Raises a number to a floating point power.

Note that this function is special in that it can return non-NaN results for NaN inputs. Forexample,f128::powf(f128::NAN, 0.0) returns1.0. However, if an input is asignalingNaN, then the result is non-deterministically either a NaN or the result that thecorresponding quiet NaN would produce.

§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

#![feature(f128)]letx =2.0_f128;letabs_difference = (x.powf(2.0) - (x * x)).abs();assert!(abs_difference <= f128::EPSILON);assert_eq!(f128::powf(1.0, f128::NAN),1.0);assert_eq!(f128::powf(f128::NAN,0.0),1.0);assert_eq!(f128::powf(0.0,0.0),1.0);

Returnse^(self), (the exponential function).

§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

#![feature(f128)]letone =1.0f128;// e^1lete = one.exp();// ln(e) - 1 == 0letabs_difference = (e.ln() -1.0).abs();assert!(abs_difference <= f128::EPSILON);

Returns2^(self).

§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

#![feature(f128)]letf =2.0f128;// 2^2 - 4 == 0letabs_difference = (f.exp2() -4.0).abs();assert!(abs_difference <= f128::EPSILON);

Returns the natural logarithm of the number.

This returns NaN when the number is negative, and negative infinity when number is zero.

§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

#![feature(f128)]letone =1.0f128;// e^1lete = one.exp();// ln(e) - 1 == 0letabs_difference = (e.ln() -1.0).abs();assert!(abs_difference <= f128::EPSILON);

Non-positive values:

#![feature(f128)]assert_eq!(0_f128.ln(), f128::NEG_INFINITY);assert!((-42_f128).ln().is_nan());

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

This returns NaN when the number is negative, and negative infinity when number is zero.

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

§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

#![feature(f128)]letfive =5.0f128;// log5(5) - 1 == 0letabs_difference = (five.log(5.0) -1.0).abs();assert!(abs_difference <= f128::EPSILON);

Non-positive values:

#![feature(f128)]assert_eq!(0_f128.log(10.0), f128::NEG_INFINITY);assert!((-42_f128).log(10.0).is_nan());

Returns the base 2 logarithm of the number.

This returns NaN when the number is negative, and negative infinity when number is zero.

§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

#![feature(f128)]lettwo =2.0f128;// log2(2) - 1 == 0letabs_difference = (two.log2() -1.0).abs();assert!(abs_difference <= f128::EPSILON);

Non-positive values:

#![feature(f128)]assert_eq!(0_f128.log2(), f128::NEG_INFINITY);assert!((-42_f128).log2().is_nan());

Returns the base 10 logarithm of the number.

This returns NaN when the number is negative, and negative infinity when number is zero.

§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

#![feature(f128)]letten =10.0f128;// log10(10) - 1 == 0letabs_difference = (ten.log10() -1.0).abs();assert!(abs_difference <= f128::EPSILON);

Non-positive values:

#![feature(f128)]assert_eq!(0_f128.log10(), f128::NEG_INFINITY);assert!((-42_f128).log10().is_nan());

Returns the cube root of a number.

§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.

This function currently corresponds to thecbrtf128 from libc on Unixand Windows. Note that this might change in the future.

§Examples

#![feature(f128)]letx =8.0f128;// x^(1/3) - 2 == 0letabs_difference = (x.cbrt() -2.0).abs();assert!(abs_difference <= f128::EPSILON);

Compute the distance between the origin and a point (x,y) on theEuclidean plane. Equivalently, compute the length of the hypotenuse of aright-angle triangle with other sides having lengthx.abs() andy.abs().

§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.

This function currently corresponds to thehypotf128 from libc on Unixand Windows. Note that this might change in the future.

§Examples

#![feature(f128)]letx =2.0f128;lety =3.0f128;// sqrt(x^2 + y^2)letabs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();assert!(abs_difference <= f128::EPSILON);

Computes the sine of a number (in 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

#![feature(f128)]letx = std::f128::consts::FRAC_PI_2;letabs_difference = (x.sin() -1.0).abs();assert!(abs_difference <= f128::EPSILON);

Computes the cosine of a number (in 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

#![feature(f128)]letx =2.0* std::f128::consts::PI;letabs_difference = (x.cos() -1.0).abs();assert!(abs_difference <= f128::EPSILON);

Computes the tangent of a number (in 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.

This function currently corresponds to thetanf128 from libc on Unix andWindows. Note that this might change in the future.

§Examples

#![feature(f128)]letx = std::f128::consts::FRAC_PI_4;letabs_difference = (x.tan() -1.0).abs();assert!(abs_difference <= f128::EPSILON);

Computes the arcsine of a number. Return value is in radians inthe range [-pi/2, pi/2] or NaN if the number is outside the range[-1, 1].

