Primitive Type f64 []

The 64-bit floating point type.

See also the std::f64 module.

However, please note that examples are shared between the f64 and f32 primitive types. So it's normal if you see usage of f32 in there.

Methods

impl f64

1.0.0fn is_nan(self) -> bool

Returns true if this value is NaN and false otherwise.

fn main() { use std::f64; let nan = f64::NAN; let f = 7.0_f64; assert!(nan.is_nan()); assert!(!f.is_nan()); }
use std::f64;

let nan = f64::NAN;
let f = 7.0_f64;

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

1.0.0fn is_infinite(self) -> bool

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

fn main() { use std::f64; let f = 7.0f64; let inf = f64::INFINITY; let neg_inf = f64::NEG_INFINITY; let nan = f64::NAN; assert!(!f.is_infinite()); assert!(!nan.is_infinite()); assert!(inf.is_infinite()); assert!(neg_inf.is_infinite()); }
use std::f64;

let f = 7.0f64;
let inf = f64::INFINITY;
let neg_inf = f64::NEG_INFINITY;
let nan = f64::NAN;

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

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

1.0.0fn is_finite(self) -> bool

Returns true if this number is neither infinite nor NaN.

fn main() { use std::f64; let f = 7.0f64; let inf: f64 = f64::INFINITY; let neg_inf: f64 = f64::NEG_INFINITY; let nan: f64 = f64::NAN; assert!(f.is_finite()); assert!(!nan.is_finite()); assert!(!inf.is_finite()); assert!(!neg_inf.is_finite()); }
use std::f64;

let f = 7.0f64;
let inf: f64 = f64::INFINITY;
let neg_inf: f64 = f64::NEG_INFINITY;
let nan: f64 = f64::NAN;

assert!(f.is_finite());

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

1.0.0fn is_normal(self) -> bool

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

fn main() { use std::f32; let min = f32::MIN_POSITIVE; // 1.17549435e-38f64 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 std::f32;

let min = f32::MIN_POSITIVE; // 1.17549435e-38f64
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());

1.0.0fn 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 main() { use std::num::FpCategory; use std::f64; let num = 12.4_f64; let inf = f64::INFINITY; assert_eq!(num.classify(), FpCategory::Normal); assert_eq!(inf.classify(), FpCategory::Infinite); }
use std::num::FpCategory;
use std::f64;

let num = 12.4_f64;
let inf = f64::INFINITY;

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

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

Unstable (float_extras #27752)

: signature is undecided

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.

#![feature(float_extras)] fn main() { let num = 2.0f64; // (8388608, -22, 1) let (mantissa, exponent, sign) = num.integer_decode(); let sign_f = sign as f64; let mantissa_f = mantissa as f64; let exponent_f = num.powf(exponent as f64); // 1 * 8388608 * 2^(-22) == 2 let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs(); assert!(abs_difference < 1e-10); }
#![feature(float_extras)]

let num = 2.0f64;

// (8388608, -22, 1)
let (mantissa, exponent, sign) = num.integer_decode();
let sign_f = sign as f64;
let mantissa_f = mantissa as f64;
let exponent_f = num.powf(exponent as f64);

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

assert!(abs_difference < 1e-10);

1.0.0fn floor(self) -> f64

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

fn main() { let f = 3.99_f64; let g = 3.0_f64; assert_eq!(f.floor(), 3.0); assert_eq!(g.floor(), 3.0); }
let f = 3.99_f64;
let g = 3.0_f64;

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

1.0.0fn ceil(self) -> f64

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

fn main() { let f = 3.01_f64; let g = 4.0_f64; assert_eq!(f.ceil(), 4.0); assert_eq!(g.ceil(), 4.0); }
let f = 3.01_f64;
let g = 4.0_f64;

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

1.0.0fn round(self) -> f64

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

fn main() { let f = 3.3_f64; let g = -3.3_f64; assert_eq!(f.round(), 3.0); assert_eq!(g.round(), -3.0); }
let f = 3.3_f64;
let g = -3.3_f64;

