diff options
| -rw-r--r-- | library/std/build.rs | 37 | ||||
| -rw-r--r-- | library/std/src/f128.rs | 1300 | ||||
| -rw-r--r-- | library/std/src/f128/tests.rs | 450 | ||||
| -rw-r--r-- | library/std/src/f16.rs | 1296 | ||||
| -rw-r--r-- | library/std/src/f16/tests.rs | 444 | ||||
| -rw-r--r-- | library/std/src/macros.rs | 2 | ||||
| -rw-r--r-- | library/std/src/sys/cmath.rs | 15 |
7 files changed, 3452 insertions, 92 deletions
diff --git a/library/std/build.rs b/library/std/build.rs index 9b58dd53ba2..18ca7b512a9 100644 --- a/library/std/build.rs +++ b/library/std/build.rs @@ -85,6 +85,11 @@ fn main() { println!("cargo:rustc-check-cfg=cfg(reliable_f16)"); println!("cargo:rustc-check-cfg=cfg(reliable_f128)"); + // This is a step beyond only having the types and basic functions available. Math functions + // aren't consistently available or correct. + println!("cargo:rustc-check-cfg=cfg(reliable_f16_math)"); + println!("cargo:rustc-check-cfg=cfg(reliable_f128_math)"); + let has_reliable_f16 = match (target_arch.as_str(), target_os.as_str()) { // Selection failure until recent LLVM <https://github.com/llvm/llvm-project/issues/93894> // FIXME(llvm19): can probably be removed at the version bump @@ -130,10 +135,42 @@ fn main() { _ => false, }; + // These are currently empty, but will fill up as some platforms move from completely + // unreliable to reliable basics but unreliable math. + + // LLVM is currenlty adding missing routines, <https://github.com/llvm/llvm-project/issues/93566> + let has_reliable_f16_math = has_reliable_f16 + && match (target_arch.as_str(), target_os.as_str()) { + // Currently nothing special. Hooray! + // This will change as platforms gain better better support for standard ops but math + // lags behind. + _ => true, + }; + + let has_reliable_f128_math = has_reliable_f128 + && match (target_arch.as_str(), target_os.as_str()) { + // LLVM lowers `fp128` math to `long double` symbols even on platforms where + // `long double` is not IEEE binary128. See + // <https://github.com/llvm/llvm-project/issues/44744>. + // + // This rules out anything that doesn't have `long double` = `binary128`; <= 32 bits + // (ld is `f64`), anything other than Linux (Windows and MacOS use `f64`), and `x86` + // (ld is 80-bit extended precision). + ("x86_64", _) => false, + (_, "linux") if target_pointer_width == 64 => true, + _ => false, + }; + if has_reliable_f16 { println!("cargo:rustc-cfg=reliable_f16"); } if has_reliable_f128 { println!("cargo:rustc-cfg=reliable_f128"); } + if has_reliable_f16_math { + println!("cargo:rustc-cfg=reliable_f16_math"); + } + if has_reliable_f128_math { + println!("cargo:rustc-cfg=reliable_f128_math"); + } } diff --git a/library/std/src/f128.rs b/library/std/src/f128.rs index a5b00d57cef..f6df6259137 100644 --- a/library/std/src/f128.rs +++ b/library/std/src/f128.rs @@ -12,25 +12,180 @@ pub use core::f128::consts; #[cfg(not(test))] use crate::intrinsics; +#[cfg(not(test))] +use crate::sys::cmath; #[cfg(not(test))] impl f128 { - /// 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(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// let f = 3.7_f128; + /// let g = 3.0_f128; + /// let h = -3.7_f128; /// - /// 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 = "f128", issue = "116909")] #[must_use = "method returns a new number and does not mutate the original value"] - pub fn powi(self, n: i32) -> f128 { - unsafe { intrinsics::powif128(self, n) } + pub fn floor(self) -> f128 { + unsafe { intrinsics::floorf128(self) } + } + + /// Returns the smallest integer greater than or equal to `self`. + /// + /// This function always returns the precise result. + /// + /// # Examples + /// + /// ``` + /// #![feature(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// let f = 3.01_f128; + /// let g = 4.0_f128; + /// + /// assert_eq!(f.ceil(), 4.0); + /// assert_eq!(g.ceil(), 4.0); + /// # } + /// ``` + #[inline] + #[doc(alias = "ceiling")] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn ceil(self) -> f128 { + unsafe { intrinsics::ceilf128(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(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn round(self) -> f128 { + unsafe { intrinsics::roundf128(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(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn round_ties_even(self) -> f128 { + unsafe { intrinsics::rintf128(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(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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); + /// # } + /// ``` + #[inline] + #[doc(alias = "truncate")] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn trunc(self) -> f128 { + unsafe { intrinsics::truncf128(self) } + } + + /// Returns the fractional part of `self`. + /// + /// This function always returns the precise result. + /// + /// # Examples + /// + /// ``` + /// #![feature(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn fract(self) -> f128 { + self - self.trunc() } /// Computes the absolute value of `self`. @@ -41,7 +196,7 @@ impl f128 { /// /// ``` /// #![feature(f128)] - /// # #[cfg(reliable_f128)] { // FIXME(f16_f128): reliable_f128 + /// # #[cfg(reliable_f128)] { /// /// let x = 3.5_f128; /// let y = -3.5_f128; @@ -61,4 +216,1129 @@ impl f128 { // We don't do this now because LLVM has lowering bugs for f128 math. Self::from_bits(self.to_bits() & !(1 << 127)) } + + /// 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)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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()); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn signum(self) -> f128 { + if self.is_nan() { Self::NAN } else { 1.0_f128.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@f128) for more info. + /// + /// # Examples + /// + /// ``` + /// #![feature(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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()); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn copysign(self, sign: f128) -> f128 { + unsafe { intrinsics::copysignf128(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(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn mul_add(self, a: f128, b: f128) -> f128 { + unsafe { intrinsics::fmaf128(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(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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 + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn div_euclid(self, rhs: f128) -> f128 { + 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(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[doc(alias = "modulo", alias = "mod")] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn rem_euclid(self, rhs: f128) -> f128 { + 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 = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn powi(self, n: i32) -> f128 { + unsafe { intrinsics::powif128(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(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// let x = 2.0_f128; + /// let abs_difference = (x.powf(2.0) - (x * x)).abs(); + /// + /// assert!