Primitive Type f32

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 not equal 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 a primitive operation (addition, subtraction, multiplication, or division) is performed on this type, the result 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).
• If the result of a sum exactly equals zero, the outcome is +0.0 unless both arguments were negative, then it is -0.0. Subtraction a - b is regarded as a sum a + (-b).

For more information on floating point numbers, see Wikipedia.

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

Implementations

impl f32

pub fn floor(self) -> f32

Returns the largest integer less than or equal to self.

Examples

let f = 3.7_f32;
let g = 3.0_f32;
let h = -3.7_f32;

assert_eq!(f.floor(), 3.0);
assert_eq!(g.floor(), 3.0);
assert_eq!(h.floor(), -4.0);

pub fn ceil(self) -> f32

Returns the smallest integer greater than or equal to self.

Examples

let f = 3.01_f32;
let g = 4.0_f32;

assert_eq!(f.ceil(), 4.0);
assert_eq!(g.ceil(), 4.0);

pub fn round(self) -> f32

Returns the nearest integer to self. If a value is half-way between two integers, round away from 0.0.

Examples

let f = 3.3_f32;
let g = -3.3_f32;
let h = -3.7_f32;
let i = 3.5_f32;
let j = 4.5_f32;

assert_eq!(f.round(), 3.0);
assert_eq!(g.round(), -3.0);
assert_eq!(h.round(), -4.0);
assert_eq!(i.round(), 4.0);
assert_eq!(j.round(), 5.0);

pub fn round_ties_even(self) -> f32

🔬This is a nightly-only experimental API. (round_ties_even #96710)

Returns the nearest integer to a number. Rounds half-way cases to the number with an even least significant digit.

Examples

#![feature(round_ties_even)]

let f = 3.3_f32;
let g = -3.3_f32;
let h = 3.5_f32;
let i = 4.5_f32;

assert_eq!(f.round_ties_even(), 3.0);
assert_eq!(g.round_ties_even(), -3.0);
assert_eq!(h.round_ties_even(), 4.0);
assert_eq!(i.round_ties_even(), 4.0);

pub fn trunc(self) -> f32

Returns the integer part of self. This means that non-integer numbers are always truncated towards zero.

Examples

let f = 3.7_f32;
let g = 3.0_f32;
let h = -3.7_f32;

assert_eq!(f.trunc(), 3.0);
assert_eq!(g.trunc(), 3.0);
assert_eq!(h.trunc(), -3.0);

pub fn fract(self) -> f32

Returns the fractional part of self.

Examples

let x = 3.6_f32;
let y = -3.6_f32;
let abs_difference_x = (x.fract() - 0.6).abs();
let abs_difference_y = (y.fract() - (-0.6)).abs();

assert!(abs_difference_x <= f32::EPSILON);
assert!(abs_difference_y <= f32::EPSILON);

pub fn abs(self) -> f32

Computes the absolute value of self.

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());

pub 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

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());

pub fn copysign(self, sign: f32) -> f32

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 bit of sign is returned. Note, however, that conserving the sign bit on NaN across arithmetical operations is not generally guaranteed. See explanation of NaN as a special value for more info.

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());

pub fn mul_add(self, a: f32, b: f32) -> f32

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);

pub fn div_euclid(self, rhs: f32) -> f32

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 * 2.0

pub fn rem_euclid(self, rhs: f32) -> f32

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) approximately.

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);

pub fn powi(self, n: i32) -> f32

Raises a number to an integer power.

Using this function is generally faster than using powf. It might have a different sequence of rounding operations than powf, so the results are not guaranteed to agree.

Examples

let x = 2.0_f32;
let abs_difference = (x.powi(2) - (x * x)).abs();

assert!(abs_difference <= f32::EPSILON);

pub fn powf(self, n: f32) -> f32

Raises a number to a floating point power.

