Struct fj_math::Scalar

#[repr(C)]
pub struct Scalar(_);

A rational, finite scalar value

This is a wrapper around f64. On construction, it checks that the f64 value is not NaN. This allows Scalar to provide implementations of Eq, Ord, and Hash, enabling Scalar (and types built on top of it), to be used as keys in hash maps, hash sets, and similar types.

Implementations

impl Scalar

pub const ZERO: Self = _

The Scalar instance that represents zero

pub const ONE: Self = _

The Scalar instance that represents one

pub const TWO: Self = _

The Scalar instance that represents two

pub const MAX: Self = _

The largest Scalar value

pub const PI: Self = _

The Scalar instance that represents pi

pub const TAU: Self = _

The Scalar instance that represents tau

pub fn from_f64(scalar: f64) -> Self

Construct a Scalar from an f64

Panics

Panics, if scalar is NaN.

Examples found in repository

src/scalar.rs (line 55)

    pub fn from_u64(scalar: u64) -> Self {
        Self::from_f64(scalar as f64)
    }

    /// Convert the scalar into an `f32`
    pub fn into_f32(self) -> f32 {
        self.0 as f32
    }

    /// Convert the scalar into an `f64`
    pub fn into_f64(self) -> f64 {
        self.0
    }

    /// Convert the scalar into a `u64`
    pub fn into_u64(self) -> u64 {
        self.0 as u64
    }

    /// Indicate whether the scalar is negative
    pub fn is_negative(self) -> bool {
        self < Self::ZERO
    }

    /// Indicate whether the scalar is positive
    pub fn is_positive(self) -> bool {
        self > Self::ZERO
    }

    /// Indicate whether the scalar is zero
    pub fn is_zero(self) -> bool {
        self == Self::ZERO
    }

    /// The sign of the scalar
    ///
    /// Return `Scalar::ZERO`, if the scalar is zero, `Scalar::ONE`, if it is
    /// positive, `-Scalar::ONE`, if it is negative.
    pub fn sign(self) -> Sign {
        if self.is_negative() {
            return Sign::Negative;
        }
        if self.is_positive() {
            return Sign::Positive;
        }
        if self.is_zero() {
            return Sign::Zero;
        }

        unreachable!("Sign is neither negative, nor positive, nor zero.")
    }

    /// Compute the absolute value of the scalar
    pub fn abs(self) -> Self {
        self.0.abs().into()
    }

    /// Compute the maximum of this and another scalar
    pub fn max(self, other: impl Into<Self>) -> Self {
        self.0.max(other.into().0).into()
    }

    /// Compute the largest integer smaller than or equal to this scalar
    pub fn floor(self) -> Self {
        self.0.floor().into()
    }

    /// Compute the smallest integer larger than or equal to this scalar
    pub fn ceil(self) -> Self {
        self.0.ceil().into()
    }

    /// Round the scalar
    pub fn round(self) -> Self {
        self.0.round().into()
    }

    /// Compute the cosine
    pub fn cos(self) -> Self {
        self.0.cos().into()
    }

    /// Compute sine and cosine
    pub fn sin_cos(self) -> (Self, Self) {
        let (sin, cos) = self.0.sin_cos();
        (sin.into(), cos.into())
    }

    /// Compute the arccosine
    pub fn acos(self) -> Self {
        self.0.acos().into()
    }

    /// Compute the four-quadrant arctangent
    pub fn atan2(self, other: Self) -> Self {
        self.0.atan2(other.0).into()
    }
}

impl PartialEq for Scalar {
    fn eq(&self, other: &Self) -> bool {
        self.0 == other.0
    }
}

impl Eq for Scalar {}

impl PartialOrd for Scalar {
    fn partial_cmp(&self, other: &Self) -> Option<cmp::Ordering> {
        self.0.partial_cmp(&other.0)
    }
}

impl Ord for Scalar {
    fn cmp(&self, other: &Self) -> cmp::Ordering {
        // Should never panic, as `from_f64` checks that the wrapped value is
        // finite.
        self.partial_cmp(other).expect("Invalid `Scalar`")
    }
}