(abs_difference <= f128::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn powf(self, n: f128) -> f128 { + unsafe { intrinsics::powf128(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(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn sqrt(self) -> f128 { + unsafe { intrinsics::sqrtf128(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(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn exp(self) -> f128 { + unsafe { intrinsics::expf128(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(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// let f = 2.0f128; + /// + /// // 2^2 - 4 == 0 + /// let abs_difference = (f.exp2() - 4.0).abs(); + /// + /// assert!(abs_difference <= f128::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn exp2(self) -> f128 { + unsafe { intrinsics::exp2f128(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(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn ln(self) -> f128 { + unsafe { intrinsics::logf128(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(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// let five = 5.0f128; + /// + /// // log5(5) - 1 == 0 + /// let abs_difference = (five.log(5.0) - 1.0).abs(); + /// + /// assert!(abs_difference <= f128::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn log(self, base: f128) -> f128 { + 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(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// let two = 2.0f128; + /// + /// // log2(2) - 1 == 0 + /// let abs_difference = (two.log2() - 1.0).abs(); + /// + /// assert!(abs_difference <= f128::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn log2(self) -> f128 { + unsafe { intrinsics::log2f128(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(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// let ten = 10.0f128; + /// + /// // log10(10) - 1 == 0 + /// let abs_difference = (ten.log10() - 1.0).abs(); + /// + /// assert!(abs_difference <= f128::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn log10(self) -> f128 { + unsafe { intrinsics::log10f128(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 `cbrtf128` from libc on Unix + /// and Windows. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// let x = 8.0f128; + /// + /// // x^(1/3) - 2 == 0 + /// let abs_difference = (x.cbrt() - 2.0).abs(); + /// + /// assert!(abs_difference <= f128::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn cbrt(self) -> f128 { + unsafe { cmath::cbrtf128(self) } + } + + /// 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)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn hypot(self, other: f128) -> f128 { + unsafe { cmath::hypotf128(self, other) } + } + + /// 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)] + /// # #[cfg(reliable_f128_math)] { + /// + /// let x = std::f128::consts::FRAC_PI_2; + /// + /// let abs_difference = (x.sin() - 1.0).abs(); + /// + /// assert!(abs_difference <= f128::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn sin(self) -> f128 { + unsafe { intrinsics::sinf128(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(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// let x = 2.0 * std::f128::consts::PI; + /// + /// let abs_difference = (x.cos() - 1.0).abs(); + /// + /// assert!(abs_difference <= f128::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn cos(self) -> f128 { + unsafe { intrinsics::cosf128(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 `tanf128` from libc on Unix and + /// Windows. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// let x = std::f128::consts::FRAC_PI_4; + /// let abs_difference = (x.tan() - 1.0).abs(); + /// + /// assert!(abs_difference <= f128::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn tan(self) -> f128 { + unsafe { cmath::tanf128(self) } + } + + /// Computes the arcsine of a number. Return value is in radians in + /// the range [-pi/2, pi/2] or NaN if the number is outside the range + /// [-1, 1]. + /// + /// # 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)] + /// # #[cfg(reliable_f128_math)] { + /// + /// let f = std::f128::consts::FRAC_PI_2; + /// + /// // asin(sin(pi/2)) + /// let abs_difference = (f.sin().asin() - std::f128::consts::FRAC_PI_2).abs(); + /// + /// assert!(abs_difference <= f128::EPSILON); + /// # } + /// ``` + #[inline] + #[doc(alias = "arcsin")] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn asin(self) -> f128 { + unsafe { cmath::asinf128(self) } + } + + /// Computes the arccosine of a number. Return value is in radians in + /// the range [0, pi] or NaN if the number is outside the range + /// [-1, 1]. + /// + /// # 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)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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); + /// # } + /// ``` + #[inline] + #[doc(alias = "arccos")] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn acos(self) -> f128 { + unsafe { cmath::acosf128(self) } + } + + /// 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)] + /// # #[cfg(reliable_f128_math)] { + /// + /// let f = 1.0f128; + /// + /// // atan(tan(1)) + /// let abs_difference = (f.tan().atan() - 1.0).abs(); + /// + /// assert!(abs_difference <= f128::EPSILON); + /// # } + /// ``` + #[inline] + #[doc(alias = "arctan")] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn atan(self) -> f128 { + unsafe { cmath::atanf128(self) } + } + + /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`) in radians. + /// + /// * `x = 0`, `y = 0`: `0` + /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]` + /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]` + /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)` + /// + /// # 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)] + /// # #[cfg(reliable_f128_math)] { + /// + /// // 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); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn atan2(self, other: f128) -> f128 { + unsafe { cmath::atan2f128(self, other) } + } + + /// 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)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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); + /// # } + /// ``` + #[inline] + #[doc(alias = "sincos")] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + pub fn sin_cos(self) -> (f128, f128) { + (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 `expm1f128` from libc on Unix + /// and Windows. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn exp_m1(self) -> f128 { + unsafe { cmath::expm1f128(self) } + } + + /// 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 `log1pf128` from libc on Unix + /// and Windows. