Struct rug::Float [−][src]
#[repr(transparent)]pub struct Float { /* fields omitted */ }
Expand description
A multi-precision floating-point number with arbitrarily large precision and correct rounding
The precision has to be set during construction. The rounding method of the required operations can be specified, and the direction of the rounding is returned.
Examples
use core::cmp::Ordering; use rug::{float::Round, ops::DivAssignRound, Float}; // A precision of 32 significant bits is specified here. // (The primitive `f32` has a precision of 24 and // `f64` has a precision of 53.) let mut two_thirds_down = Float::with_val(32, 2.0); let dir = two_thirds_down.div_assign_round(3.0, Round::Down); // since we rounded down, direction is Ordering::Less assert_eq!(dir, Ordering::Less); let mut two_thirds_up = Float::with_val(32, 2.0); let dir = two_thirds_up.div_assign_round(3.0, Round::Up); // since we rounded up, direction is Ordering::Greater assert_eq!(dir, Ordering::Greater); let diff_expected = 2.0_f64.powi(-32); let diff = two_thirds_up - two_thirds_down; assert_eq!(diff, diff_expected);
Operations on two borrowed Float
numbers result in an incomplete-computation
value that has to be assigned to a new Float
value.
use rug::Float; let a = Float::with_val(53, 10.5); let b = Float::with_val(53, -1.25); let a_b_ref = &a + &b; let a_b = Float::with_val(53, a_b_ref); assert_eq!(a_b, 9.25);
As a special case, when an incomplete-computation value is obtained from
multiplying two Float
references, it can be added to or subtracted from
another Float
(or reference). This will result in a fused multiply-accumulate
operation, with only one rounding operation taking place.
use rug::Float; // Use only 4 bits of precision for demonstration purposes. // 24 in binary is 11000. let a = Float::with_val(4, 24); // 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 + 1.5 × −13 = 4.5 let add = Float::with_val(4, &a + &mul1 * &mul2); assert_eq!(add, 4.5); // 24 − 1.5 × −13 = 43.5, rounded to 44 using four bits of precision. let sub = a - &mul1 * &mul2; assert_eq!(sub, 44); // With separate addition and multiplication: let a = Float::with_val(4, 24); // No borrows, so multiplication is computed immediately. // 1.5 × −13 = −19.5 (binary −10011.1), rounded to −20. let separate_add = a + mul1 * mul2; assert_eq!(separate_add, 4);
The incomplete-computation value obtained from multiplying two Float
references can also be added to or subtracted from another such
incomplete-computation value, so that two muliplications and an addition
are fused with only one rounding operation taking place.
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 add = Float::with_val(53, &a * &b + &c * &d); assert_eq!(add, 60); // 24 × 1.5 − 12 × 2 = 12 let sub = Float::with_val(53, &a * &b - &c * &d); assert_eq!(sub, 12);
The Float
type supports various functions. Most methods have four versions:
- The first method consumes the operand and rounds the returned
Float
to the nearest representable value. - The second method has a “
_mut
” suffix, mutates the operand and rounds it the nearest representable value. - The third method has a “
_round
” suffix, mutates the operand, applies the specified rounding method, and returns the rounding direction: - The fourth method has a “
_ref
” suffix and borrows the operand. The returned item is an incomplete-computation value that can be assigned to aFloat
; the rounding method is selected during the assignment.
use core::cmp::Ordering; use rug::{float::Round, Float}; let expected = 0.9490_f64; // 1. consume the operand, round to nearest let a = Float::with_val(53, 1.25); let sin_a = a.sin(); assert!((sin_a - expected).abs() < 0.0001); // 2. mutate the operand, round to nearest let mut b = Float::with_val(53, 1.25); b.sin_mut(); assert!((b - expected).abs() < 0.0001); // 3. mutate the operand, apply specified rounding let mut c = Float::with_val(4, 1.25); // using 4 significant bits, 0.9490 is rounded down to 0.9375 let dir = c.sin_round(Round::Nearest); assert_eq!(c, 0.9375); assert_eq!(dir, Ordering::Less); // 4. borrow the operand let d = Float::with_val(53, 1.25); let r = d.sin_ref(); let sin_d = Float::with_val(53, r); assert!((sin_d - expected).abs() < 0.0001); // d was not consumed assert_eq!(d, 1.25);
The following example is a translation of the MPFR sample found on the MPFR website. The program computes a lower bound on 1 + 1/1! + 1/2! + … + 1/100! using 200-bit precision. The program writes:
Sum is 2.7182818284590452353602874713526624977572470936999595749669131
use rug::{ float::{self, FreeCache, Round}, ops::{AddAssignRound, AssignRound, MulAssignRound}, Float, }; let mut t = Float::with_val(200, 1.0); let mut s = Float::with_val(200, 1.0); let mut u = Float::new(200); for i in 1..=100_u32 { // multiply t by i in place, round towards +∞ t.mul_assign_round(i, Round::Up); // set u to 1/t, round towards −∞ u.assign_round(t.recip_ref(), Round::Down); // increase s by u in place, round towards −∞ s.add_assign_round(&u, Round::Down); } // `None` means the number of printed digits depends on the precision let sr = s.to_string_radix_round(10, None, Round::Down); println!("Sum is {}", sr); float::free_cache(FreeCache::All);
Implementations
pub fn with_val_round<T>(prec: u32, val: T, round: Round) -> (Self, Ordering) where
Self: AssignRound<T, Round = Round, Ordering = Ordering>,
pub fn with_val_round<T>(prec: u32, val: T, round: Round) -> (Self, Ordering) where
Self: AssignRound<T, Round = Round, Ordering = Ordering>,
Create a new Float
with the specified precision and with the given
value, applying the specified rounding method.
Panics
Panics if prec
is out of the allowed range.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; let (f1, dir) = Float::with_val_round(4, 3.3, Round::Nearest); // 3.3 with precision 4 is rounded down to 3.25 assert_eq!(f1.prec(), 4); assert_eq!(f1, 3.25); assert_eq!(dir, Ordering::Less); let (f2, dir) = Float::with_val_round(4, 3.3, Round::Up); // 3.3 rounded up to 3.5 assert_eq!(f2.prec(), 4); assert_eq!(f2, 3.5); assert_eq!(dir, Ordering::Greater);
Sets the precision, applying the specified rounding method.
Panics
Panics if prec
is out of the allowed range.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // 16.25 has seven significant bits (binary 10000.01) let mut f = Float::with_val(53, 16.25); let dir = f.set_prec_round(5, Round::Up); assert_eq!(f, 17); assert_eq!(dir, Ordering::Greater); assert_eq!(f.prec(), 5);
Creates a Float
from an initialized 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. Since this function takes over ownership, no other copies of the passed value should exist.
Examples
use core::mem::MaybeUninit; use gmp_mpfr_sys::mpfr::{self, rnd_t}; use rug::Float; let f = unsafe { let mut m = MaybeUninit::uninit(); mpfr::init2(m.as_mut_ptr(), 53); let mut m = m.assume_init(); mpfr::set_d(&mut m, -14.5, rnd_t::RNDN); // m is initialized and unique Float::from_raw(m) }; assert_eq!(f, -14.5); // since f is a Float now, deallocation is automatic
Converts a Float
into an MPFR floating-point number.
The returned object should be freed to avoid memory leaks.
Examples
use gmp_mpfr_sys::mpfr::{self, rnd_t}; use rug::Float; let f = Float::with_val(53, -14.5); let mut m = f.into_raw(); unsafe { let d = mpfr::get_d(&m, rnd_t::RNDN); assert_eq!(d, -14.5); // free object to prevent memory leak mpfr::clear(&mut m); }
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);
Returns an unsafe mutable 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 mut f = Float::with_val(53, -14.5); let m_ptr = f.as_raw_mut(); unsafe { mpfr::add_ui(m_ptr, m_ptr, 10, rnd_t::RNDN); } assert_eq!(f, -4.5);
Parses a decimal string slice (&str
) or byte slice
(&[u8]
) into a Float
.
AssignRound<Src> for Float
is implemented with the
unwrapped returned incomplete-computation value as Src
.
The string can start with an optional minus or plus sign and must then
have one or more significant digits with an optional decimal point. This
can optionally be followed by an exponent; the exponent can start with a
separator “e
”, “E
” or “@
”, and is followed by an optional minus or
plus sign and by one or more decimal digits.
Alternatively, the string can indicate the special values infinity or
NaN. Infinity can be represented as "inf"
, "infinity"
, "@inf@"
or
"@infinity@"
,and NaN can be represented as "nan"
or "@nan@"
. All
of these special representations are case insensitive. The NaN
representation may also include a possibly-empty string of ASCII
letters, digits and underscores enclosed in brackets, for example
"nan(char_sequence_1)"
.
ASCII whitespace is ignored everywhere in the string except in the
substrings specified above for special values; for example " @inf@ "
is accepted but "@ inf @"
is not. Underscores are ignored anywhere in
digit strings except before the first digit and between the exponent
separator and the first digit of the exponent.
Examples
use rug::Float; let valid = Float::parse("12.25e-4"); let f = Float::with_val(53, valid.unwrap()); assert_eq!(f, 12.25e-4); let invalid = Float::parse(".e-4"); assert!(invalid.is_err());
pub fn parse_radix<S: AsRef<[u8]>>(
src: S,
radix: i32
) -> Result<ParseIncomplete, ParseFloatError>
pub fn parse_radix<S: AsRef<[u8]>>(
src: S,
radix: i32
) -> Result<ParseIncomplete, ParseFloatError>
Parses a string slice (&str
) or byte slice
(&[u8]
) into a Float
.
AssignRound<Src> for Float
is implemented with the
unwrapped returned incomplete-computation value as Src
.
The string can start with an optional minus or plus sign and must then
have one or more significant digits with an optional point. This can
optionally be followed by an exponent; the exponent can start with a
separator “e
” or “E
” if the radix ≤ 10, or “@
” for any radix, and
is followed by an optional minus or plus sign and by one or more decimal
digits.
Alternatively, the string can indicate the special values infinity or
NaN. If the radix ≤ 10, infinity can be represented as "inf"
or
"infinity"
, and NaN can be represented as "nan"
. For any radix,
infinity can also be represented as "@inf@"
or "@infinity@"
, and NaN
can be represented as "@nan@"
. All of these special representations
are case insensitive. The NaN representation may also include a
possibly-empty string of ASCII letters, digits and underscores enclosed
in brackets, for example "nan(char_sequence_1)"
.
ASCII whitespace is ignored everywhere in the string except in the
substrings specified above for special values; for example " @inf@ "
is accepted but "@ inf @"
is not. Underscores are ignored anywhere in
digit strings except before the first digit and between the exponent
separator and the first digit of the exponent.
Panics
Panics if radix
is less than 2 or greater than 36.
