Number of significant digits in base 2.

Note that the size of the mantissa in the bitwise representation is one smaller than this since the leading 1 is not stored explicitly.

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 f64 and back without loss.

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

Smallest finite f64 value.

Equal to −MAX.

Smallest positive normal f64 value.

Equal to 2^{MIN_EXP − 1}.

One greater than the minimum possible normal power of 2 exponent for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).

This corresponds to the exact minimum possible normal power of 2 exponent for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition). In other words, all normal numbers representable by this type are greater than or equal to 0.5 × 2^MIN_EXP.

One greater than the maximum possible power of 2 exponent for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).

This corresponds to the exact maximum possible power of 2 exponent for a significand bounded by 0.5 ≤ x < 1 (i.e. the C definition). In other words, all numbers representable by this type are strictly less than 2^MAX_EXP.

Minimum x for which 10^x is normal.

Equal to ceil(log₁₀ MIN_POSITIVE).

Maximum x for which 10^x is normal.

Equal to floor(log₁₀ MAX).

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) and its sign. See the specification of NaN bit patterns for more info.

This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptions that the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing is guaranteed about the specific bit pattern chosen here: both payload and sign are arbitrary. The concrete bit pattern may change across Rust versions and target platforms.

Maximum integer that can be represented exactly in an f64 value, with no other integer converting to the same floating point value.

For an integer x which satisfies MIN_EXACT_INTEGER <= x <= MAX_EXACT_INTEGER, there is a “one-to-one” mapping between i64 and f64 values. MAX_EXACT_INTEGER + 1 also converts losslessly to f64 and back to i64, but MAX_EXACT_INTEGER + 2 converts to the same f64 value (and back to MAX_EXACT_INTEGER + 1 as an integer) so there is not a “one-to-one” mapping.

#![feature(float_exact_integer_constants)]
let max_exact_int = f64::MAX_EXACT_INTEGER;
assert_eq!(max_exact_int, max_exact_int as f64 as i64);
assert_eq!(max_exact_int + 1, (max_exact_int + 1) as f64 as i64);
assert_ne!(max_exact_int + 2, (max_exact_int + 2) as f64 as i64);

// Beyond `f64::MAX_EXACT_INTEGER`, multiple integers can map to one float value
assert_eq!((max_exact_int + 1) as f64, (max_exact_int + 2) as f64);

Minimum integer that can be represented exactly in an f64 value, with no other integer converting to the same floating point value.

For an integer x which satisfies MIN_EXACT_INTEGER <= x <= MAX_EXACT_INTEGER, there is a “one-to-one” mapping between i64 and f64 values. MAX_EXACT_INTEGER + 1 also converts losslessly to f64 and back to i64, but MAX_EXACT_INTEGER + 2 converts to the same f64 value (and back to MAX_EXACT_INTEGER + 1 as an integer) so there is not a “one-to-one” mapping.

This constant is equivalent to -MAX_EXACT_INTEGER.

#![feature(float_exact_integer_constants)]
let min_exact_int = f64::MIN_EXACT_INTEGER;
assert_eq!(min_exact_int, min_exact_int as f64 as i64);
assert_eq!(min_exact_int - 1, (min_exact_int - 1) as f64 as i64);
assert_ne!(min_exact_int - 2, (min_exact_int - 2) as f64 as i64);

// Below `f64::MIN_EXACT_INTEGER`, multiple integers can map to one float value
assert_eq!((min_exact_int - 1) as f64, (min_exact_int - 2) as f64);

Returns true if this value is NaN.

let nan = f64::NAN;
let f = 7.0_f64;

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

Returns true if this value is positive infinity or negative infinity, and false otherwise.

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());

Returns true if this number is neither infinite nor NaN.

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());

Returns true if the number is subnormal.

let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308_f64
let max = f64::MAX;
let lower_than_min = 1.0e-308_f64;
let zero = 0.0_f64;

assert!(!min.is_subnormal());
assert!(!max.is_subnormal());

assert!(!zero.is_subnormal());
assert!(!f64::NAN.is_subnormal());
assert!(!f64::INFINITY.is_subnormal());
// Values between `0` and `min` are Subnormal.
assert!(lower_than_min.is_subnormal());

Returns true if the number is neither zero, infinite, subnormal, or NaN.

let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308f64
let max = f64::MAX;
let lower_than_min = 1.0e-308_f64;
let zero = 0.0f64;

assert!(min.is_normal());
assert!(max.is_normal());

assert!(!zero.is_normal());
assert!(!f64::NAN.is_normal());
assert!(!f64::INFINITY.is_normal());
// Values between `0` and `min` are Subnormal.
assert!(!lower_than_min.is_normal());

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_f64;
let inf = f64::INFINITY;

assert_eq!(num.classify(), FpCategory::Normal);
assert_eq!(inf.classify(), FpCategory::Infinite);

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 or non-portable result. See the specification of NaN bit patterns for more info. Use self.signum() == 1.0 if you need fully portable behavior (will return false for all NaNs).

let f = 7.0_f64;
let g = -7.0_f64;

assert!(f.is_sign_positive());
assert!(!g.is_sign_positive());

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 or non-portable result. See the specification of NaN bit patterns for more info. Use self.signum() == -1.0 if you need fully portable behavior (will return false for all NaNs).

let f = 7.0_f64;
let g = -7.0_f64;

assert!(!f.is_sign_negative());
assert!(g.is_sign_negative());

Returns the least number greater than self.