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

1.0.0fn trunc(self) -> f64

Returns the integer part of a number.

fn main() { let f = 3.3_f64; let g = -3.7_f64; assert_eq!(f.trunc(), 3.0); assert_eq!(g.trunc(), -3.0); }
let f = 3.3_f64;
let g = -3.7_f64;

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

1.0.0fn fract(self) -> f64

Returns the fractional part of a number.

fn main() { let x = 3.5_f64; let y = -3.5_f64; 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); }
let x = 3.5_f64;
let y = -3.5_f64;
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);

1.0.0fn abs(self) -> f64

Computes the absolute value of self. Returns NAN if the number is NAN.

fn main() { use std::f64; let x = 3.5_f64; let y = -3.5_f64; 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 std::f64;

let x = 3.5_f64;
let y = -3.5_f64;

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());

1.0.0fn signum(self) -> f64

Returns a number that represents the sign of self.

  • 1.0 if the number is positive, +0.0 or INFINITY
  • -1.0 if the number is negative, -0.0 or NEG_INFINITY
  • NAN if the number is NAN
fn main() { use std::f64; let f = 3.5_f64; assert_eq!(f.signum(), 1.0); assert_eq!(f64::NEG_INFINITY.signum(), -1.0); assert!(f64::NAN.signum().is_nan()); }
use std::f64;

let f = 3.5_f64;

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

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

1.0.0fn is_sign_positive(self) -> bool

Returns true if self's sign bit is positive, including +0.0 and INFINITY.

fn main() { use std::f64; let nan: f64 = f64::NAN; let f = 7.0_f64; let g = -7.0_f64; 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 std::f64;

let nan: f64 = f64::NAN;

let f = 7.0_f64;
let g = -7.0_f64;

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());

1.0.0fn is_positive(self) -> bool

Deprecated since 1.0.0

: renamed to is_sign_positive

1.0.0fn is_sign_negative(self) -> bool

Returns true if self's sign is negative, including -0.0 and NEG_INFINITY.

fn main() { use std::f64; let nan = f64::NAN; let f = 7.0_f64; let g = -7.0_f64; 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 std::f64;

let nan = f64::NAN;

let f = 7.0_f64;
let g = -7.0_f64;

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());

1.0.0fn is_negative(self) -> bool

Deprecated since 1.0.0

: renamed to is_sign_negative

1.0.0fn mul_add(self, a: f64, b: f64) -> f64

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.

fn main() { let m = 10.0_f64; let x = 4.0_f64; let b = 60.0_f64; // 100.0 let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs(); assert!(abs_difference < 1e-10); }
let m = 10.0_f64;
let x = 4.0_f64;
let b = 60.0_f64;

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

assert!(abs_difference < 1e-10);

1.0.0fn recip(self) -> f64

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

fn main() { let x = 2.0_f64; let abs_difference = (x.recip() - (1.0/x)).abs(); assert!(abs_difference < 1e-10); }
let x = 2.0_f64;
let abs_difference = (x.recip() - (1.0/x)).abs();

assert!(abs_difference < 1e-10);

1.0.0fn powi(self, n: i32) -> f64

Raises a number to an integer power.

Using this function is generally faster than using powf

fn main() { let x = 2.0_f64; let abs_difference = (x.powi(2) - x*x).abs(); assert!(abs_difference < 1e-10); }
let x = 2.0_f64;
let abs_difference = (x.powi(2) - x*x).abs();

assert!(abs_difference < 1e-10);

1.0.0fn powf(self, n: f64) -> f64

Raises a number to a floating point power.

fn main() { let x = 2.0_f64; let abs_difference = (x.powf(2.0) - x*x).abs(); assert!(abs_difference < 1e-10); }
let x = 2.0_f64;
let abs_difference = (x.powf(2.0) - x*x).abs();

assert!(abs_difference < 1e-10);

1.0.0fn sqrt(self) -> f64

Takes the square root of a number.

