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. For example, f128::powf(f128::NAN, 0.0) returns 1.0. However, if an input is a signaling NaN, then the result is non-deterministically either a NaN or the result that the corresponding 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)]

let x = 2.0_f128;
let abs_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);

Returns e^(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)]

let one = 1.0f128;
// e^1
let e = one.exp();

// ln(e) - 1 == 0
let abs_difference = (e.ln() - 1.0).abs();

assert!(abs_difference <= f128::EPSILON);

Returns 2^(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)]

let f = 2.0f128;

// 2^2 - 4 == 0
let abs_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)]

let one = 1.0f128;
// e^1
let e = one.exp();

// ln(e) - 1 == 0
let abs_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, and self.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)]

let five = 5.0f128;

// log5(5) - 1 == 0
let abs_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)]

let two = 2.0f128;

// log2(2) - 1 == 0
let abs_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)]

let ten = 10.0f128;

// log10(10) - 1 == 0
let abs_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 the cbrtf128 from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f128)]

let x = 8.0f128;

// x^(1/3) - 2 == 0
let abs_difference = (x.cbrt() - 2.0).abs();

assert!(abs_difference <= f128::EPSILON);

Compute the distance between the origin and a point (x, y) on the Euclidean plane. Equivalently, compute the length of the hypotenuse of a right-angle triangle with other sides having length x.abs() and y.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 the hypotf128 from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f128)]

let x = 2.0f128;
let y = 3.0f128;

// sqrt(x^2 + y^2)
let abs_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)]

let x = std::f128::consts::FRAC_PI_2;

let abs_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)]

let x = 2.0 * std::f128::consts::PI;

let abs_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 the tanf128 from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f128)]

let x = std::f128::consts::FRAC_PI_4;
let abs_difference = (x.tan() - 1.0).abs();

assert!(abs_difference <= f128::EPSILON);

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].

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 asinf128 from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f128)]

let f = std::f128::consts::FRAC_PI_4;

// asin(sin(pi/2))
let abs_difference = (f.sin().asin() - f).abs();

assert!(abs_difference <= f128::EPSILON);

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].

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 acosf128 from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f128)]

let f = std::f128::consts::FRAC_PI_4;

// acos(cos(pi/4))
let abs_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 the range [-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 the atanf128 from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f128)]

let f = 1.0f128;

// atan(tan(1))
let abs_difference = (f.tan().atan() - 1.0).abs();

assert!(abs_difference <= f128::EPSILON);

Computes the four quadrant arctangent of self (y) and other (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 the atan2f128 from libc on Unix and 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)
let x1 = 3.0f128;
let y1 = -3.0f128;

// 3pi/4 radians (135 deg counter-clockwise)
let x2 = -3.0f128;
let y2 = 3.0f128;

let abs_difference_1 = (y1.atan2(x1) - (-std::f128::consts::FRAC_PI_4)).abs();
let abs_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)]

let x = std::f128::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 <= f128::EPSILON);
assert!(abs_difference_1 <= f128::EPSILON);

Returns e^(self) - 1 in a way that is accurate even if the number 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 the expm1f128 from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f128)]

let x = 1e-8_f128;

// for very small x, e^x is approximately 1 + x + x^2 / 2
let approx = x + x * x / 2.0;
let abs_difference = (x.exp_m1() - approx).abs();

assert!(abs_difference < 1e-10);

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

This returns NaN when n < -1.0, and negative infinity when n == -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 the log1pf128 from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f128)]

let x = 1e-8_f128;

// 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-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 the sinhf128 from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f128)]

let e = std::f128::consts::E;
let x = 1.0f128;

let f = x.sinh();
// Solving sinh() at 1 gives `(e^2-1)/(2e)`
let g = ((e * e) - 1.0) / (2.0 * e);
let abs_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 the coshf128 from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f128)]

let e = std::f128::consts::E;
let x = 1.0f128;
let f = x.cosh();
// Solving cosh() at 1 gives this result
let g = ((e * e) + 1.0) / (2.0 * e);
let abs_difference = (f - g).abs();

// Same result
assert!(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 the tanhf128 from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f128)]

let e = std::f128::consts::E;
let x = 1.0f128;

let f = x.tanh();
// Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
let g = (1.0 - e.powi(-2)) / (1.0 + e.powi(-2));
let abs_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)]

let x = 1.0f128;
let f = x.sinh().asinh();

let abs_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)]

let x = 1.0f128;
let f = x.cosh().acosh();

let abs_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)]

let x = std::f128::consts::FRAC_PI_6;
let f = x.tanh().atanh();

let abs_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 the tgammaf128 from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f128)]
#![feature(float_gamma)]

let x = 5.0f128;

let abs_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 the lgammaf128_r from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f128)]
#![feature(float_gamma)]

let x = 2.0f128;

let abs_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 the erff128 from libc on Unix and 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)`).
fn within_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 deviation
assert!((within_standard_deviations(1.0) - 68.269).abs() < 0.01);
// 95% of a normal distribution is within two standard deviations
assert!((within_standard_deviations(2.0) - 95.450).abs() < 0.01);
// 99.7% of a normal distribution is within three standard deviations
assert!((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 the erfcf128 from libc on Unix and Windows. Note that this might change in the future.

