Trait num::traits::Float [] [src]

pub trait Float: Copy + NumCast + Num + Neg<Output=Self> + PartialOrd<Self> {
    fn nan() -> Self;
    fn infinity() -> Self;
    fn neg_infinity() -> Self;
    fn neg_zero() -> Self;
    fn min_value() -> Self;
    fn min_positive_value() -> Self;
    fn max_value() -> Self;
    fn is_nan(self) -> bool;
    fn is_infinite(self) -> bool;
    fn is_finite(self) -> bool;
    fn is_normal(self) -> bool;
    fn classify(self) -> FpCategory;
    fn floor(self) -> Self;
    fn ceil(self) -> Self;
    fn round(self) -> Self;
    fn trunc(self) -> Self;
    fn fract(self) -> Self;
    fn abs(self) -> Self;
    fn signum(self) -> Self;
    fn is_sign_positive(self) -> bool;
    fn is_sign_negative(self) -> bool;
    fn mul_add(self, a: Self, b: Self) -> Self;
    fn recip(self) -> Self;
    fn powi(self, n: i32) -> Self;
    fn powf(self, n: Self) -> Self;
    fn sqrt(self) -> Self;
    fn exp(self) -> Self;
    fn exp2(self) -> Self;
    fn ln(self) -> Self;
    fn log(self, base: Self) -> Self;
    fn log2(self) -> Self;
    fn log10(self) -> Self;
    fn max(self, other: Self) -> Self;
    fn min(self, other: Self) -> Self;
    fn abs_sub(self, other: Self) -> Self;
    fn cbrt(self) -> Self;
    fn hypot(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 atan2(self, other: Self) -> Self;
    fn sin_cos(self) -> (Self, Self);
    fn exp_m1(self) -> Self;
    fn ln_1p(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 integer_decode(self) -> (u64, i16, i8);
}

Required Methods

fn nan() -> Self

Returns the NaN value.

extern crate num; fn main() { use num_traits::Float; let nan: f32 = Float::nan(); assert!(nan.is_nan()); }
use num_traits::Float;

let nan: f32 = Float::nan();

assert!(nan.is_nan());

fn infinity() -> Self

Returns the infinite value.

extern crate num; fn main() { use num_traits::Float; use std::f32; let infinity: f32 = Float::infinity(); assert!(infinity.is_infinite()); assert!(!infinity.is_finite()); assert!(infinity > f32::MAX); }
use num_traits::Float;
use std::f32;

let infinity: f32 = Float::infinity();

assert!(infinity.is_infinite());
assert!(!infinity.is_finite());
assert!(infinity > f32::MAX);

fn neg_infinity() -> Self

Returns the negative infinite value.

extern crate num; fn main() { use num_traits::Float; use std::f32; let neg_infinity: f32 = Float::neg_infinity(); assert!(neg_infinity.is_infinite()); assert!(!neg_infinity.is_finite()); assert!(neg_infinity < f32::MIN); }
use num_traits::Float;
use std::f32;

let neg_infinity: f32 = Float::neg_infinity();

assert!(neg_infinity.is_infinite());
assert!(!neg_infinity.is_finite());
assert!(neg_infinity < f32::MIN);

fn neg_zero() -> Self

Returns -0.0.

extern crate num; fn main() { use num_traits::{Zero, Float}; let inf: f32 = Float::infinity(); let zero: f32 = Zero::zero(); let neg_zero: f32 = Float::neg_zero(); assert_eq!(zero, neg_zero); assert_eq!(7.0f32/inf, zero); assert_eq!(zero * 10.0, zero); }
use num_traits::{Zero, Float};

let inf: f32 = Float::infinity();
let zero: f32 = Zero::zero();
let neg_zero: f32 = Float::neg_zero();

assert_eq!(zero, neg_zero);
assert_eq!(7.0f32/inf, zero);
assert_eq!(zero * 10.0, zero);

fn min_value() -> Self

Returns the smallest finite value that this type can represent.