§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.

This function currently corresponds to theasinf128 from libc on Unixand Windows. Note that this might change in the future.

§Examples

#![feature(f128)]letf = std::f128::consts::FRAC_PI_4;// asin(sin(pi/2))letabs_difference = (f.sin().asin() - f).abs();assert!(abs_difference <= f128::EPSILON);

Computes the arccosine of a number. Return value is in radians inthe range [0, pi] or NaN if the number is outside the range[-1, 1].

§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.

This function currently corresponds to theacosf128 from libc on Unixand Windows. Note that this might change in the future.

§Examples

#![feature(f128)]letf = std::f128::consts::FRAC_PI_4;// acos(cos(pi/4))letabs_difference = (f.cos().acos() - std::f128::consts::FRAC_PI_4).abs();assert!(abs_difference <= f128::EPSILON);

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

§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.

This function currently corresponds to theatanf128 from libc on Unixand Windows. Note that this might change in the future.

§Examples

#![feature(f128)]letf =1.0f128;// atan(tan(1))letabs_difference = (f.tan().atan() -1.0).abs();assert!(abs_difference <= f128::EPSILON);

Computes the four quadrant arctangent ofself (y) andother (x) in 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.

This function currently corresponds to theatan2f128 from libc on Unixand Windows. Note that this might change in the future.

§Examples

#![feature(f128)]// Positive angles measured counter-clockwise// from positive x axis// -pi/4 radians (45 deg clockwise)letx1 =3.0f128;lety1 = -3.0f128;// 3pi/4 radians (135 deg counter-clockwise)letx2 = -3.0f128;lety2 =3.0f128;letabs_difference_1 = (y1.atan2(x1) - (-std::f128::consts::FRAC_PI_4)).abs();letabs_difference_2 = (y2.atan2(x2) - (3.0* std::f128::consts::FRAC_PI_4)).abs();assert!(abs_difference_1 <= f128::EPSILON);assert!(abs_difference_2 <= f128::EPSILON);

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

§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.

This function currently corresponds to the(f128::sin(x), f128::cos(x)). Note that this might change in the future.

§Examples

#![feature(f128)]letx = std::f128::consts::FRAC_PI_4;letf = x.sin_cos();letabs_difference_0 = (f.0- x.sin()).abs();letabs_difference_1 = (f.1- x.cos()).abs();assert!(abs_difference_0 <= f128::EPSILON);assert!(abs_difference_1 <= f128::EPSILON);

Returnse^(self) - 1 in a way that is accurate even if thenumber is close to zero.

§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.

This function currently corresponds to theexpm1f128 from libc on Unixand Windows. Note that this might change in the future.

§Examples

#![feature(f128)]letx =1e-8_f128;// for very small x, e^x is approximately 1 + x + x^2 / 2letapprox = x + x * x /2.0;letabs_difference = (x.exp_m1() - approx).abs();assert!(abs_difference <1e-10);

Returnsln(1+n) (natural logarithm) more accurately than ifthe operations were performed separately.

This returns NaN whenn < -1.0, and negative infinity whenn == -1.0.

§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.

This function currently corresponds to thelog1pf128 from libc on Unixand Windows. Note that this might change in the future.

§Examples

#![feature(f128)]letx =1e-8_f128;// for very small x, ln(1 + x) is approximately x - x^2 / 2letapprox = x - x * x /2.0;letabs_difference = (x.ln_1p() - approx).abs();assert!(abs_difference <1e-10);

Out-of-range values:

#![feature(f128)]assert_eq!((-1.0_f128).ln_1p(), f128::NEG_INFINITY);assert!((-2.0_f128).ln_1p().is_nan());

Hyperbolic sine function.

§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.

This function currently corresponds to thesinhf128 from libc on Unixand Windows. Note that this might change in the future.

§Examples

#![feature(f128)]lete = std::f128::consts::E;letx =1.0f128;letf = x.sinh();// Solving sinh() at 1 gives `(e^2-1)/(2e)`letg = ((e * e) -1.0) / (2.0* e);letabs_difference = (f - g).abs();assert!(abs_difference <= f128::EPSILON);

Hyperbolic cosine function.

§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.

This function currently corresponds to thecoshf128 from libc on Unixand Windows. Note that this might change in the future.

§Examples

#![feature(f128)]lete = std::f128::consts::E;letx =1.0f128;letf = x.cosh();// Solving cosh() at 1 gives this resultletg = ((e * e) +1.0) / (2.0* e);letabs_difference = (f - g).abs();// Same resultassert!(abs_difference <= f128::EPSILON);

Hyperbolic tangent function.

§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.

This function currently corresponds to thetanhf128 from libc on Unixand Windows. Note that this might change in the future.

