# Primitive Type f321.0.0[−]

## Expand description

A 32-bit floating point type (specifically, the “binary32” type defined in IEEE 754-2008).

This type can represent a wide range of decimal numbers, like `3.5`

, `27`

,
`-113.75`

, `0.0078125`

, `34359738368`

, `0`

, `-1`

. So unlike integer types
(such as `i32`

), floating point types can represent non-integer numbers,
too.

However, being able to represent this wide range of numbers comes at the
cost of precision: floats can only represent some of the real numbers and
calculation with floats round to a nearby representable number. For example,
`5.0`

and `1.0`

can be exactly represented as `f32`

, but `1.0 / 5.0`

results
in `0.20000000298023223876953125`

since `0.2`

cannot be exactly represented
as `f32`

. Note, however, that printing floats with `println`

and friends will
often discard insignificant digits: `println!("{}", 1.0f32 / 5.0f32)`

will
print `0.2`

.

Additionally, `f32`

can represent some special values:

- −0.0: IEEE 754 floating point numbers have a bit that indicates their sign, so −0.0 is a possible value. For comparison −0.0 = +0.0, but floating point operations can carry the sign bit through arithmetic operations. This means −0.0 × +0.0 produces −0.0 and a negative number rounded to a value smaller than a float can represent also produces −0.0.
- ∞ and
−∞: these result from calculations
like
`1.0 / 0.0`

. - NaN (not a number): this value results from
calculations like
`(-1.0).sqrt()`

. NaN has some potentially unexpected behavior: it is unequal to any float, including itself! It is also neither smaller nor greater than any float, making it impossible to sort. Lastly, it is considered infectious as almost all calculations where one of the operands is NaN will also result in NaN.

For more information on floating point numbers, see Wikipedia.

## Implementations

Computes the absolute value of `self`

. Returns `NAN`

if the
number is `NAN`

.

# Examples

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());Run

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`

# Examples

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());Run

Returns a number composed of the magnitude of `self`

and the sign of
`sign`

.

Equal to `self`

if the sign of `self`

and `sign`

are the same, otherwise
equal to `-self`

. If `self`

is a `NAN`

, then a `NAN`

with the sign of
`sign`

is returned.

# Examples

let f = 3.5_f32; assert_eq!(f.copysign(0.42), 3.5_f32); assert_eq!(f.copysign(-0.42), -3.5_f32); assert_eq!((-f).copysign(0.42), 3.5_f32); assert_eq!((-f).copysign(-0.42), -3.5_f32); assert!(f32::NAN.copysign(1.0).is_nan());Run

Fused multiply-add. Computes `(self * a) + b`

with only one rounding
error, yielding a more accurate result than an unfused multiply-add.

Using `mul_add`

*may* be more performant than an unfused multiply-add if
the target architecture has a dedicated `fma`

CPU instruction. However,
this is not always true, and will be heavily dependant on designing
algorithms with specific target hardware in mind.

# Examples

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);Run

Calculates Euclidean division, the matching method for `rem_euclid`

.

This computes the integer `n`

such that
`self = n * rhs + self.rem_euclid(rhs)`

.
In other words, the result is `self / rhs`

rounded to the integer `n`

such that `self >= n * rhs`

.

# Examples

let a: f32 = 7.0; let b = 4.0; assert_eq!(a.div_euclid(b), 1.0); // 7.0 > 4.0 * 1.0 assert_eq!((-a).div_euclid(b), -2.0); // -7.0 >= 4.0 * -2.0 assert_eq!(a.div_euclid(-b), -1.0); // 7.0 >= -4.0 * -1.0 assert_eq!((-a).div_euclid(-b), 2.0); // -7.0 >= -4.0 * 2.0Run

Calculates the least nonnegative remainder of `self (mod rhs)`

.

In particular, the return value `r`

satisfies `0.0 <= r < rhs.abs()`

in
most cases. However, due to a floating point round-off error it can
result in `r == rhs.abs()`

, violating the mathematical definition, if
`self`

is much smaller than `rhs.abs()`

in magnitude and `self < 0.0`

.
This result is not an element of the function’s codomain, but it is the
closest floating point number in the real numbers and thus fulfills the
property `self == self.div_euclid(rhs) * rhs + self.rem_euclid(rhs)`

approximatively.

# Examples

let a: f32 = 7.0; let b = 4.0; assert_eq!(a.rem_euclid(b), 3.0); assert_eq!((-a).rem_euclid(b), 1.0); assert_eq!(a.rem_euclid(-b), 3.0); assert_eq!((-a).rem_euclid(-b), 1.0); // limitation due to round-off error assert!((-f32::EPSILON).rem_euclid(3.0) != 0.0);Run

Returns the logarithm of the number with respect to an arbitrary base.

