Primitive Type f32 [-] [+]

Operations and constants for 32-bits floats (f32 type)

Methods

impl f32

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

Parses a float as with a given radix

fn is_nan(self) -> bool

Returns true if this value is NaN and false otherwise.

extern crate std; 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.

extern crate std; 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.

extern crate std; 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.

extern crate std; 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.

extern crate std; 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)

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(std_misc)] extern crate std; 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); }
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.

extern crate std; 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.

extern crate std; 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
extern crate std; 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.

extern crate std; 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.

extern crate std; 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.

extern crate std; 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.

extern crate std; 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

extern crate std; 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.

extern crate std; 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.

extern crate std; 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).

extern crate std; 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).

extern crate std; 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.

extern crate std; 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.

extern crate std; 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.

extern crate std; 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.

extern crate std; 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.

#![feature(std_misc)] extern crate std; 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.

#![feature(std_misc)] extern crate std; 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

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

#![feature(std_misc)] extern crate std; 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); }
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)

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

  • self = x * 2^exp
  • 0.5 <= abs(x) < 1.0
#![feature(std_misc)] extern crate std; 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); }
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

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

#![feature(std_misc)] extern crate std; 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); }
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);

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);

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

The positive difference of two numbers.

  • If self <= other: 0:0
  • Else: self - other
extern crate std; 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.

extern crate std; 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.

extern crate std; 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).

extern crate std; 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).

extern crate std; 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).

extern crate std; 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].

extern crate std; 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].

extern crate std; 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];

extern crate std; 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)
extern crate std; 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)).

extern crate std; 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.

extern crate std; 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.

extern crate std; 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.

extern crate std; 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.

extern crate std; 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.

extern crate std; 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.

extern crate std; 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.

extern crate std; 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 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', equivalent to '3.14'
  • '-3.14'
  • '2.5E10', or equivalently, '2.5e10'
  • '2.5E-10'
  • '.' (understood as 0)
  • '5.'
  • '.5', or, equivalently, '0.5'
  • '+inf', '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 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 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

Returns a deep copy of the value.

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>

impl SampleRange for f32

fn construct_range(low: f32, high: f32) -> Range<f32>

fn sample_range<R>(r: &Range<f32>, rng: &mut R) -> f32 where R: Rng

impl Rand for f32

fn rand<R>(rng: &mut R) -> f32 where R: Rng

Generate a floating point number in the half-open interval [0,1).

See Closed01 for the closed interval [0,1], and Open01 for the open interval (0,1).