extern crate num; fn main() { use num_traits::Float; use std::f64; let x: f64 = Float::min_value(); assert_eq!(x, f64::MIN); }
use num_traits::Float;
use std::f64;

let x: f64 = Float::min_value();

assert_eq!(x, f64::MIN);

fn min_positive_value() -> Self

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

extern crate num; fn main() { use num_traits::Float; use std::f64; let x: f64 = Float::min_positive_value(); assert_eq!(x, f64::MIN_POSITIVE); }
use num_traits::Float;
use std::f64;

let x: f64 = Float::min_positive_value();

assert_eq!(x, f64::MIN_POSITIVE);

fn max_value() -> Self

Returns the largest finite value that this type can represent.

extern crate num; fn main() { use num_traits::Float; use std::f64; let x: f64 = Float::max_value(); assert_eq!(x, f64::MAX); }
use num_traits::Float;
use std::f64;

let x: f64 = Float::max_value();
assert_eq!(x, f64::MAX);

fn is_nan(self) -> bool

Returns true if this value is NaN and false otherwise.

extern crate num; fn main() { use num_traits::Float; use std::f64; let nan = f64::NAN; let f = 7.0; assert!(nan.is_nan()); assert!(!f.is_nan()); }
use num_traits::Float;
use std::f64;

let nan = f64::NAN;
let f = 7.0;

assert!(nan.is_nan());
assert!(!f.is_nan());

fn is_infinite(self) -> bool

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

extern crate num; fn main() { use num_traits::Float; use std::f32; let f = 7.0f32; let inf: f32 = Float::infinity(); let neg_inf: f32 = Float::neg_infinity(); let nan: f32 = f32::NAN; assert!(!f.is_infinite()); assert!(!nan.is_infinite()); assert!(inf.is_infinite()); assert!(neg_inf.is_infinite()); }
use num_traits::Float;
use std::f32;

let f = 7.0f32;
let inf: f32 = Float::infinity();
let neg_inf: f32 = Float::neg_infinity();
let nan: f32 = f32::NAN;

assert!(!f.is_infinite());
assert!(!nan.is_infinite());

assert!(inf.is_infinite());
assert!(neg_inf.is_infinite());

fn is_finite(self) -> bool

Returns true if this number is neither infinite nor NaN.

extern crate num; fn main() { use num_traits::Float; use std::f32; let f = 7.0f32; let inf: f32 = Float::infinity(); let neg_inf: f32 = Float::neg_infinity(); let nan: f32 = f32::NAN; assert!(f.is_finite()); assert!(!nan.is_finite()); assert!(!inf.is_finite()); assert!(!neg_inf.is_finite()); }
use num_traits::Float;
use std::f32;

let f = 7.0f32;
let inf: f32 = Float::infinity();
let neg_inf: f32 = Float::neg_infinity();
let nan: f32 = f32::NAN;

assert!(f.is_finite());

assert!(!nan.is_finite());
assert!(!inf.is_finite());
assert!(!neg_inf.is_finite());

fn is_normal(self) -> bool

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

extern crate num; fn main() { use num_traits::Float; use std::f32; let min = f32::MIN_POSITIVE; // 1.17549435e-38f32 let max = f32::MAX; let lower_than_min = 1.0e-40_f32; let zero = 0.0f32; assert!(min.is_normal()); assert!(max.is_normal()); assert!(!zero.is_normal()); assert!(!f32::NAN.is_normal()); assert!(!f32::INFINITY.is_normal()); // Values between `0` and `min` are Subnormal. assert!(!lower_than_min.is_normal()); }
use num_traits::Float;
use std::f32;

let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
let max = f32::MAX;
let lower_than_min = 1.0e-40_f32;
let zero = 0.0f32;

assert!(min.is_normal());
assert!(max.is_normal());

assert!(!zero.is_normal());
assert!(!f32::NAN.is_normal());
assert!(!f32::INFINITY.is_normal());
// Values between `0` and `min` are Subnormal.
assert!(!lower_than_min.is_normal());

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.

