Primitive Type f32

The 32-bit floating point type.

See also the std::f32 module.

Methods

impl f32

fn from_str_radix(s: &str, radix: u32) -> Result<f32, ParseFloatError>

Deprecated since 1.4.0

: unclear how useful or correct this is

Parses a float as with a given radix

fn is_nan(self) -> bool

Returns true if this value is NaN and false otherwise.

fn main() { use std::f32; let nan = f32::NAN; let f = 7.0_f32; assert!(nan.is_nan()); assert!(!f.is_nan()); }

use std::f32;

let nan = f32::NAN;
let f = 7.0_f32;

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::f32; let f = 7.0f32; let inf = f32::INFINITY; let neg_inf = f32::NEG_INFINITY; let nan = f32::NAN; assert!(!f.is_infinite()); assert!(!nan.is_infinite()); assert!(inf.is_infinite()); assert!(neg_inf.is_infinite()); }

use std::f32;

let f = 7.0f32;
let inf = f32::INFINITY;
let neg_inf = f32::NEG_INFINITY;
let nan = 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.

fn main() { use std::f32; let f = 7.0f32; let inf = f32::INFINITY; let neg_inf = f32::NEG_INFINITY; let nan = f32::NAN; assert!(f.is_finite()); assert!(!nan.is_finite()); assert!(!inf.is_finite()); assert!(!neg_inf.is_finite()); }

use std::f32;

let f = 7.0f32;
let inf = f32::INFINITY;
let neg_inf = f32::NEG_INFINITY;
let nan = 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.

fn main() { 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 = 0.0_f32; 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-38f32
let max = f32::MAX;
let lower_than_min = 1.0e-40_f32;
let zero = 0.0_f32;

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::f32; let num = 12.4_f32; let inf = f32::INFINITY; assert_eq!(num.classify(), FpCategory::Normal); assert_eq!(inf.classify(), FpCategory::Infinite); }

use std::num::FpCategory;
use std::f32;

let num = 12.4_f32;
let inf = f32::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() { use std::f32; let num = 2.0f32; // (8388608, -22, 1) let (mantissa, exponent, sign) = num.integer_decode(); 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 <= f32::EPSILON); }

#![feature(float_extras)]

use std::f32;

let num = 2.0f32;

// (8388608, -22, 1)
let (mantissa, exponent, sign) = num.integer_decode();
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 <= f32::EPSILON);

fn floor(self) -> f32

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

fn main() { let f = 3.99_f32; let g = 3.0_f32; assert_eq!(f.floor(), 3.0); assert_eq!(g.floor(), 3.0); }

let f = 3.99_f32;
let g = 3.0_f32;

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

fn ceil(self) -> f32

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

fn main() { let f = 3.01_f32; let g = 4.0_f32; assert_eq!(f.ceil(), 4.0); assert_eq!(g.ceil(), 4.0); }

let f = 3.01_f32;
let g = 4.0_f32;

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

fn round(self) -> f32

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

fn main() { let f = 3.3_f32; let g = -3.3_f32; assert_eq!(f.round(), 3.0); assert_eq!(g.round(), -3.0); }

let f = 3.3_f32;
let g = -3.3_f32;

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

fn trunc(self) -> f32

Returns the integer part of a number.

fn main() { let f = 3.3_f32; let g = -3.7_f32; assert_eq!(f.trunc(), 3.0); assert_eq!(g.trunc(), -3.0); }

let f = 3.3_f32;
let g = -3.7_f32;

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

fn fract(self) -> f32

Returns the fractional part of a number.