impl Hash for Scalar {
    fn hash<H: std::hash::Hasher>(&self, state: &mut H) {
        // To the best of my knowledge, this matches the `PartialEq`
        // implementation.
        R64::from_inner(self.0).hash(state);
    }
}

impl From<f32> for Scalar {
    fn from(scalar: f32) -> Self {
        Self::from_f64(scalar.into())
    }
}

impl From<f64> for Scalar {
    fn from(scalar: f64) -> Self {
        Self::from_f64(scalar)
    }
}

impl From<Scalar> for f64 {
    fn from(scalar: Scalar) -> Self {
        scalar.into_f64()
    }
}

impl ops::Neg for Scalar {
    type Output = Self;

    fn neg(self) -> Self::Output {
        self.0.neg().into()
    }
}

impl<T: Into<Self>> ops::Add<T> for Scalar {
    type Output = Self;

    fn add(self, rhs: T) -> Self::Output {
        self.0.add(rhs.into().0).into()
    }
}

impl<T: Into<Self>> ops::Sub<T> for Scalar {
    type Output = Self;

    fn sub(self, rhs: T) -> Self::Output {
        self.0.sub(rhs.into().0).into()
    }
}

impl<T: Into<Self>> ops::Mul<T> for Scalar {
    type Output = Self;

    fn mul(self, rhs: T) -> Self::Output {
        self.0.mul(rhs.into().0).into()
    }
}

impl<T: Into<Self>> ops::Div<T> for Scalar {
    type Output = Self;

    fn div(self, rhs: T) -> Self::Output {
        self.0.div(rhs.into().0).into()
    }
}

impl<T: Into<Self>> ops::Rem<T> for Scalar {
    type Output = Self;

    fn rem(self, rhs: T) -> Self::Output {
        self.0.rem(rhs.into().0).into()
    }
}

impl<T: Into<Self>> ops::AddAssign<T> for Scalar {
    fn add_assign(&mut self, rhs: T) {
        self.0.add_assign(rhs.into().0);
        *self = self.0.into();
    }
}

impl<T: Into<Self>> ops::SubAssign<T> for Scalar {
    fn sub_assign(&mut self, rhs: T) {
        self.0.sub_assign(rhs.into().0);
        *self = self.0.into();
    }
}

impl<T: Into<Self>> ops::MulAssign<T> for Scalar {
    fn mul_assign(&mut self, rhs: T) {
        self.0.mul_assign(rhs.into().0);
        *self = self.0.into();
    }
}

impl<T: Into<Self>> ops::DivAssign<T> for Scalar {
    fn div_assign(&mut self, rhs: T) {
        self.0.div_assign(rhs.into().0);
        *self = self.0.into();
    }
}

impl<T: Into<Self>> ops::RemAssign<T> for Scalar {
    fn rem_assign(&mut self, rhs: T) {
        self.0.rem_assign(rhs.into().0);
        *self = self.0.into();
    }
}

impl num_traits::Zero for Scalar {
    fn zero() -> Self {
        Self::ZERO
    }

    fn is_zero(&self) -> bool {
        self.0.is_zero()
    }
}

impl num_traits::One for Scalar {
    fn one() -> Self {
        Self::ONE
    }
}

impl num_traits::Num for Scalar {
    type FromStrRadixErr = <f64 as num_traits::Num>::FromStrRadixErr;

    fn from_str_radix(
        str: &str,
        radix: u32,
    ) -> Result<Self, Self::FromStrRadixErr> {
        f64::from_str_radix(str, radix).map(Self::from_f64)
    }
}

impl num_traits::NumCast for Scalar {
    fn from<T: num_traits::ToPrimitive>(n: T) -> Option<Self> {
        Some(Self::from_f64(<f64 as num_traits::NumCast>::from(n)?))
    }
}

impl num_traits::Signed for Scalar {
    fn abs(&self) -> Self {
        self.0.abs().into()
    }

