Struct rug::float::BorrowFloat

#[repr(transparent)]
pub struct BorrowFloat<'a> { /* private fields */ }

Used to get a reference to a Float.

The struct implements Deref<Target = Float>.

No memory is unallocated when this struct is dropped.

Examples

use rug::{float::BorrowFloat, Float};
let f = Float::with_val(53, 4.2);
let neg: BorrowFloat = f.as_neg();
// f is still valid
assert_eq!(f, 4.2);
assert_eq!(*neg, -4.2);

Implementations

impl BorrowFloat<'_>

pub unsafe fn from_raw<'a>(raw: mpfr_t) -> BorrowFloat<'a>

Create a borrow from a raw MPFR floating-point number.

Safety

• The value must be initialized.
• The mpfr_t type can be considered as a kind of pointer, so there can be multiple copies of it. BorrowFloat cannot mutate the value, so there can be other copies, but none of them are allowed to mutate the value.
• The lifetime is obtained from the return type. The user must ensure the value remains valid for the duration of the lifetime.

Examples

use rug::{float::BorrowFloat, Float};
let f = Float::with_val(53, 4.2);
// Safety: f.as_raw() is a valid pointer.
let raw = unsafe { *f.as_raw() };
// Safety: f is still valid when borrow is used.
let borrow = unsafe { BorrowFloat::from_raw(raw) };
assert_eq!(f, *borrow);

Methods from Deref<Target = Float>

pub fn prec(&self) -> u32

Returns the precision.

Examples

use rug::Float;
let f = Float::new(53);
assert_eq!(f.prec(), 53);

pub fn as_raw(&self) -> *const mpfr_t

Returns a pointer to the inner MPFR floating-point number.

The returned pointer will be valid for as long as self is valid.

Examples

use gmp_mpfr_sys::mpfr::{self, rnd_t};
use rug::Float;
let f = Float::with_val(53, -14.5);
let m_ptr = f.as_raw();
unsafe {
    let d = mpfr::get_d(m_ptr, rnd_t::RNDN);
    assert_eq!(d, -14.5);
}
// f is still valid
assert_eq!(f, -14.5);

pub fn to_integer(&self) -> Option<Integer>

If the value is a finite number, converts it to an Integer rounding to the nearest.

This conversion can also be performed using

• (&float).checked_as::<Integer>()
• float.borrow().checked_as::<Integer>()

Examples

use rug::Float;
let f = Float::with_val(53, 13.7);
let i = match f.to_integer() {
    Some(i) => i,
    None => unreachable!(),
};
assert_eq!(i, 14);

pub fn to_integer_round(&self, round: Round) -> Option<(Integer, Ordering)>

If the value is a finite number, converts it to an Integer applying the specified rounding method.

Examples

use core::cmp::Ordering;
use rug::{float::Round, Float};
let f = Float::with_val(53, 13.7);
let (i, dir) = match f.to_integer_round(Round::Down) {
    Some(i_dir) => i_dir,
    None => unreachable!(),
};
assert_eq!(i, 13);
assert_eq!(dir, Ordering::Less);

pub fn to_integer_exp(&self) -> Option<(Integer, i32)>

If the value is a finite number, returns an Integer and exponent such that it is exactly equal to the integer multiplied by two raised to the power of the exponent.

Examples

use rug::{float::Special, Assign, Float};
let mut float = Float::with_val(16, 6.5);
// 6.5 in binary is 110.1
// Since the precision is 16 bits, this becomes
// 1101_0000_0000_0000 times two to the power of -12
let (int, exp) = float.to_integer_exp().unwrap();
assert_eq!(int, 0b1101_0000_0000_0000);
assert_eq!(exp, -13);

float.assign(0);
let (zero, _) = float.to_integer_exp().unwrap();
assert_eq!(zero, 0);

float.assign(Special::Infinity);
assert!(float.to_integer_exp().is_none());

pub fn to_rational(&self) -> Option<Rational>

If the value is a finite number, returns a Rational number preserving all the precision of the value.

This conversion can also be performed using

• Rational::try_from(&float)
• Rational::try_from(float)
• (&float).checked_as::<Rational>()
• float.borrow().checked_as::<Rational>()

Examples

use core::{cmp::Ordering, str::FromStr};
use rug::{float::Round, Float, Rational};

// Consider the number 123,456,789 / 10,000,000,000.
let parse = Float::parse("0.0123456789").unwrap();
let (f, f_rounding) = Float::with_val_round(35, parse, Round::Down);
assert_eq!(f_rounding, Ordering::Less);
let r = Rational::from_str("123456789/10000000000").unwrap();
// Set fr to the value of f exactly.
let fr = f.to_rational().unwrap();
// Since f == fr and f was rounded down, r != fr.
assert_ne!(r, fr);
let (frf, frf_rounding) = Float::with_val_round(35, &fr, Round::Down);
assert_eq!(frf_rounding, Ordering::Equal);
assert_eq!(frf, f);
assert_eq!(format!("{:.9}", frf), "1.23456789e-2");

In the following example, the Float values can be represented exactly.

use rug::Float;

let large_f = Float::with_val(16, 6.5);
let large_r = large_f.to_rational().unwrap();
let small_f = Float::with_val(16, -0.125);
let small_r = small_f.to_rational().unwrap();

assert_eq!(*large_r.numer(), 13);
assert_eq!(*large_r.denom(), 2);
assert_eq!(*small_r.numer(), -1);
assert_eq!(*small_r.denom(), 8);

pub fn to_i32_saturating(&self) -> Option<i32>

Converts to an i32, rounding to the nearest.

If the value is too small or too large for the target type, the minimum or maximum value allowed is returned. If the value is a NaN, None is returned.

Examples

use core::{i32, u32};
use rug::{Assign, Float};
let mut f = Float::with_val(53, -13.7);
assert_eq!(f.to_i32_saturating(), Some(-14));
f.assign(-1e40);
assert_eq!(f.to_i32_saturating(), Some(i32::MIN));
f.assign(u32::MAX);
assert_eq!(f.to_i32_saturating(), Some(i32::MAX));

pub fn to_i32_saturating_round(&self, round: Round) -> Option<i32>

Converts to an i32, applying the specified rounding method.

If the value is too small or too large for the target type, the minimum or maximum value allowed is returned. If the value is a NaN, None is returned.

Examples

use rug::{float::Round, Float};
let f = Float::with_val(53, -13.7);
assert_eq!(f.to_i32_saturating_round(Round::Up), Some(-13));

pub fn to_u32_saturating(&self) -> Option<u32>

Converts to a u32, rounding to the nearest.

If the value is too small or too large for the target type, the minimum or maximum value allowed is returned. If the value is a NaN, None is returned.

Examples

use core::u32;
use rug::{Assign, Float};
let mut f = Float::with_val(53, 13.7);
assert_eq!(f.to_u32_saturating(), Some(14));
f.assign(-1);
assert_eq!(f.to_u32_saturating(), Some(0));
f.assign(1e40);
assert_eq!(f.to_u32_saturating(), Some(u32::MAX));

pub fn to_u32_saturating_round(&self, round: Round) -> Option<u32>

Converts to a u32, applying the specified rounding method.

