Struct rug::complex::SmallComplex
source · pub struct SmallComplex { /* private fields */ }
Expand description
A small complex number that does not require any memory allocation.
This can be useful when you have real and imaginary numbers that are primitive
integers or floats and you need a reference to a Complex
.
The SmallComplex
will have a precision according to the types of the
primitives used to set its real and imaginary parts. Note that if different
types are used to set the parts, the parts can have different precisions.
i8
,u8
: the part will have eight bits of precision.i16
,u16
: the part will have 16 bits of precision.i32
,u32
: the part will have 32 bits of precision.i64
,u64
: the part will have 64 bits of precision.i128
,u128
: the part will have 128 bits of precision.isize
,usize
: the part will have 32 or 64 bits of precision, depending on the platform.f32
: the part will have 24 bits of precision.f64
: the part will have 53 bits of precision.Special
: the part will have the minimum possible precision.
The SmallComplex
type can be coerced to a Complex
, as it implements
Deref<Target = Complex>
.
Examples
use rug::complex::SmallComplex;
use rug::Complex;
// `a` requires a heap allocation
let mut a = Complex::with_val(53, (1, 2));
// `b` can reside on the stack
let b = SmallComplex::from((-10f64, -20.5f64));
a += &*b;
assert_eq!(*a.real(), -9);
assert_eq!(*a.imag(), -18.5);
Implementations
sourceimpl SmallComplex
impl SmallComplex
sourcepub const fn new() -> Self
pub const fn new() -> Self
Creates a SmallComplex
with value 0 and the minimum possible
precision.
Examples
use rug::complex::SmallComplex;
let c = SmallComplex::new();
// Borrow c as if it were Complex.
assert_eq!(*c, 0);
sourcepub unsafe fn as_nonreallocating_complex(&mut self) -> &mut Complex
pub unsafe fn as_nonreallocating_complex(&mut self) -> &mut Complex
Returns a mutable reference to a Complex
number for simple
operations that do not need to change the precision of the real or
imaginary part.
Safety
It is undefined behavior to modify the precision of the referenced
Complex
number or to swap it with another number.
Examples
use rug::complex::SmallComplex;
let mut c = SmallComplex::from((1.0f32, 3.0f32));
// rotation does not change the precision
unsafe {
c.as_nonreallocating_complex().mul_i_mut(false);
}
assert_eq!(*c, (-3.0, 1.0));
Methods from Deref<Target = Complex>
sourcepub fn prec(&self) -> (u32, u32)
pub fn prec(&self) -> (u32, u32)
Returns the precision of the real and imaginary parts.
Examples
use rug::Complex;
let r = Complex::new((24, 53));
assert_eq!(r.prec(), (24, 53));
sourcepub fn as_raw(&self) -> *const mpc_t
pub fn as_raw(&self) -> *const mpc_t
Returns a pointer to the inner MPC complex number.
The returned pointer will be valid for as long as self
is valid.