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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); + /// # } + /// ``` + #[inline] + #[doc(alias = "log1p")] + #[must_use = "method returns a new number and does not mutate the original value"] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + pub fn ln_1p(self) -> f128 { + unsafe { cmath::log1pf128(self) } + } + + /// 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)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn sinh(self) -> f128 { + unsafe { cmath::sinhf128(self) } + } + + /// 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)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn cosh(self) -> f128 { + unsafe { cmath::coshf128(self) } + } + + /// 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)] + /// # #[cfg(reliable_f128_math)] { + /// + /// 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); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn tanh(self) -> f128 { + unsafe { cmath::tanhf128(self) } + } + + /// 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)] + /// # #[cfg(reliable_f128_math)] { + /// + /// let x = 1.0f128; + /// let f = x.sinh().asinh(); + /// + /// let abs_difference = (f - x).abs(); + /// + /// assert!(abs_difference <= f128::EPSILON); + /// # } + /// ``` + #[inline] + #[doc(alias = "arcsinh")] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn asinh(self) -> f128 { + 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(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// let x = 1.0f128; + /// let f = x.cosh().acosh(); + /// + /// let abs_difference = (f - x).abs(); + /// + /// assert!(abs_difference <= f128::EPSILON); + /// # } + /// ``` + #[inline] + #[doc(alias = "arccosh")] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn acosh(self) -> f128 { + 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(f128)] + /// # #[cfg(reliable_f128_math)] { + /// + /// let e = std::f128::consts::E; + /// let f = e.tanh().atanh(); + /// + /// let abs_difference = (f - e).abs(); + /// + /// assert!(abs_difference <= 1e-5); + /// # } + /// ``` + #[inline] + #[doc(alias = "arctanh")] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn atanh(self) -> f128 { + 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 `tgammaf128` from libc on Unix + /// and Windows. Note that this might change in the future. + /// + /// # Examples + /// + /// ``` + /// #![feature(f128)] + /// #![feature(float_gamma)] + /// # #[cfg(reliable_f128_math)] { + /// + /// let x = 5.0f128; + /// + /// let abs_difference = (x.gamma() - 24.0).abs(); + /// + /// assert!(abs_difference <= f128::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn gamma(self) -> f128 { + unsafe { cmath::tgammaf128(self) } + } + + /// 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)] + /// # #[cfg(reliable_f128_math)] { + /// + /// let x = 2.0f128; + /// + /// let abs_difference = (x.ln_gamma().0 - 0.0).abs(); + /// + /// assert!(abs_difference <= f128::EPSILON); + /// # } + /// ``` + #[inline] + #[rustc_allow_incoherent_impl] + #[unstable(feature = "f128", issue = "116909")] + #[must_use = "method returns a new number and does not mutate the original value"] + pub fn ln_gamma(self) -> (f128, i32) { + let mut signgamp: i32 = 0; + let x = unsafe { cmath::lgammaf128_r(self, &mut signgamp) }; + (x, signgamp) + } } diff --git a/library/std/src/f128/tests.rs b/library/std/src/f128/tests.rs index 162c8dbad81..df806a639f6 100644 --- a/library/std/src/f128/tests.rs +++ b/library/std/src/f128/tests.rs @@ -4,6 +4,21 @@ use crate::f128::consts; use crate::num::{FpCategory as Fp, *}; +// Note these tolerances make sense around zero, but not for more extreme exponents. + +/// For operations that are near exact, usually not involving math of different +/// signs. +const TOL_PRECISE: f128 = 1e-28; + +/// Default tolerances. Works for values that should be near precise but not exact. Roughly +/// the precision carried by `100 * 100`. +const TOL: f128 = 1e-12; + +/// Tolerances for math that is allowed to be imprecise, usually due to multiple chained +/// operations. +#[cfg(reliable_f128_math)] +const TOL_IMPR: f128 = 1e-10; + /// Smallest number const TINY_BITS: u128 = 0x1; @@ -191,9 +206,100 @@ fn test_classify() { assert_eq!(1e-4932f128.classify(), Fp::Subnormal); } -// FIXME(f16_f128): add missing math functions when available +#[test] +#[cfg(reliable_f128_math)] +fn test_floor() { + assert_approx_eq!(1.0f128.floor(), 1.0f128, TOL_PRECISE); + assert_approx_eq!(1.3f128.floor(), 1.0f128, TOL_PRECISE); + assert_approx_eq!(1.5f128.floor(), 1.0f128, TOL_PRECISE); + assert_approx_eq!(1.7f128.floor(), 1.0f128, TOL_PRECISE); + assert_approx_eq!(0.0f128.floor(), 0.0f128, TOL_PRECISE); + assert_approx_eq!((-0.0f128).floor(), -0.0f128, TOL_PRECISE); + assert_approx_eq!((-1.0f128).floor(), -1.0f128, TOL_PRECISE); + assert_approx_eq!((-1.3f128).floor(), -2.0f128, TOL_PRECISE); + assert_approx_eq!((-1.5f128).floor(), -2.0f128, TOL_PRECISE); + assert_approx_eq!((-1.7f128).floor(), -2.0f128, TOL_PRECISE); +} + +#[test] +#[cfg(reliable_f128_math)] +fn test_ceil() { + assert_approx_eq!(1.0f128.ceil(), 1.0f128, TOL_PRECISE); + assert_approx_eq!(1.3f128.ceil(), 2.0f128, TOL_PRECISE); + assert_approx_eq!(1.5f128.ceil(), 2.0f128, TOL_PRECISE); + assert_approx_eq!(1.7f128.ceil(), 2.0f128, TOL_PRECISE); + assert_approx_eq!(0.0f128.ceil(), 0.0f128, TOL_PRECISE); + assert_approx_eq!((-0.0f128).ceil(), -0.0f128, TOL_PRECISE); + assert_approx_eq!((-1.0f128).ceil(), -1.0f128, TOL_PRECISE); + assert_approx_eq!((-1.3f128).ceil(), -1.0f128, TOL_PRECISE); + assert_approx_eq!((-1.5f128).ceil(), -1.0f128, TOL_PRECISE); + assert_approx_eq!((-1.7f128).ceil(), -1.0f128, TOL_PRECISE); +} + +#[test] +#[cfg(reliable_f128_math)] +fn test_round() { + assert_approx_eq!(2.5f128.round(), 3.0f128, TOL_PRECISE); + assert_approx_eq!(1.0f128.round(), 1.0f128, TOL_PRECISE); + assert_approx_eq!(1.3f128.round(), 1.0f128, TOL_PRECISE); + assert_approx_eq!(1.5f128.round(), 2.0f128, TOL_PRECISE); + assert_approx_eq!(1.7f128.round(), 2.0f128, TOL_PRECISE); + assert_approx_eq!(0.0f128.round(), 0.0f128, TOL_PRECISE); + assert_approx_eq!((-0.0f128).round(), -0.0f128, TOL_PRECISE); + assert_approx_eq!((-1.0f128).round(), -1.0f128, TOL_PRECISE); + assert_approx_eq!((-1.3f128).round(), -1.0f128, TOL_PRECISE); + assert_approx_eq!((-1.5f128).round(), -2.0f128, TOL_PRECISE); + assert_approx_eq!((-1.7f128).round(), -2.0f128, TOL_PRECISE); +} + +#[test] +#[cfg(reliable_f128_math)] +fn test_round_ties_even() { + assert_approx_eq!(2.5f128.round_ties_even(), 2.0f128, TOL_PRECISE); + assert_approx_eq!(1.0f128.round_ties_even(), 1.0f128, TOL_PRECISE); + assert_approx_eq!(1.3f128.round_ties_even(), 1.0f128, TOL_PRECISE); + assert_approx_eq!(1.5f128.round_ties_even(), 2.0f128, TOL_PRECISE); + assert_approx_eq!(1.7f128.round_ties_even(), 2.0f128, TOL_PRECISE); + assert_approx_eq!(0.0f128.round_ties_even(), 0.0f128, TOL_PRECISE); + assert_approx_eq!((-0.0f128).round_ties_even(), -0.0f128, TOL_PRECISE); + assert_approx_eq!((-1.0f128).round_ties_even(), -1.0f128, TOL_PRECISE); + assert_approx_eq!((-1.3f128).round_ties_even(), -1.0f128, TOL_PRECISE); + assert_approx_eq!((-1.5f128).round_ties_even(), -2.0f128, TOL_PRECISE); + assert_approx_eq!((-1.7f128).round_ties_even(), -2.0f128, TOL_PRECISE); +} + +#[test] +#[cfg(reliable_f128_math)] +fn test_trunc() { + assert_approx_eq!(1.0f128.trunc(), 1.0f128, TOL_PRECISE); + assert_approx_eq!(1.3f128.trunc(), 1.0f128, TOL_PRECISE); + assert_approx_eq!(1.5f128.trunc(), 1.0f128, TOL_PRECISE); + assert_approx_eq!(1.7f128.trunc(), 1.0f128, TOL_PRECISE); + assert_approx_eq!(0.0f128.trunc(), 0.0f128, TOL_PRECISE); + assert_approx_eq!