Primitive Type f64
[-] [+]
Operations and constants for 64-bits floats (f64
type)
Methods
impl f64
fn from_str_radix(s: &str, radix: u32) -> Result<f64, 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::f64; let nan = f64::NAN; let f = 7.0_f64; 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::f64; let f = 7.0f64; let inf = f64::INFINITY; let neg_inf = f64::NEG_INFINITY; let nan = f64::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::f64; let f = 7.0f64; let inf: f64 = f64::INFINITY; let neg_inf: f64 = f64::NEG_INFINITY; let nan: f64 = f64::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-38f64 let max = f32::MAX; let lower_than_min = 1.0e-40_f32; let zero = 0.0f32; 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::f64; let num = 12.4_f64; let inf = f64::INFINITY; assert_eq!(num.classify(), FpCategory::Normal); assert_eq!(inf.classify(), FpCategory::Infinite); }use std::num::FpCategory; use std::f64; let num = 12.4_f64; let inf = f64::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.
let num = 2.0f64; // (8388608, -22, 1) let (mantissa, exponent, sign) = num.integer_decode(); let sign_f = sign as f64; let mantissa_f = mantissa as f64; let exponent_f = num.powf(exponent as f64); // 1 * 8388608 * 2^(-22) == 2 let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs(); assert!(abs_difference < 1e-10);
fn floor(self) -> f64
Returns the largest integer less than or equal to a number.
fn main() { let f = 3.99_f64; let g = 3.0_f64; assert_eq!(f.floor(), 3.0); assert_eq!(g.floor(), 3.0); }let f = 3.99_f64; let g = 3.0_f64; assert_eq!(f.floor(), 3.0); assert_eq!(g.floor(), 3.0);
fn ceil(self) -> f64
Returns the smallest integer greater than or equal to a number.
fn main() { let f = 3.01_f64; let g = 4.0_f64; assert_eq!(f.ceil(), 4.0); assert_eq!(g.ceil(), 4.0); }let f = 3.01_f64; let g = 4.0_f64; assert_eq!(f.ceil(), 4.0); assert_eq!(g.ceil(), 4.0);
fn round(self) -> f64
Returns the nearest integer to a number. Round half-way cases away from
0.0
.
let f = 3.3_f64; let g = -3.3_f64; assert_eq!(f.round(), 3.0); assert_eq!(g.round(), -3.0);
fn trunc(self) -> f64
Returns the integer part of a number.
fn main() { let f = 3.3_f64; let g = -3.7_f64; assert_eq!(f.trunc(), 3.0); assert_eq!(g.trunc(), -3.0); }let f = 3.3_f64; let g = -3.7_f64; assert_eq!(f.trunc(), 3.0); assert_eq!(g.trunc(), -3.0);
fn fract(self) -> f64
Returns the fractional part of a number.
fn main() { let x = 3.5_f64; let y = -3.5_f64; let abs_difference_x = (x.fract() - 0.5).abs(); let abs_difference_y = (y.fract() - (-0.5)).abs(); assert!(abs_difference_x < 1e-10); assert!(abs_difference_y < 1e-10); }let x = 3.5_f64; let y = -3.5_f64; let abs_difference_x = (x.fract() - 0.5).abs(); let abs_difference_y = (y.fract() - (-0.5)).abs(); assert!(abs_difference_x < 1e-10); assert!(abs_difference_y < 1e-10);
fn abs(self) -> f64
Computes the absolute value of self
. Returns NAN
if the
number is NAN
.
use std::f64; let x = 3.5_f64; let y = -3.5_f64; let abs_difference_x = (x.abs() - x).abs(); let abs_difference_y = (y.abs() - (-y)).abs(); assert!(abs_difference_x < 1e-10); assert!(abs_difference_y < 1e-10); assert!(f64::NAN.abs().is_nan());
fn signum(self) -> f64
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::f64; let f = 3.5_f64; assert_eq!(f.signum(), 1.0); assert_eq!(f64::NEG_INFINITY.signum(), -1.0); assert!(f64::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::f64; let nan: f64 = f64::NAN; let f = 7.0_f64; let g = -7.0_f64; 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_positive(self) -> bool
fn is_sign_negative(self) -> bool
Returns true
if self
's sign is negative, including -0.0
and NEG_INFINITY
.
use std::f64; let nan = f64::NAN; let f = 7.0_f64; let g = -7.0_f64; 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 is_negative(self) -> bool
fn mul_add(self, a: f64, b: f64) -> f64
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.
let m = 10.0_f64; let x = 4.0_f64; let b = 60.0_f64; // 100.0 let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs(); assert!(abs_difference < 1e-10);
fn recip(self) -> f64
Takes the reciprocal (inverse) of a number, 1/x
.
let x = 2.0_f64; let abs_difference = (x.recip() - (1.0/x)).abs(); assert!(abs_difference < 1e-10);
fn powi(self, n: i32) -> f64
Raises a number to an integer power.
