| //! This module provides constants which are specific to the implementation |
| //! of the `f64` floating point data type. |
| //! |
| //! *[See also the `f64` primitive type](../../std/primitive.f64.html).* |
| //! |
| //! Mathematically significant numbers are provided in the `consts` sub-module. |
| |
| #![stable(feature = "rust1", since = "1.0.0")] |
| #![allow(missing_docs)] |
| |
| #[cfg(not(test))] |
| use crate::intrinsics; |
| #[cfg(not(test))] |
| use crate::sys::cmath; |
| |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub use core::f64::consts; |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub use core::f64::{DIGITS, EPSILON, MANTISSA_DIGITS, RADIX}; |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub use core::f64::{INFINITY, MAX_10_EXP, NAN, NEG_INFINITY}; |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub use core::f64::{MAX, MIN, MIN_POSITIVE}; |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub use core::f64::{MAX_EXP, MIN_10_EXP, MIN_EXP}; |
| |
| #[cfg(not(test))] |
| #[lang = "f64_runtime"] |
| impl f64 { |
| /// Returns the largest integer less than or equal to a number. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let f = 3.7_f64; |
| /// let g = 3.0_f64; |
| /// let h = -3.7_f64; |
| /// |
| /// assert_eq!(f.floor(), 3.0); |
| /// assert_eq!(g.floor(), 3.0); |
| /// assert_eq!(h.floor(), -4.0); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn floor(self) -> f64 { |
| unsafe { intrinsics::floorf64(self) } |
| } |
| |
| /// Returns the smallest integer greater than or equal to a number. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let f = 3.01_f64; |
| /// let g = 4.0_f64; |
| /// |
| /// assert_eq!(f.ceil(), 4.0); |
| /// assert_eq!(g.ceil(), 4.0); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn ceil(self) -> f64 { |
| unsafe { intrinsics::ceilf64(self) } |
| } |
| |
| /// Returns the nearest integer to a number. Round half-way cases away from |
| /// `0.0`. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let f = 3.3_f64; |
| /// let g = -3.3_f64; |
| /// |
| /// assert_eq!(f.round(), 3.0); |
| /// assert_eq!(g.round(), -3.0); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn round(self) -> f64 { |
| unsafe { intrinsics::roundf64(self) } |
| } |
| |
| /// Returns the integer part of a number. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let f = 3.7_f64; |
| /// let g = 3.0_f64; |
| /// let h = -3.7_f64; |
| /// |
| /// assert_eq!(f.trunc(), 3.0); |
| /// assert_eq!(g.trunc(), 3.0); |
| /// assert_eq!(h.trunc(), -3.0); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn trunc(self) -> f64 { |
| unsafe { intrinsics::truncf64(self) } |
| } |
| |
| /// Returns the fractional part of a number. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let x = 3.6_f64; |
| /// let y = -3.6_f64; |
| /// let abs_difference_x = (x.fract() - 0.6).abs(); |
| /// let abs_difference_y = (y.fract() - (-0.6)).abs(); |
| /// |
| /// assert!(abs_difference_x < 1e-10); |
| /// assert!(abs_difference_y < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn fract(self) -> f64 { |
| self - self.trunc() |
| } |
| |
| /// Computes the absolute value of `self`. Returns `NAN` if the |
| /// number is `NAN`. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let x = 3.5_f64; |
| /// let y = -3.5_f64; |
| /// |
| /// let abs_difference_x = (x.abs() - x).abs(); |
| /// let abs_difference_y = (y.abs() - (-y)).abs(); |
| /// |
| /// assert!(abs_difference_x < 1e-10); |
| /// assert!(abs_difference_y < 1e-10); |
| /// |
| /// assert!(f64::NAN.abs().is_nan()); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn abs(self) -> f64 { |
| unsafe { intrinsics::fabsf64(self) } |
| } |
| |
| /// 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 |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let f = 3.5_f64; |
| /// |
| /// assert_eq!(f.signum(), 1.0); |
| /// assert_eq!(f64::NEG_INFINITY.signum(), -1.0); |
| /// |
| /// assert!(f64::NAN.signum().is_nan()); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn signum(self) -> f64 { |
| if self.is_nan() { NAN } else { 1.0_f64.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 of |
| /// `sign` is returned. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let f = 3.5_f64; |
| /// |
| /// assert_eq!(f.copysign(0.42), 3.5_f64); |
| /// assert_eq!(f.copysign(-0.42), -3.5_f64); |
| /// assert_eq!((-f).copysign(0.42), 3.5_f64); |
| /// assert_eq!((-f).copysign(-0.42), -3.5_f64); |
| /// |
| /// assert!(f64::NAN.copysign(1.0).is_nan()); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "copysign", since = "1.35.0")] |
| #[inline] |
| pub fn copysign(self, sign: f64) -> f64 { |
| unsafe { intrinsics::copysignf64(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` can be more performant than an unfused multiply-add if |