If the value is too small or too large for the target type, the minimum or maximum value allowed is returned. If the value is a NaN, None is returned.

Examples

use rug::{float::Round, Float};
let f = Float::with_val(53, 13.7);
assert_eq!(f.to_u32_saturating_round(Round::Down), Some(13));

pub fn to_f32(&self) -> f32

Converts to an f32, rounding to the nearest.

If the value is too small or too large for the target type, the minimum or maximum value allowed is returned.

Examples

use core::f32;
use rug::{Assign, Float};
let mut f = Float::with_val(53, 13.7);
assert_eq!(f.to_f32(), 13.7);
f.assign(1e300);
assert_eq!(f.to_f32(), f32::INFINITY);
f.assign(1e-300);
assert_eq!(f.to_f32(), 0.0);

pub fn to_f32_round(&self, round: Round) -> f32

Converts to an f32, applying the specified rounding method.

If the value is too small or too large for the target type, the minimum or maximum value allowed is returned.

Examples

use core::f32;
use rug::{float::Round, Float};
let f = Float::with_val(53, 1.0 + (-50f64).exp2());
assert_eq!(f.to_f32_round(Round::Up), 1.0 + f32::EPSILON);

pub fn to_f64(&self) -> f64

Converts to an f64, rounding to the nearest.

If the value is too small or too large for the target type, the minimum or maximum value allowed is returned.

Examples

use core::f64;
use rug::{Assign, Float};
let mut f = Float::with_val(53, 13.7);
assert_eq!(f.to_f64(), 13.7);
f.assign(1e300);
f.square_mut();
assert_eq!(f.to_f64(), f64::INFINITY);

pub fn to_f64_round(&self, round: Round) -> f64

Converts to an f64, applying the specified rounding method.

If the value is too small or too large for the target type, the minimum or maximum value allowed is returned.

Examples

use core::f64;
use rug::{float::Round, Float};
// (2.0 ^ -90) + 1
let f: Float = Float::with_val(100, -90).exp2() + 1;
assert_eq!(f.to_f64_round(Round::Up), 1.0 + f64::EPSILON);

pub fn to_f32_exp(&self) -> (f32, i32)

Converts to an f32 and an exponent, rounding to the nearest.

The returned f32 is in the range 0.5 ≤ x < 1.

If the value is too small or too large for the target type, the minimum or maximum value allowed is returned.

Examples

use rug::Float;
let zero = Float::new(64);
let (d0, exp0) = zero.to_f32_exp();
assert_eq!((d0, exp0), (0.0, 0));
let three_eighths = Float::with_val(64, 0.375);
let (d3_8, exp3_8) = three_eighths.to_f32_exp();
assert_eq!((d3_8, exp3_8), (0.75, -1));

pub fn to_f32_exp_round(&self, round: Round) -> (f32, i32)

Converts to an f32 and an exponent, applying the specified rounding method.

The returned f32 is in the range 0.5 ≤ x < 1.

If the value is too small or too large for the target type, the minimum or maximum value allowed is returned.

Examples

use rug::{float::Round, Float};
let frac_10_3 = Float::with_val(64, 10) / 3u32;
let (f_down, exp_down) = frac_10_3.to_f32_exp_round(Round::Down);
assert_eq!((f_down, exp_down), (0.8333333, 2));
let (f_up, exp_up) = frac_10_3.to_f32_exp_round(Round::Up);
assert_eq!((f_up, exp_up), (0.8333334, 2));

pub fn to_f64_exp(&self) -> (f64, i32)

Converts to an f64 and an exponent, rounding to the nearest.

The returned f64 is in the range 0.5 ≤ x < 1.

If the value is too small or too large for the target type, the minimum or maximum value allowed is returned.

Examples

use rug::Float;
let zero = Float::new(64);
let (d0, exp0) = zero.to_f64_exp();
assert_eq!((d0, exp0), (0.0, 0));
let three_eighths = Float::with_val(64, 0.375);
let (d3_8, exp3_8) = three_eighths.to_f64_exp();
assert_eq!((d3_8, exp3_8), (0.75, -1));

pub fn to_f64_exp_round(&self, round: Round) -> (f64, i32)

Converts to an f64 and an exponent, applying the specified rounding method.

The returned f64 is in the range 0.5 ≤ x < 1.

If the value is too small or too large for the target type, the minimum or maximum value allowed is returned.

Examples

use rug::{float::Round, Float};
let frac_10_3 = Float::with_val(64, 10) / 3u32;
let (f_down, exp_down) = frac_10_3.to_f64_exp_round(Round::Down);
assert_eq!((f_down, exp_down), (0.8333333333333333, 2));
let (f_up, exp_up) = frac_10_3.to_f64_exp_round(Round::Up);
assert_eq!((f_up, exp_up), (0.8333333333333334, 2));

pub fn to_string_radix(&self, radix: i32, num_digits: Option<usize>) -> String

Returns a string representation of self for the specified radix rounding to the nearest.

The exponent is encoded in decimal. If the number of digits is not specified, the output string will have enough precision such that reading it again will give the exact same number.

Panics

Panics if radix is less than 2 or greater than 36.

Examples

use rug::{float::Special, Float};
let neg_inf = Float::with_val(53, Special::NegInfinity);
assert_eq!(neg_inf.to_string_radix(10, None), "-inf");
assert_eq!(neg_inf.to_string_radix(16, None), "-@inf@");
let twentythree = Float::with_val(8, 23);
assert_eq!(twentythree.to_string_radix(10, None), "23.00");
assert_eq!(twentythree.to_string_radix(16, None), "17.0");
assert_eq!(twentythree.to_string_radix(10, Some(2)), "23");
assert_eq!(twentythree.to_string_radix(16, Some(4)), "17.00");
// 2 raised to the power of 80 in hex is 1 followed by 20 zeros
let two_to_80 = Float::with_val(53, 80f64.exp2());
assert_eq!(two_to_80.to_string_radix(10, Some(3)), "1.21e24");
assert_eq!(two_to_80.to_string_radix(16, Some(3)), "1.00@20");

pub fn to_string_radix_round(
    &self,
    radix: i32,
    num_digits: Option<usize>,
    round: Round
) -> String

Returns a string representation of self for the specified radix applying the specified rounding method.

The exponent is encoded in decimal. If the number of digits is not specified, the output string will have enough precision such that reading it again will give the exact same number.

Panics

Panics if radix is less than 2 or greater than 36.

Examples

use rug::{float::Round, Float};
let twentythree = Float::with_val(8, 23.3);
let down = twentythree.to_string_radix_round(10, Some(2), Round::Down);
assert_eq!(down, "23");
let up = twentythree.to_string_radix_round(10, Some(2), Round::Up);
assert_eq!(up, "24");

pub fn to_sign_string_exp(
    &self,
    radix: i32,
    num_digits: Option<usize>
) -> (bool, String, Option<i32>)

Returns a string representation of self together with a sign and an exponent for the specified radix, rounding to the nearest.

The returned exponent is None if the Float is zero, infinite or NaN, that is if the value is not normal.

For normal values, the returned string has an implicit radix point before the first digit. If the number of digits is not specified, the output string will have enough precision such that reading it again will give the exact same number.

Panics

Panics if radix is less than 2 or greater than 36.

