nalgebra

Struct Complex

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#[repr(C)]
pub struct Complex<T> { pub re: T, pub im: T, }
Expand description

A complex number in Cartesian form.

§Representation and Foreign Function Interface Compatibility

Complex<T> is memory layout compatible with an array [T; 2].

Note that Complex<F> where F is a floating point type is only memory layout compatible with C’s complex types, not necessarily calling convention compatible. This means that for FFI you can only pass Complex<F> behind a pointer, not as a value.

§Examples

Example of extern function declaration.

use num_complex::Complex;
use std::os::raw::c_int;

extern "C" {
    fn zaxpy_(n: *const c_int, alpha: *const Complex<f64>,
              x: *const Complex<f64>, incx: *const c_int,
              y: *mut Complex<f64>, incy: *const c_int);
}

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§re: T

Real portion of the complex number

§im: T

Imaginary portion of the complex number

Implementations§

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impl<T> Complex<T>

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pub const fn new(re: T, im: T) -> Complex<T>

Create a new Complex

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impl<T> Complex<T>
where T: Clone + Num,

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pub fn i() -> Complex<T>

Returns the imaginary unit.

See also Complex::I.

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pub fn norm_sqr(&self) -> T

Returns the square of the norm (since T doesn’t necessarily have a sqrt function), i.e. re^2 + im^2.

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pub fn scale(&self, t: T) -> Complex<T>

Multiplies self by the scalar t.

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pub fn unscale(&self, t: T) -> Complex<T>

Divides self by the scalar t.

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pub fn powu(&self, exp: u32) -> Complex<T>

Raises self to an unsigned integer power.

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impl<T> Complex<T>
where T: Clone + Num + Neg<Output = T>,

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pub fn conj(&self) -> Complex<T>

Returns the complex conjugate. i.e. re - i im

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pub fn inv(&self) -> Complex<T>

Returns 1/self

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pub fn powi(&self, exp: i32) -> Complex<T>

Raises self to a signed integer power.

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impl<T> Complex<T>
where T: Clone + Signed,

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pub fn l1_norm(&self) -> T

Returns the L1 norm |re| + |im| – the Manhattan distance from the origin.

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impl<T> Complex<T>
where T: FloatCore,

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pub fn is_nan(self) -> bool

Checks if the given complex number is NaN

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pub fn is_infinite(self) -> bool

Checks if the given complex number is infinite

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pub fn is_finite(self) -> bool

Checks if the given complex number is finite

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pub fn is_normal(self) -> bool

Checks if the given complex number is normal

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impl<T> Complex<T>
where T: ConstZero,

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pub const ZERO: Complex<T> = _

A constant Complex 0.

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impl<T> Complex<T>
where T: ConstOne + ConstZero,

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pub const ONE: Complex<T> = _

A constant Complex 1.

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pub const I: Complex<T> = _

A constant Complex i, the imaginary unit.

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impl<'a, 'b, T> Add<&'b Complex<T>> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the + operator.
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fn add( self, other: &Complex<T>, ) -> <&'a Complex<T> as Add<&'b Complex<T>>>::Output

Performs the + operation. Read more
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impl<'a, T> Add<&'a Complex<T>> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the + operator.
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fn add(self, other: &Complex<T>) -> <Complex<T> as Add<&'a Complex<T>>>::Output

Performs the + operation. Read more
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impl<'a, 'b, T> Add<&'a T> for &'b Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the + operator.
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fn add(self, other: &T) -> <&'b Complex<T> as Add<&'a T>>::Output

Performs the + operation. Read more
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impl<'a, T> Add<&'a T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the + operator.
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fn add(self, other: &T) -> <Complex<T> as Add<&'a T>>::Output

Performs the + operation. Read more
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impl<'a, T> Add<Complex<T>> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the + operator.
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fn add(self, other: Complex<T>) -> <&'a Complex<T> as Add<Complex<T>>>::Output

Performs the + operation. Read more
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impl<'a, T> Add<T> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the + operator.
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fn add(self, other: T) -> <&'a Complex<T> as Add<T>>::Output

Performs the + operation. Read more
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impl<T> Add<T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the + operator.
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fn add(self, other: T) -> <Complex<T> as Add<T>>::Output

Performs the + operation. Read more
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impl<T> Add for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the + operator.
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fn add(self, other: Complex<T>) -> <Complex<T> as Add>::Output

Performs the + operation. Read more
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impl<'a, T> AddAssign<&'a Complex<T>> for Complex<T>
where T: Clone + NumAssign,

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fn add_assign(&mut self, other: &Complex<T>)

Performs the += operation. Read more
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impl<'a, T> AddAssign<&'a T> for Complex<T>
where T: Clone + NumAssign,

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fn add_assign(&mut self, other: &T)

Performs the += operation. Read more
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impl<T> AddAssign<T> for Complex<T>
where T: Clone + NumAssign,

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fn add_assign(&mut self, other: T)

Performs the += operation. Read more
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impl<T> AddAssign for Complex<T>
where T: Clone + NumAssign,

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fn add_assign(&mut self, other: Complex<T>)

Performs the += operation. Read more
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impl<T, U> AsPrimitive<U> for Complex<T>
where T: AsPrimitive<U>, U: 'static + Copy,

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fn as_(self) -> U

Convert a value to another, using the as operator.
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impl<T> Binary for Complex<T>
where T: Binary + Num + PartialOrd + Clone,

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

Formats the value using the given formatter. Read more
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impl<T> Clone for Complex<T>
where T: Clone,

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fn clone(&self) -> Complex<T>

Returns a copy of the value. Read more
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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl<N> ComplexField for Complex<N>
where N: RealField + PartialOrd,

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fn exp(self) -> Complex<N>

Computes e^(self), where e is the base of the natural logarithm.

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fn ln(self) -> Complex<N>

Computes the principal value of natural logarithm of self.

This function has one branch cut:

  • (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

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fn sqrt(self) -> Complex<N>

Computes the principal value of the square root of self.

This function has one branch cut:

  • (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

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fn powf(self, exp: <Complex<N> as ComplexField>::RealField) -> Complex<N>

Raises self to a floating point power.

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fn log(self, base: N) -> Complex<N>

Returns the logarithm of self with respect to an arbitrary base.

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fn powc(self, exp: Complex<N>) -> Complex<N>

Raises self to a complex power.

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fn sin(self) -> Complex<N>

Computes the sine of self.

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fn cos(self) -> Complex<N>

Computes the cosine of self.

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fn tan(self) -> Complex<N>

Computes the tangent of self.

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fn asin(self) -> Complex<N>

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

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fn acos(self) -> Complex<N>

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

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fn atan(self) -> Complex<N>

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

  • (-∞i, -i], continuous from the left.
  • [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

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fn sinh(self) -> Complex<N>

Computes the hyperbolic sine of self.

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fn cosh(self) -> Complex<N>

Computes the hyperbolic cosine of self.

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fn tanh(self) -> Complex<N>

Computes the hyperbolic tangent of self.

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fn asinh(self) -> Complex<N>

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

  • (-∞i, -i), continuous from the left.
  • (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

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fn acosh(self) -> Complex<N>

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

  • (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

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fn atanh(self) -> Complex<N>

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

  • (-∞, -1], continuous from above.
  • [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

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type RealField = N

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fn from_real(re: <Complex<N> as ComplexField>::RealField) -> Complex<N>

Builds a pure-real complex number from the given value.
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fn real(self) -> <Complex<N> as ComplexField>::RealField

The real part of this complex number.
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fn imaginary(self) -> <Complex<N> as ComplexField>::RealField

The imaginary part of this complex number.
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fn argument(self) -> <Complex<N> as ComplexField>::RealField

The argument of this complex number.
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fn modulus(self) -> <Complex<N> as ComplexField>::RealField

The modulus of this complex number.
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fn modulus_squared(self) -> <Complex<N> as ComplexField>::RealField

The squared modulus of this complex number.
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fn norm1(self) -> <Complex<N> as ComplexField>::RealField

The sum of the absolute value of this complex number’s real and imaginary part.
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fn recip(self) -> Complex<N>

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fn conjugate(self) -> Complex<N>

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fn scale(self, factor: <Complex<N> as ComplexField>::RealField) -> Complex<N>

Multiplies this complex number by factor.
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fn unscale(self, factor: <Complex<N> as ComplexField>::RealField) -> Complex<N>

Divides this complex number by factor.
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fn floor(self) -> Complex<N>

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fn ceil(self) -> Complex<N>

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fn round(self) -> Complex<N>

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fn trunc(self) -> Complex<N>

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fn fract(self) -> Complex<N>

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fn mul_add(self, a: Complex<N>, b: Complex<N>) -> Complex<N>

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fn abs(self) -> <Complex<N> as ComplexField>::RealField

The absolute value of this complex number: self / self.signum(). Read more
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fn exp2(self) -> Complex<N>

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fn exp_m1(self) -> Complex<N>

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fn ln_1p(self) -> Complex<N>

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fn log2(self) -> Complex<N>

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fn log10(self) -> Complex<N>

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fn cbrt(self) -> Complex<N>

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fn powi(self, n: i32) -> Complex<N>

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fn is_finite(&self) -> bool

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fn try_sqrt(self) -> Option<Complex<N>>

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fn hypot(self, b: Complex<N>) -> <Complex<N> as ComplexField>::RealField

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()
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fn sin_cos(self) -> (Complex<N>, Complex<N>)

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fn sinh_cosh(self) -> (Complex<N>, Complex<N>)

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fn to_polar(self) -> (Self::RealField, Self::RealField)

The polar form of this complex number: (modulus, arg)
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fn to_exp(self) -> (Self::RealField, Self)

The exponential form of this complex number: (modulus, e^{i arg})
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fn signum(self) -> Self

The exponential part of this complex number: self / self.modulus()
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fn sinc(self) -> Self

Cardinal sine
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fn sinhc(self) -> Self

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fn cosc(self) -> Self

Cardinal cos
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fn coshc(self) -> Self

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impl<T> ConstOne for Complex<T>
where T: Clone + Num + ConstOne + ConstZero,

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const ONE: Complex<T> = Self::ONE

The multiplicative identity element of Self, 1.
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impl<T> ConstZero for Complex<T>
where T: Clone + Num + ConstZero,

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const ZERO: Complex<T> = Self::ZERO

The additive identity element of Self, 0.
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impl<T> Debug for Complex<T>
where T: Debug,

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

Formats the value using the given formatter. Read more
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impl<T> Default for Complex<T>
where T: Default,

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fn default() -> Complex<T>

Returns the “default value” for a type. Read more
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impl<'de, T> Deserialize<'de> for Complex<T>
where T: Deserialize<'de>,

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fn deserialize<D>( deserializer: D, ) -> Result<Complex<T>, <D as Deserializer<'de>>::Error>
where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer. Read more
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impl<T> Display for Complex<T>
where T: Display + Num + PartialOrd + Clone,

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

Formats the value using the given formatter. Read more
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impl<'a, 'b, T> Div<&'b Complex<T>> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the / operator.
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fn div( self, other: &Complex<T>, ) -> <&'a Complex<T> as Div<&'b Complex<T>>>::Output

Performs the / operation. Read more
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impl<'a, T> Div<&'a Complex<T>> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the / operator.
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fn div(self, other: &Complex<T>) -> <Complex<T> as Div<&'a Complex<T>>>::Output

Performs the / operation. Read more
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impl<'a, 'b, T> Div<&'a T> for &'b Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the / operator.
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fn div(self, other: &T) -> <&'b Complex<T> as Div<&'a T>>::Output