Examples
use rug::Float; let valid1 = Float::parse_radix("12.23e-4", 4); let f1 = Float::with_val(53, valid1.unwrap()); assert_eq!(f1, (2.0 + 4.0 * 1.0 + 0.25 * (2.0 + 0.25 * 3.0)) / 256.0); let valid2 = Float::parse_radix("12.yz@2", 36); let f2 = Float::with_val(53, valid2.unwrap()); assert_eq!(f2, 35 + 36 * (34 + 36 * (2 + 36 * 1))); let invalid = Float::parse_radix("ffe-2", 16); assert!(invalid.is_err());
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);
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);
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());
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);
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));
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));
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));
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));
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);
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);
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);
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);
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));
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));
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));
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));
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");
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");
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)));
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)));
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);
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);
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(); assert_eq!(nan.cmp(nan), Ordering::Equal); let neg_inf_f = Float::with_val(53, Special::NegInfinity); let neg_inf = neg_inf_f.as_ord(); assert_eq!(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);
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));
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());
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);
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);
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));
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);
Clamps the exponent of a Float
within a specified range if the range
is valid.
This method returns None
if the specified exponent range is outside
the allowed exponent range obtained using exp_min
and exp_max
.
This method assumes that self
is the correctly rounded value of some
exact result exact, rounded according to round
in the direction
dir
. If necessary, this function then modifies self
to be within the
specified exponent range. If the exponent of self
is outside the
specified range, an underflow or overflow occurs, and the value of the
input parameter dir
is used to avoid double rounding.
Unlike most methods functions, the direction is obtained by comparing
the output self
to the unknown result exact, not to the input
value of self
.
Examples
use core::cmp::Ordering; use rug::{float::Round, ops::DivAssignRound, Float}; // use precision 4 for sake of example let mut f = Float::with_val(4, 1.0); // 1/115_000 is 8.696e-6, rounded down to 0.5625 >> 16 = 8.583e-6 let dir = f.div_assign_round(115_000, Round::Nearest); assert_eq!(f, 0.5625 / 16f32.exp2()); assert_eq!(dir, Ordering::Less); // Limiting exponent range to [-16, 16] leaves f unchanged let dir = f.clamp_exp(dir, Round::Nearest, -16, 16).unwrap(); assert_eq!(f, 0.5625 / 16f32.exp2()); assert_eq!(dir, Ordering::Less); // Limiting exponent range to [-15, 15] pushes f up to 0.5 >> 15 let dir = f.clamp_exp(dir, Round::Nearest, -15, 15).unwrap(); assert_eq!(f, 0.5 / 15f32.exp2()); assert_eq!(dir, Ordering::Greater);
The dir
parameter can be required to avoid double rounding. In the
following example, f
is 1/16, which is a tie between 0 and 1/8. With
ties rounding to even, this would be double rounded to 0, but the exact
result was actually > 1/16 as indicated by dir
saying that f
is less
than its exact value. f
can thus be rounded correctly to 1/8.
use core::cmp::Ordering; use rug::{float::Round, ops::DivAssignRound, Float}; let mut f = Float::with_val(4, 1.0); // 1/15.999 is > 1/16, rounded down to 0.5 >> 3 = 1/16 let dir = f.div_assign_round(15.999, Round::Nearest); assert_eq!(f, 0.5 / 3f32.exp2()); assert_eq!(dir, Ordering::Less); // Limiting exponent range to [-2, 2] pushes f correctly away from zero. let dir = f.clamp_exp(dir, Round::Nearest, -2, 2).unwrap(); assert_eq!(f, 0.5 / 2f32.exp2()); assert_eq!(dir, Ordering::Greater);
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);
Sets to the next value towards to
.
Examples
use rug::Float; let to = Float::with_val(8, 100); // 32.5 in binary is 100000.10 // 32.75 in binary is 100000.11 let mut f = Float::with_val(8, 32.5); f.next_toward(&to); assert_eq!(f, 32.75);
Sets to the next value towards +∞.
Examples
use rug::Float; // 32.5 in binary is 100000.10 // 32.75 in binary is 100000.11 let mut f = Float::with_val(8, 32.5); f.next_up(); assert_eq!(f, 32.75);
Sets to the next value towards −∞.
Examples
use rug::Float; // 32.5 in binary is 100000.10 // 32.25 in binary is 100000.01 let mut f = Float::with_val(8, 32.5); f.next_down(); assert_eq!(f, 32.25);
Emulate subnormal numbers for precisions specified in IEEE 754, rounding to the nearest.
Subnormalization is only performed for precisions specified in IEEE 754:
- binary16 with 16 storage bits and a precision of 11 bits,
- binary32 (single precision) with 32 storage bits and a precision of 24 bits,
- binary64 (double precision) with 64 storage bits and a precision of 53 bits,
- binary{k} with k storage bits where k is a multiple of 32 and k ≥ 128, and a precision of k − round(4 × log2 k) + 13 bits.
This method has no effect if the value is not in the subnormal range.
Examples
use core::f32; use rug::Float; // minimum single subnormal is 0.5 × 2 ^ −148 = 2 ^ −149 let single_min_subnormal = (-149f64).exp2(); assert_eq!(single_min_subnormal, single_min_subnormal as f32 as f64); let single_cannot = single_min_subnormal * 1.25; assert_eq!(single_min_subnormal, single_cannot as f32 as f64); let mut f = Float::with_val(24, single_cannot); assert_eq!(f.to_f64(), single_cannot); f.subnormalize_ieee(); assert_eq!(f.to_f64(), single_min_subnormal);
Emulate subnormal numbers for precisions specified in IEEE 754, applying the specified rounding method.
Subnormalization is only performed for precisions specified in IEEE 754:
- binary16 with 16 storage bits and a precision of 11 bits,
- binary32 (single precision) with 32 storage bits and a precision of 24 bits,
- binary64 (double precision) with 64 storage bits and a precision of 53 bits,
- binary{k} with k storage bits where k is a multiple of 32 and k ≥ 128, and a precision of k − round(4 × log2 k) + 13 bits.
This method simply propagates prev_rounding
if the value is not in the
subnormal range.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // minimum single subnormal is 0.5 × 2 ^ −148 = 2 ^ −149 let single_min_subnormal = (-149f64).exp2(); assert_eq!(single_min_subnormal, single_min_subnormal as f32 as f64); let single_cannot = single_min_subnormal * 1.25; assert_eq!(single_min_subnormal, single_cannot as f32 as f64); let mut f = Float::with_val(24, single_cannot); assert_eq!(f.to_f64(), single_cannot); let dir = f.subnormalize_ieee_round(Ordering::Equal, Round::Up); assert_eq!(f.to_f64(), single_min_subnormal * 2.0); assert_eq!(dir, Ordering::Greater);
Emulate subnormal numbers, rounding to the nearest.
Subnormalization is only performed when the exponent lies within the subnormal range, that is when
normal_exp_min
− precision + 1 ≤ exponent <
normal_exp_min
For example, for IEEE 754 single precision, the precision is 24 and
normal_exp_min
is −125, so the subnormal range would be
−148 ≤ exponent < −125.
This method has no effect if the value is not in the subnormal range.
Examples
use rug::Float; // minimum single subnormal is 0.5 × 2 ^ −148 = 2 ^ −149 let single_min_subnormal = (-149f64).exp2(); assert_eq!(single_min_subnormal, single_min_subnormal as f32 as f64); let single_cannot = single_min_subnormal * 1.25; assert_eq!(single_min_subnormal, single_cannot as f32 as f64); let mut f = Float::with_val(24, single_cannot); assert_eq!(f.to_f64(), single_cannot); f.subnormalize(-125); assert_eq!(f.to_f64(), single_min_subnormal);
Emulate subnormal numbers, applying the specified rounding method.
Subnormalization is only performed when the exponent lies within the subnormal range, that is when
normal_exp_min
− precision + 1 ≤ exponent <
normal_exp_min
For example, for IEEE 754 single precision, the precision is 24 and
normal_exp_min
is −125, so the subnormal range would be
−148 ≤ exponent < −125.
This method simply propagates prev_rounding
if the value is not in the
subnormal range.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // minimum single subnormal is 0.5 × 2 ^ −148 = 2 ^ −149 let single_min_subnormal = (-149f64).exp2(); assert_eq!(single_min_subnormal, single_min_subnormal as f32 as f64); let single_cannot = single_min_subnormal * 1.25; assert_eq!(single_min_subnormal, single_cannot as f32 as f64); let mut f = Float::with_val(24, single_cannot); assert_eq!(f.to_f64(), single_cannot); let dir = f.subnormalize_round(-125, Ordering::Equal, Round::Up); assert_eq!(f.to_f64(), single_min_subnormal * 2.0); assert_eq!(dir, Ordering::Greater);
Adds a list of Float
values with correct rounding.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Float
AssignRound<Src> for Float
AddAssign<Src> for Float
AddAssignRound<Src> for Float
Add<Src> for Float
,Add<Float> for Src
SubAssign<Src> for Float
,SubFrom<Src> for Float
SubAssignRound<Src> for Float
,SubFromRound<Src> for Float
Sub<Src> for Float
,Sub<Float> for Src
Examples
use core::cmp::Ordering; use rug::{float::Round, ops::AddAssignRound, Float}; // Give each value only 4 bits of precision for example purposes. let values = [ Float::with_val(4, 5.0), Float::with_val(4, 1024.0), Float::with_val(4, -1024.0), Float::with_val(4, -4.5), ]; // The result should still be exact if it fits. let r = Float::sum(values.iter()); let sum = Float::with_val(4, r); assert_eq!(sum, 0.5); let mut f = Float::with_val(4, 15.0); // 15.5 using 4 bits of precision becomes 16.0 let r = Float::sum(values.iter()); let dir = f.add_assign_round(r, Round::Nearest); assert_eq!(f, 16.0); assert_eq!(dir, Ordering::Greater);
Finds the dot product of a list of Float
value pairs with correct
rounding.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Float
AssignRound<Src> for Float
AddAssign<Src> for Float
AddAssignRound<Src> for Float
Add<Src> for Float
,Add<Float> for Src
SubAssign<Src> for Float
,SubFrom<Src> for Float
SubAssignRound<Src> for Float
,SubFromRound<Src> for Float
Sub<Src> for Float
,Sub<Float> for Src
This method will produce a result with correct rounding, except for some cases where underflow or overflow occurs in intermediate products.
Examples
use rug::Float; let a = [Float::with_val(53, 2.75), Float::with_val(53, -1.25)]; let b = [Float::with_val(53, 10.5), Float::with_val(53, 0.5)]; let r = Float::dot(a.iter().zip(b.iter())); let dot = Float::with_val(53, r); let expected = 2.75 * 10.5 - 1.25 * 0.5; assert_eq!(dot, expected); let r = Float::dot(b.iter().zip(a.iter())); let twice = dot + r; assert_eq!(twice, expected * 2.0);
Computes the remainder, rounding to the nearest.
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.
Examples
use rug::Float; let num = Float::with_val(53, 589.4); let den = Float::with_val(53, 100); let remainder = num.remainder(&den); let expected = -10.6_f64; assert!((remainder - expected).abs() < 0.0001); // compare to % operator let num = Float::with_val(53, 589.4); let den = Float::with_val(53, 100); let rem_op = num % &den; let expected = 89.4_f64; assert!((rem_op - expected).abs() < 0.0001);
Computes the remainder, rounding to the nearest.