Examples
use gmp_mpfr_sys::mpc;
use gmp_mpfr_sys::mpfr;
use gmp_mpfr_sys::mpfr::rnd_t;
use rug::Complex;
let c = Complex::with_val(53, (-14.5, 3.25));
let m_ptr = c.as_raw();
unsafe {
let re_ptr = mpc::realref_const(m_ptr);
let re = mpfr::get_d(re_ptr, rnd_t::RNDN);
assert_eq!(re, -14.5);
let im_ptr = mpc::imagref_const(m_ptr);
let im = mpfr::get_d(im_ptr, rnd_t::RNDN);
assert_eq!(im, 3.25);
}
// c is still valid
assert_eq!(c, (-14.5, 3.25));
sourcepub fn to_string_radix(&self, radix: i32, num_digits: Option<usize>) -> String
pub fn to_string_radix(&self, radix: i32, num_digits: Option<usize>) -> String
Returns a string representation of the value 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::Complex;
let c1 = Complex::with_val(53, 0);
assert_eq!(c1.to_string_radix(10, None), "(0 0)");
let c2 = Complex::with_val(12, (15, 5));
assert_eq!(c2.to_string_radix(16, None), "(f.000 5.000)");
let c3 = Complex::with_val(53, (10, -4));
assert_eq!(c3.to_string_radix(10, Some(3)), "(10.0 -4.00)");
assert_eq!(c3.to_string_radix(5, Some(3)), "(20.0 -4.00)");
// 2 raised to the power of 80 in hex is 1 followed by 20 zeros
let c4 = Complex::with_val(53, (80f64.exp2(), 0.25));
assert_eq!(c4.to_string_radix(10, Some(3)), "(1.21e24 2.50e-1)");
assert_eq!(c4.to_string_radix(16, Some(3)), "(1.00@20 4.00@-1)");
sourcepub fn to_string_radix_round(
&self,
radix: i32,
num_digits: Option<usize>,
round: (Round, Round)
) -> String
pub fn to_string_radix_round(
&self,
radix: i32,
num_digits: Option<usize>,
round: (Round, Round)
) -> String
Returns a string representation of the value 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;
use rug::Complex;
let c = Complex::with_val(10, 10.4);
let down = (Round::Down, Round::Down);
let nearest = (Round::Nearest, Round::Nearest);
let up = (Round::Up, Round::Up);
let nd = c.to_string_radix_round(10, None, down);
assert_eq!(nd, "(10.406 0)");
let nu = c.to_string_radix_round(10, None, up);
assert_eq!(nu, "(10.407 0)");
let sd = c.to_string_radix_round(10, Some(2), down);
assert_eq!(sd, "(10 0)");
let sn = c.to_string_radix_round(10, Some(2), nearest);
assert_eq!(sn, "(10 0)");
let su = c.to_string_radix_round(10, Some(2), up);
assert_eq!(su, "(11 0)");
sourcepub fn as_neg(&self) -> BorrowComplex<'_>
pub fn as_neg(&self) -> BorrowComplex<'_>
Borrows a negated copy of the Complex
number.
The returned object implements Deref<Target = Complex>
.
This method performs a shallow copy and negates it, and negation does not change the allocated data.
Examples
use rug::Complex;
let c = Complex::with_val(53, (4.2, -2.3));
let neg_c = c.as_neg();
assert_eq!(*neg_c, (-4.2, 2.3));
// methods taking &self can be used on the returned object
let reneg_c = neg_c.as_neg();
assert_eq!(*reneg_c, (4.2, -2.3));
assert_eq!(*reneg_c, c);
sourcepub fn as_conj(&self) -> BorrowComplex<'_>
pub fn as_conj(&self) -> BorrowComplex<'_>
Borrows a conjugate copy of the Complex
number.
The returned object implements Deref<Target = Complex>
.
This method performs a shallow copy and negates its imaginary part, and negation does not change the allocated data.
Examples
use rug::Complex;
let c = Complex::with_val(53, (4.2, -2.3));
let conj_c = c.as_conj();
assert_eq!(*conj_c, (4.2, 2.3));
// methods taking &self can be used on the returned object
let reconj_c = conj_c.as_conj();
assert_eq!(*reconj_c, (4.2, -2.3));
assert_eq!(*reconj_c, c);
sourcepub fn as_mul_i(&self, negative: bool) -> BorrowComplex<'_>
pub fn as_mul_i(&self, negative: bool) -> BorrowComplex<'_>
Borrows a rotated copy of the Complex
number.
The returned object implements Deref<Target = Complex>
.
This method operates by performing some shallow copying; unlike the
mul_i
method and friends, this method swaps the
precision of the real and imaginary parts if they have unequal
precisions.