Let TINY be the smallest representable positive f64. 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.

// f64::EPSILON is the difference between 1.0 and the next number up.
assert_eq!(1.0f64.next_up(), 1.0 + f64::EPSILON);
// But not for most numbers.
assert!(0.1f64.next_up() < 0.1 + f64::EPSILON);
assert_eq!(9007199254740992f64.next_up(), 9007199254740994.0);

This operation corresponds to IEEE-754 nextUp.

Returns the greatest number less than self.

Let TINY be the smallest representable positive f64. 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.

let x = 1.0f64;
// Clamp value into range [0, 1).
let clamped = x.clamp(0.0, 1.0f64.next_down());
assert!(clamped < 1.0);
assert_eq!(clamped.next_up(), 1.0);

This operation corresponds to IEEE-754 nextDown.

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);

Converts radians to degrees.

§Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

§Examples

let angle = std::f64::consts::PI;

let abs_difference = (angle.to_degrees() - 180.0).abs();

assert!(abs_difference < 1e-10);

Converts degrees to radians.

§Unspecified precision

The precision of this function is non-deterministic. This means it varies by platform, Rust version, and can even differ within the same execution from one invocation to the next.

§Examples

let angle = 180.0_f64;

let abs_difference = (angle.to_radians() - std::f64::consts::PI).abs();

assert!(abs_difference < 1e-10);

Returns the maximum of the two numbers, ignoring NaN.

If exactly one of the arguments is NaN (quiet or signaling), then the other argument is returned. If both arguments are NaN, the return value is NaN, with the bit pattern picked using the usual rules for arithmetic operations. If the inputs compare equal (such as for the case of +0.0 and -0.0), either input may be returned non-deterministically.

The handling of NaNs follows the IEEE 754-2019 semantics for maximumNumber, treating all NaNs the same way to ensure the operation is associative. The handling of signed zeros follows the IEEE 754-2008 semantics for maxNum.

let x = 1.0_f64;
let y = 2.0_f64;

assert_eq!(x.max(y), y);
assert_eq!(x.max(f64::NAN), x);

Returns the minimum of the two numbers, ignoring NaN.

If exactly one of the arguments is NaN (quiet or signaling), then the other argument is returned. If both arguments are NaN, the return value is NaN, with the bit pattern picked using the usual rules for arithmetic operations. If the inputs compare equal (such as for the case of +0.0 and -0.0), either input may be returned non-deterministically.

The handling of NaNs follows the IEEE 754-2019 semantics for minimumNumber, treating all NaNs the same way to ensure the operation is associative. The handling of signed zeros follows the IEEE 754-2008 semantics for minNum.

let x = 1.0_f64;
let y = 2.0_f64;

assert_eq!(x.min(y), x);
assert_eq!(x.min(f64::NAN), x);

Returns the maximum of the two numbers, propagating NaN.

If at least one of the arguments is NaN, the return value is NaN, with the bit pattern picked using the usual rules for arithmetic operations. Furthermore, -0.0 is considered to be less than +0.0, making this function fully deterministic for non-NaN inputs.

This is in contrast to f64::max which only returns NaN when both arguments are NaN, and which does not reliably order -0.0 and +0.0.

This follows the IEEE 754-2019 semantics for maximum.

#![feature(float_minimum_maximum)]
let x = 1.0_f64;
let y = 2.0_f64;

assert_eq!(x.maximum(y), y);
assert!(x.maximum(f64::NAN).is_nan());

Returns the minimum of the two numbers, propagating NaN.

If at least one of the arguments is NaN, the return value is NaN, with the bit pattern picked using the usual rules for arithmetic operations. Furthermore, -0.0 is considered to be less than +0.0, making this function fully deterministic for non-NaN inputs.

This is in contrast to f64::min which only returns NaN when both arguments are NaN, and which does not reliably order -0.0 and +0.0.

This follows the IEEE 754-2019 semantics for minimum.

#![feature(float_minimum_maximum)]
let x = 1.0_f64;
let y = 2.0_f64;

assert_eq!(x.minimum(y), x);
assert!(x.minimum(f64::NAN).is_nan());

Calculates the midpoint (average) between self and rhs.

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

§Examples

assert_eq!(1f64.midpoint(4.0), 2.5);
assert_eq!((-5.5f64).midpoint(8.0), 1.25);

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_f64;
let rounded = unsafe { value.to_int_unchecked::<u16>() };
assert_eq!(rounded, 4);

let value = -128.9_f64;
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

Raw transmutation to u64.

This is currently identical to transmute::<f64, u64>(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!((1f64).to_bits() != 1f64 as u64); // to_bits() is not casting!
assert_eq!((12.5f64).to_bits(), 0x4029000000000000);

Raw transmutation from u64.