Examples

use rug::{float::Special, Float};
let inf = Float::with_val(53, Special::Infinity);
let (sign, s, exp) = inf.to_sign_string_exp(10, None);
assert_eq!((sign, &*s, exp), (false, "inf", None));
let (sign, s, exp) = (-inf).to_sign_string_exp(16, None);
assert_eq!((sign, &*s, exp), (true, "@inf@", None));

let (sign, s, exp) = Float::with_val(8, -0.0625).to_sign_string_exp(10, None);
assert_eq!((sign, &*s, exp), (true, "6250", Some(-1)));
let (sign, s, exp) = Float::with_val(8, -0.625).to_sign_string_exp(10, None);
assert_eq!((sign, &*s, exp), (true, "6250", Some(0)));
let (sign, s, exp) = Float::with_val(8, -6.25).to_sign_string_exp(10, None);
assert_eq!((sign, &*s, exp), (true, "6250", Some(1)));
// -4.8e4 = 48_000, which is rounded to 48_128 using 8 bits of precision
let (sign, s, exp) = Float::with_val(8, -4.8e4).to_sign_string_exp(10, None);
assert_eq!((sign, &*s, exp), (true, "4813", Some(5)));

pub fn to_sign_string_exp_round(
    &self,
    radix: i32,
    num_digits: Option<usize>,
    round: Round
) -> (bool, String, Option<i32>)

Returns a string representation of self together with a sign and an exponent for the specified radix, applying the specified rounding method.

The returned exponent is None if the Float is zero, infinite or NaN, that is if the value is not normal.

For normal values, the returned string has an implicit radix point before the first digit. If the number of digits is not specified, the output string will have enough precision such that reading it again will give the exact same number.

Panics

Panics if radix is less than 2 or greater than 36.

Examples

use rug::{float::Round, Float};
let val = Float::with_val(53, -0.0625);
// rounding -0.0625 to two significant digits towards -∞ gives -0.063
let (sign, s, exp) = val.to_sign_string_exp_round(10, Some(2), Round::Down);
assert_eq!((sign, &*s, exp), (true, "63", Some(-1)));
// rounding -0.0625 to two significant digits towards +∞ gives -0.062
let (sign, s, exp) = val.to_sign_string_exp_round(10, Some(2), Round::Up);
assert_eq!((sign, &*s, exp), (true, "62", Some(-1)));

let val = Float::with_val(53, 6.25e4);
// rounding 6.25e4 to two significant digits towards -∞ gives 6.2e4
let (sign, s, exp) = val.to_sign_string_exp_round(10, Some(2), Round::Down);
assert_eq!((sign, &*s, exp), (false, "62", Some(5)));
// rounding 6.25e4 to two significant digits towards +∞ gives 6.3e4
let (sign, s, exp) = val.to_sign_string_exp_round(10, Some(2), Round::Up);
assert_eq!((sign, &*s, exp), (false, "63", Some(5)));

pub fn as_neg(&self) -> BorrowFloat<'_>

Borrows a negated copy of the Float.

The returned object implements Deref<Target = Float>.

This method performs a shallow copy and negates it, and negation does not change the allocated data.

Examples

use rug::Float;
let f = Float::with_val(53, 4.2);
let neg_f = f.as_neg();
assert_eq!(*neg_f, -4.2);
// methods taking &self can be used on the returned object
let reneg_f = neg_f.as_neg();
assert_eq!(*reneg_f, 4.2);
assert_eq!(*reneg_f, f);

pub fn as_abs(&self) -> BorrowFloat<'_>

Borrows an absolute copy of the Float.

The returned object implements Deref<Target = Float>.

This method performs a shallow copy and possibly negates it, and negation does not change the allocated data.

Examples

use rug::Float;
let f = Float::with_val(53, -4.2);
let abs_f = f.as_abs();
assert_eq!(*abs_f, 4.2);
// methods taking &self can be used on the returned object
let reabs_f = abs_f.as_abs();
assert_eq!(*reabs_f, 4.2);
assert_eq!(*reabs_f, *abs_f);

pub fn as_ord(&self) -> &OrdFloat

Borrows the Float as an ordered floating-point number of type OrdFloat.

The same result can be obtained using the implementation of AsRef<OrdFloat> which is provided for Float.

Examples

use core::cmp::Ordering;
use rug::{float::Special, Float};

let nan_f = Float::with_val(53, Special::Nan);
let nan = nan_f.as_ord();
let neg_nan_f = nan_f.as_neg();
let neg_nan = neg_nan_f.as_ord();
assert_eq!(nan.cmp(nan), Ordering::Equal);
assert_eq!(neg_nan.cmp(nan), Ordering::Less);

let inf_f = Float::with_val(53, Special::Infinity);
let inf = inf_f.as_ord();
let neg_inf_f = Float::with_val(53, Special::NegInfinity);
let neg_inf = neg_inf_f.as_ord();
assert_eq!(nan.cmp(inf), Ordering::Greater);
assert_eq!(neg_nan.cmp(neg_inf), Ordering::Less);

let zero_f = Float::with_val(53, Special::Zero);
let zero = zero_f.as_ord();
let neg_zero_f = Float::with_val(53, Special::NegZero);
let neg_zero = neg_zero_f.as_ord();
assert_eq!(zero.cmp(neg_zero), Ordering::Greater);

pub fn as_complex(&self) -> BorrowComplex<'_>

Borrows a copy of the Float as a Complex number.

The returned object implements Deref<Target = Complex>.

The imaginary part of the return value has the same precision as the real part. While this has no effect for the zero value of the returned complex number, it could have an effect if the return value is cloned.

Examples

use rug::Float;
let f = Float::with_val(53, 4.2);
let c = f.as_complex();
assert_eq!(*c, (4.2, 0.0));
// methods taking &self can be used on the returned object
let c_mul_i = c.as_mul_i(false);
assert_eq!(*c_mul_i, (0.0, 4.2));

pub fn is_integer(&self) -> bool

Returns true if self is an integer.

Examples

use rug::Float;
let mut f = Float::with_val(53, 13.5);
assert!(!f.is_integer());
f *= 2;
assert!(f.is_integer());

pub fn is_nan(&self) -> bool

Returns true if self is not a number.

Examples

use rug::Float;
let mut f = Float::with_val(53, 0);
assert!(!f.is_nan());
f /= 0;
assert!(f.is_nan());

pub fn is_infinite(&self) -> bool

Returns true if self is plus or minus infinity.

Examples

use rug::Float;
let mut f = Float::with_val(53, 1);
assert!(!f.is_infinite());
f /= 0;
assert!(f.is_infinite());

pub fn is_finite(&self) -> bool

Returns true if self is a finite number, that is neither NaN nor infinity.

Examples

use rug::Float;
let mut f = Float::with_val(53, 1);
assert!(f.is_finite());
f /= 0;
assert!(!f.is_finite());

pub fn is_zero(&self) -> bool

Returns true if self is plus or minus zero.

Examples

use rug::{float::Special, Assign, Float};
let mut f = Float::with_val(53, Special::Zero);
assert!(f.is_zero());
f.assign(Special::NegZero);
assert!(f.is_zero());
f += 1;
assert!(!f.is_zero());

pub fn is_normal(&self) -> bool

Returns true if self is a normal number, that is neither NaN, nor infinity, nor zero. Note that Float cannot be subnormal.