((-0.0f128).trunc(), -0.0f128, TOL_PRECISE); + assert_approx_eq!((-1.0f128).trunc(), -1.0f128, TOL_PRECISE); + assert_approx_eq!((-1.3f128).trunc(), -1.0f128, TOL_PRECISE); + assert_approx_eq!((-1.5f128).trunc(), -1.0f128, TOL_PRECISE); + assert_approx_eq!((-1.7f128).trunc(), -1.0f128, TOL_PRECISE); +} + +#[test] +#[cfg(reliable_f128_math)] +fn test_fract() { + assert_approx_eq!(1.0f128.fract(), 0.0f128, TOL_PRECISE); + assert_approx_eq!(1.3f128.fract(), 0.3f128, TOL_PRECISE); + assert_approx_eq!(1.5f128.fract(), 0.5f128, TOL_PRECISE); + assert_approx_eq!(1.7f128.fract(), 0.7f128, TOL_PRECISE); + assert_approx_eq!(0.0f128.fract(), 0.0f128, TOL_PRECISE); + assert_approx_eq!((-0.0f128).fract(), -0.0f128, TOL_PRECISE); + assert_approx_eq!((-1.0f128).fract(), -0.0f128, TOL_PRECISE); + assert_approx_eq!((-1.3f128).fract(), -0.3f128, TOL_PRECISE); + assert_approx_eq!((-1.5f128).fract(), -0.5f128, TOL_PRECISE); + assert_approx_eq!((-1.7f128).fract(), -0.7f128, TOL_PRECISE); +} #[test] +#[cfg(reliable_f128_math)] fn test_abs() { assert_eq!(f128::INFINITY.abs(), f128::INFINITY); assert_eq!(1f128.abs(), 1f128); @@ -293,6 +399,24 @@ fn test_next_down() { } #[test] +#[cfg(reliable_f128_math)] +fn test_mul_add() { + let nan: f128 = f128::NAN; + let inf: f128 = f128::INFINITY; + let neg_inf: f128 = f128::NEG_INFINITY; + assert_approx_eq!(12.3f128.mul_add(4.5, 6.7), 62.05, TOL_PRECISE); + assert_approx_eq!((-12.3f128).mul_add(-4.5, -6.7), 48.65, TOL_PRECISE); + assert_approx_eq!(0.0f128.mul_add(8.9, 1.2), 1.2, TOL_PRECISE); + assert_approx_eq!(3.4f128.mul_add(-0.0, 5.6), 5.6, TOL_PRECISE); + assert!(nan.mul_add(7.8, 9.0).is_nan()); + assert_eq!(inf.mul_add(7.8, 9.0), inf); + assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf); + assert_eq!(8.9f128.mul_add(inf, 3.2), inf); + assert_eq!((-3.2f128).mul_add(2.4, neg_inf), neg_inf); +} + +#[test] +#[cfg(reliable_f16_math)] fn test_recip() { let nan: f128 = f128::NAN; let inf: f128 = f128::INFINITY; @@ -301,11 +425,161 @@ fn test_recip() { assert_eq!(2.0f128.recip(), 0.5); assert_eq!((-0.4f128).recip(), -2.5); assert_eq!(0.0f128.recip(), inf); + assert_approx_eq!( + f128::MAX.recip(), + 8.40525785778023376565669454330438228902076605e-4933, + 1e-4900 + ); assert!(nan.recip().is_nan()); assert_eq!(inf.recip(), 0.0); assert_eq!(neg_inf.recip(), 0.0); } +// Many math functions allow for less accurate results, so the next tolerance up is used + +#[test] +#[cfg(reliable_f128_math)] +fn test_powi() { + let nan: f128 = f128::NAN; + let inf: f128 = f128::INFINITY; + let neg_inf: f128 = f128::NEG_INFINITY; + assert_eq!(1.0f128.powi(1), 1.0); + assert_approx_eq!((-3.1f128).powi(2), 9.6100000000000005506706202140776519387, TOL); + assert_approx_eq!(5.9f128.powi(-2), 0.028727377190462507313100483690639638451, TOL); + assert_eq!(8.3f128.powi(0), 1.0); + assert!(nan.powi(2).is_nan()); + assert_eq!(inf.powi(3), inf); + assert_eq!(neg_inf.powi(2), inf); +} + +#[test] +#[cfg(reliable_f128_math)] +fn test_powf() { + let nan: f128 = f128::NAN; + let inf: f128 = f128::INFINITY; + let neg_inf: f128 = f128::NEG_INFINITY; + assert_eq!(1.0f128.powf(1.0), 1.0); + assert_approx_eq!(3.4f128.powf(4.5), 246.40818323761892815995637964326426756, TOL_IMPR); + assert_approx_eq!(2.7f128.powf(-3.2), 0.041652009108526178281070304373500889273, TOL_IMPR); + assert_approx_eq!((-3.1f128).powf(2.0), 9.6100000000000005506706202140776519387, TOL_IMPR); + assert_approx_eq!(5.9f128.powf(-2.0), 0.028727377190462507313100483690639638451, TOL_IMPR); + assert_eq!(8.3f128.powf(0.0), 1.0); + assert!(nan.powf(2.0).is_nan()); + assert_eq!(inf.powf(2.0), inf); + assert_eq!(neg_inf.powf(3.0), neg_inf); +} + +#[test] +#[cfg(reliable_f128_math)] +fn test_sqrt_domain() { + assert!(f128::NAN.sqrt().is_nan()); + assert!(f128::NEG_INFINITY.sqrt().is_nan()); + assert!((-1.0f128).sqrt().is_nan()); + assert_eq!((-0.0f128).sqrt(), -0.0); + assert_eq!(0.0f128.sqrt(), 0.0); + assert_eq!(1.0f128.sqrt(), 1.0); + assert_eq!(f128::INFINITY.sqrt(), f128::INFINITY); +} + +#[test] +#[cfg(reliable_f128_math)] +fn test_exp() { + assert_eq!(1.0, 0.0f128.exp()); + assert_approx_eq!(consts::E, 1.0f128.exp(), TOL); + assert_approx_eq!(148.41315910257660342111558004055227962348775, 5.0f128.exp(), TOL); + + let inf: f128 = f128::INFINITY; + let neg_inf: f128 = f128::NEG_INFINITY; + let nan: f128 = f128::NAN; + assert_eq!(inf, inf.exp()); + assert_eq!(0.0, neg_inf.exp()); + assert!(nan.exp().is_nan()); +} + +#[test] +#[cfg(reliable_f128_math)] +fn test_exp2() { + assert_eq!(32.0, 5.0f128.exp2()); + assert_eq!(1.0, 0.0f128.exp2()); + + let inf: f128 = f128::INFINITY; + let neg_inf: f128 = f128::NEG_INFINITY; + let nan: f128 = f128::NAN; + assert_eq!(inf, inf.exp2()); + assert_eq!(0.0, neg_inf.exp2()); + assert!(nan.exp2().is_nan()); +} + +#[test] +#[cfg(reliable_f128_math)] +fn test_ln() { + let nan: f128 = f128::NAN; + let inf: f128 = f128::INFINITY; + let neg_inf: f128 = f128::NEG_INFINITY; + assert_approx_eq!(1.0f128.exp().ln(), 1.0, TOL); + assert!(nan.ln().is_nan()); + assert_eq!(inf.ln(), inf); + assert!(neg_inf.ln().is_nan()); + assert!((-2.3f128).ln().is_nan()); + assert_eq!((-0.0f128).ln(), neg_inf); + assert_eq!(0.0f128.ln(), neg_inf); + assert_approx_eq!(4.0f128.ln(), 1.3862943611198906188344642429163531366, TOL); +} + +#[test] +#[cfg(reliable_f128_math)] +fn test_log() { + let nan: f128 = f128::NAN; + let inf: f128 = f128::INFINITY; + let neg_inf: f128 = f128::NEG_INFINITY; + assert_eq!(10.0f128.log(10.0), 1.0); + assert_approx_eq!(2.3f128.log(3.5), 0.66485771361478710036766645911922010272, TOL); + assert_eq!(1.0f128.exp().log(1.0f128.exp()), 1.0); + assert!(1.0f128.log(1.0).is_nan()); + assert!(1.0f128.log(-13.9).is_nan()); + assert!(nan.log(2.3).is_nan()); + assert_eq!(inf.log(10.0), inf); + assert!(neg_inf.log(8.8).is_nan()); + assert!((-2.3f128).log(0.1).is_nan()); + assert_eq!((-0.0f128).log(2.0), neg_inf); + assert_eq!(0.0f128.log(7.0), neg_inf); +} + +#[test] +#[cfg(reliable_f128_math)] +fn test_log2() { + let nan: f128 = f128::NAN; + let inf: f128 = f128::INFINITY; + let neg_inf: f128 = f128::NEG_INFINITY; + assert_approx_eq!(10.0f128.log2(), 3.32192809488736234787031942948939017, TOL); + assert_approx_eq!(2.3f128.log2(), 1.2016338611696504130002982471978765921, TOL); + assert_approx_eq!(1.0f128.exp().log2(), 1.4426950408889634073599246810018921381, TOL); + assert!(nan.log2().is_nan()); + assert_eq!(inf.log2(), inf); + assert!(neg_inf.log2().is_nan()); + assert!((-2.3f128).log2().is_nan()); + assert_eq!((-0.0f128).log2(), neg_inf); + assert_eq!(0.0f128.log2(), neg_inf); +} + +#[test] +#[cfg(reliable_f128_math)] +fn test_log10() { + let nan: f128 = f128::NAN; + let inf: f128 = f128::INFINITY; + let neg_inf: f128 = f128::NEG_INFINITY; + assert_eq!(10.0f128.log10(), 1.0); + assert_approx_eq!(2.3f128.log10(), 0.36172783601759284532595218865859309898, TOL); + assert_approx_eq!(1.0f128.exp().log10(), 0.43429448190325182765112891891660508222, TOL); + assert_eq!(1.0f128.log10(), 0.0); + assert!(nan.log10().is_nan()); + assert_eq!(inf.log10(), inf); + assert!(neg_inf.log10().is_nan()); + assert!((-2.3f128).log10().is_nan()); + assert_eq!((-0.0f128).log10(), neg_inf); + assert_eq!