Trait ExtFloat

pub trait ExtFloat: ExtFloatConst + Sized {
    // Required methods
    fn floor(self) -> Self;
    fn ceil(self) -> Self;
    fn round(self) -> Self;
    fn round_ties_away(self) -> Self;
    fn round_ties_even(self) -> Self;
    fn round_ties_odd(self) -> Self;
    fn trunc(self) -> Self;
    fn fract(self) -> Self;
    fn split(self) -> (Self, Self) ;
    fn abs(self) -> Self;
    fn neg_abs(self) -> Self;
    fn sign(self) -> Sign;
    fn sign_nonzero(self) -> Sign;
    fn signum(self) -> Self;
    fn flip_sign(self) -> Self;
    fn is_sign_positive(self) -> bool;
    fn is_sign_negative(self) -> bool;
    fn is_zero(self) -> bool;
    fn is_sign_positive_nonzero(self) -> bool;
    fn is_sign_negative_nonzero(self) -> bool;
    fn copysign(self, sign: Self) -> Self;
    fn mul_add(self, mul: Self, add: Self) -> Self;
    fn div_euclid(self, rhs: Self) -> Self;
    fn rem_euclid(self, rhs: Self) -> Self;
    fn scale(self, min: Self, max: Self, u: Self, v: Self) -> Self;
    fn lerp(self, u: Self, v: Self) -> Self;
    fn powf(self, y: Self) -> Self;
    fn powi(self, p: i32) -> Self;
    fn sqrt(self) -> Self;
    fn sqrt_fisr(self) -> Self;
    fn fisr(self) -> Self;
    fn cbrt(self) -> Self;
    fn hypot(self, rhs: Self) -> Self;
    fn exp(self) -> Self;
    fn exp2(self) -> Self;
    fn exp_m1(self) -> Self;
    fn ln(self) -> Self;
    fn ln_1p(self) -> Self;
    fn log(self, base: Self) -> Self;
    fn log2(self) -> Self;
    fn log10(self) -> Self;
    fn factorial(n: u32) -> Self;
    fn sin(self) -> Self;
    fn cos(self) -> Self;
    fn sin_cos(self) -> (Self, Self) ;
    fn tan(self) -> Self;
    fn asin(self) -> Self;
    fn acos(self) -> Self;
    fn atan(self) -> Self;
    fn atan2(self, other: 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 clamp_nan(self, min: Self, max: Self) -> Self;
    fn max_nan(self, other: Self) -> Self;
    fn min_nan(self, other: Self) -> Self;
    fn clamp_total(self, min: Self, max: Self) -> Self;
    fn max_total(self, other: Self) -> Self;
    fn min_total(self, other: Self) -> Self;
    fn eval_poly(self, coefficients: &[Self]) -> Self;
    fn derivative<F>(f: F, x: Self, h: Self) -> Self
       where F: Fn(Self) -> Self;
    fn integrate<F>(f: F, x: Self, y: Self, n: usize) -> Self
       where F: Fn(Self) -> Self;
    fn partial_derivative_x<F>(f: F, x: Self, y: Self, h: Self) -> Self
       where F: Fn(Self, Self) -> Self;
    fn partial_derivative_y<F>(f: F, x: Self, y: Self, h: Self) -> Self
       where F: Fn(Self, Self) -> Self;
}

Extension trait for floating-point types. Associated methods.

This trait can be more convenient to use than the Float struct, for non-const operations over primitive floating-point types.

Features

It depends on having any _float_f[32|64] features enabled.

Float has a few more methods implemented if the dep_libm feature is enabled.

Required Methods

fn floor(self) -> Self

The largest integer less than or equal to self.

Formula

$$ \large \lfloor x \rfloor = \max { n \in \mathbb{Z} ,|, n \leq x } $$

fn ceil(self) -> Self

The smallest integer greater than or equal to self.

