| //! Constants specific to the `f64` double-precision floating point type. |
| //! |
| //! *[See also the `f64` primitive type](primitive@f64).* |
| //! |
| //! Mathematically significant numbers are provided in the `consts` sub-module. |
| //! |
| //! For the constants defined directly in this module |
| //! (as distinct from those defined in the `consts` sub-module), |
| //! new code should instead use the associated constants |
| //! defined directly on the `f64` type. |
| |
| #![stable(feature = "rust1", since = "1.0.0")] |
| #![allow(missing_docs)] |
| |
| #[cfg(test)] |
| mod tests; |
| |
| #[cfg(not(test))] |
| use crate::intrinsics; |
| #[cfg(not(test))] |
| use crate::sys::cmath; |
| |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[allow(deprecated, deprecated_in_future)] |
| pub use core::f64::{ |
| consts, DIGITS, EPSILON, INFINITY, MANTISSA_DIGITS, MAX, MAX_10_EXP, MAX_EXP, MIN, MIN_10_EXP, |
| MIN_EXP, MIN_POSITIVE, NAN, NEG_INFINITY, RADIX, |
| }; |
| |
| #[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 |
| /// |
| /// ``` |
| /// 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 |
| /// |
| /// ``` |
| /// 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() { Self::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 |
| /// |
| /// ``` |
| /// 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` *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. |
| /// |
| /// # 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!((-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 other than `-0.0`. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let positive = 4.0_f64; |
| /// let negative = -4.0_f64; |
| /// let negative_zero = -0.0_f64; |
| /// |
| /// let abs_difference = (positive.sqrt() - 2.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// assert!(negative.sqrt().is_nan()); |
| /// assert!(negative_zero.sqrt() == negative_zero); |
| /// ``` |
| #[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 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. |
| /// |
| /// # 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 cube 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 |
| /// |
| /// ``` |
| /// let x = std::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 |
| /// |
| /// ``` |
| /// let x = 2.0 * std::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 |
| /// |
| /// ``` |
| /// let x = std::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 |
| /// |
| /// ``` |
| /// let f = std::f64::consts::FRAC_PI_2; |
| /// |
| /// // asin(sin(pi/2)) |
| /// let abs_difference = (f.sin().asin() - std::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 |
| /// |
| /// ``` |
| /// let f = std::f64::consts::FRAC_PI_4; |
| /// |
| /// // acos(cos(pi/4)) |
| /// let abs_difference = (f.cos().acos() - std::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 |
| /// |
| /// ``` |
| /// // 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) - (-std::f64::consts::FRAC_PI_4)).abs(); |
| /// let abs_difference_2 = (y2.atan2(x2) - (3.0 * std::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 |
| /// |
| /// ``` |
| /// let x = std::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 = 1e-16_f64; |
| /// |
| /// // 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-20); |
| /// ``` |
| #[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 |
| /// |
| /// ``` |
| /// let x = 1e-16_f64; |
| /// |
| /// // 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-20); |
| /// ``` |
| #[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 |
| /// |
| /// ``` |
| /// let e = std::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 |
| /// |
| /// ``` |
| /// let e = std::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 |
| /// |
| /// ``` |
| /// let e = std::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 { |
| (self.abs() + ((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 { Self::NAN } else { (self + ((self * self) - 1.0).sqrt()).ln() } |
| } |
| |
| /// Inverse hyperbolic tangent function. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// let e = std::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() |
| } |
| |
| /// Linear interpolation between `start` and `end`. |
| /// |
| /// This enables linear interpolation between `start` and `end`, where start is represented by |
| /// `self == 0.0` and `end` is represented by `self == 1.0`. This is the basis of all |
| /// "transition", "easing", or "step" functions; if you change `self` from 0.0 to 1.0 |
| /// at a given rate, the result will change from `start` to `end` at a similar rate. |
| /// |
| /// Values below 0.0 or above 1.0 are allowed, allowing you to extrapolate values outside the |
| /// range from `start` to `end`. This also is useful for transition functions which might |
| /// move slightly past the end or start for a desired effect. Mathematically, the values |
| /// returned are equivalent to `start + self * (end - start)`, although we make a few specific |
| /// guarantees that are useful specifically to linear interpolation. |
| /// |
| /// These guarantees are: |
| /// |
| /// * If `start` and `end` are [finite], the value at 0.0 is always `start` and the |
| /// value at 1.0 is always `end`. (exactness) |
| /// * If `start` and `end` are [finite], the values will always move in the direction from |
| /// `start` to `end` (monotonicity) |
| /// * If `self` is [finite] and `start == end`, the value at any point will always be |
| /// `start == end`. (consistency) |
| /// |
| /// [finite]: #method.is_finite |
| #[must_use = "method returns a new number and does not mutate the original value"] |
| #[unstable(feature = "float_interpolation", issue = "86269")] |
| pub fn lerp(self, start: f64, end: f64) -> f64 { |
| // consistent |
| if start == end { |
| start |
| |
| // exact/monotonic |
| } else { |
| self.mul_add(end, (-self).mul_add(start, start)) |
| } |
| } |
| |
| // 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!(any(target_os = "solaris", target_os = "illumos")) { |
| log_fn(self) |
| } else if self.is_finite() { |
| if self > 0.0 { |
| log_fn(self) |
| } else if self == 0.0 { |
| Self::NEG_INFINITY // log(0) = -Inf |
| } else { |
| Self::NAN // log(-n) = NaN |
| } |
| } else if self.is_nan() { |
| self // log(NaN) = NaN |
| } else if self > 0.0 { |
| self // log(Inf) = Inf |
| } else { |
| Self::NAN // log(-Inf) = NaN |
| } |
| } |
| } |