§Examples

#![feature(f128)]lete = std::f128::consts::E;letx =1.0f128;letf = x.tanh();// Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`letg = (1.0- e.powi(-2)) / (1.0+ e.powi(-2));letabs_difference = (f - g).abs();assert!(abs_difference <= f128::EPSILON);

Inverse hyperbolic sine function.

§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

#![feature(f128)]letx =1.0f128;letf = x.sinh().asinh();letabs_difference = (f - x).abs();assert!(abs_difference <= f128::EPSILON);

Inverse hyperbolic cosine function.

§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

#![feature(f128)]letx =1.0f128;letf = x.cosh().acosh();letabs_difference = (f - x).abs();assert!(abs_difference <= f128::EPSILON);

Inverse hyperbolic tangent function.

§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

#![feature(f128)]letx = std::f128::consts::FRAC_PI_6;letf = x.tanh().atanh();letabs_difference = (f - x).abs();assert!(abs_difference <=1e-5);

Gamma function.

§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.

This function currently corresponds to thetgammaf128 from libc on Unixand Windows. Note that this might change in the future.

§Examples

#![feature(f128)]#![feature(float_gamma)]letx =5.0f128;letabs_difference = (x.gamma() -24.0).abs();assert!(abs_difference <= f128::EPSILON);

Natural logarithm of the absolute value of the gamma function

The integer part of the tuple indicates the sign of the gamma function.

§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.

This function currently corresponds to thelgammaf128_r from libc on Unixand Windows. Note that this might change in the future.

§Examples

#![feature(f128)]#![feature(float_gamma)]letx =2.0f128;letabs_difference = (x.ln_gamma().0-0.0).abs();assert!(abs_difference <= f128::EPSILON);

Error function.

§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.

This function currently corresponds to theerff128 from libc on Unixand Windows. Note that this might change in the future.

§Examples

#![feature(f128)]#![feature(float_erf)]/// The error function relates what percent of a normal distribution lies/// within `x` standard deviations (scaled by `1/sqrt(2)`).fnwithin_standard_deviations(x: f128) -> f128 {    (x * std::f128::consts::FRAC_1_SQRT_2).erf() *100.0}// 68% of a normal distribution is within one standard deviationassert!((within_standard_deviations(1.0) -68.269).abs() <0.01);// 95% of a normal distribution is within two standard deviationsassert!((within_standard_deviations(2.0) -95.450).abs() <0.01);// 99.7% of a normal distribution is within three standard deviationsassert!((within_standard_deviations(3.0) -99.730).abs() <0.01);

Complementary error function.

§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.

This function currently corresponds to theerfcf128 from libc on Unixand Windows. Note that this might change in the future.

§Examples

#![feature(f128)]#![feature(float_erf)]letx: f128 =0.123;letone = x.erf() + x.erfc();letabs_difference = (one -1.0).abs();assert!(abs_difference <= f128::EPSILON);

The radix or base of the internal representation off128.

Number of significant digits in base 2.

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

Approximate number of significant digits in base 10.

This is the maximumx such that any decimal number withxsignificant digits can be converted tof128 and back without loss.

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

Machine epsilon value forf128.

This is the difference between1.0 and the next larger representable number.

Equal to 2^{1 − MANTISSA_DIGITS}.

Smallest finitef128 value.

Equal to −MAX.

Smallest positive normalf128 value.

Equal to 2^{MIN_EXP − 1}.

Largest finitef128 value.

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

One greater than the minimum possiblenormal power of 2 exponentfor a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).

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

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

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

Minimumx for which 10^x is normal.

Equal to ceil(log₁₀ MIN_POSITIVE).

Maximumx 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 areconsidered to be NaN. Furthermore, the standard makes a difference between a “signaling” anda “quiet” NaN, and allows inspecting its “payload” (the unspecified bits in the bit pattern)and its sign. See thespecification of NaN bit patterns for moreinfo.

This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptionsthat the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing isguaranteed 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.

Infinity (∞).

Negative infinity (−∞).

Returnstrue if this value is NaN.

#![feature(f128)]letnan = f128::NAN;letf =7.0_f128;assert!(nan.is_nan());assert!(!f.is_nan());

Returnstrue if this value is positive infinity or negative infinity, andfalse otherwise.

#![feature(f128)]letf =7.0f128;letinf = f128::INFINITY;letneg_inf = f128::NEG_INFINITY;letnan = f128::NAN;assert!(!f.is_infinite());assert!(!nan.is_infinite());assert!(inf.is_infinite());assert!(neg_inf.is_infinite());

Returnstrue if this number is neither infinite nor NaN.