(0.0f128.log10(), neg_inf); +} + #[test] fn test_to_degrees() { let pi: f128 = consts::PI; @@ -313,8 +587,8 @@ fn test_to_degrees() { let inf: f128 = f128::INFINITY; let neg_inf: f128 = f128::NEG_INFINITY; assert_eq!(0.0f128.to_degrees(), 0.0); - assert_approx_eq!((-5.8f128).to_degrees(), -332.315521); - assert_eq!(pi.to_degrees(), 180.0); + assert_approx_eq!((-5.8f128).to_degrees(), -332.31552117587745090765431723855668471, TOL); + assert_approx_eq!(pi.to_degrees(), 180.0, TOL); assert!(nan.to_degrees().is_nan()); assert_eq!(inf.to_degrees(), inf); assert_eq!(neg_inf.to_degrees(), neg_inf); @@ -328,19 +602,122 @@ fn test_to_radians() { let inf: f128 = f128::INFINITY; let neg_inf: f128 = f128::NEG_INFINITY; assert_eq!(0.0f128.to_radians(), 0.0); - assert_approx_eq!(154.6f128.to_radians(), 2.698279); - assert_approx_eq!((-332.31f128).to_radians(), -5.799903); + assert_approx_eq!(154.6f128.to_radians(), 2.6982790235832334267135442069489767804, TOL); + assert_approx_eq!((-332.31f128).to_radians(), -5.7999036373023566567593094812182763013, TOL); // check approx rather than exact because round trip for pi doesn't fall on an exactly // representable value (unlike `f32` and `f64`). - assert_approx_eq!(180.0f128.to_radians(), pi); + assert_approx_eq!(180.0f128.to_radians(), pi, TOL_PRECISE); assert!(nan.to_radians().is_nan()); assert_eq!(inf.to_radians(), inf); assert_eq!(neg_inf.to_radians(), neg_inf); } #[test] +#[cfg(reliable_f128_math)] +fn test_asinh() { + // Lower accuracy results are allowed, use increased tolerances + assert_eq!(0.0f128.asinh(), 0.0f128); + assert_eq!((-0.0f128).asinh(), -0.0f128); + + let inf: f128 = f128::INFINITY; + let neg_inf: f128 = f128::NEG_INFINITY; + let nan: f128 = f128::NAN; + assert_eq!(inf.asinh(), inf); + assert_eq!(neg_inf.asinh(), neg_inf); + assert!(nan.asinh().is_nan()); + assert!((-0.0f128).asinh().is_sign_negative()); + + // issue 63271 + assert_approx_eq!(2.0f128.asinh(), 1.443635475178810342493276740273105f128, TOL_IMPR); + assert_approx_eq!((-2.0f128).asinh(), -1.443635475178810342493276740273105f128, TOL_IMPR); + // regression test for the catastrophic cancellation fixed in 72486 + assert_approx_eq!( + (-67452098.07139316f128).asinh(), + -18.720075426274544393985484294000831757220, + TOL_IMPR + ); + + // test for low accuracy from issue 104548 + assert_approx_eq!(60.0f128, 60.0f128.sinh().asinh(), TOL_IMPR); + // mul needed for approximate comparison to be meaningful + assert_approx_eq!(1.0f128, 1e-15f128.sinh().asinh() * 1e15f128, TOL_IMPR); +} + +#[test] +#[cfg(reliable_f128_math)] +fn test_acosh() { + assert_eq!(1.0f128.acosh(), 0.0f128); + assert!(0.999f128.acosh().is_nan()); + + let inf: f128 = f128::INFINITY; + let neg_inf: f128 = f128::NEG_INFINITY; + let nan: f128 = f128::NAN; + assert_eq!(inf.acosh(), inf); + assert!(neg_inf.acosh().is_nan()); + assert!(nan.acosh().is_nan()); + assert_approx_eq!(2.0f128.acosh(), 1.31695789692481670862504634730796844f128, TOL_IMPR); + assert_approx_eq!(3.0f128.acosh(), 1.76274717403908605046521864995958461f128, TOL_IMPR); + + // test for low accuracy from issue 104548 + assert_approx_eq!(60.0f128, 60.0f128.cosh().acosh(), TOL_IMPR); +} + +#[test] +#[cfg(reliable_f128_math)] +fn test_atanh() { + assert_eq!(0.0f128.atanh(), 0.0f128); + assert_eq!((-0.0f128).atanh(), -0.0f128); + + let inf: f128 = f128::INFINITY; + let neg_inf: f128 = f128::NEG_INFINITY; + let nan: f128 = f128::NAN; + assert_eq!(1.0f128.atanh(), inf); + assert_eq!((-1.0f128).atanh(), neg_inf); + assert!(2f128.atanh().atanh().is_nan()); + assert!((-2f128).atanh().atanh().is_nan()); + assert!(inf.atanh().is_nan()); + assert!(neg_inf.atanh().is_nan()); + assert!(nan.atanh().is_nan()); + assert_approx_eq!(0.5f128.atanh(), 0.54930614433405484569762261846126285f128, TOL_IMPR); + assert_approx_eq!((-0.5f128).atanh(), -0.54930614433405484569762261846126285f128, TOL_IMPR); +} + +#[test] +#[cfg(reliable_f128_math)] +fn test_gamma() { + // precision can differ among platforms + assert_approx_eq!(1.0f128.gamma(), 1.0f128, TOL_IMPR); + assert_approx_eq!(2.0f128.gamma(), 1.0f128, TOL_IMPR); + assert_approx_eq!(3.0f128.gamma(), 2.0f128, TOL_IMPR); + assert_approx_eq!(4.0f128.gamma(), 6.0f128, TOL_IMPR); + assert_approx_eq!(5.0f128.gamma(), 24.0f128, TOL_IMPR); + assert_approx_eq!(0.5f128.gamma(), consts::PI.sqrt(), TOL_IMPR); + assert_approx_eq!((-0.5f128).gamma(), -2.0 * consts::PI.sqrt(), TOL_IMPR); + assert_eq!(0.0f128.gamma(), f128::INFINITY); + assert_eq!((-0.0f128).gamma(), f128::NEG_INFINITY); + assert!((-1.0f128).gamma().is_nan()); + assert!((-2.0f128).gamma().is_nan()); + assert!(f128::NAN.gamma().is_nan()); + assert!(f128::NEG_INFINITY.gamma().is_nan()); + assert_eq!(f128::INFINITY.gamma(), f128::INFINITY); + assert_eq!(1760.9f128.gamma(), f128::INFINITY); +} + +#[test] +#[cfg(reliable_f128_math)] +fn test_ln_gamma() { + assert_approx_eq!(1.0f128.ln_gamma().0, 0.0f128, TOL_IMPR); + assert_eq!(1.0f128.ln_gamma().1, 1); + assert_approx_eq!(2.0f128.ln_gamma().0, 0.0f128, TOL_IMPR); + assert_eq!(2.0f128.ln_gamma().1, 1); + assert_approx_eq!(3.0f128.ln_gamma().0, 2.0f128.ln(), TOL_IMPR); + assert_eq!(3.0f128.ln_gamma().1, 1); + assert_approx_eq!((-0.5f128).ln_gamma().0, (2.0 * consts::PI.sqrt()).ln(), TOL_IMPR); + assert_eq!((-0.5f128).ln_gamma().1, -1); +} + +#[test] fn test_real_consts() { - // FIXME(f16_f128): add math tests when available use super::consts; let pi: f128 = consts::PI; @@ -351,29 +728,34 @@ fn test_real_consts() { let frac_pi_8: f128 = consts::FRAC_PI_8; let frac_1_pi: f128 = consts::FRAC_1_PI; let frac_2_pi: f128 = consts::FRAC_2_PI; - // let frac_2_sqrtpi: f128 = consts::FRAC_2_SQRT_PI; - // let sqrt2: f128 = consts::SQRT_2; - // let frac_1_sqrt2: f128 = consts::FRAC_1_SQRT_2; - // let e: f128 = consts::E; - // let log2_e: f128 = consts::LOG2_E; - // let log10_e: f128 = consts::LOG10_E; - // let ln_2: f128 = consts::LN_2; - // let ln_10: f128 = consts::LN_10; - - assert_approx_eq!(frac_pi_2, pi / 2f128); - assert_approx_eq!(frac_pi_3, pi / 3f128); - assert_approx_eq!(frac_pi_4, pi / 4f128); - assert_approx_eq!(frac_pi_6, pi / 6f128); - assert_approx_eq!(frac_pi_8, pi / 8f128); - assert_approx_eq!(frac_1_pi, 1f128 / pi); - assert_approx_eq!(frac_2_pi, 2f128 / pi); - // assert_approx_eq!(frac_2_sqrtpi, 2f128 / pi.sqrt()); - // assert_approx_eq!(sqrt2, 2f128.sqrt()); - // assert_approx_eq!(frac_1_sqrt2, 1f128 / 2f128.sqrt()); - // assert_approx_eq!(log2_e, e.log2()); - // assert_approx_eq!(log10_e, e.log10()); - // assert_approx_eq!(ln_2, 2f128.ln()); - // assert_approx_eq!(ln_10, 10f128.ln()); + + assert_approx_eq!(frac_pi_2, pi / 2f128, TOL_PRECISE); + assert_approx_eq!(frac_pi_3, pi / 3f128, TOL_PRECISE); + assert_approx_eq!(frac_pi_4, pi / 4f128, TOL_PRECISE); + assert_approx_eq!(frac_pi_6, pi / 6f128, TOL_PRECISE); + assert_approx_eq!(frac_pi_8, pi / 8f128, TOL_PRECISE); + assert_approx_eq!(frac_1_pi, 1f128 / pi, TOL_PRECISE); + assert_approx_eq!(frac_2_pi, 2f128 / pi, TOL_PRECISE); + + #[cfg(reliable_f128_math)] + { + let frac_2_sqrtpi: f128 = consts::FRAC_2_SQRT_PI; + let sqrt2: f128 = consts::SQRT_2; + let frac_1_sqrt2: f128 = consts::FRAC_1_SQRT_2; + let e: f128 = consts::E; + let log2_e: f128 = consts::LOG2_E; + let log10_e: f128 = consts::LOG10_E; + let ln_2: f128 = consts::LN_2; + let ln_10: f128 = consts::LN_10; + + assert_approx_eq!