Examples

use rug::{float::Special, Assign, Float};
let mut f = Float::with_val(53, Special::Zero);
assert!(!f.is_normal());
f += 5.2;
assert!(f.is_normal());
f.assign(Special::Infinity);
assert!(!f.is_normal());
f.assign(Special::Nan);
assert!(!f.is_normal());

pub fn classify(&self) -> FpCategory

Returns the floating-point category of the number. Note that Float cannot be subnormal.

Examples

use core::num::FpCategory;
use rug::{float::Special, Float};
let nan = Float::with_val(53, Special::Nan);
let infinite = Float::with_val(53, Special::Infinity);
let zero = Float::with_val(53, Special::Zero);
let normal = Float::with_val(53, 2.3);
assert_eq!(nan.classify(), FpCategory::Nan);
assert_eq!(infinite.classify(), FpCategory::Infinite);
assert_eq!(zero.classify(), FpCategory::Zero);
assert_eq!(normal.classify(), FpCategory::Normal);

pub fn cmp0(&self) -> Option<Ordering>

Returns the same result as self.partial_cmp(&0), but is faster.

Examples

use core::cmp::Ordering;
use rug::{float::Special, Assign, Float};
let mut f = Float::with_val(53, Special::NegZero);
assert_eq!(f.cmp0(), Some(Ordering::Equal));
f += 5.2;
assert_eq!(f.cmp0(), Some(Ordering::Greater));
f.assign(Special::NegInfinity);
assert_eq!(f.cmp0(), Some(Ordering::Less));
f.assign(Special::Nan);
assert_eq!(f.cmp0(), None);

pub fn cmp_abs(&self, other: &Self) -> Option<Ordering>

Compares the absolute values of self and other.

Examples

use core::cmp::Ordering;
use rug::Float;
let a = Float::with_val(53, -10);
let b = Float::with_val(53, 4);
assert_eq!(a.partial_cmp(&b), Some(Ordering::Less));
assert_eq!(a.cmp_abs(&b), Some(Ordering::Greater));

pub fn total_cmp(&self, other: &Float) -> Ordering

Returns the total ordering between self and other.

Negative zero is ordered as less than positive zero. Negative NaN is ordered as less than negative infinity, while positive NaN is ordered as greater than positive infinity. Comparing two negative NaNs or two positive NaNs produces equality.

Examples

use rug::{float::Special, Float};
let mut values = vec![
    Float::with_val(53, Special::Zero),
    Float::with_val(53, Special::NegZero),
    Float::with_val(53, Special::Infinity),
    Float::with_val(53, Special::NegInfinity),
    Float::with_val(53, Special::Nan),
    -Float::with_val(53, Special::Nan),
];

values.sort_by(Float::total_cmp);

// NaN with negative sign
assert!(values[0].is_nan() && values[0].is_sign_negative());
// -∞
assert!(values[1].is_infinite() && values[1].is_sign_negative());
// -0
assert!(values[2].is_zero() && values[2].is_sign_negative());
// +0
assert!(values[3].is_zero() && values[3].is_sign_positive());
// +∞
assert!(values[4].is_infinite() && values[4].is_sign_positive());
// NaN with positive sign
assert!(values[5].is_nan() && values[5].is_sign_positive());

pub fn get_exp(&self) -> Option<i32>

If the value is a normal number, returns its exponent.

The significand is assumed to be in the range 0.5 ≤ x < 1.

Examples

use rug::{Assign, Float};
// -(2.0 ^ 32) == -(0.5 × 2 ^ 33)
let mut f = Float::with_val(53, -32f64.exp2());
assert_eq!(f.get_exp(), Some(33));
// 0.8 × 2 ^ -39
f.assign(0.8 * (-39f64).exp2());
assert_eq!(f.get_exp(), Some(-39));
f.assign(0);
assert_eq!(f.get_exp(), None);

pub fn get_significand(&self) -> Option<BorrowInteger<'_>>

If the value is a normal number, returns a reference to its significand as an Integer.

The unwrapped returned object implements Deref<Target = Integer>.

The number of significant bits of a returned significand is at least equal to the precision, but can be larger. It is usually rounded up to a multiple of 32 or 64 depending on the implementation; in this case, the extra least significant bits will be zero. The value of self is exactly equal to the returned Integer divided by two raised to the power of the number of significant bits and multiplied by two raised to the power of the exponent of self.

Unlike the to_integer_exp method which returns an owned Integer, this method only performs a shallow copy and does not allocate any memory.

Examples

use rug::Float;
let float = Float::with_val(16, 6.5);
// 6.5 in binary is 110.1 = 0.1101 times two to the power of 3
let exp = float.get_exp().unwrap();
assert_eq!(exp, 3);
let significand = float.get_significand().unwrap();
let sig_bits = significand.significant_bits();
// sig_bits must be greater or equal to precision
assert!(sig_bits >= 16);
let (check_int, check_exp) = float.to_integer_exp().unwrap();
assert_eq!(check_int << sig_bits << (check_exp - exp), *significand);

pub fn is_sign_positive(&self) -> bool

Returns true if the value is positive, +0 or NaN without a negative sign.

Examples

use rug::Float;
let pos = Float::with_val(53, 1.0);
let neg = Float::with_val(53, -1.0);
assert!(pos.is_sign_positive());
assert!(!neg.is_sign_positive());

pub fn is_sign_negative(&self) -> bool

Returns true if the value is negative, −0 or NaN with a negative sign.

Examples

use rug::Float;
let neg = Float::with_val(53, -1.0);
let pos = Float::with_val(53, 1.0);
assert!(neg.is_sign_negative());
assert!(!pos.is_sign_negative());

pub fn remainder_ref<'a>(&'a self, divisor: &'a Self) -> RemainderIncomplete<'_>

Computes the remainder.

The remainder is the value of self − n × divisor, where n is the integer quotient of self / divisor rounded to the nearest integer (ties rounded to even). This is different from the remainder obtained using the % operator or the Rem trait, where n is truncated instead of rounded to the nearest.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 589.4);
let g = Float::with_val(53, 100);
let remainder = Float::with_val(53, f.remainder_ref(&g));
let expected = -10.6_f64;
assert!((remainder - expected).abs() < 0.0001);

// compare to % operator
let f = Float::with_val(53, 589.4);
let g = Float::with_val(53, 100);
let rem_op = Float::with_val(53, &f % &g);
let expected = 89.4_f64;
assert!((rem_op - expected).abs() < 0.0001);

pub fn mul_add_ref<'a>(
    &'a self,
    mul: &'a Self,
    add: &'a Self
) -> AddMulIncomplete<'a>

Multiplies and adds in one fused operation.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

a.mul_add_ref(&b, &c) produces the exact same result as &a * &b + &c.