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
RemAssign
trait, where n is truncated
instead of rounded to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 589.4); let g = Float::with_val(53, 100); f.remainder_mut(&g); let expected = -10.6_f64; assert!((f - expected).abs() < 0.0001); // compare to %= operator let mut f = Float::with_val(53, 589.4); let g = Float::with_val(53, 100); f %= &g; let expected = 89.4_f64; assert!((f - expected).abs() < 0.0001);
Computes the remainder, applying the specified rounding method.
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
RemAssignRound
trait, where n is
truncated instead of rounded to the nearest.
Examples
use core::cmp::Ordering; use rug::{float::Round, ops::RemAssignRound, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 128); let g = Float::with_val(6, 49); // remainder of 128 / 49 is 128 − 3 × 49 = −19 // using 4 significant bits: −20 let dir = f.remainder_round(&g, Round::Nearest); assert_eq!(f, -20.0); assert_eq!(dir, Ordering::Less); // compare to RemAssignRound::rem_assign_round let mut f = Float::with_val(4, 128); let g = Float::with_val(6, 49); // with RemAssignRound, remainder of 128 / 49 is 128 − 2 × 49 = 30 // using 4 significant bits: 30 let dir = f.rem_assign_round(&g, Round::Nearest); assert_eq!(f, 30.0); assert_eq!(dir, Ordering::Equal);
Computes the remainder, rounding to the nearest.
The remainder is the value of dividend
− n × self
, where
n is the integer quotient of dividend
/ self
rounded to the
nearest integer (ties rounded to even). This is different from the
remainder obtained using the RemFrom
trait, where n is
truncated instead of rounded to the nearest.
Examples
use rug::{ops::RemFrom, Float}; let f = Float::with_val(53, 589.4); let mut g = Float::with_val(53, 100); g.remainder_from(&f); let expected = -10.6_f64; assert!((g - expected).abs() < 0.0001); // compare to RemFrom::rem_from let f = Float::with_val(53, 589.4); let mut g = Float::with_val(53, 100); g.rem_from(&f); let expected = 89.4_f64; assert!((g - expected).abs() < 0.0001);
Computes the remainder, applying the specified rounding method.
The remainder is the value of dividend
− n × self
, where
n is the integer quotient of dividend
/ self
rounded to the
nearest integer (ties rounded to even). This is different from the
remainder obtained using the RemFromRound
trait, where n is truncated instead of rounded to the nearest.
Examples
use core::cmp::Ordering; use rug::{float::Round, ops::RemFromRound, Float}; // Use only 4 bits of precision to show rounding. let f = Float::with_val(8, 171); let mut g = Float::with_val(4, 64); // remainder of 171 / 64 is 171 − 3 × 64 = −21 // using 4 significant bits: −20 let dir = g.remainder_from_round(&f, Round::Nearest); assert_eq!(g, -20.0); assert_eq!(dir, Ordering::Greater); // compare to RemFromRound::rem_from_round let f = Float::with_val(8, 171); let mut g = Float::with_val(4, 64); // with RemFromRound, remainder of 171 / 64 is 171 − 2 × 64 = 43 // using 4 significant bits: 44 let dir = g.rem_from_round(&f, Round::Nearest); assert_eq!(g, 44.0); assert_eq!(dir, Ordering::Greater);
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
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);
Multiplies and adds in one fused operation, rounding to the nearest with only one rounding error.
a.mul_add(&b, &c)
produces a result like &a * &b + &c
, but a
is
consumed and the result produced uses its precision.
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 mul_add = mul1.mul_add(&mul2, &add); assert_eq!(mul_add, 4.5);
Multiplies and adds in one fused operation, rounding to the nearest with only one rounding error.
a.mul_add_mut(&b, &c)
produces a result like &a * &b + &c
, but
stores the result in a
using its precision.
Examples
use rug::Float; // Use only 4 bits of precision for demonstration purposes. // 1.5 in binary is 1.1. let mut 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 mul1.mul_add_mut(&mul2, &add); assert_eq!(mul1, 4.5);
Multiplies and adds in one fused operation, applying the specified rounding method with only one rounding error.
a.mul_add_round(&b, &c, round)
produces a result like
ans.assign_round(&a * &b + &c, round)
, but stores the result in a
using its precision rather than in another Float
like ans
.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision for demonstration purposes. // 1.5 in binary is 1.1. let mut 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 dir = mul1.mul_add_round(&mul2, &add, Round::Nearest); assert_eq!(mul1, 4.5); assert_eq!(dir, Ordering::Equal);
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
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);
Multiplies and subtracts in one fused operation, rounding to the nearest with only one rounding error.
a.mul_sub(&b, &c)
produces a result like &a * &b - &c
, but a
is
consumed and the result produced uses its precision.
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 mul_sub = mul1.mul_sub(&mul2, &sub); assert_eq!(mul_sub, -44);
Multiplies and subtracts in one fused operation, rounding to the nearest with only one rounding error.
a.mul_sub_mut(&b, &c)
produces a result like &a * &b - &c
, but
stores the result in a
using its precision.
Examples
use rug::Float; // Use only 4 bits of precision for demonstration purposes. // 1.5 in binary is 1.1. let mut 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. mul1.mul_sub_mut(&mul2, &sub); assert_eq!(mul1, -44);
Multiplies and subtracts in one fused operation, applying the specified rounding method with only one rounding error.
a.mul_sub_round(&b, &c, round)
produces a result like
ans.assign_round(&a * &b - &c, round)
, but stores the result in a
using its precision rather than in another Float
like ans
.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision for demonstration purposes. // 1.5 in binary is 1.1. let mut 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 dir = mul1.mul_sub_round(&mul2, &sub, Round::Nearest); assert_eq!(mul1, -44); assert_eq!(dir, Ordering::Less);
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
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);
Multiplies two products and adds them in one fused operation, rounding to the nearest with only one rounding error.
a.mul_add_mul(&b, &c, &d)
produces a result like &a * &b + &c * &d
,
but a
is consumed and the result produced uses its precision.
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 mul_add_mul = a.mul_add_mul(&b, &c, &d); assert_eq!(mul_add_mul, 60);
Multiplies two products and adds them in one fused operation, rounding to the nearest with only one rounding error.
a.mul_add_mul_mut(&b, &c, &d)
produces a result like &a * &b + &c * &d
, but stores the result in a
using its precision.
Examples
use rug::Float; let mut 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 a.mul_add_mul_mut(&b, &c, &d); assert_eq!(a, 60);
Multiplies two produces and adds them in one fused operation, applying the specified rounding method with only one rounding error.
a.mul_add_mul_round(&b, &c, &d, round)
produces a result like
ans.assign_round(&a * &b + &c * &d, round)
, but stores the result in
a
using its precision rather than in another Float
like ans
.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; let mut 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 dir = a.mul_add_mul_round(&b, &c, &d, Round::Nearest); assert_eq!(a, 60); assert_eq!(dir, Ordering::Equal);
pub fn mul_add_mul_ref<'a>(
&'a self,
mul: &'a Self,
add_mul1: &'a Self,
add_mul2: &'a Self
) -> MulAddMulIncomplete<'a>
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
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);
Multiplies two products and subtracts them in one fused operation, rounding to the nearest with only one rounding error.
a.mul_sub_mul(&b, &c, &d)
produces a result like &a * &b - &c * &d
,
but a
is consumed and the result produced uses its precision.
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 mul_sub_mul = a.mul_sub_mul(&b, &c, &d); assert_eq!(mul_sub_mul, 12);
Multiplies two products and subtracts them in one fused operation, rounding to the nearest with only one rounding error.
a.mul_sub_mul_mut(&b, &c, &d)
produces a result like &a * &b - &c * &d
, but stores the result in a
using its precision.
Examples
use rug::Float; let mut 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 a.mul_sub_mul_mut(&b, &c, &d); assert_eq!(a, 12);
Multiplies two produces and subtracts them in one fused operation, applying the specified rounding method with only one rounding error.
a.mul_sub_mul_round(&b, &c, &d, round)
produces a result like
ans.assign_round(&a * &b - &c * &d, round)
, but stores the result in
a
using its precision rather than in another Float
like ans
.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; let mut 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 dir = a.mul_sub_mul_round(&b, &c, &d, Round::Nearest); assert_eq!(a, 12); assert_eq!(dir, Ordering::Equal);
pub fn mul_sub_mul_ref<'a>(
&'a self,
mul: &'a Self,
sub_mul1: &'a Self,
sub_mul2: &'a Self
) -> MulSubMulIncomplete<'a>
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
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);
Multiplies u
by 2exp
.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Float
AssignRound<Src> for Float
You can also compare the returned value to a Float
;
the following are also implemented with the returned
incomplete-computation value as Src
:
PartialEq<Src> for Float
PartialEq<Float> for Src
PartialOrd<Src> for Float
PartialOrd<Float> for Src
Examples
use rug::Float; let v = Float::u_exp(120, -100); let f = Float::with_val(53, v); assert_eq!(f, 120.0 * (-100f64).exp2()); let same = Float::u_exp(120 << 2, -100 - 2); assert_eq!(f, same);
Multiplies i
by 2exp
.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Float
AssignRound<Src> for Float
You can also compare the returned value to a Float
; the following
are also implemented with the returned incomplete-computation
value as Src
:
PartialEq<Src> for Float
PartialEq<Float> for Src
PartialOrd<Src> for Float
PartialOrd<Float> for Src
Examples
use rug::Float; let v = Float::i_exp(-120, -100); let f = Float::with_val(53, v); assert_eq!(f, -120.0 * (-100f64).exp2()); let same = Float::i_exp(-120 << 2, -100 - 2); assert_eq!(f, same);
Raises base
to the power of exponent
.
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 p = Float::u_pow_u(13, 6); let f = Float::with_val(53, p); assert_eq!(f, 13u32.pow(6));
Raises base
to the power of exponent
.
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 p = Float::i_pow_u(-13, 5); let f = Float::with_val(53, p); assert_eq!(f, -13i32.pow(5));
Computes the square, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 5.0); let square = f.square(); assert_eq!(square, 25.0);
Computes the square, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 5.0); f.square_mut(); assert_eq!(f, 25.0);
Computes the square, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // 5 in binary is 101 let mut f = Float::with_val(3, 5.0); // 25 in binary is 11001 (more than 3 bits of precision). // 25 (11001) is rounded up to 28 (11100). let dir = f.square_round(Round::Up); assert_eq!(f, 28.0); assert_eq!(dir, Ordering::Greater);
Computes the square.
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, 5.0); let r = f.square_ref(); let square = Float::with_val(53, r); assert_eq!(square, 25.0);
Computes the square root, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 25.0); let sqrt = f.sqrt(); assert_eq!(sqrt, 5.0);
Computes the square root, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 25.0); f.sqrt_mut(); assert_eq!(f, 5.0);
Computes the square root, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // 5 in binary is 101 let mut f = Float::with_val(4, 5.0); // sqrt(5) in binary is 10.00111100... // sqrt(5) is rounded to 2.25 (10.01). let dir = f.sqrt_round(Round::Nearest); assert_eq!(f, 2.25); assert_eq!(dir, Ordering::Greater);
Computes the square root.
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, 25.0); let r = f.sqrt_ref(); let sqrt = Float::with_val(53, r); assert_eq!(sqrt, 5.0);
Computes the square root of u
.