| /// the target architecture has a dedicated `fma` CPU instruction. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let m = 10.0_f64; |
| /// let x = 4.0_f64; |
| /// let b = 60.0_f64; |
| /// |
| /// // 100.0 |
| /// let abs_difference = (m.mul_add(x, b) - ((m * x) + b)).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn mul_add(self, a: f64, b: f64) -> f64 { |
| unsafe { intrinsics::fmaf64(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`. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let a: f64 = 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 |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[inline] |
| #[stable(feature = "euclidean_division", since = "1.38.0")] |
| pub fn div_euclid(self, rhs: f64) -> f64 { |
| 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)` |
| /// approximatively. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let a: f64 = 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!((-std::f64::EPSILON).rem_euclid(3.0) != 0.0); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[inline] |
| #[stable(feature = "euclidean_division", since = "1.38.0")] |
| pub fn rem_euclid(self, rhs: f64) -> f64 { |
| 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` |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let x = 2.0_f64; |
| /// let abs_difference = (x.powi(2) - (x * x)).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn powi(self, n: i32) -> f64 { |
| unsafe { intrinsics::powif64(self, n) } |
| } |
| |
| /// Raises a number to a floating point power. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let x = 2.0_f64; |
| /// let abs_difference = (x.powf(2.0) - (x * x)).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn powf(self, n: f64) -> f64 { |
| unsafe { intrinsics::powf64(self, n) } |
| } |
| |
| /// Returns the square root of a number. |
| /// |
| /// Returns NaN if `self` is a negative number. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let positive = 4.0_f64; |
| /// let negative = -4.0_f64; |
| /// |
| /// let abs_difference = (positive.sqrt() - 2.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// assert!(negative.sqrt().is_nan()); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn sqrt(self) -> f64 { |
| unsafe { intrinsics::sqrtf64(self) } |
| } |
| |
| /// Returns `e^(self)`, (the exponential function). |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let one = 1.0_f64; |
| /// // e^1 |
| /// let e = one.exp(); |
| /// |
| /// // ln(e) - 1 == 0 |
| /// let abs_difference = (e.ln() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn exp(self) -> f64 { |
| unsafe { intrinsics::expf64(self) } |
| } |
| |
| /// Returns `2^(self)`. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let f = 2.0_f64; |
| /// |
| /// // 2^2 - 4 == 0 |
| /// let abs_difference = (f.exp2() - 4.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn exp2(self) -> f64 { |
| unsafe { intrinsics::exp2f64(self) } |
| } |
| |
| /// Returns the natural logarithm of the number. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let one = 1.0_f64; |
| /// // e^1 |
| /// let e = one.exp(); |
| /// |
| /// // ln(e) - 1 == 0 |
| /// let abs_difference = (e.ln() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn ln(self) -> f64 { |
| self.log_wrapper(|n| unsafe { intrinsics::logf64(n) }) |
| } |
| |
| /// Returns the logarithm of the number with respect to an arbitrary base. |
| /// |
| /// The result may not be correctly rounded owing to implementation details; |
| /// `self.log2()` can produce more accurate results for base 2, and |
| /// `self.log10()` can produce more accurate results for base 10. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let twenty_five = 25.0_f64; |
| /// |
| /// // log5(25) - 2 == 0 |
| /// let abs_difference = (twenty_five.log(5.0) - 2.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn log(self, base: f64) -> f64 { |
| self.ln() / base.ln() |
| } |
| |
| /// Returns the base 2 logarithm of the number. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let four = 4.0_f64; |
| /// |
| /// // log2(4) - 2 == 0 |
| /// let abs_difference = (four.log2() - 2.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn log2(self) -> f64 { |
| self.log_wrapper(|n| { |
| #[cfg(target_os = "android")] |
| return crate::sys::android::log2f64(n); |
| #[cfg(not(target_os = "android"))] |
| return unsafe { intrinsics::log2f64(n) }; |
| }) |
| } |
| |
| /// Returns the base 10 logarithm of the number. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let hundred = 100.0_f64; |
| /// |
| /// // log10(100) - 2 == 0 |
| /// let abs_difference = (hundred.log10() - 2.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn log10(self) -> f64 { |