#![feature(f128)]letf =7.0f128;letinf: f128 = f128::INFINITY;letneg_inf: f128 = f128::NEG_INFINITY;letnan: f128 = f128::NAN;assert!(f.is_finite());assert!(!nan.is_finite());assert!(!inf.is_finite());assert!(!neg_inf.is_finite());

Returnstrue if the number issubnormal.

#![feature(f128)]letmin = f128::MIN_POSITIVE;// 3.362103143e-4932f128letmax = f128::MAX;letlower_than_min =1.0e-4960_f128;letzero =0.0_f128;assert!(!min.is_subnormal());assert!(!max.is_subnormal());assert!(!zero.is_subnormal());assert!(!f128::NAN.is_subnormal());assert!(!f128::INFINITY.is_subnormal());// Values between `0` and `min` are Subnormal.assert!(lower_than_min.is_subnormal());

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

#![feature(f128)]letmin = f128::MIN_POSITIVE;// 3.362103143e-4932f128letmax = f128::MAX;letlower_than_min =1.0e-4960_f128;letzero =0.0_f128;assert!(min.is_normal());assert!(max.is_normal());assert!(!zero.is_normal());assert!(!f128::NAN.is_normal());assert!(!f128::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 propertyis going to be tested, it is generally faster to use the specificpredicate instead.

#![feature(f128)]usestd::num::FpCategory;letnum =12.4_f128;letinf = f128::INFINITY;assert_eq!(num.classify(), FpCategory::Normal);assert_eq!(inf.classify(), FpCategory::Infinite);

Returnstrue ifself has a positive sign, including+0.0, NaNs withpositive sign bit and positive infinity.

Note that IEEE 754 doesn’t assign any meaning to the sign bit in case ofa NaN, and as Rust doesn’t guarantee that the bit pattern of NaNs areconserved over arithmetic operations, the result ofis_sign_positive ona NaN might produce an unexpected or non-portable result. See thespecificationof NaN bit patterns for more info. Useself.signum() == 1.0if you need fully portable behavior (will returnfalse for all NaNs).

#![feature(f128)]letf =7.0_f128;letg = -7.0_f128;assert!(f.is_sign_positive());assert!(!g.is_sign_positive());

Returnstrue ifself has a negative sign, including-0.0, NaNs withnegative sign bit and negative infinity.

Note that IEEE 754 doesn’t assign any meaning to the sign bit in case ofa NaN, and as Rust doesn’t guarantee that the bit pattern of NaNs areconserved over arithmetic operations, the result ofis_sign_negative ona NaN might produce an unexpected or non-portable result. See thespecificationof NaN bit patterns for more info. Useself.signum() == -1.0if you need fully portable behavior (will returnfalse for all NaNs).

#![feature(f128)]letf =7.0_f128;letg = -7.0_f128;assert!(!f.is_sign_negative());assert!(g.is_sign_negative());

Returns the least number greater thanself.

LetTINY be the smallest representable positivef128. Then,

• ifself.is_nan(), this returnsself;
• ifself isNEG_INFINITY, this returnsMIN;
• ifself is-TINY, this returns -0.0;
• ifself is -0.0 or +0.0, this returnsTINY;
• ifself isMAX orINFINITY, this returnsINFINITY;
• otherwise the unique least value greater thanself is returned.

The identityx.next_up() == -(-x).next_down() holds for all non-NaNx. Whenxis finitex == x.next_up().next_down() also holds.

#![feature(f128)]// f128::EPSILON is the difference between 1.0 and the next number up.assert_eq!(1.0f128.next_up(),1.0+ f128::EPSILON);// But not for most numbers.assert!(0.1f128.next_up() <0.1+ f128::EPSILON);assert_eq!(4611686018427387904f128.next_up(),4611686018427387904.000000000000001);

This operation corresponds to IEEE-754nextUp.

Returns the greatest number less thanself.

LetTINY be the smallest representable positivef128. Then,

• ifself.is_nan(), this returnsself;
• ifself isINFINITY, this returnsMAX;
• ifself isTINY, this returns 0.0;
• ifself is -0.0 or +0.0, this returns-TINY;
• ifself isMIN orNEG_INFINITY, this returnsNEG_INFINITY;
• otherwise the unique greatest value less thanself is returned.

The identityx.next_down() == -(-x).next_up() holds for all non-NaNx. Whenxis finitex == x.next_down().next_up() also holds.

#![feature(f128)]letx =1.0f128;// Clamp value into range [0, 1).letclamped = x.clamp(0.0,1.0f128.next_down());assert!(clamped <1.0);assert_eq!(clamped.next_up(),1.0);

This operation corresponds to IEEE-754nextDown.