Examples
use rug::Complex;
let c = Complex::with_val(53, (4.2, -2.3));
let mul_i_c = c.as_mul_i(false);
assert_eq!(*mul_i_c, (2.3, 4.2));
// methods taking &self can be used on the returned object
let mul_ii_c = mul_i_c.as_mul_i(false);
assert_eq!(*mul_ii_c, (-4.2, 2.3));
let mul_1_c = mul_i_c.as_mul_i(true);
assert_eq!(*mul_1_c, (4.2, -2.3));
assert_eq!(*mul_1_c, c);
sourcepub fn as_ord(&self) -> &OrdComplex
pub fn as_ord(&self) -> &OrdComplex
Borrows the Complex
number as an ordered complex number of type
OrdComplex
.
The same result can be obtained using the implementation of
AsRef<OrdComplex>
which is provided for Complex
.
Examples
use core::cmp::Ordering;
use rug::float::Special;
use rug::Complex;
let nan_c = Complex::with_val(53, (Special::Nan, Special::Nan));
let nan = nan_c.as_ord();
assert_eq!(nan.cmp(nan), Ordering::Equal);
let one_neg0_c = Complex::with_val(53, (1, Special::NegZero));
let one_neg0 = one_neg0_c.as_ord();
let one_pos0_c = Complex::with_val(53, (1, Special::Zero));
let one_pos0 = one_pos0_c.as_ord();
assert_eq!(one_neg0.cmp(one_pos0), Ordering::Less);
let zero_inf_s = (Special::Zero, Special::Infinity);
let zero_inf_c = Complex::with_val(53, zero_inf_s);
let zero_inf = zero_inf_c.as_ord();
assert_eq!(one_pos0.cmp(zero_inf), Ordering::Greater);
sourcepub fn cmp_abs(&self, other: &Self) -> Option<Ordering>
pub fn cmp_abs(&self, other: &Self) -> Option<Ordering>
Compares the absolute values of self
and other
.
Examples
use core::cmp::Ordering;
use rug::Complex;
let five = Complex::with_val(53, (5, 0));
let five_rotated = Complex::with_val(53, (3, -4));
let greater_than_five = Complex::with_val(53, (-4, -4));
let has_nan = Complex::with_val(53, (5, 0.0 / 0.0));
assert_eq!(five.cmp_abs(&five_rotated), Some(Ordering::Equal));
assert_eq!(five.cmp_abs(&greater_than_five), Some(Ordering::Less));
assert_eq!(five.cmp_abs(&has_nan), None);
sourcepub fn total_cmp(&self, other: &Complex) -> Ordering
pub fn total_cmp(&self, other: &Complex) -> Ordering
Returns the total ordering between self
and other
.
For ordering, the real part has precedence over the imaginary part. Negative zero is ordered as less than positive zero. Negative NaN is ordered as less than negative infinity, while positive NaN is ordered as greater than positive infinity. Comparing two negative NaNs or two positive NaNs produces equality.
Examples
use rug::float::Special;
use rug::Complex;
let mut values = vec![
Complex::with_val(53, (Special::Zero, Special::Zero)),
Complex::with_val(53, (Special::Zero, Special::NegZero)),
Complex::with_val(53, (Special::NegZero, Special::Infinity)),
];
values.sort_by(Complex::total_cmp);
// (-0, +∞)
assert!(values[0].real().is_zero() && values[0].real().is_sign_negative());
assert!(values[0].imag().is_infinite() && values[0].imag().is_sign_positive());
// (+0, -0)
assert!(values[1].real().is_zero() && values[1].real().is_sign_positive());
assert!(values[1].imag().is_zero() && values[1].imag().is_sign_negative());
// (+0, +0)
assert!(values[2].real().is_zero() && values[2].real().is_sign_positive());
assert!(values[2].imag().is_zero() && values[2].imag().is_sign_positive());
sourcepub fn mul_add_ref<'a>(
&'a self,
mul: &'a Self,
add: &'a Self
) -> AddMulIncomplete<'a>
pub fn mul_add_ref<'a>(
&'a self,
mul: &'a Self,
add: &'a Self
) -> AddMulIncomplete<'a>
Multiplies and adds in one fused operation.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
a.mul_add_ref(&b, &c)
produces the exact same result as
&a * &b + &c
.