Examples

use rug::Float;
// Use only 4 bits of precision for demonstration purposes.
// 1.5 in binary is 1.1.
let mul1 = Float::with_val(4, 1.5);
// -13 in binary is -1101.
let mul2 = Float::with_val(4, -13);
// 24 in binary is 11000.
let add = Float::with_val(4, 24);

// 1.5 × -13 + 24 = 4.5
let ans = Float::with_val(4, mul1.mul_add_ref(&mul2, &add));
assert_eq!(ans, 4.5);

pub fn mul_sub_ref<'a>(
    &'a self,
    mul: &'a Self,
    sub: &'a Self
) -> SubMulFromIncomplete<'a>

Multiplies and subtracts in one fused operation.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

a.mul_sub_ref(&b, &c) produces the exact same result as &a * &b - &c.

Examples

use rug::Float;
// Use only 4 bits of precision for demonstration purposes.
// 1.5 in binary is 1.1.
let mul1 = Float::with_val(4, 1.5);
// -13 in binary is -1101.
let mul2 = Float::with_val(4, -13);
// 24 in binary is 11000.
let sub = Float::with_val(4, 24);

// 1.5 × -13 - 24 = -43.5, rounded to 44 using four bits of precision.
let ans = Float::with_val(4, mul1.mul_sub_ref(&mul2, &sub));
assert_eq!(ans, -44);

pub fn mul_add_mul_ref<'a>(
    &'a self,
    mul: &'a Self,
    add_mul1: &'a Self,
    add_mul2: &'a Self
) -> MulAddMulIncomplete<'a>

Multiplies two products and adds them in one fused operation.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

a.mul_add_mul_ref(&b, &c, &d) produces the exact same result as &a * &b + &c * &d.

Examples

use rug::Float;
let a = Float::with_val(53, 24);
let b = Float::with_val(53, 1.5);
let c = Float::with_val(53, 12);
let d = Float::with_val(53, 2);
// 24 × 1.5 + 12 × 2 = 60
let ans = Float::with_val(53, a.mul_add_mul_ref(&b, &c, &d));
assert_eq!(ans, 60);

pub fn mul_sub_mul_ref<'a>(
    &'a self,
    mul: &'a Self,
    sub_mul1: &'a Self,
    sub_mul2: &'a Self
) -> MulSubMulIncomplete<'a>

Multiplies two products and subtracts them in one fused operation.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

a.mul_sub_mul_ref(&b, &c, &d) produces the exact same result as &a * &b - &c * &d.

Examples

use rug::Float;
let a = Float::with_val(53, 24);
let b = Float::with_val(53, 1.5);
let c = Float::with_val(53, 12);
let d = Float::with_val(53, 2);
// 24 × 1.5 - 12 × 2 = 12
let ans = Float::with_val(53, a.mul_sub_mul_ref(&b, &c, &d));
assert_eq!(ans, 12);

pub fn square_ref(&self) -> SquareIncomplete<'_>

Computes the square.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 5.0);
let r = f.square_ref();
let square = Float::with_val(53, r);
assert_eq!(square, 25.0);

pub fn sqrt_ref(&self) -> SqrtIncomplete<'_>

Computes the square root.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 25.0);
let r = f.sqrt_ref();
let sqrt = Float::with_val(53, r);
assert_eq!(sqrt, 5.0);

pub fn recip_sqrt_ref(&self) -> RecipSqrtIncomplete<'_>

Computes the reciprocal square root.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 16.0);
let r = f.recip_sqrt_ref();
let recip_sqrt = Float::with_val(53, r);
assert_eq!(recip_sqrt, 0.25);

pub fn cbrt_ref(&self) -> CbrtIncomplete<'_>

Computes the cube root.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 125.0);
let r = f.cbrt_ref();
let cbrt = Float::with_val(53, r);
assert_eq!(cbrt, 5.0);

pub fn root_ref(&self, k: u32) -> RootIncomplete<'_>

Computes the kth root.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 625.0);
let r = f.root_ref(4);
let root = Float::with_val(53, r);
assert_eq!(root, 5.0);

pub fn abs_ref(&self) -> AbsIncomplete<'_>

Computes the absolute value.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, -23.5);
let r = f.abs_ref();
let abs = Float::with_val(53, r);
assert_eq!(abs, 23.5);

pub fn signum_ref(&self) -> SignumIncomplete<'_>

Computes the signum.

• 1.0 if the value is positive, +0.0 or +∞
• −1.0 if the value is negative, −0.0 or −∞
• NaN if the value is NaN

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, -23.5);
let r = f.signum_ref();
let signum = Float::with_val(53, r);
assert_eq!(signum, -1);

pub fn copysign_ref<'a>(&'a self, y: &'a Self) -> CopysignIncomplete<'_>

Computes a number with the magnitude of self and the sign of y.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let x = Float::with_val(53, 23.0);
let y = Float::with_val(53, -1.0);
let r = x.copysign_ref(&y);
let copysign = Float::with_val(53, r);
assert_eq!(copysign, -23.0);

pub fn clamp_ref<'min, 'max, Min, Max>(
    &self,
    min: &'min Min,
    max: &'max Max
) -> ClampIncomplete<'_, 'min, 'max, Min, Max> where
    Self: PartialOrd<Min> + PartialOrd<Max> + for<'a> AssignRound<&'a Min, Round = Round, Ordering = Ordering> + for<'a> AssignRound<&'a Max, Round = Round, Ordering = Ordering>, 

Clamps the value within the specified bounds.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Panics

Panics if the maximum value is less than the minimum value, unless assigning any of them to the target produces the same value with the same rounding direction.

Examples

use rug::Float;
let min = -1.5;
let max = 1.5;
let too_small = Float::with_val(53, -2.5);
let r1 = too_small.clamp_ref(&min, &max);
let clamped1 = Float::with_val(53, r1);
assert_eq!(clamped1, -1.5);
let in_range = Float::with_val(53, 0.5);
let r2 = in_range.clamp_ref(&min, &max);
let clamped2 = Float::with_val(53, r2);
assert_eq!(clamped2, 0.5);

pub fn recip_ref(&self) -> RecipIncomplete<'_>

Computes the reciprocal.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, -0.25);
let r = f.recip_ref();
let recip = Float::with_val(53, r);
assert_eq!(recip, -4.0);

pub fn min_ref<'a>(&'a self, other: &'a Self) -> MinIncomplete<'_>

Finds the minimum.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let a = Float::with_val(53, 5.2);
let b = Float::with_val(53, -2);
let r = a.min_ref(&b);
let min = Float::with_val(53, r);
assert_eq!(min, -2);

pub fn max_ref<'a>(&'a self, other: &'a Self) -> MaxIncomplete<'_>

Finds the maximum.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let a = Float::with_val(53, 5.2);
let b = Float::with_val(53, 12.5);
let r = a.max_ref(&b);
let max = Float::with_val(53, r);
assert_eq!(max, 12.5);

pub fn positive_diff_ref<'a>(
    &'a self,
    other: &'a Self
) -> PositiveDiffIncomplete<'_>

Computes the positive difference.