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

#![feature(f128)]letx =2.0_f128;letabs_difference = (x.recip() - (1.0/ x)).abs();assert!(abs_difference <= f128::EPSILON);

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

#![feature(f128)]letangle = std::f128::consts::PI;letabs_difference = (angle.to_degrees() -180.0).abs();assert!(abs_difference <= f128::EPSILON);

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

#![feature(f128)]letangle =180.0f128;letabs_difference = (angle.to_radians() - std::f128::consts::PI).abs();assert!(abs_difference <=1e-30);

Returns the maximum of the two numbers, ignoring NaN.

If exactly one of the arguments is NaN, then the other argument is returned. If botharguments are NaN, the return value is NaN, with the bit pattern picked using the usualrules for arithmetic operations. If the inputs compare equal (suchas for the case of+0.0 and-0.0), either input may be returned non-deterministically.

This follows the IEEE 754-2008 semantics formaxNum, except for handling of signaling NaNs;this function handles all NaNs the same way and avoidsmaxNum’s problems with associativity.This also matches the behavior of libm’sfmax.

#![feature(f128)]letx =1.0f128;lety =2.0f128;assert_eq!(x.max(y), y);assert_eq!(x.max(f128::NAN), x);

Returns the minimum of the two numbers, ignoring NaN.

If exactly one of the arguments is NaN, then the other argument is returned. If botharguments are NaN, the return value is NaN, with the bit pattern picked using the usualrules for arithmetic operations. If the inputs compare equal (suchas for the case of+0.0 and-0.0), either input may be returned non-deterministically.

This follows the IEEE 754-2008 semantics forminNum, except for handling of signaling NaNs;this function handles all NaNs the same way and avoidsminNum’s problems with associativity.This also matches the behavior of libm’sfmin.

#![feature(f128)]letx =1.0f128;lety =2.0f128;assert_eq!(x.min(y), x);assert_eq!(x.min(f128::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 patternpicked using the usualrules for arithmetic operations. Furthermore,-0.0 is considered to be less than+0.0, making this function fully deterministic fornon-NaN inputs.

This is in contrast tof128::max which only returns NaN whenboth arguments are NaN,and which does not reliably order-0.0 and+0.0.

This follows the IEEE 754-2019 semantics formaximum.

#![feature(f128)]#![feature(float_minimum_maximum)]letx =1.0f128;lety =2.0f128;assert_eq!(x.maximum(y), y);assert!(x.maximum(f128::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 patternpicked using the usualrules for arithmetic operations. Furthermore,-0.0 is considered to be less than+0.0, making this function fully deterministic fornon-NaN inputs.

This is in contrast tof128::min which only returns NaN whenboth arguments are NaN,and which does not reliably order-0.0 and+0.0.

This follows the IEEE 754-2019 semantics forminimum.

#![feature(f128)]#![feature(float_minimum_maximum)]letx =1.0f128;lety =2.0f128;assert_eq!(x.minimum(y), x);assert!(x.minimum(f128::NAN).is_nan());

Calculates the midpoint (average) betweenself andrhs.

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

§Examples

#![feature(f128)]assert_eq!(1f128.midpoint(4.0),2.5);assert_eq!((-5.5f128).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.

#![feature(f128)]letvalue =4.6_f128;letrounded =unsafe{ value.to_int_unchecked::<u16>() };assert_eq!(rounded,4);letvalue = -128.9_f128;letrounded =unsafe{ value.to_int_unchecked::<i8>() };assert_eq!(rounded, i8::MIN);

§Safety

The value must:

• Not beNaN
• Not be infinite
• Be representable in the return typeInt, after truncating off its fractional part

Raw transmutation tou128.

This is currently identical totransmute::<f128, u128>(self) on all platforms.

Seefrom_bits for some discussion of theportability of this operation (there are almost no issues).

Note that this function is distinct fromas casting, which attempts topreserve thenumeric value, and not the bitwise value.

#![feature(f128)]assert_eq!((12.5f128).to_bits(),0x40029000000000000000000000000000);

Raw transmutation fromu128.

This is currently identical totransmute::<u128, f128>(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, howto interpret the NaN signaling bit wasn’t actually specified. Most platforms(notably x86 and ARM) picked the interpretation that was ultimatelystandardized in 2008, but some didn’t (notably MIPS). As a result, allsignaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.

Rather than trying to preserve signaling-ness cross-platform, thisimplementation favors preserving the exact bits. This means thatany payloads encoded in NaNs will be preserved even if the result ofthis 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 samearchitecture 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 noportability concern.

Note that this function is distinct fromas casting, which attempts topreserve thenumeric value, and not the bitwise value.

#![feature(f128)]letv = f128::from_bits(0x40029000000000000000000000000000);assert_eq!(v,12.5);

Returns the memory representation of this floating point number as a byte array inbig-endian (network) byte order.

Seefrom_bits for some discussion of theportability of this operation (there are almost no issues).