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 s = Float::sqrt_u(25); let f = Float::with_val(53, s); assert_eq!(f, 5.0);
Computes the reciprocal square root, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 16.0); let recip_sqrt = f.recip_sqrt(); assert_eq!(recip_sqrt, 0.25);
Computes the reciprocal square root, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 16.0); f.recip_sqrt_mut(); assert_eq!(f, 0.25);
Computes the reciprocal square root, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // 5 in binary is 101 let mut f = Float::with_val(4, 5.0); // 1 / √5 in binary is 0.01110010... // 1 / √5 is rounded to 0.4375 (0.01110). let dir = f.recip_sqrt_round(Round::Nearest); assert_eq!(f, 0.4375); assert_eq!(dir, Ordering::Less);
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
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);
Computes the cube root, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 125.0); let cbrt = f.cbrt(); assert_eq!(cbrt, 5.0);
Computes the cube root, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 125.0); f.cbrt_mut(); assert_eq!(f, 5.0);
Computes the cube root, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // 5 in binary is 101 let mut f = Float::with_val(4, 5.0); // cbrt(5) in binary is 1.101101... // cbrt(5) is rounded to 1.75 (1.110). let dir = f.cbrt_round(Round::Nearest); assert_eq!(f, 1.75); assert_eq!(dir, Ordering::Greater);
Computes the cube root.
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, 125.0); let r = f.cbrt_ref(); let cbrt = Float::with_val(53, r); assert_eq!(cbrt, 5.0);
Computes the kth root, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 625.0); let root = f.root(4); assert_eq!(root, 5.0);
Computes the kth root, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 625.0); f.root_mut(4); assert_eq!(f, 5.0);
Computes the kth root, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // 5 in binary is 101 let mut f = Float::with_val(4, 5.0); // fourth root of 5 in binary is 1.01111... // fourth root of 5 is rounded to 1.5 (1.100). let dir = f.root_round(4, Round::Nearest); assert_eq!(f, 1.5); assert_eq!(dir, Ordering::Greater);
Computes the kth root.
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, 625.0); let r = f.root_ref(4); let root = Float::with_val(53, r); assert_eq!(root, 5.0);
Computes the absolute value.
Examples
use rug::Float; let f = Float::with_val(53, -23.5); let abs = f.abs(); assert_eq!(abs, 23.5);
Computes the absolute value.
Examples
use rug::Float; let mut f = Float::with_val(53, -23.5); f.abs_mut(); assert_eq!(f, 23.5);
Computes the absolute 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, -23.5); let r = f.abs_ref(); let abs = Float::with_val(53, r); assert_eq!(abs, 23.5);
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
Examples
use rug::Float; assert_eq!(Float::with_val(53, -23.5).signum(), -1); assert_eq!(Float::with_val(53, -0.0).signum(), -1); assert_eq!(Float::with_val(53, 0.0).signum(), 1); assert_eq!(Float::with_val(53, 23.5).signum(), 1);
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
Examples
use rug::Float; let mut f = Float::with_val(53, -23.5); f.signum_mut(); assert_eq!(f, -1);
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
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);
Returns a number with the magnitude of self
and the sign of y
.
Examples
use rug::Float; let x = Float::with_val(53, 23.0); let y = Float::with_val(53, -1.0); let copysign = x.copysign(&y); assert_eq!(copysign, -23.0);
Retains the magnitude of self
and copies the sign of y
.
Examples
use rug::Float; let mut x = Float::with_val(53, 23.0); let y = Float::with_val(53, -1.0); x.copysign_mut(&y); assert_eq!(x, -23.0);
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
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<Min, Max>(self, min: &Min, max: &Max) -> Self where
Self: PartialOrd<Min> + PartialOrd<Max> + for<'a> AssignRound<&'a Min, Round = Round, Ordering = Ordering> + for<'a> AssignRound<&'a Max, Round = Round, Ordering = Ordering>,
pub fn clamp<Min, Max>(self, min: &Min, max: &Max) -> Self 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, rounding to the nearest.
Panics
Panics if the maximum value is less than the minimum value, unless
assigning any of them to self
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 clamped1 = too_small.clamp(&min, &max); assert_eq!(clamped1, -1.5); let in_range = Float::with_val(53, 0.5); let clamped2 = in_range.clamp(&min, &max); assert_eq!(clamped2, 0.5);
pub fn clamp_mut<Min, Max>(&mut self, min: &Min, max: &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>,
pub fn clamp_mut<Min, Max>(&mut self, min: &Min, max: &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, rounding to the nearest.
Panics
Panics if the maximum value is less than the minimum value, unless
assigning any of them to self
produces the same value with the same
rounding direction.
Examples
use rug::Float; let min = -1.5; let max = 1.5; let mut too_small = Float::with_val(53, -2.5); too_small.clamp_mut(&min, &max); assert_eq!(too_small, -1.5); let mut in_range = Float::with_val(53, 0.5); in_range.clamp_mut(&min, &max); assert_eq!(in_range, 0.5);
pub fn clamp_round<Min, Max>(
&mut self,
min: &Min,
max: &Max,
round: Round
) -> Ordering where
Self: PartialOrd<Min> + PartialOrd<Max> + for<'a> AssignRound<&'a Min, Round = Round, Ordering = Ordering> + for<'a> AssignRound<&'a Max, Round = Round, Ordering = Ordering>,
pub fn clamp_round<Min, Max>(
&mut self,
min: &Min,
max: &Max,
round: Round
) -> Ordering 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, applying the specified rounding method.
Panics
Panics if the maximum value is less than the minimum value, unless
assigning any of them to self
produces the same value with the same
rounding direction.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; let min = Float::with_val(53, -1.5); let max = Float::with_val(53, 1.5); let mut too_small = Float::with_val(53, -2.5); let dir1 = too_small.clamp_round(&min, &max, Round::Nearest); assert_eq!(too_small, -1.5); assert_eq!(dir1, Ordering::Equal); let mut in_range = Float::with_val(53, 0.5); let dir2 = in_range.clamp_round(&min, &max, Round::Nearest); assert_eq!(in_range, 0.5); assert_eq!(dir2, Ordering::Equal);
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>,
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
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);
Computes the reciprocal, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, -0.25); let recip = f.recip(); assert_eq!(recip, -4.0);
Computes the reciprocal, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, -0.25); f.recip_mut(); assert_eq!(f, -4.0);
Computes the reciprocal, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // 5 in binary is 101 let mut f = Float::with_val(4, -5.0); // 1/5 in binary is 0.00110011... // 1/5 is rounded to 0.203125 (0.001101). let dir = f.recip_round(Round::Nearest); assert_eq!(f, -0.203125); assert_eq!(dir, Ordering::Less);
Computes the reciprocal.
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, -0.25); let r = f.recip_ref(); let recip = Float::with_val(53, r); assert_eq!(recip, -4.0);
Finds the minimum, rounding to the nearest.
Examples
use rug::Float; let a = Float::with_val(53, 5.2); let b = Float::with_val(53, -2); let min = a.min(&b); assert_eq!(min, -2);
Finds the minimum, rounding to the nearest.
Examples
use rug::Float; let mut a = Float::with_val(53, 5.2); let b = Float::with_val(53, -2); a.min_mut(&b); assert_eq!(a, -2);
Finds the minimum, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; let mut a = Float::with_val(53, 5.2); let b = Float::with_val(53, -2); let dir = a.min_round(&b, Round::Nearest); assert_eq!(a, -2); assert_eq!(dir, Ordering::Equal);
Finds the minimum.
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 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);
Finds the maximum, rounding to the nearest.
Examples
use rug::Float; let a = Float::with_val(53, 5.2); let b = Float::with_val(53, 12.5); let max = a.max(&b); assert_eq!(max, 12.5);
Finds the maximum, rounding to the nearest.
Examples
use rug::Float; let mut a = Float::with_val(53, 5.2); let b = Float::with_val(53, 12.5); a.max_mut(&b); assert_eq!(a, 12.5);
Finds the maximum, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; let mut a = Float::with_val(53, 5.2); let b = Float::with_val(53, 12.5); let dir = a.max_round(&b, Round::Nearest); assert_eq!(a, 12.5); assert_eq!(dir, Ordering::Equal);
Finds the maximum.
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 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);
Computes the positive difference between self
and other
, rounding to
the nearest.
The positive difference is self
− other
if self
> other
, zero if
self
≤ other
, or NaN if any operand is NaN.
Examples
use rug::Float; let a = Float::with_val(53, 12.5); let b = Float::with_val(53, 7.3); let diff1 = a.positive_diff(&b); assert_eq!(diff1, 5.2); let diff2 = diff1.positive_diff(&b); assert_eq!(diff2, 0);
Computes the positive difference between self
and other
, rounding to
the nearest.
The positive difference is self
− other
if self
> other
, zero if
self
≤ other
, or NaN if any operand is NaN.
Examples
use rug::Float; let mut a = Float::with_val(53, 12.5); let b = Float::with_val(53, 7.3); a.positive_diff_mut(&b); assert_eq!(a, 5.2); a.positive_diff_mut(&b); assert_eq!(a, 0);
Computes the positive difference between self
and other
, applying
the specified rounding method.
The positive difference is self
− other
if self
> other
, zero if
self
≤ other
, or NaN if any operand is NaN.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; let mut a = Float::with_val(53, 12.5); let b = Float::with_val(53, 7.3); let dir = a.positive_diff_round(&b, Round::Nearest); assert_eq!(a, 5.2); assert_eq!(dir, Ordering::Equal); let dir = a.positive_diff_round(&b, Round::Nearest); assert_eq!(a, 0); assert_eq!(dir, Ordering::Equal);
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
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);
Computes the natural logarithm, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.5); let ln = f.ln(); let expected = 0.4055_f64; assert!((ln - expected).abs() < 0.0001);
Computes the natural logarithm, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.5); f.ln_mut(); let expected = 0.4055_f64; assert!((f - expected).abs() < 0.0001);
Computes the natural logarithm, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.5); // ln(1.5) = 0.4055 // using 4 significant bits: 0.40625 let dir = f.ln_round(Round::Nearest); assert_eq!(f, 0.40625); assert_eq!(dir, Ordering::Greater);
Computes the natural logarithm.
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, 1.5); let ln = Float::with_val(53, f.ln_ref()); let expected = 0.4055_f64; assert!((ln - expected).abs() < 0.0001);
Computes the natural logarithm of u
.
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 l = Float::ln_u(3); let f = Float::with_val(53, l); let expected = 1.0986f64; assert!((f - expected).abs() < 0.0001);
Computes the logarithm to base 2, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.5); let log2 = f.log2(); let expected = 0.5850_f64; assert!((log2 - expected).abs() < 0.0001);
Computes the logarithm to base 2, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.5); f.log2_mut(); let expected = 0.5850_f64; assert!((f - expected).abs() < 0.0001);
Computes the logarithm to base 2, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.5); // log2(1.5) = 0.5850 // using 4 significant bits: 0.5625 let dir = f.log2_round(Round::Nearest); assert_eq!(f, 0.5625); assert_eq!(dir, Ordering::Less);
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
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);
Computes the logarithm to base 10, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.5); let log10 = f.log10(); let expected = 0.1761_f64; assert!((log10 - expected).abs() < 0.0001);
Computes the logarithm to base 10, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.5); f.log10_mut(); let expected = 0.1761_f64; assert!((f - expected).abs() < 0.0001);
Computes the logarithm to base 10, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.5); // log10(1.5) = 0.1761 // using 4 significant bits: 0.171875 let dir = f.log10_round(Round::Nearest); assert_eq!(f, 0.171875); assert_eq!(dir, Ordering::Less);
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
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);
Computes the exponential, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.5); let exp = f.exp(); let expected = 4.4817_f64; assert!((exp - expected).abs() < 0.0001);
Computes the exponential, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.5); f.exp_mut(); let expected = 4.4817_f64; assert!((f - expected).abs() < 0.0001);
Computes the exponential, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.5); // exp(1.5) = 4.4817 // using 4 significant bits: 4.5 let dir = f.exp_round(Round::Nearest); assert_eq!(f, 4.5); assert_eq!(dir, Ordering::Greater);
Computes the exponential.
