Trait funty::Floating[−][src]

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

Show 30 associated constants and 52 methods
    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;

    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;

}
Expand description

Declare that a type is a floating-point number.

Associated Types

The unsigned integer type of the same width as Self.

Associated Constants

The radix or base of the internal representation of f32.

Number of significant digits in base 2.

Approximate number of significant digits in base 10.

Machine epsilon value for f32.

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

Smallest finite f32 value.

Smallest positive normal f32 value.

Largest finite f32 value.

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

Maximum possible power of 2 exponent.

Minimum possible normal power of 10 exponent.

Maximum possible power of 10 exponent.

Not a Number (NaN).

Infinity (∞).

Negative infinity (−∞).

Archimedes’ constant (π)

π/2

π/3

π/4

π/6

π/8

1/π

2/π

2/sqrt(π)

sqrt(2)

1/sqrt(2)

Euler’s number (e)

log2(e)

log10(e)

ln(2)

ln(10)

Required methods

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

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

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

Returns the integer part of a number.

Returns the fractional part of a number.

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

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.

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.

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.

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.

Raises a number to an integer power.

Using this function is generally faster than using powf

Raises a number to a floating point power.

Returns the square root of a number.

Returns NaN if self is a negative number.

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

Returns 2^(self).

Returns the natural logarithm of the number.

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.

Returns the base 2 logarithm of the number.

Returns the base 10 logarithm of the number.

Returns the cubic root of a number.

Computes the sine of a number (in radians).

Computes the sine of a number (in radians).

Computes the cosine of a number (in radians).

Computes the tangent of a number (in radians).

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].

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].

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

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)

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

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

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

Hyperbolic sine function.

Hyperbolic cosine function.

Hyperbolic tangent function.

Inverse hyperbolic sine function.

Inverse hyperbolic cosine function.

Inverse hyperbolic tangent function.

Returns true if this value is NaN.

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

Returns true if this number is neither infinite nor NaN.

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

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.

Returns true if self has a positive sign, including +0.0, NaNs with positive sign bit and positive infinity.

Returns true if self has a negative sign, including -0.0, NaNs with negative sign bit and negative infinity.

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

Converts radians to degrees.

Converts degrees to radians.

Returns the maximum of the two numbers.

Returns the minimum of the two numbers.

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.

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.

Implementations on Foreign Types

Implementors