fn main() { use std::f32; let x = 3.5_f32; let y = -3.5_f32; let abs_difference_x = (x.fract() - 0.5).abs(); let abs_difference_y = (y.fract() - (-0.5)).abs(); assert!(abs_difference_x <= f32::EPSILON); assert!(abs_difference_y <= f32::EPSILON); }

use std::f32;

let x = 3.5_f32;
let y = -3.5_f32;
let abs_difference_x = (x.fract() - 0.5).abs();
let abs_difference_y = (y.fract() - (-0.5)).abs();

assert!(abs_difference_x <= f32::EPSILON);
assert!(abs_difference_y <= f32::EPSILON);

fn abs(self) -> f32

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

fn main() { use std::f32; let x = 3.5_f32; let y = -3.5_f32; let abs_difference_x = (x.abs() - x).abs(); let abs_difference_y = (y.abs() - (-y)).abs(); assert!(abs_difference_x <= f32::EPSILON); assert!(abs_difference_y <= f32::EPSILON); assert!(f32::NAN.abs().is_nan()); }

use std::f32;

let x = 3.5_f32;
let y = -3.5_f32;

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

assert!(abs_difference_x <= f32::EPSILON);
assert!(abs_difference_y <= f32::EPSILON);

assert!(f32::NAN.abs().is_nan());

fn signum(self) -> f32

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::f32; let f = 3.5_f32; assert_eq!(f.signum(), 1.0); assert_eq!(f32::NEG_INFINITY.signum(), -1.0); assert!(f32::NAN.signum().is_nan()); }

use std::f32;

let f = 3.5_f32;

assert_eq!(f.signum(), 1.0);
assert_eq!(f32::NEG_INFINITY.signum(), -1.0);

assert!(f32::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::f32; let nan = f32::NAN; let f = 7.0_f32; let g = -7.0_f32; 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::f32;

let nan = f32::NAN;
let f = 7.0_f32;
let g = -7.0_f32;

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's sign is negative, including -0.0 and NEG_INFINITY.

fn main() { use std::f32; let nan = f32::NAN; let f = 7.0f32; let g = -7.0f32; 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::f32;

let nan = f32::NAN;
let f = 7.0f32;
let g = -7.0f32;

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: f32, b: f32) -> f32

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() { use std::f32; let m = 10.0_f32; let x = 4.0_f32; let b = 60.0_f32; // 100.0 let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs(); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let m = 10.0_f32;
let x = 4.0_f32;
let b = 60.0_f32;

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

assert!(abs_difference <= f32::EPSILON);

fn recip(self) -> f32

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

fn main() { use std::f32; let x = 2.0_f32; let abs_difference = (x.recip() - (1.0/x)).abs(); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let x = 2.0_f32;
let abs_difference = (x.recip() - (1.0/x)).abs();

assert!(abs_difference <= f32::EPSILON);

fn powi(self, n: i32) -> f32

Raises a number to an integer power.

Using this function is generally faster than using powf

fn main() { use std::f32; let x = 2.0_f32; let abs_difference = (x.powi(2) - x*x).abs(); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let x = 2.0_f32;
let abs_difference = (x.powi(2) - x*x).abs();

assert!(abs_difference <= f32::EPSILON);

fn powf(self, n: f32) -> f32

Raises a number to a floating point power.

fn main() { use std::f32; let x = 2.0_f32; let abs_difference = (x.powf(2.0) - x*x).abs(); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let x = 2.0_f32;
let abs_difference = (x.powf(2.0) - x*x).abs();

assert!(abs_difference <= f32::EPSILON);

fn sqrt(self) -> f32

Takes the square root of a number.

Returns NaN if self is a negative number.

fn main() { use std::f32; let positive = 4.0_f32; let negative = -4.0_f32; let abs_difference = (positive.sqrt() - 2.0).abs(); assert!(abs_difference <= f32::EPSILON); assert!(negative.sqrt().is_nan()); }

use std::f32;

let positive = 4.0_f32;
let negative = -4.0_f32;

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

assert!(abs_difference <= f32::EPSILON);
assert!(negative.sqrt().is_nan());

fn exp(self) -> f32

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

fn main() { use std::f32; let one = 1.0f32; // e^1 let e = one.exp(); // ln(e) - 1 == 0 let abs_difference = (e.ln() - 1.0).abs(); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let one = 1.0f32;
// e^1
let e = one.exp();

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

assert!(abs_difference <= f32::EPSILON);

fn exp2(self) -> f32

Returns 2^(self).

