Expand description
A 64-bit floating point type (specifically, the “binary64” type defined in IEEE 754-2008).
This type is very similar to f32
, but has increased
precision by using twice as many bits. Please see the documentation for
f32
or Wikipedia on double precision
values for more information.
Implementations
Computes the absolute value of self
. Returns NAN
if the
number is NAN
.
Examples
let x = 3.5_f64;
let y = -3.5_f64;
let abs_difference_x = (x.abs() - x).abs();
let abs_difference_y = (y.abs() - (-y)).abs();
assert!(abs_difference_x < 1e-10);
assert!(abs_difference_y < 1e-10);
assert!(f64::NAN.abs().is_nan());
RunReturns a number that represents the sign of self
.
1.0
if the number is positive,+0.0
orINFINITY
-1.0
if the number is negative,-0.0
orNEG_INFINITY
NAN
if the number isNAN
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());
RunReturns a number composed of the magnitude of self
and the sign of
sign
.
Equal to self
if the sign of self
and sign
are the same, otherwise
equal to -self
. If self
is a NAN
, then a NAN
with the sign of
sign
is returned.
Examples
let f = 3.5_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());
RunFused 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_f64;
let x = 4.0_f64;
let b = 60.0_f64;
// 100.0
let abs_difference = (m.mul_add(x, b) - ((m * x) + b)).abs();
assert!(abs_difference < 1e-10);
RunCalculates 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: f64 = 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
RunCalculates the least nonnegative remainder of self (mod rhs)
.
In particular, the return value r
satisfies 0.0 <= r < rhs.abs()
in
most cases. However, due to a floating point round-off error it can
result in r == rhs.abs()
, violating the mathematical definition, if
self
is much smaller than rhs.abs()
in magnitude and self < 0.0
.
This result is not an element of the function’s codomain, but it is the
closest floating point number in the real numbers and thus fulfills the
property self == self.div_euclid(rhs) * rhs + self.rem_euclid(rhs)
approximatively.
Examples
let a: f64 = 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!((-f64::EPSILON).rem_euclid(3.0) != 0.0);
RunReturns the square root of a number.
Returns NaN if self
is a negative number other than -0.0
.
Examples
let positive = 4.0_f64;
let negative = -4.0_f64;
let negative_zero = -0.0_f64;
let abs_difference = (positive.sqrt() - 2.0).abs();
assert!(abs_difference < 1e-10);
assert!(negative.sqrt().is_nan());
assert!(negative_zero.sqrt() == negative_zero);
RunReturns 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 twenty_five = 25.0_f64;
// log5(25) - 2 == 0
let abs_difference = (twenty_five.log(5.0) - 2.0).abs();
assert!(abs_difference < 1e-10);
Run👎 Deprecated since 1.10.0: you probably meant (self - other).abs()
: this operation is (self - other).max(0.0)
except that abs_sub
also propagates NaNs (also known as fdim
in C). If you truly need the positive difference, consider using that expression or the C function fdim
, depending on how you wish to handle NaN (please consider filing an issue describing your use-case too).
you probably meant (self - other).abs()
: this operation is (self - other).max(0.0)
except that abs_sub
also propagates NaNs (also known as fdim
in C). If you truly need the positive difference, consider using that expression or the C function fdim
, 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 = 3.0_f64;
let y = -3.0_f64;
let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
assert!(abs_difference_x < 1e-10);
assert!(abs_difference_y < 1e-10);
RunComputes 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::f64::consts::FRAC_PI_2;
// asin(sin(pi/2))
let abs_difference = (f.sin().asin() - std::f64::consts::FRAC_PI_2).abs();
assert!(abs_difference < 1e-10);
RunComputes 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::f64::consts::FRAC_PI_4;
// acos(cos(pi/4))
let abs_difference = (f.cos().acos() - std::f64::consts::FRAC_PI_4).abs();
assert!(abs_difference < 1e-10);
RunComputes 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 = 3.0_f64;
let y1 = -3.0_f64;
// 3pi/4 radians (135 deg counter-clockwise)
let x2 = -3.0_f64;
let y2 = 3.0_f64;
let abs_difference_1 = (y1.atan2(x1) - (-std::f64::consts::FRAC_PI_4)).abs();
let abs_difference_2 = (y2.atan2(x2) - (3.0 * std::f64::consts::FRAC_PI_4)).abs();
assert!(abs_difference_1 < 1e-10);
assert!(abs_difference_2 < 1e-10);
RunSimultaneously computes the sine and cosine of the number, x
. Returns
(sin(x), cos(x))
.
Examples
let x = std::f64::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 < 1e-10);
assert!(abs_difference_1 < 1e-10);
RunReturns ln(1+n)
(natural logarithm) more accurately than if
the operations were performed separately.
Examples
let x = 1e-16_f64;
// 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-20);
RunNumber of significant digits in base 2.
Machine epsilon value for f64
.
This is the difference between 1.0
and the next larger representable number.
Smallest positive normal f64
value.
One greater than the minimum possible normal power of 2 exponent.
Minimum possible normal power of 10 exponent.
Maximum possible power of 10 exponent.
Negative infinity (−∞).