The positive difference is self − other if self > other, zero if self ≤ other, or NaN if any operand is NaN.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let a = Float::with_val(53, 12.5);
let b = Float::with_val(53, 7.3);
let rab = a.positive_diff_ref(&b);
let ab = Float::with_val(53, rab);
assert_eq!(ab, 5.2);
let rba = b.positive_diff_ref(&a);
let ba = Float::with_val(53, rba);
assert_eq!(ba, 0);

pub fn ln_ref(&self) -> LnIncomplete<'_>

Computes the natural logarithm.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.5);
let ln = Float::with_val(53, f.ln_ref());
let expected = 0.4055_f64;
assert!((ln - expected).abs() < 0.0001);

pub fn log2_ref(&self) -> Log2Incomplete<'_>

Computes the logarithm to base 2.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.5);
let log2 = Float::with_val(53, f.log2_ref());
let expected = 0.5850_f64;
assert!((log2 - expected).abs() < 0.0001);

pub fn log10_ref(&self) -> Log10Incomplete<'_>

Computes the logarithm to base 10.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.5);
let log10 = Float::with_val(53, f.log10_ref());
let expected = 0.1761_f64;
assert!((log10 - expected).abs() < 0.0001);

pub fn exp_ref(&self) -> ExpIncomplete<'_>

Computes the exponential.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.5);
let exp = Float::with_val(53, f.exp_ref());
let expected = 4.4817_f64;
assert!((exp - expected).abs() < 0.0001);

pub fn exp2_ref(&self) -> Exp2Incomplete<'_>

Computes 2 to the power of the value.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.5);
let exp2 = Float::with_val(53, f.exp2_ref());
let expected = 2.8284_f64;
assert!((exp2 - expected).abs() < 0.0001);

pub fn exp10_ref(&self) -> Exp10Incomplete<'_>

Computes 10 to the power of the value.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.5);
let exp10 = Float::with_val(53, f.exp10_ref());
let expected = 31.6228_f64;
assert!((exp10 - expected).abs() < 0.0001);

pub fn sin_ref(&self) -> SinIncomplete<'_>

Computes the sine.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let sin = Float::with_val(53, f.sin_ref());
let expected = 0.9490_f64;
assert!((sin - expected).abs() < 0.0001);

pub fn cos_ref(&self) -> CosIncomplete<'_>

Computes the cosine.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let cos = Float::with_val(53, f.cos_ref());
let expected = 0.3153_f64;
assert!((cos - expected).abs() < 0.0001);

pub fn tan_ref(&self) -> TanIncomplete<'_>

Computes the tangent.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let tan = Float::with_val(53, f.tan_ref());
let expected = 3.0096_f64;
assert!((tan - expected).abs() < 0.0001);

pub fn sin_cos_ref(&self) -> SinCosIncomplete<'_>

Computes the sine and cosine.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for (Float, Float)
• Assign<Src> for (&mut Float, &mut Float)
• AssignRound<Src> for (Float, Float)
• AssignRound<Src> for (&mut Float, &mut Float)
• CompleteRound<Completed = (Float, Float)> for Src

Examples

use core::cmp::Ordering;
use rug::{float::Round, ops::AssignRound, Assign, Float};
let phase = Float::with_val(53, 1.25);

let (mut sin, mut cos) = (Float::new(53), Float::new(53));
let sin_cos = phase.sin_cos_ref();
(&mut sin, &mut cos).assign(sin_cos);
let expected_sin = 0.9490_f64;
let expected_cos = 0.3153_f64;
assert!((sin - expected_sin).abs() < 0.0001);
assert!((cos - expected_cos).abs() < 0.0001);

// using 4 significant bits: sin = 0.9375
// using 4 significant bits: cos = 0.3125
let (mut sin_4, mut cos_4) = (Float::new(4), Float::new(4));
let sin_cos = phase.sin_cos_ref();
let (dir_sin, dir_cos) = (&mut sin_4, &mut cos_4)
    .assign_round(sin_cos, Round::Nearest);
assert_eq!(sin_4, 0.9375);
assert_eq!(dir_sin, Ordering::Less);
assert_eq!(cos_4, 0.3125);
assert_eq!(dir_cos, Ordering::Less);

pub fn sec_ref(&self) -> SecIncomplete<'_>

Computes the secant.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let sec = Float::with_val(53, f.sec_ref());
let expected = 3.1714_f64;
assert!((sec - expected).abs() < 0.0001);

pub fn csc_ref(&self) -> CscIncomplete<'_>

Computes the cosecant.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let csc = Float::with_val(53, f.csc_ref());
let expected = 1.0538_f64;
assert!((csc - expected).abs() < 0.0001);

pub fn cot_ref(&self) -> CotIncomplete<'_>

Computes the cotangent.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let cot = Float::with_val(53, f.cot_ref());
let expected = 0.3323_f64;
assert!((cot - expected).abs() < 0.0001);

pub fn asin_ref(&self) -> AsinIncomplete<'_>

Computes the arc-sine.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, -0.75);
let asin = Float::with_val(53, f.asin_ref());
let expected = -0.8481_f64;
assert!((asin - expected).abs() < 0.0001);

pub fn acos_ref(&self) -> AcosIncomplete<'_>

Computes the arc-cosine.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, -0.75);
let acos = Float::with_val(53, f.acos_ref());
let expected = 2.4189_f64;
assert!((acos - expected).abs() < 0.0001);

pub fn atan_ref(&self) -> AtanIncomplete<'_>

Computes the arc-tangent.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, -0.75);
let atan = Float::with_val(53, f.atan_ref());
let expected = -0.6435_f64;
assert!((atan - expected).abs() < 0.0001);

pub fn atan2_ref<'a>(&'a self, x: &'a Self) -> Atan2Incomplete<'_>

Computes the arc-tangent.

This is similar to the arc-tangent of self / x, but has an output range of 2π rather than π.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let y = Float::with_val(53, 3.0);
let x = Float::with_val(53, -4.0);
let r = y.atan2_ref(&x);
let atan2 = Float::with_val(53, r);
let expected = 2.4981_f64;
assert!((atan2 - expected).abs() < 0.0001);

pub fn sinh_ref(&self) -> SinhIncomplete<'_>

Computes the hyperbolic sine.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let sinh = Float::with_val(53, f.sinh_ref());
let expected = 1.6019_f64;
assert!((sinh - expected).abs() < 0.0001);

pub fn cosh_ref(&self) -> CoshIncomplete<'_>

Computes the hyperbolic cosine.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let cosh = Float::with_val(53, f.cosh_ref());
let expected = 1.8884_f64;
assert!((cosh - expected).abs() < 0.0001);

pub fn tanh_ref(&self) -> TanhIncomplete<'_>

Computes the hyperbolic tangent.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let tanh = Float::with_val(53, f.tanh_ref());
let expected = 0.8483_f64;
assert!((tanh - expected).abs() < 0.0001);

pub fn sinh_cosh_ref(&self) -> SinhCoshIncomplete<'_>

Computes the hyperbolic sine and cosine.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for (Float, Float)
• Assign<Src> for (&mut Float, &mut Float)
• AssignRound<Src> for (Float, Float)
• AssignRound<Src> for (&mut Float, &mut Float)
• CompleteRound<Completed = (Float, Float)> for Src

Examples

use core::cmp::Ordering;
use rug::{float::Round, ops::AssignRound, Assign, Float};
let phase = Float::with_val(53, 1.25);

let (mut sinh, mut cosh) = (Float::new(53), Float::new(53));
let sinh_cosh = phase.sinh_cosh_ref();
(&mut sinh, &mut cosh).assign(sinh_cosh);
let expected_sinh = 1.6019_f64;
let expected_cosh = 1.8884_f64;
assert!((sinh - expected_sinh).abs() < 0.0001);
assert!((cosh - expected_cosh).abs() < 0.0001);