| self.log_wrapper(|n| unsafe { intrinsics::log10f64(n) }) |
| } |
| |
| /// The positive difference of two numbers. |
| /// |
| /// * If `self <= other`: `0:0` |
| /// * Else: `self - other` |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let x = 3.0_f64; |
| /// let y = -3.0_f64; |
| /// |
| /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs(); |
| /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs(); |
| /// |
| /// assert!(abs_difference_x < 1e-10); |
| /// assert!(abs_difference_y < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| #[rustc_deprecated( |
| since = "1.10.0", |
| reason = "you probably meant `(self - other).abs()`: \ |
| this operation is `(self - other).max(0.0)` \ |
| except that `abs_sub` also propagates NaNs (also \ |
| known as `fdim` in C). If you truly need the positive \ |
| difference, consider using that expression or the C function \ |
| `fdim`, depending on how you wish to handle NaN (please consider \ |
| filing an issue describing your use-case too)." |
| )] |
| pub fn abs_sub(self, other: f64) -> f64 { |
| unsafe { cmath::fdim(self, other) } |
| } |
| |
| /// Returns the cubic root of a number. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let x = 8.0_f64; |
| /// |
| /// // x^(1/3) - 2 == 0 |
| /// let abs_difference = (x.cbrt() - 2.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn cbrt(self) -> f64 { |
| unsafe { cmath::cbrt(self) } |
| } |
| |
| /// Calculates the length of the hypotenuse of a right-angle triangle given |
| /// legs of length `x` and `y`. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let x = 2.0_f64; |
| /// let y = 3.0_f64; |
| /// |
| /// // sqrt(x^2 + y^2) |
| /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn hypot(self, other: f64) -> f64 { |
| unsafe { cmath::hypot(self, other) } |
| } |
| |
| /// Computes the sine of a number (in radians). |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let x = f64::consts::FRAC_PI_2; |
| /// |
| /// let abs_difference = (x.sin() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn sin(self) -> f64 { |
| unsafe { intrinsics::sinf64(self) } |
| } |
| |
| /// Computes the cosine of a number (in radians). |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let x = 2.0 * f64::consts::PI; |
| /// |
| /// let abs_difference = (x.cos() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn cos(self) -> f64 { |
| unsafe { intrinsics::cosf64(self) } |
| } |
| |
| /// Computes the tangent of a number (in radians). |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let x = f64::consts::FRAC_PI_4; |
| /// let abs_difference = (x.tan() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-14); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn tan(self) -> f64 { |
| unsafe { cmath::tan(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]. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let f = f64::consts::FRAC_PI_2; |
| /// |
| /// // asin(sin(pi/2)) |
| /// let abs_difference = (f.sin().asin() - f64::consts::FRAC_PI_2).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn asin(self) -> f64 { |
| unsafe { cmath::asin(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]. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let f = f64::consts::FRAC_PI_4; |
| /// |
| /// // acos(cos(pi/4)) |
| /// let abs_difference = (f.cos().acos() - f64::consts::FRAC_PI_4).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn acos(self) -> f64 { |
| unsafe { cmath::acos(self) } |
| } |
| |
| /// Computes the arctangent of a number. Return value is in radians in the |
| /// range [-pi/2, pi/2]; |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let f = 1.0_f64; |
| /// |
| /// // atan(tan(1)) |
| /// let abs_difference = (f.tan().atan() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn atan(self) -> f64 { |
| unsafe { cmath::atan(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)` |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// // Positive angles measured counter-clockwise |
| /// // from positive x axis |
| /// // -pi/4 radians (45 deg clockwise) |
| /// let x1 = 3.0_f64; |
| /// let y1 = -3.0_f64; |
| /// |
| /// // 3pi/4 radians (135 deg counter-clockwise) |
| /// let x2 = -3.0_f64; |
| /// let y2 = 3.0_f64; |
| /// |
| /// let abs_difference_1 = (y1.atan2(x1) - (-f64::consts::FRAC_PI_4)).abs(); |
| /// let abs_difference_2 = (y2.atan2(x2) - (3.0 * f64::consts::FRAC_PI_4)).abs(); |
| /// |
| /// assert!(abs_difference_1 < 1e-10); |
| /// assert!(abs_difference_2 < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn atan2(self, other: f64) -> f64 { |
| unsafe { cmath::atan2(self, other) } |
| } |
| |
| /// Simultaneously computes the sine and cosine of the number, `x`. Returns |