Returns NaN if self is a negative number.

fn main() { let positive = 4.0_f64; let negative = -4.0_f64; let abs_difference = (positive.sqrt() - 2.0).abs(); assert!(abs_difference < 1e-10); assert!(negative.sqrt().is_nan()); }
let positive = 4.0_f64;
let negative = -4.0_f64;

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

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

1.0.0fn exp(self) -> f64

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

fn main() { let one = 1.0_f64; // e^1 let e = one.exp(); // ln(e) - 1 == 0 let abs_difference = (e.ln() - 1.0).abs(); assert!(abs_difference < 1e-10); }
let one = 1.0_f64;
// e^1
let e = one.exp();

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

assert!(abs_difference < 1e-10);

1.0.0fn exp2(self) -> f64

Returns 2^(self).

fn main() { let f = 2.0_f64; // 2^2 - 4 == 0 let abs_difference = (f.exp2() - 4.0).abs(); assert!(abs_difference < 1e-10); }
let f = 2.0_f64;

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

assert!(abs_difference < 1e-10);

1.0.0fn ln(self) -> f64

Returns the natural logarithm of the number.

fn main() { let one = 1.0_f64; // e^1 let e = one.exp(); // ln(e) - 1 == 0 let abs_difference = (e.ln() - 1.0).abs(); assert!(abs_difference < 1e-10); }
let one = 1.0_f64;
// e^1
let e = one.exp();

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

assert!(abs_difference < 1e-10);

1.0.0fn log(self, base: f64) -> f64

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

fn main() { let ten = 10.0_f64; let two = 2.0_f64; // 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); }
let ten = 10.0_f64;
let two = 2.0_f64;

// 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);

1.0.0fn log2(self) -> f64

Returns the base 2 logarithm of the number.

fn main() { let two = 2.0_f64; // log2(2) - 1 == 0 let abs_difference = (two.log2() - 1.0).abs(); assert!(abs_difference < 1e-10); }
let two = 2.0_f64;

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

assert!(abs_difference < 1e-10);

1.0.0fn log10(self) -> f64

Returns the base 10 logarithm of the number.

fn main() { let ten = 10.0_f64; // log10(10) - 1 == 0 let abs_difference = (ten.log10() - 1.0).abs(); assert!(abs_difference < 1e-10); }
let ten = 10.0_f64;

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

assert!(abs_difference < 1e-10);

1.0.0fn to_degrees(self) -> f64

Converts radians to degrees.

fn main() { use std::f64::consts; let angle = consts::PI; let abs_difference = (angle.to_degrees() - 180.0).abs(); assert!(abs_difference < 1e-10); }
use std::f64::consts;

let angle = consts::PI;

let abs_difference = (angle.to_degrees() - 180.0).abs();

assert!(abs_difference < 1e-10);

1.0.0fn to_radians(self) -> f64

Converts degrees to radians.

fn main() { use std::f64::consts; let angle = 180.0_f64; let abs_difference = (angle.to_radians() - consts::PI).abs(); assert!(abs_difference < 1e-10); }
use std::f64::consts;

let angle = 180.0_f64;

let abs_difference = (angle.to_radians() - consts::PI).abs();

assert!(abs_difference < 1e-10);

fn ldexp(x: f64, exp: isize) -> f64

Unstable (float_extras #27752)

: pending integer conventions

Constructs a floating point number of x*2^exp.

#![feature(float_extras)] fn main() { // 3*2^2 - 12 == 0 let abs_difference = (f64::ldexp(3.0, 2) - 12.0).abs(); assert!(abs_difference < 1e-10); }
#![feature(float_extras)]

// 3*2^2 - 12 == 0
let abs_difference = (f64::ldexp(3.0, 2) - 12.0).abs();

assert!(abs_difference < 1e-10);

fn frexp(self) -> (f64, isize)

Unstable (float_extras #27752)

: pending integer conventions

Breaks the number into a normalized fraction and a base-2 exponent, satisfying:

  • self = x * 2^exp
  • 0.5 <= abs(x) < 1.0
#![feature(float_extras)] fn main() { let x = 4.0_f64; // (1/2)*2^3 -> 1 * 8/2 -> 4.0 let f = x.frexp(); let abs_difference_0 = (f.0 - 0.5).abs(); let abs_difference_1 = (f.1 as f64 - 3.0).abs(); assert!(abs_difference_0 < 1e-10); assert!(abs_difference_1 < 1e-10); }
#![feature(float_extras)]

let x = 4.0_f64;

// (1/2)*2^3 -> 1 * 8/2 -> 4.0
let f = x.frexp();
let abs_difference_0 = (f.0 - 0.5).abs();
let abs_difference_1 = (f.1 as f64 - 3.0).abs();

assert!(abs_difference_0 < 1e-10);
assert!(abs_difference_1 < 1e-10);

fn next_after(self, other: f64) -> f64

Unstable (float_extras #27752)

: unsure about its place in the world

Returns the next representable floating-point value in the direction of other.

#![feature(float_extras)] fn main() { let x = 1.0f32; let abs_diff = (x.next_after(2.0) - 1.00000011920928955078125_f32).abs(); assert!(abs_diff < 1e-10); }
#![feature(float_extras)]

let x = 1.0f32;

let abs_diff = (x.next_after(2.0) - 1.00000011920928955078125_f32).abs();

assert!(abs_diff < 1e-10);

1.0.0fn max(self, other: f64) -> f64

Returns the maximum of the two numbers.

fn main() { let x = 1.0_f64; let y = 2.0_f64; assert_eq!(x.max(y), y); }
let x = 1.0_f64;
let y = 2.0_f64;

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

If one of the arguments is NaN, then the other argument is returned.

1.0.0fn min(self, other: f64) -> f64

Returns the minimum of the two numbers.

fn main() { let x = 1.0_f64; let y = 2.0_f64; assert_eq!(x.min(y), x); }
let x = 1.0_f64;
let y = 2.0_f64;

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

If one of the arguments is NaN, then the other argument is returned.

1.0.0fn abs_sub(self, other: f64) -> f64

The positive difference of two numbers.

  • If self <= other: 0:0
  • Else: self - other
fn main() { let x = 3.0_f64; let y = -3.0_f64; 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); }
let x = 3.0_f64;
let y = -3.0_f64;

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);

1.0.0fn cbrt(self) -> f64

Takes the cubic root of a number.

fn main() { let x = 8.0_f64; // x^(1/3) - 2 == 0 let abs_difference = (x.cbrt() - 2.0).abs(); assert!(abs_difference < 1e-10); }
let x = 8.0_f64;

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

assert!(abs_difference < 1e-10);

1.0.0fn hypot(self, other: f64) -> f64

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

fn main() { let x = 2.0_f64; let y = 3.0_f64; // sqrt(x^2 + y^2) let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs(); assert!(abs_difference < 1e-10); }
let x = 2.0_f64;
let y = 3.0_f64;

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

assert!(abs_difference < 1e-10);

1.0.0fn sin(self) -> f64

Computes the sine of a number (in radians).

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

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

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

assert!(abs_difference < 1e-10);

1.0.0fn cos(self) -> f64

Computes the cosine of a number (in radians).

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

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

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

assert!(abs_difference < 1e-10);

1.0.0fn tan(self) -> f64

Computes the tangent of a number (in radians).

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

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

assert!(abs_difference < 1e-14);

1.0.0fn asin(self) -> f64

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 main() { 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 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);

1.0.0fn acos(self) -> f64

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 main() { 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 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);

1.0.0fn atan(self) -> f64

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

fn main() { let f = 1.0_f64; // atan(tan(1)) let abs_difference = (f.tan().atan() - 1.0).abs(); assert!(abs_difference < 1e-10); }
let f = 1.0_f64;

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

assert!(abs_difference < 1e-10);