    fn abs_sub(&self, other: &Self) -> Self {
        <f64 as num_traits::Signed>::abs_sub(&self.0, &other.0).into()
    }

    fn signum(&self) -> Self {
        <f64 as num_traits::Signed>::signum(&self.0).into()
    }

    fn is_positive(&self) -> bool {
        <f64 as num_traits::Signed>::is_positive(&self.0)
    }

    fn is_negative(&self) -> bool {
        <f64 as num_traits::Signed>::is_negative(&self.0)
    }
}

impl num_traits::ToPrimitive for Scalar {
    fn to_i64(&self) -> Option<i64> {
        self.0.to_i64()
    }

    fn to_u64(&self) -> Option<u64> {
        self.0.to_u64()
    }
}

impl num_traits::Float for Scalar {
    fn nan() -> Self {
        panic!("`Scalar` can not represent NaN")
    }

    fn infinity() -> Self {
        Self::from_f64(f64::infinity())
    }

    fn neg_infinity() -> Self {
        Self::from_f64(f64::neg_infinity())
    }

    fn neg_zero() -> Self {
        Self::from_f64(f64::neg_zero())
    }

    fn min_value() -> Self {
        Self::from_f64(f64::min_value())
    }

    fn min_positive_value() -> Self {
        Self::from_f64(f64::min_positive_value())
    }

    fn max_value() -> Self {
        Self::from_f64(f64::max_value())
    }

    fn is_nan(self) -> bool {
        self.0.is_nan()
    }

    fn is_infinite(self) -> bool {
        self.0.is_infinite()
    }

    fn is_finite(self) -> bool {
        self.0.is_finite()
    }

    fn is_normal(self) -> bool {
        self.0.is_normal()
    }

    fn classify(self) -> std::num::FpCategory {
        self.0.classify()
    }

    fn floor(self) -> Self {
        Self::from_f64(self.0.floor())
    }

    fn ceil(self) -> Self {
        Self::from_f64(self.0.ceil())
    }

    fn round(self) -> Self {
        Self::from_f64(self.0.round())
    }

    fn trunc(self) -> Self {
        Self::from_f64(self.0.trunc())
    }

    fn fract(self) -> Self {
        Self::from_f64(self.0.fract())
    }

    fn abs(self) -> Self {
        Self::from_f64(self.0.abs())
    }

    fn signum(self) -> Self {
        Self::from_f64(self.0.signum())
    }

    fn is_sign_positive(self) -> bool {
        self.0.is_sign_positive()
    }

    fn is_sign_negative(self) -> bool {
        self.0.is_sign_negative()
    }

    fn mul_add(self, a: Self, b: Self) -> Self {
        Self::from_f64(self.0.mul_add(a.0, b.0))
    }

    fn recip(self) -> Self {
        Self::from_f64(self.0.recip())
    }

    fn powi(self, n: i32) -> Self {
        Self::from_f64(self.0.powi(n))
    }

    fn powf(self, n: Self) -> Self {
        Self::from_f64(self.0.powf(n.0))
    }

    fn sqrt(self) -> Self {
        Self::from_f64(self.0.sqrt())
    }

    fn exp(self) -> Self {
        Self::from_f64(self.0.exp())
    }

    fn exp2(self) -> Self {
        Self::from_f64(self.0.exp2())
    }

    fn ln(self) -> Self {
        Self::from_f64(self.0.ln())
    }

    fn log(self, base: Self) -> Self {
        Self::from_f64(self.0.log(base.0))
    }

    fn log2(self) -> Self {
        Self::from_f64(self.0.log2())
    }

    fn log10(self) -> Self {
        Self::from_f64(self.0.log10())
    }

    fn max(self, other: Self) -> Self {
        Self::from_f64(self.0.max(other.0))
    }

    fn min(self, other: Self) -> Self {
        Self::from_f64(self.0.min(other.0))
    }

    fn abs_sub(self, other: Self) -> Self {
        (self - other).abs()
    }

    fn cbrt(self) -> Self {
        Self::from_f64(self.0.cbrt())
    }

    fn hypot(self, other: Self) -> Self {
        Self::from_f64(self.0.hypot(other.0))
    }