| /// `(sin(x), cos(x))`. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let x = f64::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 < 1e-10); |
| /// assert!(abs_difference_1 < 1e-10); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn sin_cos(self) -> (f64, f64) { |
| (self.sin(), self.cos()) |
| } |
| |
| /// Returns `e^(self) - 1` in a way that is accurate even if the |
| /// number is close to zero. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let x = 7.0_f64; |
| /// |
| /// // e^(ln(7)) - 1 |
| /// let abs_difference = (x.ln().exp_m1() - 6.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn exp_m1(self) -> f64 { |
| unsafe { cmath::expm1(self) } |
| } |
| |
| /// Returns `ln(1+n)` (natural logarithm) more accurately than if |
| /// the operations were performed separately. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let x = f64::consts::E - 1.0; |
| /// |
| /// // ln(1 + (e - 1)) == ln(e) == 1 |
| /// let abs_difference = (x.ln_1p() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn ln_1p(self) -> f64 { |
| unsafe { cmath::log1p(self) } |
| } |
| |
| /// Hyperbolic sine function. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let e = f64::consts::E; |
| /// let x = 1.0_f64; |
| /// |
| /// 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 < 1e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn sinh(self) -> f64 { |
| unsafe { cmath::sinh(self) } |
| } |
| |
| /// Hyperbolic cosine function. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let e = f64::consts::E; |
| /// let x = 1.0_f64; |
| /// 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 < 1.0e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn cosh(self) -> f64 { |
| unsafe { cmath::cosh(self) } |
| } |
| |
| /// Hyperbolic tangent function. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let e = f64::consts::E; |
| /// let x = 1.0_f64; |
| /// |
| /// 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 < 1.0e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn tanh(self) -> f64 { |
| unsafe { cmath::tanh(self) } |
| } |
| |
| /// Inverse hyperbolic sine function. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let x = 1.0_f64; |
| /// let f = x.sinh().asinh(); |
| /// |
| /// let abs_difference = (f - x).abs(); |
| /// |
| /// assert!(abs_difference < 1.0e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn asinh(self) -> f64 { |
| if self == NEG_INFINITY { |
| NEG_INFINITY |
| } else { |
| (self + ((self * self) + 1.0).sqrt()).ln().copysign(self) |
| } |
| } |
| |
| /// Inverse hyperbolic cosine function. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let x = 1.0_f64; |
| /// let f = x.cosh().acosh(); |
| /// |
| /// let abs_difference = (f - x).abs(); |
| /// |
| /// assert!(abs_difference < 1.0e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn acosh(self) -> f64 { |
| if self < 1.0 { NAN } else { (self + ((self * self) - 1.0).sqrt()).ln() } |
| } |
| |
| /// Inverse hyperbolic tangent function. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let e = f64::consts::E; |
| /// let f = e.tanh().atanh(); |
| /// |
| /// let abs_difference = (f - e).abs(); |
| /// |
| /// assert!(abs_difference < 1.0e-10); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn atanh(self) -> f64 { |
| 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p() |
| } |
| |
| /// Restrict a value to a certain interval unless it is NaN. |
| /// |
| /// Returns `max` if `self` is greater than `max`, and `min` if `self` is |
| /// less than `min`. Otherwise this returns `self`. |
| /// |
| /// Not that this function returns NaN if the initial value was NaN as |
| /// well. |
| /// |
| /// # Panics |
| /// |
| /// Panics if `min > max`, `min` is NaN, or `max` is NaN. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// #![feature(clamp)] |
| /// assert!((-3.0f64).clamp(-2.0, 1.0) == -2.0); |
| /// assert!((0.0f64).clamp(-2.0, 1.0) == 0.0); |
| /// assert!((2.0f64).clamp(-2.0, 1.0) == 1.0); |
| /// assert!((std::f64::NAN).clamp(-2.0, 1.0).is_nan()); |
| /// ``` |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[unstable(feature = "clamp", issue = "44095")] |
| #[inline] |
| pub fn clamp(self, min: f64, max: f64) -> f64 { |
| assert!(min <= max); |
| let mut x = self; |
| if x < min { |
| x = min; |
| } |
| if x > max { |
| x = max; |
| } |
| x |
| } |
| |
| // Solaris/Illumos requires a wrapper around log, log2, and log10 functions |
| // because of their non-standard behavior (e.g., log(-n) returns -Inf instead |
| // of expected NaN). |
| fn log_wrapper<F: Fn(f64) -> f64>(self, log_fn: F) -> f64 { |
| if !cfg!(target_os = "solaris") { |
| log_fn(self) |
| } else { |
| if self.is_finite() { |
| if self > 0.0 { |
| log_fn(self) |
| } else if self == 0.0 { |
| NEG_INFINITY // log(0) = -Inf |
| } else { |
| NAN // log(-n) = NaN |
