Trait Floating

pub trait Floating:
    Numeric
    + LowerExp
    + UpperExp
    + Neg
    + From<f32>
    + From<i8>
    + From<i16>
    + From<u8>
    + From<u16> {
    type Raw: Unsigned;

    const RADIX: u32;
    const MANTISSA_DIGITS: u32;
    const DIGITS: u32;
    const EPSILON: Self;
    const MIN: Self;
    const MIN_POSITIVE: Self;
    const MAX: Self;
    const MIN_EXP: i32;
    const MAX_EXP: i32;
    const MIN_10_EXP: i32;
    const MAX_10_EXP: i32;
    const NAN: Self;
    const INFINITY: Self;
    const NEG_INFINITY: Self;
    const PI: Self;
    const FRAC_PI_2: Self;
    const FRAC_PI_3: Self;
    const FRAC_PI_4: Self;
    const FRAC_PI_6: Self;
    const FRAC_PI_8: Self;
    const FRAC_1_PI: Self;
    const FRAC_2_PI: Self;
    const FRAC_2_SQRT_PI: Self;
    const SQRT_2: Self;
    const FRAC_1_SQRT_2: Self;
    const E: Self;
    const LOG2_E: Self;
    const LOG10_E: Self;
    const LN_2: Self;
    const LN_10: Self;

    // Required methods
    fn floor(self) -> Self;
    fn ceil(self) -> Self;
    fn round(self) -> Self;
    fn trunc(self) -> Self;
    fn fract(self) -> Self;
    fn abs(self) -> Self;
    fn signum(self) -> Self;
    fn copysign(self, sign: Self) -> Self;
    fn mul_add(self, a: Self, b: Self) -> Self;
    fn div_euclid(self, rhs: Self) -> Self;
    fn rem_euclid(self, rhs: Self) -> Self;
    fn powi(self, n: i32) -> Self;
    fn powf(self, n: Self) -> Self;
    fn sqrt(self) -> Self;
    fn exp(self) -> Self;
    fn exp2(self) -> Self;
    fn ln(self) -> Self;
    fn log(self, base: Self) -> Self;
    fn log2(self) -> Self;
    fn log10(self) -> Self;
    fn cbrt(self) -> Self;
    fn hypot(self, other: Self) -> Self;
    fn sin(self) -> Self;
    fn cos(self) -> Self;
    fn tan(self) -> Self;
    fn asin(self) -> Self;
    fn acos(self) -> Self;
    fn atan(self) -> Self;
    fn atan2(self, other: Self) -> Self;
    fn sin_cos(self) -> (Self, Self);
    fn exp_m1(self) -> Self;
    fn ln_1p(self) -> Self;
    fn sinh(self) -> Self;
    fn cosh(self) -> Self;
    fn tanh(self) -> Self;
    fn asinh(self) -> Self;
    fn acosh(self) -> Self;
    fn atanh(self) -> Self;
    fn is_nan(self) -> bool;
    fn is_infinite(self) -> bool;
    fn is_finite(self) -> bool;
    fn is_normal(self) -> bool;
    fn classify(self) -> FpCategory;
    fn is_sign_positive(self) -> bool;
    fn is_sign_negative(self) -> bool;
    fn recip(self) -> Self;
    fn to_degrees(self) -> Self;
    fn to_radians(self) -> Self;
    fn max(self, other: Self) -> Self;
    fn min(self, other: Self) -> Self;
    fn to_bits(self) -> Self::Raw;
    fn from_bits(bits: Self::Raw) -> Self;
}

Declare that a type is a floating-point number.

Required Associated Constants

const RADIX: u32

The radix or base of the internal representation of f32.

const MANTISSA_DIGITS: u32

Number of significant digits in base 2.

const DIGITS: u32

Approximate number of significant digits in base 10.

const EPSILON: Self

Machine epsilon value for f32.