(frac_2_sqrtpi, 2f128 / pi.sqrt(), TOL_PRECISE); + assert_approx_eq!(sqrt2, 2f128.sqrt(), TOL_PRECISE); + assert_approx_eq!(frac_1_sqrt2, 1f128 / 2f128.sqrt(), TOL_PRECISE); + assert_approx_eq!(log2_e, e.log2(), TOL_PRECISE); + assert_approx_eq!(log10_e, e.log10(), TOL_PRECISE); + assert_approx_eq!(ln_2, 2f128.ln(), TOL_PRECISE); + assert_approx_eq!(ln_10, 10f128.ln(), TOL_PRECISE); + } } #[test] @@ -382,10 +764,10 @@ fn test_float_bits_conv() { assert_eq!((12.5f128).to_bits(), 0x40029000000000000000000000000000); assert_eq!((1337f128).to_bits(), 0x40094e40000000000000000000000000); assert_eq!((-14.25f128).to_bits(), 0xc002c800000000000000000000000000); - assert_approx_eq!(f128::from_bits(0x3fff0000000000000000000000000000), 1.0); - assert_approx_eq!(f128::from_bits(0x40029000000000000000000000000000), 12.5); - assert_approx_eq!(f128::from_bits(0x40094e40000000000000000000000000), 1337.0); - assert_approx_eq!(f128::from_bits(0xc002c800000000000000000000000000), -14.25); + assert_approx_eq!(f128::from_bits(0x3fff0000000000000000000000000000), 1.0, TOL_PRECISE); + assert_approx_eq!(f128::from_bits(0x40029000000000000000000000000000), 12.5, TOL_PRECISE); + assert_approx_eq!(f128::from_bits(0x40094e40000000000000000000000000), 1337.0, TOL_PRECISE); + assert_approx_eq!(f128::from_bits(0xc002c800000000000000000000000000), -14.25, TOL_PRECISE); // Check that NaNs roundtrip their bits regardless of signaling-ness // 0xA is 0b1010; 0x5 is 0b0101 -- so these two together clobbers all the mantissa bits 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) + } } diff --git a/library/std/src/f16/tests.rs b/library/std/src/f16/tests.rs index f73bdf68e82..f0ef807dac1 100644 --- a/library/std/src/f16/tests.rs +++ b/library/std/src/f16/tests.rs @@ -4,11 +4,21 @@ use crate::f16::consts; use crate::num::{FpCategory as Fp, *}; -// We run out of precision pretty quickly with f16 -// const F16_APPROX_L1: f16 = 0.001; -const F16_APPROX_L2: f16 = 0.01; -// const F16_APPROX_L3: f16 = 0.1; -const F16_APPROX_L4: f16 = 0.5; +/// Tolerance for results on the order of 10.0e-2; +#[cfg(reliable_f16_math)] +const TOL_N2: f16 = 0.0001; + +/// Tolerance for results on the order of 10.0e+0 +#[cfg(reliable_f16_math)] +const TOL_0: f16 = 0.01; + +/// Tolerance for results on the order of 10.0e+2 +#[cfg(reliable_f16_math)] +const TOL_P2: f16 = 0.5; + +/// Tolerance for results on the order of 10.0e+4 +#[cfg(reliable_f16_math)] +const TOL_P4: f16 = 10.0; /// Smallest number const TINY_BITS: u16 = 0x1; @@ -197,9 +207,100 @@ fn test_classify() { assert_eq!(1e-5f16.classify(), Fp::Subnormal); } -// FIXME(f16_f128): add missing math functions when available +#[test] +#[cfg(reliable_f16_math)] +fn test_floor() { + assert_approx_eq!(1.0f16.floor(), 1.0f16, TOL_0); + assert_approx_eq!(1.3f16.floor(), 1.0f16, TOL_0); + assert_approx_eq!(1.5f16.floor(), 1.0f16, TOL_0); + assert_approx_eq!(1.7f16.floor(), 1.0f16, TOL_0); + assert_approx_eq!(0.0f16.floor(), 0.0f16, TOL_0); + assert_approx_eq!((-0.0f16).floor(), -0.0f16, TOL_0); + assert_approx_eq!((-1.0f16).floor(), -1.0f16, TOL_0); + assert_approx_eq!((-1.3f16).floor(), -2.0f16, TOL_0); + assert_approx_eq!((-1.5f16).floor(), -2.0f16, TOL_0); + assert_approx_eq!((-1.7f16).floor(), -2.0f16, TOL_0); +} + +#[test] +#[cfg(reliable_f16_math)] +fn test_ceil() { + assert_approx_eq!(1.0f16.ceil(), 1.0f16, TOL_0); + assert_approx_eq!(1.3f16.ceil(), 2.0f16, TOL_0); + assert_approx_eq!(1.5f16.ceil(), 2.0f16, TOL_0); + assert_approx_eq!(1.7f16.ceil(), 2.0f16, TOL_0); + assert_approx_eq!(0.0f16.ceil(), 0.0f16, TOL_0); + assert_approx_eq!((-0.0f16).ceil(), -0.0f16, TOL_0); + assert_approx_eq!((-1.0f16).ceil(), -1.0f16, TOL_0); + assert_approx_eq!((-1.3f16).ceil(), -1.0f16, TOL_0); + assert_approx_eq!((-1.5f16).ceil(), -1.0f16, TOL_0); + assert_approx_eq!((-1.7f16).ceil(), -1.0f16, TOL_0); +} + +#[test] +#[cfg(reliable_f16_math)] +fn test_round() { + assert_approx_eq!(2.5f16.round(), 3.0f16, TOL_0); + assert_approx_eq!(1.0f16.round(), 1.0f16, TOL_0); + assert_approx_eq!(1.3f16.round(), 1.0f16, TOL_0); + assert_approx_eq!(1.5f16.round(), 2.0f16, TOL_0); + assert_approx_eq!(1.7f16.round(), 2.0f16, TOL_0); + assert_approx_eq!(0.0f16.round(), 0.0f16, TOL_0); + assert_approx_eq!((-0.0f16).round(), -0.0f16, TOL_0); + assert_approx_eq!((-1.0f16).round(), -1.0f16, TOL_0); + assert_approx_eq!((-1.3f16).round(), -1.0f16, TOL_0); + assert_approx_eq!((-1.5f16).round(), -2.0f16, TOL_0); + assert_approx_eq!((-1.7f16).round(), -2.0f16, TOL_0); +} + +#[test] +#[cfg(reliable_f16_math)] +fn test_round_ties_even() { + assert_approx_eq!(2.5f16.round_ties_even(), 2.0f16, TOL_0); + assert_approx_eq!(1.0f16.round_ties_even(), 1.0f16, TOL_0); + assert_approx_eq!(1.3f16.round_ties_even(), 1.0f16, TOL_0); + assert_approx_eq!(1.5f16.round_ties_even(), 2.0f16, TOL_0); + assert_approx_eq!(1.7f16.round_ties_even(), 2.0f16, TOL_0); + assert_approx_eq!(0.0f16.round_ties_even(), 0.0f16, TOL_0); + assert_approx_eq!((-0.0f16).round_ties_even(), -0.0f16, TOL_0); + assert_approx_eq!((-1.0f16).round_ties_even(), -1.0f16, TOL_0); + assert_approx_eq!((-1.3f16).round_ties_even(), -1.0f16, TOL_0); + assert_approx_eq!((-1.5f16).round_ties_even(), -2.0f16, TOL_0); + assert_approx_eq!((-1.7f16).round_ties_even(), -2.0f16, TOL_0); +} #[test] +#[cfg(reliable_f16_math)] +fn test_trunc() { + assert_approx_eq!(1.0f16.trunc(), 1.0f16, TOL_0); + assert_approx_eq!(1.3f16.trunc(), 1.0f16, TOL_0); + assert_approx_eq!(1.5f16.trunc(), 1.0f16, TOL_0); + assert_approx_eq!(1.7f16.trunc(), 1.0f16, TOL_0); + assert_approx_eq!(0.0f16.trunc(), 0.0f16, TOL_0); + assert_approx_eq!((-0.0f16).trunc(), -0.0f16, TOL_0); + assert_approx_eq!((-1.0f16).trunc(), -1.0f16, TOL_0); + assert_approx_eq!((-1.3f16).trunc(), -1.0f16, TOL_0); + assert_approx_eq!((-1.5f16).trunc(), -1.0f16, TOL_0); + assert_approx_eq!((-1.7f16).trunc(), -1.0f16, TOL_0); +} + +#[test] +#[cfg(reliable_f16_math)] +fn test_fract() { + assert_approx_eq!(1.0f16.fract(), 0.0f16, TOL_0); + assert_approx_eq!(1.3f16.fract(), 0.3f16, TOL_0); + assert_approx_eq!(1.5f16.fract(), 0.5f16, TOL_0); + assert_approx_eq!(1.7f16.fract(), 0.7f16, TOL_0); + assert_approx_eq!(0.0f16.fract(), 0.0f16, TOL_0); + assert_approx_eq!((-0.0f16).fract(), -0.0f16, TOL_0); + assert_approx_eq!((-1.0f16).fract(), -0.0f16, TOL_0); + assert_approx_eq!((-1.3f16).fract(), -0.3f16, TOL_0); + assert_approx_eq!((-1.5f16).fract(), -0.5f16, TOL_0); + assert_approx_eq!((-1.7f16).fract(), -0.7f16, TOL_0); +} + +#[test] +#[cfg(reliable_f16_math)] fn test_abs() { assert_eq!(f16::INFINITY.abs(), f16::INFINITY); assert_eq!(1f16.abs(), 1f16); @@ -299,6 +400,24 @@ fn test_next_down() { } #[test] +#[cfg(reliable_f16_math)] +fn test_mul_add() { + let nan: f16 = f16::NAN; + let inf: f16 = f16::INFINITY; + let neg_inf: f16 = f16::NEG_INFINITY; + assert_approx_eq!(12.3f16.mul_add(4.5, 6.7), 62.05, TOL_P2); + assert_approx_eq!((-12.3f16).mul_add(-4.5, -6.7), 48.65, TOL_P2); + assert_approx_eq!(0.0f16.mul_add(8.9, 1.2), 1.2, TOL_0); + assert_approx_eq!