Examples

let x = 2.0_f32;
let abs_difference = (x.powf(2.0) - (x * x)).abs();

assert!(abs_difference <= f32::EPSILON);

pub fn sqrt(self) -> f32

Returns the square root of a number.

Returns NaN if self is a negative number other than -0.0.

Examples

let positive = 4.0_f32;
let negative = -4.0_f32;
let negative_zero = -0.0_f32;

let abs_difference = (positive.sqrt() - 2.0).abs();

assert!(abs_difference <= f32::EPSILON);
assert!(negative.sqrt().is_nan());
assert!(negative_zero.sqrt() == negative_zero);

pub fn exp(self) -> f32

Returns e^(self), (the exponential function).

Examples

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);

pub fn exp2(self) -> f32

Returns 2^(self).

Examples

let f = 2.0f32;

// 2^2 - 4 == 0
let abs_difference = (f.exp2() - 4.0).abs();

assert!(abs_difference <= f32::EPSILON);

pub fn ln(self) -> f32

Returns the natural logarithm of the number.

Examples

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);

pub fn log(self, base: f32) -> f32

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

The result might 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);

pub fn log2(self) -> f32

Returns the base 2 logarithm of the number.

Examples

let two = 2.0f32;

// log2(2) - 1 == 0
let abs_difference = (two.log2() - 1.0).abs();

assert!(abs_difference <= f32::EPSILON);

pub fn log10(self) -> f32

Returns the base 10 logarithm of the number.

Examples

let ten = 10.0f32;

// log10(10) - 1 == 0
let abs_difference = (ten.log10() - 1.0).abs();

assert!(abs_difference <= f32::EPSILON);

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

👎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).

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);

pub fn cbrt(self) -> f32

Returns the cube root of a number.

Examples

let x = 8.0f32;

// x^(1/3) - 2 == 0
let abs_difference = (x.cbrt() - 2.0).abs();

assert!(abs_difference <= f32::EPSILON);

pub fn hypot(self, other: f32) -> f32

Compute the distance between the origin and a point (x, y) on the Euclidean plane. Equivalently, compute the length of the hypotenuse of a right-angle triangle with other sides having length x.abs() and y.abs().

Examples

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);

pub fn sin(self) -> f32

Computes the sine of a number (in radians).

Examples

let x = std::f32::consts::FRAC_PI_2;

let abs_difference = (x.sin() - 1.0).abs();

assert!(abs_difference <= f32::EPSILON);

pub fn cos(self) -> f32

Computes the cosine of a number (in radians).

Examples

let x = 2.0 * std::f32::consts::PI;

let abs_difference = (x.cos() - 1.0).abs();

assert!(abs_difference <= f32::EPSILON);

pub fn tan(self) -> f32

Computes the tangent of a number (in radians).

Examples

let x = std::f32::consts::FRAC_PI_4;
let abs_difference = (x.tan() - 1.0).abs();

assert!(abs_difference <= f32::EPSILON);

pub 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].

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);

pub 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].

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);

pub fn atan(self) -> f32

Computes the arctangent of a number. Return value is in radians in the range [-pi/2, pi/2];

Examples

let f = 1.0f32;

// atan(tan(1))
let abs_difference = (f.tan().atan() - 1.0).abs();

assert!(abs_difference <= f32::EPSILON);

pub fn atan2(self, other: f32) -> f32

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);

pub fn sin_cos(self) -> (f32, f32)

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);

pub fn exp_m1(self) -> f32

Returns e^(self) - 1 in a way that is accurate even if the number is close to zero.

Examples

let x = 1e-8_f32;

// for very small x, e^x is approximately 1 + x + x^2 / 2
let approx = x + x * x / 2.0;
let abs_difference = (x.exp_m1() - approx).abs();

assert!(abs_difference < 1e-10);

pub fn ln_1p(self) -> f32

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);

pub fn sinh(self) -> f32

Hyperbolic sine function.

Examples

let e = std::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);

pub fn cosh(self) -> f32

Hyperbolic cosine function.