§Examples

#![feature(f128)]letbytes =12.5f128.to_be_bytes();assert_eq!(    bytes,    [0x40,0x02,0x90,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00]);

Returns the memory representation of this floating point number as a byte array inlittle-endian byte order.

Seefrom_bits for some discussion of theportability of this operation (there are almost no issues).

§Examples

#![feature(f128)]letbytes =12.5f128.to_le_bytes();assert_eq!(    bytes,    [0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x90,0x02,0x40]);

Returns the memory representation of this floating point number as a byte array innative byte order.

As the target platform’s native endianness is used, portable codeshould useto_be_bytes orto_le_bytes, as appropriate, instead.

Seefrom_bits for some discussion of theportability of this operation (there are almost no issues).

§Examples

#![feature(f128)]letbytes =12.5f128.to_ne_bytes();assert_eq!(    bytes,ifcfg!(target_endian ="big") {        [0x40,0x02,0x90,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00]    }else{        [0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x90,0x02,0x40]    });

Creates a floating point value from its representation as a byte array in big endian.

Seefrom_bits for some discussion of theportability of this operation (there are almost no issues).

§Examples

#![feature(f128)]letvalue = f128::from_be_bytes(    [0x40,0x02,0x90,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00]);assert_eq!(value,12.5);

Creates a floating point value from its representation as a byte array in little endian.

Seefrom_bits for some discussion of theportability of this operation (there are almost no issues).

§Examples

#![feature(f128)]letvalue = f128::from_le_bytes(    [0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x90,0x02,0x40]);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 codelikely wants to usefrom_be_bytes orfrom_le_bytes, asappropriate instead.

Seefrom_bits for some discussion of theportability of this operation (there are almost no issues).

§Examples

#![feature(f128)]letvalue = f128::from_ne_bytes(ifcfg!(target_endian ="big") {    [0x40,0x02,0x90,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00]}else{    [0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x90,0x02,0x40]});assert_eq!(value,12.5);

Returns the ordering betweenself andother.

Unlike the standard partial comparison between floating point numbers,this comparison always produces an ordering in accordance tothetotalOrder 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 thePartialOrd andPartialEq implementations off128. For example,they consider negative and positive zero equal, whiletotal_cmpdoesn’t.

The interpretation of the signaling NaN bit follows the definition inthe IEEE 754 standard, which may not match the interpretation by some ofthe older, non-conformant (e.g. MIPS) hardware implementations.

§Example

#![feature(f128)]structGoodBoy {    name:&'staticstr,    weight: f128,}letmutbois =vec![    GoodBoy { name:"Pucci", weight:0.1},    GoodBoy { name:"Woofer", weight:99.0},    GoodBoy { name:"Yapper", weight:10.0},    GoodBoy { name:"Chonk", weight: f128::INFINITY },    GoodBoy { name:"Abs. Unit", weight: f128::NAN },    GoodBoy { name:"Floaty", weight: -5.0},];bois.sort_by(|a, b| a.weight.total_cmp(&b.weight));// `f128::NAN` could be positive or negative, which will affect the sort order.iff128::NAN.is_sign_negative() {    bois.into_iter().map(|b| b.weight)        .zip([f128::NAN, -5.0,0.1,10.0,99.0, f128::INFINITY].iter())        .for_each(|(a, b)|assert_eq!(a.to_bits(), b.to_bits()))}else{    bois.into_iter().map(|b| b.weight)        .zip([-5.0,0.1,10.0,99.0, f128::INFINITY, f128::NAN].iter())        .for_each(|(a, b)|assert_eq!(a.to_bits(), b.to_bits()))}

Restrict a value to a certain interval unless it is NaN.

Returnsmax ifself is greater thanmax, andmin ifself isless thanmin. Otherwise this returnsself.

Note that this function returns NaN if the initial value was NaN aswell. If the result is zero and among the three inputsself,min, andmax there arezeros with different sign, either0.0 or-0.0 is returned non-deterministically.

§Panics

Panics ifmin > max,min is NaN, ormax is NaN.

§Examples

#![feature(f128)]assert!((-3.0f128).clamp(-2.0,1.0) == -2.0);assert!((0.0f128).clamp(-2.0,1.0) ==0.0);assert!((2.0f128).clamp(-2.0,1.0) ==1.0);assert!((f128::NAN).clamp(-2.0,1.0).is_nan());// These always returns zero, but the sign (which is ignored by `==`) is non-deterministic.assert!((0.0f128).clamp(-0.0, -0.0) ==0.0);assert!((1.0f128).clamp(-0.0,0.0) ==0.0);// This is definitely a negative zero.assert!((-1.0f128).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 mostlimit.

This is functionally equivalent toself.clamp(-limit, limit), but is moreexplicit about the intent.