    fn sin(self) -> Self {
        Self::from_f64(self.0.sin())
    }

    fn cos(self) -> Self {
        Self::from_f64(self.0.cos())
    }

    fn tan(self) -> Self {
        Self::from_f64(self.0.tan())
    }

    fn asin(self) -> Self {
        Self::from_f64(self.0.asin())
    }

    fn acos(self) -> Self {
        Self::from_f64(self.0.acos())
    }

    fn atan(self) -> Self {
        Self::from_f64(self.0.atan())
    }

    fn atan2(self, other: Self) -> Self {
        Self::from_f64(self.0.atan2(other.0))
    }

    fn sin_cos(self) -> (Self, Self) {
        let (sin, cos) = self.0.sin_cos();
        (Self::from_f64(sin), Self::from_f64(cos))
    }

    fn exp_m1(self) -> Self {
        Self::from_f64(self.0.exp_m1())
    }

    fn ln_1p(self) -> Self {
        Self::from_f64(self.0.ln_1p())
    }

    fn sinh(self) -> Self {
        Self::from_f64(self.0.sinh())
    }

    fn cosh(self) -> Self {
        Self::from_f64(self.0.cosh())
    }

    fn tanh(self) -> Self {
        Self::from_f64(self.0.tanh())
    }

    fn asinh(self) -> Self {
        Self::from_f64(self.0.asinh())
    }

    fn acosh(self) -> Self {
        Self::from_f64(self.0.acosh())
    }

    fn atanh(self) -> Self {
        Self::from_f64(self.0.atanh())
    }

pub fn from_u64(scalar: u64) -> Self

Construct a Scalar from a u64

pub fn into_f32(self) -> f32

Convert the scalar into an f32

Examples found in repository

src/vector.rs (line 263)

    fn from(vector: Vector<D>) -> Self {
        vector.components.map(|scalar| scalar.into_f32())
    }

pub fn into_f64(self) -> f64

Convert the scalar into an f64

Examples found in repository

src/scalar.rs (line 197)

    fn from(scalar: Scalar) -> Self {
        scalar.into_f64()
    }

src/vector.rs (line 269)

    fn from(vector: Vector<D>) -> Self {
        vector.components.map(|scalar| scalar.into_f64())
    }
}

impl<const D: usize> From<Vector<D>> for [Scalar; D] {
    fn from(vector: Vector<D>) -> Self {
        vector.components
    }
}

impl<const D: usize> From<Vector<D>> for nalgebra::SVector<f64, D> {
    fn from(vector: Vector<D>) -> Self {
        vector.to_na()
    }
}

impl<const D: usize> ops::Neg for Vector<D> {
    type Output = Self;

    fn neg(self) -> Self::Output {
        self.to_na().neg().into()
    }
}

impl<V, const D: usize> ops::Add<V> for Vector<D>
where
    V: Into<Self>,
{
    type Output = Self;

    fn add(self, rhs: V) -> Self::Output {
        self.to_na().add(rhs.into().to_na()).into()
    }
}

impl<V, const D: usize> ops::Sub<V> for Vector<D>
where
    V: Into<Self>,
{
    type Output = Self;

    fn sub(self, rhs: V) -> Self::Output {
        self.to_na().sub(rhs.into().to_na()).into()
    }
}

impl<S, const D: usize> ops::Mul<S> for Vector<D>
where
    S: Into<Scalar>,
{
    type Output = Self;

    fn mul(self, rhs: S) -> Self::Output {
        self.to_na().mul(rhs.into().into_f64()).into()
    }
}

impl<S, const D: usize> ops::Div<S> for Vector<D>
where
    S: Into<Scalar>,
{
    type Output = Self;

    fn div(self, rhs: S) -> Self::Output {
        self.to_na().div(rhs.into().into_f64()).into()
    }

pub fn into_u64(self) -> u64

Convert the scalar into a u64

pub fn is_negative(self) -> bool

Indicate whether the scalar is negative

Examples found in repository

src/scalar.rs (line 93)