Examples

let e = std::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 - g).abs();

// Same result
assert!(abs_difference <= f32::EPSILON);

pub fn tanh(self) -> f32

Hyperbolic tangent function.

Examples

let e = std::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);

pub fn asinh(self) -> f32

Inverse hyperbolic sine function.

Examples

let x = 1.0f32;
let f = x.sinh().asinh();

let abs_difference = (f - x).abs();

assert!(abs_difference <= f32::EPSILON);

pub fn acosh(self) -> f32

Inverse hyperbolic cosine function.

Examples

let x = 1.0f32;
let f = x.cosh().acosh();

let abs_difference = (f - x).abs();

assert!(abs_difference <= f32::EPSILON);

pub fn atanh(self) -> f32

Inverse hyperbolic tangent function.

Examples

let e = std::f32::consts::E;
let f = e.tanh().atanh();

let abs_difference = (f - e).abs();

assert!(abs_difference <= 1e-5);

pub fn gamma(self) -> f32

🔬This is a nightly-only experimental API. (float_gamma #99842)

Gamma function.

Examples

#![feature(float_gamma)]
let x = 5.0f32;

let abs_difference = (x.gamma() - 24.0).abs();

assert!(abs_difference <= f32::EPSILON);

pub fn ln_gamma(self) -> (f32, i32)

🔬This is a nightly-only experimental API. (float_gamma #99842)

Natural logarithm of the absolute value of the gamma function

The integer part of the tuple indicates the sign of the gamma function.

Examples

#![feature(float_gamma)]
let x = 2.0f32;

let abs_difference = (x.ln_gamma().0 - 0.0).abs();

assert!(abs_difference <= f32::EPSILON);

impl f32

pub const RADIX: u32 = 2u32

The radix or base of the internal representation of f32.

pub const MANTISSA_DIGITS: u32 = 24u32

Number of significant digits in base 2.

pub const DIGITS: u32 = 6u32

Approximate number of significant digits in base 10.

This is the maximum x such that any decimal number with x significant digits can be converted to f32 and back without loss.

Equal to floor(log₁₀ 2^{MANTISSA_DIGITS − 1}).

pub const EPSILON: f32 = 1.1920929E-7f32

Machine epsilon value for f32.

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

Equal to 2^{1 − MANTISSA_DIGITS}.

pub const MIN: f32 = -3.40282347E+38f32

Smallest finite f32 value.

Equal to −MAX.

pub const MIN_POSITIVE: f32 = 1.17549435E-38f32

Smallest positive normal f32 value.

Equal to 2^{MIN_EXP − 1}.

pub const MAX: f32 = 3.40282347E+38f32

Largest finite f32 value.

Equal to (1 − 2^{−MANTISSA_DIGITS}) 2^MAX_EXP.

pub const MIN_EXP: i32 = -125i32

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

If x = MIN_EXP, then normal numbers ≥ 0.5 × 2^x.

pub const MAX_EXP: i32 = 128i32

Maximum possible power of 2 exponent.

If x = MAX_EXP, then normal numbers < 1 × 2^x.

pub const MIN_10_EXP: i32 = -37i32

Minimum x for which 10^x is normal.

Equal to ceil(log₁₀ MIN_POSITIVE).

pub const MAX_10_EXP: i32 = 38i32

Maximum x for which 10^x is normal.

Equal to floor(log₁₀ MAX).

pub const NAN: f32 = NaNf32

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.

pub const INFINITY: f32 = +Inff32

Infinity (∞).

pub const NEG_INFINITY: f32 = -Inff32

Negative infinity (−∞).

pub fn is_nan(self) -> bool

Returns true if this value is NaN.

let nan = f32::NAN;
let f = 7.0_f32;

assert!(nan.is_nan());
assert!(!f.is_nan());

pub fn is_infinite(self) -> bool

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());

pub fn is_finite(self) -> bool

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());

pub fn is_subnormal(self) -> bool

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());

pub fn is_normal(self) -> bool

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());

pub 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.