Formula

$$ $$ \lceil x \rceil = \min { n \in \mathbb{Z} ,|, n \geq x } $$

fn round(self) -> Self

The nearest integer to self, default rounding, same as round_ties_away

fn round_ties_away(self) -> Self

The nearest integer to self, rounding ties away from 0.0.

Formula

$$ \text{round\_ties\_away}(x) = \begin{cases} \lceil x \rceil, & \text{if } x - \lfloor x \rfloor > 0.5 \text{ or } (x - \lfloor x \rfloor = 0.5 \text{ and } x > 0) \cr \lfloor x \rfloor, & \text{if } x - \lfloor x \rfloor < 0.5 \text{ or } (x - \lfloor x \rfloor = 0.5 \text{ and } x < 0) \end{cases} $$

fn round_ties_even(self) -> Self

The nearest integer to self, rounding ties to the nearest even integer.

Formula

$$ \text{round\_ties\_even}(x) = \begin{cases} \lceil x \rceil, & \text{if } x - \lfloor x \rfloor > 0.5 \cr \lfloor x \rfloor, & \text{if } x - \lfloor x \rfloor < 0.5 \cr \lfloor x \rfloor, & \text{if } x - \lfloor x \rfloor = 0.5 \text{ and } \lfloor x \rfloor \text{ is even} \cr \lceil x \rceil, & \text{if } x - \lfloor x \rfloor = 0.5 \text{ and } \lfloor x \rfloor \text{ is odd} \end{cases} $$

fn round_ties_odd(self) -> Self

The nearest integer to self, rounding ties to the nearest odd integer.

Formula

$$ \text{round\_ties\_odd}(x) = \begin{cases} \lceil x \rceil, & \text{if } x - \lfloor x \rfloor > 0.5 \cr \lfloor x \rfloor, & \text{if } x - \lfloor x \rfloor < 0.5 \cr \lfloor x \rfloor, & \text{if } x - \lfloor x \rfloor = 0.5 \text{ and } \lfloor x \rfloor \text{ is odd} \cr \lceil x \rceil, & \text{if } x - \lfloor x \rfloor = 0.5 \text{ and } \lfloor x \rfloor \text{ is even} \end{cases} $$

fn trunc(self) -> Self

The integral part of self.

Formula

$$ \text{trunc}(x) = \begin{cases} \lfloor x \rfloor, & \text{if } x \geq 0 \ \lceil x \rceil, & \text{if } x < 0 \end{cases} $$

fn fract(self) -> Self

The fractional part of self.

Formula

$$ \text{fract}(x) = x - \text{trunc}(x) $$

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

The integral and fractional parts ox self.

Formula

$$ \text{split}(x) = (\text{trunc}(x), \text{fract}(x)) $$

fn abs(self) -> Self

The absolute value of self.

fn neg_abs(self) -> Self

The negative absolute value of self.

fn sign(self) -> Sign

Returns the Sign of self.

fn sign_nonzero(self) -> Sign

Returns the Sign of self, except for zero.

fn signum(self) -> Self

A number that represents the sign of self.

fn flip_sign(self) -> Self

Flips the sign of self.

fn is_sign_positive(self) -> bool

Returns true if self has a positive sign.

fn is_sign_negative(self) -> bool

Returns true if self has a negative sign.

fn is_zero(self) -> bool

Returns true if self is either 0.0 or -0.0.

fn is_sign_positive_nonzero(self) -> bool

Returns true if self has a positive sign and is not zero.

fn is_sign_negative_nonzero(self) -> bool

Returns true if self has a negative sign and is not zero.

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

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

fn mul_add(self, mul: Self, add: Self) -> Self

Fused multiply-add. Computes (self * mul) + add with only one rounding error.