§Panics

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

§Examples

#![feature(f128)]#![feature(clamp_magnitude)]assert_eq!(5.0f128.clamp_magnitude(3.0),3.0);assert_eq!((-5.0f128).clamp_magnitude(3.0), -3.0);assert_eq!(2.0f128.clamp_magnitude(3.0),2.0);assert_eq!((-2.0f128).clamp_magnitude(3.0), -2.0);

Computes the absolute value ofself.

This function always returns the precise result.

§Examples

#![feature(f128)]letx =3.5_f128;lety = -3.5_f128;assert_eq!(x.abs(), x);assert_eq!(y.abs(), -y);assert!(f128::NAN.abs().is_nan());

Returns a number that represents the sign ofself.

• 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 is NaN

§Examples

#![feature(f128)]letf =3.5_f128;assert_eq!(f.signum(),1.0);assert_eq!(f128::NEG_INFINITY.signum(), -1.0);assert!(f128::NAN.signum().is_nan());

Returns a number composed of the magnitude ofself and the sign ofsign.

Equal toself if the sign ofself andsign are the same, otherwise equal to-self.Ifself is a NaN, then a NaN with the same payload asself and the sign bit ofsign isreturned.

Ifsign is a NaN, then this operation will still carry over its sign into the result. Notethat IEEE 754 doesn’t assign any meaning to the sign bit in case of a NaN, and as Rustdoesn’t guarantee that the bit pattern of NaNs are conserved over arithmetic operations, theresult ofcopysign withsign being a NaN might produce an unexpected or non-portableresult. See thespecification of NaN bit patterns for moreinfo.

§Examples

#![feature(f128)]letf =3.5_f128;assert_eq!(f.copysign(0.42),3.5_f128);assert_eq!(f.copysign(-0.42), -3.5_f128);assert_eq!((-f).copysign(0.42),3.5_f128);assert_eq!((-f).copysign(-0.42), -3.5_f128);assert!(f128::NAN.copysign(1.0).is_nan());

Float addition that allows optimizations based on algebraic rules.

Seealgebraic operators for more info.

Float subtraction that allows optimizations based on algebraic rules.

Seealgebraic operators for more info.

Float multiplication that allows optimizations based on algebraic rules.

Seealgebraic operators for more info.

Float division that allows optimizations based on algebraic rules.

Seealgebraic operators for more info.

Float remainder that allows optimizations based on algebraic rules.

Seealgebraic operators for more info.

Returns the largest integer less than or equal toself.

This function always returns the precise result.

§Examples

#![feature(f128)]letf =3.7_f128;letg =3.0_f128;leth = -3.7_f128;assert_eq!(f.floor(),3.0);assert_eq!(g.floor(),3.0);assert_eq!(h.floor(), -4.0);

Returns the smallest integer greater than or equal toself.

This function always returns the precise result.

§Examples

#![feature(f128)]letf =3.01_f128;letg =4.0_f128;assert_eq!(f.ceil(),4.0);assert_eq!(g.ceil(),4.0);

Returns the nearest integer toself. If a value is half-way between twointegers, round away from0.0.

This function always returns the precise result.

§Examples

#![feature(f128)]letf =3.3_f128;letg = -3.3_f128;leth = -3.7_f128;leti =3.5_f128;letj =4.5_f128;assert_eq!(f.round(),3.0);assert_eq!(g.round(), -3.0);assert_eq!(h.round(), -4.0);assert_eq!(i.round(),4.0);assert_eq!(j.round(),5.0);

Returns the nearest integer to a number. Rounds half-way cases to the numberwith an even least significant digit.

This function always returns the precise result.

§Examples

#![feature(f128)]letf =3.3_f128;letg = -3.3_f128;leth =3.5_f128;leti =4.5_f128;assert_eq!(f.round_ties_even(),3.0);assert_eq!(g.round_ties_even(), -3.0);assert_eq!(h.round_ties_even(),4.0);assert_eq!(i.round_ties_even(),4.0);

Returns the integer part ofself.This means that non-integer numbers are always truncated towards zero.

This function always returns the precise result.

§Examples

#![feature(f128)]letf =3.7_f128;letg =3.0_f128;leth = -3.7_f128;assert_eq!(f.trunc(),3.0);assert_eq!(g.trunc(),3.0);assert_eq!(h.trunc(), -3.0);

Returns the fractional part ofself.

This function always returns the precise result.

§Examples

#![feature(f128)]letx =3.6_f128;lety = -3.6_f128;letabs_difference_x = (x.fract() -0.6).abs();letabs_difference_y = (y.fract() - (-0.6)).abs();assert!(abs_difference_x <= f128::EPSILON);assert!(abs_difference_y <= f128::EPSILON);

Fused multiply-add. Computes(self * a) + b with only one roundingerror, yielding a more accurate result than an unfused multiply-add.