Examples
use rug::Complex;
let a = Complex::with_val(53, (10, 0));
let b = Complex::with_val(53, (1, -1));
let c = Complex::with_val(53, (1000, 1000));
// (10 + 0i) × (1 - i) + (1000 + 1000i) = (1010 + 990i)
let ans = Complex::with_val(53, a.mul_add_ref(&b, &c));
assert_eq!(ans, (1010, 990));
sourcepub fn mul_sub_ref<'a>(
&'a self,
mul: &'a Self,
sub: &'a Self
) -> SubMulFromIncomplete<'a>
pub fn mul_sub_ref<'a>(
&'a self,
mul: &'a Self,
sub: &'a Self
) -> SubMulFromIncomplete<'a>
Multiplies and subtracts in one fused operation.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
a.mul_sub_ref(&b, &c)
produces the exact same result as &a * &b - &c
.
Examples
use rug::Complex;
let a = Complex::with_val(53, (10, 0));
let b = Complex::with_val(53, (1, -1));
let c = Complex::with_val(53, (1000, 1000));
// (10 + 0i) × (1 - i) - (1000 + 1000i) = (-990 - 1010i)
let ans = Complex::with_val(53, a.mul_sub_ref(&b, &c));
assert_eq!(ans, (-990, -1010));
sourcepub fn proj_ref(&self) -> ProjIncomplete<'_>
pub fn proj_ref(&self) -> ProjIncomplete<'_>
Computes the projection onto the Riemann sphere.
If no parts of the number are infinite, the result is unchanged. If any part is infinite, the real part of the result is set to +∞ and the imaginary part of the result is set to 0 with the same sign as the imaginary part of the input.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use core::f64;
use rug::Complex;
let c1 = Complex::with_val(53, (f64::INFINITY, 50));
let proj1 = Complex::with_val(53, c1.proj_ref());
assert_eq!(proj1, (f64::INFINITY, 0.0));
let c2 = Complex::with_val(53, (f64::NAN, f64::NEG_INFINITY));
let proj2 = Complex::with_val(53, c2.proj_ref());
assert_eq!(proj2, (f64::INFINITY, 0.0));
// imaginary was negative, so now it is minus zero
assert!(proj2.imag().is_sign_negative());
sourcepub fn square_ref(&self) -> SquareIncomplete<'_>
pub fn square_ref(&self) -> SquareIncomplete<'_>
Computes the square.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use core::cmp::Ordering;
use rug::float::Round;
use rug::Complex;
let c = Complex::with_val(53, (1.25, 1.25));
// (1.25 + 1.25i) squared is (0 + 3.125i).
let r = c.square_ref();
// With 4 bits of precision, 3.125 is rounded down to 3.
let round = (Round::Down, Round::Down);
let (square, dir) = Complex::with_val_round(4, r, round);
assert_eq!(square, (0, 3));
assert_eq!(dir, (Ordering::Equal, Ordering::Less));
sourcepub fn sqrt_ref(&self) -> SqrtIncomplete<'_>
pub fn sqrt_ref(&self) -> SqrtIncomplete<'_>
Computes the square root.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use core::cmp::Ordering;
use rug::float::Round;
use rug::Complex;
let c = Complex::with_val(53, (2, 2.25));
// Square root of (2 + 2.25i) is (1.5828 + 0.7108i).
