Primitive Type f32 []

The 32-bit floating point type.

See also the std::f32 module.

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

Methods

impl f32

1.0.0fn 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());

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::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());

1.0.0fn 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());

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-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());

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::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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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());

1.0.0fn 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());

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::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());

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::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());

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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());

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.7.0fn to_degrees(self) -> f32

Converts radians to degrees.

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

let angle = consts::PI;

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

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

1.7.0fn to_radians(self) -> f32

Converts degrees to radians.

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); }
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);

1.0.0fn 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.

1.0.0fn 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.

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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);

1.0.0fn 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 Zero for f32

fn zero() -> f32

impl One for f32

fn one() -> f32

impl From<i8> for f321.5.0

fn from(small: i8) -> f32

impl From<i16> for f321.5.0

fn from(small: i16) -> f32

impl From<u8> for f321.5.0

fn from(small: u8) -> f32

impl From<u16> for f321.5.0

fn from(small: u16) -> f32

impl Add<f32> for f321.0.0

type Output = f32

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

impl<'a> Add<f32> for &'a f321.0.0

type Output = f32::Output

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

impl<'a> Add<&'a f32> for f321.0.0

type Output = f32::Output

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

impl<'a, 'b> Add<&'a f32> for &'b f321.0.0

type Output = f32::Output

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

impl Sub<f32> for f321.0.0

type Output = f32

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

impl<'a> Sub<f32> for &'a f321.0.0

type Output = f32::Output

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

impl<'a> Sub<&'a f32> for f321.0.0

type Output = f32::Output

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

impl<'a, 'b> Sub<&'a f32> for &'b f321.0.0

type Output = f32::Output

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

impl Mul<f32> for f321.0.0

type Output = f32

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

impl<'a> Mul<f32> for &'a f321.0.0

type Output = f32::Output

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

impl<'a> Mul<&'a f32> for f321.0.0

type Output = f32::Output

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

impl<'a, 'b> Mul<&'a f32> for &'b f321.0.0

type Output = f32::Output

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

impl Div<f32> for f321.0.0

type Output = f32

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

impl<'a> Div<f32> for &'a f321.0.0

type Output = f32::Output

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

impl<'a> Div<&'a f32> for f321.0.0

type Output = f32::Output

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

impl<'a, 'b> Div<&'a f32> for &'b f321.0.0

type Output = f32::Output

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

impl Rem<f32> for f321.0.0

type Output = f32

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

impl<'a> Rem<f32> for &'a f321.0.0

type Output = f32::Output

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

impl<'a> Rem<&'a f32> for f321.0.0

type Output = f32::Output

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

impl<'a, 'b> Rem<&'a f32> for &'b f321.0.0

type Output = f32::Output

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

impl Neg for f321.0.0

type Output = f32

fn neg(self) -> f32

impl<'a> Neg for &'a f321.0.0

type Output = f32::Output

fn neg(self) -> f32::Output

impl AddAssign<f32> for f321.8.0

fn add_assign(&mut self, other: f32)

impl SubAssign<f32> for f321.8.0

fn sub_assign(&mut self, other: f32)

impl MulAssign<f32> for f321.8.0

fn mul_assign(&mut self, other: f32)

impl DivAssign<f32> for f321.8.0

fn div_assign(&mut self, other: f32)

impl RemAssign<f32> for f321.8.0

fn rem_assign(&mut self, other: f32)

impl PartialEq<f32> for f321.0.0

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

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

impl PartialOrd<f32> for f321.0.0

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 f321.0.0

fn clone(&self) -> f32

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

impl Default for f321.0.0

fn default() -> f32

impl Debug for f321.0.0

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

impl Display for f321.0.0

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

impl LowerExp for f321.0.0

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

impl UpperExp for f321.0.0

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