(3.4f16.mul_add(-0.0, 5.6), 5.6, TOL_0); + assert!(nan.mul_add(7.8, 9.0).is_nan()); + assert_eq!(inf.mul_add(7.8, 9.0), inf); + assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf); + assert_eq!(8.9f16.mul_add(inf, 3.2), inf); + assert_eq!((-3.2f16).mul_add(2.4, neg_inf), neg_inf); +} + +#[test] +#[cfg(reliable_f16_math)] fn test_recip() { let nan: f16 = f16::NAN; let inf: f16 = f16::INFINITY; @@ -307,20 +426,166 @@ fn test_recip() { assert_eq!(2.0f16.recip(), 0.5); assert_eq!((-0.4f16).recip(), -2.5); assert_eq!(0.0f16.recip(), inf); + assert_approx_eq!(f16::MAX.recip(), 1.526624e-5f16, 1e-4); assert!(nan.recip().is_nan()); assert_eq!(inf.recip(), 0.0); assert_eq!(neg_inf.recip(), 0.0); } #[test] +#[cfg(reliable_f16_math)] +fn test_powi() { + // FIXME(llvm19): LLVM misoptimizes `powi.f16` + // <https://github.com/llvm/llvm-project/issues/98665> + // let nan: f16 = f16::NAN; + // let inf: f16 = f16::INFINITY; + // let neg_inf: f16 = f16::NEG_INFINITY; + // assert_eq!(1.0f16.powi(1), 1.0); + // assert_approx_eq!((-3.1f16).powi(2), 9.61, TOL_0); + // assert_approx_eq!(5.9f16.powi(-2), 0.028727, TOL_N2); + // assert_eq!(8.3f16.powi(0), 1.0); + // assert!(nan.powi(2).is_nan()); + // assert_eq!(inf.powi(3), inf); + // assert_eq!(neg_inf.powi(2), inf); +} + +#[test] +#[cfg(reliable_f16_math)] +fn test_powf() { + let nan: f16 = f16::NAN; + let inf: f16 = f16::INFINITY; + let neg_inf: f16 = f16::NEG_INFINITY; + assert_eq!(1.0f16.powf(1.0), 1.0); + assert_approx_eq!(3.4f16.powf(4.5), 246.408183, TOL_P2); + assert_approx_eq!(2.7f16.powf(-3.2), 0.041652, TOL_N2); + assert_approx_eq!((-3.1f16).powf(2.0), 9.61, TOL_P2); + assert_approx_eq!(5.9f16.powf(-2.0), 0.028727, TOL_N2); + assert_eq!(8.3f16.powf(0.0), 1.0); + assert!(nan.powf(2.0).is_nan()); + assert_eq!(inf.powf(2.0), inf); + assert_eq!(neg_inf.powf(3.0), neg_inf); +} + +#[test] +#[cfg(reliable_f16_math)] +fn test_sqrt_domain() { + assert!(f16::NAN.sqrt().is_nan()); + assert!(f16::NEG_INFINITY.sqrt().is_nan()); + assert!((-1.0f16).sqrt().is_nan()); + assert_eq!((-0.0f16).sqrt(), -0.0); + assert_eq!(0.0f16.sqrt(), 0.0); + assert_eq!(1.0f16.sqrt(), 1.0); + assert_eq!(f16::INFINITY.sqrt(), f16::INFINITY); +} + +#[test] +#[cfg(reliable_f16_math)] +fn test_exp() { + assert_eq!(1.0, 0.0f16.exp()); + assert_approx_eq!(2.718282, 1.0f16.exp(), TOL_0); + assert_approx_eq!(148.413159, 5.0f16.exp(), TOL_0); + + let inf: f16 = f16::INFINITY; + let neg_inf: f16 = f16::NEG_INFINITY; + let nan: f16 = f16::NAN; + assert_eq!(inf, inf.exp()); + assert_eq!(0.0, neg_inf.exp()); + assert!(nan.exp().is_nan()); +} + +#[test] +#[cfg(reliable_f16_math)] +fn test_exp2() { + assert_eq!(32.0, 5.0f16.exp2()); + assert_eq!(1.0, 0.0f16.exp2()); + + let inf: f16 = f16::INFINITY; + let neg_inf: f16 = f16::NEG_INFINITY; + let nan: f16 = f16::NAN; + assert_eq!(inf, inf.exp2()); + assert_eq!(0.0, neg_inf.exp2()); + assert!(nan.exp2().is_nan()); +} + +#[test] +#[cfg(reliable_f16_math)] +fn test_ln() { + let nan: f16 = f16::NAN; + let inf: f16 = f16::INFINITY; + let neg_inf: f16 = f16::NEG_INFINITY; + assert_approx_eq!(1.0f16.exp().ln(), 1.0, TOL_0); + assert!(nan.ln().is_nan()); + assert_eq!(inf.ln(), inf); + assert!(neg_inf.ln().is_nan()); + assert!((-2.3f16).ln().is_nan()); + assert_eq!((-0.0f16).ln(), neg_inf); + assert_eq!(0.0f16.ln(), neg_inf); + assert_approx_eq!(4.0f16.ln(), 1.386294, TOL_0); +} + +#[test] +#[cfg(reliable_f16_math)] +fn test_log() { + let nan: f16 = f16::NAN; + let inf: f16 = f16::INFINITY; + let neg_inf: f16 = f16::NEG_INFINITY; + assert_eq!(10.0f16.log(10.0), 1.0); + assert_approx_eq!(2.3f16.log(3.5), 0.664858, TOL_0); + assert_eq!(1.0f16.exp().log(1.0f16.exp()), 1.0); + assert!(1.0f16.log(1.0).is_nan()); + assert!(1.0f16.log(-13.9).is_nan()); + assert!(nan.log(2.3).is_nan()); + assert_eq!(inf.log(10.0), inf); + assert!(neg_inf.log(8.8).is_nan()); + assert!((-2.3f16).log(0.1).is_nan()); + assert_eq!((-0.0f16).log(2.0), neg_inf); + assert_eq!(0.0f16.log(7.0), neg_inf); +} + +#[test] +#[cfg(reliable_f16_math)] +fn test_log2() { + let nan: f16 = f16::NAN; + let inf: f16 = f16::INFINITY; + let neg_inf: f16 = f16::NEG_INFINITY; + assert_approx_eq!(10.0f16.log2(), 3.321928, TOL_0); + assert_approx_eq!(2.3f16.log2(), 1.201634, TOL_0); + assert_approx_eq!(1.0f16.exp().log2(), 1.442695, TOL_0); + assert!(nan.log2().is_nan()); + assert_eq!(inf.log2(), inf); + assert!(neg_inf.log2().is_nan()); + assert!((-2.3f16).log2().is_nan()); + assert_eq!((-0.0f16).log2(), neg_inf); + assert_eq!(0.0f16.log2(), neg_inf); +} + +#[test] +#[cfg(reliable_f16_math)] +fn test_log10() { + let nan: f16 = f16::NAN; + let inf: f16 = f16::INFINITY; + let neg_inf: f16 = f16::NEG_INFINITY; + assert_eq!(10.0f16.log10(), 1.0); + assert_approx_eq!(2.3f16.log10(), 0.361728, TOL_0); + assert_approx_eq!(1.0f16.exp().log10(), 0.434294, TOL_0); + assert_eq!(1.0f16.log10(), 0.0); + assert!(nan.log10().is_nan()); + assert_eq!(inf.log10(), inf); + assert!(neg_inf.log10().is_nan()); + assert!((-2.3f16).log10().is_nan()); + assert_eq!((-0.0f16).log10(), neg_inf); + assert_eq!(0.0f16.log10(), neg_inf); +} + +#[test] fn test_to_degrees() { let pi: f16 = consts::PI; let nan: f16 = f16::NAN; let inf: f16 = f16::INFINITY; let neg_inf: f16 = f16::NEG_INFINITY; assert_eq!(0.0f16.to_degrees(), 0.0); - assert_approx_eq!((-5.8f16).to_degrees(), -332.315521); - assert_approx_eq!(pi.to_degrees(), 180.0, F16_APPROX_L4); + assert_approx_eq!((-5.8f16).to_degrees(), -332.315521, TOL_P2); + assert_approx_eq!(pi.to_degrees(), 180.0, TOL_P2); assert!(nan.to_degrees().is_nan()); assert_eq!(inf.to_degrees(), inf); assert_eq!(neg_inf.to_degrees(), neg_inf); @@ -334,15 +599,113 @@ fn test_to_radians() { let inf: f16 = f16::INFINITY; let neg_inf: f16 = f16::NEG_INFINITY; assert_eq!(0.0f16.to_radians(), 0.0); - assert_approx_eq!(154.6f16.to_radians(), 2.698279); - assert_approx_eq!((-332.31f16).to_radians(), -5.799903); - assert_approx_eq!(180.0f16.to_radians(), pi, F16_APPROX_L2); + assert_approx_eq!(154.6f16.to_radians(), 2.698279, TOL_0); + assert_approx_eq!((-332.31f16).to_radians(), -5.799903, TOL_0); + assert_approx_eq!(180.0f16.to_radians(), pi, TOL_0); assert!(nan.to_radians().is_nan()); assert_eq!(inf.to_radians(), inf); assert_eq!(neg_inf.to_radians(), neg_inf); } #[test] +#[cfg(reliable_f16_math)] +fn test_asinh() { + assert_eq!(0.0f16.asinh(), 0.0f16); + assert_eq!((-0.0f16).asinh(), -0.0f16); + + let inf: f16 = f16::INFINITY; + let neg_inf: f16 = f16::NEG_INFINITY; + let nan: f16 = f16::NAN; + assert_eq!(inf.asinh(), inf); + assert_eq!(neg_inf.asinh(), neg_inf); + assert!(nan.asinh().is_nan()); + assert!((-0.0f16).asinh().is_sign_negative()); + // issue 63271 + assert_approx_eq!(2.0f16.asinh(), 1.443635475178810342493276740273105f16, TOL_0); + assert_approx_eq!((-2.0f16).asinh(), -1.443635475178810342493276740273105f16, TOL_0); + // regression test for the catastrophic cancellation fixed in 72486 + assert_approx_eq!((-200.0f16).asinh(), -5.991470797049389, TOL_0); + + // test for low accuracy from issue 104548 + assert_approx_eq!(10.0f16, 10.0f16.sinh().asinh(), TOL_0); + // mul needed for approximate comparison to be meaningful + assert_approx_eq!