1.0.0fn atan2(self, other: f64) -> f64

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)
fn main() { use std::f64; let pi = f64::consts::PI; // All angles from horizontal right (+x) // 45 deg counter-clockwise let x1 = 3.0_f64; let y1 = -3.0_f64; // 135 deg clockwise let x2 = -3.0_f64; let y2 = 3.0_f64; 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 std::f64;

let pi = f64::consts::PI;
// All angles from horizontal right (+x)
// 45 deg counter-clockwise
let x1 = 3.0_f64;
let y1 = -3.0_f64;

// 135 deg clockwise
let x2 = -3.0_f64;
let y2 = 3.0_f64;

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);

1.0.0fn sin_cos(self) -> (f64, f64)

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

fn main() { 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 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);

1.0.0fn exp_m1(self) -> f64

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

fn main() { let x = 7.0_f64; // e^(ln(7)) - 1 let abs_difference = (x.ln().exp_m1() - 6.0).abs(); assert!(abs_difference < 1e-10); }
let x = 7.0_f64;

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

assert!(abs_difference < 1e-10);

1.0.0fn ln_1p(self) -> f64

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

fn main() { 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 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);

1.0.0fn sinh(self) -> f64

Hyperbolic sine function.

fn main() { use std::f64; let e = f64::consts::E; let x = 1.0_f64; 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 std::f64;

let e = f64::consts::E;
let x = 1.0_f64;

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);

1.0.0fn cosh(self) -> f64

Hyperbolic cosine function.

fn main() { use std::f64; let e = f64::consts::E; let x = 1.0_f64; 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 std::f64;

let e = f64::consts::E;
let x = 1.0_f64;
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);

1.0.0fn tanh(self) -> f64

Hyperbolic tangent function.

fn main() { use std::f64; let e = f64::consts::E; let x = 1.0_f64; 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 std::f64;

let e = f64::consts::E;
let x = 1.0_f64;

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);

1.0.0fn asinh(self) -> f64

Inverse hyperbolic sine function.

fn main() { let x = 1.0_f64; let f = x.sinh().asinh(); let abs_difference = (f - x).abs(); assert!(abs_difference < 1.0e-10); }
let x = 1.0_f64;
let f = x.sinh().asinh();

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

assert!(abs_difference < 1.0e-10);

1.0.0fn acosh(self) -> f64

Inverse hyperbolic cosine function.

fn main() { let x = 1.0_f64; let f = x.cosh().acosh(); let abs_difference = (f - x).abs(); assert!(abs_difference < 1.0e-10); }
let x = 1.0_f64;
let f = x.cosh().acosh();

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

assert!(abs_difference < 1.0e-10);

1.0.0fn atanh(self) -> f64

Inverse hyperbolic tangent function.

fn main() { 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 std::f64;

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

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

assert!(abs_difference < 1.0e-10);