fn main() { use std::f32; let f = 2.0f32; // 2^2 - 4 == 0 let abs_difference = (f.exp2() - 4.0).abs(); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let f = 2.0f32;

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

assert!(abs_difference <= f32::EPSILON);

fn ln(self) -> f32

Returns the natural logarithm of the number.

fn main() { use std::f32; let one = 1.0f32; // e^1 let e = one.exp(); // ln(e) - 1 == 0 let abs_difference = (e.ln() - 1.0).abs(); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let one = 1.0f32;
// e^1
let e = one.exp();

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

assert!(abs_difference <= f32::EPSILON);

fn log(self, base: f32) -> f32

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

fn main() { use std::f32; let ten = 10.0f32; let two = 2.0f32; // 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 <= f32::EPSILON); assert!(abs_difference_2 <= f32::EPSILON); }

use std::f32;

let ten = 10.0f32;
let two = 2.0f32;

// 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 <= f32::EPSILON);
assert!(abs_difference_2 <= f32::EPSILON);

fn log2(self) -> f32

Returns the base 2 logarithm of the number.

fn main() { use std::f32; let two = 2.0f32; // log2(2) - 1 == 0 let abs_difference = (two.log2() - 1.0).abs(); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let two = 2.0f32;

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

assert!(abs_difference <= f32::EPSILON);

fn log10(self) -> f32

Returns the base 10 logarithm of the number.

fn main() { use std::f32; let ten = 10.0f32; // log10(10) - 1 == 0 let abs_difference = (ten.log10() - 1.0).abs(); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let ten = 10.0f32;

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

assert!(abs_difference <= f32::EPSILON);

fn to_degrees(self) -> f32

Unstable (float_extras #27752)

: desirability is unclear

Converts radians to degrees.

#![feature(float_extras)] fn main() { use std::f32::{self, consts}; let angle = consts::PI; let abs_difference = (angle.to_degrees() - 180.0).abs(); assert!(abs_difference <= f32::EPSILON); }

#![feature(float_extras)]

use std::f32::{self, consts};

let angle = consts::PI;

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

assert!(abs_difference <= f32::EPSILON);

fn to_radians(self) -> f32

Unstable (float_extras #27752)

: desirability is unclear

Converts degrees to radians.

#![feature(float_extras)] fn main() { use std::f32::{self, consts}; let angle = 180.0f32; let abs_difference = (angle.to_radians() - consts::PI).abs(); assert!(abs_difference <= f32::EPSILON); }

#![feature(float_extras)]

use std::f32::{self, consts};

let angle = 180.0f32;

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

assert!(abs_difference <= f32::EPSILON);

fn ldexp(x: f32, exp: isize) -> f32

Unstable (float_extras #27752)

: pending integer conventions

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

#![feature(float_extras)] fn main() { use std::f32; // 3*2^2 - 12 == 0 let abs_difference = (f32::ldexp(3.0, 2) - 12.0).abs(); assert!(abs_difference <= f32::EPSILON); }

#![feature(float_extras)]

use std::f32;
// 3*2^2 - 12 == 0
let abs_difference = (f32::ldexp(3.0, 2) - 12.0).abs();

assert!(abs_difference <= f32::EPSILON);

fn frexp(self) -> (f32, 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() { use std::f32; let x = 4.0f32; // (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 f32 - 3.0).abs(); assert!(abs_difference_0 <= f32::EPSILON); assert!(abs_difference_1 <= f32::EPSILON); }

#![feature(float_extras)]

use std::f32;

let x = 4.0f32;

// (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 f32 - 3.0).abs();

assert!(abs_difference_0 <= f32::EPSILON);
assert!(abs_difference_1 <= f32::EPSILON);

fn next_after(self, other: f32) -> f32

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() { use std::f32; let x = 1.0f32; let abs_diff = (x.next_after(2.0) - 1.00000011920928955078125_f32).abs(); assert!(abs_diff <= f32::EPSILON); }

#![feature(float_extras)]

use std::f32;

let x = 1.0f32;

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

assert!(abs_diff <= f32::EPSILON);

fn max(self, other: f32) -> f32

Returns the maximum of the two numbers.

fn main() { let x = 1.0f32; let y = 2.0f32; assert_eq!(x.max(y), y); }

let x = 1.0f32;
let y = 2.0f32;

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

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

fn min(self, other: f32) -> f32

Returns the minimum of the two numbers.

fn main() { let x = 1.0f32; let y = 2.0f32; assert_eq!(x.min(y), x); }

let x = 1.0f32;
let y = 2.0f32;

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

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

fn abs_sub(self, other: f32) -> f32

The positive difference of two numbers.