| } |
| } else if self.is_nan() { |
| self // log(NaN) = NaN |
| } else if self > 0.0 { |
| self // log(Inf) = Inf |
| } else { |
| NAN // log(-Inf) = NaN |
| } |
| } |
| } |
| } |
| |
| #[cfg(test)] |
| mod tests { |
| use crate::f64; |
| use crate::f64::*; |
| use crate::num::FpCategory as Fp; |
| use crate::num::*; |
| |
| #[test] |
| fn test_num_f64() { |
| test_num(10f64, 2f64); |
| } |
| |
| #[test] |
| fn test_min_nan() { |
| assert_eq!(NAN.min(2.0), 2.0); |
| assert_eq!(2.0f64.min(NAN), 2.0); |
| } |
| |
| #[test] |
| fn test_max_nan() { |
| assert_eq!(NAN.max(2.0), 2.0); |
| assert_eq!(2.0f64.max(NAN), 2.0); |
| } |
| |
| #[test] |
| fn test_nan() { |
| let nan: f64 = NAN; |
| assert!(nan.is_nan()); |
| assert!(!nan.is_infinite()); |
| assert!(!nan.is_finite()); |
| assert!(!nan.is_normal()); |
| assert!(nan.is_sign_positive()); |
| assert!(!nan.is_sign_negative()); |
| assert_eq!(Fp::Nan, nan.classify()); |
| } |
| |
| #[test] |
| fn test_infinity() { |
| let inf: f64 = INFINITY; |
| assert!(inf.is_infinite()); |
| assert!(!inf.is_finite()); |
| assert!(inf.is_sign_positive()); |
| assert!(!inf.is_sign_negative()); |
| assert!(!inf.is_nan()); |
| assert!(!inf.is_normal()); |
| assert_eq!(Fp::Infinite, inf.classify()); |
| } |
| |
| #[test] |
| fn test_neg_infinity() { |
| let neg_inf: f64 = NEG_INFINITY; |
| assert!(neg_inf.is_infinite()); |
| assert!(!neg_inf.is_finite()); |
| assert!(!neg_inf.is_sign_positive()); |
| assert!(neg_inf.is_sign_negative()); |
| assert!(!neg_inf.is_nan()); |
| assert!(!neg_inf.is_normal()); |
| assert_eq!(Fp::Infinite, neg_inf.classify()); |
| } |
| |
| #[test] |
| fn test_zero() { |
| let zero: f64 = 0.0f64; |
| assert_eq!(0.0, zero); |
| assert!(!zero.is_infinite()); |
| assert!(zero.is_finite()); |
| assert!(zero.is_sign_positive()); |
| assert!(!zero.is_sign_negative()); |
| assert!(!zero.is_nan()); |
| assert!(!zero.is_normal()); |
| assert_eq!(Fp::Zero, zero.classify()); |
| } |
| |
| #[test] |
| fn test_neg_zero() { |
| let neg_zero: f64 = -0.0; |
| assert_eq!(0.0, neg_zero); |
| assert!(!neg_zero.is_infinite()); |
| assert!(neg_zero.is_finite()); |
| assert!(!neg_zero.is_sign_positive()); |
| assert!(neg_zero.is_sign_negative()); |
| assert!(!neg_zero.is_nan()); |
| assert!(!neg_zero.is_normal()); |
| assert_eq!(Fp::Zero, neg_zero.classify()); |
| } |
| |
| #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630 |
| #[test] |
| fn test_one() { |
| let one: f64 = 1.0f64; |
| assert_eq!(1.0, one); |
| assert!(!one.is_infinite()); |
| assert!(one.is_finite()); |
| assert!(one.is_sign_positive()); |
| assert!(!one.is_sign_negative()); |
| assert!(!one.is_nan()); |
| assert!(one.is_normal()); |
| assert_eq!(Fp::Normal, one.classify()); |
| } |
| |
| #[test] |
| fn test_is_nan() { |
| let nan: f64 = NAN; |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| assert!(nan.is_nan()); |
| assert!(!0.0f64.is_nan()); |
| assert!(!5.3f64.is_nan()); |
| assert!(!(-10.732f64).is_nan()); |
| assert!(!inf.is_nan()); |
| assert!(!neg_inf.is_nan()); |
| } |
| |
| #[test] |
| fn test_is_infinite() { |
| let nan: f64 = NAN; |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| assert!(!nan.is_infinite()); |
| assert!(inf.is_infinite()); |
| assert!(neg_inf.is_infinite()); |
| assert!(!0.0f64.is_infinite()); |
| assert!(!42.8f64.is_infinite()); |
| assert!(!(-109.2f64).is_infinite()); |
| } |
| |
| #[test] |
| fn test_is_finite() { |
| let nan: f64 = NAN; |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| assert!(!nan.is_finite()); |
| assert!(!inf.is_finite()); |
| assert!(!neg_inf.is_finite()); |
| assert!(0.0f64.is_finite()); |
| assert!(42.8f64.is_finite()); |
| assert!((-109.2f64).is_finite()); |
| } |
| |
| #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630 |
| #[test] |
| fn test_is_normal() { |
| let nan: f64 = NAN; |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| let zero: f64 = 0.0f64; |
| let neg_zero: f64 = -0.0; |
| assert!(!nan.is_normal()); |
| assert!(!inf.is_normal()); |
| assert!(!neg_inf.is_normal()); |
| assert!(!zero.is_normal()); |
| assert!(!neg_zero.is_normal()); |
| assert!(1f64.is_normal()); |
| assert!(1e-307f64.is_normal()); |
| assert!(!1e-308f64.is_normal()); |
| } |
| |
| #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630 |
| #[test] |
| fn test_classify() { |
| let nan: f64 = NAN; |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| let zero: f64 = 0.0f64; |
| let neg_zero: f64 = -0.0; |
| assert_eq!(nan.classify(), Fp::Nan); |
| assert_eq!(inf.classify(), Fp::Infinite); |
| assert_eq!(neg_inf.classify(), Fp::Infinite); |
| assert_eq!(zero.classify(), Fp::Zero); |
| assert_eq!(neg_zero.classify(), Fp::Zero); |
| assert_eq!(1e-307f64.classify(), Fp::Normal); |
| assert_eq!(1e-308f64.classify(), Fp::Subnormal); |
