Primitive Type f32

1.0.0 · [−]
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! This is the reason f32 doesn’t implement the Eq trait.
    • It is also neither smaller nor greater than any float, making it impossible to sort by the default comparison operation, which is the reason f32 doesn’t implement the Ord trait.
    • It is also considered infectious as almost all calculations where one of the operands is NaN will also result in NaN. The explanations on this page only explicitly document behavior on NaN operands if this default is deviated from.
    • Lastly, there are multiple bit patterns that are considered NaN. Rust does not currently guarantee that the bit patterns of NaN are preserved over arithmetic operations, and they are not guaranteed to be portable or even fully deterministic! This means that there may be some surprising results upon inspecting the bit patterns, as the same calculations might produce NaNs with different bit patterns.

When the number resulting from a primitive operation (addition, subtraction, multiplication, or division) on this type is not exactly representable as f32, it is rounded according to the roundTiesToEven direction defined in IEEE 754-2008. That means:

  • The result is the representable value closest to the true value, if there is a unique closest representable value.
  • If the true value is exactly half-way between two representable values, the result is the one with an even least-significant binary digit.
  • If the true value’s magnitude is ≥ f32::MAX + 2(f32::MAX_EXP − f32::MANTISSA_DIGITS − 1), the result is ∞ or −∞ (preserving the true value’s sign).

For more information on floating point numbers, see Wikipedia.

See also the std::f32::consts module.

Implementations

The radix or base of the internal representation of f32.

Number of significant digits in base 2.

Approximate number of significant digits in base 10.

Machine epsilon value for f32.

This is the difference between 1.0 and the next larger representable number.

Smallest finite f32 value.

Smallest positive normal f32 value.

Largest finite f32 value.

One greater than the minimum possible normal power of 2 exponent.

Maximum possible power of 2 exponent.

Minimum possible normal power of 10 exponent.

Maximum possible power of 10 exponent.

Not a Number (NaN).

Note that IEEE 754 doesn’t define just a single NaN value; a plethora of bit patterns are considered to be NaN. Furthermore, the standard makes a difference between a “signaling” and a “quiet” NaN, and allows inspecting its “payload” (the unspecified bits in the bit pattern). This constant isn’t guaranteed to equal to any specific NaN bitpattern, and the stability of its representation over Rust versions and target platforms isn’t guaranteed.

Infinity (∞).

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, NaNs with positive sign bit and positive infinity. Note that IEEE 754 doesn’t assign any meaning to the sign bit in case of a NaN, and as Rust doesn’t guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the result of is_sign_positive on a NaN might produce an unexpected result in some cases. See explanation of NaN as a special value for more info.

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, NaNs with negative sign bit and negative infinity. Note that IEEE 754 doesn’t assign any meaning to the sign bit in case of a NaN, and as Rust doesn’t guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the result of is_sign_negative on a NaN might produce an unexpected result in some cases. See explanation of NaN as a special value for more info.

let f = 7.0f32;
let g = -7.0f32;

assert!(!f.is_sign_negative());
assert!(g.is_sign_negative());
Run
🔬This is a nightly-only experimental API. (float_next_up_down #91399)

Returns the least number greater than self.

Let TINY be the smallest representable positive f32. Then,

  • if self.is_nan(), this returns self;
  • if self is NEG_INFINITY, this returns MIN;
  • if self is -TINY, this returns -0.0;
  • if self is -0.0 or +0.0, this returns TINY;
  • if self is MAX or INFINITY, this returns INFINITY;
  • otherwise the unique least value greater than self is returned.

The identity x.next_up() == -(-x).next_down() holds for all non-NaN x. When x is finite x == x.next_up().next_down() also holds.

#![feature(float_next_up_down)]
// f32::EPSILON is the difference between 1.0 and the next number up.
assert_eq!(1.0f32.next_up(), 1.0 + f32::EPSILON);
// But not for most numbers.
assert!(0.1f32.next_up() < 0.1 + f32::EPSILON);
assert_eq!(16777216f32.next_up(), 16777218.0);
Run
🔬This is a nightly-only experimental API. (float_next_up_down #91399)

Returns the greatest number less than self.

Let TINY be the smallest representable positive f32. Then,

  • if self.is_nan(), this returns self;
  • if self is INFINITY, this returns MAX;
  • if self is TINY, this returns 0.0;
  • if self is -0.0 or +0.0, this returns -TINY;
  • if self is MIN or NEG_INFINITY, this returns NEG_INFINITY;
  • otherwise the unique greatest value less than self is returned.

The identity x.next_down() == -(-x).next_up() holds for all non-NaN x. When x is finite x == x.next_down().next_up() also holds.

#![feature(float_next_up_down)]
let x = 1.0f32;
// Clamp value into range [0, 1).
let clamped = x.clamp(0.0, 1.0f32.next_down());
assert!(clamped < 1.0);
assert_eq!(clamped.next_up(), 1.0);
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, ignoring NaN.

If one of the arguments is NaN, then the other argument is returned. This follows the IEEE 754-2008 semantics for maxNum, except for handling of signaling NaNs; this function handles all NaNs the same way and avoids maxNum’s problems with associativity. This also matches the behavior of libm’s fmax.

let x = 1.0f32;
let y = 2.0f32;

assert_eq!(x.max(y), y);
Run

Returns the minimum of the two numbers, ignoring NaN.