Examples

#![feature(f128)]
#![feature(float_erf)]
let x: f128 = 0.123;

let one = x.erf() + x.erfc();
let abs_difference = (one - 1.0).abs();

assert!(abs_difference <= f128::EPSILON);

The radix or base of the internal representation of f128.

Number of significant digits in base 2.

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

Approximate number of significant digits in base 10.

This is the maximum x such that any decimal number with x significant digits can be converted to f128 and back without loss.

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

Machine epsilon value for f128.

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

Equal to 2^{1 − MANTISSA_DIGITS}.

Smallest finite f128 value.

Equal to −MAX.

Smallest positive normal f128 value.

Equal to 2^{MIN_EXP − 1}.

Largest finite f128 value.

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

One greater than the minimum possible normal power of 2 exponent for a significand bounded by 1 ≤ x < 2 (i.e. the IEEE definition).

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

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

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

Minimum x for which 10^x is normal.

Equal to ceil(log₁₀ MIN_POSITIVE).

Maximum x 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 are considered to be NaN. Furthermore, the standard makes a difference between a “signaling” and a “quiet” NaN, and allows inspecting its “payload” (the unspecified bits in the bit pattern) and its sign. See the specification of NaN bit patterns for more info.

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

Returns true if this value is NaN.

#![feature(f128)]

let nan = f128::NAN;
let f = 7.0_f128;

assert!(nan.is_nan());
assert!(!f.is_nan());

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

#![feature(f128)]

let f = 7.0f128;
let inf = f128::INFINITY;
let neg_inf = f128::NEG_INFINITY;
let nan = f128::NAN;

assert!(!f.is_infinite());
assert!(!nan.is_infinite());

assert!(inf.is_infinite());
assert!(neg_inf.is_infinite());

Returns true if this number is neither infinite nor NaN.

#![feature(f128)]

let f = 7.0f128;
let inf: f128 = f128::INFINITY;
let neg_inf: f128 = f128::NEG_INFINITY;
let nan: f128 = f128::NAN;

assert!(f.is_finite());

assert!(!nan.is_finite());
assert!(!inf.is_finite());
assert!(!neg_inf.is_finite());

Returns true if the number is subnormal.

#![feature(f128)]

let min = f128::MIN_POSITIVE; // 3.362103143e-4932f128
let max = f128::MAX;
let lower_than_min = 1.0e-4960_f128;
let zero = 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());

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

#![feature(f128)]

let min = f128::MIN_POSITIVE; // 3.362103143e-4932f128
let max = f128::MAX;
let lower_than_min = 1.0e-4960_f128;
let zero = 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 property is going to be tested, it is generally faster to use the specific predicate instead.

#![feature(f128)]

use std::num::FpCategory;

let num = 12.4_f128;
let inf = f128::INFINITY;

assert_eq!(num.classify(), FpCategory::Normal);
assert_eq!(inf.classify(), FpCategory::Infinite);

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

Note that IEEE 754 doesn’t assign any meaning to the sign bit in case of a NaN, and as Rust doesn’t guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the result of is_sign_positive on a NaN might produce an unexpected or non-portable result. See the specification of NaN bit patterns for more info. Use self.signum() == 1.0 if you need fully portable behavior (will return false for all NaNs).

#![feature(f128)]

let f = 7.0_f128;
let g = -7.0_f128;

assert!(f.is_sign_positive());
assert!(!g.is_sign_positive());

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

Note that IEEE 754 doesn’t assign any meaning to the sign bit in case of a NaN, and as Rust doesn’t guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the result of is_sign_negative on a NaN might produce an unexpected or non-portable result. See the specification of NaN bit patterns for more info. Use self.signum() == -1.0 if you need fully portable behavior (will return false for all NaNs).

#![feature(f128)]

let f = 7.0_f128;
let g = -7.0_f128;

assert!(!f.is_sign_negative());
assert!(g.is_sign_negative());

Returns the least number greater than self.

Let TINY be the smallest representable positive f128. Then,

• if self.is_nan(), this returns self;
• if self is NEG_INFINITY, this returns MIN;
• if self is -TINY, this returns -0.0;
• if self is -0.0 or +0.0, this returns TINY;
• if self is MAX or INFINITY, this returns INFINITY;
• otherwise the unique least value greater than self is returned.

