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.
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.
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
.
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
.
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.
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
.
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
.
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
orINFINITY
-1.0
if the number is negative,-0.0
orNEG_INFINITY
NAN
if the number isNAN
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
.
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
.
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.
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
.
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
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.
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).
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)
.
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
.
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
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
.
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
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
.
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)
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))
.
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.
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.
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
impl One for 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
.