extern crate num; fn main() { use num_traits::Float; use std::num::FpCategory; use std::f32; let num = 12.4f32; let inf = f32::INFINITY; assert_eq!(num.classify(), FpCategory::Normal); assert_eq!(inf.classify(), FpCategory::Infinite); }
use num_traits::Float;
use std::num::FpCategory;
use std::f32;

let num = 12.4f32;
let inf = f32::INFINITY;

assert_eq!(num.classify(), FpCategory::Normal);
assert_eq!(inf.classify(), FpCategory::Infinite);

fn floor(self) -> Self

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

extern crate num; fn main() { use num_traits::Float; let f = 3.99; let g = 3.0; assert_eq!(f.floor(), 3.0); assert_eq!(g.floor(), 3.0); }
use num_traits::Float;

let f = 3.99;
let g = 3.0;

assert_eq!(f.floor(), 3.0);
assert_eq!(g.floor(), 3.0);

fn ceil(self) -> Self

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

extern crate num; fn main() { use num_traits::Float; let f = 3.01; let g = 4.0; assert_eq!(f.ceil(), 4.0); assert_eq!(g.ceil(), 4.0); }
use num_traits::Float;

let f = 3.01;
let g = 4.0;

assert_eq!(f.ceil(), 4.0);
assert_eq!(g.ceil(), 4.0);

fn round(self) -> Self

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

extern crate num; fn main() { use num_traits::Float; let f = 3.3; let g = -3.3; assert_eq!(f.round(), 3.0); assert_eq!(g.round(), -3.0); }
use num_traits::Float;

let f = 3.3;
let g = -3.3;

assert_eq!(f.round(), 3.0);
assert_eq!(g.round(), -3.0);

fn trunc(self) -> Self

Return the integer part of a number.

extern crate num; fn main() { use num_traits::Float; let f = 3.3; let g = -3.7; assert_eq!(f.trunc(), 3.0); assert_eq!(g.trunc(), -3.0); }
use num_traits::Float;

let f = 3.3;
let g = -3.7;

assert_eq!(f.trunc(), 3.0);
assert_eq!(g.trunc(), -3.0);

fn fract(self) -> Self

Returns the fractional part of a number.

extern crate num; fn main() { use num_traits::Float; let x = 3.5; let y = -3.5; let abs_difference_x = (x.fract() - 0.5).abs(); let abs_difference_y = (y.fract() - (-0.5)).abs(); assert!(abs_difference_x < 1e-10); assert!(abs_difference_y < 1e-10); }
use num_traits::Float;

let x = 3.5;
let y = -3.5;
let abs_difference_x = (x.fract() - 0.5).abs();
let abs_difference_y = (y.fract() - (-0.5)).abs();

assert!(abs_difference_x < 1e-10);
assert!(abs_difference_y < 1e-10);

fn abs(self) -> Self

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

extern crate num; fn main() { use num_traits::Float; use std::f64; let x = 3.5; let y = -3.5; let abs_difference_x = (x.abs() - x).abs(); let abs_difference_y = (y.abs() - (-y)).abs(); assert!(abs_difference_x < 1e-10); assert!(abs_difference_y < 1e-10); assert!(f64::NAN.abs().is_nan()); }
use num_traits::Float;
use std::f64;

let x = 3.5;
let y = -3.5;

let abs_difference_x = (x.abs() - x).abs();
let abs_difference_y = (y.abs() - (-y)).abs();

assert!(abs_difference_x < 1e-10);
assert!(abs_difference_y < 1e-10);

assert!(f64::NAN.abs().is_nan());

fn signum(self) -> Self

Returns a number that represents the sign of self.

  • 1.0 if the number is positive, +0.0 or Float::infinity()
  • -1.0 if the number is negative, -0.0 or Float::neg_infinity()
  • Float::nan() if the number is Float::nan()
extern crate num; fn main() { use num_traits::Float; use std::f64; let f = 3.5; assert_eq!(f.signum(), 1.0); assert_eq!(f64::NEG_INFINITY.signum(), -1.0); assert!(f64::NAN.signum().is_nan()); }
use num_traits::Float;
use std::f64;

let f = 3.5;

assert_eq!(f.signum(), 1.0);
assert_eq!(f64::NEG_INFINITY.signum(), -1.0);

assert!(f64::NAN.signum().is_nan());

fn is_sign_positive(self) -> bool

Returns true if self is positive, including +0.0 and Float::infinity().

