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

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

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);

fn 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);

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_1 <= 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_1 <= 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 UpperExp for f32

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

impl LowerExp for f32

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

impl Display for f32

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

impl Debug for f32

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

impl Default for f32

fn default() -> f32

impl Clone for f32

fn clone(&self) -> f32

Returns a deep copy of the value.

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

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 PartialEq<f32> for f32

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

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

impl RemAssign<f32> for f32

fn rem_assign(&mut self, other: f32)

impl DivAssign<f32> for f32

fn div_assign(&mut self, other: f32)

impl MulAssign<f32> for f32

fn mul_assign(&mut self, other: f32)

impl SubAssign<f32> for f32

fn sub_assign(&mut self, other: f32)

impl AddAssign<f32> for f32

fn add_assign(&mut self, other: f32)

impl<'a> Neg for &'a f32

type Output = f32::Output

fn neg(self) -> f32::Output

impl Neg for f32

type Output = f32

fn neg(self) -> f32

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

type Output = f32::Output

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

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

type Output = f32::Output

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

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

type Output = f32::Output

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

impl Rem<f32> for f32

type Output = f32

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

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

type Output = f32::Output

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

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

type Output = f32::Output

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

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

type Output = f32::Output

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

impl Div<f32> for f32

type Output = f32

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

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

type Output = f32::Output

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

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

type Output = f32::Output

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

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

type Output = f32::Output

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

impl Mul<f32> for f32

type Output = f32

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

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

type Output = f32::Output

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

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

type Output = f32::Output

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

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

type Output = f32::Output

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

impl Sub<f32> for f32

type Output = f32

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

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

type Output = f32::Output

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

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

type Output = f32::Output

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

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

type Output = f32::Output

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

impl Add<f32> for f32

type Output = f32

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

impl From<u16> for f32

fn from(small: u16) -> f32

impl From<u8> for f32

fn from(small: u8) -> f32

impl From<i16> for f32

fn from(small: i16) -> f32

impl From<i8> for f32

fn from(small: i8) -> f32

impl One for f32

fn one() -> f32

Unstable (zero_one #27739)

: unsure of placement, wants to use associated constants

impl Zero for f32

fn zero() -> f32

Unstable (zero_one #27739)

: unsure of placement, wants to use associated constants

impl FromStr for f32

type Err = ParseFloatError

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