With either std or dep_libm enabled it leverages compiler intrinsics, otherwise it uses mul_add_fallback.

fn div_euclid(self, rhs: Self) -> Self

The euclidean division.

fn rem_euclid(self, rhs: Self) -> Self

The least nonnegative remainder of self % rhs.

fn scale(self, min: Self, max: Self, u: Self, v: Self) -> Self

Returns self between [min..=max] scaled to a new range [u..=v].

Values of self outside [min..=max] are not clamped and will result in extrapolation.

Formula

$$ \large \text{scale}(x, min, max, u, v) = (v - u) \frac{x - min}{max - min} + u $$

fn lerp(self, u: Self, v: Self) -> Self

Calculates a linearly interpolated value between u..=v based on the percentage self between [0..=1].

Values of self outside [0..=1] are not clamped and will result in extrapolation.

Formula

$$ \large \text{lerp}(x, u, v) = (1 - x) \cdot u + x \cdot v $$

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

Raises self to the y floating point power.

With either std or dep_libm enabled it leverages compiler intrinsics, otherwise it’s equal to powf_series.

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

Raises self to the p integer power.

fn sqrt(self) -> Self

The square root.

With either std or dep_libm enabled it leverages compiler intrinsics, otherwise it’s equal to sqrt_nr.

fn sqrt_fisr(self) -> Self

The square root calculated using the fast inverse square root algorithm.

fn fisr(self) -> Self

$ 1 / \sqrt{x} $ the fast inverse square root algorithm.

fn cbrt(self) -> Self

The cubic root.

With either std or dep_libm enabled it leverages compiler intrinsics, otherwise it’s equal to cbrt_nr.

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

The hypothenuse (the euclidean distance).

With either std or dep_libm enabled it leverages compiler intrinsics, otherwise it’s equal to hypot_nr.

fn exp(self) -> Self

$e^x$ (the exponential function).

The maximum values with a representable result are: 88.722… for f32 and 709.782… for f64.

With both std and dep_libm disabled it leverages exp_series with exp_series_terms.

fn exp2(self) -> Self

$2^x$.

With both std and dep_libm disabled it leverages exp2_series with exp2_series_terms.

fn exp_m1(self) -> Self

The exponential minus 1, more accurately.

With both std and dep_libm disabled it leverages exp_m1_series with exp_series_terms.

fn ln(self) -> Self

The natural logarithm of self.

With both std and dep_libm disabled it leverages ln_series with ln_series_terms.

fn ln_1p(self) -> Self

The natural logarithm of self plus 1, more accurately.

With both std and dep_libm disabled it leverages ln_1p_series with ln_series_terms.

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

The logarithm of self with respect to an arbitrary base.

With both std and dep_libm disabled it leverages log_series with ln_series_terms.

fn log2(self) -> Self

The base 2 logarithm of self.

With both std and dep_libm disabled it leverages log2_series with ln_series_terms.

fn log10(self) -> Self

The base 10 logarithm of self.

With both std and dep_libm disabled it leverages log10_series with ln_series_terms.

fn factorial(n: u32) -> Self

The factorial.

The maximum values with a representable result are: 34 for f32 and 170 for f64.

fn sin(self) -> Self

The sine.

With both std and dep_libm disabled it leverages sin_series with 8 terms.

fn cos(self) -> Self

The cosine.

With both std and dep_libm disabled it leverages cos_series with 8 terms.

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

Both the sine and cosine.

With both std and dep_libm disabled it leverages sin_cos_series with 8 terms.

fn tan(self) -> Self

The tangent.

With both std and dep_libm disabled it leverages tan_series with 8 terms.

fn asin(self) -> Self

The arc sine.

With both std and dep_libm disabled it leverages asin_series with asin_series_terms.

fn acos(self) -> Self

The arc cosine.

With both std and dep_libm disabled it leverages acos_series with acos_series_terms.

fn atan(self) -> Self

The arc tangent.

With both std and dep_libm disabled it leverages atan_series with atan_series_terms.

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

The arc tangent of two variables.