extern crate num; fn main() { use num_traits::Float; use std::f64; let nan: f64 = f64::NAN; let f = 7.0; let g = -7.0; assert!(f.is_sign_positive()); assert!(!g.is_sign_positive()); // Requires both tests to determine if is `NaN` assert!(!nan.is_sign_positive() && !nan.is_sign_negative()); }
use num_traits::Float;
use std::f64;

let nan: f64 = f64::NAN;

let f = 7.0;
let g = -7.0;

assert!(f.is_sign_positive());
assert!(!g.is_sign_positive());
// Requires both tests to determine if is `NaN`
assert!(!nan.is_sign_positive() && !nan.is_sign_negative());

fn is_sign_negative(self) -> bool

Returns true if self is negative, including -0.0 and Float::neg_infinity().

extern crate num; fn main() { use num_traits::Float; use std::f64; let nan = f64::NAN; let f = 7.0; let g = -7.0; assert!(!f.is_sign_negative()); assert!(g.is_sign_negative()); // Requires both tests to determine if is `NaN`. assert!(!nan.is_sign_positive() && !nan.is_sign_negative()); }
use num_traits::Float;
use std::f64;

let nan = f64::NAN;

let f = 7.0;
let g = -7.0;

assert!(!f.is_sign_negative());
assert!(g.is_sign_negative());
// Requires both tests to determine if is `NaN`.
assert!(!nan.is_sign_positive() && !nan.is_sign_negative());

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

Fused multiply-add. Computes (self * a) + b with only one rounding error. This produces a more accurate result with better performance than a separate multiplication operation followed by an add.

extern crate num; fn main() { use num_traits::Float; let m = 10.0; let x = 4.0; let b = 60.0; // 100.0 let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;

let m = 10.0;
let x = 4.0;
let b = 60.0;

// 100.0
let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();

assert!(abs_difference < 1e-10);

fn recip(self) -> Self

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

extern crate num; fn main() { use num_traits::Float; let x = 2.0; let abs_difference = (x.recip() - (1.0/x)).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;

let x = 2.0;
let abs_difference = (x.recip() - (1.0/x)).abs();

assert!(abs_difference < 1e-10);

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

Raise a number to an integer power.

Using this function is generally faster than using powf

extern crate num; fn main() { use num_traits::Float; let x = 2.0; let abs_difference = (x.powi(2) - x*x).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;

let x = 2.0;
let abs_difference = (x.powi(2) - x*x).abs();

assert!(abs_difference < 1e-10);

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

Raise a number to a floating point power.

extern crate num; fn main() { use num_traits::Float; let x = 2.0; let abs_difference = (x.powf(2.0) - x*x).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;

let x = 2.0;
let abs_difference = (x.powf(2.0) - x*x).abs();

assert!(abs_difference < 1e-10);

fn sqrt(self) -> Self

Take the square root of a number.

Returns NaN if self is a negative number.

extern crate num; fn main() { use num_traits::Float; let positive = 4.0; let negative = -4.0; let abs_difference = (positive.sqrt() - 2.0).abs(); assert!(abs_difference < 1e-10); assert!(negative.sqrt().is_nan()); }
use num_traits::Float;

let positive = 4.0;
let negative = -4.0;

let abs_difference = (positive.sqrt() - 2.0).abs();

assert!(abs_difference < 1e-10);
assert!(negative.sqrt().is_nan());

fn exp(self) -> Self

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

extern crate num; fn main() { use num_traits::Float; let one = 1.0; // e^1 let e = one.exp(); // ln(e) - 1 == 0 let abs_difference = (e.ln() - 1.0).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;

let one = 1.0;
// e^1
let e = one.exp();

// ln(e) - 1 == 0
let abs_difference = (e.ln() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn exp2(self) -> Self

Returns 2^(self).

extern crate num; fn main() { use num_traits::Float; let f = 2.0; // 2^2 - 4 == 0 let abs_difference = (f.exp2() - 4.0).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;

let f = 2.0;

// 2^2 - 4 == 0
let abs_difference = (f.exp2() - 4.0).abs();

assert!(abs_difference < 1e-10);

fn ln(self) -> Self

Returns the natural logarithm of the number.