Performs the / operation. Read more
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impl<'a, T> Div<&'a T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the / operator.
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fn div(self, other: &T) -> <Complex<T> as Div<&'a T>>::Output

Performs the / operation. Read more
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impl<'a, T> Div<Complex<T>> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the / operator.
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fn div(self, other: Complex<T>) -> <&'a Complex<T> as Div<Complex<T>>>::Output

Performs the / operation. Read more
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impl<'a, T> Div<T> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the / operator.
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fn div(self, other: T) -> <&'a Complex<T> as Div<T>>::Output

Performs the / operation. Read more
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impl<T> Div<T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the / operator.
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fn div(self, other: T) -> <Complex<T> as Div<T>>::Output

Performs the / operation. Read more
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impl<T> Div for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the / operator.
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fn div(self, other: Complex<T>) -> <Complex<T> as Div>::Output

Performs the / operation. Read more
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impl<'a, T> DivAssign<&'a Complex<T>> for Complex<T>
where T: Clone + NumAssign,

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fn div_assign(&mut self, other: &Complex<T>)

Performs the /= operation. Read more
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impl<'a, T> DivAssign<&'a T> for Complex<T>
where T: Clone + NumAssign,

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fn div_assign(&mut self, other: &T)

Performs the /= operation. Read more
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impl<T> DivAssign<T> for Complex<T>
where T: Clone + NumAssign,

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fn div_assign(&mut self, other: T)

Performs the /= operation. Read more
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impl<T> DivAssign for Complex<T>
where T: Clone + NumAssign,

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fn div_assign(&mut self, other: Complex<T>)

Performs the /= operation. Read more
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impl<'a, T> From<&'a T> for Complex<T>
where T: Clone + Num,

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fn from(re: &T) -> Complex<T>

Converts to this type from the input type.
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impl<T> From<T> for Complex<T>
where T: Clone + Num,

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fn from(re: T) -> Complex<T>

Converts to this type from the input type.
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impl<T> FromPrimitive for Complex<T>
where T: FromPrimitive + Num,

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fn from_usize(n: usize) -> Option<Complex<T>>

Converts a usize to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_isize(n: isize) -> Option<Complex<T>>

Converts an isize to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_u8(n: u8) -> Option<Complex<T>>

Converts an u8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_u16(n: u16) -> Option<Complex<T>>

Converts an u16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_u32(n: u32) -> Option<Complex<T>>

Converts an u32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_u64(n: u64) -> Option<Complex<T>>

Converts an u64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_i8(n: i8) -> Option<Complex<T>>

Converts an i8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_i16(n: i16) -> Option<Complex<T>>

Converts an i16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_i32(n: i32) -> Option<Complex<T>>

Converts an i32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_i64(n: i64) -> Option<Complex<T>>

Converts an i64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_u128(n: u128) -> Option<Complex<T>>

Converts an u128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more
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fn from_i128(n: i128) -> Option<Complex<T>>

Converts an i128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more
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fn from_f32(n: f32) -> Option<Complex<T>>

Converts a f32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.
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fn from_f64(n: f64) -> Option<Complex<T>>

Converts a f64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned. Read more
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impl<T> FromStr for Complex<T>
where T: FromStr + Num + Clone,

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fn from_str(s: &str) -> Result<Complex<T>, <Complex<T> as FromStr>::Err>

Parses a +/- bi; ai +/- b; a; or bi where a and b are of type T

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type Err = ParseComplexError<<T as FromStr>::Err>

The associated error which can be returned from parsing.
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impl<T> Hash for Complex<T>
where T: Hash,

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fn hash<__H>(&self, state: &mut __H)
where __H: Hasher,

Feeds this value into the given Hasher. Read more
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fn hash_slice<H>(data: &[Self], state: &mut H)
where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher. Read more
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impl<'a, T> Inv for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn inv(self) -> <&'a Complex<T> as Inv>::Output

Returns the multiplicative inverse of self. Read more
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impl<T> Inv for Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn inv(self) -> <Complex<T> as Inv>::Output

Returns the multiplicative inverse of self. Read more
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impl<T> LowerExp for Complex<T>
where T: LowerExp + Num + PartialOrd + Clone,

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

Formats the value using the given formatter. Read more
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impl<T> LowerHex for Complex<T>
where T: LowerHex + Num + PartialOrd + Clone,

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

Formats the value using the given formatter. Read more
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impl<'a, 'b, T> Mul<&'b Complex<T>> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the * operator.
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fn mul( self, other: &Complex<T>, ) -> <&'a Complex<T> as Mul<&'b Complex<T>>>::Output

Performs the * operation. Read more
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impl<'a, T> Mul<&'a Complex<T>> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the * operator.
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fn mul(self, other: &Complex<T>) -> <Complex<T> as Mul<&'a Complex<T>>>::Output

Performs the * operation. Read more
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impl<'a, 'b, T> Mul<&'a T> for &'b Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the * operator.
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fn mul(self, other: &T) -> <&'b Complex<T> as Mul<&'a T>>::Output

Performs the * operation. Read more
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impl<'a, T> Mul<&'a T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the * operator.
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fn mul(self, other: &T) -> <Complex<T> as Mul<&'a T>>::Output

Performs the * operation. Read more
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impl<'a, T> Mul<Complex<T>> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the * operator.
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fn mul(self, other: Complex<T>) -> <&'a Complex<T> as Mul<Complex<T>>>::Output

Performs the * operation. Read more
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impl<'a, T> Mul<T> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the * operator.
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fn mul(self, other: T) -> <&'a Complex<T> as Mul<T>>::Output

Performs the * operation. Read more
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impl<T> Mul<T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the * operator.
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fn mul(self, other: T) -> <Complex<T> as Mul<T>>::Output

Performs the * operation. Read more
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impl<T> Mul for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the * operator.
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fn mul(self, other: Complex<T>) -> <Complex<T> as Mul>::Output

Performs the * operation. Read more
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impl<'a, 'b, T> MulAdd<&'b Complex<T>> for &'a Complex<T>
where T: Clone + Num + MulAdd<Output = T>,

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type Output = Complex<T>

The resulting type after applying the fused multiply-add.
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fn mul_add(self, other: &Complex<T>, add: &Complex<T>) -> Complex<T>

Performs the fused multiply-add operation (self * a) + b
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impl<T> MulAdd for Complex<T>
where T: Clone + Num + MulAdd<Output = T>,

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type Output = Complex<T>

The resulting type after applying the fused multiply-add.
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fn mul_add(self, other: Complex<T>, add: Complex<T>) -> Complex<T>

Performs the fused multiply-add operation (self * a) + b
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impl<'a, 'b, T> MulAddAssign<&'a Complex<T>, &'b Complex<T>> for Complex<T>

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fn mul_add_assign(&mut self, other: &Complex<T>, add: &Complex<T>)

Performs the fused multiply-add assignment operation *self = (*self * a) + b
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impl<T> MulAddAssign for Complex<T>

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fn mul_add_assign(&mut self, other: Complex<T>, add: Complex<T>)

Performs the fused multiply-add assignment operation *self = (*self * a) + b
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impl<'a, T> MulAssign<&'a Complex<T>> for Complex<T>
where T: Clone + NumAssign,

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fn mul_assign(&mut self, other: &Complex<T>)

Performs the *= operation. Read more
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impl<'a, T> MulAssign<&'a T> for Complex<T>
where T: Clone + NumAssign,

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fn mul_assign(&mut self, other: &T)

Performs the *= operation. Read more
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impl<T> MulAssign<T> for Complex<T>
where T: Clone + NumAssign,

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fn mul_assign(&mut self, other: T)

Performs the *= operation. Read more
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impl<T> MulAssign for Complex<T>
where T: Clone + NumAssign,

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fn mul_assign(&mut self, other: Complex<T>)

Performs the *= operation. Read more
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impl<'a, T> Neg for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn neg(self) -> <&'a Complex<T> as Neg>::Output

Performs the unary - operation. Read more
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impl<T> Neg for Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn neg(self) -> <Complex<T> as Neg>::Output

Performs the unary - operation. Read more
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impl<T: SimdRealField> Normed for Complex<T>

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type Norm = <T as SimdComplexField>::SimdRealField

The type of the norm.
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fn norm(&self) -> T::SimdRealField

Computes the norm.
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fn norm_squared(&self) -> T::SimdRealField

Computes the squared norm.
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fn scale_mut(&mut self, n: Self::Norm)

Multiply self by n.
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fn unscale_mut(&mut self, n: Self::Norm)

Divides self by n.
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impl<T> Num for Complex<T>
where T: Num + Clone,

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fn from_str_radix( s: &str, radix: u32, ) -> Result<Complex<T>, <Complex<T> as Num>::FromStrRadixErr>

Parses a +/- bi; ai +/- b; a; or bi where a and b are of type T

radix must be <= 18; larger radix would include i and j as digits, which cannot be supported.

The conversion returns an error if 18 <= radix <= 36; it panics if radix > 36.

The elements of T are parsed using Num::from_str_radix too, and errors (or panics) from that are reflected here as well.

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type FromStrRadixErr = ParseComplexError<<T as Num>::FromStrRadixErr>

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impl<T> NumCast for Complex<T>
where T: NumCast + Num,

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fn from<U>(n: U) -> Option<Complex<T>>
where U: ToPrimitive,

Creates a number from another value that can be converted into a primitive via the ToPrimitive trait. If the source value cannot be represented by the target type, then None is returned. Read more
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impl<T> Octal for Complex<T>
where T: Octal + Num + PartialOrd + Clone,

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

Formats the value using the given formatter. Read more
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impl<T> One for Complex<T>
where T: Clone + Num,

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fn one() -> Complex<T>

Returns the multiplicative identity element of Self, 1. Read more
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fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity. Read more
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fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.
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impl<T> PartialEq for Complex<T>
where T: PartialEq,

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fn eq(&self, other: &Complex<T>) -> bool

Tests for self and other values to be equal, and is used by ==.
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fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl<'a, 'b, T> Pow<&'b i128> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &i128) -> <&'a Complex<T> as Pow<&'b i128>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b i16> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &i16) -> <&'a Complex<T> as Pow<&'b i16>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b i32> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &i32) -> <&'a Complex<T> as Pow<&'b i32>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b i64> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &i64) -> <&'a Complex<T> as Pow<&'b i64>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b i8> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &i8) -> <&'a Complex<T> as Pow<&'b i8>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b isize> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &isize) -> <&'a Complex<T> as Pow<&'b isize>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b u128> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &u128) -> <&'a Complex<T> as Pow<&'b u128>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b u16> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &u16) -> <&'a Complex<T> as Pow<&'b u16>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b u32> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &u32) -> <&'a Complex<T> as Pow<&'b u32>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b u64> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &u64) -> <&'a Complex<T> as Pow<&'b u64>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b u8> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &u8) -> <&'a Complex<T> as Pow<&'b u8>>::Output

Returns self to the power rhs. Read more
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impl<'a, 'b, T> Pow<&'b usize> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: &usize) -> <&'a Complex<T> as Pow<&'b usize>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<i128> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: i128) -> <&'a Complex<T> as Pow<i128>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<i16> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: i16) -> <&'a Complex<T> as Pow<i16>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<i32> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: i32) -> <&'a Complex<T> as Pow<i32>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<i64> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: i64) -> <&'a Complex<T> as Pow<i64>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<i8> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: i8) -> <&'a Complex<T> as Pow<i8>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<isize> for &'a Complex<T>
where T: Clone + Num + Neg<Output = T>,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: isize) -> <&'a Complex<T> as Pow<isize>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<u128> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: u128) -> <&'a Complex<T> as Pow<u128>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<u16> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: u16) -> <&'a Complex<T> as Pow<u16>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<u32> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: u32) -> <&'a Complex<T> as Pow<u32>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<u64> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: u64) -> <&'a Complex<T> as Pow<u64>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<u8> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: u8) -> <&'a Complex<T> as Pow<u8>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Pow<usize> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The result after applying the operator.
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fn pow(self, exp: usize) -> <&'a Complex<T> as Pow<usize>>::Output