The identity x.next_up() == -(-x).next_down() holds for all non-NaN x. When x is finite x == 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-754 nextUp.

Returns the greatest number less than self.

Let TINY be the smallest representable positive f128. Then,

• if self.is_nan(), this returns self;
• if self is INFINITY, this returns MAX;
• if self is TINY, this returns 0.0;
• if self is -0.0 or +0.0, this returns -TINY;
• if self is MIN or NEG_INFINITY, this returns NEG_INFINITY;
• otherwise the unique greatest value less than self is returned.

The identity x.next_down() == -(-x).next_up() holds for all non-NaN x. When x is finite x == x.next_down().next_up() also holds.

#![feature(f128)]

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

This operation corresponds to IEEE-754 nextDown.

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

#![feature(f128)]

let x = 2.0_f128;
let abs_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)]

let angle = std::f128::consts::PI;

let abs_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)]

let angle = 180.0f128;

let abs_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 both arguments are NaN, the return value is NaN, with the bit pattern picked using the usual rules for arithmetic operations. If the inputs compare equal (such as for the case of +0.0 and -0.0), either input may be returned non-deterministically.

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

#![feature(f128)]

let x = 1.0f128;
let y = 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 both arguments are NaN, the return value is NaN, with the bit pattern picked using the usual rules for arithmetic operations. If the inputs compare equal (such as for the case of +0.0 and -0.0), either input may be returned non-deterministically.

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

#![feature(f128)]

let x = 1.0f128;
let y = 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 pattern picked using the usual rules for arithmetic operations. Furthermore, -0.0 is considered to be less than +0.0, making this function fully deterministic for non-NaN inputs.

This is in contrast to f128::max which only returns NaN when both arguments are NaN, and which does not reliably order -0.0 and +0.0.

This follows the IEEE 754-2019 semantics for maximum.

#![feature(f128)]
#![feature(float_minimum_maximum)]

let x = 1.0f128;
let y = 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 pattern picked using the usual rules for arithmetic operations. Furthermore, -0.0 is considered to be less than +0.0, making this function fully deterministic for non-NaN inputs.

This is in contrast to f128::min which only returns NaN when both arguments are NaN, and which does not reliably order -0.0 and +0.0.

This follows the IEEE 754-2019 semantics for minimum.

#![feature(f128)]
#![feature(float_minimum_maximum)]

let x = 1.0f128;
let y = 2.0f128;

assert_eq!(x.minimum(y), x);
assert!(x.minimum(f128::NAN).is_nan());

Calculates the midpoint (average) between self and rhs.

This returns NaN when either 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)]

let value = 4.6_f128;
let rounded = unsafe { value.to_int_unchecked::<u16>() };
assert_eq!(rounded, 4);

let value = -128.9_f128;
let rounded = unsafe { value.to_int_unchecked::<i8>() };
assert_eq!(rounded, i8::MIN);

Safety

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 u128.

This is currently identical to transmute::<f128, u128>(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.

#![feature(f128)]

assert_eq!((12.5f128).to_bits(), 0x40029000000000000000000000000000);

Raw transmutation from u128.

This is currently identical to transmute::<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, 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.

#![feature(f128)]

let v = f128::from_bits(0x40029000000000000000000000000000);
assert_eq!(v, 12.5);

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

See from_bits for some discussion of the portability of this operation (there are almost no issues).

Examples

#![feature(f128)]

let bytes = 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 in little-endian byte order.

See from_bits for some discussion of the portability of this operation (there are almost no issues).

Examples

#![feature(f128)]

let bytes = 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 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.

See from_bits for some discussion of the portability of this operation (there are almost no issues).

Examples

#![feature(f128)]

let bytes = 12.5f128.to_ne_bytes();
assert_eq!(
    bytes,
    if cfg!(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.

See from_bits for some discussion of the portability of this operation (there are almost no issues).

Examples

#![feature(f128)]

let value = 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.

See from_bits for some discussion of the portability of this operation (there are almost no issues).

Examples

#![feature(f128)]

let value = 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 code likely wants to use from_be_bytes or from_le_bytes, as appropriate instead.

See from_bits for some discussion of the portability of this operation (there are almost no issues).

Examples

#![feature(f128)]

let value = f128::from_ne_bytes(if cfg!(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 between self and other.

Unlike the standard partial comparison between floating point numbers, this comparison always produces an ordering in accordance to the totalOrder 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 the PartialOrd and PartialEq implementations of f128. For example, they consider negative and positive zero equal, while total_cmp doesn’t.

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

Example

#![feature(f128)]

struct GoodBoy {
    name: &'static str,
    weight: f128,
}

let mut bois = 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.
if f128::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.

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. If the result is zero and among the three inputs self, min, and max there are zeros with different sign, either 0.0 or -0.0 is returned non-deterministically.