extern crate num; fn main() { use num_traits::Float; let one = 1.0; // e^1 let e = one.exp(); // ln(e) - 1 == 0 let abs_difference = (e.ln() - 1.0).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;

let one = 1.0;
// e^1
let e = one.exp();

// ln(e) - 1 == 0
let abs_difference = (e.ln() - 1.0).abs();

assert!(abs_difference < 1e-10);

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

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

extern crate num; fn main() { use num_traits::Float; let ten = 10.0; let two = 2.0; // log10(10) - 1 == 0 let abs_difference_10 = (ten.log(10.0) - 1.0).abs(); // log2(2) - 1 == 0 let abs_difference_2 = (two.log(2.0) - 1.0).abs(); assert!(abs_difference_10 < 1e-10); assert!(abs_difference_2 < 1e-10); }
use num_traits::Float;

let ten = 10.0;
let two = 2.0;

// log10(10) - 1 == 0
let abs_difference_10 = (ten.log(10.0) - 1.0).abs();

// log2(2) - 1 == 0
let abs_difference_2 = (two.log(2.0) - 1.0).abs();

assert!(abs_difference_10 < 1e-10);
assert!(abs_difference_2 < 1e-10);

fn log2(self) -> Self

Returns the base 2 logarithm of the number.

extern crate num; fn main() { use num_traits::Float; let two = 2.0; // log2(2) - 1 == 0 let abs_difference = (two.log2() - 1.0).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;

let two = 2.0;

// log2(2) - 1 == 0
let abs_difference = (two.log2() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn log10(self) -> Self

Returns the base 10 logarithm of the number.

extern crate num; fn main() { use num_traits::Float; let ten = 10.0; // log10(10) - 1 == 0 let abs_difference = (ten.log10() - 1.0).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;

let ten = 10.0;

// log10(10) - 1 == 0
let abs_difference = (ten.log10() - 1.0).abs();

assert!(abs_difference < 1e-10);

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

Returns the maximum of the two numbers.

extern crate num; fn main() { use num_traits::Float; let x = 1.0; let y = 2.0; assert_eq!(x.max(y), y); }
use num_traits::Float;

let x = 1.0;
let y = 2.0;

assert_eq!(x.max(y), y);

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

Returns the minimum of the two numbers.

extern crate num; fn main() { use num_traits::Float; let x = 1.0; let y = 2.0; assert_eq!(x.min(y), x); }
use num_traits::Float;

let x = 1.0;
let y = 2.0;

assert_eq!(x.min(y), x);

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

The positive difference of two numbers.

  • If self <= other: 0:0
  • Else: self - other
extern crate num; fn main() { use num_traits::Float; let x = 3.0; let y = -3.0; let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs(); let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs(); assert!(abs_difference_x < 1e-10); assert!(abs_difference_y < 1e-10); }
use num_traits::Float;

let x = 3.0;
let y = -3.0;

let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();

assert!(abs_difference_x < 1e-10);
assert!(abs_difference_y < 1e-10);

fn cbrt(self) -> Self

Take the cubic root of a number.

extern crate num; fn main() { use num_traits::Float; let x = 8.0; // x^(1/3) - 2 == 0 let abs_difference = (x.cbrt() - 2.0).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;

let x = 8.0;

// x^(1/3) - 2 == 0
let abs_difference = (x.cbrt() - 2.0).abs();

assert!(abs_difference < 1e-10);

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

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

extern crate num; fn main() { use num_traits::Float; let x = 2.0; let y = 3.0; // sqrt(x^2 + y^2) let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;

let x = 2.0;
let y = 3.0;

// sqrt(x^2 + y^2)
let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();

assert!(abs_difference < 1e-10);

fn sin(self) -> Self

Computes the sine of a number (in radians).

extern crate num; fn main() { use num_traits::Float; use std::f64; let x = f64::consts::PI/2.0; let abs_difference = (x.sin() - 1.0).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;
use std::f64;

let x = f64::consts::PI/2.0;

let abs_difference = (x.sin() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn cos(self) -> Self

Computes the cosine of a number (in radians).

extern crate num; fn main() { use num_traits::Float; use std::f64; let x = 2.0*f64::consts::PI; let abs_difference = (x.cos() - 1.0).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;
use std::f64;

let x = 2.0*f64::consts::PI;

let abs_difference = (x.cos() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn tan(self) -> Self

