Trait Numeric 

pub trait Numeric:
    Copy
    + Clone
    + PartialEq
    + PartialOrd
    + Debug
    + Add<Output = Self>
    + Sub<Output = Self>
    + Mul<Output = Self>
    + Div<Output = Self>
    + Neg<Output = Self>
    + AddAssign
    + SubAssign
    + MulAssign
    + DivAssign {
    const ZERO: Self;
    const ONE: Self;
    const TWO: Self;
    const HALF: Self;
    const PI: Self;
    const EPSILON: Self;
    const NAN: Self;
    const INFINITY: Self;
    const NEG_INFINITY: Self;
    const MAX: Self;
    const MIN_POSITIVE: Self;

    // Required methods
    fn from_f64(value: f64) -> Self;
    fn from_u64(value: u64) -> Self;
    fn from_usize(value: usize) -> Self;
    fn abs(self) -> Self;
    fn sqrt(self) -> Self;
    fn sin(self) -> Self;
    fn cos(self) -> Self;
    fn tan(self) -> Self;
    fn exp(self) -> Self;
    fn ln(self) -> Self;
    fn atan2(self, other: Self) -> Self;
    fn copysign(self, sign: Self) -> Self;
    fn floor(self) -> Self;
    fn is_nan(self) -> bool;
    fn is_finite(self) -> bool;

    // Provided methods
    fn signum(self) -> Self { ... }
    fn max(self, other: Self) -> Self { ... }
    fn min(self, other: Self) -> Self { ... }
    fn atan(self) -> Self { ... }
    fn asin(self) -> Self { ... }
    fn acos(self) -> Self { ... }
    fn sinh(self) -> Self { ... }
    fn cosh(self) -> Self { ... }
    fn tanh(self) -> Self { ... }
    fn hypot(self, other: Self) -> Self { ... }
    fn powf(self, n: Self) -> Self { ... }
    fn mul_add(self, a: Self, b: Self) -> Self { ... }
    fn recip(self) -> Self { ... }
    fn powi(self, n: i32) -> Self { ... }
}

A floating-point scalar usable by the differentiation, integration, and approximation modules. Transcendentals come from libm, so the trait works without std.

Required Associated Constants

const ZERO: Self

The value 0.

const ONE: Self

The value 1.

const TWO: Self

The value 2.

const HALF: Self

The value 0.5.

const PI: Self

Archimedes’ constant, π.

const EPSILON: Self

The difference between 1 and the next larger representable value.

const NAN: Self

Not a Number.

const INFINITY: Self

Positive infinity.

const NEG_INFINITY: Self

Negative infinity.

const MAX: Self

The largest finite value.

use multicalc::Numeric;
assert_eq!(<f64 as Numeric>::MAX, f64::MAX);

const MIN_POSITIVE: Self

The smallest positive normal value.

use multicalc::Numeric;
assert_eq!(<f64 as Numeric>::MIN_POSITIVE, f64::MIN_POSITIVE);

Required Methods

fn from_f64(value: f64) -> Self

Converts from f64, narrowing if necessary. Used for table values and literals.

fn from_u64(value: u64) -> Self

Converts from u64, e.g. an iteration count.

fn from_usize(value: usize) -> Self

Converts from usize, e.g. a point or variable count.

fn abs(self) -> Self

Absolute value.

fn sqrt(self) -> Self

Square root.

fn sin(self) -> Self

Sine, with self in radians.

fn cos(self) -> Self

Cosine, with self in radians.

fn tan(self) -> Self

Tangent, with self in radians.

fn exp(self) -> Self

e raised to the power self.

fn ln(self) -> Self

Natural logarithm of self.

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

Four-quadrant arctangent of self / other, in radians, taking self as the y coordinate and other as the x coordinate. Result in (-π, π].

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

A value with the magnitude of self and the sign of sign.

fn floor(self) -> Self

The largest integer less than or equal to self.

A step function, so its derivative is zero everywhere it is differentiable; the dual implementations therefore carry a zero derivative.

fn is_nan(self) -> bool

Returns true if self is NaN.

fn is_finite(self) -> bool

Returns true if self is neither infinite nor NaN.

Provided Methods

fn signum(self) -> Self

Sign of self: 1 for positive, -1 for negative, 0 at zero.

The derivative is zero wherever it is defined. This default maps NaN and both zeros to 0; the f32/f64 impls override to match the primitive signum (NaN maps to NaN, signed zeros are preserved).

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

The larger of self and other, compared with >.

On the autodiff scalars this selects the larger operand together with its full derivative payload. The f32/f64 impls override to match the primitive max, which returns the non-NaN operand.

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

The smaller of self and other, compared with <.