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);

pub fn is_sign_positive(self) -> bool

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());

pub fn is_sign_negative(self) -> bool

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());

pub fn next_up(self) -> f32

🔬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);

pub fn next_down(self) -> f32

🔬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);

pub fn recip(self) -> f32

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);

pub fn to_degrees(self) -> f32

Converts radians to degrees.

let angle = std::f32::consts::PI;

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

pub fn to_radians(self) -> f32

Converts degrees to radians.

let angle = 180.0f32;

let abs_difference = (angle.to_radians() - std::f32::consts::PI).abs();

assert!(abs_difference <= f32::EPSILON);

pub fn max(self, other: f32) -> f32

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);

pub fn min(self, other: f32) -> f32

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);

pub fn maximum(self, other: f32) -> f32

🔬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());

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.

pub fn minimum(self, other: f32) -> f32

🔬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());

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.

pub fn midpoint(self, other: f32) -> f32

🔬This is a nightly-only experimental API. (num_midpoint #110840)

Calculates the middle point of self and rhs.

This returns NaN when either argument is NaN or if a combination of +inf and -inf is provided as arguments.

Examples

#![feature(num_midpoint)]
assert_eq!(1f32.midpoint(4.0), 2.5);
assert_eq!((-5.5f32).midpoint(8.0), 1.25);

pub unsafe fn to_int_unchecked<Int>(self) -> Intwhere f32: FloatToInt<Int>,

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);

Safety

The value must:

• Not be NaN
• Not be infinite
• Be representable in the return type Int, after truncating off its fractional part

pub fn to_bits(self) -> u32

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);

pub fn from_bits(v: u32) -> f32

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);

pub fn to_be_bytes(self) -> [u8; 4]

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]);

pub fn to_le_bytes(self) -> [u8; 4]

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]);

pub fn to_ne_bytes(self) -> [u8; 4]

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]
    }
);

pub fn from_be_bytes(bytes: [u8; 4]) -> f32

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);

pub fn from_le_bytes(bytes: [u8; 4]) -> f32

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);

pub fn from_ne_bytes(bytes: [u8; 4]) -> f32

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);

pub fn total_cmp(&self, other: &f32) -> Ordering

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));

// `f32::NAN` could be positive or negative, which will affect the sort order.
if f32::NAN.is_sign_negative() {
    assert!(bois.into_iter().map(|b| b.weight)
        .zip([f32::NAN, -5.0, 0.1, 10.0, 99.0, f32::INFINITY].iter())
        .all(|(a, b)| a.to_bits() == b.to_bits()))
} else {
    assert!(bois.into_iter().map(|b| b.weight)
        .zip([-5.0, 0.1, 10.0, 99.0, f32::INFINITY, f32::NAN].iter())
        .all(|(a, b)| a.to_bits() == b.to_bits()))
}

pub fn clamp(self, min: f32, max: f32) -> f32

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());

Trait Implementations

impl Add<&f32> for &f32

type Output = <f32 as Add>::Output

The resulting type after applying the + operator.

fn add(self, other: &f32) -> <f32 as Add>::Output

Performs the + operation.

impl Add<&f32> for f32

type Output = <f32 as Add>::Output

The resulting type after applying the + operator.

fn add(self, other: &f32) -> <f32 as Add>::Output

Performs the + operation.

impl<'a> Add<f32> for &'a f32

type Output = <f32 as Add>::Output

The resulting type after applying the + operator.

fn add(self, other: f32) -> <f32 as Add>::Output

Performs the + operation.

impl Add for f32

type Output = f32

The resulting type after applying the + operator.