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, 1.5); let exp = Float::with_val(53, f.exp_ref()); let expected = 4.4817_f64; assert!((exp - expected).abs() < 0.0001);
Computes 2 to the power of self
, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.5); let exp2 = f.exp2(); let expected = 2.8284_f64; assert!((exp2 - expected).abs() < 0.0001);
Computes 2 to the power of self
, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.5); f.exp2_mut(); let expected = 2.8284_f64; assert!((f - expected).abs() < 0.0001);
Computes 2 to the power of self
, applying the specified rounding
method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.5); // exp2(1.5) = 2.8284 // using 4 significant bits: 2.75 let dir = f.exp2_round(Round::Nearest); assert_eq!(f, 2.75); assert_eq!(dir, Ordering::Less);
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
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);
Computes 10 to the power of self
, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.5); let exp10 = f.exp10(); let expected = 31.6228_f64; assert!((exp10 - expected).abs() < 0.0001);
Computes 10 to the power of self
, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.5); f.exp10_mut(); let expected = 31.6228_f64; assert!((f - expected).abs() < 0.0001);
Computes 10 to the power of self
, applying the specified rounding
method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.5); // exp10(1.5) = 31.6228 // using 4 significant bits: 32 let dir = f.exp10_round(Round::Nearest); assert_eq!(f, 32); assert_eq!(dir, Ordering::Greater);
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
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);
Computes the sine, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let sin = f.sin(); let expected = 0.9490_f64; assert!((sin - expected).abs() < 0.0001);
Computes the sine, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.sin_mut(); let expected = 0.9490_f64; assert!((f - expected).abs() < 0.0001);
Computes the sine, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // sin(1.25) = 0.9490 // using 4 significant bits: 0.9375 let dir = f.sin_round(Round::Nearest); assert_eq!(f, 0.9375); assert_eq!(dir, Ordering::Less);
Computes the sine.
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 sin = Float::with_val(53, f.sin_ref()); let expected = 0.9490_f64; assert!((sin - expected).abs() < 0.0001);
Computes the cosine, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let cos = f.cos(); let expected = 0.3153_f64; assert!((cos - expected).abs() < 0.0001);
Computes the cosine, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.cos_mut(); let expected = 0.3153_f64; assert!((f - expected).abs() < 0.0001);
Computes the cosine, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // cos(1.25) = 0.3153 // using 4 significant bits: 0.3125 let dir = f.cos_round(Round::Nearest); assert_eq!(f, 0.3125); assert_eq!(dir, Ordering::Less);
Computes the cosine.
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 cos = Float::with_val(53, f.cos_ref()); let expected = 0.3153_f64; assert!((cos - expected).abs() < 0.0001);
Computes the tangent, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let tan = f.tan(); let expected = 3.0096_f64; assert!((tan - expected).abs() < 0.0001);
Computes the tangent, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.tan_mut(); let expected = 3.0096_f64; assert!((f - expected).abs() < 0.0001);
Computes the tangent, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // tan(1.25) = 3.0096 // using 4 significant bits: 3.0 let dir = f.tan_round(Round::Nearest); assert_eq!(f, 3.0); assert_eq!(dir, Ordering::Less);
Computes the tangent.
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 tan = Float::with_val(53, f.tan_ref()); let expected = 3.0096_f64; assert!((tan - expected).abs() < 0.0001);
Computes the sine and cosine of self
, rounding to the nearest.
The sine is stored in self
and keeps its precision, while the cosine
is stored in cos
keeping its precision.
The initial value of cos
is ignored.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let (sin, cos) = f.sin_cos(Float::new(53)); 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);
Computes the sine and cosine of self
, rounding to the nearest.
The sine is stored in self
and keeps its precision, while the cosine
is stored in cos
keeping its precision.
The initial value of cos
is ignored.
Examples
use rug::Float; let mut sin = Float::with_val(53, 1.25); let mut cos = Float::new(53); sin.sin_cos_mut(&mut 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);
Computes the sine and cosine of self
, applying the specified rounding
method.
The sine is stored in self
and keeps its precision, while the cosine
is stored in cos
keeping its precision.
The initial value of cos
is ignored.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut sin = Float::with_val(4, 1.25); let mut cos = Float::new(4); // sin(1.25) = 0.9490, using 4 significant bits: 0.9375 // cos(1.25) = 0.3153, using 4 significant bits: 0.3125 let (dir_sin, dir_cos) = sin.sin_cos_round(&mut cos, Round::Nearest); assert_eq!(sin, 0.9375); assert_eq!(dir_sin, Ordering::Less); assert_eq!(cos, 0.3125); assert_eq!(dir_cos, Ordering::Less);
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)
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);
Computes the secant, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let sec = f.sec(); let expected = 3.1714_f64; assert!((sec - expected).abs() < 0.0001);
Computes the secant, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.sec_mut(); let expected = 3.1714_f64; assert!((f - expected).abs() < 0.0001);
Computes the secant, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // sec(1.25) = 3.1714 // using 4 significant bits: 3.25 let dir = f.sec_round(Round::Nearest); assert_eq!(f, 3.25); assert_eq!(dir, Ordering::Greater);
Computes the secant.
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 sec = Float::with_val(53, f.sec_ref()); let expected = 3.1714_f64; assert!((sec - expected).abs() < 0.0001);
Computes the cosecant, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let csc = f.csc(); let expected = 1.0538_f64; assert!((csc - expected).abs() < 0.0001);
Computes the cosecant, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.csc_mut(); let expected = 1.0538_f64; assert!((f - expected).abs() < 0.0001);
Computes the cosecant, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // csc(1.25) = 1.0538 // using 4 significant bits: 1.0 let dir = f.csc_round(Round::Nearest); assert_eq!(f, 1.0); assert_eq!(dir, Ordering::Less);
Computes the cosecant.
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 csc = Float::with_val(53, f.csc_ref()); let expected = 1.0538_f64; assert!((csc - expected).abs() < 0.0001);
Computes the cotangent, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let cot = f.cot(); let expected = 0.3323_f64; assert!((cot - expected).abs() < 0.0001);
Computes the cotangent, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.cot_mut(); let expected = 0.3323_f64; assert!((f - expected).abs() < 0.0001);
Computes the cotangent, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // cot(1.25) = 0.3323 // using 4 significant bits: 0.34375 let dir = f.cot_round(Round::Nearest); assert_eq!(f, 0.34375); assert_eq!(dir, Ordering::Greater);
Computes the cotangent.
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 cot = Float::with_val(53, f.cot_ref()); let expected = 0.3323_f64; assert!((cot - expected).abs() < 0.0001);
Computes the arc-sine, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, -0.75); let asin = f.asin(); let expected = -0.8481_f64; assert!((asin - expected).abs() < 0.0001);
Computes the arc-sine, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, -0.75); f.asin_mut(); let expected = -0.8481_f64; assert!((f - expected).abs() < 0.0001);
Computes the arc-sine, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, -0.75); // asin(−0.75) = −0.8481 // using 4 significant bits: −0.875 let dir = f.asin_round(Round::Nearest); assert_eq!(f, -0.875); assert_eq!(dir, Ordering::Less);
Computes the arc-sine.
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, -0.75); let asin = Float::with_val(53, f.asin_ref()); let expected = -0.8481_f64; assert!((asin - expected).abs() < 0.0001);
Computes the arc-cosine, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, -0.75); let acos = f.acos(); let expected = 2.4189_f64; assert!((acos - expected).abs() < 0.0001);
Computes the arc-cosine, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, -0.75); f.acos_mut(); let expected = 2.4189_f64; assert!((f - expected).abs() < 0.0001);
Computes the arc-cosine, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, -0.75); // acos(−0.75) = 2.4189 // using 4 significant bits: 2.5 let dir = f.acos_round(Round::Nearest); assert_eq!(f, 2.5); assert_eq!(dir, Ordering::Greater);
Computes the arc-cosine.
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, -0.75); let acos = Float::with_val(53, f.acos_ref()); let expected = 2.4189_f64; assert!((acos - expected).abs() < 0.0001);
Computes the arc-tangent, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, -0.75); let atan = f.atan(); let expected = -0.6435_f64; assert!((atan - expected).abs() < 0.0001);
Computes the arc-tangent, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, -0.75); f.atan_mut(); let expected = -0.6435_f64; assert!((f - expected).abs() < 0.0001);
Computes the arc-tangent, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, -0.75); // atan(−0.75) = −0.6435 // using 4 significant bits: −0.625 let dir = f.atan_round(Round::Nearest); assert_eq!(f, -0.625); assert_eq!(dir, Ordering::Greater);
Computes the arc-tangent.
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, -0.75); let atan = Float::with_val(53, f.atan_ref()); let expected = -0.6435_f64; assert!((atan - expected).abs() < 0.0001);
Computes the arc-tangent2 of self
and x
, rounding to the nearest.
This is similar to the arc-tangent of self / x
, but has an output
range of 2π rather than π.
Examples
use rug::Float; let y = Float::with_val(53, 3.0); let x = Float::with_val(53, -4.0); let atan2 = y.atan2(&x); let expected = 2.4981_f64; assert!((atan2 - expected).abs() < 0.0001);
Computes the arc-tangent2 of self
and x
, rounding to the nearest.
This is similar to the arc-tangent of self / x
, but has an output
range of 2π rather than π.
Examples
use rug::Float; let mut y = Float::with_val(53, 3.0); let x = Float::with_val(53, -4.0); y.atan2_mut(&x); let expected = 2.4981_f64; assert!((y - expected).abs() < 0.0001);
Computes the arc-tangent2 of self
and x
, applying the specified
rounding method.
This is similar to the arc-tangent of self / x
, but has an output
range of 2π rather than π.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut y = Float::with_val(4, 3.0); let x = Float::with_val(4, -4.0); // atan2(3.0, −4.0) = 2.4981 // using 4 significant bits: 2.5 let dir = y.atan2_round(&x, Round::Nearest); assert_eq!(y, 2.5); assert_eq!(dir, Ordering::Greater);
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
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);
Computes the hyperbolic sine, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let sinh = f.sinh(); let expected = 1.6019_f64; assert!((sinh - expected).abs() < 0.0001);
Computes the hyperbolic sine, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.sinh_mut(); let expected = 1.6019_f64; assert!((f - expected).abs() < 0.0001);
Computes the hyperbolic sine, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // sinh(1.25) = 1.6019 // using 4 significant bits: 1.625 let dir = f.sinh_round(Round::Nearest); assert_eq!(f, 1.625); assert_eq!(dir, Ordering::Greater);
Computes the hyperbolic sine.