    pub fn sign(self) -> Sign {
        if self.is_negative() {
            return Sign::Negative;
        }
        if self.is_positive() {
            return Sign::Positive;
        }
        if self.is_zero() {
            return Sign::Zero;
        }

        unreachable!("Sign is neither negative, nor positive, nor zero.")
    }

pub fn is_positive(self) -> bool

Indicate whether the scalar is positive

Examples found in repository

src/scalar.rs (line 96)

    pub fn sign(self) -> Sign {
        if self.is_negative() {
            return Sign::Negative;
        }
        if self.is_positive() {
            return Sign::Positive;
        }
        if self.is_zero() {
            return Sign::Zero;
        }

        unreachable!("Sign is neither negative, nor positive, nor zero.")
    }

pub fn is_zero(self) -> bool

Indicate whether the scalar is zero

Examples found in repository

src/scalar.rs (line 99)

    pub fn sign(self) -> Sign {
        if self.is_negative() {
            return Sign::Negative;
        }
        if self.is_positive() {
            return Sign::Positive;
        }
        if self.is_zero() {
            return Sign::Zero;
        }

        unreachable!("Sign is neither negative, nor positive, nor zero.")
    }

pub fn sign(self) -> Sign

The sign of the scalar

Return Scalar::ZERO, if the scalar is zero, Scalar::ONE, if it is positive, -Scalar::ONE, if it is negative.

pub fn abs(self) -> Self

Compute the absolute value of the scalar

Examples found in repository

src/scalar.rs (line 487)

    fn abs_sub(self, other: Self) -> Self {
        (self - other).abs()
    }

pub fn max(self, other: impl Into<Self>) -> Self

Compute the maximum of this and another scalar

pub fn floor(self) -> Self

Compute the largest integer smaller than or equal to this scalar

pub fn ceil(self) -> Self

Compute the smallest integer larger than or equal to this scalar

pub fn round(self) -> Self

Round the scalar

pub fn cos(self) -> Self

Compute the cosine

pub fn sin_cos(self) -> (Self, Self)

Compute sine and cosine

Examples found in repository

src/circle.rs (line 150)

    pub fn vector_from_circle_coords(
        &self,
        vector: impl Into<Vector<1>>,
    ) -> Vector<D> {
        let angle = vector.into().t;
        let (sin, cos) = angle.sin_cos();

        self.a * cos + self.b * sin
    }

pub fn acos(self) -> Self

Compute the arccosine

pub fn atan2(self, other: Self) -> Self

Compute the four-quadrant arctangent

Examples found in repository

src/circle.rs (line 127)

    pub fn point_to_circle_coords(
        &self,
        point: impl Into<Point<D>>,
    ) -> Point<1> {
        let vector = (point.into() - self.center).to_uv();
        let atan = Scalar::atan2(vector.v, vector.u);
        let coord = if atan >= Scalar::ZERO {
            atan
        } else {
            atan + Scalar::TAU
        };
        Point::from([coord])
    }

Trait Implementations

impl AbsDiffEq<Scalar> for Scalar

type Epsilon = Scalar

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together.

fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of AbsDiffEq::abs_diff_eq.

impl<T: Into<Self>> Add<T> for Scalar

type Output = Scalar

The resulting type after applying the + operator.

fn add(self, rhs: T) -> Self::Output

Performs the + operation.

impl<T: Into<Self>> AddAssign<T> for Scalar

fn add_assign(&mut self, rhs: T)

Performs the += operation.

impl Clone for Scalar

fn clone(&self) -> Scalar

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for Scalar

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

Formats the value using the given formatter.

impl Default for Scalar

fn default() -> Scalar

Returns the “default value” for a type.

impl Display for Scalar

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

Formats the value using the given formatter.

impl<T: Into<Self>> Div<T> for Scalar

type Output = Scalar

The resulting type after applying the / operator.

fn div(self, rhs: T) -> Self::Output

Performs the / operation.

impl<T: Into<Self>> DivAssign<T> for Scalar

fn div_assign(&mut self, rhs: T)