This is currently identical to transmute::<u64, f64>(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 signaling-ness (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 = f64::from_bits(0x4029000000000000);
assert_eq!(v, 12.5);

Returns 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 = 12.5f64.to_be_bytes();
assert_eq!(bytes, [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);

Returns 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 = 12.5f64.to_le_bytes();
assert_eq!(bytes, [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);

Returns 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 = 12.5f64.to_ne_bytes();
assert_eq!(
    bytes,
    if cfg!(target_endian = "big") {
        [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
    } else {
        [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
    }
);

Creates 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 = f64::from_be_bytes([0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
assert_eq!(value, 12.5);

Creates 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 = f64::from_le_bytes([0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]);
assert_eq!(value, 12.5);

Creates 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 = f64::from_ne_bytes(if cfg!(target_endian = "big") {
    [0x40, 0x29, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]
} else {
    [0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x29, 0x40]
});
assert_eq!(value, 12.5);

Returns 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 f64. 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: f64,
}

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: f64::INFINITY },
    GoodBoy { name: "Abs. Unit".to_owned(), weight: f64::NAN },
    GoodBoy { name: "Floaty".to_owned(), weight: -5.0 },
];

bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));

// `f64::NAN` could be positive or negative, which will affect the sort order.
if f64::NAN.is_sign_negative() {
    assert!(bois.into_iter().map(|b| b.weight)
        .zip([f64::NAN, -5.0, 0.1, 10.0, 99.0, f64::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, f64::INFINITY, f64::NAN].iter())
        .all(|(a, b)| a.to_bits() == b.to_bits()))
}

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. If the result is zero and among the three inputs self, min, and max there are zeros with different sign, either 0.0 or -0.0 is returned non-deterministically.

§Panics

Panics if min > max, min is NaN, or max is NaN.

§Examples

assert!((-3.0f64).clamp(-2.0, 1.0) == -2.0);
assert!((0.0f64).clamp(-2.0, 1.0) == 0.0);
assert!((2.0f64).clamp(-2.0, 1.0) == 1.0);
assert!((f64::NAN).clamp(-2.0, 1.0).is_nan());

// These always returns zero, but the sign (which is ignored by `==`) is non-deterministic.
assert!((0.0f64).clamp(-0.0, -0.0) == 0.0);
assert!((1.0f64).clamp(-0.0, 0.0) == 0.0);
// This is definitely a negative zero.
assert!((-1.0f64).clamp(-0.0, 1.0).is_sign_negative());

Clamps this number to a symmetric range centered around zero.

The method clamps the number’s magnitude (absolute value) to be at most limit.

This is functionally equivalent to self.clamp(-limit, limit), but is more explicit about the intent.

§Panics

Panics if limit is negative or NaN, as this indicates a logic error.

§Examples

#![feature(clamp_magnitude)]
assert_eq!(5.0f64.clamp_magnitude(3.0), 3.0);
assert_eq!((-5.0f64).clamp_magnitude(3.0), -3.0);
assert_eq!(2.0f64.clamp_magnitude(3.0), 2.0);
assert_eq!((-2.0f64).clamp_magnitude(3.0), -2.0);

Computes the absolute value of self.

This function always returns the precise result.

§Examples

let x = 3.5_f64;
let y = -3.5_f64;

assert_eq!(x.abs(), x);
assert_eq!(y.abs(), -y);

assert!(f64::NAN.abs().is_nan());

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_f64;

assert_eq!(f.signum(), 1.0);
assert_eq!(f64::NEG_INFINITY.signum(), -1.0);

assert!(f64::NAN.signum().is_nan());

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 same payload as self and the sign bit of sign is returned.

If sign is a NaN, then this operation will still carry over its sign into the result. 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 copysign with sign being a NaN might produce an unexpected or non-portable result. See the specification of NaN bit patterns for more info.

§Examples

let f = 3.5_f64;

assert_eq!(f.copysign(0.42), 3.5_f64);
assert_eq!(f.copysign(-0.42), -3.5_f64);
assert_eq!((-f).copysign(0.42), 3.5_f64);
assert_eq!((-f).copysign(-0.42), -3.5_f64);

assert!(f64::NAN.copysign(1.0).is_nan());

Float addition that allows optimizations based on algebraic rules.

See algebraic operators for more info.

Float subtraction that allows optimizations based on algebraic rules.

See algebraic operators for more info.

Float multiplication that allows optimizations based on algebraic rules.

See algebraic operators for more info.

Float division that allows optimizations based on algebraic rules.

See algebraic operators for more info.

Float remainder that allows optimizations based on algebraic rules.

See algebraic operators for more info.

Converts a bool to f64 losslessly. The resulting value is positive 0.0 for false and 1.0 for true values.

§Examples

let x: f64 = false.into();
assert_eq!(x, 0.0);
assert!(x.is_sign_positive());

let y: f64 = true.into();
assert_eq!(y, 1.0);

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’
• ‘7’
• ‘007’
• ‘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).