With both std and dep_libm disabled it leverages atan2_series with atan_series_terms.

fn sinh(self) -> Self

The hyperbolic sine.

With both std and dep_libm disabled it leverages sinh_series with exp_series_terms.

fn cosh(self) -> Self

The hyperbolic cosine.

With both std and dep_libm disabled it leverages cosh_series with exp_series_terms.

fn tanh(self) -> Self

The hyperbolic tangent.

With both std and dep_libm disabled it leverages cosh_series with exp_series_terms.

fn asinh(self) -> Self

The inverse hyperbolic sine of self.

With both std and dep_libm disabled it leverages asinh_series with ln_series_terms.

fn acosh(self) -> Self

The inverse hyperbolic cosine of self.

With both std and dep_libm disabled it leverages acosh_series with ln_series_terms.

fn atanh(self) -> Self

The inverse hyperbolic tangent of self.

With both std and dep_libm disabled it leverages atanh_series with ln_series_terms.

fn clamp_nan(self, min: Self, max: Self) -> Self

The clamped value, propagating NaN.

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

The maximum of two numbers, propagating NaN.

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

The minimum of two numbers, propagating NaN.

fn clamp_total(self, min: Self, max: Self) -> Self

The clamped value, using total order.

Features

This will only work if the corresponding _cmp_[f32|f64] feature is enabled, otherwise it will return NaN.

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

The maximum of two numbers using total order.

Features

This will only work if the corresponding _cmp_[f32|f64] feature is enabled, otherwise it will return NaN.

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

The minimum of two numbers using total order.

Features

This will only work if the corresponding _cmp_[f32|f64] feature is enabled, otherwise it will return NaN.

fn eval_poly(self, coefficients: &[Self]) -> Self

Evaluates a polynomial at the self point value, using Horner’s method.

fn derivative<F>(f: F, x: Self, h: Self) -> Self

where F: Fn(Self) -> Self,

Approximates the derivative of the 1D function f at x point using step size h.

Uses the finite difference method.

See also the [autodiff] attr macro, enabled with the nightly_autodiff feature.

fn integrate<F>(f: F, x: Self, y: Self, n: usize) -> Self

where F: Fn(Self) -> Self,

Approximates the integral of the 1D function f over the range [x, y] using n subdivisions.

Uses the Riemann Sum.

fn partial_derivative_x<F>(f: F, x: Self, y: Self, h: Self) -> Self

where F: Fn(Self, Self) -> Self,

Approximates the partial derivative of the 2D function f at point (x, y) with step size h, differentiating over x.

fn partial_derivative_y<F>(f: F, x: Self, y: Self, h: Self) -> Self

where F: Fn(Self, Self) -> Self,

Approximates the partial derivative of the 2D function f at point (x, y) with step size h, differentiating over x.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementations on Foreign Types

impl ExtFloat for f32

Available on crate feature _float_f32 only.