Using this function is generally faster than using powf
let x = 2.0_f64; let abs_difference = (x.powi(2) - x*x).abs(); assert!(abs_difference < 1e-10);
fn powf(self, n: f64) -> f64
Raises a number to a floating point power.
fn main() { let x = 2.0_f64; let abs_difference = (x.powf(2.0) - x*x).abs(); assert!(abs_difference < 1e-10); }let x = 2.0_f64; let abs_difference = (x.powf(2.0) - x*x).abs(); assert!(abs_difference < 1e-10);
fn sqrt(self) -> f64
Takes the square root of a number.
Returns NaN if self
is a negative number.
let positive = 4.0_f64; let negative = -4.0_f64; let abs_difference = (positive.sqrt() - 2.0).abs(); assert!(abs_difference < 1e-10); assert!(negative.sqrt().is_nan());
fn exp(self) -> f64
Returns e^(self)
, (the exponential function).
let one = 1.0_f64; // e^1 let e = one.exp(); // ln(e) - 1 == 0 let abs_difference = (e.ln() - 1.0).abs(); assert!(abs_difference < 1e-10);
fn exp2(self) -> f64
Returns 2^(self)
.
let f = 2.0_f64; // 2^2 - 4 == 0 let abs_difference = (f.exp2() - 4.0).abs(); assert!(abs_difference < 1e-10);
fn ln(self) -> f64
Returns the natural logarithm of the number.
fn main() { let one = 1.0_f64; // e^1 let e = one.exp(); // ln(e) - 1 == 0 let abs_difference = (e.ln() - 1.0).abs(); assert!(abs_difference < 1e-10); }let one = 1.0_f64; // e^1 let e = one.exp(); // ln(e) - 1 == 0 let abs_difference = (e.ln() - 1.0).abs(); assert!(abs_difference < 1e-10);
fn log(self, base: f64) -> f64
Returns the logarithm of the number with respect to an arbitrary base.
fn main() { let ten = 10.0_f64; let two = 2.0_f64; // 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 < 1e-10); assert!(abs_difference_2 < 1e-10); }let ten = 10.0_f64; let two = 2.0_f64; // 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 < 1e-10); assert!(abs_difference_2 < 1e-10);
fn log2(self) -> f64
Returns the base 2 logarithm of the number.
fn main() { let two = 2.0_f64; // log2(2) - 1 == 0 let abs_difference = (two.log2() - 1.0).abs(); assert!(abs_difference < 1e-10); }let two = 2.0_f64; // log2(2) - 1 == 0 let abs_difference = (two.log2() - 1.0).abs(); assert!(abs_difference < 1e-10);
fn log10(self) -> f64
Returns the base 10 logarithm of the number.
fn main() { let ten = 10.0_f64; // log10(10) - 1 == 0 let abs_difference = (ten.log10() - 1.0).abs(); assert!(abs_difference < 1e-10); }let ten = 10.0_f64; // log10(10) - 1 == 0 let abs_difference = (ten.log10() - 1.0).abs(); assert!(abs_difference < 1e-10);
fn to_degrees(self) -> f64
Converts radians to degrees.
extern crate std; fn main() { use std::f64::consts; let angle = consts::PI; let abs_difference = (angle.to_degrees() - 180.0).abs(); assert!(abs_difference < 1e-10); }use std::f64::consts; let angle = consts::PI; let abs_difference = (angle.to_degrees() - 180.0).abs(); assert!(abs_difference < 1e-10);
fn to_radians(self) -> f64
Converts degrees to radians.
extern crate std; fn main() { use std::f64::consts; let angle = 180.0_f64; let abs_difference = (angle.to_radians() - consts::PI).abs(); assert!(abs_difference < 1e-10); }use std::f64::consts; let angle = 180.0_f64; let abs_difference = (angle.to_radians() - consts::PI).abs(); assert!(abs_difference < 1e-10);
fn ldexp(x: f64, exp: isize) -> f64
Constructs a floating point number of x*2^exp
.