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

Performs the + operation.

impl AddAssign<&f32> for f32

fn add_assign(&mut self, other: &f32)

Performs the += operation.

impl AddAssign for f32

fn add_assign(&mut self, other: f32)

Performs the += operation.

impl Clone for f32

fn clone(&self) -> f32

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for f32

fn fmt(&self, fmt: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl Default for f32

fn default() -> f32

Returns the default value of 0.0

impl Display for f32

fn fmt(&self, fmt: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl Div<&f32> for &f32

type Output = <f32 as Div>::Output

The resulting type after applying the / operator.

fn div(self, other: &f32) -> <f32 as Div>::Output

Performs the / operation.

impl Div<&f32> for f32

type Output = <f32 as Div>::Output

The resulting type after applying the / operator.

fn div(self, other: &f32) -> <f32 as Div>::Output

Performs the / operation.

impl<'a> Div<f32> for &'a f32

type Output = <f32 as Div>::Output

The resulting type after applying the / operator.

fn div(self, other: f32) -> <f32 as Div>::Output

Performs the / operation.

impl Div for f32

type Output = f32

The resulting type after applying the / operator.

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

Performs the / operation.

impl DivAssign<&f32> for f32

fn div_assign(&mut self, other: &f32)

Performs the /= operation.

impl DivAssign for f32

fn div_assign(&mut self, other: f32)

Performs the /= operation.

impl From<bool> for f32

fn from(small: bool) -> f32

Converts bool to f32 losslessly. The resulting value is positive 0.0 for false and 1.0 for true values.

Examples

let x: f32 = false.into();
assert_eq!(x, 0.0);
assert!(x.is_sign_positive());

let y: f32 = true.into();
assert_eq!(y, 1.0);

impl From<f32> for f64

fn from(small: f32) -> f64

Converts f32 to f64 losslessly.

impl From<i16> for f32

fn from(small: i16) -> f32

Converts i16 to f32 losslessly.

impl From<i8> for f32

fn from(small: i8) -> f32

Converts i8 to f32 losslessly.

impl From<u16> for f32

fn from(small: u16) -> f32

Converts u16 to f32 losslessly.

impl From<u8> for f32

fn from(small: u8) -> f32

Converts u8 to f32 losslessly.

impl FromStr for f32

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’
• ‘2.5E10’, or equivalently, ‘2.5e10’
• ‘2.5E-10’
• ‘5.’
• ‘.5’, or, equivalently, ‘0.5’
• ‘inf’, ‘-inf’, ‘+infinity’, ‘NaN’

Note that alphabetical characters are not case-sensitive.

Leading and trailing whitespace represent an error.

Grammar

All strings that adhere to the following EBNF grammar when lowercased will result in an Ok being returned:

Float  ::= Sign? ( 'inf' | 'infinity' | 'nan' | Number )
Number ::= ( Digit+ |
             Digit+ '.' Digit* |
             Digit* '.' Digit+ ) Exp?
Exp    ::= 'e' Sign? Digit+
Sign   ::= [+-]
Digit  ::= [0-9]

Arguments

• src - A string

Return value

Err(ParseFloatError) if the string did not represent a valid number. Otherwise, Ok(n) where n is the closest representable floating-point number to the number represented by src (following the same rules for rounding as for the results of primitive operations).

type Err = ParseFloatError

The associated error which can be returned from parsing.

impl LowerExp for f32

fn fmt(&self, fmt: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl Mul<&f32> for &f32

type Output = <f32 as Mul>::Output

The resulting type after applying the * operator.

fn mul(self, other: &f32) -> <f32 as Mul>::Output

Performs the * operation.

impl Mul<&f32> for f32

type Output = <f32 as Mul>::Output

The resulting type after applying the * operator.

fn mul(self, other: &f32) -> <f32 as Mul>::Output

Performs the * operation.

impl<'a> Mul<f32> for &'a f32

type Output = <f32 as Mul>::Output

The resulting type after applying the * operator.

fn mul(self, other: f32) -> <f32 as Mul>::Output

Performs the * operation.

impl Mul for f32

type Output = f32

The resulting type after applying the * operator.