• If self <= other: 0:0
• Else: self - other

fn main() { use std::f32; let x = 3.0f32; let y = -3.0f32; 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 <= f32::EPSILON); assert!(abs_difference_y <= f32::EPSILON); }

use std::f32;

let x = 3.0f32;
let y = -3.0f32;

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 <= f32::EPSILON);
assert!(abs_difference_y <= f32::EPSILON);

fn cbrt(self) -> f32

Takes the cubic root of a number.

fn main() { use std::f32; let x = 8.0f32; // x^(1/3) - 2 == 0 let abs_difference = (x.cbrt() - 2.0).abs(); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let x = 8.0f32;

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

assert!(abs_difference <= f32::EPSILON);

fn hypot(self, other: f32) -> f32

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

fn main() { use std::f32; let x = 2.0f32; let y = 3.0f32; // sqrt(x^2 + y^2) let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs(); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let x = 2.0f32;
let y = 3.0f32;

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

assert!(abs_difference <= f32::EPSILON);

fn sin(self) -> f32

Computes the sine of a number (in radians).

fn main() { use std::f32; let x = f32::consts::PI/2.0; let abs_difference = (x.sin() - 1.0).abs(); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let x = f32::consts::PI/2.0;

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

assert!(abs_difference <= f32::EPSILON);

fn cos(self) -> f32

Computes the cosine of a number (in radians).

fn main() { use std::f32; let x = 2.0*f32::consts::PI; let abs_difference = (x.cos() - 1.0).abs(); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let x = 2.0*f32::consts::PI;

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

assert!(abs_difference <= f32::EPSILON);

fn tan(self) -> f32

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-10); }

use std::f64;

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

assert!(abs_difference < 1e-10);

fn asin(self) -> f32

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::f32; let f = f32::consts::PI / 2.0; // asin(sin(pi/2)) let abs_difference = f.sin().asin().abs_sub(f32::consts::PI / 2.0); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let f = f32::consts::PI / 2.0;

// asin(sin(pi/2))
let abs_difference = f.sin().asin().abs_sub(f32::consts::PI / 2.0);

assert!(abs_difference <= f32::EPSILON);

fn acos(self) -> f32

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::f32; let f = f32::consts::PI / 4.0; // acos(cos(pi/4)) let abs_difference = f.cos().acos().abs_sub(f32::consts::PI / 4.0); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let f = f32::consts::PI / 4.0;

// acos(cos(pi/4))
let abs_difference = f.cos().acos().abs_sub(f32::consts::PI / 4.0);

assert!(abs_difference <= f32::EPSILON);

fn atan(self) -> f32

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

fn main() { use std::f32; let f = 1.0f32; // atan(tan(1)) let abs_difference = f.tan().atan().abs_sub(1.0); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let f = 1.0f32;

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

assert!(abs_difference <= f32::EPSILON);

fn atan2(self, other: f32) -> f32

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::f32; let pi = f32::consts::PI; // All angles from horizontal right (+x) // 45 deg counter-clockwise let x1 = 3.0f32; let y1 = -3.0f32; // 135 deg clockwise let x2 = -3.0f32; let y2 = 3.0f32; 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 <= f32::EPSILON); assert!(abs_difference_2 <= f32::EPSILON); }

use std::f32;

let pi = f32::consts::PI;
// All angles from horizontal right (+x)
// 45 deg counter-clockwise
let x1 = 3.0f32;
let y1 = -3.0f32;

// 135 deg clockwise
let x2 = -3.0f32;
let y2 = 3.0f32;