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 sinh = Float::with_val(53, f.sinh_ref()); let expected = 1.6019_f64; assert!((sinh - expected).abs() < 0.0001);
Computes the hyperbolic cosine, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let cosh = f.cosh(); let expected = 1.8884_f64; assert!((cosh - expected).abs() < 0.0001);
Computes the hyperbolic cosine, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.cosh_mut(); let expected = 1.8884_f64; assert!((f - expected).abs() < 0.0001);
Computes the hyperbolic cosine, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // cosh(1.25) = 1.8884 // using 4 significant bits: 1.875 let dir = f.cosh_round(Round::Nearest); assert_eq!(f, 1.875); assert_eq!(dir, Ordering::Less);
Computes the hyperbolic cosine.
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 cosh = Float::with_val(53, f.cosh_ref()); let expected = 1.8884_f64; assert!((cosh - expected).abs() < 0.0001);
Computes the hyperbolic tangent, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let tanh = f.tanh(); let expected = 0.8483_f64; assert!((tanh - expected).abs() < 0.0001);
Computes the hyperbolic tangent, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.tanh_mut(); let expected = 0.8483_f64; assert!((f - expected).abs() < 0.0001);
Computes the hyperbolic tangent, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // tanh(1.25) = 0.8483 // using 4 significant bits: 0.875 let dir = f.tanh_round(Round::Nearest); assert_eq!(f, 0.875); assert_eq!(dir, Ordering::Greater);
Computes the hyperbolic tangent.
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 tanh = Float::with_val(53, f.tanh_ref()); let expected = 0.8483_f64; assert!((tanh - expected).abs() < 0.0001);
Computes the hyperbolic sine and cosine of self
, rounding to the
nearest.
The sine is stored in self
and keeps its precision, while the cosine
is stored in cos
keeping its precision.
The initial value of cos
is ignored.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let (sinh, cosh) = f.sinh_cosh(Float::new(53)); 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);
Computes the hyperbolic sine and cosine of self
, rounding to the
nearest.
The sine is stored in self
and keeps its precision, while the cosine
is stored in cos
keeping its precision.
The initial value of cos
is ignored.
Examples
use rug::Float; let mut sinh = Float::with_val(53, 1.25); let mut cosh = Float::new(53); sinh.sinh_cosh_mut(&mut 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);
Computes the hyperbolic sine and cosine of self
, applying the
specified rounding method.
The sine is stored in self
and keeps its precision, while the cosine
is stored in cos
keeping its precision.
The initial value of cos
is ignored.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut sinh = Float::with_val(4, 1.25); let mut cosh = Float::new(4); // sinh(1.25) = 1.6019, using 4 significant bits: 1.625 // cosh(1.25) = 1.8884, using 4 significant bits: 1.875 let (dir_sinh, dir_cosh) = sinh.sinh_cosh_round(&mut cosh, Round::Nearest); assert_eq!(sinh, 1.625); assert_eq!(dir_sinh, Ordering::Greater); assert_eq!(cosh, 1.875); assert_eq!(dir_cosh, Ordering::Less);
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)
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);
Computes the hyperbolic secant, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let sech = f.sech(); let expected = 0.5295_f64; assert!((sech - expected).abs() < 0.0001);
Computes the hyperbolic secant, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.sech_mut(); let expected = 0.5295_f64; assert!((f - expected).abs() < 0.0001);
Computes the hyperbolic secant, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // sech(1.25) = 0.5295 // using 4 significant bits: 0.5 let dir = f.sech_round(Round::Nearest); assert_eq!(f, 0.5); assert_eq!(dir, Ordering::Less);
Computes the hyperbolic secant.
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 sech = Float::with_val(53, f.sech_ref()); let expected = 0.5295_f64; assert!((sech - expected).abs() < 0.0001);
Computes the hyperbolic cosecant, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let csch = f.csch(); let expected = 0.6243_f64; assert!((csch - expected).abs() < 0.0001);
Computes the hyperbolic cosecant, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.csch_mut(); let expected = 0.6243_f64; assert!((f - expected).abs() < 0.0001);
Computes the hyperbolic cosecant, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // csch(1.25) = 0.6243 // using 4 significant bits: 0.625 let dir = f.csch_round(Round::Nearest); assert_eq!(f, 0.625); assert_eq!(dir, Ordering::Greater);
Computes the hyperbolic cosecant.
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 csch = Float::with_val(53, f.csch_ref()); let expected = 0.6243_f64; assert!((csch - expected).abs() < 0.0001);
Computes the hyperbolic cotangent, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let coth = f.coth(); let expected = 1.1789_f64; assert!((coth - expected).abs() < 0.0001);
Computes the hyperbolic cotangent, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.coth_mut(); let expected = 1.1789_f64; assert!((f - expected).abs() < 0.0001);
Computes the hyperbolic cotangent, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // coth(1.25) = 1.1789 // using 4 significant bits: 1.125 let dir = f.coth_round(Round::Nearest); assert_eq!(f, 1.125); assert_eq!(dir, Ordering::Less);
Computes the hyperbolic cotangent.
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 coth = Float::with_val(53, f.coth_ref()); let expected = 1.1789_f64; assert!((coth - expected).abs() < 0.0001);
Computes the inverse hyperbolic sine, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let asinh = f.asinh(); let expected = 1.0476_f64; assert!((asinh - expected).abs() < 0.0001);
Computes the inverse hyperbolic sine, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.asinh_mut(); let expected = 1.0476_f64; assert!((f - expected).abs() < 0.0001);
Computes the inverse hyperbolic sine, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // asinh(1.25) = 1.0476 // using 4 significant bits: 1.0 let dir = f.asinh_round(Round::Nearest); assert_eq!(f, 1.0); assert_eq!(dir, Ordering::Less);
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
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);
Computes the inverse hyperbolic cosine, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let acosh = f.acosh(); let expected = 0.6931_f64; assert!((acosh - expected).abs() < 0.0001);
Computes the inverse hyperbolic cosine, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.acosh_mut(); let expected = 0.6931_f64; assert!((f - expected).abs() < 0.0001);
Computes the inverse hyperbolic cosine, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // acosh(1.25) = 0.6931 // using 4 significant bits: 0.6875 let dir = f.acosh_round(Round::Nearest); assert_eq!(f, 0.6875); assert_eq!(dir, Ordering::Less);
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
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);
Computes the inverse hyperbolic tangent, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 0.75); let atanh = f.atanh(); let expected = 0.9730_f64; assert!((atanh - expected).abs() < 0.0001);
Computes the inverse hyperbolic tangent, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 0.75); f.atanh_mut(); let expected = 0.9730_f64; assert!((f - expected).abs() < 0.0001);
Computes the inverse hyperbolic tangent, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 0.75); // atanh(0.75) = 0.9730 // using 4 significant bits: 1.0 let dir = f.atanh_round(Round::Nearest); assert_eq!(f, 1.0); assert_eq!(dir, Ordering::Greater);
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
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);
Computes the factorial of 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; // 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 let n = Float::factorial(10); let f = Float::with_val(53, n); assert_eq!(f, 3628800.0);
Computes the natural logarithm of one plus self
, rounding to the
nearest.
Examples
use rug::Float; let two_to_m10 = (-10f64).exp2(); let f = Float::with_val(53, 1.5 * two_to_m10); let ln_1p = f.ln_1p(); let expected = 1.4989_f64 * two_to_m10; assert!((ln_1p - expected).abs() < 0.0001 * two_to_m10);
Computes the natural logarithm of one plus self
, rounding to the
nearest.
Examples
use rug::Float; let two_to_m10 = (-10f64).exp2(); let mut f = Float::with_val(53, 1.5 * two_to_m10); f.ln_1p_mut(); let expected = 1.4989_f64 * two_to_m10; assert!((f - expected).abs() < 0.0001 * two_to_m10);
Computes the natural logarithm of one plus self
, applying the
specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; let two_to_m10 = (-10f64).exp2(); // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.5 * two_to_m10); // ln_1p(1.5 × 2 ^ −10) = 1.4989 × 2 ^ −10 // using 4 significant bits: 1.5 × 2 ^ −10 let dir = f.ln_1p_round(Round::Nearest); assert_eq!(f, 1.5 * two_to_m10); assert_eq!(dir, Ordering::Greater);
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
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);
Subtracts one from the exponential of self
, rounding to the nearest.
Examples
use rug::Float; let two_to_m10 = (-10f64).exp2(); let f = Float::with_val(53, 1.5 * two_to_m10); let exp_m1 = f.exp_m1(); let expected = 1.5011_f64 * two_to_m10; assert!((exp_m1 - expected).abs() < 0.0001 * two_to_m10);
Subtracts one from the exponential of self
, rounding to the nearest.
Examples
use rug::Float; let two_to_m10 = (-10f64).exp2(); let mut f = Float::with_val(53, 1.5 * two_to_m10); f.exp_m1_mut(); let expected = 1.5011_f64 * two_to_m10; assert!((f - expected).abs() < 0.0001 * two_to_m10);
Subtracts one from the exponential of self
, applying the specified
rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; let two_to_m10 = (-10f64).exp2(); // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.5 * two_to_m10); // exp_m1(1.5 × 2 ^ −10) = 1.5011 × 2 ^ −10 // using 4 significant bits: 1.5 × 2 ^ −10 let dir = f.exp_m1_round(Round::Nearest); assert_eq!(f, 1.5 * two_to_m10); assert_eq!(dir, Ordering::Less);
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
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);
Computes the exponential integral, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let eint = f.eint(); let expected = 2.5810_f64; assert!((eint - expected).abs() < 0.0001);
Computes the exponential integral, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.eint_mut(); let expected = 2.5810_f64; assert!((f - expected).abs() < 0.0001);
Computes the exponential integral, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // eint(1.25) = 2.5810 // using 4 significant bits: 2.5 let dir = f.eint_round(Round::Nearest); assert_eq!(f, 2.5); assert_eq!(dir, Ordering::Less);
Computes the exponential integral.