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

Performs the * operation.

impl MulAssign<&f32> for f32

fn mul_assign(&mut self, other: &f32)

Performs the *= operation.

impl MulAssign for f32

fn mul_assign(&mut self, other: f32)

Performs the *= operation.

impl Neg for &f32

type Output = <f32 as Neg>::Output

The resulting type after applying the - operator.

fn neg(self) -> <f32 as Neg>::Output

Performs the unary - operation.

impl Neg for f32

type Output = f32

The resulting type after applying the - operator.

fn neg(self) -> f32

Performs the unary - operation.

impl PartialEq for f32

fn eq(&self, other: &f32) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &f32) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl PartialOrd for f32

fn partial_cmp(&self, other: &f32) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &f32) -> bool

This method tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &f32) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

fn ge(&self, other: &f32) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

fn gt(&self, other: &f32) -> bool

This method tests greater than (for self and other) and is used by the > operator.

impl<'a> Product<&'a f32> for f32

fn product<I>(iter: I) -> f32where I: Iterator<Item = &'a f32>,

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl Product for f32

fn product<I>(iter: I) -> f32where I: Iterator<Item = f32>,

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl Rem<&f32> for &f32

type Output = <f32 as Rem>::Output

The resulting type after applying the % operator.

fn rem(self, other: &f32) -> <f32 as Rem>::Output

Performs the % operation.

impl Rem<&f32> for f32

type Output = <f32 as Rem>::Output

The resulting type after applying the % operator.

fn rem(self, other: &f32) -> <f32 as Rem>::Output

Performs the % operation.

impl<'a> Rem<f32> for &'a f32

type Output = <f32 as Rem>::Output

The resulting type after applying the % operator.

fn rem(self, other: f32) -> <f32 as Rem>::Output

Performs the % operation.

impl Rem for f32

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);

type Output = f32

The resulting type after applying the % operator.

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

Performs the % operation.

impl RemAssign<&f32> for f32

fn rem_assign(&mut self, other: &f32)

Performs the %= operation.

impl RemAssign for f32

fn rem_assign(&mut self, other: f32)

Performs the %= operation.

impl SimdElement for f32

type Mask = i32

🔬This is a nightly-only experimental API. (portable_simd #86656)

The mask element type corresponding to this element type.

impl Sub<&f32> for &f32

type Output = <f32 as Sub>::Output

The resulting type after applying the - operator.

fn sub(self, other: &f32) -> <f32 as Sub>::Output

Performs the - operation.

impl Sub<&f32> for f32

type Output = <f32 as Sub>::Output

The resulting type after applying the - operator.

fn sub(self, other: &f32) -> <f32 as Sub>::Output

Performs the - operation.

impl<'a> Sub<f32> for &'a f32

type Output = <f32 as Sub>::Output

The resulting type after applying the - operator.

fn sub(self, other: f32) -> <f32 as Sub>::Output

Performs the - operation.

impl Sub for f32

type Output = f32

The resulting type after applying the - operator.

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

Performs the - operation.

impl SubAssign<&f32> for f32

fn sub_assign(&mut self, other: &f32)

Performs the -= operation.

impl SubAssign for f32

fn sub_assign(&mut self, other: f32)

Performs the -= operation.

impl<'a> Sum<&'a f32> for f32

fn sum<I>(iter: I) -> f32where I: Iterator<Item = &'a f32>,

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl Sum for f32

fn sum<I>(iter: I) -> f32where I: Iterator<Item = f32>,

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl UpperExp for f32

fn fmt(&self, fmt: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl Copy for f32

impl FloatToInt<i128> for f32

impl FloatToInt<i16> for f32

impl FloatToInt<i32> for f32

impl FloatToInt<i64> for f32

impl FloatToInt<i8> for f32

impl FloatToInt<isize> for f32

impl FloatToInt<u128> for f32

impl FloatToInt<u16> for f32

impl FloatToInt<u32> for f32

impl FloatToInt<u64> for f32

impl FloatToInt<u8> for f32

impl FloatToInt<usize> for f32

impl SimdCast for f32