Trait Real 

pub trait Real:
    Clone
    + Debug
    + Display
    + PartialEq
    + PartialOrd
    + From<f64>
    + From<i32>
    + Send
    + Sync
    + 'static
    + Neg<Output = Self>
    + Add<Self, Output = Self>
    + Sub<Self, Output = Self>
    + Mul<Self, Output = Self>
    + Div<Self, Output = Self>
    + Add<Self::Passive, Output = Self>
    + Sub<Self::Passive, Output = Self>
    + Mul<Self::Passive, Output = Self>
    + Div<Self::Passive, Output = Self> {
    type Passive: Passive + Add<Self, Output = Self> + Sub<Self, Output = Self> + Mul<Self, Output = Self> + Div<Self, Output = Self>;

    // Required methods
    fn value(&self) -> Self::Passive;
    fn zero() -> Self;
    fn one() -> Self;
    fn powf(&self, exponent: Self) -> Self;
    fn powi(&self, exponent: i32) -> Self;
    fn sin(&self) -> Self;
    fn cos(&self) -> Self;
    fn tan(&self) -> Self;
    fn asin(&self) -> Self;
    fn acos(&self) -> Self;
    fn atan(&self) -> Self;
    fn sinh(&self) -> Self;
    fn cosh(&self) -> Self;
    fn tanh(&self) -> Self;
    fn asinh(&self) -> Self;
    fn acosh(&self) -> Self;
    fn atanh(&self) -> Self;
    fn exp(&self) -> Self;
    fn exp2(&self) -> Self;
    fn ln(&self) -> Self;
    fn log2(&self) -> Self;
    fn log10(&self) -> Self;
    fn ln_1p(&self) -> Self;
    fn exp_m1(&self) -> Self;
    fn sqrt(&self) -> Self;
    fn cbrt(&self) -> Self;
    fn abs(&self) -> Self;
    fn erf(&self) -> Self;
    fn erfc(&self) -> Self;
    fn norm_cdf(&self) -> Self;
    fn norm_pdf(&self) -> Self;
    fn inv_norm_cdf(&self) -> Self;
    fn sum(xs: &[Self]) -> Self;
    fn dot(xs: &[Self], ys: &[Self]) -> Self;
    fn weighted_sum(ws: &[Self::Passive], xs: &[Self]) -> Self;
    fn weighted_dot(ws: &[Self::Passive], xs: &[Self], ys: &[Self]) -> Self;
    fn max(&self, other: &Self) -> Self;
    fn min(&self, other: &Self) -> Self;
}

Required Associated Types

type Passive: Passive + Add<Self, Output = Self> + Sub<Self, Output = Self> + Mul<Self, Output = Self> + Div<Self, Output = Self>

Required Methods

fn value(&self) -> Self::Passive

fn zero() -> Self

fn one() -> Self

fn powf(&self, exponent: Self) -> Self

fn powi(&self, exponent: i32) -> Self

fn sin(&self) -> Self

Sine.

fn cos(&self) -> Self

Cosine.

fn tan(&self) -> Self

Tangent. f' = 1 + tan², f'' = 2·tan·f'.

fn asin(&self) -> Self

Inverse sine. f' = 1/√(1-x²), f'' = x·f'³.

fn acos(&self) -> Self

Inverse cosine. f' = -1/√(1-x²), f'' = x·f'³.

fn atan(&self) -> Self

Inverse tangent. f' = 1/(1+x²), f'' = -2x·f'².

fn sinh(&self) -> Self

Hyperbolic sine.

fn cosh(&self) -> Self

Hyperbolic cosine.

fn tanh(&self) -> Self

Hyperbolic tangent. f' = 1 - tanh², f'' = -2·tanh·f'.

fn asinh(&self) -> Self

Inverse hyperbolic sine. f' = 1/√(x²+1), f'' = -x·f'³.

fn acosh(&self) -> Self

Inverse hyperbolic cosine. f' = 1/√(x²-1), f'' = -x·f'³.

fn atanh(&self) -> Self

Inverse hyperbolic tangent. f' = 1/(1-x²), f'' = 2x·f'².