let r = c.sqrt_ref();
// Nearest with 4 bits of precision: (1.625 + 0.6875i)
let nearest = (Round::Nearest, Round::Nearest);
let (sqrt, dir) = Complex::with_val_round(4, r, nearest);
assert_eq!(sqrt, (1.625, 0.6875));
assert_eq!(dir, (Ordering::Greater, Ordering::Less));
sourcepub fn conj_ref(&self) -> ConjIncomplete<'_>
pub fn conj_ref(&self) -> ConjIncomplete<'_>
Computes the complex conjugate.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::Complex;
let c = Complex::with_val(53, (1.5, 2.5));
let conj = Complex::with_val(53, c.conj_ref());
assert_eq!(conj, (1.5, -2.5));
sourcepub fn abs_ref(&self) -> AbsIncomplete<'_>
pub fn abs_ref(&self) -> AbsIncomplete<'_>
Computes the absolute value.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Float
Assign<Src> for Complex
AssignRound<Src> for Float
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::{Complex, Float};
let c = Complex::with_val(53, (30, 40));
let f = Float::with_val(53, c.abs_ref());
assert_eq!(f, 50);
sourcepub fn arg_ref(&self) -> ArgIncomplete<'_>
pub fn arg_ref(&self) -> ArgIncomplete<'_>
Computes the argument.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Float
Assign<Src> for Complex
AssignRound<Src> for Float
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use core::f64;
use rug::{Assign, Complex, Float};
// f has precision 53, just like f64, so PI constants match.
let mut arg = Float::new(53);
let c_pos = Complex::with_val(53, 1);
arg.assign(c_pos.arg_ref());
assert!(arg.is_zero());
let c_neg = Complex::with_val(53, -1.3);
arg.assign(c_neg.arg_ref());
assert_eq!(arg, f64::consts::PI);
let c_pi_4 = Complex::with_val(53, (1.333, 1.333));
arg.assign(c_pi_4.arg_ref());
assert_eq!(arg, f64::consts::FRAC_PI_4);
sourcepub fn mul_i_ref(&self, negative: bool) -> MulIIncomplete<'_>
pub fn mul_i_ref(&self, negative: bool) -> MulIIncomplete<'_>
Multiplies the complex number by ±i.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::Complex;
let c = Complex::with_val(53, (13, 24));
let rotated = Complex::with_val(53, c.mul_i_ref(false));
assert_eq!(rotated, (-24, 13));
sourcepub fn recip_ref(&self) -> RecipIncomplete<'_>
pub fn recip_ref(&self) -> RecipIncomplete<'_>
Computes the reciprocal.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::Complex;
let c = Complex::with_val(53, (1, 1));
// 1/(1 + i) = (0.5 - 0.5i)
let recip = Complex::with_val(53, c.recip_ref());
assert_eq!(recip, (0.5, -0.5));
sourcepub fn norm_ref(&self) -> NormIncomplete<'_>
pub fn norm_ref(&self) -> NormIncomplete<'_>
Computes the norm, that is the square of the absolute value.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Float
Assign<Src> for Complex
AssignRound<Src> for Float
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::{Complex, Float};
let c = Complex::with_val(53, (3, 4));
let f = Float::with_val(53, c.norm_ref());
assert_eq!(f, 25);
sourcepub fn ln_ref(&self) -> LnIncomplete<'_>
pub fn ln_ref(&self) -> LnIncomplete<'_>
Computes the natural logarithm.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::Complex;
let c = Complex::with_val(53, (1.5, -0.5));
let ln = Complex::with_val(53, c.ln_ref());
let expected = Complex::with_val(53, (0.4581, -0.3218));
assert!(*(ln - expected).abs().real() < 0.0001);
sourcepub fn log10_ref(&self) -> Log10Incomplete<'_>
pub fn log10_ref(&self) -> Log10Incomplete<'_>
Computes the logarithm to base 10.
