), RoundingMode::Ceiling, Some((1.3333334, -2)));
/// test(Rational::from_signeds(1, 3), RoundingMode::Up, Some((1.3333334, -2)));
/// test(Rational::from_signeds(1, 3), RoundingMode::Nearest, Some((1.3333334, -2)));
/// test(Rational::from_signeds(1, 3), RoundingMode::Exact, None);
/// ```
pub fn sci_mantissa_and_exponent_with_rounding<T: PrimitiveFloat>(
mut self,
rm: RoundingMode,
) -> Option<(T, i64)> {
assert!(self != 0);
let mut exponent = i64::exact_from(self.numerator.significant_bits())
- i64::exact_from(self.denominator.significant_bits());
if self.numerator.cmp_normalized(&self.denominator) == Ordering::Less {
exponent -= 1;
}
self >>= exponent - i64::wrapping_from(T::MANTISSA_WIDTH);
let (n, d) = self.into_numerator_and_denominator();
if rm == RoundingMode::Exact && d != 1u32 {
return None;
}
let mut mantissa = n.div_round(d, rm);
let mut bits = mantissa.significant_bits();
if bits > T::MANTISSA_WIDTH + 1 {
bits -= 1;
mantissa >>= 1;
exponent += 1;
}
assert_eq!(bits, T::MANTISSA_WIDTH + 1);
mantissa.clear_bit(T::MANTISSA_WIDTH);
Some((
T::from_raw_mantissa_and_exponent(
u64::exact_from(&mantissa),
u64::wrapping_from(T::MAX_EXPONENT),
),
exponent,
))
}
/// Returns a [`Rational`]'s scientific mantissa and exponent, taking the [`Rational`] by
/// reference.
///
/// When $x$ is positive, we can write $x = 2^{e_s}m_s$, where $e_s$ is an integer and $m_s$ is
/// a rational number with $1 \leq m_s < 2$. We represent the rational mantissa as a float. The
/// conversion might not be exact, so we round to the nearest float using the provided rounding
/// mode. If the rounding mode is `Exact` but the conversion is not exact, `None` is returned.
/// $$
/// f(x, r) \approx \left (\frac{x}{2^{\lfloor \log_2 x \rfloor}},
/// \lfloor \log_2 x \rfloor\right ).
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// extern crate malachite_base;
///
/// use malachite_base::num::arithmetic::traits::Pow;
/// use malachite_base::num::conversion::traits::SciMantissaAndExponent;
/// use malachite_base::num::float::NiceFloat;
/// use malachite_base::rounding_modes::RoundingMode;
/// use malachite_q::Rational;
///
/// let test = |n: Rational, rm: RoundingMode, out: Option<(f32, i64)>| {
/// assert_eq!(
/// (&n).sci_mantissa_and_exponent_with_rounding_ref(rm)
/// .map(|(m, e)| (NiceFloat(m), e)),
/// out.map(|(m, e)| (NiceFloat(m), e))
/// );
/// };
/// test(Rational::from(3u32), RoundingMode::Down, Some((1.5, 1)));
/// test(Rational::from(3u32), RoundingMode::Ceiling, Some((1.5, 1)));
/// test(Rational::from(3u32), RoundingMode::Up, Some((1.5, 1)));
/// test(Rational::from(3u32), RoundingMode::Nearest, Some((1.5, 1)));
/// test(Rational::from(3u32), RoundingMode::Exact, Some((1.5, 1)));
///
/// test(Rational::from_signeds(1, 3), RoundingMode::Floor, Some((1.3333333, -2)));
/// test(Rational::from_signeds(1, 3), RoundingMode::Down, Some((1.3333333, -2)));
/// test(Rational::from_signeds(1, 3), RoundingMode::Ceiling, Some((1.3333334, -2)));
/// test(Rational::from_signeds(1, 3), RoundingMode::Up, Some((1.3333334, -2)));
/// test(Rational::from_signeds(1, 3), RoundingMode::Nearest, Some((1.3333334, -2)));
/// test(Rational::from_signeds(1, 3), RoundingMode::Exact, None);
/// ```
pub fn sci_mantissa_and_exponent_with_rounding_ref<T: PrimitiveFloat>(
&self,
rm: RoundingMode,
