diff options
Diffstat (limited to 'library/std/src/f16.rs')
| -rw-r--r-- | library/std/src/f16.rs | 1296 |
1 files changed, 1287 insertions, 9 deletions
diff --git a/library/std/src/f16.rs b/library/std/src/f16.rs index e3024defed7..10908332762 100644 --- a/library/std/src/f16.rs +++ b/library/std/src/f16.rs @@ -12,25 +12,180 @@ pub use core::f16::consts; #[cfg(not(test))] use crate::intrinsics; +#[cfg(not(test))] +use crate::sys::cmath; #[cfg(not(test))] impl f16 { - /// Raises a number to an integer power. + /// Returns the largest integer less than or equal to `self`. /// - /// 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. + /// This function always returns the precise result. /// - /// # Unspecified precision + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let f = 3.7_f16; + /// let g = 3.0_f16; + /// let h = -3.7_f16; /// - /// 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. + /// assert_eq!(f.floor(), 3.0); + /// assert_eq!(g.floor(), 3.0); + /// assert_eq!(h.floor(), -4.0); + /// # } + /// ``` #[inline] #[rustc_allow_incoherent_impl] #[unstable(feature = "f16", issue = "116909")] #[must_use = "method returns a new number and does not mutate the original value"] - pub fn powi(self, n: i32) -> f16 { - unsafe { intrinsics::powif16(self, n) } + pub fn floor(self) -> f16 { + unsafe { intrinsics::floorf16(self) } + } + + /// Returns the smallest integer greater than or equal to `self`. + /// + /// This function always returns the precise result. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let f = 3.01_f16; + /// let g = 4.0_f16; + /// + /// assert_eq!(f.ceil(), 4.0); + /// assert_eq!(g.ceil(), 4.0); + /// # } + /// ``` + #[inline] + #[doc(alias = "ceiling")] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn ceil(self) -> f16 { + unsafe { intrinsics::ceilf16(self) } + } + + /// 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(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let f = 3.3_f16; + /// let g = -3.3_f16; + /// let h = -3.7_f16; + /// let i = 3.5_f16; + /// let j = 4.5_f16; + /// + /// 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); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn round(self) -> f16 { + unsafe { intrinsics::roundf16(self) } + } + + /// 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(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let f = 3.3_f16; + /// let g = -3.3_f16; + /// let h = 3.5_f16; + /// let i = 4.5_f16; + /// + /// 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); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn round_ties_even(self) -> f16 { + unsafe { intrinsics::rintf16(self) } + } + + /// 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(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let f = 3.7_f16; + /// let g = 3.0_f16; + /// let h = -3.7_f16; + /// + /// assert_eq!(f.trunc(), 3.0); + /// assert_eq!(g.trunc(), 3.0); + /// assert_eq!(h.trunc(), -3.0); + /// # } + /// ``` + #[inline] + #[doc(alias = "truncate")] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn trunc(self) -> f16 { + unsafe { intrinsics::truncf16(self) } + } + + /// Returns the fractional part of `self`. + /// + /// This function always returns the precise result. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let x = 3.6_f16; + /// let y = -3.6_f16; + /// let abs_difference_x = (x.fract() - 0.6).abs(); + /// let abs_difference_y = (y.fract() - (-0.6)).abs(); + /// + /// assert!(abs_difference_x <= f16::EPSILON); + /// assert!(abs_difference_y <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn fract(self) -> f16 { + self - self.trunc() } /// Computes the absolute value of `self`. @@ -60,4 +215,1127 @@ impl f16 { // FIXME(f16_f128): replace with `intrinsics::fabsf16` when available Self::from_bits(self.to_bits() & !(1 << 15)) } + + /// 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(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let f = 3.5_f16; + /// + /// assert_eq!(f.signum(), 1.0); + /// assert_eq!(f16::NEG_INFINITY.signum(), -1.0); + /// + /// assert!(f16::NAN.signum().is_nan()); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn signum(self) -> f16 { + if self.is_nan() { Self::NAN } else { 1.0_f16.copysign(self) } + } + + /// Returns a number composed of the magnitude of `self` and the sign of + /// `sign`. + /// + /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise + /// equal to `-self`. If `self` is a NaN, then a NaN with the sign bit of + /// `sign` is returned. Note, however, that conserving the sign bit on NaN + /// across arithmetical operations is not generally guaranteed. + /// See [explanation of NaN as a special value](primitive@f16) for more info. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let f = 3.5_f16; + /// + /// assert_eq!(f.copysign(0.42), 3.5_f16); + /// assert_eq!(f.copysign(-0.42), -3.5_f16); + /// assert_eq!((-f).copysign(0.42), 3.5_f16); + /// assert_eq!((-f).copysign(-0.42), -3.5_f16); + /// + /// assert!