The result may not be correctly rounded owing to implementation details;
`self.log2()`

can produce more accurate results for base 2, and
`self.log10()`

can produce more accurate results for base 10.

# Examples

let five = 5.0f32; // log5(5) - 1 == 0 let abs_difference = (five.log(5.0) - 1.0).abs(); assert!(abs_difference <= f32::EPSILON);Run

## 👎 Deprecated since 1.10.0: you probably meant `(self - other).abs()`

: this operation is `(self - other).max(0.0)`

except that `abs_sub`

also propagates NaNs (also known as `fdimf`

in C). If you truly need the positive difference, consider using that expression or the C function `fdimf`

, depending on how you wish to handle NaN (please consider filing an issue describing your use-case too).

you probably meant `(self - other).abs()`

: this operation is `(self - other).max(0.0)`

except that `abs_sub`

also propagates NaNs (also known as `fdimf`

in C). If you truly need the positive difference, consider using that expression or the C function `fdimf`

, depending on how you wish to handle NaN (please consider filing an issue describing your use-case too).

The positive difference of two numbers.

- If
`self <= other`

:`0:0`

- Else:
`self - other`

# Examples

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);Run

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].

# Examples

let f = std::f32::consts::FRAC_PI_2; // asin(sin(pi/2)) let abs_difference = (f.sin().asin() - std::f32::consts::FRAC_PI_2).abs(); assert!(abs_difference <= f32::EPSILON);Run

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].

# Examples

let f = std::f32::consts::FRAC_PI_4; // acos(cos(pi/4)) let abs_difference = (f.cos().acos() - std::f32::consts::FRAC_PI_4).abs(); assert!(abs_difference <= f32::EPSILON);Run

Computes the four quadrant arctangent of `self`

(`y`

) and `other`

(`x`

) in radians.

`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)`

# Examples

// Positive angles measured counter-clockwise // from positive x axis // -pi/4 radians (45 deg clockwise) let x1 = 3.0f32; let y1 = -3.0f32; // 3pi/4 radians (135 deg counter-clockwise) let x2 = -3.0f32; let y2 = 3.0f32; let abs_difference_1 = (y1.atan2(x1) - (-std::f32::consts::FRAC_PI_4)).abs(); let abs_difference_2 = (y2.atan2(x2) - (3.0 * std::f32::consts::FRAC_PI_4)).abs(); assert!(abs_difference_1 <= f32::EPSILON); assert!(abs_difference_2 <= f32::EPSILON);Run

Simultaneously computes the sine and cosine of the number, `x`

. Returns
`(sin(x), cos(x))`

.

# Examples

let x = std::f32::consts::FRAC_PI_4; 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);Run

Returns `ln(1+n)`

(natural logarithm) more accurately than if
the operations were performed separately.

# Examples

let x = 1e-8_f32; // for very small x, ln(1 + x) is approximately x - x^2 / 2 let approx = x - x * x / 2.0; let abs_difference = (x.ln_1p() - approx).abs(); assert!(abs_difference < 1e-10);Run

Linear interpolation between `start`

and `end`

.

This enables linear interpolation between `start`

and `end`

, where start is represented by
`self == 0.0`

and `end`

is represented by `self == 1.0`

. This is the basis of all
“transition”, “easing”, or “step” functions; if you change `self`

from 0.0 to 1.0
at a given rate, the result will change from `start`

to `end`

at a similar rate.

Values below 0.0 or above 1.0 are allowed, allowing you to extrapolate values outside the
range from `start`

to `end`

. This also is useful for transition functions which might
move slightly past the end or start for a desired effect. Mathematically, the values
returned are equivalent to `start + self * (end - start)`

, although we make a few specific
guarantees that are useful specifically to linear interpolation.

These guarantees are:

- If
`start`

and`end`

are finite, the value at 0.0 is always`start`

and the value at 1.0 is always`end`

. (exactness) - If
`start`

and`end`

are finite, the values will always move in the direction from`start`

to`end`

(monotonicity) - If
`self`

is finite and`start == end`

, the value at any point will always be`start == end`

. (consistency)

Number of significant digits in base 2.

Machine epsilon value for `f32`

.

This is the difference between `1.0`

and the next larger representable number.

Smallest positive normal `f32`

value.

Minimum possible normal power of 10 exponent.

Maximum possible power of 10 exponent.

Negative infinity (−∞).

Returns `true`

if this value is `NaN`

.

let nan = f32::NAN; let f = 7.0_f32; assert!(nan.is_nan()); assert!(!f.is_nan());Run

Returns `true`

if this value is positive infinity or negative infinity, and
`false`

otherwise.

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());Run

Returns `true`

if this number is neither infinite nor `NaN`

.