Usingmul_addmay be more performant than an unfused multiply-add ifthe target architecture has a dedicatedfma CPU instruction. However,this is not always true, and will be heavily dependant on designingalgorithms with specific target hardware in mind.

§Precision

The result of this operation is guaranteed to be the roundedinfinite-precision result. It is specified by IEEE 754 asfusedMultiplyAdd and guaranteed not to change.

§Examples

#![feature(f128)]letm =10.0_f128;letx =4.0_f128;letb =60.0_f128;assert_eq!(m.mul_add(x, b),100.0);assert_eq!(m * x + b,100.0);letone_plus_eps =1.0_f128+ f128::EPSILON;letone_minus_eps =1.0_f128- f128::EPSILON;letminus_one = -1.0_f128;// The exact result (1 + eps) * (1 - eps) = 1 - eps * eps.assert_eq!(one_plus_eps.mul_add(one_minus_eps, minus_one), -f128::EPSILON * f128::EPSILON);// Different rounding with the non-fused multiply and add.assert_eq!(one_plus_eps * one_minus_eps + minus_one,0.0);

Calculates Euclidean division, the matching method forrem_euclid.

This computes the integern such thatself = n * rhs + self.rem_euclid(rhs).In other words, the result isself / rhs rounded to the integernsuch thatself >= n * rhs.

§Precision

The result of this operation is guaranteed to be the roundedinfinite-precision result.

§Examples

#![feature(f128)]leta: f128 =7.0;letb =4.0;assert_eq!(a.div_euclid(b),1.0);// 7.0 > 4.0 * 1.0assert_eq!((-a).div_euclid(b), -2.0);// -7.0 >= 4.0 * -2.0assert_eq!(a.div_euclid(-b), -1.0);// 7.0 >= -4.0 * -1.0assert_eq!((-a).div_euclid(-b),2.0);// -7.0 >= -4.0 * 2.0

Calculates the least nonnegative remainder ofself (mod rhs).

In particular, the return valuer satisfies0.0 <= r < rhs.abs() inmost cases. However, due to a floating point round-off error it canresult inr == rhs.abs(), violating the mathematical definition, ifself is much smaller thanrhs.abs() in magnitude andself < 0.0.This result is not an element of the function’s codomain, but it is theclosest floating point number in the real numbers and thus fulfills thepropertyself == self.div_euclid(rhs) * rhs + self.rem_euclid(rhs)approximately.

§Precision

The result of this operation is guaranteed to be the roundedinfinite-precision result.

§Examples

#![feature(f128)]leta: f128 =7.0;letb =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 errorassert!((-f128::EPSILON).rem_euclid(3.0) !=0.0);

Raises a number to an integer power.

Using this function is generally faster than usingpowf.It might have a different sequence of rounding operations thanpowf,so the results are not guaranteed to agree.

Note that this function is special in that it can return non-NaN results for NaN inputs. Forexample,f128::powi(f128::NAN, 0) returns1.0. However, if an input is asignalingNaN, then the result is non-deterministically either a NaN or the result that thecorresponding quiet NaN would produce.

§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

#![feature(f128)]letx =2.0_f128;letabs_difference = (x.powi(2) - (x * x)).abs();assert!(abs_difference <= f128::EPSILON);assert_eq!(f128::powi(f128::NAN,0),1.0);assert_eq!(f128::powi(0.0,0),1.0);

Returns the square root of a number.

Returns NaN ifself is a negative number other than-0.0.

§Precision

The result of this operation is guaranteed to be the roundedinfinite-precision result. It is specified by IEEE 754 assquareRootand guaranteed not to change.

§Examples

#![feature(f128)]letpositive =4.0_f128;letnegative = -4.0_f128;letnegative_zero = -0.0_f128;assert_eq!(positive.sqrt(),2.0);assert!(negative.sqrt().is_nan());assert!(negative_zero.sqrt() == negative_zero);

Returns the default value of0.0

Converts abool tof128 losslessly.The resulting value is positive0.0 forfalse and1.0 fortrue values.

§Examples

#![feature(f128)]letx: f128 =false.into();assert_eq!(x,0.0);assert!(x.is_sign_positive());lety: f128 =true.into();assert_eq!(y,1.0);

Convertsf16 tof128 losslessly.

Convertsf32 tof128 losslessly.

Convertsf64 tof128 losslessly.

Convertsi16 tof128 losslessly.

Convertsi32 tof128 losslessly.

Convertsi8 tof128 losslessly.

Convertsu16 tof128 losslessly.

Convertsu32 tof128 losslessly.

Convertsu8 tof128 losslessly.

Returns the argument unchanged.

CallsU::from(self).

That is, this conversion is whatever the implementation ofFrom<T> for U chooses to do.