| } |
| |
| #[test] |
| fn test_floor() { |
| assert_approx_eq!(1.0f64.floor(), 1.0f64); |
| assert_approx_eq!(1.3f64.floor(), 1.0f64); |
| assert_approx_eq!(1.5f64.floor(), 1.0f64); |
| assert_approx_eq!(1.7f64.floor(), 1.0f64); |
| assert_approx_eq!(0.0f64.floor(), 0.0f64); |
| assert_approx_eq!((-0.0f64).floor(), -0.0f64); |
| assert_approx_eq!((-1.0f64).floor(), -1.0f64); |
| assert_approx_eq!((-1.3f64).floor(), -2.0f64); |
| assert_approx_eq!((-1.5f64).floor(), -2.0f64); |
| assert_approx_eq!((-1.7f64).floor(), -2.0f64); |
| } |
| |
| #[test] |
| fn test_ceil() { |
| assert_approx_eq!(1.0f64.ceil(), 1.0f64); |
| assert_approx_eq!(1.3f64.ceil(), 2.0f64); |
| assert_approx_eq!(1.5f64.ceil(), 2.0f64); |
| assert_approx_eq!(1.7f64.ceil(), 2.0f64); |
| assert_approx_eq!(0.0f64.ceil(), 0.0f64); |
| assert_approx_eq!((-0.0f64).ceil(), -0.0f64); |
| assert_approx_eq!((-1.0f64).ceil(), -1.0f64); |
| assert_approx_eq!((-1.3f64).ceil(), -1.0f64); |
| assert_approx_eq!((-1.5f64).ceil(), -1.0f64); |
| assert_approx_eq!((-1.7f64).ceil(), -1.0f64); |
| } |
| |
| #[test] |
| fn test_round() { |
| assert_approx_eq!(1.0f64.round(), 1.0f64); |
| assert_approx_eq!(1.3f64.round(), 1.0f64); |
| assert_approx_eq!(1.5f64.round(), 2.0f64); |
| assert_approx_eq!(1.7f64.round(), 2.0f64); |
| assert_approx_eq!(0.0f64.round(), 0.0f64); |
| assert_approx_eq!((-0.0f64).round(), -0.0f64); |
| assert_approx_eq!((-1.0f64).round(), -1.0f64); |
| assert_approx_eq!((-1.3f64).round(), -1.0f64); |
| assert_approx_eq!((-1.5f64).round(), -2.0f64); |
| assert_approx_eq!((-1.7f64).round(), -2.0f64); |
| } |
| |
| #[test] |
| fn test_trunc() { |
| assert_approx_eq!(1.0f64.trunc(), 1.0f64); |
| assert_approx_eq!(1.3f64.trunc(), 1.0f64); |
| assert_approx_eq!(1.5f64.trunc(), 1.0f64); |
| assert_approx_eq!(1.7f64.trunc(), 1.0f64); |
| assert_approx_eq!(0.0f64.trunc(), 0.0f64); |
| assert_approx_eq!((-0.0f64).trunc(), -0.0f64); |
| assert_approx_eq!((-1.0f64).trunc(), -1.0f64); |
| assert_approx_eq!((-1.3f64).trunc(), -1.0f64); |
| assert_approx_eq!((-1.5f64).trunc(), -1.0f64); |
| assert_approx_eq!((-1.7f64).trunc(), -1.0f64); |
| } |
| |
| #[test] |
| fn test_fract() { |
| assert_approx_eq!(1.0f64.fract(), 0.0f64); |
| assert_approx_eq!(1.3f64.fract(), 0.3f64); |
| assert_approx_eq!(1.5f64.fract(), 0.5f64); |
| assert_approx_eq!(1.7f64.fract(), 0.7f64); |
| assert_approx_eq!(0.0f64.fract(), 0.0f64); |
| assert_approx_eq!((-0.0f64).fract(), -0.0f64); |
| assert_approx_eq!((-1.0f64).fract(), -0.0f64); |
| assert_approx_eq!((-1.3f64).fract(), -0.3f64); |
| assert_approx_eq!((-1.5f64).fract(), -0.5f64); |
| assert_approx_eq!((-1.7f64).fract(), -0.7f64); |
| } |
| |
| #[test] |
| fn test_abs() { |
| assert_eq!(INFINITY.abs(), INFINITY); |
| assert_eq!(1f64.abs(), 1f64); |
| assert_eq!(0f64.abs(), 0f64); |
| assert_eq!((-0f64).abs(), 0f64); |
| assert_eq!((-1f64).abs(), 1f64); |
| assert_eq!(NEG_INFINITY.abs(), INFINITY); |
| assert_eq!((1f64 / NEG_INFINITY).abs(), 0f64); |
| assert!(NAN.abs().is_nan()); |
| } |
| |
| #[test] |
| fn test_signum() { |
| assert_eq!(INFINITY.signum(), 1f64); |
| assert_eq!(1f64.signum(), 1f64); |
| assert_eq!(0f64.signum(), 1f64); |
| assert_eq!((-0f64).signum(), -1f64); |
| assert_eq!((-1f64).signum(), -1f64); |
| assert_eq!(NEG_INFINITY.signum(), -1f64); |
| assert_eq!((1f64 / NEG_INFINITY).signum(), -1f64); |
| assert!(NAN.signum().is_nan()); |
| } |
| |
| #[test] |
| fn test_is_sign_positive() { |
| assert!(INFINITY.is_sign_positive()); |
| assert!(1f64.is_sign_positive()); |
| assert!(0f64.is_sign_positive()); |
| assert!(!(-0f64).is_sign_positive()); |
| assert!(!(-1f64).is_sign_positive()); |
| assert!(!NEG_INFINITY.is_sign_positive()); |
| assert!(!(1f64 / NEG_INFINITY).is_sign_positive()); |
| assert!(NAN.is_sign_positive()); |
| assert!(!(-NAN).is_sign_positive()); |
| } |
| |
| #[test] |
| fn test_is_sign_negative() { |
| assert!(!INFINITY.is_sign_negative()); |
| assert!(!1f64.is_sign_negative()); |
| assert!(!0f64.is_sign_negative()); |
| assert!((-0f64).is_sign_negative()); |
| assert!((-1f64).is_sign_negative()); |
| assert!(NEG_INFINITY.is_sign_negative()); |
| assert!((1f64 / NEG_INFINITY).is_sign_negative()); |
| assert!(!NAN.is_sign_negative()); |
| assert!((-NAN).is_sign_negative()); |
| } |
| |
| #[test] |
| fn test_mul_add() { |
| let nan: f64 = NAN; |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| assert_approx_eq!(12.3f64.mul_add(4.5, 6.7), 62.05); |
| assert_approx_eq!((-12.3f64).mul_add(-4.5, -6.7), 48.65); |
| assert_approx_eq!(0.0f64.mul_add(8.9, 1.2), 1.2); |
| assert_approx_eq!(3.4f64.mul_add(-0.0, 5.6), 5.6); |
| 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!(8.9f64.mul_add(inf, 3.2), inf); |
| assert_eq!((-3.2f64).mul_add(2.4, neg_inf), neg_inf); |