(f16::NAN.copysign(1.0).is_nan()); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn copysign(self, sign: f16) -> f16 { + unsafe { intrinsics::copysignf16(self, sign) } + } + + /// 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(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let m = 10.0_f16; + /// let x = 4.0_f16; + /// let b = 60.0_f16; + /// + /// assert_eq!(m.mul_add(x, b), 100.0); + /// assert_eq!(m * x + b, 100.0); + /// + /// let one_plus_eps = 1.0_f16 + f16::EPSILON; + /// let one_minus_eps = 1.0_f16 - f16::EPSILON; + /// let minus_one = -1.0_f16; + /// + /// // The exact result (1 + eps) * (1 - eps) = 1 - eps * eps. + /// assert_eq!(one_plus_eps.mul_add(one_minus_eps, minus_one), -f16::EPSILON * f16::EPSILON); + /// // Different rounding with the non-fused multiply and add. + /// assert_eq!(one_plus_eps * one_minus_eps + minus_one, 0.0); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn mul_add(self, a: f16, b: f16) -> f16 { + unsafe { intrinsics::fmaf16(self, a, b) } + } + + /// 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(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let a: f16 = 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 + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn div_euclid(self, rhs: f16) -> f16 { + let q = (self / rhs).trunc(); + if self % rhs < 0.0 { + return if rhs > 0.0 { q - 1.0 } else { q + 1.0 }; + } + q + } + + /// 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(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let a: f16 = 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!((-f16::EPSILON).rem_euclid(3.0) != 0.0); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[doc(alias = "modulo", alias = "mod")] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn rem_euclid(self, rhs: f16) -> f16 { + let r = self % rhs; + if r < 0.0 { r + rhs.abs() } else { r } + } + + /// 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. + /// + /// # 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. + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn powi(self, n: i32) -> f16 { + unsafe { intrinsics::powif16(self, n) } + } + + /// Raises a number to a floating point power. + /// + /// # 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(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let x = 2.0_f16; + /// let abs_difference = (x.powf(2.0) - (x * x)).abs(); + /// + /// assert!(abs_difference <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn powf(self, n: f16) -> f16 { + unsafe { intrinsics::powf16(self, n) } + } + + /// 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(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let positive = 4.0_f16; + /// let negative = -4.0_f16; + /// let negative_zero = -0.0_f16; + /// + /// assert_eq!(positive.sqrt(), 2.0); + /// assert!(negative.sqrt().is_nan()); + /// assert!(negative_zero.sqrt() == negative_zero); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn sqrt(self) -> f16 { + unsafe { intrinsics::sqrtf16(self) } + } + + /// 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(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let one = 1.0f16; + /// // e^1 + /// let e = one.exp(); + /// + /// // ln(e) - 1 == 0 + /// let abs_difference = (e.ln() - 1.0).abs(); + /// + /// assert!(abs_difference <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn exp(self) -> f16 { + unsafe { intrinsics::expf16(self) } + } + + /// 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(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let f = 2.0f16; + /// + /// // 2^2 - 4 == 0 + /// let abs_difference = (f.exp2() - 4.0).abs(); + /// + /// assert!(abs_difference <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn exp2(self) -> f16 { + unsafe { intrinsics::exp2f16(self) } + } + + /// Returns the natural logarithm of the 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. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let one = 1.0f16; + /// // e^1 + /// let e = one.exp(); + /// + /// // ln(e) - 1 == 0 + /// let abs_difference = (e.ln() - 1.0).abs(); + /// + /// assert!(abs_difference <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn ln(self) -> f16 { + unsafe { intrinsics::logf16(self) } + } + + /// Returns the logarithm of the number with respect to an arbitrary base. + /// + /// 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(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let five = 5.0f16; + /// + /// // log5(5) - 1 == 0 + /// let abs_difference = (five.log(5.0) - 1.0).abs(); + /// + /// assert!(abs_difference <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn log(self, base: f16) -> f16 { + self.ln() / base.ln() + } + + /// Returns the base 2 logarithm of the 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. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let two = 2.0f16; + /// + /// // log2(2) - 1 == 0 + /// let abs_difference = (two.log2() - 1.0).abs(); + /// + /// assert!(abs_difference <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn log2(self) -> f16 { + unsafe { intrinsics::log2f16(self) } + } + + /// Returns the base 10 logarithm of the 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. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let ten = 10.0f16; + /// + /// // log10(10) - 1 == 0 + /// let abs_difference = (ten.log10() - 1.0).abs(); + /// + /// assert!(abs_difference <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn log10(self) -> f16 { + unsafe { intrinsics::log10f16(self) } + } + + /// 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 `cbrtf` from libc on Unix + /// and Windows. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let x = 8.0f16; + /// + /// // x^(1/3) - 2 == 0 + /// let abs_difference = (x.cbrt() - 2.0).abs(); + /// + /// assert!(abs_difference <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn cbrt(self) -> f16 { + (unsafe { cmath::cbrtf(self as f32) }) as f16 + } + + /// 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 `hypotf` from libc on Unix + /// and Windows. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let x = 2.0f16; + /// let y = 3.0f16; + /// + /// // sqrt(x^2 + y^2) + /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs(); + /// + /// assert!(abs_difference <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn hypot(self, other: f16) -> f16 { + (unsafe { cmath::hypotf(self as f32, other as f32) }) as f16 + } + + /// 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(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let x = std::f16::consts::FRAC_PI_2; + /// + /// let abs_difference = (x.sin() - 1.0).abs(); + /// + /// assert!(abs_difference <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn sin(self) -> f16 { + unsafe { intrinsics::sinf16(self) } + } + + /// 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(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let x = 2.0 * std::f16::consts::PI; + /// + /// let abs_difference = (x.cos() - 1.0).abs(); + /// + /// assert!(abs_difference <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn cos(self) -> f16 { + unsafe { intrinsics::cosf16(self) } + } + + /// 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 `tanf` from libc on Unix and + /// Windows. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let x = std::f16::consts::FRAC_PI_4; + /// let abs_difference = (x.tan() - 1.0).abs(); + /// + /// assert!(abs_difference <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn tan(self) -> f16 { + (unsafe { cmath::tanf(self as f32) }) as f16 + } + + /// 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 `asinf` from libc on Unix + /// and Windows. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let f = std::f16::consts::FRAC_PI_2; + /// + /// // asin(sin(pi/2)) + /// let abs_difference = (f.sin().asin() - std::f16::consts::FRAC_PI_2).abs(); + /// + /// assert!(abs_difference <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[doc(alias = "arcsin")] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn asin(self) -> f16 { + (unsafe { cmath::asinf(self as f32) }) as f16 + } + + /// 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 `acosf` from libc on Unix + /// and Windows. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let f = std::f16::consts::FRAC_PI_4; + /// + /// // acos(cos(pi/4)) + /// let abs_difference = (f.cos().acos() - std::f16::consts::FRAC_PI_4).abs(); + /// + /// assert!(abs_difference <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[doc(alias = "arccos")] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn acos(self) -> f16 { + (unsafe { cmath::acosf(self as f32) }) as f16 + } + + /// 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 `atanf` from libc on Unix + /// and Windows. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let f = 1.0f16; + /// + /// // atan(tan(1)) + /// let abs_difference = (f.tan().atan() - 1.0).abs(); + /// + /// assert!(abs_difference <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[doc(alias = "arctan")] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn atan(self) -> f16 { + (unsafe { cmath::atanf(self as f32) }) as f16 + } + + /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`) in radians. + /// + /// * `x = 0`, `y = 0`: `0` + /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]` + /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]` + /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)` + /// + /// # 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 `atan2f` from libc on Unix + /// and Windows. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// // Positive angles measured counter-clockwise + /// // from positive x axis + /// // -pi/4 radians (45 deg clockwise) + /// let x1 = 3.0f16; + /// let y1 = -3.0f16; + /// + /// // 3pi/4 radians (135 deg counter-clockwise) + /// let x2 = -3.0f16; + /// let y2 = 3.0f16; + /// + /// let abs_difference_1 = (y1.atan2(x1) - (-std::f16::consts::FRAC_PI_4)).abs(); + /// let abs_difference_2 = (y2.atan2(x2) - (3.0 * std::f16::consts::FRAC_PI_4)).abs(); + /// + /// assert!(abs_difference_1 <= f16::EPSILON); + /// assert!(abs_difference_2 <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn atan2(self, other: f16) -> f16 { + (unsafe { cmath::atan2f(self as f32, other as f32) }) as f16 + } + + /// 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 `(f16::sin(x), + /// f16::cos(x))`. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let x = std::f16::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 <= f16::EPSILON); + /// assert!(abs_difference_1 <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[doc(alias = "sincos")] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + pub fn sin_cos(self) -> (f16, f16) { + (self.sin(), self.cos()) + } + + /// 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 `expm1f` from libc on Unix + /// and Windows. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let x = 1e-4_f16; + /// + /// // 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-4); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn exp_m1(self) -> f16 { + (unsafe { cmath::expm1f(self as f32) }) as f16 + } + + /// Returns `ln(1+n)` (natural logarithm) more accurately than if + /// the operations were performed separately. + /// + /// # 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 `log1pf` from libc on Unix + /// and Windows. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let x = 1e-4_f16; + /// + /// // 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-4); + /// # } + /// ``` + #[inline] + #[doc(alias = "log1p")] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn ln_1p(self) -> f16 { + (unsafe { cmath::log1pf(self as f32) }) as f16 + } + + /// 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 `sinhf` from libc on Unix + /// and Windows. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let e = std::f16::consts::E; + /// let x = 1.0f16; + /// + /// 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 <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn sinh(self) -> f16 { + (unsafe { cmath::sinhf(self as f32) }) as f16 + } + + /// 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 `coshf` from libc on Unix + /// and Windows. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let e = std::f16::consts::E; + /// let x = 1.0f16; + /// 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 <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn cosh(self) -> f16 { + (unsafe { cmath::coshf(self as f32) }) as f16 + } + + /// 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 `tanhf` from libc on Unix + /// and Windows. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let e = std::f16::consts::E; + /// let x = 1.0f16; + /// + /// 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 <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn tanh(self) -> f16 { + (unsafe { cmath::tanhf(self as f32) }) as f16 + } + + /// 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(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let x = 1.0f16; + /// let f = x.sinh().asinh(); + /// + /// let abs_difference = (f - x).abs(); + /// + /// assert!(abs_difference <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[doc(alias = "arcsinh")] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn asinh(self) -> f16 { + let ax = self.abs(); + let ix = 1.0 / ax; + (ax + (ax / (Self::hypot(1.0, ix) + ix))).ln_1p().copysign(self) + } + + /// 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(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let x = 1.0f16; + /// let f = x.cosh().acosh(); + /// + /// let abs_difference = (f - x).abs(); + /// + /// assert!(abs_difference <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[doc(alias = "arccosh")] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn acosh(self) -> f16 { + if self < 1.0 { + Self::NAN + } else { + (self + ((self - 1.0).sqrt() * (self + 1.0).sqrt())).ln() + } + } + + /// 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(f16)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let e = std::f16::consts::E; + /// let f = e.tanh().atanh(); + /// + /// let abs_difference = (f - e).abs(); + /// + /// assert!(abs_difference <= 0.01); + /// # } + /// ``` + #[inline] + #[doc(alias = "arctanh")] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn atanh(self) -> f16 { + 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p() + } + + /// 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 `tgammaf` from libc on Unix + /// and Windows. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// #![feature(float_gamma)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let x = 5.0f16; + /// + /// let abs_difference = (x.gamma() - 24.0).abs(); + /// + /// assert!(abs_difference <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn gamma(self) -> f16 { + (unsafe { cmath::tgammaf(self as f32) }) as f16 + } + + /// 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 `lgamma_r` from libc on Unix + /// and Windows. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f16)] + /// #![feature(float_gamma)] + /// # #[cfg(reliable_f16_math)] { + /// + /// let x = 2.0f16; + /// + /// let abs_difference = (x.ln_gamma().0 - 0.0).abs(); + /// + /// assert!(abs_difference <= f16::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f16", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn ln_gamma(self) -> (f16, i32) { + let mut signgamp: i32 = 0; + let x = (unsafe { cmath::lgammaf_r(self as f32, &mut signgamp) }) as f16; + (x, signgamp) + } } |