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 eint = Float::with_val(53, f.eint_ref()); let expected = 2.5810_f64; assert!((eint - expected).abs() < 0.0001);
Computes the real part of the dilogarithm of self
, rounding to the
nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let li2 = f.li2(); let expected = 2.1902_f64; assert!((li2 - expected).abs() < 0.0001);
Computes the real part of the dilogarithm of self
, rounding to the
nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.li2_mut(); let expected = 2.1902_f64; assert!((f - expected).abs() < 0.0001);
Computes the real part of the dilogarithm of self
, applying the
specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // li2(1.25) = 2.1902 // using 4 significant bits: 2.25 let dir = f.li2_round(Round::Nearest); assert_eq!(f, 2.25); assert_eq!(dir, Ordering::Greater);
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
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);
Computes the value of the gamma function on self
, rounding to the
nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let gamma = f.gamma(); let expected = 0.9064_f64; assert!((gamma - expected).abs() < 0.0001);
Computes the value of the gamma function on self
, rounding to the
nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.gamma_mut(); let expected = 0.9064_f64; assert!((f - expected).abs() < 0.0001);
Computes the value of the gamma function on self
, applying the
specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // gamma(1.25) = 0.9064 // using 4 significant bits: 0.9375 let dir = f.gamma_round(Round::Nearest); assert_eq!(f, 0.9375); assert_eq!(dir, Ordering::Greater);
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
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);
Computes the value of the upper incomplete gamma function on self
and
x
, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let x = Float::with_val(53, 2.5); let gamma_inc = f.gamma_inc(&x); let expected = 0.1116_f64; assert!((gamma_inc - expected).abs() < 0.0001);
Computes the value of the upper incomplete gamma function on self
,
rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); let x = Float::with_val(53, 2.5); f.gamma_inc_mut(&x); let expected = 0.1116_f64; assert!((f - expected).abs() < 0.0001);
Computes the value of the upper incomplete gamma function on self
,
applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); let x = Float::with_val(53, 2.5); // gamma_inc(1.25, 2.5) = 0.1116 // using 4 significant bits: 0.109375 let dir = f.gamma_inc_round(&x, Round::Nearest); assert_eq!(f, 0.109375); assert_eq!(dir, Ordering::Less);
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
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);
Computes the logarithm of the gamma function on self
, rounding to the
nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let ln_gamma = f.ln_gamma(); let expected = -0.0983_f64; assert!((ln_gamma - expected).abs() < 0.0001);
Computes the logarithm of the gamma function on self
, rounding to the
nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.ln_gamma_mut(); let expected = -0.0983_f64; assert!((f - expected).abs() < 0.0001);
Computes the logarithm of the gamma function on self
, applying the
specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // ln_gamma(1.25) = −0.0983 // using 4 significant bits: −0.1015625 let dir = f.ln_gamma_round(Round::Nearest); assert_eq!(f, -0.1015625); assert_eq!(dir, Ordering::Less);
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
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);
Computes the logarithm of the absolute value of the gamma function on
self
, rounding to the nearest.
Returns Ordering::Less
if the gamma
function is negative, or
Ordering::Greater
if the gamma
function is positive.
Examples
use core::cmp::Ordering; use rug::{float::Constant, Float}; // gamma of 1/2 is √π let ln_gamma_64 = Float::with_val(64, Constant::Pi).sqrt().ln(); let f = Float::with_val(53, 0.5); let (ln_gamma, sign) = f.ln_abs_gamma(); // gamma of 1/2 is positive assert_eq!(sign, Ordering::Greater); // check to 53 significant bits assert_eq!(ln_gamma, Float::with_val(53, &ln_gamma_64));
If the gamma function is negative, the sign returned is
Ordering::Less
.
use core::cmp::Ordering; use rug::{float::Constant, Float}; // 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(); let f = Float::with_val(53, -0.5); let (ln_gamma, sign) = f.ln_abs_gamma(); // gamma of −1/2 is negative assert_eq!(sign, Ordering::Less); // check to 53 significant bits assert_eq!(ln_gamma, Float::with_val(53, &ln_gamma_64));
Computes the logarithm of the absolute value of the gamma function on
self
, rounding to the nearest.
Returns Ordering::Less
if the gamma
function is negative, or
Ordering::Greater
if the gamma
function is positive.
Examples
use core::cmp::Ordering; use rug::{float::Constant, Float}; // 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(); let mut f = Float::with_val(53, -0.5); let sign = f.ln_abs_gamma_mut(); // 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));
Computes the logarithm of the absolute value of the gamma function on
self
, applying the specified rounding method.
The returned tuple contains:
- The logarithm of the absolute value of the gamma function.
- The rounding direction.
Examples
use core::cmp::Ordering; use rug::{ float::{Constant, Round}, Float, }; // 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(); let mut f = Float::with_val(53, -0.5); let (sign, dir) = f.ln_abs_gamma_round(Round::Nearest); // gamma of −1/2 is negative assert_eq!(sign, Ordering::Less); // check is correct to 53 significant bits let (check, check_dir) = Float::with_val_round(53, &ln_gamma_64, Round::Nearest); assert_eq!(f, check); assert_eq!(dir, check_dir);
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)
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));
Computes the value of the Digamma function on self
, rounding to the
nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let digamma = f.digamma(); let expected = -0.2275_f64; assert!((digamma - expected).abs() < 0.0001);
Computes the value of the Digamma function on self
, rounding to the
nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.digamma_mut(); let expected = -0.2275_f64; assert!((f - expected).abs() < 0.0001);
Computes the value of the Digamma function on self
, applying the
specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // digamma(1.25) = −0.2275 // using 4 significant bits: −0.234375 let dir = f.digamma_round(Round::Nearest); assert_eq!(f, -0.234375); assert_eq!(dir, Ordering::Less);
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);
Computes the value of the Riemann Zeta function on self
, rounding to
the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let zeta = f.zeta(); let expected = 4.5951_f64; assert!((zeta - expected).abs() < 0.0001);
Computes the value of the Riemann Zeta function on self
, rounding to
the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.zeta_mut(); let expected = 4.5951_f64; assert!((f - expected).abs() < 0.0001);
Computes the value of the Riemann Zeta function on self
, applying the
specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // zeta(1.25) = 4.5951 // using 4 significant bits: 4.5 let dir = f.zeta_round(Round::Nearest); assert_eq!(f, 4.5); assert_eq!(dir, Ordering::Less);
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);
Computes the Riemann Zeta function on u.
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 z = Float::zeta_u(3); let f = Float::with_val(53, z); let expected = 1.2021_f64; assert!((f - expected).abs() < 0.0001);
Computes the value of the error function, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let erf = f.erf(); let expected = 0.9229_f64; assert!((erf - expected).abs() < 0.0001);
Computes the value of the error function, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.erf_mut(); let expected = 0.9229_f64; assert!((f - expected).abs() < 0.0001);
Computes the value of the error function, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // erf(1.25) = 0.9229 // using 4 significant bits: 0.9375 let dir = f.erf_round(Round::Nearest); assert_eq!(f, 0.9375); assert_eq!(dir, Ordering::Greater);
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);
Computes the value of the complementary error function, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let erfc = f.erfc(); let expected = 0.0771_f64; assert!((erfc - expected).abs() < 0.0001);
Computes the value of the complementary error function, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.erfc_mut(); let expected = 0.0771_f64; assert!((f - expected).abs() < 0.0001);
Computes the value of the complementary error function, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // erfc(1.25) = 0.0771 // using 4 significant bits: 0.078125 let dir = f.erfc_round(Round::Nearest); assert_eq!(f, 0.078125); assert_eq!(dir, Ordering::Greater);
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);
Computes the value of the first kind Bessel function of order 0, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let j0 = f.j0(); let expected = 0.6459_f64; assert!((j0 - expected).abs() < 0.0001);
Computes the value of the first kind Bessel function of order 0, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.j0_mut(); let expected = 0.6459_f64; assert!((f - expected).abs() < 0.0001);
Computes the value of the first kind Bessel function of order 0, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // j0(1.25) = 0.6459 // using 4 significant bits: 0.625 let dir = f.j0_round(Round::Nearest); assert_eq!(f, 0.625); assert_eq!(dir, Ordering::Less);
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);
Computes the value of the first kind Bessel function of order 1, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let j1 = f.j1(); let expected = 0.5106_f64; assert!((j1 - expected).abs() < 0.0001);
Computes the value of the first kind Bessel function of order 1, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.j1_mut(); let expected = 0.5106_f64; assert!((f - expected).abs() < 0.0001);
Computes the value of the first kind Bessel function of order 1, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // j1(1.25) = 0.5106 // using 4 significant bits: 0.5 let dir = f.j1_round(Round::Nearest); assert_eq!(f, 0.5); assert_eq!(dir, Ordering::Less);
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);
Computes the value of the first kind Bessel function of order n, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let j2 = f.jn(2); let expected = 0.1711_f64; assert!((j2 - expected).abs() < 0.0001);
Computes the value of the first kind Bessel function of order n, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.jn_mut(2); let expected = 0.1711_f64; assert!((f - expected).abs() < 0.0001);
Computes the value of the first kind Bessel function of order n, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // j2(1.25) = 0.1711 // using 4 significant bits: 0.171875 let dir = f.jn_round(2, Round::Nearest); assert_eq!(f, 0.171875); assert_eq!(dir, Ordering::Greater);
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);
Computes the value of the second kind Bessel function of order 0, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let y0 = f.y0(); let expected = 0.2582_f64; assert!((y0 - expected).abs() < 0.0001);
Computes the value of the second kind Bessel function of order 0, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.y0_mut(); let expected = 0.2582_f64; assert!((f - expected).abs() < 0.0001);
Computes the value of the second kind Bessel function of order 0, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // y0(1.25) = 0.2582 // using 4 significant bits: 0.25 let dir = f.y0_round(Round::Nearest); assert_eq!(f, 0.25); assert_eq!(dir, Ordering::Less);
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);
Computes the value of the second kind Bessel function of order 1, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let y1 = f.y1(); let expected = -0.5844_f64; assert!((y1 - expected).abs() < 0.0001);
Computes the value of the second kind Bessel function of order 1, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.y1_mut(); let expected = -0.5844_f64; assert!((f - expected).abs() < 0.0001);
Computes the value of the second kind Bessel function of order 1, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // y1(1.25) = −0.5844 // using 4 significant bits: −0.5625 let dir = f.y1_round(Round::Nearest); assert_eq!(f, -0.5625); assert_eq!(dir, Ordering::Greater);
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);
Computes the value of the second kind Bessel function of order n, rounding to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let y2 = f.yn(2); let expected = -1.1932_f64; assert!((y2 - expected).abs() < 0.0001);
Computes the value of the second kind Bessel function of order n, rounding to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.yn_mut(2); let expected = -1.1932_f64; assert!((f - expected).abs() < 0.0001);
Computes the value of the second kind Bessel function of order n, applying the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // y2(1.25) = −1.1932 // using 4 significant bits: −1.25 let dir = f.yn_round(2, Round::Nearest); assert_eq!(f, -1.25); assert_eq!(dir, Ordering::Less);
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);
Computes the arithmetic-geometric mean of self
and other
, rounding
to the nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let g = Float::with_val(53, 3.75); let agm = f.agm(&g); let expected = 2.3295_f64; assert!((agm - expected).abs() < 0.0001);
Computes the arithmetic-geometric mean of self
and other
, rounding
to the nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); let g = Float::with_val(53, 3.75); f.agm_mut(&g); let expected = 2.3295_f64; assert!((f - expected).abs() < 0.0001);
Computes the arithmetic-geometric mean of self
and other
, applying
the specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); let g = Float::with_val(4, 3.75); // agm(1.25, 3.75) = 2.3295 // using 4 significant bits: 2.25 let dir = f.agm_round(&g, Round::Nearest); assert_eq!(f, 2.25); assert_eq!(dir, Ordering::Less);
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);
Computes the Euclidean norm of self
and other
, rounding to the
nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let g = Float::with_val(53, 3.75); let hypot = f.hypot(&g); let expected = 3.9528_f64; assert!((hypot - expected).abs() < 0.0001);
Computes the Euclidean norm of self
and other
, rounding to the
nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); let g = Float::with_val(53, 3.75); f.hypot_mut(&g); let expected = 3.9528_f64; assert!((f - expected).abs() < 0.0001);
Computes the Euclidean norm of self
and other
, applying the
specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); let g = Float::with_val(4, 3.75); // hypot(1.25) = 3.9528 // using 4 significant bits: 4.0 let dir = f.hypot_round(&g, Round::Nearest); assert_eq!(f, 4.0); assert_eq!(dir, Ordering::Greater);
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);
Computes the value of the Airy function Ai on self
, rounding to the
nearest.