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());Run

Returns `true`

if the number is subnormal.

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_subnormal()); assert!(!max.is_subnormal()); assert!(!zero.is_subnormal()); assert!(!f32::NAN.is_subnormal()); assert!(!f32::INFINITY.is_subnormal()); // Values between `0` and `min` are Subnormal. assert!(lower_than_min.is_subnormal());Run

Returns `true`

if the number is neither zero, infinite,
subnormal, or `NaN`

.

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());Run

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.

use std::num::FpCategory; let num = 12.4_f32; let inf = f32::INFINITY; assert_eq!(num.classify(), FpCategory::Normal); assert_eq!(inf.classify(), FpCategory::Infinite);Run

Returns `true`

if `self`

has a positive sign, including `+0.0`

, `NaN`

s with
positive sign bit and positive infinity.

let f = 7.0_f32; let g = -7.0_f32; assert!(f.is_sign_positive()); assert!(!g.is_sign_positive());Run

Returns `true`

if `self`

has a negative sign, including `-0.0`

, `NaN`

s with
negative sign bit and negative infinity.

let f = 7.0f32; let g = -7.0f32; assert!(!f.is_sign_negative()); assert!(g.is_sign_negative());Run

Takes the reciprocal (inverse) of a number, `1/x`

.

let x = 2.0_f32; let abs_difference = (x.recip() - (1.0 / x)).abs(); assert!(abs_difference <= f32::EPSILON);Run

Converts radians to degrees.

let angle = std::f32::consts::PI; let abs_difference = (angle.to_degrees() - 180.0).abs(); assert!(abs_difference <= f32::EPSILON);Run

Converts degrees to radians.

let angle = 180.0f32; let abs_difference = (angle.to_radians() - std::f32::consts::PI).abs(); assert!(abs_difference <= f32::EPSILON);Run

Returns the maximum of the two numbers.

let x = 1.0f32; let y = 2.0f32; assert_eq!(x.max(y), y);Run

If one of the arguments is NaN, then the other argument is returned.

Returns the minimum of the two numbers.

let x = 1.0f32; let y = 2.0f32; assert_eq!(x.min(y), x);Run

If one of the arguments is NaN, then the other argument is returned.

Rounds toward zero and converts to any primitive integer type, assuming that the value is finite and fits in that type.

let value = 4.6_f32; let rounded = unsafe { value.to_int_unchecked::<u16>() }; assert_eq!(rounded, 4); let value = -128.9_f32; let rounded = unsafe { value.to_int_unchecked::<i8>() }; assert_eq!(rounded, i8::MIN);Run

# Safety

The value must:

- Not be
`NaN`

- Not be infinite
- Be representable in the return type
`Int`

, after truncating off its fractional part

Raw transmutation to `u32`

.

This is currently identical to `transmute::<f32, u32>(self)`

on all platforms.

See `from_bits`

for some discussion of the
portability of this operation (there are almost no issues).

Note that this function is distinct from `as`

casting, which attempts to
preserve the *numeric* value, and not the bitwise value.

# Examples

assert_ne!((1f32).to_bits(), 1f32 as u32); // to_bits() is not casting! assert_eq!((12.5f32).to_bits(), 0x41480000);Run

Raw transmutation from `u32`

.

This is currently identical to `transmute::<u32, f32>(v)`

on all platforms.
It turns out this is incredibly portable, for two reasons:

- Floats and Ints have the same endianness on all supported platforms.
- IEEE-754 very precisely specifies the bit layout of floats.

However there is one caveat: prior to the 2008 version of IEEE-754, how to interpret the NaN signaling bit wasn’t actually specified. Most platforms (notably x86 and ARM) picked the interpretation that was ultimately standardized in 2008, but some didn’t (notably MIPS). As a result, all signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.

Rather than trying to preserve signaling-ness cross-platform, this implementation favors preserving the exact bits. This means that any payloads encoded in NaNs will be preserved even if the result of this method is sent over the network from an x86 machine to a MIPS one.

If the results of this method are only manipulated by the same architecture that produced them, then there is no portability concern.

If the input isn’t NaN, then there is no portability concern.

If you don’t care about signalingness (very likely), then there is no portability concern.

Note that this function is distinct from `as`

casting, which attempts to
preserve the *numeric* value, and not the bitwise value.

# Examples

let v = f32::from_bits(0x41480000); assert_eq!(v, 12.5);Run

Return the memory representation of this floating point number as a byte array in native byte order.

As the target platform’s native endianness is used, portable code
should use `to_be_bytes`

or `to_le_bytes`

, as appropriate, instead.