Returns self to the power rhs. Read more
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impl<'a, T> Product<&'a Complex<T>> for Complex<T>
where T: 'a + Num + Clone,

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fn product<I>(iter: I) -> Complex<T>
where I: Iterator<Item = &'a Complex<T>>,

Takes an iterator and generates Self from the elements by multiplying the items.
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impl<T> Product for Complex<T>
where T: Num + Clone,

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fn product<I>(iter: I) -> Complex<T>
where I: Iterator<Item = Complex<T>>,

Takes an iterator and generates Self from the elements by multiplying the items.
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impl<'a, 'b, T> Rem<&'b Complex<T>> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the % operator.
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fn rem( self, other: &Complex<T>, ) -> <&'a Complex<T> as Rem<&'b Complex<T>>>::Output

Performs the % operation. Read more
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impl<'a, T> Rem<&'a Complex<T>> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the % operator.
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fn rem(self, other: &Complex<T>) -> <Complex<T> as Rem<&'a Complex<T>>>::Output

Performs the % operation. Read more
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impl<'a, 'b, T> Rem<&'a T> for &'b Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the % operator.
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fn rem(self, other: &T) -> <&'b Complex<T> as Rem<&'a T>>::Output

Performs the % operation. Read more
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impl<'a, T> Rem<&'a T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the % operator.
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fn rem(self, other: &T) -> <Complex<T> as Rem<&'a T>>::Output

Performs the % operation. Read more
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impl<'a, T> Rem<Complex<T>> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the % operator.
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fn rem(self, other: Complex<T>) -> <&'a Complex<T> as Rem<Complex<T>>>::Output

Performs the % operation. Read more
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impl<'a, T> Rem<T> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the % operator.
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fn rem(self, other: T) -> <&'a Complex<T> as Rem<T>>::Output

Performs the % operation. Read more
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impl<T> Rem<T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the % operator.
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fn rem(self, other: T) -> <Complex<T> as Rem<T>>::Output

Performs the % operation. Read more
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impl<T> Rem for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the % operator.
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fn rem(self, modulus: Complex<T>) -> <Complex<T> as Rem>::Output

Performs the % operation. Read more
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impl<'a, T> RemAssign<&'a Complex<T>> for Complex<T>
where T: Clone + NumAssign,

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fn rem_assign(&mut self, other: &Complex<T>)

Performs the %= operation. Read more
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impl<'a, T> RemAssign<&'a T> for Complex<T>
where T: Clone + NumAssign,

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fn rem_assign(&mut self, other: &T)

Performs the %= operation. Read more
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impl<T> RemAssign<T> for Complex<T>
where T: Clone + NumAssign,

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fn rem_assign(&mut self, other: T)

Performs the %= operation. Read more
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impl<T> RemAssign for Complex<T>
where T: Clone + NumAssign,

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fn rem_assign(&mut self, modulus: Complex<T>)

Performs the %= operation. Read more
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impl<T> Serialize for Complex<T>
where T: Serialize,

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fn serialize<S>( &self, serializer: S, ) -> Result<<S as Serializer>::Ok, <S as Serializer>::Error>
where S: Serializer,

Serialize this value into the given Serde serializer. Read more
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impl SimdComplexField for Complex<AutoSimd<[f32; 16]>>

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fn simd_exp(self) -> Complex<AutoSimd<[f32; 16]>>

Computes e^(self), where e is the base of the natural logarithm.

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fn simd_ln(self) -> Complex<AutoSimd<[f32; 16]>>

Computes the principal value of natural logarithm of self.

This function has one branch cut:

  • (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

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fn simd_sqrt(self) -> Complex<AutoSimd<[f32; 16]>>

Computes the principal value of the square root of self.

This function has one branch cut:

  • (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

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fn simd_powf( self, exp: <Complex<AutoSimd<[f32; 16]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f32; 16]>>

Raises self to a floating point power.

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fn simd_log(self, base: AutoSimd<[f32; 16]>) -> Complex<AutoSimd<[f32; 16]>>

Returns the logarithm of self with respect to an arbitrary base.

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fn simd_powc( self, exp: Complex<AutoSimd<[f32; 16]>>, ) -> Complex<AutoSimd<[f32; 16]>>

Raises self to a complex power.

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fn simd_sin(self) -> Complex<AutoSimd<[f32; 16]>>

Computes the sine of self.

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fn simd_cos(self) -> Complex<AutoSimd<[f32; 16]>>

Computes the cosine of self.

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fn simd_tan(self) -> Complex<AutoSimd<[f32; 16]>>

Computes the tangent of self.

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fn simd_asin(self) -> Complex<AutoSimd<[f32; 16]>>

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

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fn simd_acos(self) -> Complex<AutoSimd<[f32; 16]>>

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

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fn simd_atan(self) -> Complex<AutoSimd<[f32; 16]>>

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

  • (-∞i, -i], continuous from the left.
  • [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

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fn simd_sinh(self) -> Complex<AutoSimd<[f32; 16]>>

Computes the hyperbolic sine of self.

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fn simd_cosh(self) -> Complex<AutoSimd<[f32; 16]>>

Computes the hyperbolic cosine of self.

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fn simd_tanh(self) -> Complex<AutoSimd<[f32; 16]>>

Computes the hyperbolic tangent of self.

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fn simd_asinh(self) -> Complex<AutoSimd<[f32; 16]>>

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

  • (-∞i, -i), continuous from the left.
  • (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

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fn simd_acosh(self) -> Complex<AutoSimd<[f32; 16]>>

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

  • (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

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fn simd_atanh(self) -> Complex<AutoSimd<[f32; 16]>>

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

  • (-∞, -1], continuous from above.
  • [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

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type SimdRealField = AutoSimd<[f32; 16]>

Type of the coefficients of a complex number.
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fn simd_horizontal_sum( self, ) -> <Complex<AutoSimd<[f32; 16]>> as SimdValue>::Element

Computes the sum of all the lanes of self.
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fn simd_horizontal_product( self, ) -> <Complex<AutoSimd<[f32; 16]>> as SimdValue>::Element

Computes the product of all the lanes of self.
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fn from_simd_real( re: <Complex<AutoSimd<[f32; 16]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f32; 16]>>

Builds a pure-real complex number from the given value.
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fn simd_real( self, ) -> <Complex<AutoSimd<[f32; 16]>> as SimdComplexField>::SimdRealField

The real part of this complex number.
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fn simd_imaginary( self, ) -> <Complex<AutoSimd<[f32; 16]>> as SimdComplexField>::SimdRealField

The imaginary part of this complex number.
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fn simd_argument( self, ) -> <Complex<AutoSimd<[f32; 16]>> as SimdComplexField>::SimdRealField

The argument of this complex number.
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fn simd_modulus( self, ) -> <Complex<AutoSimd<[f32; 16]>> as SimdComplexField>::SimdRealField

The modulus of this complex number.
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fn simd_modulus_squared( self, ) -> <Complex<AutoSimd<[f32; 16]>> as SimdComplexField>::SimdRealField

The squared modulus of this complex number.
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fn simd_norm1( self, ) -> <Complex<AutoSimd<[f32; 16]>> as SimdComplexField>::SimdRealField

The sum of the absolute value of this complex number’s real and imaginary part.
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fn simd_recip(self) -> Complex<AutoSimd<[f32; 16]>>

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fn simd_conjugate(self) -> Complex<AutoSimd<[f32; 16]>>

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fn simd_scale( self, factor: <Complex<AutoSimd<[f32; 16]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f32; 16]>>

Multiplies this complex number by factor.
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fn simd_unscale( self, factor: <Complex<AutoSimd<[f32; 16]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f32; 16]>>

Divides this complex number by factor.
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fn simd_floor(self) -> Complex<AutoSimd<[f32; 16]>>

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fn simd_ceil(self) -> Complex<AutoSimd<[f32; 16]>>

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fn simd_round(self) -> Complex<AutoSimd<[f32; 16]>>

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fn simd_trunc(self) -> Complex<AutoSimd<[f32; 16]>>

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fn simd_fract(self) -> Complex<AutoSimd<[f32; 16]>>

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fn simd_mul_add( self, a: Complex<AutoSimd<[f32; 16]>>, b: Complex<AutoSimd<[f32; 16]>>, ) -> Complex<AutoSimd<[f32; 16]>>

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fn simd_abs( self, ) -> <Complex<AutoSimd<[f32; 16]>> as SimdComplexField>::SimdRealField

The absolute value of this complex number: self / self.signum(). Read more
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fn simd_exp2(self) -> Complex<AutoSimd<[f32; 16]>>

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fn simd_exp_m1(self) -> Complex<AutoSimd<[f32; 16]>>

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fn simd_ln_1p(self) -> Complex<AutoSimd<[f32; 16]>>

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fn simd_log2(self) -> Complex<AutoSimd<[f32; 16]>>

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fn simd_log10(self) -> Complex<AutoSimd<[f32; 16]>>

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fn simd_cbrt(self) -> Complex<AutoSimd<[f32; 16]>>

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fn simd_powi(self, n: i32) -> Complex<AutoSimd<[f32; 16]>>

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fn simd_hypot( self, b: Complex<AutoSimd<[f32; 16]>>, ) -> <Complex<AutoSimd<[f32; 16]>> as SimdComplexField>::SimdRealField

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()
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fn simd_sin_cos( self, ) -> (Complex<AutoSimd<[f32; 16]>>, Complex<AutoSimd<[f32; 16]>>)

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fn simd_sinh_cosh( self, ) -> (Complex<AutoSimd<[f32; 16]>>, Complex<AutoSimd<[f32; 16]>>)

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fn simd_to_polar(self) -> (Self::SimdRealField, Self::SimdRealField)

The polar form of this complex number: (modulus, arg)
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fn simd_to_exp(self) -> (Self::SimdRealField, Self)

The exponential form of this complex number: (modulus, e^{i arg})
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fn simd_signum(self) -> Self

The exponential part of this complex number: self / self.modulus()
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fn simd_sinc(self) -> Self

Cardinal sine
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fn simd_sinhc(self) -> Self

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fn simd_cosc(self) -> Self

Cardinal cos
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fn simd_coshc(self) -> Self

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impl SimdComplexField for Complex<AutoSimd<[f32; 2]>>

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fn simd_exp(self) -> Complex<AutoSimd<[f32; 2]>>

Computes e^(self), where e is the base of the natural logarithm.

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fn simd_ln(self) -> Complex<AutoSimd<[f32; 2]>>

Computes the principal value of natural logarithm of self.

This function has one branch cut:

  • (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

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fn simd_sqrt(self) -> Complex<AutoSimd<[f32; 2]>>

Computes the principal value of the square root of self.

This function has one branch cut:

  • (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

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fn simd_powf( self, exp: <Complex<AutoSimd<[f32; 2]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f32; 2]>>

Raises self to a floating point power.

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fn simd_log(self, base: AutoSimd<[f32; 2]>) -> Complex<AutoSimd<[f32; 2]>>

Returns the logarithm of self with respect to an arbitrary base.