// 3*2^2 - 12 == 0 let abs_difference = (f64::ldexp(3.0, 2) - 12.0).abs(); assert!(abs_difference < 1e-10);
fn frexp(self) -> (f64, isize)
Breaks the number into a normalized fraction and a base-2 exponent, satisfying:
self = x * 2^exp
0.5 <= abs(x) < 1.0
let x = 4.0_f64; // (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 f64 - 3.0).abs(); assert!(abs_difference_0 < 1e-10); assert!(abs_difference_1 < 1e-10);
fn next_after(self, other: f64) -> f64
Returns the next representable floating-point value in the direction of
other
.
let x = 1.0f32; let abs_diff = (x.next_after(2.0) - 1.00000011920928955078125_f32).abs(); assert!(abs_diff < 1e-10);
fn max(self, other: f64) -> f64
Returns the maximum of the two numbers.
fn main() { let x = 1.0_f64; let y = 2.0_f64; assert_eq!(x.max(y), y); }let x = 1.0_f64; let y = 2.0_f64; assert_eq!(x.max(y), y);
fn min(self, other: f64) -> f64
Returns the minimum of the two numbers.
fn main() { let x = 1.0_f64; let y = 2.0_f64; assert_eq!(x.min(y), x); }let x = 1.0_f64; let y = 2.0_f64; assert_eq!(x.min(y), x);
fn abs_sub(self, other: f64) -> f64
The positive difference of two numbers.
- If
self <= other
:0:0
- Else:
self - other
let x = 3.0_f64; let y = -3.0_f64; 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 < 1e-10); assert!(abs_difference_y < 1e-10);
fn cbrt(self) -> f64
Takes the cubic root of a number.
fn main() { let x = 8.0_f64; // x^(1/3) - 2 == 0 let abs_difference = (x.cbrt() - 2.0).abs(); assert!(abs_difference < 1e-10); }let x = 8.0_f64; // x^(1/3) - 2 == 0 let abs_difference = (x.cbrt() - 2.0).abs(); assert!(abs_difference < 1e-10);
fn hypot(self, other: f64) -> f64
Calculates the length of the hypotenuse of a right-angle triangle given
legs of length x
and y
.
let x = 2.0_f64; let y = 3.0_f64; // sqrt(x^2 + y^2) let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs(); assert!(abs_difference < 1e-10);
fn sin(self) -> f64
Computes the sine of a number (in radians).
extern crate std; fn main() { use std::f64; let x = f64::consts::PI/2.0; let abs_difference = (x.sin() - 1.0).abs(); assert!(abs_difference < 1e-10); }use std::f64; let x = f64::consts::PI/2.0; let abs_difference = (x.sin() - 1.0).abs(); assert!(abs_difference < 1e-10);
fn cos(self) -> f64
Computes the cosine of a number (in radians).
extern crate std; fn main() { use std::f64; let x = 2.0*f64::consts::PI; let abs_difference = (x.cos() - 1.0).abs(); assert!(abs_difference < 1e-10); }use std::f64; let x = 2.0*f64::consts::PI; let abs_difference = (x.cos() - 1.0).abs(); assert!(abs_difference < 1e-10);
fn tan(self) -> f64
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-14); }use std::f64; let x = f64::consts::PI/4.0; let abs_difference = (x.tan() - 1.0).abs(); assert!(abs_difference < 1e-14);
fn asin(self) -> f64
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::f64; let f = f64::consts::PI / 2.0; // asin(sin(pi/2)) let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs(); assert!(abs_difference < 1e-10); }use std::f64; let f = f64::consts::PI / 2.0; // asin(sin(pi/2)) let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs(); assert!(abs_difference < 1e-10);
fn acos(self) -> f64
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::f64; let f = f64::consts::PI / 4.0; // acos(cos(pi/4)) let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs(); assert!(abs_difference < 1e-10); }use std::f64; let f = f64::consts::PI / 4.0; // acos(cos(pi/4)) let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs(); assert!(abs_difference < 1e-10);
fn atan(self) -> f64
Computes the arctangent of a number. Return value is in radians in the range [-pi/2, pi/2];
fn main() { let f = 1.0_f64; // atan(tan(1)) let abs_difference = (f.tan().atan() - 1.0).abs(); assert!(abs_difference < 1e-10); }let f = 1.0_f64; // atan(tan(1)) let abs_difference = (f.tan().atan() - 1.0).abs(); assert!(abs_difference < 1e-10);
fn atan2(self, other: f64) -> f64
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::f64; let pi = f64::consts::PI; // All angles from horizontal right (+x) // 45 deg counter-clockwise let x1 = 3.0_f64; let y1 = -3.0_f64; // 135 deg clockwise let x2 = -3.0_f64; let y2 = 3.0_f64; 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 < 1e-10); assert!(abs_difference_2 < 1e-10);
fn sin_cos(self) -> (f64, f64)
Simultaneously computes the sine and cosine of the number, x
. Returns
(sin(x), cos(x))
.