fn floor(self) -> Self

fn ceil(self) -> Self

fn round(self) -> Self

fn round_ties_away(self) -> Self

fn round_ties_even(self) -> Self

fn round_ties_odd(self) -> Self

fn trunc(self) -> Self

fn fract(self) -> Self

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

fn abs(self) -> Self

fn neg_abs(self) -> Self

fn sign(self) -> Sign

fn sign_nonzero(self) -> Sign

fn signum(self) -> Self

fn flip_sign(self) -> Self

fn is_sign_positive(self) -> bool

fn is_sign_negative(self) -> bool

fn is_zero(self) -> bool

fn is_sign_positive_nonzero(self) -> bool

fn is_sign_negative_nonzero(self) -> bool

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

fn mul_add(self, mul: Self, add: Self) -> Self

fn div_euclid(self, rhs: Self) -> Self

fn rem_euclid(self, rhs: Self) -> Self

fn scale(self, min: Self, max: Self, u: Self, v: Self) -> Self

fn lerp(self, u: Self, v: Self) -> Self

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

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

fn sqrt(self) -> Self

fn sqrt_fisr(self) -> Self

fn fisr(self) -> Self

fn cbrt(self) -> Self

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

fn exp(self) -> Self

fn exp2(self) -> Self

fn exp_m1(self) -> Self

fn ln(self) -> Self

fn ln_1p(self) -> Self

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

fn log2(self) -> Self

fn log10(self) -> Self

fn factorial(a: u32) -> Self

fn sin(self) -> Self

fn cos(self) -> Self

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

fn tan(self) -> Self

fn asin(self) -> Self

fn acos(self) -> Self

fn atan(self) -> Self

fn atan2(self, other: 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 clamp_nan(self, min: Self, max: Self) -> Self

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

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

fn clamp_total(self, min: Self, max: Self) -> Self

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

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

fn eval_poly(self, coefficients: &[Self]) -> Self

fn derivative<F>(f: F, x: Self, h: Self) -> Self

where F: Fn(Self) -> Self,

fn integrate<F>(f: F, x: Self, y: Self, n: usize) -> Self

where F: Fn(Self) -> Self,

fn partial_derivative_x<F>(f: F, x: Self, y: Self, h: Self) -> Self

where F: Fn(Self, Self) -> Self,

fn partial_derivative_y<F>(f: F, x: Self, y: Self, h: Self) -> Self

where F: Fn(Self, Self) -> Self,

impl ExtFloat for f64

Available on crate feature _float_f64 only.

fn floor(self) -> Self

fn ceil(self) -> Self

fn round(self) -> Self

fn round_ties_away(self) -> Self

fn round_ties_even(self) -> Self

fn round_ties_odd(self) -> Self

fn trunc(self) -> Self

fn fract(self) -> Self

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

fn abs(self) -> Self

fn neg_abs(self) -> Self

fn sign(self) -> Sign

fn sign_nonzero(self) -> Sign

fn signum(self) -> Self

fn flip_sign(self) -> Self

fn is_sign_positive(self) -> bool

fn is_sign_negative(self) -> bool

fn is_zero(self) -> bool

fn is_sign_positive_nonzero(self) -> bool

fn is_sign_negative_nonzero(self) -> bool

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

fn mul_add(self, mul: Self, add: Self) -> Self

fn div_euclid(self, rhs: Self) -> Self

fn rem_euclid(self, rhs: Self) -> Self

fn scale(self, min: Self, max: Self, u: Self, v: Self) -> Self

fn lerp(self, u: Self, v: Self) -> Self

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

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

fn sqrt(self) -> Self

fn sqrt_fisr(self) -> Self

fn fisr(self) -> Self

fn cbrt(self) -> Self

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

fn exp(self) -> Self

fn exp2(self) -> Self

fn exp_m1(self) -> Self

fn ln(self) -> Self

fn ln_1p(self) -> Self

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

fn log2(self) -> Self

fn log10(self) -> Self

fn factorial(a: u32) -> Self

fn sin(self) -> Self

fn cos(self) -> Self

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

fn tan(self) -> Self

fn asin(self) -> Self

fn acos(self) -> Self

fn atan(self) -> Self

fn atan2(self, other: 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 clamp_nan(self, min: Self, max: Self) -> Self

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

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

fn clamp_total(self, min: Self, max: Self) -> Self

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

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

fn eval_poly(self, coefficients: &[Self]) -> Self

fn derivative<F>(f: F, x: Self, h: Self) -> Self

where F: Fn(Self) -> Self,

fn integrate<F>(f: F, x: Self, y: Self, n: usize) -> Self

where F: Fn(Self) -> Self,

fn partial_derivative_x<F>(f: F, x: Self, y: Self, h: Self) -> Self

where F: Fn(Self, Self) -> Self,

fn partial_derivative_y<F>(f: F, x: Self, y: Self, h: Self) -> Self

where F: Fn(Self, Self) -> Self,

Implementors