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fn simd_powc( self, exp: Complex<AutoSimd<[f32; 2]>>, ) -> Complex<AutoSimd<[f32; 2]>>

Raises self to a complex power.

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fn simd_sin(self) -> Complex<AutoSimd<[f32; 2]>>

Computes the sine of self.

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fn simd_cos(self) -> Complex<AutoSimd<[f32; 2]>>

Computes the cosine of self.

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fn simd_tan(self) -> Complex<AutoSimd<[f32; 2]>>

Computes the tangent of self.

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fn simd_asin(self) -> Complex<AutoSimd<[f32; 2]>>

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

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fn simd_acos(self) -> Complex<AutoSimd<[f32; 2]>>

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

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fn simd_atan(self) -> Complex<AutoSimd<[f32; 2]>>

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

  • (-∞i, -i], continuous from the left.
  • [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

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fn simd_sinh(self) -> Complex<AutoSimd<[f32; 2]>>

Computes the hyperbolic sine of self.

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fn simd_cosh(self) -> Complex<AutoSimd<[f32; 2]>>

Computes the hyperbolic cosine of self.

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fn simd_tanh(self) -> Complex<AutoSimd<[f32; 2]>>

Computes the hyperbolic tangent of self.

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fn simd_asinh(self) -> Complex<AutoSimd<[f32; 2]>>

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

  • (-∞i, -i), continuous from the left.
  • (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

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fn simd_acosh(self) -> Complex<AutoSimd<[f32; 2]>>

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

  • (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

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fn simd_atanh(self) -> Complex<AutoSimd<[f32; 2]>>

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

  • (-∞, -1], continuous from above.
  • [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

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type SimdRealField = AutoSimd<[f32; 2]>

Type of the coefficients of a complex number.
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fn simd_horizontal_sum( self, ) -> <Complex<AutoSimd<[f32; 2]>> as SimdValue>::Element

Computes the sum of all the lanes of self.
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fn simd_horizontal_product( self, ) -> <Complex<AutoSimd<[f32; 2]>> as SimdValue>::Element

Computes the product of all the lanes of self.
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fn from_simd_real( re: <Complex<AutoSimd<[f32; 2]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f32; 2]>>

Builds a pure-real complex number from the given value.
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fn simd_real( self, ) -> <Complex<AutoSimd<[f32; 2]>> as SimdComplexField>::SimdRealField

The real part of this complex number.
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fn simd_imaginary( self, ) -> <Complex<AutoSimd<[f32; 2]>> as SimdComplexField>::SimdRealField

The imaginary part of this complex number.
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fn simd_argument( self, ) -> <Complex<AutoSimd<[f32; 2]>> as SimdComplexField>::SimdRealField

The argument of this complex number.
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fn simd_modulus( self, ) -> <Complex<AutoSimd<[f32; 2]>> as SimdComplexField>::SimdRealField

The modulus of this complex number.
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fn simd_modulus_squared( self, ) -> <Complex<AutoSimd<[f32; 2]>> as SimdComplexField>::SimdRealField

The squared modulus of this complex number.
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fn simd_norm1( self, ) -> <Complex<AutoSimd<[f32; 2]>> as SimdComplexField>::SimdRealField

The sum of the absolute value of this complex number’s real and imaginary part.
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fn simd_recip(self) -> Complex<AutoSimd<[f32; 2]>>

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fn simd_conjugate(self) -> Complex<AutoSimd<[f32; 2]>>

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fn simd_scale( self, factor: <Complex<AutoSimd<[f32; 2]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f32; 2]>>

Multiplies this complex number by factor.
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fn simd_unscale( self, factor: <Complex<AutoSimd<[f32; 2]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f32; 2]>>

Divides this complex number by factor.
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fn simd_floor(self) -> Complex<AutoSimd<[f32; 2]>>

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fn simd_ceil(self) -> Complex<AutoSimd<[f32; 2]>>

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fn simd_round(self) -> Complex<AutoSimd<[f32; 2]>>

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fn simd_trunc(self) -> Complex<AutoSimd<[f32; 2]>>

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fn simd_fract(self) -> Complex<AutoSimd<[f32; 2]>>

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fn simd_mul_add( self, a: Complex<AutoSimd<[f32; 2]>>, b: Complex<AutoSimd<[f32; 2]>>, ) -> Complex<AutoSimd<[f32; 2]>>

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fn simd_abs( self, ) -> <Complex<AutoSimd<[f32; 2]>> as SimdComplexField>::SimdRealField

The absolute value of this complex number: self / self.signum(). Read more
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fn simd_exp2(self) -> Complex<AutoSimd<[f32; 2]>>

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fn simd_exp_m1(self) -> Complex<AutoSimd<[f32; 2]>>

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fn simd_ln_1p(self) -> Complex<AutoSimd<[f32; 2]>>

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fn simd_log2(self) -> Complex<AutoSimd<[f32; 2]>>

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fn simd_log10(self) -> Complex<AutoSimd<[f32; 2]>>

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fn simd_cbrt(self) -> Complex<AutoSimd<[f32; 2]>>

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fn simd_powi(self, n: i32) -> Complex<AutoSimd<[f32; 2]>>

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fn simd_hypot( self, b: Complex<AutoSimd<[f32; 2]>>, ) -> <Complex<AutoSimd<[f32; 2]>> as SimdComplexField>::SimdRealField

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()
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fn simd_sin_cos( self, ) -> (Complex<AutoSimd<[f32; 2]>>, Complex<AutoSimd<[f32; 2]>>)

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fn simd_sinh_cosh( self, ) -> (Complex<AutoSimd<[f32; 2]>>, Complex<AutoSimd<[f32; 2]>>)

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fn simd_to_polar(self) -> (Self::SimdRealField, Self::SimdRealField)

The polar form of this complex number: (modulus, arg)
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fn simd_to_exp(self) -> (Self::SimdRealField, Self)

The exponential form of this complex number: (modulus, e^{i arg})
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fn simd_signum(self) -> Self

The exponential part of this complex number: self / self.modulus()
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fn simd_sinc(self) -> Self

Cardinal sine
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fn simd_sinhc(self) -> Self

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fn simd_cosc(self) -> Self

Cardinal cos
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fn simd_coshc(self) -> Self

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impl SimdComplexField for Complex<AutoSimd<[f32; 4]>>

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fn simd_exp(self) -> Complex<AutoSimd<[f32; 4]>>

Computes e^(self), where e is the base of the natural logarithm.

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fn simd_ln(self) -> Complex<AutoSimd<[f32; 4]>>

Computes the principal value of natural logarithm of self.

This function has one branch cut:

  • (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

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fn simd_sqrt(self) -> Complex<AutoSimd<[f32; 4]>>

Computes the principal value of the square root of self.

This function has one branch cut:

  • (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

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fn simd_powf( self, exp: <Complex<AutoSimd<[f32; 4]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f32; 4]>>

Raises self to a floating point power.

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fn simd_log(self, base: AutoSimd<[f32; 4]>) -> Complex<AutoSimd<[f32; 4]>>

Returns the logarithm of self with respect to an arbitrary base.

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fn simd_powc( self, exp: Complex<AutoSimd<[f32; 4]>>, ) -> Complex<AutoSimd<[f32; 4]>>

Raises self to a complex power.

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fn simd_sin(self) -> Complex<AutoSimd<[f32; 4]>>

Computes the sine of self.

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fn simd_cos(self) -> Complex<AutoSimd<[f32; 4]>>

Computes the cosine of self.

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fn simd_tan(self) -> Complex<AutoSimd<[f32; 4]>>

Computes the tangent of self.

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fn simd_asin(self) -> Complex<AutoSimd<[f32; 4]>>

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

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fn simd_acos(self) -> Complex<AutoSimd<[f32; 4]>>

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

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fn simd_atan(self) -> Complex<AutoSimd<[f32; 4]>>

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

  • (-∞i, -i], continuous from the left.
  • [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

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fn simd_sinh(self) -> Complex<AutoSimd<[f32; 4]>>

Computes the hyperbolic sine of self.

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fn simd_cosh(self) -> Complex<AutoSimd<[f32; 4]>>

Computes the hyperbolic cosine of self.

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fn simd_tanh(self) -> Complex<AutoSimd<[f32; 4]>>

Computes the hyperbolic tangent of self.

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fn simd_asinh(self) -> Complex<AutoSimd<[f32; 4]>>

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

  • (-∞i, -i), continuous from the left.
  • (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

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fn simd_acosh(self) -> Complex<AutoSimd<[f32; 4]>>

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

  • (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

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fn simd_atanh(self) -> Complex<AutoSimd<[f32; 4]>>

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

  • (-∞, -1], continuous from above.
  • [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

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type SimdRealField = AutoSimd<[f32; 4]>

Type of the coefficients of a complex number.
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fn simd_horizontal_sum( self, ) -> <Complex<AutoSimd<[f32; 4]>> as SimdValue>::Element

Computes the sum of all the lanes of self.
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fn simd_horizontal_product( self, ) -> <Complex<AutoSimd<[f32; 4]>> as SimdValue>::Element

Computes the product of all the lanes of self.
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fn from_simd_real( re: <Complex<AutoSimd<[f32; 4]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f32; 4]>>

Builds a pure-real complex number from the given value.
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fn simd_real( self, ) -> <Complex<AutoSimd<[f32; 4]>> as SimdComplexField>::SimdRealField

The real part of this complex number.
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fn simd_imaginary( self, ) -> <Complex<AutoSimd<[f32; 4]>> as SimdComplexField>::SimdRealField

The imaginary part of this complex number.
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fn simd_argument( self, ) -> <Complex<AutoSimd<[f32; 4]>> as SimdComplexField>::SimdRealField

The argument of this complex number.
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fn simd_modulus( self, ) -> <Complex<AutoSimd<[f32; 4]>> as SimdComplexField>::SimdRealField

The modulus of this complex number.
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fn simd_modulus_squared( self, ) -> <Complex<AutoSimd<[f32; 4]>> as SimdComplexField>::SimdRealField

The squared modulus of this complex number.
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fn simd_norm1( self, ) -> <Complex<AutoSimd<[f32; 4]>> as SimdComplexField>::SimdRealField

The sum of the absolute value of this complex number’s real and imaginary part.
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fn simd_recip(self) -> Complex<AutoSimd<[f32; 4]>>

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fn simd_conjugate(self) -> Complex<AutoSimd<[f32; 4]>>

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fn simd_scale( self, factor: <Complex<AutoSimd<[f32; 4]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f32; 4]>>

Multiplies this complex number by factor.
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fn simd_unscale( self, factor: <Complex<AutoSimd<[f32; 4]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f32; 4]>>

Divides this complex number by factor.
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fn simd_floor(self) -> Complex<AutoSimd<[f32; 4]>>

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fn simd_ceil(self) -> Complex<AutoSimd<[f32; 4]>>

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fn simd_round(self) -> Complex<AutoSimd<[f32; 4]>>

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fn simd_trunc(self) -> Complex<AutoSimd<[f32; 4]>>

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fn simd_fract(self) -> Complex<AutoSimd<[f32; 4]>>

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fn simd_mul_add( self, a: Complex<AutoSimd<[f32; 4]>>, b: Complex<AutoSimd<[f32; 4]>>, ) -> Complex<AutoSimd<[f32; 4]>>

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fn simd_abs( self, ) -> <Complex<AutoSimd<[f32; 4]>> as SimdComplexField>::SimdRealField

The absolute value of this complex number: self / self.signum(). Read more
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fn simd_exp2(self) -> Complex<AutoSimd<[f32; 4]>>