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

const MIN: Self

Smallest finite f32 value.

const MIN_POSITIVE: Self

Smallest positive normal f32 value.

const MAX: Self

Largest finite f32 value.

const MIN_EXP: i32

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

const MAX_EXP: i32

Maximum possible power of 2 exponent.

const MIN_10_EXP: i32

Minimum possible normal power of 10 exponent.

const MAX_10_EXP: i32

Maximum possible power of 10 exponent.

const NAN: Self

Not a Number (NaN).

const INFINITY: Self

Infinity (∞).

const NEG_INFINITY: Self

Negative infinity (−∞).

const PI: Self

Archimedes’ constant (π)

const FRAC_PI_2: Self

π/2

const FRAC_PI_3: Self

π/3

const FRAC_PI_4: Self

π/4

const FRAC_PI_6: Self

π/6

const FRAC_PI_8: Self

π/8

const FRAC_1_PI: Self

1/π

const FRAC_2_PI: Self

2/π

const FRAC_2_SQRT_PI: Self

2/sqrt(π)

const SQRT_2: Self

sqrt(2)

const FRAC_1_SQRT_2: Self

1/sqrt(2)

const E: Self

Euler’s number (e)

const LOG2_E: Self

log₂(e)

const LOG10_E: Self

log₁₀(e)

const LN_2: Self

ln(2)

const LN_10: Self

ln(10)

Required Associated Types

type Raw: Unsigned

The unsigned integer type of the same width as Self.

Required Methods

fn floor(self) -> Self

Returns the largest integer less than or equal to a number.

fn ceil(self) -> Self

Returns the smallest integer greater than or equal to a number.

fn round(self) -> Self

Returns the nearest integer to a number. Round half-way cases away from 0.0.

fn trunc(self) -> Self

Returns the integer part of a number.

fn fract(self) -> Self

Returns the fractional part of a number.

fn abs(self) -> Self

Computes the absolute value of self. Returns NAN if the number is NAN.

fn signum(self) -> Self

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

fn copysign(self, sign: Self) -> Self

Returns a number composed of the magnitude of self and the sign of sign.

Equal to self if the sign of self and sign are the same, otherwise equal to -self. If self is a NAN, then a NAN with the sign of sign is returned.

fn mul_add(self, a: Self, b: Self) -> Self

Fused multiply-add. Computes (self * a) + b with only one rounding error, yielding a more accurate result than an un-fused multiply-add.

Using mul_add can be more performant than an un-fused multiply-add if the target architecture has a dedicated fma CPU instruction.

fn div_euclid(self, rhs: Self) -> Self

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.

fn rem_euclid(self, rhs: Self) -> Self

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

In particular, the return value r satisfies 0.0 <= r < rhs.abs() in most cases. However, due to a floating point round-off error it can result in r == rhs.abs(), violating the mathematical definition, if self is much smaller than rhs.abs() in magnitude and self < 0.0. This result is not an element of the function’s codomain, but it is the closest floating point number in the real numbers and thus fulfills the property self == self.div_euclid(rhs) * rhs + self.rem_euclid(rhs) approximatively.

fn powi(self, n: i32) -> Self

Raises a number to an integer power.

Using this function is generally faster than using powf

fn powf(self, n: Self) -> Self

Raises a number to a floating point power.

fn sqrt(self) -> Self

Returns the square root of a number.

Returns NaN if self is a negative number.

fn exp(self) -> Self

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

fn exp2(self) -> Self

Returns 2^(self).

fn ln(self) -> Self

Returns the natural logarithm of the number.

fn log(self, base: Self) -> Self

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

The result may not be correctly rounded owing to implementation details; self.log2() can produce more accurate results for base 2, and self.log10() can produce more accurate results for base 10.

fn log2(self) -> Self

Returns the base 2 logarithm of the number.

fn log10(self) -> Self

Returns the base 10 logarithm of the number.

fn cbrt(self) -> Self

Returns the cubic root of a number.

fn hypot(self, other: Self) -> Self

Computes the sine of a number (in radians).

fn sin(self) -> Self

Computes the sine of a number (in radians).

fn cos(self) -> Self

Computes the cosine of a number (in radians).

fn tan(self) -> Self

Computes the tangent of a number (in radians).

fn asin(self) -> Self

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].

fn acos(self) -> Self

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].

fn atan(self) -> Self

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

fn atan2(self, other: Self) -> Self

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)

fn sin_cos(self) -> (Self, Self)

Simultaneously computes the sine and cosine of the number, x. Returns (sin(x), cos(x)).

