[−][src]Trait funty::IsFloat
Declare that a type is a floating-point number.
Associated Types
type Raw
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 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
orINFINITY
-1.0
if the number is negative,-0.0
orNEG_INFINITY
NAN
if the number isNAN
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 unfused multiply-add.
Using mul_add
can be more performant than an unfused 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
, NaN
s
with positive sign bit and positive infinity.
fn is_sign_negative(self) -> bool
Returns true
if self
has a negative sign, including -0.0
, NaN
s
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.