The following are implemented with the returned
incomplete-computation value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::Complex;
let c = Complex::with_val(53, (1.5, -0.5));
let log10 = Complex::with_val(53, c.log10_ref());
let expected = Complex::with_val(53, (0.1990, -0.1397));
assert!(*(log10 - expected).abs().real() < 0.0001);
sourcepub fn exp_ref(&self) -> ExpIncomplete<'_>
pub fn exp_ref(&self) -> ExpIncomplete<'_>
Computes the exponential.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::Complex;
let c = Complex::with_val(53, (0.5, -0.75));
let exp = Complex::with_val(53, c.exp_ref());
let expected = Complex::with_val(53, (1.2064, -1.1238));
assert!(*(exp - expected).abs().real() < 0.0001);
sourcepub fn sin_ref(&self) -> SinIncomplete<'_>
pub fn sin_ref(&self) -> SinIncomplete<'_>
Computes the sine.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::Complex;
let c = Complex::with_val(53, (1, 1));
let sin = Complex::with_val(53, c.sin_ref());
let expected = Complex::with_val(53, (1.2985, 0.6350));
assert!(*(sin - expected).abs().real() < 0.0001);
sourcepub fn cos_ref(&self) -> CosIncomplete<'_>
pub fn cos_ref(&self) -> CosIncomplete<'_>
Computes the cosine.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::Complex;
let c = Complex::with_val(53, (1, 1));
let cos = Complex::with_val(53, c.cos_ref());
let expected = Complex::with_val(53, (0.8337, -0.9889));
assert!(*(cos - expected).abs().real() < 0.0001);
sourcepub fn sin_cos_ref(&self) -> SinCosIncomplete<'_>
pub fn sin_cos_ref(&self) -> SinCosIncomplete<'_>
Computes the sine and cosine.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for (Complex, Complex)
Assign<Src> for (&mut Complex, &mut Complex)
AssignRound<Src> for (Complex, Complex)
AssignRound<Src> for (&mut Complex, &mut Complex)
CompleteRound<Completed = (Complex, Complex)> for Src
Examples
use core::cmp::Ordering;
use rug::float::Round;
use rug::ops::AssignRound;
use rug::{Assign, Complex};
let phase = Complex::with_val(53, (1, 1));
let (mut sin, mut cos) = (Complex::new(53), Complex::new(53));
let sin_cos = phase.sin_cos_ref();
(&mut sin, &mut cos).assign(sin_cos);
let expected_sin = Complex::with_val(53, (1.2985, 0.6350));
let expected_cos = Complex::with_val(53, (0.8337, -0.9889));
assert!(*(sin - expected_sin).abs().real() < 0.0001);
assert!(*(cos - expected_cos).abs().real() < 0.0001);
// using 4 significant bits: sin = (1.25 + 0.625i)
// using 4 significant bits: cos = (0.8125 - i)
let (mut sin_4, mut cos_4) = (Complex::new(4), Complex::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, Round::Nearest));
assert_eq!(sin_4, (1.25, 0.625));
assert_eq!(dir_sin, (Ordering::Less, Ordering::Less));
assert_eq!(cos_4, (0.8125, -1));
assert_eq!(dir_cos, (Ordering::Less, Ordering::Less));
sourcepub fn tan_ref(&self) -> TanIncomplete<'_>
pub fn tan_ref(&self) -> TanIncomplete<'_>
Computes the tangent.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::Complex;
let c = Complex::with_val(53, (1, 1));
let tan = Complex::with_val(53, c.tan_ref());
let expected = Complex::with_val(53, (0.2718, 1.0839));
assert!(*(tan - expected).abs().real() < 0.0001);
sourcepub fn sinh_ref(&self) -> SinhIncomplete<'_>
pub fn sinh_ref(&self) -> SinhIncomplete<'_>
Computes the hyperbolic sine.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::Complex;
let c = Complex::with_val(53, (1, 1));
let sinh = Complex::with_val(53, c.sinh_ref());
let expected = Complex::with_val(53, (0.6350, 1.2985));
assert!(*(sinh - expected).abs().real() < 0.0001);
sourcepub fn cosh_ref(&self) -> CoshIncomplete<'_>
pub fn cosh_ref(&self) -> CoshIncomplete<'_>