Examples
use rug::Float; let f = Float::with_val(53, 1.25); let ai = f.ai(); let expected = 0.0996_f64; assert!((ai - expected).abs() < 0.0001);
Computes the value of the Airy function Ai on self
, rounding to the
nearest.
Examples
use rug::Float; let mut f = Float::with_val(53, 1.25); f.ai_mut(); let expected = 0.0996_f64; assert!((f - expected).abs() < 0.0001);
Computes the value of the Airy function Ai on self
, applying the
specified rounding method.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // Use only 4 bits of precision to show rounding. let mut f = Float::with_val(4, 1.25); // ai(1.25) = 0.0996 // using 4 significant bits: 0.1015625 let dir = f.ai_round(Round::Nearest); assert_eq!(f, 0.1015625); assert_eq!(dir, Ordering::Greater);
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);
Rounds up to the next higher integer.
Examples
use rug::Float; let f1 = Float::with_val(53, -23.75); let ceil1 = f1.ceil(); assert_eq!(ceil1, -23); let f2 = Float::with_val(53, 23.75); let ceil2 = f2.ceil(); assert_eq!(ceil2, 24);
Rounds up to the next higher integer.
Examples
use rug::Float; let mut f1 = Float::with_val(53, -23.75); f1.ceil_mut(); assert_eq!(f1, -23); let mut f2 = Float::with_val(53, 23.75); f2.ceil_mut(); assert_eq!(f2, 24);
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);
Rounds down to the next lower integer.
Examples
use rug::Float; let f1 = Float::with_val(53, -23.75); let floor1 = f1.floor(); assert_eq!(floor1, -24); let f2 = Float::with_val(53, 23.75); let floor2 = f2.floor(); assert_eq!(floor2, 23);
Rounds down to the next lower integer.
Examples
use rug::Float; let mut f1 = Float::with_val(53, -23.75); f1.floor_mut(); assert_eq!(f1, -24); let mut f2 = Float::with_val(53, 23.75); f2.floor_mut(); assert_eq!(f2, 23);
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);
Rounds to the nearest integer, rounding half-way cases away from zero.
Examples
use rug::Float; let f1 = Float::with_val(53, -23.75); let round1 = f1.round(); assert_eq!(round1, -24); let f2 = Float::with_val(53, 23.75); let round2 = f2.round(); assert_eq!(round2, 24);
Rounds to the nearest integer, rounding half-way cases away from zero.
Examples
use rug::Float; let mut f1 = Float::with_val(53, -23.75); f1.round_mut(); assert_eq!(f1, -24); let mut f2 = Float::with_val(53, 23.75); f2.round_mut(); assert_eq!(f2, 24);
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);
Rounds to the nearest integer, rounding half-way cases to even.
Examples
use rug::Float; let f1 = Float::with_val(53, 23.5); let round1 = f1.round_even(); assert_eq!(round1, 24); let f2 = Float::with_val(53, 24.5); let round2 = f2.round_even(); assert_eq!(round2, 24);
Rounds to the nearest integer, rounding half-way cases to even.
Examples
use rug::Float; let mut f1 = Float::with_val(53, 23.5); f1.round_even_mut(); assert_eq!(f1, 24); let mut f2 = Float::with_val(53, 24.5); f2.round_even_mut(); assert_eq!(f2, 24);
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);
Rounds to the next integer towards zero.
Examples
use rug::Float; let f1 = Float::with_val(53, -23.75); let trunc1 = f1.trunc(); assert_eq!(trunc1, -23); let f2 = Float::with_val(53, 23.75); let trunc2 = f2.trunc(); assert_eq!(trunc2, 23);
Rounds to the next integer towards zero.
Examples
use rug::Float; let mut f1 = Float::with_val(53, -23.75); f1.trunc_mut(); assert_eq!(f1, -23); let mut f2 = Float::with_val(53, 23.75); f2.trunc_mut(); assert_eq!(f2, 23);
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);
Gets the fractional part of the number.
Examples
use rug::Float; let f1 = Float::with_val(53, -23.75); let fract1 = f1.fract(); assert_eq!(fract1, -0.75); let f2 = Float::with_val(53, 23.75); let fract2 = f2.fract(); assert_eq!(fract2, 0.75);
Gets the fractional part of the number.
Examples
use rug::Float; let mut f1 = Float::with_val(53, -23.75); f1.fract_mut(); assert_eq!(f1, -0.75); let mut f2 = Float::with_val(53, 23.75); f2.fract_mut(); assert_eq!(f2, 0.75);
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);
Gets the integer and fractional parts of the number, rounding to the nearest.
The integer part is stored in self
and keeps its precision, while the
fractional part is stored in fract
keeping its precision.
The initial value of fract
is ignored.
Examples
use rug::Float; let f1 = Float::with_val(53, -23.75); let (trunc1, fract1) = f1.trunc_fract(Float::new(53)); assert_eq!(trunc1, -23); assert_eq!(fract1, -0.75); let f2 = Float::with_val(53, 23.75); let (trunc2, fract2) = f2.trunc_fract(Float::new(53)); assert_eq!(trunc2, 23); assert_eq!(fract2, 0.75);
Gets the integer and fractional parts of the number, rounding to the nearest.
The integer part is stored in self
and keeps its precision, while the
fractional part is stored in fract
keeping its precision.
The initial value of fract
is ignored.
Examples
use rug::Float; let mut f1 = Float::with_val(53, -23.75); let mut fract1 = Float::new(53); f1.trunc_fract_mut(&mut fract1); assert_eq!(f1, -23); assert_eq!(fract1, -0.75); let mut f2 = Float::with_val(53, 23.75); let mut fract2 = Float::new(53); f2.trunc_fract_mut(&mut fract2); assert_eq!(f2, 23); assert_eq!(fract2, 0.75);
Gets the integer and fractional parts of the number, applying the specified rounding method.
The first element of the returned tuple of rounding directions is always
Ordering::Equal
, as truncating a value
in place will always be exact.
The integer part is stored in self
and keeps its precision, while the
fractional part is stored in fract
keeping its precision.
The initial value of fract
is ignored.
Examples
use core::cmp::Ordering; use rug::{float::Round, Float}; // 0.515625 in binary is 0.100001 let mut f1 = Float::with_val(53, -23.515625); let mut fract1 = Float::new(4); let dir1 = f1.trunc_fract_round(&mut fract1, Round::Nearest); assert_eq!(f1, -23); assert_eq!(fract1, -0.5); assert_eq!(dir1, (Ordering::Equal, Ordering::Greater)); let mut f2 = Float::with_val(53, 23.515625); let mut fract2 = Float::new(4); let dir2 = f2.trunc_fract_round(&mut fract2, Round::Nearest); assert_eq!(f2, 23); assert_eq!(fract2, 0.5); assert_eq!(dir2, (Ordering::Equal, Ordering::Less));
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);
Generates a random number in the range 0 ≤ x < 1.
This is equivalent to generating a random integer in the range 0 ≤ x < 2p, where 2p is two raised to the power of the precision, and then dividing the integer by 2p. The smallest non-zero result will thus be 2−p, and will only have one bit set. In the smaller possible results, many bits will be zero, and not all the precision will be used.
There is a corner case where the generated random number is converted to NaN: if the precision is very large, the generated random number could have an exponent less than the allowed minimum exponent, and NaN is used to indicate this. For this to occur in practice, the minimum exponent has to be set to have a very small magnitude using the low-level MPFR interface, or the random number generator has to be designed specifically to trigger this case.
Assign<Src> for Float
is implemented with the returned
incomplete-computation value as Src
.
Examples
use rug::{rand::RandState, Assign, Float}; let mut rand = RandState::new(); let mut f = Float::new(2); f.assign(Float::random_bits(&mut rand)); assert!(f == 0.0 || f == 0.25 || f == 0.5 || f == 0.75); println!("0.0 ≤ {} < 1.0", f);
Generates a random number in the continuous range 0 ≤ x < 1.
The result can be rounded up to be equal to one. Unlike the
random_bits
method which generates a discrete
random number at intervals depending on the precision, this method is
equivalent to generating a continuous random number with infinite
precision and then rounding the result. This means that even the smaller
numbers will be using all the available precision bits, and rounding is
performed in all cases, not in some corner case.
Rounding directions for generated random numbers cannot be
Ordering::Equal
, as the random numbers
generated can be considered to have infinite precision before rounding.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Float
AssignRound<Src> for Float
Examples
use rug::{rand::RandState, Float}; let mut rand = RandState::new(); let f = Float::with_val(2, Float::random_cont(&mut rand)); // The significand is either 0b10 or 0b11 assert!( f == 1.0 || f == 0.75 || f == 0.5 || f == 0.375 || f == 0.25 || f <= 0.1875 );
Generates a random number according to a standard normal Gaussian distribution, rounding to the nearest.
Rounding directions for generated random numbers cannot be
Ordering::Equal
, as the random numbers
generated can be considered to have infinite precision before rounding.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Float
AssignRound<Src> for Float
Examples
use rug::{rand::RandState, Float}; let mut rand = RandState::new(); let f = Float::with_val(53, Float::random_normal(&mut rand)); println!("Normal random number: {}", f);
Generates a random number according to an exponential distribution with mean one, rounding to the nearest.
Rounding directions for generated random numbers cannot be
Ordering::Equal
, as the random numbers
generated can be considered to have infinite precision before rounding.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Float
AssignRound<Src> for Float
Examples
use rug::{rand::RandState, Float}; let mut rand = RandState::new(); let f = Float::with_val(53, Float::random_exp(&mut rand)); println!("Exponential random number: {}", f);
Trait Implementations
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Deserialize this value from the given Serde deserializer. Read more
fn deserialize_in_place<D: Deserializer<'de>>(
deserializer: D,
place: &mut Float
) -> Result<(), D::Error>
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
Performs the *=
operation. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than (for self
and other
) and is used by the >
operator. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Peforms the power operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Performs the %=
operation. Read more
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Performs the <<=
operation. Read more
Performs the <<=
operation. Read more
Performs the <<=
operation. Read more
Performs the <<=
operation. Read more
Performs the >>=
operation. Read more
Performs the >>=
operation. Read more
Performs the >>=
operation. Read more
Performs the >>=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more
type Error = TryFromFloatError
type Error = TryFromFloatError
The type returned in the event of a conversion error.
Performs the conversion.
type Error = TryFromFloatError
type Error = TryFromFloatError
The type returned in the event of a conversion error.
Performs the conversion.
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Auto Trait Implementations
Blanket Implementations
Mutably borrows from an owned value. Read more
Casts the value.
Casts the value.
Casts the value.
Casts the value.
Casts the value.