Trait simba::simd::SimdComplexField

source · [−]
pub trait SimdComplexField: SubsetOf<Self> + SupersetOf<f64> + Field + Copy + Neg<Output = Self> + Send + Sync + Any + 'static + Debug + NumAssignOps + NumOps + PartialEq {
    type SimdRealField: SimdRealField<SimdBool = <Self as SimdValue>::SimdBool>;

Show 55 methods    fn from_simd_real(re: Self::SimdRealField) -> Self;

    fn simd_real(self) -> Self::SimdRealField;

    fn simd_imaginary(self) -> Self::SimdRealField;

    fn simd_modulus(self) -> Self::SimdRealField;

    fn simd_modulus_squared(self) -> Self::SimdRealField;

    fn simd_argument(self) -> Self::SimdRealField;

    fn simd_norm1(self) -> Self::SimdRealField;

    fn simd_scale(self, factor: Self::SimdRealField) -> Self;

    fn simd_unscale(self, factor: Self::SimdRealField) -> Self;

    fn simd_floor(self) -> Self;

    fn simd_ceil(self) -> Self;

    fn simd_round(self) -> Self;

    fn simd_trunc(self) -> Self;

    fn simd_fract(self) -> Self;

    fn simd_mul_add(self, a: Self, b: Self) -> Self;

    fn simd_abs(self) -> Self::SimdRealField;

    fn simd_hypot(self, other: Self) -> Self::SimdRealField;

    fn simd_recip(self) -> Self;

    fn simd_conjugate(self) -> Self;

    fn simd_sin(self) -> Self;

    fn simd_cos(self) -> Self;

    fn simd_sin_cos(self) -> (Self, Self);

    fn simd_tan(self) -> Self;

    fn simd_asin(self) -> Self;

    fn simd_acos(self) -> Self;

    fn simd_atan(self) -> Self;

    fn simd_sinh(self) -> Self;

    fn simd_cosh(self) -> Self;

    fn simd_tanh(self) -> Self;

    fn simd_asinh(self) -> Self;

    fn simd_acosh(self) -> Self;

    fn simd_atanh(self) -> Self;

    fn simd_log(self, base: Self::SimdRealField) -> Self;

    fn simd_log2(self) -> Self;

    fn simd_log10(self) -> Self;

    fn simd_ln(self) -> Self;

    fn simd_ln_1p(self) -> Self;

    fn simd_sqrt(self) -> Self;

    fn simd_exp(self) -> Self;

    fn simd_exp2(self) -> Self;

    fn simd_exp_m1(self) -> Self;

    fn simd_powi(self, n: i32) -> Self;

    fn simd_powf(self, n: Self::SimdRealField) -> Self;

    fn simd_powc(self, n: Self) -> Self;

    fn simd_cbrt(self) -> Self;

    fn simd_horizontal_sum(self) -> Self::Element;

    fn simd_horizontal_product(self) -> Self::Element;

    fn simd_to_polar(self) -> (Self::SimdRealField, Self::SimdRealField) { ... }

    fn simd_to_exp(self) -> (Self::SimdRealField, Self) { ... }

    fn simd_signum(self) -> Self { ... }

    fn simd_sinh_cosh(self) -> (Self, Self) { ... }

    fn simd_sinc(self) -> Self { ... }

    fn simd_sinhc(self) -> Self { ... }

    fn simd_cosc(self) -> Self { ... }

    fn simd_coshc(self) -> Self { ... }

}
Expand description

Lane-wise generalisation of ComplexField for SIMD complex fields.

Each lane of an SIMD complex field should contain one complex field.

Associated Types

Type of the coefficients of a complex number.

Required methods

Builds a pure-real complex number from the given value.

The real part of this complex number.

The imaginary part of this complex number.

The modulus of this complex number.

The squared modulus of this complex number.

The argument of this complex number.

The sum of the absolute value of this complex number’s real and imaginary part.

Multiplies this complex number by factor.

Divides this complex number by factor.

The absolute value of this complex number: self / self.signum().

This is equivalent to self.modulus().

Computes (self.conjugate() * self + other.conjugate() * other).sqrt()

Computes the sum of all the lanes of self.

Computes the product of all the lanes of self.

Provided methods

The polar form of this complex number: (modulus, arg)

The exponential form of this complex number: (modulus, e^{i arg})

The exponential part of this complex number: self / self.modulus()

Cardinal sine

Cardinal cos

Implementations on Foreign Types

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

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.

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.

Raises self to a floating point power.

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

Raises self to a complex power.

Computes the sine of self.

Computes the cosine of self.

Computes the tangent of self.

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.

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.

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.

Computes the hyperbolic sine of self.

Computes the hyperbolic cosine of self.

Computes the hyperbolic tangent of self.

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.

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)) < ∞.

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.

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

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.

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.

Raises self to a floating point power.

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

Raises self to a complex power.

Computes the sine of self.

Computes the cosine of self.

Computes the tangent of self.

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.

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.

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.

Computes the hyperbolic sine of self.

Computes the hyperbolic cosine of self.

Computes the hyperbolic tangent of self.

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.

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)) < ∞.

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.

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

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.

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.

Raises self to a floating point power.

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

Raises self to a complex power.

Computes the sine of self.

Computes the cosine of self.

Computes the tangent of self.

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.

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.

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.

Computes the hyperbolic sine of self.

Computes the hyperbolic cosine of self.

Computes the hyperbolic tangent of self.

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.

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)) < ∞.

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.

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

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.

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.

Raises self to a floating point power.

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

Raises self to a complex power.

Computes the sine of self.

Computes the cosine of self.

Computes the tangent of self.

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.

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.

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.

Computes the hyperbolic sine of self.

Computes the hyperbolic cosine of self.

Computes the hyperbolic tangent of self.

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.

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)) < ∞.

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.

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

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.

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.

Raises self to a floating point power.

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

Raises self to a complex power.

Computes the sine of self.

Computes the cosine of self.

Computes the tangent of self.

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.

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.

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.

Computes the hyperbolic sine of self.

Computes the hyperbolic cosine of self.

Computes the hyperbolic tangent of self.

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.

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)) < ∞.

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.

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

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.

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.

Raises self to a floating point power.

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

Raises self to a complex power.

Computes the sine of self.

Computes the cosine of self.

Computes the tangent of self.

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.

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.

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.

Computes the hyperbolic sine of self.

Computes the hyperbolic cosine of self.

Computes the hyperbolic tangent of self.

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.

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)) < ∞.

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.

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

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.

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.

Raises self to a floating point power.

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

Raises self to a complex power.

Computes the sine of self.

Computes the cosine of self.

Computes the tangent of self.

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.

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.

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.

Computes the hyperbolic sine of self.

Computes the hyperbolic cosine of self.

Computes the hyperbolic tangent of self.

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.

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)) < ∞.

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.

Implementors