Computes the hyperbolic cosine.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::Complex;
let c = Complex::with_val(53, (1, 1));
let cosh = Complex::with_val(53, c.cosh_ref());
let expected = Complex::with_val(53, (0.8337, 0.9889));
assert!(*(cosh - expected).abs().real() < 0.0001);
sourcepub fn tanh_ref(&self) -> TanhIncomplete<'_>
pub fn tanh_ref(&self) -> TanhIncomplete<'_>
Computes the hyperbolic tangent.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::Complex;
let c = Complex::with_val(53, (1, 1));
let tanh = Complex::with_val(53, c.tanh_ref());
let expected = Complex::with_val(53, (1.0839, 0.2718));
assert!(*(tanh - expected).abs().real() < 0.0001);
sourcepub fn asin_ref(&self) -> AsinIncomplete<'_>
pub fn asin_ref(&self) -> AsinIncomplete<'_>
Computes the inverse sine.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::Complex;
let c = Complex::with_val(53, (1, 1));
let asin = Complex::with_val(53, c.asin_ref());
let expected = Complex::with_val(53, (0.6662, 1.0613));
assert!(*(asin - expected).abs().real() < 0.0001);
sourcepub fn acos_ref(&self) -> AcosIncomplete<'_>
pub fn acos_ref(&self) -> AcosIncomplete<'_>
Computes the inverse cosine.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::Complex;
let c = Complex::with_val(53, (1, 1));
let acos = Complex::with_val(53, c.acos_ref());
let expected = Complex::with_val(53, (0.9046, -1.0613));
assert!(*(acos - expected).abs().real() < 0.0001);
sourcepub fn atan_ref(&self) -> AtanIncomplete<'_>
pub fn atan_ref(&self) -> AtanIncomplete<'_>
Computes the inverse tangent.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::Complex;
let c = Complex::with_val(53, (1, 1));
let atan = Complex::with_val(53, c.atan_ref());
let expected = Complex::with_val(53, (1.0172, 0.4024));
assert!(*(atan - expected).abs().real() < 0.0001);
sourcepub fn asinh_ref(&self) -> AsinhIncomplete<'_>
pub fn asinh_ref(&self) -> AsinhIncomplete<'_>
Computes the inverse hyperboic sine.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::Complex;
let c = Complex::with_val(53, (1, 1));
let asinh = Complex::with_val(53, c.asinh_ref());
let expected = Complex::with_val(53, (1.0613, 0.6662));
assert!(*(asinh - expected).abs().real() < 0.0001);
sourcepub fn acosh_ref(&self) -> AcoshIncomplete<'_>
pub fn acosh_ref(&self) -> AcoshIncomplete<'_>
Computes the inverse hyperbolic cosine.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::Complex;
let c = Complex::with_val(53, (1, 1));
let acosh = Complex::with_val(53, c.acosh_ref());
let expected = Complex::with_val(53, (1.0613, 0.9046));
assert!(*(acosh - expected).abs().real() < 0.0001);
sourcepub fn atanh_ref(&self) -> AtanhIncomplete<'_>
pub fn atanh_ref(&self) -> AtanhIncomplete<'_>
Computes the inverse hyperbolic tangent.
The following are implemented with the returned incomplete-computation
value as Src
:
Assign<Src> for Complex
AssignRound<Src> for Complex
CompleteRound<Completed = Complex> for Src
Examples
use rug::Complex;
let c = Complex::with_val(53, (1, 1));
let atanh = Complex::with_val(53, c.atanh_ref());
let expected = Complex::with_val(53, (0.4024, 1.0172));
assert!(*(atanh - expected).abs().real() < 0.0001);
Trait Implementations
sourceimpl Assign<&SmallComplex> for SmallComplex
impl Assign<&SmallComplex> for SmallComplex
sourceimpl<Re: ToSmall> Assign<Re> for SmallComplex
impl<Re: ToSmall> Assign<Re> for SmallComplex
sourceimpl Assign<SmallComplex> for SmallComplex
impl Assign<SmallComplex> for SmallComplex
sourceimpl Clone for SmallComplex
impl Clone for SmallComplex
sourcefn clone(&self) -> SmallComplex
fn clone(&self) -> SmallComplex
1.0.0 · sourcefn clone_from(&mut self, source: &Self)
fn clone_from(&mut self, source: &Self)
source
. Read more