Computes the tangent of a number (in radians).

extern crate num; fn main() { use num_traits::Float; use std::f64; let x = f64::consts::PI/4.0; let abs_difference = (x.tan() - 1.0).abs(); assert!(abs_difference < 1e-14); }
use num_traits::Float;
use std::f64;

let x = f64::consts::PI/4.0;
let abs_difference = (x.tan() - 1.0).abs();

assert!(abs_difference < 1e-14);

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].

extern crate num; fn main() { use num_traits::Float; use std::f64; let f = f64::consts::PI / 2.0; // asin(sin(pi/2)) let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;
use std::f64;

let f = f64::consts::PI / 2.0;

// asin(sin(pi/2))
let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs();

assert!(abs_difference < 1e-10);

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].

extern crate num; fn main() { use num_traits::Float; use std::f64; let f = f64::consts::PI / 4.0; // acos(cos(pi/4)) let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;
use std::f64;

let f = f64::consts::PI / 4.0;

// acos(cos(pi/4))
let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs();

assert!(abs_difference < 1e-10);

fn atan(self) -> Self

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

extern crate num; fn main() { use num_traits::Float; let f = 1.0; // atan(tan(1)) let abs_difference = (f.tan().atan() - 1.0).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;

let f = 1.0;

// atan(tan(1))
let abs_difference = (f.tan().atan() - 1.0).abs();

assert!(abs_difference < 1e-10);

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

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

  • x = 0, y = 0: 0
  • x >= 0: arctan(y/x) -> [-pi/2, pi/2]
  • y >= 0: arctan(y/x) + pi -> (pi/2, pi]
  • y < 0: arctan(y/x) - pi -> (-pi, -pi/2)
extern crate num; fn main() { use num_traits::Float; use std::f64; let pi = f64::consts::PI; // All angles from horizontal right (+x) // 45 deg counter-clockwise let x1 = 3.0; let y1 = -3.0; // 135 deg clockwise let x2 = -3.0; let y2 = 3.0; let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs(); let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs(); assert!(abs_difference_1 < 1e-10); assert!(abs_difference_2 < 1e-10); }
use num_traits::Float;
use std::f64;

let pi = f64::consts::PI;
// All angles from horizontal right (+x)
// 45 deg counter-clockwise
let x1 = 3.0;
let y1 = -3.0;

// 135 deg clockwise
let x2 = -3.0;
let y2 = 3.0;

let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();

assert!(abs_difference_1 < 1e-10);
assert!(abs_difference_2 < 1e-10);

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

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

extern crate num; fn main() { use num_traits::Float; use std::f64; let x = f64::consts::PI/4.0; let f = x.sin_cos(); let abs_difference_0 = (f.0 - x.sin()).abs(); let abs_difference_1 = (f.1 - x.cos()).abs(); assert!(abs_difference_0 < 1e-10); assert!(abs_difference_0 < 1e-10); }
use num_traits::Float;
use std::f64;

let x = f64::consts::PI/4.0;
let f = x.sin_cos();

let abs_difference_0 = (f.0 - x.sin()).abs();
let abs_difference_1 = (f.1 - x.cos()).abs();

assert!(abs_difference_0 < 1e-10);
assert!(abs_difference_0 < 1e-10);

fn exp_m1(self) -> Self

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

extern crate num; fn main() { use num_traits::Float; let x = 7.0; // e^(ln(7)) - 1 let abs_difference = (x.ln().exp_m1() - 6.0).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;

let x = 7.0;

// e^(ln(7)) - 1
let abs_difference = (x.ln().exp_m1() - 6.0).abs();

assert!(abs_difference < 1e-10);

fn ln_1p(self) -> Self

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

extern crate num; fn main() { use num_traits::Float; use std::f64; let x = f64::consts::E - 1.0; // ln(1 + (e - 1)) == ln(e) == 1 let abs_difference = (x.ln_1p() - 1.0).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;
use std::f64;

let x = f64::consts::E - 1.0;

// ln(1 + (e - 1)) == ln(e) == 1
let abs_difference = (x.ln_1p() - 1.0).abs();

assert!(abs_difference < 1e-10);

fn sinh(self) -> Self

Hyperbolic sine function.