If one of the arguments is NaN, then the other argument is returned. This follows the IEEE 754-2008 semantics for minNum, except for handling of signaling NaNs; this function handles all NaNs the same way and avoids minNum’s problems with associativity. This also matches the behavior of libm’s fmin.

let x = 1.0f32;
let y = 2.0f32;

assert_eq!(x.min(y), x);
Run
🔬This is a nightly-only experimental API. (float_minimum_maximum #91079)

Returns the maximum of the two numbers, propagating NaN.

This returns NaN when either argument is NaN, as opposed to f32::max which only returns NaN when both arguments are NaN.

#![feature(float_minimum_maximum)]
let x = 1.0f32;
let y = 2.0f32;

assert_eq!(x.maximum(y), y);
assert!(x.maximum(f32::NAN).is_nan());
Run

If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater of the two numbers. For this operation, -0.0 is considered to be less than +0.0. Note that this follows the semantics specified in IEEE 754-2019.

Also note that “propagation” of NaNs here doesn’t necessarily mean that the bitpattern of a NaN operand is conserved; see explanation of NaN as a special value for more info.

🔬This is a nightly-only experimental API. (float_minimum_maximum #91079)

Returns the minimum of the two numbers, propagating NaN.

This returns NaN when either argument is NaN, as opposed to f32::min which only returns NaN when both arguments are NaN.

#![feature(float_minimum_maximum)]
let x = 1.0f32;
let y = 2.0f32;

assert_eq!(x.minimum(y), x);
assert!(x.minimum(f32::NAN).is_nan());
Run

If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser of the two numbers. For this operation, -0.0 is considered to be less than +0.0. Note that this follows the semantics specified in IEEE 754-2019.

Also note that “propagation” of NaNs here doesn’t necessarily mean that the bitpattern of a NaN operand is conserved; see explanation of NaN as a special value for more info.

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 big-endian (network) byte order.

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

Examples
let bytes = 12.5f32.to_be_bytes();
assert_eq!(bytes, [0x41, 0x48, 0x00, 0x00]);
Run

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

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

Examples
let bytes = 12.5f32.to_le_bytes();
assert_eq!(bytes, [0x00, 0x00, 0x48, 0x41]);
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.

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

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 big endian.

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

Examples
let value = f32::from_be_bytes([0x41, 0x48, 0x00, 0x00]);
assert_eq!(value, 12.5);
Run

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

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

Examples
let value = f32::from_le_bytes([0x00, 0x00, 0x48, 0x41]);
assert_eq!(value, 12.5);
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.

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

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

Return the ordering between self and other.

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

  • 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.

The ordering established by this function does not always agree with the PartialOrd and PartialEq implementations of f32. For example, they consider negative and positive zero equal, while total_cmp doesn’t.

The interpretation of the signaling NaN bit follows the definition in the IEEE 754 standard, which may not match the interpretation by some of the older, non-conformant (e.g. MIPS) hardware implementations.

Example
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

The resulting type after applying the + operator.
Performs the + operation. Read more
The resulting type after applying the + operator.
Performs the + operation. Read more
The resulting type after applying the + operator.
Performs the + operation. Read more
The resulting type after applying the + operator.
Performs the + operation. Read more
Performs the += operation. Read more
Performs the += operation. Read more
Returns a copy of the value. Read more
Performs copy-assignment from source. Read more
Formats the value using the given formatter. Read more

Returns the default value of 0.0

The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
The resulting type after applying the / operator.
Performs the / operation. Read more
Performs the /= operation. Read more
Performs the /= operation. Read more

Converts f32 to f64 losslessly.

Converts i16 to f32 losslessly.

Converts i8 to f32 losslessly.

Converts u16 to f32 losslessly.

Converts u8 to f32 losslessly.

The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
The resulting type after applying the * operator.
Performs the * operation. Read more
Performs the *= operation. Read more
Performs the *= operation. Read more
The resulting type after applying the - operator.
Performs the unary - operation. Read more
The resulting type after applying the - operator.
Performs the unary - operation. Read more
This method tests for self and other values to be equal, and is used by ==. Read more
This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason. 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
This method tests greater than (for self and other) and is used by the > operator. Read more
Method which takes an iterator and generates Self from the elements by multiplying the items. Read more
Method which takes an iterator and generates Self from the elements by multiplying the items. Read more
The resulting type after applying the % operator.
Performs the % operation. Read more
The resulting type after applying the % operator.
Performs the % operation. Read more
The resulting type after applying the % operator.
Performs the % operation. 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
The resulting type after applying the % operator.
Performs the % operation. Read more
Performs the %= operation. Read more
Performs the %= operation. Read more
🔬This is a nightly-only experimental API. (portable_simd #86656)
The mask element type corresponding to this element type.
The resulting type after applying the - operator.
Performs the - operation. Read more
The resulting type after applying the - operator.
Performs the - operation. Read more
The resulting type after applying the - operator.
Performs the - operation. Read more
The resulting type after applying the - operator.
Performs the - operation. Read more
Performs the -= operation. Read more
Performs the -= operation. Read more
Method which takes an iterator and generates Self from the elements by “summing up” the items. Read more
Method which takes an iterator and generates Self from the elements by “summing up” the items. Read more

Auto Trait Implementations

Blanket Implementations

Gets the TypeId of self. Read more
Immutably borrows from an owned value. Read more
Mutably borrows from an owned value. Read more

Returns the argument unchanged.

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

The type returned in the event of a conversion error.
Performs the conversion.
The type returned in the event of a conversion error.
Performs the conversion.
This documentation is an old archive. Please see https://rust.docs.kernel.org instead.