) -> Option<(T, i64)> {
assert!(*self != 0);
let mut exponent = i64::exact_from(self.numerator.significant_bits())
- i64::exact_from(self.denominator.significant_bits());
if self.numerator.cmp_normalized(&self.denominator) == Ordering::Less {
exponent -= 1;
}
let x = self >> (exponent - i64::wrapping_from(T::MANTISSA_WIDTH));
let (n, d) = x.into_numerator_and_denominator();
if rm == RoundingMode::Exact && d != 1u32 {
return None;
}
let mut mantissa = n.div_round(d, rm);
let mut bits = mantissa.significant_bits();
if bits > T::MANTISSA_WIDTH + 1 {
bits -= 1;
mantissa >>= 1;
exponent += 1;
}
assert_eq!(bits, T::MANTISSA_WIDTH + 1);
mantissa.clear_bit(T::MANTISSA_WIDTH);
Some((
T::from_raw_mantissa_and_exponent(
u64::exact_from(&mantissa),
u64::wrapping_from(T::MAX_EXPONENT),
),
exponent,
))
}
}
macro_rules! impl_mantissa_and_exponent {
($t:ident) => {
impl SciMantissaAndExponent<$t, i64> for Rational {
/// Returns a [`Rational`]'s scientific mantissa and exponent, taking the [`Rational`]
/// by value.
///
/// When $x$ is positive, we can write $x = 2^{e_s}m_s$, where $e_s$ is an integer and
/// $m_s$ is a rational number with $1 \leq m_s < 2$. We represent the rational
/// mantissa as a float. The conversion might not be exact, so we round to the nearest
/// float using the `Nearest` rounding mode. To use other rounding modes, use
/// [`sci_mantissa_and_exponent_with_rounding`](Rational::sci_mantissa_and_exponent_with_rounding).
/// $$
/// f(x) \approx (\frac{x}{2^{\lfloor \log_2 x \rfloor}}, \lfloor \log_2 x \rfloor).
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// See [here](super::mantissa_and_exponent#sci_mantissa_and_exponent).
#[inline]
fn sci_mantissa_and_exponent(self) -> ($t, i64) {
self.sci_mantissa_and_exponent_with_rounding(RoundingMode::Nearest)
.unwrap()
}
/// Returns a [`Rational`]'s scientific exponent, taking the [`Rational`] by value.
///
/// When $x$ is positive, we can write $x = 2^{e_s}m_s$, where $e_s$ is an integer and
/// $m_s$ is a rational number with $1 \leq m_s < 2$. We represent the rational
/// mantissa as a float. The conversion might not be exact, so we round to the nearest
/// float using the `Nearest` rounding mode. To use other rounding modes, use
/// [`sci_mantissa_and_exponent_with_rounding`](Rational::sci_mantissa_and_exponent_with_rounding).
/// $$
/// f(x) \approx \lfloor \log_2 x \rfloor.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// See [here](super::mantissa_and_exponent#sci_exponent).
fn sci_exponent(mut self) -> i64 {
assert!(self != 0);
let mut exponent = i64::exact_from(self.numerator.significant_bits())
- i64::exact_from(self.denominator.significant_bits());
if self.numerator.cmp_normalized(&self.denominator) == Ordering::Less {
exponent -= 1;
}
self >>= exponent - i64::wrapping_from($t::MANTISSA_WIDTH);
let (n, d) = self.into_numerator_and_denominator();
if n.div_round(d, RoundingMode::Nearest).significant_bits() > $t::MANTISSA_WIDTH + 1
{
exponent + 1
} else {
exponent
}
}
/// Constructs a [`Rational`] from its scientific mantissa and exponent.
///
/// When $x$ is positive, we can write $x = 2^{e_s}m_s$, where $e_s$ is an integer and
/// $m_s$ is a rational number with $1 \leq m_s < 2$. Here, the rational mantissa is
/// provided as a float. If the mantissa is outside the range $[1, 2)$, `None` is
/// returned.