Returns true
if this value is NaN
.
let nan = f64::NAN;
let f = 7.0_f64;
assert!(nan.is_nan());
assert!(!f.is_nan());
RunReturns 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());
RunReturns 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());
RunReturns 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());
RunReturns 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());
RunReturns 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);
RunReturns true
if self
has a positive sign, including +0.0
, NaN
s with
positive sign bit and positive infinity.
let f = 7.0_f64;
let g = -7.0_f64;
assert!(f.is_sign_positive());
assert!(!g.is_sign_positive());
RunReturns true
if self
has a negative sign, including -0.0
, NaN
s with
negative sign bit and negative infinity.
let f = 7.0_f64;
let g = -7.0_f64;
assert!(!f.is_sign_negative());
assert!(g.is_sign_negative());
RunTakes 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);
RunConverts radians to degrees.
let angle = std::f64::consts::PI;
let abs_difference = (angle.to_degrees() - 180.0).abs();
assert!(abs_difference < 1e-10);
RunConverts degrees to radians.
let angle = 180.0_f64;
let abs_difference = (angle.to_radians() - std::f64::consts::PI).abs();
assert!(abs_difference < 1e-10);
RunReturns the maximum of the two numbers.
Follows the IEEE-754 2008 semantics for maxNum, except for handling of signaling NaNs. This matches the behavior of libm’s fmax.
let x = 1.0_f64;
let y = 2.0_f64;
assert_eq!(x.max(y), y);
RunIf one of the arguments is NaN, then the other argument is returned.
Returns the minimum of the two numbers.
Follows the IEEE-754 2008 semantics for minNum, except for handling of signaling NaNs. This matches the behavior of libm’s fmin.
let x = 1.0_f64;
let y = 2.0_f64;
assert_eq!(x.min(y), x);
RunIf one of the arguments is NaN, then the other argument is returned.
Returns the maximum of the two numbers, propagating NaNs.
This returns NaN when either argument is NaN, as opposed to
f64::max
which only returns NaN when both arguments are NaN.
#![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());
RunIf 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.
Returns the minimum of the two numbers, propagating NaNs.
This returns NaN when either argument is NaN, as opposed to
f64::min
which only returns NaN when both arguments are NaN.
#![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());
RunIf 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.
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);
RunSafety
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);
RunRaw 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);
RunReturn the memory representation of this floating point number as a byte array in native byte order.
As the target platform’s native endianness is used, portable code
should use to_be_bytes
or to_le_bytes
, as appropriate, instead.
Examples
let bytes = 12.5f64.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]
}
);
RunCreate a floating point value from its representation as a byte array in native endian.
As the target platform’s native endianness is used, portable code
likely wants to use from_be_bytes
or from_le_bytes
, as
appropriate instead.
Examples
let value = 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);
RunReturns an ordering between self and other values. Unlike the standard partial comparison between floating point numbers, this comparison always produces an ordering in accordance to the totalOrder predicate as defined in IEEE 754 (2008 revision) floating point standard. The values are ordered in following order:
- Negative quiet NaN
- Negative signaling NaN
- Negative infinity
- Negative numbers
- Negative subnormal numbers
- Negative zero
- Positive zero
- Positive subnormal numbers
- Positive numbers
- Positive infinity
- Positive signaling NaN
- Positive quiet NaN
Note that this function does not always agree with the PartialOrd
and PartialEq
implementations of f64
. In particular, they regard
negative and positive zero as equal, while total_cmp
doesn’t.
Example
#![feature(total_cmp)]
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));
RunRestrict 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!((-3.0f64).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());
RunTrait Implementations
Performs the +=
operation. Read more
Performs the +=
operation. Read more
Performs the /=
operation. Read more
Performs the /=
operation. Read more
Converts a string in base 10 to a float. Accepts an optional decimal exponent.
This function accepts strings such as
- ‘3.14’
- ‘-3.14’
- ‘2.5E10’, or equivalently, ‘2.5e10’
- ‘2.5E-10’
- ‘5.’
- ‘.5’, or, equivalently, ‘0.5’
- ‘inf’, ‘-inf’, ‘NaN’
Leading and trailing whitespace represent an error.
Grammar
All strings that adhere to the following EBNF grammar
will result in an Ok
being returned:
Float ::= Sign? ( 'inf' | 'NaN' | Number )
Number ::= ( Digit+ |
Digit+ '.' Digit* |
Digit* '.' Digit+ ) Exp?
Exp ::= [eE] Sign? Digit+
Sign ::= [+-]
Digit ::= [0-9]
Arguments
- src - A string
Return value
Err(ParseFloatError)
if the string did not represent a valid
number. Otherwise, Ok(n)
where n
is the floating-point
number represented by src
.
type Err = ParseFloatError
type Err = ParseFloatError
The associated error which can be returned from parsing.
Performs the *=
operation. Read more
Performs the *=
operation. Read more
This method returns an ordering between self
and other
values if one exists. Read more
This method tests less than (for self
and other
) and is used by the <
operator. Read more
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
This method tests greater than or equal to (for self
and other
) and is used by the >=
operator. Read more
The remainder from the division of two floats.
The remainder has the same sign as the dividend and is computed as:
x - (x / y).trunc() * y
.
Examples
let x: f32 = 50.50;
let y: f32 = 8.125;
let remainder = x - (x / y).trunc() * y;
// The answer to both operations is 1.75
assert_eq!(x % y, remainder);
RunPerforms the %=
operation. Read more
Performs the %=
operation. Read more
Performs the -=
operation. Read more
Performs the -=
operation. Read more