Performs the /= operation.

impl Float for Scalar

fn nan() -> Self

Returns the NaN value.

fn infinity() -> Self

Returns the infinite value.

fn neg_infinity() -> Self

Returns the negative infinite value.

fn neg_zero() -> Self

Returns -0.0.

fn min_value() -> Self

Returns the smallest finite value that this type can represent.

fn min_positive_value() -> Self

Returns the smallest positive, normalized value that this type can represent.

fn max_value() -> Self

Returns the largest finite value that this type can represent.

fn is_nan(self) -> bool

Returns true if this value is NaN and false otherwise.

fn is_infinite(self) -> bool

Returns true if this value is positive infinity or negative infinity and false otherwise.

fn is_finite(self) -> bool

Returns true if this number is neither infinite nor NaN.

fn is_normal(self) -> bool

Returns true if the number is neither zero, infinite, subnormal, or NaN.

fn classify(self) -> FpCategory

Returns the floating point category of the number. If only one property is going to be tested, it is generally faster to use the specific predicate instead.

fn floor(self) -> Self

Returns the largest integer less than or equal to a number.

fn ceil(self) -> Self

Returns the smallest integer greater than or equal to a number.

fn round(self) -> Self

Returns the nearest integer to a number. Round half-way cases away from 0.0.

fn trunc(self) -> Self

Return the integer part of a number.

fn fract(self) -> Self

Returns the fractional part of a number.

fn abs(self) -> Self

Computes the absolute value of self. Returns Float::nan() if the number is Float::nan().

fn signum(self) -> Self

Returns a number that represents the sign of self.

fn is_sign_positive(self) -> bool

Returns true if self is positive, including +0.0, Float::infinity(), and since Rust 1.20 also Float::nan().

fn is_sign_negative(self) -> bool

Returns true if self is negative, including -0.0, Float::neg_infinity(), and since Rust 1.20 also -Float::nan().

fn mul_add(self, a: Self, b: Self) -> Self

Fused multiply-add. Computes (self * a) + b with only one rounding error, yielding a more accurate result than an unfused multiply-add.

fn recip(self) -> Self

Take the reciprocal (inverse) of a number, 1/x.

fn powi(self, n: i32) -> Self

Raise a number to an integer power.

fn powf(self, n: Self) -> Self

Raise a number to a floating point power.

fn sqrt(self) -> Self

Take the square root of a number.

fn exp(self) -> Self

Returns e^(self), (the exponential function).

fn exp2(self) -> Self

Returns 2^(self).

fn ln(self) -> Self

Returns the natural logarithm of the number.

fn log(self, base: Self) -> Self

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

fn log2(self) -> Self

Returns the base 2 logarithm of the number.

fn log10(self) -> Self

Returns the base 10 logarithm of the number.

fn max(self, other: Self) -> Self

Returns the maximum of the two numbers.

fn min(self, other: Self) -> Self

Returns the minimum of the two numbers.

fn abs_sub(self, other: Self) -> Self

The positive difference of two numbers.

fn cbrt(self) -> Self

Take the cubic root of a number.

fn hypot(self, other: Self) -> Self

Calculate the length of the hypotenuse of a right-angle triangle given legs of length x and y.

fn sin(self) -> Self

Computes the sine of a number (in radians).

fn cos(self) -> Self

Computes the cosine of a number (in radians).

fn tan(self) -> Self

Computes the tangent of a number (in radians).

fn asin(self) -> Self

Computes the arcsine of a number. Return value is in radians in the range [-pi/2, pi/2] or NaN if the number is outside the range [-1, 1].

fn acos(self) -> Self

Computes the arccosine of a number. Return value is in radians in the range [0, pi] or NaN if the number is outside the range [-1, 1].

fn atan(self) -> Self

Computes the arctangent of a number. Return value is in radians in the range [-pi/2, pi/2];

fn atan2(self, other: Self) -> Self

Computes the four quadrant arctangent of self (y) and other (x).

fn sin_cos(self) -> (Self, Self)

