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

fn 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());

fn 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());

fn 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());

fn 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());

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.

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);

fn 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);

fn 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);

fn 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);

fn 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);

fn 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);

fn 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());

fn 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());

fn 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());

fn is_positive(self) -> bool

fn 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());

fn is_negative(self) -> bool

fn 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);

fn 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);

fn 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);

fn 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);

fn 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());

fn 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);

fn 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);

fn 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);

fn 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);

fn 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);

fn 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);

fn 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);

fn 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);

fn 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.

fn 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.

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

Deprecated since 1.10.0

: you probably meant (self - other).abs(): this operation is (self - other).max(0.0) (also known as fdim in C). If you truly need the positive difference, consider using that expression or the C function fdim, depending on how you wish to handle NaN (please consider filing an issue describing your use-case too).

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);

fn 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);

fn 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);

fn 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);

fn 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);

fn 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);

fn 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);

fn 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);

fn 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);

fn 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);

fn 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_1 < 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_1 < 1e-10);

fn 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);

fn 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);

fn 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);

fn 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);

fn 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);

fn 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);

fn 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);

fn 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 FromStr for f64

type Err = ParseFloatError

The associated error which can be returned from parsing.

fn from_str(src: &str) -> Result<f64, ParseFloatError>

Converts a string in base 10 to a float. Accepts an optional decimal exponent.

This function accepts strings such as

• '3.14'
• '-3.14'
• '2.5E10', or equivalently, '2.5e10'
• '2.5E-10'
• '.' (understood as 0)
• '5.'
• '.5', or, equivalently, '0.5'
• 'inf', '-inf', 'NaN'

Leading and trailing whitespace represent an error.

Arguments

• src - A string

Return value

Err(ParseFloatError) if the string did not represent a valid number. Otherwise, Ok(n) where n is the floating-point number represented by src.

impl Zero for f64

fn zero() -> f64

The "zero" (usually, additive identity) for this type.

impl One for f64

fn one() -> f64

The "one" (usually, multiplicative identity) for this type.

impl From<i8> for f64

fn from(small: i8) -> f64

Performs the conversion.

impl From<i16> for f64

fn from(small: i16) -> f64

Performs the conversion.

impl From<i32> for f64

fn from(small: i32) -> f64

Performs the conversion.

impl From<u8> for f64

fn from(small: u8) -> f64

Performs the conversion.

impl From<u16> for f64

fn from(small: u16) -> f64

Performs the conversion.

impl From<u32> for f64

fn from(small: u32) -> f64

Performs the conversion.

impl From<f32> for f64

fn from(small: f32) -> f64

Performs the conversion.

impl Add<f64> for f64

type Output = f64

The resulting type after applying the + operator

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

The method for the + operator

impl<'a> Add<f64> for &'a f64

type Output = f64::Output

The resulting type after applying the + operator

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

The method for the + operator

impl<'a> Add<&'a f64> for f64

type Output = f64::Output

The resulting type after applying the + operator

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

The method for the + operator

impl<'a, 'b> Add<&'a f64> for &'b f64

type Output = f64::Output

The resulting type after applying the + operator

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

The method for the + operator

impl Sub<f64> for f64

type Output = f64

The resulting type after applying the - operator

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

The method for the - operator

impl<'a> Sub<f64> for &'a f64

type Output = f64::Output

The resulting type after applying the - operator

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

The method for the - operator

impl<'a> Sub<&'a f64> for f64

type Output = f64::Output

The resulting type after applying the - operator

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

The method for the - operator

impl<'a, 'b> Sub<&'a f64> for &'b f64

type Output = f64::Output

The resulting type after applying the - operator

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

The method for the - operator

impl Mul<f64> for f64

type Output = f64

The resulting type after applying the * operator

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

The method for the * operator

impl<'a> Mul<f64> for &'a f64

type Output = f64::Output

The resulting type after applying the * operator

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

The method for the * operator

impl<'a> Mul<&'a f64> for f64

type Output = f64::Output

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, 'b> Mul<&'a f64> for &'b f64

type Output = f64::Output

The resulting type after applying the * operator

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

The method for the * operator

impl Div<f64> for f64

type Output = f64

The resulting type after applying the / operator

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

The method for the / operator

impl<'a> Div<f64> for &'a f64

type Output = f64::Output

The resulting type after applying the / operator

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

The method for the / operator

impl<'a> Div<&'a f64> for f64

type Output = f64::Output

The resulting type after applying the / operator

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

The method for the / operator

impl<'a, 'b> Div<&'a f64> for &'b f64

type Output = f64::Output

The resulting type after applying the / operator

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

The method for the / operator

impl Rem<f64> for f64

type Output = f64

The resulting type after applying the % operator

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

The method for the % operator

impl<'a> Rem<f64> for &'a f64

type Output = f64::Output

The resulting type after applying the % operator

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

The method for the % operator

impl<'a> Rem<&'a f64> for f64

type Output = f64::Output

The resulting type after applying the % operator

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

The method for the % operator

impl<'a, 'b> Rem<&'a f64> for &'b f64

type Output = f64::Output

The resulting type after applying the % operator

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

The method for the % operator

impl Neg for f64

type Output = f64

The resulting type after applying the - operator

fn neg(self) -> f64

The method for the unary - operator

impl<'a> Neg for &'a f64

type Output = f64::Output

The resulting type after applying the - operator

fn neg(self) -> f64::Output

The method for the unary - operator

impl AddAssign<f64> for f64

fn add_assign(&mut self, other: f64)

The method for the += operator

impl SubAssign<f64> for f64

fn sub_assign(&mut self, other: f64)

The method for the -= operator

impl MulAssign<f64> for f64

fn mul_assign(&mut self, other: f64)

The method for the *= operator

impl DivAssign<f64> for f64

fn div_assign(&mut self, other: f64)

The method for the /= operator

impl RemAssign<f64> for f64

fn rem_assign(&mut self, other: f64)

The method for the %= operator

impl PartialEq<f64> for f64

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

This method tests for self and other values to be equal, and is used by ==.

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

This method tests for !=.

impl PartialOrd<f64> for f64

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

This method returns an ordering between self and other values if one exists.

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

This method tests less than (for self and other) and is used by the < operator.

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

This method tests less than or equal to (for self and other) and is used by the <= operator.

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

This method tests greater than or equal to (for self and other) and is used by the >= operator.

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

This method tests greater than (for self and other) and is used by the > operator.

impl Clone for f64

fn clone(&self) -> f64

Returns a deep copy of the value.

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

Performs copy-assignment from source.

impl Default for f64

fn default() -> f64

Returns the "default value" for a type.

impl Debug for f64

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

Formats the value using the given formatter.

impl Display for f64

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

Formats the value using the given formatter.

impl LowerExp for f64

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

Formats the value using the given formatter.

impl UpperExp for f64

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

Formats the value using the given formatter.