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fn simd_exp_m1(self) -> Complex<AutoSimd<[f32; 4]>>

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fn simd_ln_1p(self) -> Complex<AutoSimd<[f32; 4]>>

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fn simd_log2(self) -> Complex<AutoSimd<[f32; 4]>>

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fn simd_log10(self) -> Complex<AutoSimd<[f32; 4]>>

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fn simd_cbrt(self) -> Complex<AutoSimd<[f32; 4]>>

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fn simd_powi(self, n: i32) -> Complex<AutoSimd<[f32; 4]>>

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fn simd_hypot( self, b: Complex<AutoSimd<[f32; 4]>>, ) -> <Complex<AutoSimd<[f32; 4]>> as SimdComplexField>::SimdRealField

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()
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fn simd_sin_cos( self, ) -> (Complex<AutoSimd<[f32; 4]>>, Complex<AutoSimd<[f32; 4]>>)

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fn simd_sinh_cosh( self, ) -> (Complex<AutoSimd<[f32; 4]>>, Complex<AutoSimd<[f32; 4]>>)

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fn simd_to_polar(self) -> (Self::SimdRealField, Self::SimdRealField)

The polar form of this complex number: (modulus, arg)
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fn simd_to_exp(self) -> (Self::SimdRealField, Self)

The exponential form of this complex number: (modulus, e^{i arg})
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fn simd_signum(self) -> Self

The exponential part of this complex number: self / self.modulus()
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fn simd_sinc(self) -> Self

Cardinal sine
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fn simd_sinhc(self) -> Self

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fn simd_cosc(self) -> Self

Cardinal cos
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fn simd_coshc(self) -> Self

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impl SimdComplexField for Complex<AutoSimd<[f32; 8]>>

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fn simd_exp(self) -> Complex<AutoSimd<[f32; 8]>>

Computes e^(self), where e is the base of the natural logarithm.

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fn simd_ln(self) -> Complex<AutoSimd<[f32; 8]>>

Computes the principal value of natural logarithm of self.

This function has one branch cut:

  • (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

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fn simd_sqrt(self) -> Complex<AutoSimd<[f32; 8]>>

Computes the principal value of the square root of self.

This function has one branch cut:

  • (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

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fn simd_powf( self, exp: <Complex<AutoSimd<[f32; 8]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f32; 8]>>

Raises self to a floating point power.

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fn simd_log(self, base: AutoSimd<[f32; 8]>) -> Complex<AutoSimd<[f32; 8]>>

Returns the logarithm of self with respect to an arbitrary base.

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fn simd_powc( self, exp: Complex<AutoSimd<[f32; 8]>>, ) -> Complex<AutoSimd<[f32; 8]>>

Raises self to a complex power.

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fn simd_sin(self) -> Complex<AutoSimd<[f32; 8]>>

Computes the sine of self.

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fn simd_cos(self) -> Complex<AutoSimd<[f32; 8]>>

Computes the cosine of self.

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fn simd_tan(self) -> Complex<AutoSimd<[f32; 8]>>

Computes the tangent of self.

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fn simd_asin(self) -> Complex<AutoSimd<[f32; 8]>>

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

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fn simd_acos(self) -> Complex<AutoSimd<[f32; 8]>>

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

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fn simd_atan(self) -> Complex<AutoSimd<[f32; 8]>>

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

  • (-∞i, -i], continuous from the left.
  • [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

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fn simd_sinh(self) -> Complex<AutoSimd<[f32; 8]>>

Computes the hyperbolic sine of self.

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fn simd_cosh(self) -> Complex<AutoSimd<[f32; 8]>>

Computes the hyperbolic cosine of self.

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fn simd_tanh(self) -> Complex<AutoSimd<[f32; 8]>>

Computes the hyperbolic tangent of self.

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fn simd_asinh(self) -> Complex<AutoSimd<[f32; 8]>>

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

  • (-∞i, -i), continuous from the left.
  • (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

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fn simd_acosh(self) -> Complex<AutoSimd<[f32; 8]>>

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

  • (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

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fn simd_atanh(self) -> Complex<AutoSimd<[f32; 8]>>

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

  • (-∞, -1], continuous from above.
  • [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

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type SimdRealField = AutoSimd<[f32; 8]>

Type of the coefficients of a complex number.
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fn simd_horizontal_sum( self, ) -> <Complex<AutoSimd<[f32; 8]>> as SimdValue>::Element

Computes the sum of all the lanes of self.
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fn simd_horizontal_product( self, ) -> <Complex<AutoSimd<[f32; 8]>> as SimdValue>::Element

Computes the product of all the lanes of self.
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fn from_simd_real( re: <Complex<AutoSimd<[f32; 8]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f32; 8]>>

Builds a pure-real complex number from the given value.
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fn simd_real( self, ) -> <Complex<AutoSimd<[f32; 8]>> as SimdComplexField>::SimdRealField

The real part of this complex number.
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fn simd_imaginary( self, ) -> <Complex<AutoSimd<[f32; 8]>> as SimdComplexField>::SimdRealField

The imaginary part of this complex number.
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fn simd_argument( self, ) -> <Complex<AutoSimd<[f32; 8]>> as SimdComplexField>::SimdRealField

The argument of this complex number.
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fn simd_modulus( self, ) -> <Complex<AutoSimd<[f32; 8]>> as SimdComplexField>::SimdRealField

The modulus of this complex number.
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fn simd_modulus_squared( self, ) -> <Complex<AutoSimd<[f32; 8]>> as SimdComplexField>::SimdRealField

The squared modulus of this complex number.
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fn simd_norm1( self, ) -> <Complex<AutoSimd<[f32; 8]>> as SimdComplexField>::SimdRealField

The sum of the absolute value of this complex number’s real and imaginary part.
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fn simd_recip(self) -> Complex<AutoSimd<[f32; 8]>>

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fn simd_conjugate(self) -> Complex<AutoSimd<[f32; 8]>>

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fn simd_scale( self, factor: <Complex<AutoSimd<[f32; 8]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f32; 8]>>

Multiplies this complex number by factor.
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fn simd_unscale( self, factor: <Complex<AutoSimd<[f32; 8]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f32; 8]>>

Divides this complex number by factor.
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fn simd_floor(self) -> Complex<AutoSimd<[f32; 8]>>

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fn simd_ceil(self) -> Complex<AutoSimd<[f32; 8]>>

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fn simd_round(self) -> Complex<AutoSimd<[f32; 8]>>

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fn simd_trunc(self) -> Complex<AutoSimd<[f32; 8]>>

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fn simd_fract(self) -> Complex<AutoSimd<[f32; 8]>>

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fn simd_mul_add( self, a: Complex<AutoSimd<[f32; 8]>>, b: Complex<AutoSimd<[f32; 8]>>, ) -> Complex<AutoSimd<[f32; 8]>>

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fn simd_abs( self, ) -> <Complex<AutoSimd<[f32; 8]>> as SimdComplexField>::SimdRealField

The absolute value of this complex number: self / self.signum(). Read more
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fn simd_exp2(self) -> Complex<AutoSimd<[f32; 8]>>

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fn simd_exp_m1(self) -> Complex<AutoSimd<[f32; 8]>>

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fn simd_ln_1p(self) -> Complex<AutoSimd<[f32; 8]>>

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fn simd_log2(self) -> Complex<AutoSimd<[f32; 8]>>

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fn simd_log10(self) -> Complex<AutoSimd<[f32; 8]>>

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fn simd_cbrt(self) -> Complex<AutoSimd<[f32; 8]>>

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fn simd_powi(self, n: i32) -> Complex<AutoSimd<[f32; 8]>>

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fn simd_hypot( self, b: Complex<AutoSimd<[f32; 8]>>, ) -> <Complex<AutoSimd<[f32; 8]>> as SimdComplexField>::SimdRealField

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()
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fn simd_sin_cos( self, ) -> (Complex<AutoSimd<[f32; 8]>>, Complex<AutoSimd<[f32; 8]>>)

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fn simd_sinh_cosh( self, ) -> (Complex<AutoSimd<[f32; 8]>>, Complex<AutoSimd<[f32; 8]>>)

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fn simd_to_polar(self) -> (Self::SimdRealField, Self::SimdRealField)

The polar form of this complex number: (modulus, arg)
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fn simd_to_exp(self) -> (Self::SimdRealField, Self)

The exponential form of this complex number: (modulus, e^{i arg})
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fn simd_signum(self) -> Self

The exponential part of this complex number: self / self.modulus()
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fn simd_sinc(self) -> Self

Cardinal sine
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fn simd_sinhc(self) -> Self

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fn simd_cosc(self) -> Self

Cardinal cos
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fn simd_coshc(self) -> Self

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impl SimdComplexField for Complex<AutoSimd<[f64; 2]>>

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fn simd_exp(self) -> Complex<AutoSimd<[f64; 2]>>

Computes e^(self), where e is the base of the natural logarithm.

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fn simd_ln(self) -> Complex<AutoSimd<[f64; 2]>>

Computes the principal value of natural logarithm of self.

This function has one branch cut:

  • (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

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fn simd_sqrt(self) -> Complex<AutoSimd<[f64; 2]>>

Computes the principal value of the square root of self.

This function has one branch cut:

  • (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

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fn simd_powf( self, exp: <Complex<AutoSimd<[f64; 2]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f64; 2]>>

Raises self to a floating point power.

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fn simd_log(self, base: AutoSimd<[f64; 2]>) -> Complex<AutoSimd<[f64; 2]>>

Returns the logarithm of self with respect to an arbitrary base.

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fn simd_powc( self, exp: Complex<AutoSimd<[f64; 2]>>, ) -> Complex<AutoSimd<[f64; 2]>>

Raises self to a complex power.

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fn simd_sin(self) -> Complex<AutoSimd<[f64; 2]>>

Computes the sine of self.

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fn simd_cos(self) -> Complex<AutoSimd<[f64; 2]>>

Computes the cosine of self.

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fn simd_tan(self) -> Complex<AutoSimd<[f64; 2]>>

Computes the tangent of self.

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fn simd_asin(self) -> Complex<AutoSimd<[f64; 2]>>

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

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fn simd_acos(self) -> Complex<AutoSimd<[f64; 2]>>

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

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fn simd_atan(self) -> Complex<AutoSimd<[f64; 2]>>

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

  • (-∞i, -i], continuous from the left.
  • [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

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fn simd_sinh(self) -> Complex<AutoSimd<[f64; 2]>>

Computes the hyperbolic sine of self.

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fn simd_cosh(self) -> Complex<AutoSimd<[f64; 2]>>

Computes the hyperbolic cosine of self.

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fn simd_tanh(self) -> Complex<AutoSimd<[f64; 2]>>

Computes the hyperbolic tangent of self.