# Examples

let bytes = 12.5f32.to_ne_bytes(); assert_eq!( bytes, if cfg!(target_endian = "big") { [0x41, 0x48, 0x00, 0x00] } else { [0x00, 0x00, 0x48, 0x41] } );Run

Create a floating point value from its representation as a byte array in native endian.

As the target platform’s native endianness is used, portable code
likely wants to use `from_be_bytes`

or `from_le_bytes`

, as
appropriate instead.

# Examples

let value = f32::from_ne_bytes(if cfg!(target_endian = "big") { [0x41, 0x48, 0x00, 0x00] } else { [0x00, 0x00, 0x48, 0x41] }); assert_eq!(value, 12.5);Run

Returns an ordering between self and other values. Unlike the standard partial comparison between floating point numbers, this comparison always produces an ordering in accordance to the totalOrder predicate as defined in IEEE 754 (2008 revision) floating point standard. The values are ordered in following order:

- Negative quiet NaN
- Negative signaling NaN
- Negative infinity
- Negative numbers
- Negative subnormal numbers
- Negative zero
- Positive zero
- Positive subnormal numbers
- Positive numbers
- Positive infinity
- Positive signaling NaN
- Positive quiet NaN

Note that this function does not always agree with the `PartialOrd`

and `PartialEq`

implementations of `f32`

. In particular, they regard
negative and positive zero as equal, while `total_cmp`

doesn’t.

# Example

#![feature(total_cmp)] struct GoodBoy { name: String, weight: f32, } let mut bois = vec![ GoodBoy { name: "Pucci".to_owned(), weight: 0.1 }, GoodBoy { name: "Woofer".to_owned(), weight: 99.0 }, GoodBoy { name: "Yapper".to_owned(), weight: 10.0 }, GoodBoy { name: "Chonk".to_owned(), weight: f32::INFINITY }, GoodBoy { name: "Abs. Unit".to_owned(), weight: f32::NAN }, GoodBoy { name: "Floaty".to_owned(), weight: -5.0 }, ]; bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));Run

Restrict a value to a certain interval unless it is NaN.

Returns `max`

if `self`

is greater than `max`

, and `min`

if `self`

is
less than `min`

. Otherwise this returns `self`

.

Note that this function returns NaN if the initial value was NaN as well.

# Panics

Panics if `min > max`

, `min`

is NaN, or `max`

is NaN.

# Examples

assert!((-3.0f32).clamp(-2.0, 1.0) == -2.0); assert!((0.0f32).clamp(-2.0, 1.0) == 0.0); assert!((2.0f32).clamp(-2.0, 1.0) == 1.0); assert!((f32::NAN).clamp(-2.0, 1.0).is_nan());Run

## Trait Implementations

Performs the `+=`

operation. Read more

Performs the `+=`

operation. Read more

Performs the `/=`

operation. Read more

Performs the `/=`

operation. Read more

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’
- ‘5.’
- ‘.5’, or, equivalently, ‘0.5’
- ‘inf’, ‘-inf’, ‘NaN’

Leading and trailing whitespace represent an error.

# Grammar

All strings that adhere to the following EBNF grammar
will result in an `Ok`

being returned:

```
Float ::= Sign? ( 'inf' | 'NaN' | Number )
Number ::= ( Digit+ |
Digit+ '.' Digit* |
Digit* '.' Digit+ ) Exp?
Exp ::= [eE] Sign? Digit+
Sign ::= [+-]
Digit ::= [0-9]
```

# Known bugs

In some situations, some strings that should create a valid float instead return an error. See issue #31407 for details.

# 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`

.

`type Err = ParseFloatError`

`type Err = ParseFloatError`

The associated error which can be returned from parsing.

Performs the `*=`

operation. Read more

Performs the `*=`

operation. Read more

This method returns an ordering between `self`

and `other`

values if one exists. Read more

This method tests less than (for `self`

and `other`

) and is used by the `<`

operator. Read more

This method tests less than or equal to (for `self`

and `other`

) and is used by the `<=`

operator. Read more

This method tests greater than or equal to (for `self`

and `other`

) and is used by the `>=`

operator. Read more

The remainder from the division of two floats.

The remainder has the same sign as the dividend and is computed as:
`x - (x / y).trunc() * y`

.

# Examples

let x: f32 = 50.50; let y: f32 = 8.125; let remainder = x - (x / y).trunc() * y; // The answer to both operations is 1.75 assert_eq!(x % y, remainder);Run

Performs the `%=`

operation. Read more

Performs the `%=`

operation. Read more

Performs the `-=`

operation. Read more

Performs the `-=`

operation. Read more

## Auto Trait Implementations

`impl RefUnwindSafe for f32`

`impl UnwindSafe for f32`

## Blanket Implementations

Mutably borrows from an owned value. Read more