///
/// All finite floats can be represented using [`Rational`]s, so no rounding is needed.
///
/// $$
/// f(x) \approx 2^{e_s}m_s.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `sci_exponent`.
#[allow(clippy::manual_range_contains)]
#[inline]
fn from_sci_mantissa_and_exponent(
sci_mantissa: $t,
sci_exponent: i64,
) -> Option<Rational> {
assert_ne!(sci_mantissa, 0.0);
if sci_mantissa < 1.0 || sci_mantissa >= 2.0 {
None
} else {
let m = sci_mantissa.integer_mantissa();
Some(
Rational::from(m)
<< (sci_exponent - i64::exact_from(m.significant_bits()) + 1),
)
}
}
}
impl<'a> SciMantissaAndExponent<$t, i64, Rational> for &'a Rational {
/// Returns a [`Rational`]'s scientific mantissa and exponent, taking the [`Rational`]
/// by reference.
///
/// When $x$ is positive, we can write $x = 2^{e_s}m_s$, where $e_s$ is an integer and
/// $m_s$ is a rational number with $1 \leq m_s < 2$. We represent the rational
/// mantissa as a float. The conversion might not be exact, so we round to the nearest
/// float using the `Nearest` rounding mode. To use other rounding modes, use
/// [`sci_mantissa_and_exponent_with_rounding`](Rational::sci_mantissa_and_exponent_with_rounding).
/// $$
/// f(x) \approx (\frac{x}{2^{\lfloor \log_2 x \rfloor}}, \lfloor \log_2 x \rfloor).
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// See [here](super::mantissa_and_exponent#sci_mantissa_and_exponent).
#[inline]
fn sci_mantissa_and_exponent(self) -> ($t, i64) {
self.sci_mantissa_and_exponent_with_rounding_ref(RoundingMode::Nearest)
.unwrap()
}
/// Returns a [`Rational`]'s scientific exponent, taking the [`Rational`] by reference.
///
/// When $x$ is positive, we can write $x = 2^{e_s}m_s$, where $e_s$ is an integer and
/// $m_s$ is a rational number with $1 \leq m_s < 2$. We represent the rational
/// mantissa as a float. The conversion might not be exact, so we round to the nearest
/// float using the `Nearest` rounding mode. To use other rounding modes, use
/// [`sci_mantissa_and_exponent_with_rounding`](Rational::sci_mantissa_and_exponent_with_rounding).
/// $$
/// f(x) \approx \lfloor \log_2 x \rfloor.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
fn sci_exponent(self) -> i64 {
assert!(*self != 0);
let mut exponent = i64::exact_from(self.numerator.significant_bits())
- i64::exact_from(self.denominator.significant_bits());
if self.numerator.cmp_normalized(&self.denominator) == Ordering::Less {
exponent -= 1;
}
let x = self >> exponent - i64::wrapping_from($t::MANTISSA_WIDTH);
let (n, d) = x.into_numerator_and_denominator();
if n.div_round(d, RoundingMode::Nearest).significant_bits() > $t::MANTISSA_WIDTH + 1
{
exponent + 1
} else {
exponent
}
}
/// Constructs a [`Rational`] from its scientific mantissa and exponent.
///
/// When $x$ is positive, we can write $x = 2^{e_s}m_s$, where $e_s$ is an integer and
/// $m_s$ is a rational number with $1 \leq m_s < 2$. Here, the rational mantissa is
/// provided as a float. If the mantissa is outside the range $[1, 2)$, `None` is
/// returned.
///
/// All finite floats can be represented using [`Rational`]s, so no rounding is needed.
///
/// $$
/// f(x) \approx 2^{e_s}m_s.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `sci_exponent`.
///
/// See [here](super::mantissa_and_exponent#from_sci_mantissa_and_exponent).
#[inline]
fn from_sci_mantissa_and_exponent(
sci_mantissa: $t,
sci_exponent: i64,
) -> Option<Rational> {
Rational::from_sci_mantissa_and_exponent(sci_mantissa, sci_exponent)
}
}
};
}
apply_to_primitive_floats!(impl_mantissa_and_exponent);