fn exp_m1(self) -> Self

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

fn ln_1p(self) -> Self

Returns ln(1+n) (natural logarithm) more accurately than if the operations were performed separately.

fn sinh(self) -> Self

Hyperbolic sine function.

fn cosh(self) -> Self

Hyperbolic cosine function.

fn tanh(self) -> Self

Hyperbolic tangent function.

fn asinh(self) -> Self

Inverse hyperbolic sine function.

fn acosh(self) -> Self

Inverse hyperbolic cosine function.

fn atanh(self) -> Self

Inverse hyperbolic tangent function.

fn is_nan(self) -> bool

Returns true if this value is NaN.

fn is_infinite(self) -> bool

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

fn is_finite(self) -> bool

Returns true if this number is neither infinite nor NaN.

fn is_normal(self) -> bool

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

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.

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.

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.

fn recip(self) -> Self

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

fn to_degrees(self) -> Self

Converts radians to degrees.

fn to_radians(self) -> Self

Converts degrees to radians.

fn max(self, other: Self) -> Self

Returns the maximum of the two numbers.

fn min(self, other: Self) -> Self

Returns the minimum of the two numbers.

fn to_bits(self) -> Self::Raw

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.

fn from_bits(bits: Self::Raw) -> Self

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.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementations on Foreign Types

impl Floating for f32

const RADIX: u32 = 2u32

const MANTISSA_DIGITS: u32 = 24u32

const DIGITS: u32 = 6u32

const EPSILON: Self = 1.1920929E-7f32

const MIN: Self = -3.40282347E+38f32

const MIN_POSITIVE: Self = 1.17549435E-38f32

const MAX: Self = 3.40282347E+38f32

const MIN_EXP: i32 = -125i32

const MAX_EXP: i32 = 128i32

const MIN_10_EXP: i32 = -37i32

const MAX_10_EXP: i32 = 38i32

const NAN: Self = NaN_f32

const INFINITY: Self = +Inf_f32

const NEG_INFINITY: Self = -Inf_f32

const PI: Self = 3.14159274f32

const FRAC_PI_2: Self = 1.57079637f32

const FRAC_PI_3: Self = 1.04719758f32

const FRAC_PI_4: Self = 0.785398185f32

const FRAC_PI_6: Self = 0.52359879f32

const FRAC_PI_8: Self = 0.392699093f32

const FRAC_1_PI: Self = 0.318309873f32

const FRAC_2_PI: Self = 0.636619746f32

const FRAC_2_SQRT_PI: Self = 1.12837923f32

const SQRT_2: Self = 1.41421354f32

const FRAC_1_SQRT_2: Self = 0.707106769f32

const E: Self = 2.71828175f32

const LOG2_E: Self = 1.44269502f32

const LOG10_E: Self = 0.434294492f32

const LN_2: Self = 0.693147182f32

const LN_10: Self = 2.30258512f32

type Raw = u32

fn floor(self) -> Self

fn ceil(self) -> Self

fn round(self) -> Self

fn trunc(self) -> Self

fn fract(self) -> Self

fn abs(self) -> Self

fn signum(self) -> Self

fn copysign(self, sign: Self) -> Self

fn mul_add(self, a: Self, b: Self) -> Self

fn div_euclid(self, rhs: Self) -> Self

fn rem_euclid(self, rhs: Self) -> Self

fn powi(self, n: i32) -> Self

fn powf(self, n: Self) -> Self

fn sqrt(self) -> Self

fn exp(self) -> Self

fn exp2(self) -> Self

fn ln(self) -> Self

fn log(self, base: Self) -> Self

fn log2(self) -> Self

fn log10(self) -> Self

fn cbrt(self) -> Self

fn hypot(self, other: Self) -> Self

fn sin(self) -> Self

fn cos(self) -> Self

fn tan(self) -> Self

fn asin(self) -> Self

fn acos(self) -> Self

fn atan(self) -> Self

fn atan2(self, other: Self) -> Self

fn sin_cos(self) -> (Self, Self)