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fn simd_asinh(self) -> Complex<AutoSimd<[f64; 2]>>

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

  • (-∞i, -i), continuous from the left.
  • (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

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fn simd_acosh(self) -> Complex<AutoSimd<[f64; 2]>>

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

  • (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

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fn simd_atanh(self) -> Complex<AutoSimd<[f64; 2]>>

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

  • (-∞, -1], continuous from above.
  • [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

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type SimdRealField = AutoSimd<[f64; 2]>

Type of the coefficients of a complex number.
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fn simd_horizontal_sum( self, ) -> <Complex<AutoSimd<[f64; 2]>> as SimdValue>::Element

Computes the sum of all the lanes of self.
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fn simd_horizontal_product( self, ) -> <Complex<AutoSimd<[f64; 2]>> as SimdValue>::Element

Computes the product of all the lanes of self.
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fn from_simd_real( re: <Complex<AutoSimd<[f64; 2]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f64; 2]>>

Builds a pure-real complex number from the given value.
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fn simd_real( self, ) -> <Complex<AutoSimd<[f64; 2]>> as SimdComplexField>::SimdRealField

The real part of this complex number.
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fn simd_imaginary( self, ) -> <Complex<AutoSimd<[f64; 2]>> as SimdComplexField>::SimdRealField

The imaginary part of this complex number.
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fn simd_argument( self, ) -> <Complex<AutoSimd<[f64; 2]>> as SimdComplexField>::SimdRealField

The argument of this complex number.
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fn simd_modulus( self, ) -> <Complex<AutoSimd<[f64; 2]>> as SimdComplexField>::SimdRealField

The modulus of this complex number.
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fn simd_modulus_squared( self, ) -> <Complex<AutoSimd<[f64; 2]>> as SimdComplexField>::SimdRealField

The squared modulus of this complex number.
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fn simd_norm1( self, ) -> <Complex<AutoSimd<[f64; 2]>> as SimdComplexField>::SimdRealField

The sum of the absolute value of this complex number’s real and imaginary part.
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fn simd_recip(self) -> Complex<AutoSimd<[f64; 2]>>

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fn simd_conjugate(self) -> Complex<AutoSimd<[f64; 2]>>

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fn simd_scale( self, factor: <Complex<AutoSimd<[f64; 2]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f64; 2]>>

Multiplies this complex number by factor.
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fn simd_unscale( self, factor: <Complex<AutoSimd<[f64; 2]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f64; 2]>>

Divides this complex number by factor.
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fn simd_floor(self) -> Complex<AutoSimd<[f64; 2]>>

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fn simd_ceil(self) -> Complex<AutoSimd<[f64; 2]>>

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fn simd_round(self) -> Complex<AutoSimd<[f64; 2]>>

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fn simd_trunc(self) -> Complex<AutoSimd<[f64; 2]>>

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fn simd_fract(self) -> Complex<AutoSimd<[f64; 2]>>

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fn simd_mul_add( self, a: Complex<AutoSimd<[f64; 2]>>, b: Complex<AutoSimd<[f64; 2]>>, ) -> Complex<AutoSimd<[f64; 2]>>

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fn simd_abs( self, ) -> <Complex<AutoSimd<[f64; 2]>> as SimdComplexField>::SimdRealField

The absolute value of this complex number: self / self.signum(). Read more
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fn simd_exp2(self) -> Complex<AutoSimd<[f64; 2]>>

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fn simd_exp_m1(self) -> Complex<AutoSimd<[f64; 2]>>

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fn simd_ln_1p(self) -> Complex<AutoSimd<[f64; 2]>>

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fn simd_log2(self) -> Complex<AutoSimd<[f64; 2]>>

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fn simd_log10(self) -> Complex<AutoSimd<[f64; 2]>>

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fn simd_cbrt(self) -> Complex<AutoSimd<[f64; 2]>>

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fn simd_powi(self, n: i32) -> Complex<AutoSimd<[f64; 2]>>

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fn simd_hypot( self, b: Complex<AutoSimd<[f64; 2]>>, ) -> <Complex<AutoSimd<[f64; 2]>> as SimdComplexField>::SimdRealField

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()
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fn simd_sin_cos( self, ) -> (Complex<AutoSimd<[f64; 2]>>, Complex<AutoSimd<[f64; 2]>>)

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fn simd_sinh_cosh( self, ) -> (Complex<AutoSimd<[f64; 2]>>, Complex<AutoSimd<[f64; 2]>>)

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fn simd_to_polar(self) -> (Self::SimdRealField, Self::SimdRealField)

The polar form of this complex number: (modulus, arg)
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fn simd_to_exp(self) -> (Self::SimdRealField, Self)

The exponential form of this complex number: (modulus, e^{i arg})
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fn simd_signum(self) -> Self

The exponential part of this complex number: self / self.modulus()
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fn simd_sinc(self) -> Self

Cardinal sine
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fn simd_sinhc(self) -> Self

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fn simd_cosc(self) -> Self

Cardinal cos
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fn simd_coshc(self) -> Self

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impl SimdComplexField for Complex<AutoSimd<[f64; 4]>>

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fn simd_exp(self) -> Complex<AutoSimd<[f64; 4]>>

Computes e^(self), where e is the base of the natural logarithm.

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fn simd_ln(self) -> Complex<AutoSimd<[f64; 4]>>

Computes the principal value of natural logarithm of self.

This function has one branch cut:

  • (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

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fn simd_sqrt(self) -> Complex<AutoSimd<[f64; 4]>>

Computes the principal value of the square root of self.

This function has one branch cut:

  • (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

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fn simd_powf( self, exp: <Complex<AutoSimd<[f64; 4]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f64; 4]>>

Raises self to a floating point power.

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fn simd_log(self, base: AutoSimd<[f64; 4]>) -> Complex<AutoSimd<[f64; 4]>>

Returns the logarithm of self with respect to an arbitrary base.

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fn simd_powc( self, exp: Complex<AutoSimd<[f64; 4]>>, ) -> Complex<AutoSimd<[f64; 4]>>

Raises self to a complex power.

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fn simd_sin(self) -> Complex<AutoSimd<[f64; 4]>>

Computes the sine of self.

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fn simd_cos(self) -> Complex<AutoSimd<[f64; 4]>>

Computes the cosine of self.

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fn simd_tan(self) -> Complex<AutoSimd<[f64; 4]>>

Computes the tangent of self.

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fn simd_asin(self) -> Complex<AutoSimd<[f64; 4]>>

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

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fn simd_acos(self) -> Complex<AutoSimd<[f64; 4]>>

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

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fn simd_atan(self) -> Complex<AutoSimd<[f64; 4]>>

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

  • (-∞i, -i], continuous from the left.
  • [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

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fn simd_sinh(self) -> Complex<AutoSimd<[f64; 4]>>

Computes the hyperbolic sine of self.

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fn simd_cosh(self) -> Complex<AutoSimd<[f64; 4]>>

Computes the hyperbolic cosine of self.

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fn simd_tanh(self) -> Complex<AutoSimd<[f64; 4]>>

Computes the hyperbolic tangent of self.

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fn simd_asinh(self) -> Complex<AutoSimd<[f64; 4]>>

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

  • (-∞i, -i), continuous from the left.
  • (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

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fn simd_acosh(self) -> Complex<AutoSimd<[f64; 4]>>

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

  • (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

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fn simd_atanh(self) -> Complex<AutoSimd<[f64; 4]>>

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

  • (-∞, -1], continuous from above.
  • [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

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type SimdRealField = AutoSimd<[f64; 4]>

Type of the coefficients of a complex number.
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fn simd_horizontal_sum( self, ) -> <Complex<AutoSimd<[f64; 4]>> as SimdValue>::Element

Computes the sum of all the lanes of self.
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fn simd_horizontal_product( self, ) -> <Complex<AutoSimd<[f64; 4]>> as SimdValue>::Element

Computes the product of all the lanes of self.
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fn from_simd_real( re: <Complex<AutoSimd<[f64; 4]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f64; 4]>>

Builds a pure-real complex number from the given value.
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fn simd_real( self, ) -> <Complex<AutoSimd<[f64; 4]>> as SimdComplexField>::SimdRealField

The real part of this complex number.
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fn simd_imaginary( self, ) -> <Complex<AutoSimd<[f64; 4]>> as SimdComplexField>::SimdRealField

The imaginary part of this complex number.
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fn simd_argument( self, ) -> <Complex<AutoSimd<[f64; 4]>> as SimdComplexField>::SimdRealField

The argument of this complex number.
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fn simd_modulus( self, ) -> <Complex<AutoSimd<[f64; 4]>> as SimdComplexField>::SimdRealField

The modulus of this complex number.
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fn simd_modulus_squared( self, ) -> <Complex<AutoSimd<[f64; 4]>> as SimdComplexField>::SimdRealField

The squared modulus of this complex number.
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fn simd_norm1( self, ) -> <Complex<AutoSimd<[f64; 4]>> as SimdComplexField>::SimdRealField

The sum of the absolute value of this complex number’s real and imaginary part.
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fn simd_recip(self) -> Complex<AutoSimd<[f64; 4]>>

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fn simd_conjugate(self) -> Complex<AutoSimd<[f64; 4]>>

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fn simd_scale( self, factor: <Complex<AutoSimd<[f64; 4]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f64; 4]>>

Multiplies this complex number by factor.
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fn simd_unscale( self, factor: <Complex<AutoSimd<[f64; 4]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f64; 4]>>

Divides this complex number by factor.
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fn simd_floor(self) -> Complex<AutoSimd<[f64; 4]>>

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fn simd_ceil(self) -> Complex<AutoSimd<[f64; 4]>>

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fn simd_round(self) -> Complex<AutoSimd<[f64; 4]>>

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fn simd_trunc(self) -> Complex<AutoSimd<[f64; 4]>>

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fn simd_fract(self) -> Complex<AutoSimd<[f64; 4]>>

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fn simd_mul_add( self, a: Complex<AutoSimd<[f64; 4]>>, b: Complex<AutoSimd<[f64; 4]>>, ) -> Complex<AutoSimd<[f64; 4]>>

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fn simd_abs( self, ) -> <Complex<AutoSimd<[f64; 4]>> as SimdComplexField>::SimdRealField

The absolute value of this complex number: self / self.signum(). Read more
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fn simd_exp2(self) -> Complex<AutoSimd<[f64; 4]>>

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fn simd_exp_m1(self) -> Complex<AutoSimd<[f64; 4]>>

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fn simd_ln_1p(self) -> Complex<AutoSimd<[f64; 4]>>

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fn simd_log2(self) -> Complex<AutoSimd<[f64; 4]>>

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fn simd_log10(self) -> Complex<AutoSimd<[f64; 4]>>

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fn simd_cbrt(self) -> Complex<AutoSimd<[f64; 4]>>

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fn simd_powi(self, n: i32) -> Complex<AutoSimd<[f64; 4]>>

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fn simd_hypot( self, b: Complex<AutoSimd<[f64; 4]>>, ) -> <Complex<AutoSimd<[f64; 4]>> as SimdComplexField>::SimdRealField

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()
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fn simd_sin_cos( self, ) -> (Complex<AutoSimd<[f64; 4]>>, Complex<AutoSimd<[f64; 4]>>)

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fn simd_sinh_cosh( self, ) -> (Complex<AutoSimd<[f64; 4]>>, Complex<AutoSimd<[f64; 4]>>)

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fn simd_to_polar(self) -> (Self::SimdRealField, Self::SimdRealField)

The polar form of this complex number: (modulus, arg)
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fn simd_to_exp(self) -> (Self::SimdRealField, Self)

The exponential form of this complex number: (modulus, e^{i arg})
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fn simd_signum(self) -> Self

The exponential part of this complex number: self / self.modulus()
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fn simd_sinc(self) -> Self

Cardinal sine
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fn simd_sinhc(self) -> Self

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fn simd_cosc(self) -> Self

Cardinal cos
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fn simd_coshc(self) -> Self

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impl SimdComplexField for Complex<AutoSimd<[f64; 8]>>

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fn simd_exp(self) -> Complex<AutoSimd<[f64; 8]>>

Computes e^(self), where e is the base of the natural logarithm.

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fn simd_ln(self) -> Complex<AutoSimd<[f64; 8]>>

Computes the principal value of natural logarithm of self.

This function has one branch cut:

  • (-∞, 0], continuous from above.