Trait Implementations

impl Zero for f64

fn zero() -> f64

impl One for f64

fn one() -> f64

impl From<i8> for f641.5.0

fn from(small: i8) -> f64

impl From<i16> for f641.5.0

fn from(small: i16) -> f64

impl From<i32> for f641.5.0

fn from(small: i32) -> f64

impl From<u8> for f641.5.0

fn from(small: u8) -> f64

impl From<u16> for f641.5.0

fn from(small: u16) -> f64

impl From<u32> for f641.5.0

fn from(small: u32) -> f64

impl From<f32> for f641.5.0

fn from(small: f32) -> f64

impl Add<f64> for f641.0.0

type Output = f64

fn add(self, other: f64) -> f64

impl<'a> Add<f64> for &'a f641.0.0

type Output = f64::Output

fn add(self, other: f64) -> f64::Output

impl<'a> Add<&'a f64> for f641.0.0

type Output = f64::Output

fn add(self, other: &'a f64) -> f64::Output

impl<'a, 'b> Add<&'a f64> for &'b f641.0.0

type Output = f64::Output

fn add(self, other: &'a f64) -> f64::Output

impl Sub<f64> for f641.0.0

type Output = f64

fn sub(self, other: f64) -> f64

impl<'a> Sub<f64> for &'a f641.0.0

type Output = f64::Output

fn sub(self, other: f64) -> f64::Output

impl<'a> Sub<&'a f64> for f641.0.0

type Output = f64::Output

fn sub(self, other: &'a f64) -> f64::Output

impl<'a, 'b> Sub<&'a f64> for &'b f641.0.0

type Output = f64::Output

fn sub(self, other: &'a f64) -> f64::Output

impl Mul<f64> for f641.0.0

type Output = f64

fn mul(self, other: f64) -> f64

impl<'a> Mul<f64> for &'a f641.0.0

type Output = f64::Output

fn mul(self, other: f64) -> f64::Output

impl<'a> Mul<&'a f64> for f641.0.0

type Output = f64::Output

fn mul(self, other: &'a f64) -> f64::Output

impl<'a, 'b> Mul<&'a f64> for &'b f641.0.0

type Output = f64::Output

fn mul(self, other: &'a f64) -> f64::Output

impl Div<f64> for f641.0.0

type Output = f64

fn div(self, other: f64) -> f64

impl<'a> Div<f64> for &'a f641.0.0

type Output = f64::Output

fn div(self, other: f64) -> f64::Output

impl<'a> Div<&'a f64> for f641.0.0

type Output = f64::Output

fn div(self, other: &'a f64) -> f64::Output

impl<'a, 'b> Div<&'a f64> for &'b f641.0.0

type Output = f64::Output

fn div(self, other: &'a f64) -> f64::Output

impl Rem<f64> for f641.0.0

type Output = f64

fn rem(self, other: f64) -> f64

impl<'a> Rem<f64> for &'a f641.0.0

type Output = f64::Output

fn rem(self, other: f64) -> f64::Output

impl<'a> Rem<&'a f64> for f641.0.0

type Output = f64::Output

fn rem(self, other: &'a f64) -> f64::Output

impl<'a, 'b> Rem<&'a f64> for &'b f641.0.0

type Output = f64::Output

fn rem(self, other: &'a f64) -> f64::Output

impl Neg for f641.0.0

type Output = f64

fn neg(self) -> f64

impl<'a> Neg for &'a f641.0.0

type Output = f64::Output

fn neg(self) -> f64::Output

impl AddAssign<f64> for f641.8.0

fn add_assign(&mut self, other: f64)

impl SubAssign<f64> for f641.8.0

fn sub_assign(&mut self, other: f64)

impl MulAssign<f64> for f641.8.0

fn mul_assign(&mut self, other: f64)

impl DivAssign<f64> for f641.8.0

fn div_assign(&mut self, other: f64)

impl RemAssign<f64> for f641.8.0

fn rem_assign(&mut self, other: f64)

impl PartialEq<f64> for f641.0.0

fn eq(&self, other: &f64) -> bool

fn ne(&self, other: &f64) -> bool

impl PartialOrd<f64> for f641.0.0

fn partial_cmp(&self, other: &f64) -> Option<Ordering>

fn lt(&self, other: &f64) -> bool

fn le(&self, other: &f64) -> bool

fn ge(&self, other: &f64) -> bool

fn gt(&self, other: &f64) -> bool

impl Clone for f641.0.0

fn clone(&self) -> f64

1.0.0fn clone_from(&mut self, source: &Self)

impl Default for f641.0.0

fn default() -> f64

impl Debug for f641.0.0

fn fmt(&self, fmt: &mut Formatter) -> Result<(), Error>

impl Display for f641.0.0

fn fmt(&self, fmt: &mut Formatter) -> Result<(), Error>

impl LowerExp for f641.0.0

fn fmt(&self, fmt: &mut Formatter) -> Result<(), Error>

impl UpperExp for f641.0.0

fn fmt(&self, fmt: &mut Formatter) -> Result<(), Error>

impl FloatMath for f64

fn exp(self) -> f64

fn ln(self) -> f64

fn powf(self, n: f64) -> f64

fn sqrt(self) -> f64