(1.0f16, 1e-3f16.sinh().asinh() * 1e3f16, TOL_0); +} + +#[test] +#[cfg(reliable_f16_math)] +fn test_acosh() { + assert_eq!(1.0f16.acosh(), 0.0f16); + assert!(0.999f16.acosh().is_nan()); + + let inf: f16 = f16::INFINITY; + let neg_inf: f16 = f16::NEG_INFINITY; + let nan: f16 = f16::NAN; + assert_eq!(inf.acosh(), inf); + assert!(neg_inf.acosh().is_nan()); + assert!(nan.acosh().is_nan()); + assert_approx_eq!(2.0f16.acosh(), 1.31695789692481670862504634730796844f16, TOL_0); + assert_approx_eq!(3.0f16.acosh(), 1.76274717403908605046521864995958461f16, TOL_0); + + // test for low accuracy from issue 104548 + assert_approx_eq!(10.0f16, 10.0f16.cosh().acosh(), TOL_P2); +} + +#[test] +#[cfg(reliable_f16_math)] +fn test_atanh() { + assert_eq!(0.0f16.atanh(), 0.0f16); + assert_eq!((-0.0f16).atanh(), -0.0f16); + + let inf: f16 = f16::INFINITY; + let neg_inf: f16 = f16::NEG_INFINITY; + let nan: f16 = f16::NAN; + assert_eq!(1.0f16.atanh(), inf); + assert_eq!((-1.0f16).atanh(), neg_inf); + assert!(2f16.atanh().atanh().is_nan()); + assert!((-2f16).atanh().atanh().is_nan()); + assert!(inf.atanh().is_nan()); + assert!(neg_inf.atanh().is_nan()); + assert!(nan.atanh().is_nan()); + assert_approx_eq!(0.5f16.atanh(), 0.54930614433405484569762261846126285f16, TOL_0); + assert_approx_eq!((-0.5f16).atanh(), -0.54930614433405484569762261846126285f16, TOL_0); +} + +#[test] +#[cfg(reliable_f16_math)] +fn test_gamma() { + // precision can differ among platforms + assert_approx_eq!(1.0f16.gamma(), 1.0f16, TOL_0); + assert_approx_eq!(2.0f16.gamma(), 1.0f16, TOL_0); + assert_approx_eq!(3.0f16.gamma(), 2.0f16, TOL_0); + assert_approx_eq!(4.0f16.gamma(), 6.0f16, TOL_0); + assert_approx_eq!(5.0f16.gamma(), 24.0f16, TOL_0); + assert_approx_eq!(0.5f16.gamma(), consts::PI.sqrt(), TOL_0); + assert_approx_eq!((-0.5f16).gamma(), -2.0 * consts::PI.sqrt(), TOL_0); + assert_eq!(0.0f16.gamma(), f16::INFINITY); + assert_eq!((-0.0f16).gamma(), f16::NEG_INFINITY); + assert!((-1.0f16).gamma().is_nan()); + assert!((-2.0f16).gamma().is_nan()); + assert!(f16::NAN.gamma().is_nan()); + assert!(f16::NEG_INFINITY.gamma().is_nan()); + assert_eq!(f16::INFINITY.gamma(), f16::INFINITY); + assert_eq!(171.71f16.gamma(), f16::INFINITY); +} + +#[test] +#[cfg(reliable_f16_math)] +fn test_ln_gamma() { + assert_approx_eq!(1.0f16.ln_gamma().0, 0.0f16, TOL_0); + assert_eq!(1.0f16.ln_gamma().1, 1); + assert_approx_eq!(2.0f16.ln_gamma().0, 0.0f16, TOL_0); + assert_eq!(2.0f16.ln_gamma().1, 1); + assert_approx_eq!(3.0f16.ln_gamma().0, 2.0f16.ln(), TOL_0); + assert_eq!(3.0f16.ln_gamma().1, 1); + assert_approx_eq!((-0.5f16).ln_gamma().0, (2.0 * consts::PI.sqrt()).ln(), TOL_0); + assert_eq!((-0.5f16).ln_gamma().1, -1); +} + +#[test] fn test_real_consts() { // FIXME(f16_f128): add math tests when available use super::consts; @@ -355,29 +718,34 @@ fn test_real_consts() { let frac_pi_8: f16 = consts::FRAC_PI_8; let frac_1_pi: f16 = consts::FRAC_1_PI; let frac_2_pi: f16 = consts::FRAC_2_PI; - // let frac_2_sqrtpi: f16 = consts::FRAC_2_SQRT_PI; - // let sqrt2: f16 = consts::SQRT_2; - // let frac_1_sqrt2: f16 = consts::FRAC_1_SQRT_2; - // let e: f16 = consts::E; - // let log2_e: f16 = consts::LOG2_E; - // let log10_e: f16 = consts::LOG10_E; - // let ln_2: f16 = consts::LN_2; - // let ln_10: f16 = consts::LN_10; - - assert_approx_eq!(frac_pi_2, pi / 2f16); - assert_approx_eq!(frac_pi_3, pi / 3f16); - assert_approx_eq!(frac_pi_4, pi / 4f16); - assert_approx_eq!(frac_pi_6, pi / 6f16); - assert_approx_eq!(frac_pi_8, pi / 8f16); - assert_approx_eq!(frac_1_pi, 1f16 / pi); - assert_approx_eq!(frac_2_pi, 2f16 / pi); - // assert_approx_eq!(frac_2_sqrtpi, 2f16 / pi.sqrt()); - // assert_approx_eq!(sqrt2, 2f16.sqrt()); - // assert_approx_eq!(frac_1_sqrt2, 1f16 / 2f16.sqrt()); - // assert_approx_eq!(log2_e, e.log2()); - // assert_approx_eq!(log10_e, e.log10()); - // assert_approx_eq!(ln_2, 2f16.ln()); - // assert_approx_eq!(ln_10, 10f16.ln()); + + assert_approx_eq!(frac_pi_2, pi / 2f16, TOL_0); + assert_approx_eq!(frac_pi_3, pi / 3f16, TOL_0); + assert_approx_eq!(frac_pi_4, pi / 4f16, TOL_0); + assert_approx_eq!(frac_pi_6, pi / 6f16, TOL_0); + assert_approx_eq!(frac_pi_8, pi / 8f16, TOL_0); + assert_approx_eq!(frac_1_pi, 1f16 / pi, TOL_0); + assert_approx_eq!(frac_2_pi, 2f16 / pi, TOL_0); + + #[cfg(reliable_f16_math)] + { + let frac_2_sqrtpi: f16 = consts::FRAC_2_SQRT_PI; + let sqrt2: f16 = consts::SQRT_2; + let frac_1_sqrt2: f16 = consts::FRAC_1_SQRT_2; + let e: f16 = consts::E; + let log2_e: f16 = consts::LOG2_E; + let log10_e: f16 = consts::LOG10_E; + let ln_2: f16 = consts::LN_2; + let ln_10: f16 = consts::LN_10; + + assert_approx_eq!(frac_2_sqrtpi, 2f16 / pi.sqrt(), TOL_0); + assert_approx_eq!(sqrt2, 2f16.sqrt(), TOL_0); + assert_approx_eq!(frac_1_sqrt2, 1f16 / 2f16.sqrt(), TOL_0); + assert_approx_eq!(log2_e, e.log2(), TOL_0); + assert_approx_eq!(log10_e, e.log10(), TOL_0); + assert_approx_eq!(ln_2, 2f16.ln(), TOL_0); + assert_approx_eq!(ln_10, 10f16.ln(), TOL_0); + } } #[test] @@ -386,10 +754,10 @@ fn test_float_bits_conv() { assert_eq!((12.5f16).to_bits(), 0x4a40); assert_eq!((1337f16).to_bits(), 0x6539); assert_eq!((-14.25f16).to_bits(), 0xcb20); - assert_approx_eq!(f16::from_bits(0x3c00), 1.0); - assert_approx_eq!(f16::from_bits(0x4a40), 12.5); - assert_approx_eq!(f16::from_bits(0x6539), 1337.0); - assert_approx_eq!(f16::from_bits(0xcb20), -14.25); + assert_approx_eq!(f16::from_bits(0x3c00), 1.0, TOL_0); + assert_approx_eq!(f16::from_bits(0x4a40), 12.5, TOL_0); + assert_approx_eq!(f16::from_bits(0x6539), 1337.0, TOL_P4); + assert_approx_eq!(f16::from_bits(0xcb20), -14.25, TOL_0); // Check that NaNs roundtrip their bits regardless of signaling-ness let masked_nan1 = f16::NAN.to_bits() ^ NAN_MASK1; diff --git a/library/std/src/macros.rs b/library/std/src/macros.rs index ba519afc62b..1b0d7f3dbf2 100644 --- a/library/std/src/macros.rs +++ b/library/std/src/macros.rs @@ -382,7 +382,7 @@ macro_rules! assert_approx_eq { let diff = (*a - *b).abs(); assert!( diff < $lim, - "{a:?} is not approximately equal to {b:?} (threshold {lim:?}, actual {diff:?})", + "{a:?} is not approximately equal to {b:?} (threshold {lim:?}, difference {diff:?})", lim = $lim ); }}; diff --git a/library/std/src/sys/cmath.rs b/library/std/src/sys/cmath.rs index 99df503b82d..2997e908fa1 100644 --- a/library/std/src/sys/cmath.rs +++ b/library/std/src/sys/cmath.rs @@ -28,6 +28,21 @@ extern "C" { pub fn lgamma_r(n: f64, s: &mut i32) -> f64; pub fn lgammaf_r(n: f32, s: &mut i32) -> f32; + pub fn acosf128(n: f128) -> f128; + pub fn asinf128(n: f128) -> f128; + pub fn atanf128(n: f128) -> f128; + pub fn atan2f128(a: f128, b: f128) -> f128; + pub fn cbrtf128(n: f128) -> f128; + pub fn coshf128(n: f128) -> f128; + pub fn expm1f128(n: f128) -> f128; + pub fn hypotf128(x: f128, y: f128) -> f128; + pub fn log1pf128(n: f128) -> f128; + pub fn sinhf128(n: f128) -> f128; + pub fn tanf128(n: f128) -> f128; + pub fn tanhf128(n: f128) -> f128; + pub fn tgammaf128(n: f128) -> f128; + pub fn lgammaf128_r(n: f128, s: &mut i32) -> f128; + cfg_if::cfg_if! { if #[cfg(not(all(target_os = "windows", target_env = "msvc", target_arch = "x86")))] { pub fn acosf(n: f32) -> f32; |