fn exp_m1(self) -> Self

fn ln_1p(self) -> Self

fn sinh(self) -> Self

fn cosh(self) -> Self

fn tanh(self) -> Self

fn asinh(self) -> Self

fn acosh(self) -> Self

fn atanh(self) -> Self

fn is_nan(self) -> bool

fn is_infinite(self) -> bool

fn is_finite(self) -> bool

fn is_normal(self) -> bool

fn classify(self) -> FpCategory

fn is_sign_positive(self) -> bool

fn is_sign_negative(self) -> bool

fn recip(self) -> Self

fn to_degrees(self) -> Self

fn to_radians(self) -> Self

fn max(self, other: Self) -> Self

fn min(self, other: Self) -> Self

fn to_bits(self) -> Self::Raw

fn from_bits(bits: Self::Raw) -> Self

impl Floating for f64

const RADIX: u32 = 2u32

const MANTISSA_DIGITS: u32 = 53u32

const DIGITS: u32 = 15u32

const EPSILON: Self = 2.2204460492503131E-16f64

const MIN: Self = -1.7976931348623157E+308f64

const MIN_POSITIVE: Self = 2.2250738585072014E-308f64

const MAX: Self = 1.7976931348623157E+308f64

const MIN_EXP: i32 = -1_021i32

const MAX_EXP: i32 = 1_024i32

const MIN_10_EXP: i32 = -307i32

const MAX_10_EXP: i32 = 308i32

const NAN: Self = NaN_f64

const INFINITY: Self = +Inf_f64

const NEG_INFINITY: Self = -Inf_f64

const PI: Self = 3.1415926535897931f64

const FRAC_PI_2: Self = 1.5707963267948966f64

const FRAC_PI_3: Self = 1.0471975511965979f64

const FRAC_PI_4: Self = 0.78539816339744828f64

const FRAC_PI_6: Self = 0.52359877559829893f64

const FRAC_PI_8: Self = 0.39269908169872414f64

const FRAC_1_PI: Self = 0.31830988618379069f64

const FRAC_2_PI: Self = 0.63661977236758138f64

const FRAC_2_SQRT_PI: Self = 1.1283791670955126f64

const SQRT_2: Self = 1.4142135623730951f64

const FRAC_1_SQRT_2: Self = 0.70710678118654757f64

const E: Self = 2.7182818284590451f64

const LOG2_E: Self = 1.4426950408889634f64

const LOG10_E: Self = 0.43429448190325182f64

const LN_2: Self = 0.69314718055994529f64

const LN_10: Self = 2.3025850929940459f64

type Raw = u64

fn floor(self) -> Self

fn ceil(self) -> Self

fn round(self) -> Self

fn trunc(self) -> Self

fn fract(self) -> Self

fn abs(self) -> Self

fn signum(self) -> Self

fn copysign(self, sign: Self) -> Self

fn mul_add(self, a: Self, b: Self) -> Self

fn div_euclid(self, rhs: Self) -> Self

fn rem_euclid(self, rhs: Self) -> Self

fn powi(self, n: i32) -> Self

fn powf(self, n: Self) -> Self

fn sqrt(self) -> Self

fn exp(self) -> Self

fn exp2(self) -> Self

fn ln(self) -> Self

fn log(self, base: Self) -> Self

fn log2(self) -> Self

fn log10(self) -> Self

fn cbrt(self) -> Self

fn hypot(self, other: Self) -> Self

fn sin(self) -> Self

fn cos(self) -> Self

fn tan(self) -> Self

fn asin(self) -> Self

fn acos(self) -> Self

fn atan(self) -> Self

fn atan2(self, other: Self) -> Self

fn sin_cos(self) -> (Self, Self)

fn exp_m1(self) -> Self

fn ln_1p(self) -> Self

fn sinh(self) -> Self

fn cosh(self) -> Self

fn tanh(self) -> Self

fn asinh(self) -> Self

fn acosh(self) -> Self

fn atanh(self) -> Self

fn is_nan(self) -> bool

fn is_infinite(self) -> bool

fn is_finite(self) -> bool

fn is_normal(self) -> bool

fn classify(self) -> FpCategory

fn is_sign_positive(self) -> bool

fn is_sign_negative(self) -> bool

fn recip(self) -> Self

fn to_degrees(self) -> Self

fn to_radians(self) -> Self

fn max(self, other: Self) -> Self

fn min(self, other: Self) -> Self

fn to_bits(self) -> Self::Raw

fn from_bits(bits: Self::Raw) -> Self

Implementors