Panics

Panics if min > max, min is NaN, or max 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 most limit.

This is functionally equivalent to self.clamp(-limit, limit), but is more explicit about the intent.

Panics

Panics if limit 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 of self.

This function always returns the precise result.

Examples

#![feature(f128)]

let x = 3.5_f128;
let y = -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 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

Examples

#![feature(f128)]

let f = 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 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 same payload as self and the sign bit of sign is returned.

If sign is a NaN, then this operation will still carry over its sign into the result. Note that IEEE 754 doesn’t assign any meaning to the sign bit in case of a NaN, and as Rust doesn’t guarantee that the bit pattern of NaNs are conserved over arithmetic operations, the result of copysign with sign being a NaN might produce an unexpected or non-portable result. See the specification of NaN bit patterns for more info.

Examples

#![feature(f128)]

let f = 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.

See algebraic operators for more info.

Float subtraction that allows optimizations based on algebraic rules.

See algebraic operators for more info.

Float multiplication that allows optimizations based on algebraic rules.

See algebraic operators for more info.

Float division that allows optimizations based on algebraic rules.

See algebraic operators for more info.

Float remainder that allows optimizations based on algebraic rules.

See algebraic operators for more info.

Returns the largest integer less than or equal to self.

This function always returns the precise result.

Examples

#![feature(f128)]

let f = 3.7_f128;
let g = 3.0_f128;
let h = -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 to self.

This function always returns the precise result.

Examples

#![feature(f128)]

let f = 3.01_f128;
let g = 4.0_f128;

assert_eq!(f.ceil(), 4.0);
assert_eq!(g.ceil(), 4.0);

Returns the nearest integer to self. If a value is half-way between two integers, round away from 0.0.

This function always returns the precise result.

Examples

#![feature(f128)]

let f = 3.3_f128;
let g = -3.3_f128;
let h = -3.7_f128;
let i = 3.5_f128;
let j = 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 number with an even least significant digit.

This function always returns the precise result.

Examples

#![feature(f128)]

let f = 3.3_f128;
let g = -3.3_f128;
let h = 3.5_f128;
let i = 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 of self. This means that non-integer numbers are always truncated towards zero.

This function always returns the precise result.

Examples

#![feature(f128)]

let f = 3.7_f128;
let g = 3.0_f128;
let h = -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 of self.

This function always returns the precise result.

Examples

#![feature(f128)]

let x = 3.6_f128;
let y = -3.6_f128;
let abs_difference_x = (x.fract() - 0.6).abs();
let abs_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 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.

Precision

The result of this operation is guaranteed to be the rounded infinite-precision result. It is specified by IEEE 754 as fusedMultiplyAdd and guaranteed not to change.

Examples

#![feature(f128)]

let m = 10.0_f128;
let x = 4.0_f128;
let b = 60.0_f128;

assert_eq!(m.mul_add(x, b), 100.0);
assert_eq!(m * x + b, 100.0);

let one_plus_eps = 1.0_f128 + f128::EPSILON;
let one_minus_eps = 1.0_f128 - f128::EPSILON;
let minus_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 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.

Precision

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

Examples

#![feature(f128)]

let a: f128 = 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

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) approximately.

Precision

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

Examples

#![feature(f128)]

let a: f128 = 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!((-f128::EPSILON).rem_euclid(3.0) != 0.0);

Raises a number to an integer power.

Using this function is generally faster than using powf. It might have a different sequence of rounding operations than powf, 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. For example, f128::powi(f128::NAN, 0) returns 1.0. However, if an input is a signaling NaN, then the result is non-deterministically either a NaN or the result that the corresponding 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)]

let x = 2.0_f128;
let abs_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 if self is a negative number other than -0.0.

Precision

The result of this operation is guaranteed to be the rounded infinite-precision result. It is specified by IEEE 754 as squareRoot and guaranteed not to change.

Examples

#![feature(f128)]

let positive = 4.0_f128;
let negative = -4.0_f128;
let negative_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 of 0.0

Converts a bool to f128 losslessly. The resulting value is positive 0.0 for false and 1.0 for true values.

Examples

#![feature(f128)]

let x: f128 = false.into();
assert_eq!(x, 0.0);
assert!(x.is_sign_positive());

let y: f128 = true.into();
assert_eq!(y, 1.0);

Converts f16 to f128 losslessly.

Converts f32 to f128 losslessly.

Converts f64 to f128 losslessly.

Converts i16 to f128 losslessly.

Converts i32 to f128 losslessly.

Converts i8 to f128 losslessly.

Converts u16 to f128 losslessly.

Converts u32 to f128 losslessly.

Converts u8 to f128 losslessly.

Returns the argument unchanged.

Calls U::from(self).

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