fn exp(&self) -> Self

Exponential. f = f' = f''.

fn exp2(&self) -> Self

Base-2 exponential. f' = f·ln 2, f'' = f·(ln 2)².

fn ln(&self) -> Self

Natural logarithm. f' = 1/x, f'' = -1/x².

fn log2(&self) -> Self

Base-2 logarithm. f' = 1/(x·ln 2), f'' = -f'/x.

fn log10(&self) -> Self

Base-10 logarithm. f' = 1/(x·ln 10), f'' = -f'/x.

fn ln_1p(&self) -> Self

ln(1 + x). f' = 1/(1+x), f'' = -f'².

fn exp_m1(&self) -> Self

exp(x) - 1. f' = f'' = exp(x) = f + 1.

fn sqrt(&self) -> Self

Square root. f' = 1/(2√x), f'' = -1/(4·x·√x).

fn cbrt(&self) -> Self

Cube root. f' = 1/(3·f²), f'' = -2/(9·x·f²).

fn abs(&self) -> Self

Absolute value. f' = sign(x), f'' = 0 (away from 0). At x = 0 the derivative is not defined; every surface takes the sub-gradient f'(0) = +1 (the x >= 0 branch), matching the winning-branch convention max/min use for payoffs.

fn erf(&self) -> Self

Gaussian error function. f' = (2/√π)·e^{-x²}, f'' = -2x·f'.

fn erfc(&self) -> Self

Complementary error function 1 - erf(x). f' = -(2/√π)·e^{-x²}.

fn norm_cdf(&self) -> Self

Standard normal CDF Φ(x). f' = φ(x), f'' = -x·φ(x).

fn norm_pdf(&self) -> Self

Standard normal density φ(x). f' = -x·φ(x), f'' = (x² − 1)·φ(x).

fn inv_norm_cdf(&self) -> Self

Inverse standard normal CDF Φ⁻¹(p). f' = 1/φ(f), f'' = f·f'².

fn sum(xs: &[Self]) -> Self

fn dot(xs: &[Self], ys: &[Self]) -> Self

fn weighted_sum(ws: &[Self::Passive], xs: &[Self]) -> Self

fn weighted_dot(ws: &[Self::Passive], xs: &[Self], ys: &[Self]) -> Self

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

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

Dyn Compatibility

This trait is not dyn compatible.

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

Implementations on Foreign Types

impl Real for f64

type Passive = f64

fn value(&self) -> f64

fn zero() -> Self

fn one() -> Self

fn powf(&self, exponent: Self) -> Self

fn powi(&self, exponent: i32) -> Self

fn sum(xs: &[Self]) -> Self

fn dot(xs: &[Self], ys: &[Self]) -> Self

fn weighted_sum(ws: &[Self::Passive], xs: &[Self]) -> Self

fn weighted_dot(ws: &[Self::Passive], xs: &[Self], ys: &[Self]) -> Self

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

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

fn sin(&self) -> Self

fn cos(&self) -> Self

fn tan(&self) -> Self

fn asin(&self) -> Self

fn acos(&self) -> Self

fn atan(&self) -> Self

fn sinh(&self) -> Self

fn cosh(&self) -> Self

fn tanh(&self) -> Self

fn asinh(&self) -> Self

fn acosh(&self) -> Self

fn atanh(&self) -> Self

fn exp(&self) -> Self

fn exp2(&self) -> Self

fn ln(&self) -> Self

fn log2(&self) -> Self

fn log10(&self) -> Self

fn ln_1p(&self) -> Self

fn exp_m1(&self) -> Self

fn sqrt(&self) -> Self

fn cbrt(&self) -> Self

fn abs(&self) -> Self

fn erf(&self) -> Self

fn erfc(&self) -> Self

fn norm_cdf(&self) -> Self

fn norm_pdf(&self) -> Self

fn inv_norm_cdf(&self) -> Self

Implementors

impl Real for AReal<f64>

type Passive = f64

impl Real for Jet1<f64>

type Passive = f64

impl Real for Jet2<f64>

type Passive = f64

impl<const K: usize> Real for JetK<f64, K>

type Passive = f64