| } |
| |
| #[test] |
| fn test_recip() { |
| let nan: f64 = NAN; |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| assert_eq!(1.0f64.recip(), 1.0); |
| assert_eq!(2.0f64.recip(), 0.5); |
| assert_eq!((-0.4f64).recip(), -2.5); |
| assert_eq!(0.0f64.recip(), inf); |
| assert!(nan.recip().is_nan()); |
| assert_eq!(inf.recip(), 0.0); |
| assert_eq!(neg_inf.recip(), 0.0); |
| } |
| |
| #[test] |
| fn test_powi() { |
| let nan: f64 = NAN; |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| assert_eq!(1.0f64.powi(1), 1.0); |
| assert_approx_eq!((-3.1f64).powi(2), 9.61); |
| assert_approx_eq!(5.9f64.powi(-2), 0.028727); |
| assert_eq!(8.3f64.powi(0), 1.0); |
| assert!(nan.powi(2).is_nan()); |
| assert_eq!(inf.powi(3), inf); |
| assert_eq!(neg_inf.powi(2), inf); |
| } |
| |
| #[test] |
| fn test_powf() { |
| let nan: f64 = NAN; |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| assert_eq!(1.0f64.powf(1.0), 1.0); |
| assert_approx_eq!(3.4f64.powf(4.5), 246.408183); |
| assert_approx_eq!(2.7f64.powf(-3.2), 0.041652); |
| assert_approx_eq!((-3.1f64).powf(2.0), 9.61); |
| assert_approx_eq!(5.9f64.powf(-2.0), 0.028727); |
| assert_eq!(8.3f64.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] |
| fn test_sqrt_domain() { |
| assert!(NAN.sqrt().is_nan()); |
| assert!(NEG_INFINITY.sqrt().is_nan()); |
| assert!((-1.0f64).sqrt().is_nan()); |
| assert_eq!((-0.0f64).sqrt(), -0.0); |
| assert_eq!(0.0f64.sqrt(), 0.0); |
| assert_eq!(1.0f64.sqrt(), 1.0); |
| assert_eq!(INFINITY.sqrt(), INFINITY); |
| } |
| |
| #[test] |
| fn test_exp() { |
| assert_eq!(1.0, 0.0f64.exp()); |
| assert_approx_eq!(2.718282, 1.0f64.exp()); |
| assert_approx_eq!(148.413159, 5.0f64.exp()); |
| |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| let nan: f64 = NAN; |
| assert_eq!(inf, inf.exp()); |
| assert_eq!(0.0, neg_inf.exp()); |
| assert!(nan.exp().is_nan()); |
| } |
| |
| #[test] |
| fn test_exp2() { |
| assert_eq!(32.0, 5.0f64.exp2()); |
| assert_eq!(1.0, 0.0f64.exp2()); |
| |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| let nan: f64 = NAN; |
| assert_eq!(inf, inf.exp2()); |
| assert_eq!(0.0, neg_inf.exp2()); |
| assert!(nan.exp2().is_nan()); |
| } |
| |
| #[test] |
| fn test_ln() { |
| let nan: f64 = NAN; |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| assert_approx_eq!(1.0f64.exp().ln(), 1.0); |
| assert!(nan.ln().is_nan()); |
| assert_eq!(inf.ln(), inf); |
| assert!(neg_inf.ln().is_nan()); |
| assert!((-2.3f64).ln().is_nan()); |
| assert_eq!((-0.0f64).ln(), neg_inf); |
| assert_eq!(0.0f64.ln(), neg_inf); |
| assert_approx_eq!(4.0f64.ln(), 1.386294); |
| } |
| |
| #[test] |
| fn test_log() { |
| let nan: f64 = NAN; |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| assert_eq!(10.0f64.log(10.0), 1.0); |
| assert_approx_eq!(2.3f64.log(3.5), 0.664858); |
| assert_eq!(1.0f64.exp().log(1.0f64.exp()), 1.0); |
| assert!(1.0f64.log(1.0).is_nan()); |
| assert!(1.0f64.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!((-2.3f64).log(0.1).is_nan()); |
| assert_eq!((-0.0f64).log(2.0), neg_inf); |
| assert_eq!(0.0f64.log(7.0), neg_inf); |
| } |
| |
| #[test] |
| fn test_log2() { |
| let nan: f64 = NAN; |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| assert_approx_eq!(10.0f64.log2(), 3.321928); |
| assert_approx_eq!(2.3f64.log2(), 1.201634); |
| assert_approx_eq!(1.0f64.exp().log2(), 1.442695); |
| assert!(nan.log2().is_nan()); |
| assert_eq!(inf.log2(), inf); |
| assert!(neg_inf.log2().is_nan()); |
| assert!((-2.3f64).log2().is_nan()); |
| assert_eq!((-0.0f64).log2(), neg_inf); |
| assert_eq!(0.0f64.log2(), neg_inf); |
| } |
| |
| #[test] |
| fn test_log10() { |
| let nan: f64 = NAN; |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| assert_eq!(10.0f64.log10(), 1.0); |
| assert_approx_eq!(2.3f64.log10(), 0.361728); |
| assert_approx_eq!(1.0f64.exp().log10(), 0.434294); |
| assert_eq!(1.0f64.log10(), 0.0); |
| assert!(nan.log10().is_nan()); |
| assert_eq!(inf.log10(), inf); |
| assert!(neg_inf.log10().is_nan()); |
| assert!((-2.3f64).log10().is_nan()); |
| assert_eq!((-0.0f64).log10(), neg_inf); |
| assert_eq!(0.0f64.log10(), neg_inf); |
| } |
| |
| #[test] |
| fn test_to_degrees() { |
| let pi: f64 = consts::PI; |
| let nan: f64 = NAN; |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| assert_eq!(0.0f64.to_degrees(), 0.0); |
| assert_approx_eq!((-5.8f64).to_degrees(), -332.315521); |
| assert_eq!(pi.to_degrees(), 180.0); |
| assert!(nan.to_degrees().is_nan()); |
| assert_eq!(inf.to_degrees(), inf); |
| assert_eq!(neg_inf.to_degrees(), neg_inf); |
| } |
| |
| #[test] |
| fn test_to_radians() { |
| let pi: f64 = consts::PI; |
| let nan: f64 = NAN; |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| assert_eq!(0.0f64.to_radians(), 0.0); |