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 <= f32::EPSILON);
assert!(abs_difference_2 <= f32::EPSILON);

fn sin_cos(self) -> (f32, f32)

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

fn main() { use std::f32; let x = f32::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 <= f32::EPSILON); assert!(abs_difference_0 <= f32::EPSILON); }

use std::f32;

let x = f32::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 <= f32::EPSILON);
assert!(abs_difference_0 <= f32::EPSILON);

fn exp_m1(self) -> f32

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

fn main() { let x = 7.0f64; // e^(ln(7)) - 1 let abs_difference = x.ln().exp_m1().abs_sub(6.0); assert!(abs_difference < 1e-10); }

let x = 7.0f64;

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

assert!(abs_difference < 1e-10);

fn ln_1p(self) -> f32

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

fn main() { use std::f32; let x = f32::consts::E - 1.0; // ln(1 + (e - 1)) == ln(e) == 1 let abs_difference = (x.ln_1p() - 1.0).abs(); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let x = f32::consts::E - 1.0;

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

assert!(abs_difference <= f32::EPSILON);

fn sinh(self) -> f32

Hyperbolic sine function.

fn main() { use std::f32; let e = f32::consts::E; let x = 1.0f32; 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 <= f32::EPSILON); }

use std::f32;

let e = f32::consts::E;
let x = 1.0f32;

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 <= f32::EPSILON);

fn cosh(self) -> f32

Hyperbolic cosine function.

fn main() { use std::f32; let e = f32::consts::E; let x = 1.0f32; let f = x.cosh(); // Solving cosh() at 1 gives this result let g = (e*e + 1.0)/(2.0*e); let abs_difference = f.abs_sub(g); // Same result assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let e = f32::consts::E;
let x = 1.0f32;
let f = x.cosh();
// Solving cosh() at 1 gives this result
let g = (e*e + 1.0)/(2.0*e);
let abs_difference = f.abs_sub(g);

// Same result
assert!(abs_difference <= f32::EPSILON);

fn tanh(self) -> f32

Hyperbolic tangent function.

fn main() { use std::f32; let e = f32::consts::E; let x = 1.0f32; 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 <= f32::EPSILON); }

use std::f32;

let e = f32::consts::E;
let x = 1.0f32;

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 <= f32::EPSILON);

fn asinh(self) -> f32

Inverse hyperbolic sine function.

fn main() { use std::f32; let x = 1.0f32; let f = x.sinh().asinh(); let abs_difference = (f - x).abs(); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let x = 1.0f32;
let f = x.sinh().asinh();

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

assert!(abs_difference <= f32::EPSILON);

fn acosh(self) -> f32

Inverse hyperbolic cosine function.

fn main() { use std::f32; let x = 1.0f32; let f = x.cosh().acosh(); let abs_difference = (f - x).abs(); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let x = 1.0f32;
let f = x.cosh().acosh();

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

assert!(abs_difference <= f32::EPSILON);

fn atanh(self) -> f32

Inverse hyperbolic tangent function.

fn main() { use std::f32; let e = f32::consts::E; let f = e.tanh().atanh(); let abs_difference = f.abs_sub(e); assert!(abs_difference <= f32::EPSILON); }

use std::f32;

let e = f32::consts::E;
let f = e.tanh().atanh();

let abs_difference = f.abs_sub(e);

assert!(abs_difference <= f32::EPSILON);