The branch satisfies -π ≤ arg(ln(z)) ≤ π.

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fn simd_sqrt(self) -> Complex<AutoSimd<[f64; 8]>>

Computes the principal value of the square root of self.

This function has one branch cut:

  • (-∞, 0), continuous from above.

The branch satisfies -π/2 ≤ arg(sqrt(z)) ≤ π/2.

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fn simd_powf( self, exp: <Complex<AutoSimd<[f64; 8]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f64; 8]>>

Raises self to a floating point power.

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fn simd_log(self, base: AutoSimd<[f64; 8]>) -> Complex<AutoSimd<[f64; 8]>>

Returns the logarithm of self with respect to an arbitrary base.

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fn simd_powc( self, exp: Complex<AutoSimd<[f64; 8]>>, ) -> Complex<AutoSimd<[f64; 8]>>

Raises self to a complex power.

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fn simd_sin(self) -> Complex<AutoSimd<[f64; 8]>>

Computes the sine of self.

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fn simd_cos(self) -> Complex<AutoSimd<[f64; 8]>>

Computes the cosine of self.

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fn simd_tan(self) -> Complex<AutoSimd<[f64; 8]>>

Computes the tangent of self.

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fn simd_asin(self) -> Complex<AutoSimd<[f64; 8]>>

Computes the principal value of the inverse sine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Re(asin(z)) ≤ π/2.

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fn simd_acos(self) -> Complex<AutoSimd<[f64; 8]>>

Computes the principal value of the inverse cosine of self.

This function has two branch cuts:

  • (-∞, -1), continuous from above.
  • (1, ∞), continuous from below.

The branch satisfies 0 ≤ Re(acos(z)) ≤ π.

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fn simd_atan(self) -> Complex<AutoSimd<[f64; 8]>>

Computes the principal value of the inverse tangent of self.

This function has two branch cuts:

  • (-∞i, -i], continuous from the left.
  • [i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Re(atan(z)) ≤ π/2.

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fn simd_sinh(self) -> Complex<AutoSimd<[f64; 8]>>

Computes the hyperbolic sine of self.

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fn simd_cosh(self) -> Complex<AutoSimd<[f64; 8]>>

Computes the hyperbolic cosine of self.

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fn simd_tanh(self) -> Complex<AutoSimd<[f64; 8]>>

Computes the hyperbolic tangent of self.

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fn simd_asinh(self) -> Complex<AutoSimd<[f64; 8]>>

Computes the principal value of inverse hyperbolic sine of self.

This function has two branch cuts:

  • (-∞i, -i), continuous from the left.
  • (i, ∞i), continuous from the right.

The branch satisfies -π/2 ≤ Im(asinh(z)) ≤ π/2.

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fn simd_acosh(self) -> Complex<AutoSimd<[f64; 8]>>

Computes the principal value of inverse hyperbolic cosine of self.

This function has one branch cut:

  • (-∞, 1), continuous from above.

The branch satisfies -π ≤ Im(acosh(z)) ≤ π and 0 ≤ Re(acosh(z)) < ∞.

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fn simd_atanh(self) -> Complex<AutoSimd<[f64; 8]>>

Computes the principal value of inverse hyperbolic tangent of self.

This function has two branch cuts:

  • (-∞, -1], continuous from above.
  • [1, ∞), continuous from below.

The branch satisfies -π/2 ≤ Im(atanh(z)) ≤ π/2.

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type SimdRealField = AutoSimd<[f64; 8]>

Type of the coefficients of a complex number.
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fn simd_horizontal_sum( self, ) -> <Complex<AutoSimd<[f64; 8]>> as SimdValue>::Element

Computes the sum of all the lanes of self.
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fn simd_horizontal_product( self, ) -> <Complex<AutoSimd<[f64; 8]>> as SimdValue>::Element

Computes the product of all the lanes of self.
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fn from_simd_real( re: <Complex<AutoSimd<[f64; 8]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f64; 8]>>

Builds a pure-real complex number from the given value.
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fn simd_real( self, ) -> <Complex<AutoSimd<[f64; 8]>> as SimdComplexField>::SimdRealField

The real part of this complex number.
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fn simd_imaginary( self, ) -> <Complex<AutoSimd<[f64; 8]>> as SimdComplexField>::SimdRealField

The imaginary part of this complex number.
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fn simd_argument( self, ) -> <Complex<AutoSimd<[f64; 8]>> as SimdComplexField>::SimdRealField

The argument of this complex number.
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fn simd_modulus( self, ) -> <Complex<AutoSimd<[f64; 8]>> as SimdComplexField>::SimdRealField

The modulus of this complex number.
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fn simd_modulus_squared( self, ) -> <Complex<AutoSimd<[f64; 8]>> as SimdComplexField>::SimdRealField

The squared modulus of this complex number.
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fn simd_norm1( self, ) -> <Complex<AutoSimd<[f64; 8]>> as SimdComplexField>::SimdRealField

The sum of the absolute value of this complex number’s real and imaginary part.
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fn simd_recip(self) -> Complex<AutoSimd<[f64; 8]>>

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fn simd_conjugate(self) -> Complex<AutoSimd<[f64; 8]>>

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fn simd_scale( self, factor: <Complex<AutoSimd<[f64; 8]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f64; 8]>>

Multiplies this complex number by factor.
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fn simd_unscale( self, factor: <Complex<AutoSimd<[f64; 8]>> as SimdComplexField>::SimdRealField, ) -> Complex<AutoSimd<[f64; 8]>>

Divides this complex number by factor.
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fn simd_floor(self) -> Complex<AutoSimd<[f64; 8]>>

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fn simd_ceil(self) -> Complex<AutoSimd<[f64; 8]>>

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fn simd_round(self) -> Complex<AutoSimd<[f64; 8]>>

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fn simd_trunc(self) -> Complex<AutoSimd<[f64; 8]>>

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fn simd_fract(self) -> Complex<AutoSimd<[f64; 8]>>

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fn simd_mul_add( self, a: Complex<AutoSimd<[f64; 8]>>, b: Complex<AutoSimd<[f64; 8]>>, ) -> Complex<AutoSimd<[f64; 8]>>

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fn simd_abs( self, ) -> <Complex<AutoSimd<[f64; 8]>> as SimdComplexField>::SimdRealField

The absolute value of this complex number: self / self.signum(). Read more
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fn simd_exp2(self) -> Complex<AutoSimd<[f64; 8]>>

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fn simd_exp_m1(self) -> Complex<AutoSimd<[f64; 8]>>

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fn simd_ln_1p(self) -> Complex<AutoSimd<[f64; 8]>>

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fn simd_log2(self) -> Complex<AutoSimd<[f64; 8]>>

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fn simd_log10(self) -> Complex<AutoSimd<[f64; 8]>>

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fn simd_cbrt(self) -> Complex<AutoSimd<[f64; 8]>>

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fn simd_powi(self, n: i32) -> Complex<AutoSimd<[f64; 8]>>

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fn simd_hypot( self, b: Complex<AutoSimd<[f64; 8]>>, ) -> <Complex<AutoSimd<[f64; 8]>> as SimdComplexField>::SimdRealField

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()
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fn simd_sin_cos( self, ) -> (Complex<AutoSimd<[f64; 8]>>, Complex<AutoSimd<[f64; 8]>>)

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fn simd_sinh_cosh( self, ) -> (Complex<AutoSimd<[f64; 8]>>, Complex<AutoSimd<[f64; 8]>>)

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fn simd_to_polar(self) -> (Self::SimdRealField, Self::SimdRealField)

The polar form of this complex number: (modulus, arg)
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fn simd_to_exp(self) -> (Self::SimdRealField, Self)

The exponential form of this complex number: (modulus, e^{i arg})
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fn simd_signum(self) -> Self

The exponential part of this complex number: self / self.modulus()
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fn simd_sinc(self) -> Self

Cardinal sine
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fn simd_sinhc(self) -> Self

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fn simd_cosc(self) -> Self

Cardinal cos
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fn simd_coshc(self) -> Self

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impl<N> SimdValue for Complex<N>
where N: SimdValue,

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const LANES: usize = N::LANES

The number of lanes of this SIMD value.
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type Element = Complex<<N as SimdValue>::Element>

The type of the elements of each lane of this SIMD value.
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type SimdBool = <N as SimdValue>::SimdBool

Type of the result of comparing two SIMD values like self.
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fn splat(val: <Complex<N> as SimdValue>::Element) -> Complex<N>

Initializes an SIMD value with each lanes set to val.
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fn extract(&self, i: usize) -> <Complex<N> as SimdValue>::Element

Extracts the i-th lane of self. Read more
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unsafe fn extract_unchecked( &self, i: usize, ) -> <Complex<N> as SimdValue>::Element

Extracts the i-th lane of self without bound-checking. Read more
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fn replace(&mut self, i: usize, val: <Complex<N> as SimdValue>::Element)

Replaces the i-th lane of self by val. Read more
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unsafe fn replace_unchecked( &mut self, i: usize, val: <Complex<N> as SimdValue>::Element, )

Replaces the i-th lane of self by val without bound-checking. Read more
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fn select( self, cond: <Complex<N> as SimdValue>::SimdBool, other: Complex<N>, ) -> Complex<N>

Merges self and other depending on the lanes of cond. Read more
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fn map_lanes(self, f: impl Fn(Self::Element) -> Self::Element) -> Self
where Self: Clone,

Applies a function to each lane of self. Read more
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fn zip_map_lanes( self, b: Self, f: impl Fn(Self::Element, Self::Element) -> Self::Element, ) -> Self
where Self: Clone,

Applies a function to each lane of self paired with the corresponding lane of b. Read more
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impl<'a, 'b, T> Sub<&'b Complex<T>> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn sub( self, other: &Complex<T>, ) -> <&'a Complex<T> as Sub<&'b Complex<T>>>::Output

Performs the - operation. Read more
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impl<'a, T> Sub<&'a Complex<T>> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn sub(self, other: &Complex<T>) -> <Complex<T> as Sub<&'a Complex<T>>>::Output

Performs the - operation. Read more
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impl<'a, 'b, T> Sub<&'a T> for &'b Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn sub(self, other: &T) -> <&'b Complex<T> as Sub<&'a T>>::Output

Performs the - operation. Read more
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impl<'a, T> Sub<&'a T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn sub(self, other: &T) -> <Complex<T> as Sub<&'a T>>::Output

Performs the - operation. Read more
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impl<'a, T> Sub<Complex<T>> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn sub(self, other: Complex<T>) -> <&'a Complex<T> as Sub<Complex<T>>>::Output

Performs the - operation. Read more
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impl<'a, T> Sub<T> for &'a Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn sub(self, other: T) -> <&'a Complex<T> as Sub<T>>::Output

Performs the - operation. Read more
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impl<T> Sub<T> for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn sub(self, other: T) -> <Complex<T> as Sub<T>>::Output

Performs the - operation. Read more
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impl<T> Sub for Complex<T>
where T: Clone + Num,

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type Output = Complex<T>

The resulting type after applying the - operator.
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fn sub(self, other: Complex<T>) -> <Complex<T> as Sub>::Output

Performs the - operation. Read more
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impl<'a, T> SubAssign<&'a Complex<T>> for Complex<T>
where T: Clone + NumAssign,

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fn sub_assign(&mut self, other: &Complex<T>)

Performs the -= operation. Read more
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impl<'a, T> SubAssign<&'a T> for Complex<T>
where T: Clone + NumAssign,

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fn sub_assign(&mut self, other: &T)