// using 4 significant bits: sin = 1.625
// using 4 significant bits: cos = 1.875
let (mut sinh_4, mut cosh_4) = (Float::new(4), Float::new(4));
let sinh_cosh = phase.sinh_cosh_ref();
let (dir_sinh, dir_cosh) = (&mut sinh_4, &mut cosh_4)
    .assign_round(sinh_cosh, Round::Nearest);
assert_eq!(sinh_4, 1.625);
assert_eq!(dir_sinh, Ordering::Greater);
assert_eq!(cosh_4, 1.875);
assert_eq!(dir_cosh, Ordering::Less);

pub fn sech_ref(&self) -> SechIncomplete<'_>

Computes the hyperbolic secant.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let sech = Float::with_val(53, f.sech_ref());
let expected = 0.5295_f64;
assert!((sech - expected).abs() < 0.0001);

pub fn csch_ref(&self) -> CschIncomplete<'_>

Computes the hyperbolic cosecant.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let csch = Float::with_val(53, f.csch_ref());
let expected = 0.6243_f64;
assert!((csch - expected).abs() < 0.0001);

pub fn coth_ref(&self) -> CothIncomplete<'_>

Computes the hyperbolic cotangent.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let coth = Float::with_val(53, f.coth_ref());
let expected = 1.1789_f64;
assert!((coth - expected).abs() < 0.0001);

pub fn asinh_ref(&self) -> AsinhIncomplete<'_>

Computes the inverse hyperbolic sine.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let asinh = Float::with_val(53, f.asinh_ref());
let expected = 1.0476_f64;
assert!((asinh - expected).abs() < 0.0001);

pub fn acosh_ref(&self) -> AcoshIncomplete<'_>

Computes the inverse hyperbolic cosine

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let acosh = Float::with_val(53, f.acosh_ref());
let expected = 0.6931_f64;
assert!((acosh - expected).abs() < 0.0001);

pub fn atanh_ref(&self) -> AtanhIncomplete<'_>

Computes the inverse hyperbolic tangent.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 0.75);
let atanh = Float::with_val(53, f.atanh_ref());
let expected = 0.9730_f64;
assert!((atanh - expected).abs() < 0.0001);

pub fn ln_1p_ref(&self) -> Ln1pIncomplete<'_>

Computes the natural logorithm of one plus the value.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let two_to_m10 = (-10f64).exp2();
let f = Float::with_val(53, 1.5 * two_to_m10);
let ln_1p = Float::with_val(53, f.ln_1p_ref());
let expected = 1.4989_f64 * two_to_m10;
assert!((ln_1p - expected).abs() < 0.0001 * two_to_m10);

pub fn exp_m1_ref(&self) -> ExpM1Incomplete<'_>

Computes one less than the exponential of the value.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let two_to_m10 = (-10f64).exp2();
let f = Float::with_val(53, 1.5 * two_to_m10);
let exp_m1 = Float::with_val(53, f.exp_m1_ref());
let expected = 1.5011_f64 * two_to_m10;
assert!((exp_m1 - expected).abs() < 0.0001 * two_to_m10);

pub fn eint_ref(&self) -> EintIncomplete<'_>

Computes the exponential integral.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let eint = Float::with_val(53, f.eint_ref());
let expected = 2.5810_f64;
assert!((eint - expected).abs() < 0.0001);

pub fn li2_ref(&self) -> Li2Incomplete<'_>

Computes the real part of the dilogarithm of the value.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let li2 = Float::with_val(53, f.li2_ref());
let expected = 2.1902_f64;
assert!((li2 - expected).abs() < 0.0001);

pub fn gamma_ref(&self) -> GammaIncomplete<'_>

Computes the gamma function on the value.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let gamma = Float::with_val(53, f.gamma_ref());
let expected = 0.9064_f64;
assert!((gamma - expected).abs() < 0.0001);

pub fn gamma_inc_ref<'a>(&'a self, x: &'a Self) -> GammaIncIncomplete<'_>

Computes the upper incomplete gamma function on the value.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let x = Float::with_val(53, 2.5);
let gamma_inc = Float::with_val(53, f.gamma_inc_ref(&x));
let expected = 0.1116_f64;
assert!((gamma_inc - expected).abs() < 0.0001);

pub fn ln_gamma_ref(&self) -> LnGammaIncomplete<'_>

Computes the logarithm of the gamma function on the value.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float
• CompleteRound<Completed = Float> for Src

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let ln_gamma = Float::with_val(53, f.ln_gamma_ref());
let expected = -0.0983_f64;
assert!((ln_gamma - expected).abs() < 0.0001);

pub fn ln_abs_gamma_ref(&self) -> LnAbsGammaIncomplete<'_>

Computes the logarithm of the absolute value of the gamma function on val.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for (Float, Ordering)
• Assign<Src> for (&mut Float, &mut Ordering)
• AssignRound<Src> for (Float, Ordering)
• AssignRound<Src> for (&mut Float, &mut Ordering)
• CompleteRound<Completed = (Float, Float)> for Src

Examples

use core::cmp::Ordering;
use rug::{float::Constant, Assign, Float};

let neg1_2 = Float::with_val(53, -0.5);
// gamma of -1/2 is -2√π
let abs_gamma_64 = Float::with_val(64, Constant::Pi).sqrt() * 2u32;
let ln_gamma_64 = abs_gamma_64.ln();

// Assign rounds to the nearest
let r = neg1_2.ln_abs_gamma_ref();
let (mut f, mut sign) = (Float::new(53), Ordering::Equal);
(&mut f, &mut sign).assign(r);
// gamma of -1/2 is negative
assert_eq!(sign, Ordering::Less);
// check to 53 significant bits
assert_eq!(f, Float::with_val(53, &ln_gamma_64));

pub fn digamma_ref(&self) -> DigammaIncomplete<'_>

Computes the Digamma function on the value.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let digamma = Float::with_val(53, f.digamma_ref());
let expected = -0.2275_f64;
assert!((digamma - expected).abs() < 0.0001);

pub fn zeta_ref(&self) -> ZetaIncomplete<'_>

Computes the Riemann Zeta function on the value.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let zeta = Float::with_val(53, f.zeta_ref());
let expected = 4.5951_f64;
assert!((zeta - expected).abs() < 0.0001);

pub fn erf_ref(&self) -> ErfIncomplete<'_>

Computes the error function.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let erf = Float::with_val(53, f.erf_ref());
let expected = 0.9229_f64;
assert!((erf - expected).abs() < 0.0001);

pub fn erfc_ref(&self) -> ErfcIncomplete<'_>

Computes the complementary error function.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let erfc = Float::with_val(53, f.erfc_ref());
let expected = 0.0771_f64;
assert!((erfc - expected).abs() < 0.0001);

pub fn j0_ref(&self) -> J0Incomplete<'_>

Computes the first kind Bessel function of order 0.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let j0 = Float::with_val(53, f.j0_ref());
let expected = 0.6459_f64;
assert!((j0 - expected).abs() < 0.0001);