extern crate num; fn main() { use num_traits::Float; use std::f64; let e = f64::consts::E; let x = 1.0; let f = x.sinh(); // Solving sinh() at 1 gives `(e^2-1)/(2e)` let g = (e*e - 1.0)/(2.0*e); let abs_difference = (f - g).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;
use std::f64;

let e = f64::consts::E;
let x = 1.0;

let f = x.sinh();
// Solving sinh() at 1 gives `(e^2-1)/(2e)`
let g = (e*e - 1.0)/(2.0*e);
let abs_difference = (f - g).abs();

assert!(abs_difference < 1e-10);

fn cosh(self) -> Self

Hyperbolic cosine function.

extern crate num; fn main() { use num_traits::Float; use std::f64; let e = f64::consts::E; let x = 1.0; let f = x.cosh(); // Solving cosh() at 1 gives this result let g = (e*e + 1.0)/(2.0*e); let abs_difference = (f - g).abs(); // Same result assert!(abs_difference < 1.0e-10); }
use num_traits::Float;
use std::f64;

let e = f64::consts::E;
let x = 1.0;
let f = x.cosh();
// Solving cosh() at 1 gives this result
let g = (e*e + 1.0)/(2.0*e);
let abs_difference = (f - g).abs();

// Same result
assert!(abs_difference < 1.0e-10);

fn tanh(self) -> Self

Hyperbolic tangent function.

extern crate num; fn main() { use num_traits::Float; use std::f64; let e = f64::consts::E; let x = 1.0; let f = x.tanh(); // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))` let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2)); let abs_difference = (f - g).abs(); assert!(abs_difference < 1.0e-10); }
use num_traits::Float;
use std::f64;

let e = f64::consts::E;
let x = 1.0;

let f = x.tanh();
// Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
let abs_difference = (f - g).abs();

assert!(abs_difference < 1.0e-10);

fn asinh(self) -> Self

Inverse hyperbolic sine function.

extern crate num; fn main() { use num_traits::Float; let x = 1.0; let f = x.sinh().asinh(); let abs_difference = (f - x).abs(); assert!(abs_difference < 1.0e-10); }
use num_traits::Float;

let x = 1.0;
let f = x.sinh().asinh();

let abs_difference = (f - x).abs();

assert!(abs_difference < 1.0e-10);

fn acosh(self) -> Self

Inverse hyperbolic cosine function.

extern crate num; fn main() { use num_traits::Float; let x = 1.0; let f = x.cosh().acosh(); let abs_difference = (f - x).abs(); assert!(abs_difference < 1.0e-10); }
use num_traits::Float;

let x = 1.0;
let f = x.cosh().acosh();

let abs_difference = (f - x).abs();

assert!(abs_difference < 1.0e-10);

fn atanh(self) -> Self

Inverse hyperbolic tangent function.

extern crate num; fn main() { use num_traits::Float; use std::f64; let e = f64::consts::E; let f = e.tanh().atanh(); let abs_difference = (f - e).abs(); assert!(abs_difference < 1.0e-10); }
use num_traits::Float;
use std::f64;

let e = f64::consts::E;
let f = e.tanh().atanh();

let abs_difference = (f - e).abs();

assert!(abs_difference < 1.0e-10);

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. The floating point encoding is documented in the Reference.

extern crate num; fn main() { use num_traits::Float; let num = 2.0f32; // (8388608, -22, 1) let (mantissa, exponent, sign) = Float::integer_decode(num); let sign_f = sign as f32; let mantissa_f = mantissa as f32; let exponent_f = num.powf(exponent as f32); // 1 * 8388608 * 2^(-22) == 2 let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs(); assert!(abs_difference < 1e-10); }
use num_traits::Float;

let num = 2.0f32;

// (8388608, -22, 1)
let (mantissa, exponent, sign) = Float::integer_decode(num);
let sign_f = sign as f32;
let mantissa_f = mantissa as f32;
let exponent_f = num.powf(exponent as f32);

// 1 * 8388608 * 2^(-22) == 2
let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs();

assert!(abs_difference < 1e-10);

Implementors