On the autodiff scalars this selects the smaller operand together with its full derivative payload. The f32/f64 impls override to match the primitive min, which returns the non-NaN operand.

fn atan(self) -> Self

Arctangent, in radians.

fn asin(self) -> Self

Arcsine, in radians, for self in [-1, 1].

fn acos(self) -> Self

Arccosine, in radians, for self in [-1, 1].

fn sinh(self) -> Self

Hyperbolic sine.

fn cosh(self) -> Self

Hyperbolic cosine.

fn tanh(self) -> Self

Hyperbolic tangent.

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

Euclidean distance √(self² + other²), scaled to avoid overflow and underflow.

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

self raised to a floating-point power, via exp(n · ln self). Defined for self > 0; the f32/f64 impls override for negative bases and edge cases.

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

self * a + b. The f32/f64 impls fuse the operation for extra precision.

fn recip(self) -> Self

The reciprocal 1 / self.

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

self raised to an integer power, by exponentiation-by-squaring.

The zero exponent gives Numeric::ONE; a negative exponent inverts the result. Built from * and / alone, so any Numeric (including a dual number) gets a correct derivative without overriding this method.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety".

Implementations on Foreign Types

impl Numeric for f32

const ZERO: Self = 0.0

const ONE: Self = 1.0

const TWO: Self = 2.0

const HALF: Self = 0.5

const PI: Self = core::f32::consts::PI

const EPSILON: Self = f32::EPSILON

const NAN: Self = f32::NAN

const INFINITY: Self = f32::INFINITY

const NEG_INFINITY: Self = f32::NEG_INFINITY

const MAX: Self = f32::MAX

const MIN_POSITIVE: Self = f32::MIN_POSITIVE

fn from_f64(value: f64) -> Self

fn from_u64(value: u64) -> Self

fn from_usize(value: usize) -> Self

fn abs(self) -> Self

fn sqrt(self) -> Self

fn sin(self) -> Self

fn cos(self) -> Self

fn tan(self) -> Self

fn exp(self) -> Self

fn ln(self) -> Self

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

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

fn floor(self) -> Self

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

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

fn signum(self) -> Self

fn atan(self) -> Self

fn asin(self) -> Self

fn acos(self) -> Self

fn sinh(self) -> Self

fn cosh(self) -> Self

fn tanh(self) -> Self

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

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

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

fn recip(self) -> Self

fn is_nan(self) -> bool

fn is_finite(self) -> bool

impl Numeric for f64

const ZERO: Self = 0.0

const ONE: Self = 1.0

const TWO: Self = 2.0

const HALF: Self = 0.5

const PI: Self = core::f64::consts::PI

const EPSILON: Self = f64::EPSILON

const NAN: Self = f64::NAN

const INFINITY: Self = f64::INFINITY

const NEG_INFINITY: Self = f64::NEG_INFINITY

const MAX: Self = f64::MAX

const MIN_POSITIVE: Self = f64::MIN_POSITIVE

fn from_f64(value: f64) -> Self

fn from_u64(value: u64) -> Self

fn from_usize(value: usize) -> Self

fn abs(self) -> Self

fn sqrt(self) -> Self

fn sin(self) -> Self

fn cos(self) -> Self

fn tan(self) -> Self

fn exp(self) -> Self

fn ln(self) -> Self

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

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

fn floor(self) -> Self

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

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

fn signum(self) -> Self

fn atan(self) -> Self

fn asin(self) -> Self

fn acos(self) -> Self

fn sinh(self) -> Self

fn cosh(self) -> Self

fn tanh(self) -> Self

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

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

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

fn recip(self) -> Self

fn is_nan(self) -> bool

fn is_finite(self) -> bool

Implementors

impl<T: Numeric, const N: usize> Numeric for Jet<T, N>

const ZERO: Self

const ONE: Self

const TWO: Self

const HALF: Self

const PI: Self

const EPSILON: Self

const NAN: Self

const INFINITY: Self

const NEG_INFINITY: Self

const MAX: Self

const MIN_POSITIVE: Self

impl<T: Numeric> Numeric for Dual<T>

const ZERO: Self

const ONE: Self

const TWO: Self

const HALF: Self

const PI: Self

const EPSILON: Self

const NAN: Self

const INFINITY: Self

const NEG_INFINITY: Self

const MAX: Self

const MIN_POSITIVE: Self

impl<T: Numeric> Numeric for HyperDual<T>

const ZERO: Self

const ONE: Self

const TWO: Self

const HALF: Self

const PI: Self

const EPSILON: Self

const NAN: Self

const INFINITY: Self

const NEG_INFINITY: Self

const MAX: Self

const MIN_POSITIVE: Self