Performs the -= operation. Read more
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impl<T> SubAssign<T> for Complex<T>
where T: Clone + NumAssign,

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fn sub_assign(&mut self, other: T)

Performs the -= operation. Read more
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impl<T> SubAssign for Complex<T>
where T: Clone + NumAssign,

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fn sub_assign(&mut self, other: Complex<T>)

Performs the -= operation. Read more
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impl<N1, N2> SubsetOf<Complex<N2>> for Complex<N1>
where N2: SupersetOf<N1>,

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fn to_superset(&self) -> Complex<N2>

The inclusion map: converts self to the equivalent element of its superset.
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fn from_superset_unchecked(element: &Complex<N2>) -> Complex<N1>

Use with care! Same as self.to_superset but without any property checks. Always succeeds.
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fn is_in_subset(c: &Complex<N2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).
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fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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impl<'a, T> Sum<&'a Complex<T>> for Complex<T>
where T: 'a + Num + Clone,

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fn sum<I>(iter: I) -> Complex<T>
where I: Iterator<Item = &'a Complex<T>>,

Takes an iterator and generates Self from the elements by “summing up” the items.
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impl<T> Sum for Complex<T>
where T: Num + Clone,

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fn sum<I>(iter: I) -> Complex<T>
where I: Iterator<Item = Complex<T>>,

Takes an iterator and generates Self from the elements by “summing up” the items.
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impl<T> ToPrimitive for Complex<T>
where T: ToPrimitive + Num,

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fn to_usize(&self) -> Option<usize>

Converts the value of self to a usize. If the value cannot be represented by a usize, then None is returned.
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fn to_isize(&self) -> Option<isize>

Converts the value of self to an isize. If the value cannot be represented by an isize, then None is returned.
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fn to_u8(&self) -> Option<u8>

Converts the value of self to a u8. If the value cannot be represented by a u8, then None is returned.
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fn to_u16(&self) -> Option<u16>

Converts the value of self to a u16. If the value cannot be represented by a u16, then None is returned.
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fn to_u32(&self) -> Option<u32>

Converts the value of self to a u32. If the value cannot be represented by a u32, then None is returned.
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fn to_u64(&self) -> Option<u64>

Converts the value of self to a u64. If the value cannot be represented by a u64, then None is returned.
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fn to_i8(&self) -> Option<i8>

Converts the value of self to an i8. If the value cannot be represented by an i8, then None is returned.
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fn to_i16(&self) -> Option<i16>

Converts the value of self to an i16. If the value cannot be represented by an i16, then None is returned.
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fn to_i32(&self) -> Option<i32>

Converts the value of self to an i32. If the value cannot be represented by an i32, then None is returned.
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fn to_i64(&self) -> Option<i64>

Converts the value of self to an i64. If the value cannot be represented by an i64, then None is returned.
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fn to_u128(&self) -> Option<u128>

Converts the value of self to a u128. If the value cannot be represented by a u128 (u64 under the default implementation), then None is returned. Read more
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fn to_i128(&self) -> Option<i128>

Converts the value of self to an i128. If the value cannot be represented by an i128 (i64 under the default implementation), then None is returned. Read more
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fn to_f32(&self) -> Option<f32>

Converts the value of self to an f32. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f32.
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fn to_f64(&self) -> Option<f64>

Converts the value of self to an f64. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f64. Read more
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impl<T> UpperExp for Complex<T>
where T: UpperExp + Num + PartialOrd + Clone,

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

Formats the value using the given formatter. Read more
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impl<T> UpperHex for Complex<T>
where T: UpperHex + Num + PartialOrd + Clone,

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

Formats the value using the given formatter. Read more
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impl<T> Zero for Complex<T>
where T: Clone + Num,

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fn zero() -> Complex<T>

Returns the additive identity element of Self, 0. Read more
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fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.
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fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.
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impl<T> Copy for Complex<T>
where T: Copy,

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impl<T> Eq for Complex<T>
where T: Eq,

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impl<N> Field for Complex<N>

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impl<N> PrimitiveSimdValue for Complex<N>

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impl<T> StructuralPartialEq for Complex<T>

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impl<T> Freeze for Complex<T>
where T: Freeze,

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impl<T> RefUnwindSafe for Complex<T>
where T: RefUnwindSafe,

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impl<T> Send for Complex<T>
where T: Send,

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impl<T> Sync for Complex<T>
where T: Sync,

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impl<T> Unpin for Complex<T>
where T: Unpin,

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impl<T> UnwindSafe for Complex<T>
where T: UnwindSafe,

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impl<T> Any for T
where T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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impl<T> Borrow<T> for T
where T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for T
where T: ?Sized,

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fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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impl<T> CloneToUninit for T
where T: Clone,

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unsafe fn clone_to_uninit(&self, dst: *mut T)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dst. Read more
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into<U> for T
where U: From<T>,

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fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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impl<T> Same for T

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type Output = T

Should always be Self
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impl<T> SimdComplexField for T
where T: ComplexField,

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type SimdRealField = <T as ComplexField>::RealField

Type of the coefficients of a complex number.
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fn from_simd_real(re: <T as SimdComplexField>::SimdRealField) -> T

Builds a pure-real complex number from the given value.
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fn simd_real(self) -> <T as SimdComplexField>::SimdRealField

The real part of this complex number.
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fn simd_imaginary(self) -> <T as SimdComplexField>::SimdRealField

The imaginary part of this complex number.
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fn simd_modulus(self) -> <T as SimdComplexField>::SimdRealField

The modulus of this complex number.
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fn simd_modulus_squared(self) -> <T as SimdComplexField>::SimdRealField

The squared modulus of this complex number.
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fn simd_argument(self) -> <T as SimdComplexField>::SimdRealField

The argument of this complex number.
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fn simd_norm1(self) -> <T as SimdComplexField>::SimdRealField

The sum of the absolute value of this complex number’s real and imaginary part.
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fn simd_scale(self, factor: <T as SimdComplexField>::SimdRealField) -> T

Multiplies this complex number by factor.
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fn simd_unscale(self, factor: <T as SimdComplexField>::SimdRealField) -> T

Divides this complex number by factor.
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fn simd_to_polar( self, ) -> (<T as SimdComplexField>::SimdRealField, <T as SimdComplexField>::SimdRealField)

The polar form of this complex number: (modulus, arg)
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fn simd_to_exp(self) -> (<T as SimdComplexField>::SimdRealField, T)

The exponential form of this complex number: (modulus, e^{i arg})
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fn simd_signum(self) -> T

The exponential part of this complex number: self / self.modulus()
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fn simd_floor(self) -> T

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fn simd_ceil(self) -> T

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fn simd_round(self) -> T

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fn simd_trunc(self) -> T

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fn simd_fract(self) -> T

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fn simd_mul_add(self, a: T, b: T) -> T

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fn simd_abs(self) -> <T as SimdComplexField>::SimdRealField

The absolute value of this complex number: self / self.signum(). Read more
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fn simd_hypot(self, other: T) -> <T as SimdComplexField>::SimdRealField

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()
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fn simd_recip(self) -> T

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fn simd_conjugate(self) -> T

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fn simd_sin(self) -> T

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fn simd_cos(self) -> T

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fn simd_sin_cos(self) -> (T, T)

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fn simd_sinh_cosh(self) -> (T, T)

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fn simd_tan(self) -> T

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fn simd_asin(self) -> T

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fn simd_acos(self) -> T

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fn simd_atan(self) -> T

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fn simd_sinh(self) -> T

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fn simd_cosh(self) -> T

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fn simd_tanh(self) -> T

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fn simd_asinh(self) -> T

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fn simd_acosh(self) -> T

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fn simd_atanh(self) -> T

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fn simd_sinc(self) -> T

Cardinal sine
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fn simd_sinhc(self) -> T

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fn simd_cosc(self) -> T

Cardinal cos
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fn simd_coshc(self) -> T

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fn simd_log(self, base: <T as SimdComplexField>::SimdRealField) -> T

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fn simd_log2(self) -> T

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fn simd_log10(self) -> T

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fn simd_ln(self) -> T

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fn simd_ln_1p(self) -> T

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fn simd_sqrt(self) -> T

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fn simd_exp(self) -> T

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fn simd_exp2(self) -> T

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fn simd_exp_m1(self) -> T

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fn simd_powi(self, n: i32) -> T

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fn simd_powf(self, n: <T as SimdComplexField>::SimdRealField) -> T

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fn simd_powc(self, n: T) -> T

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fn simd_cbrt(self) -> T

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fn simd_horizontal_sum(self) -> <T as SimdValue>::Element

Computes the sum of all the lanes of self.
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fn simd_horizontal_product(self) -> <T as SimdValue>::Element

Computes the product of all the lanes of self.
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impl<SS, SP> SupersetOf<SS> for SP
where SS: SubsetOf<SP>,

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fn to_subset(&self) -> Option<SS>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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fn is_in_subset(&self) -> bool

Checks if self is actually part of its subset T (and can be converted to it).
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fn to_subset_unchecked(&self) -> SS

Use with care! Same as self.to_subset but without any property checks. Always succeeds.
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fn from_subset(element: &SS) -> SP

The inclusion map: converts self to the equivalent element of its superset.
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impl<T> ToOwned for T
where T: Clone,

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type Owned = T

The resulting type after obtaining ownership.
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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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impl<T> ToString for T
where T: Display + ?Sized,

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default fn to_string(&self) -> String

Converts the given value to a String. Read more
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impl<T, U> TryFrom<U> for T
where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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impl<T, Right> ClosedAdd<Right> for T
where T: Add<Right, Output = T> + AddAssign<Right>,

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impl<T, Right> ClosedAddAssign<Right> for T
where T: ClosedAdd<Right> + AddAssign<Right>,

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impl<T, Right> ClosedDiv<Right> for T
where T: Div<Right, Output = T> + DivAssign<Right>,

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impl<T, Right> ClosedDivAssign<Right> for T
where T: ClosedDiv<Right> + DivAssign<Right>,

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impl<T, Right> ClosedMul<Right> for T
where T: Mul<Right, Output = T> + MulAssign<Right>,

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impl<T, Right> ClosedMulAssign<Right> for T
where T: ClosedMul<Right> + MulAssign<Right>,

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impl<T> ClosedNeg for T
where T: Neg<Output = T>,

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impl<T, Right> ClosedSub<Right> for T
where T: Sub<Right, Output = T> + SubAssign<Right>,

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impl<T, Right> ClosedSubAssign<Right> for T
where T: ClosedSub<Right> + SubAssign<Right>,

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impl<T> DeserializeOwned for T
where T: for<'de> Deserialize<'de>,

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impl<T> NumAssign for T
where T: Num + NumAssignOps,

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impl<T, Rhs> NumAssignOps<Rhs> for T
where T: AddAssign<Rhs> + SubAssign<Rhs> + MulAssign<Rhs> + DivAssign<Rhs> + RemAssign<Rhs>,

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impl<T> NumAssignRef for T
where T: NumAssign + for<'r> NumAssignOps<&'r T>,

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impl<T, Rhs, Output> NumOps<Rhs, Output> for T
where T: Sub<Rhs, Output = Output> + Mul<Rhs, Output = Output> + Div<Rhs, Output = Output> + Add<Rhs, Output = Output> + Rem<Rhs, Output = Output>,

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impl<T> NumRef for T
where T: Num + for<'r> NumOps<&'r T>,

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impl<T, Base> RefNum<Base> for T
where T: NumOps<Base, Base> + for<'r> NumOps<&'r Base, Base>,

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impl<T> Scalar for T
where T: 'static + Clone + PartialEq + Debug,