pub fn j1_ref(&self) -> J1Incomplete<'_>

Computes the first kind Bessel function of order 1.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let j1 = Float::with_val(53, f.j1_ref());
let expected = 0.5106_f64;
assert!((j1 - expected).abs() < 0.0001);

pub fn jn_ref(&self, n: i32) -> JnIncomplete<'_>

Computes the first kind Bessel function of order n.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let j2 = Float::with_val(53, f.jn_ref(2));
let expected = 0.1711_f64;
assert!((j2 - expected).abs() < 0.0001);

pub fn y0_ref(&self) -> Y0Incomplete<'_>

Computes the second kind Bessel function of order 0.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let y0 = Float::with_val(53, f.y0_ref());
let expected = 0.2582_f64;
assert!((y0 - expected).abs() < 0.0001);

pub fn y1_ref(&self) -> Y1Incomplete<'_>

Computes the second kind Bessel function of order 1.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let y1 = Float::with_val(53, f.y1_ref());
let expected = -0.5844_f64;
assert!((y1 - expected).abs() < 0.0001);

pub fn yn_ref(&self, n: i32) -> YnIncomplete<'_>

Computes the second kind Bessel function of order n.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let y2 = Float::with_val(53, f.yn_ref(2));
let expected = -1.1932_f64;
assert!((y2 - expected).abs() < 0.0001);

pub fn agm_ref<'a>(&'a self, other: &'a Self) -> AgmIncomplete<'_>

Computes the arithmetic-geometric mean.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let g = Float::with_val(53, 3.75);
let agm = Float::with_val(53, f.agm_ref(&g));
let expected = 2.3295_f64;
assert!((agm - expected).abs() < 0.0001);

pub fn hypot_ref<'a>(&'a self, other: &'a Self) -> HypotIncomplete<'_>

Computes the Euclidean norm.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let g = Float::with_val(53, 3.75);
let hypot = Float::with_val(53, f.hypot_ref(&g));
let expected = 3.9528_f64;
assert!((hypot - expected).abs() < 0.0001);

pub fn ai_ref(&self) -> AiIncomplete<'_>

Computes the Airy function Ai on the value.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float

Examples

use rug::Float;
let f = Float::with_val(53, 1.25);
let ai = Float::with_val(53, f.ai_ref());
let expected = 0.0996_f64;
assert!((ai - expected).abs() < 0.0001);

pub fn ceil_ref(&self) -> CeilIncomplete<'_>

Rounds up to the next higher integer. The result may be rounded again when assigned to the target.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float

Examples

use rug::Float;
let f1 = Float::with_val(53, -23.75);
let ceil1 = Float::with_val(53, f1.ceil_ref());
assert_eq!(ceil1, -23);
let f2 = Float::with_val(53, 23.75);
let ceil2 = Float::with_val(53, f2.ceil_ref());
assert_eq!(ceil2, 24);

pub fn floor_ref(&self) -> FloorIncomplete<'_>

Rounds down to the next lower integer. The result may be rounded again when assigned to the target.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float

Examples

use rug::Float;
let f1 = Float::with_val(53, -23.75);
let floor1 = Float::with_val(53, f1.floor_ref());
assert_eq!(floor1, -24);
let f2 = Float::with_val(53, 23.75);
let floor2 = Float::with_val(53, f2.floor_ref());
assert_eq!(floor2, 23);

pub fn round_ref(&self) -> RoundIncomplete<'_>

Rounds to the nearest integer, rounding half-way cases away from zero. The result may be rounded again when assigned to the target.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float

Examples

use rug::Float;
let f1 = Float::with_val(53, -23.75);
let round1 = Float::with_val(53, f1.round_ref());
assert_eq!(round1, -24);
let f2 = Float::with_val(53, 23.75);
let round2 = Float::with_val(53, f2.round_ref());
assert_eq!(round2, 24);

Double rounding may happen when assigning to a target with a precision less than the number of significant bits for the truncated integer.

use rug::{float::Round, Float};
use rug::ops::AssignRound;
let f = Float::with_val(53, 6.5);
// 6.5 (binary 110.1) is rounded to 7 (binary 111)
let r = f.round_ref();
// use only 2 bits of precision in destination
let mut dst = Float::new(2);
// 7 (binary 111) is rounded to 8 (binary 1000) by
// round-even rule in order to store in 2-bit Float, even
// though 6 (binary 110) is closer to original 6.5).
dst.assign_round(r, Round::Nearest);
assert_eq!(dst, 8);

pub fn round_even_ref(&self) -> RoundEvenIncomplete<'_>

Rounds to the nearest integer, rounding half-way cases to even. The result may be rounded again when assigned to the target.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float

Examples

use rug::Float;
let f1 = Float::with_val(53, 23.5);
let round1 = Float::with_val(53, f1.round_even_ref());
assert_eq!(round1, 24);
let f2 = Float::with_val(53, 24.5);
let round2 = Float::with_val(53, f2.round_even_ref());
assert_eq!(round2, 24);

pub fn trunc_ref(&self) -> TruncIncomplete<'_>

Rounds to the next integer towards zero. The result may be rounded again when assigned to the target.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float

Examples

use rug::Float;
let f1 = Float::with_val(53, -23.75);
let trunc1 = Float::with_val(53, f1.trunc_ref());
assert_eq!(trunc1, -23);
let f2 = Float::with_val(53, 23.75);
let trunc2 = Float::with_val(53, f2.trunc_ref());
assert_eq!(trunc2, 23);

pub fn fract_ref(&self) -> FractIncomplete<'_>

Gets the fractional part of the number.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for Float
• AssignRound<Src> for Float

Examples

use rug::Float;
let f1 = Float::with_val(53, -23.75);
let fract1 = Float::with_val(53, f1.fract_ref());
assert_eq!(fract1, -0.75);
let f2 = Float::with_val(53, 23.75);
let fract2 = Float::with_val(53, f2.fract_ref());
assert_eq!(fract2, 0.75);

pub fn trunc_fract_ref(&self) -> TruncFractIncomplete<'_>

Gets the integer and fractional parts of the number.

The following are implemented with the returned incomplete-computation value as Src:

• Assign<Src> for (Float, Float)
• Assign<Src> for (&mut Float, &mut Float)
• AssignRound<Src> for (Float, Float)
• AssignRound<Src> for (&mut Float, &mut Float)

Examples

use rug::{Assign, Float};
let f1 = Float::with_val(53, -23.75);
let r1 = f1.trunc_fract_ref();
let (mut trunc1, mut fract1) = (Float::new(53), Float::new(53));
(&mut trunc1, &mut fract1).assign(r1);
assert_eq!(trunc1, -23);
assert_eq!(fract1, -0.75);
let f2 = Float::with_val(53, -23.75);
let r2 = f2.trunc_fract_ref();
let (mut trunc2, mut fract2) = (Float::new(53), Float::new(53));
(&mut trunc2, &mut fract2).assign(r2);
assert_eq!(trunc2, -23);
assert_eq!(fract2, -0.75);

Trait Implementations

impl<'a> Debug for BorrowFloat<'a>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Deref for BorrowFloat<'_>

type Target = Float

The resulting type after dereferencing.

fn deref(&self) -> &Float

Dereferences the value.