| assert_approx_eq!(154.6f64.to_radians(), 2.698279); |
| assert_approx_eq!((-332.31f64).to_radians(), -5.799903); |
| assert_eq!(180.0f64.to_radians(), pi); |
| assert!(nan.to_radians().is_nan()); |
| assert_eq!(inf.to_radians(), inf); |
| assert_eq!(neg_inf.to_radians(), neg_inf); |
| } |
| |
| #[test] |
| fn test_asinh() { |
| assert_eq!(0.0f64.asinh(), 0.0f64); |
| assert_eq!((-0.0f64).asinh(), -0.0f64); |
| |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| let nan: f64 = NAN; |
| assert_eq!(inf.asinh(), inf); |
| assert_eq!(neg_inf.asinh(), neg_inf); |
| assert!(nan.asinh().is_nan()); |
| assert!((-0.0f64).asinh().is_sign_negative()); |
| // issue 63271 |
| assert_approx_eq!(2.0f64.asinh(), 1.443635475178810342493276740273105f64); |
| assert_approx_eq!((-2.0f64).asinh(), -1.443635475178810342493276740273105f64); |
| } |
| |
| #[test] |
| fn test_acosh() { |
| assert_eq!(1.0f64.acosh(), 0.0f64); |
| assert!(0.999f64.acosh().is_nan()); |
| |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| let nan: f64 = NAN; |
| assert_eq!(inf.acosh(), inf); |
| assert!(neg_inf.acosh().is_nan()); |
| assert!(nan.acosh().is_nan()); |
| assert_approx_eq!(2.0f64.acosh(), 1.31695789692481670862504634730796844f64); |
| assert_approx_eq!(3.0f64.acosh(), 1.76274717403908605046521864995958461f64); |
| } |
| |
| #[test] |
| fn test_atanh() { |
| assert_eq!(0.0f64.atanh(), 0.0f64); |
| assert_eq!((-0.0f64).atanh(), -0.0f64); |
| |
| let inf: f64 = INFINITY; |
| let neg_inf: f64 = NEG_INFINITY; |
| let nan: f64 = NAN; |
| assert_eq!(1.0f64.atanh(), inf); |
| assert_eq!((-1.0f64).atanh(), neg_inf); |
| assert!(2f64.atanh().atanh().is_nan()); |
| assert!((-2f64).atanh().atanh().is_nan()); |
| assert!(inf.atanh().is_nan()); |
| assert!(neg_inf.atanh().is_nan()); |
| assert!(nan.atanh().is_nan()); |
| assert_approx_eq!(0.5f64.atanh(), 0.54930614433405484569762261846126285f64); |
| assert_approx_eq!((-0.5f64).atanh(), -0.54930614433405484569762261846126285f64); |
| } |
| |
| #[test] |
| fn test_real_consts() { |
| use super::consts; |
| let pi: f64 = consts::PI; |
| let frac_pi_2: f64 = consts::FRAC_PI_2; |
| let frac_pi_3: f64 = consts::FRAC_PI_3; |
| let frac_pi_4: f64 = consts::FRAC_PI_4; |
| let frac_pi_6: f64 = consts::FRAC_PI_6; |
| let frac_pi_8: f64 = consts::FRAC_PI_8; |
| let frac_1_pi: f64 = consts::FRAC_1_PI; |
| let frac_2_pi: f64 = consts::FRAC_2_PI; |
| let frac_2_sqrtpi: f64 = consts::FRAC_2_SQRT_PI; |
| let sqrt2: f64 = consts::SQRT_2; |
| let frac_1_sqrt2: f64 = consts::FRAC_1_SQRT_2; |
| let e: f64 = consts::E; |
| let log2_e: f64 = consts::LOG2_E; |
| let log10_e: f64 = consts::LOG10_E; |
| let ln_2: f64 = consts::LN_2; |
| let ln_10: f64 = consts::LN_10; |
| |
| assert_approx_eq!(frac_pi_2, pi / 2f64); |
| assert_approx_eq!(frac_pi_3, pi / 3f64); |
| assert_approx_eq!(frac_pi_4, pi / 4f64); |
| assert_approx_eq!(frac_pi_6, pi / 6f64); |
| assert_approx_eq!(frac_pi_8, pi / 8f64); |
| assert_approx_eq!(frac_1_pi, 1f64 / pi); |
| assert_approx_eq!(frac_2_pi, 2f64 / pi); |
| assert_approx_eq!(frac_2_sqrtpi, 2f64 / pi.sqrt()); |
| assert_approx_eq!(sqrt2, 2f64.sqrt()); |
| assert_approx_eq!(frac_1_sqrt2, 1f64 / 2f64.sqrt()); |
| assert_approx_eq!(log2_e, e.log2()); |
| assert_approx_eq!(log10_e, e.log10()); |
| assert_approx_eq!(ln_2, 2f64.ln()); |
| assert_approx_eq!(ln_10, 10f64.ln()); |
| } |
| |
| #[test] |
| fn test_float_bits_conv() { |
| assert_eq!((1f64).to_bits(), 0x3ff0000000000000); |
| assert_eq!((12.5f64).to_bits(), 0x4029000000000000); |
| assert_eq!((1337f64).to_bits(), 0x4094e40000000000); |
| assert_eq!((-14.25f64).to_bits(), 0xc02c800000000000); |
| assert_approx_eq!(f64::from_bits(0x3ff0000000000000), 1.0); |
| assert_approx_eq!(f64::from_bits(0x4029000000000000), 12.5); |
| assert_approx_eq!(f64::from_bits(0x4094e40000000000), 1337.0); |
| assert_approx_eq!(f64::from_bits(0xc02c800000000000), -14.25); |
| |
| // Check that NaNs roundtrip their bits regardless of signalingness |
| // 0xA is 0b1010; 0x5 is 0b0101 -- so these two together clobbers all the mantissa bits |
| let masked_nan1 = f64::NAN.to_bits() ^ 0x000A_AAAA_AAAA_AAAA; |
| let masked_nan2 = f64::NAN.to_bits() ^ 0x0005_5555_5555_5555; |
| assert!(f64::from_bits(masked_nan1).is_nan()); |
| assert!(f64::from_bits(masked_nan2).is_nan()); |
| |
| assert_eq!(f64::from_bits(masked_nan1).to_bits(), masked_nan1); |
| assert_eq!(f64::from_bits(masked_nan2).to_bits(), masked_nan2); |
| } |
| |
| #[test] |
| #[should_panic] |
| fn test_clamp_min_greater_than_max() { |
| let _ = 1.0f64.clamp(3.0, 1.0); |
| } |
| |
| #[test] |
| #[should_panic] |
| fn test_clamp_min_is_nan() { |
| let _ = 1.0f64.clamp(NAN, 1.0); |
| } |
| |
| #[test] |
| #[should_panic] |
| fn test_clamp_max_is_nan() { |
| let _ = 1.0f64.clamp(3.0, NAN); |
| } |
| } |