use std::f64; let x = f64::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 < 1e-10); assert!(abs_difference_0 < 1e-10);
fn exp_m1(self) -> f64
Returns e^(self) - 1
in a way that is accurate even if the
number is close to zero.
let x = 7.0_f64; // e^(ln(7)) - 1 let abs_difference = (x.ln().exp_m1() - 6.0).abs(); assert!(abs_difference < 1e-10);
fn ln_1p(self) -> f64
Returns ln(1+n)
(natural logarithm) more accurately than if
the operations were performed separately.
use std::f64; let x = f64::consts::E - 1.0; // ln(1 + (e - 1)) == ln(e) == 1 let abs_difference = (x.ln_1p() - 1.0).abs(); assert!(abs_difference < 1e-10);
fn sinh(self) -> f64
Hyperbolic sine function.
extern crate std; fn main() { use std::f64; let e = f64::consts::E; let x = 1.0_f64; 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 < 1e-10); }use std::f64; let e = f64::consts::E; let x = 1.0_f64; 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 < 1e-10);
fn cosh(self) -> f64
Hyperbolic cosine function.
extern crate std; fn main() { use std::f64; let e = f64::consts::E; let x = 1.0_f64; let f = x.cosh(); // Solving cosh() at 1 gives this result let g = (e*e + 1.0)/(2.0*e); let abs_difference = (f - g).abs(); // Same result assert!(abs_difference < 1.0e-10); }use std::f64; let e = f64::consts::E; let x = 1.0_f64; let f = x.cosh(); // Solving cosh() at 1 gives this result let g = (e*e + 1.0)/(2.0*e); let abs_difference = (f - g).abs(); // Same result assert!(abs_difference < 1.0e-10);
fn tanh(self) -> f64
Hyperbolic tangent function.
extern crate std; fn main() { use std::f64; let e = f64::consts::E; let x = 1.0_f64; 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 < 1.0e-10); }use std::f64; let e = f64::consts::E; let x = 1.0_f64; 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 < 1.0e-10);
fn asinh(self) -> f64
Inverse hyperbolic sine function.
fn main() { let x = 1.0_f64; let f = x.sinh().asinh(); let abs_difference = (f - x).abs(); assert!(abs_difference < 1.0e-10); }let x = 1.0_f64; let f = x.sinh().asinh(); let abs_difference = (f - x).abs(); assert!(abs_difference < 1.0e-10);
fn acosh(self) -> f64
Inverse hyperbolic cosine function.
fn main() { let x = 1.0_f64; let f = x.cosh().acosh(); let abs_difference = (f - x).abs(); assert!(abs_difference < 1.0e-10); }let x = 1.0_f64; let f = x.cosh().acosh(); let abs_difference = (f - x).abs(); assert!(abs_difference < 1.0e-10);
fn atanh(self) -> f64
Inverse hyperbolic tangent function.
extern crate std; fn main() { use std::f64; let e = f64::consts::E; let f = e.tanh().atanh(); let abs_difference = (f - e).abs(); assert!(abs_difference < 1.0e-10); }use std::f64; let e = f64::consts::E; let f = e.tanh().atanh(); let abs_difference = (f - e).abs(); assert!(abs_difference < 1.0e-10);
Trait Implementations
impl Zero for f64
impl One for f64
impl FromStr for f64
type Err = ParseFloatError
fn from_str(src: &str) -> Result<f64, 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
.