Trait Implementations

impl DecodableFloat for f32

fn min_pos_norm_value() -> f32

impl RawFloat for f32

fn sig_bits() -> u8

fn exp_bits() -> u8

fn ceil_log5_of_max_sig() -> i16

fn transmute(self) -> u64

fn from_bits(bits: u64) -> f32

fn unpack(self) -> Unpacked

fn from_int(x: u64) -> f32

fn max_normal_digits() -> usize

fn inf_cutoff() -> i64

fn zero_cutoff() -> i64

impl FromStr for f32

type Err = ParseFloatError

fn from_str(src: &str) -> Result<f32, ParseFloatError>

impl Zero for f32

fn zero() -> f32

impl One for f32

fn one() -> f32

impl From<i8> for f32

fn from(small: i8) -> f32

impl From<i16> for f32

fn from(small: i16) -> f32

impl From<u8> for f32

fn from(small: u8) -> f32

impl From<u16> for f32

fn from(small: u16) -> f32

impl Add<f32> for f32

type Output = f32

fn add(self, other: f32) -> f32

impl<'a> Add<f32> for &'a f32

type Output = f32::Output

fn add(self, other: f32) -> f32::Output

impl<'a> Add<&'a f32> for f32

type Output = f32::Output

fn add(self, other: &'a f32) -> f32::Output

impl<'a, 'b> Add<&'a f32> for &'b f32

type Output = f32::Output

fn add(self, other: &'a f32) -> f32::Output

impl Sub<f32> for f32

type Output = f32

fn sub(self, other: f32) -> f32

impl<'a> Sub<f32> for &'a f32

type Output = f32::Output

fn sub(self, other: f32) -> f32::Output

impl<'a> Sub<&'a f32> for f32

type Output = f32::Output

fn sub(self, other: &'a f32) -> f32::Output

impl<'a, 'b> Sub<&'a f32> for &'b f32

type Output = f32::Output

fn sub(self, other: &'a f32) -> f32::Output

impl Mul<f32> for f32

type Output = f32

fn mul(self, other: f32) -> f32

impl<'a> Mul<f32> for &'a f32

type Output = f32::Output

fn mul(self, other: f32) -> f32::Output

impl<'a> Mul<&'a f32> for f32

type Output = f32::Output

fn mul(self, other: &'a f32) -> f32::Output

impl<'a, 'b> Mul<&'a f32> for &'b f32

type Output = f32::Output

fn mul(self, other: &'a f32) -> f32::Output

impl Div<f32> for f32

type Output = f32

fn div(self, other: f32) -> f32

impl<'a> Div<f32> for &'a f32

type Output = f32::Output

fn div(self, other: f32) -> f32::Output

impl<'a> Div<&'a f32> for f32

type Output = f32::Output

fn div(self, other: &'a f32) -> f32::Output

impl<'a, 'b> Div<&'a f32> for &'b f32

type Output = f32::Output

fn div(self, other: &'a f32) -> f32::Output

impl Rem<f32> for f32

type Output = f32

fn rem(self, other: f32) -> f32

impl<'a> Rem<f32> for &'a f32

type Output = f32::Output

fn rem(self, other: f32) -> f32::Output

impl<'a> Rem<&'a f32> for f32

type Output = f32::Output

fn rem(self, other: &'a f32) -> f32::Output

impl<'a, 'b> Rem<&'a f32> for &'b f32

type Output = f32::Output

fn rem(self, other: &'a f32) -> f32::Output

impl Neg for f32

type Output = f32

fn neg(self) -> f32

impl<'a> Neg for &'a f32

type Output = f32::Output

fn neg(self) -> f32::Output

impl AddAssign<f32> for f32

fn add_assign(&mut self, other: f32)

impl SubAssign<f32> for f32

fn sub_assign(&mut self, other: f32)

impl MulAssign<f32> for f32

fn mul_assign(&mut self, other: f32)

impl DivAssign<f32> for f32

fn div_assign(&mut self, other: f32)

impl RemAssign<f32> for f32

fn rem_assign(&mut self, other: f32)

impl PartialEq<f32> for f32

fn eq(&self, other: &f32) -> bool

fn ne(&self, other: &f32) -> bool

impl PartialOrd<f32> for f32

fn partial_cmp(&self, other: &f32) -> Option<Ordering>

fn lt(&self, other: &f32) -> bool

fn le(&self, other: &f32) -> bool

fn ge(&self, other: &f32) -> bool

fn gt(&self, other: &f32) -> bool

impl Clone for f32

fn clone(&self) -> f32

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

impl Default for f32

fn default() -> f32

impl Debug for f32

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

impl Display for f32

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

impl LowerExp for f32

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

impl UpperExp for f32

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