Simultaneously computes the sine and cosine of the number, x. Returns (sin(x), cos(x)).

fn exp_m1(self) -> Self

Returns e^(self) - 1 in a way that is accurate even if the number is close to zero.

fn ln_1p(self) -> Self

Returns ln(1+n) (natural logarithm) more accurately than if the operations were performed separately.

fn sinh(self) -> Self

Hyperbolic sine function.

fn cosh(self) -> Self

Hyperbolic cosine function.

fn tanh(self) -> Self

Hyperbolic tangent function.

fn asinh(self) -> Self

Inverse hyperbolic sine function.

fn acosh(self) -> Self

Inverse hyperbolic cosine function.

fn atanh(self) -> Self

Inverse hyperbolic tangent function.

fn integer_decode(self) -> (u64, i16, i8)

Returns the mantissa, base 2 exponent, and sign as integers, respectively. The original number can be recovered by sign * mantissa * 2 ^ exponent.

fn epsilon() -> Self

Returns epsilon, a small positive value.

fn to_degrees(self) -> Self

Converts radians to degrees.

fn to_radians(self) -> Self

Converts degrees to radians.

fn copysign(self, sign: Self) -> Self

Returns a number composed of the magnitude of self and the sign of sign.

impl From<Scalar> for f64

fn from(scalar: Scalar) -> Self

Converts to this type from the input type.

impl From<f32> for Scalar

fn from(scalar: f32) -> Self

Converts to this type from the input type.

impl From<f64> for Scalar

fn from(scalar: f64) -> Self

Converts to this type from the input type.

impl Hash for Scalar

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

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)where
    H: Hasher,
    Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<T: Into<Self>> Mul<T> for Scalar

type Output = Scalar

The resulting type after applying the * operator.

fn mul(self, rhs: T) -> Self::Output

Performs the * operation.

impl<T: Into<Self>> MulAssign<T> for Scalar

fn mul_assign(&mut self, rhs: T)

Performs the *= operation.

impl Neg for Scalar

type Output = Scalar

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl Num for Scalar

type FromStrRadixErr = <f64 as Num>::FromStrRadixErr

fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr>

Convert from a string and radix (typically 2..=36).

impl NumCast for Scalar

fn from<T: ToPrimitive>(n: T) -> Option<Self>

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.

impl One for Scalar

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

fn is_one(&self) -> boolwhere
    Self: PartialEq<Self>,

Returns true if self is equal to the multiplicative identity.

impl Ord for Scalar

fn cmp(&self, other: &Self) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Selfwhere
    Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Selfwhere
    Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Selfwhere
    Self: Sized + PartialOrd<Self>,

Restrict a value to a certain interval.

impl PartialEq<Scalar> for Scalar

fn eq(&self, other: &Self) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl PartialOrd<Scalar> for Scalar

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

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

This method tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

This method tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl<T: Into<Self>> Rem<T> for Scalar

type Output = Scalar

The resulting type after applying the % operator.

fn rem(self, rhs: T) -> Self::Output

Performs the % operation.

impl<T: Into<Self>> RemAssign<T> for Scalar

fn rem_assign(&mut self, rhs: T)

Performs the %= operation.

impl Signed for Scalar

fn abs(&self) -> Self

Computes the absolute value.

fn abs_sub(&self, other: &Self) -> Self

The positive difference of two numbers.

fn signum(&self) -> Self

Returns the sign of the number.

fn is_positive(&self) -> bool

Returns true if the number is positive and false if the number is zero or negative.

fn is_negative(&self) -> bool

Returns true if the number is negative and false if the number is zero or positive.

impl<T: Into<Self>> Sub<T> for Scalar

type Output = Scalar

The resulting type after applying the - operator.

fn sub(self, rhs: T) -> Self::Output

Performs the - operation.

impl<T: Into<Self>> SubAssign<T> for Scalar

fn sub_assign(&mut self, rhs: T)

Performs the -= operation.

impl ToPrimitive for Scalar

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

impl Zero for Scalar

fn zero() -> Self

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl Copy for Scalar

impl Eq for Scalar