| // Copyright 2012-2015 The Rust Project Developers. See the COPYRIGHT |
| // file at the top-level directory of this distribution and at |
| // http://rust-lang.org/COPYRIGHT. |
| // |
| // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or |
| // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license |
| // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your |
| // option. This file may not be copied, modified, or distributed |
| // except according to those terms. |
| |
| //! This module provides constants which are specific to the implementation |
| //! of the `f64` floating point data type. |
| //! |
| //! Mathematically significant numbers are provided in the `consts` sub-module. |
| //! |
| //! *[See also the `f64` primitive type](../../std/primitive.f64.html).* |
| |
| #![stable(feature = "rust1", since = "1.0.0")] |
| #![allow(missing_docs)] |
| |
| #[cfg(not(test))] |
| use core::num; |
| #[cfg(not(test))] |
| use intrinsics; |
| #[cfg(not(test))] |
| use num::FpCategory; |
| #[cfg(not(test))] |
| use sys::cmath; |
| |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub use core::f64::{RADIX, MANTISSA_DIGITS, DIGITS, EPSILON}; |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub use core::f64::{MIN_EXP, MAX_EXP, MIN_10_EXP}; |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub use core::f64::{MAX_10_EXP, NAN, INFINITY, NEG_INFINITY}; |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub use core::f64::{MIN, MIN_POSITIVE, MAX}; |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub use core::f64::consts; |
| |
| #[cfg(not(test))] |
| #[lang = "f64"] |
| impl f64 { |
| /// Returns `true` if this value is `NaN` and false otherwise. |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let nan = f64::NAN; |
| /// let f = 7.0_f64; |
| /// |
| /// assert!(nan.is_nan()); |
| /// assert!(!f.is_nan()); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn is_nan(self) -> bool { num::Float::is_nan(self) } |
| |
| /// Returns `true` if this value is positive infinity or negative infinity and |
| /// false otherwise. |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let f = 7.0f64; |
| /// let inf = f64::INFINITY; |
| /// let neg_inf = f64::NEG_INFINITY; |
| /// let nan = f64::NAN; |
| /// |
| /// assert!(!f.is_infinite()); |
| /// assert!(!nan.is_infinite()); |
| /// |
| /// assert!(inf.is_infinite()); |
| /// assert!(neg_inf.is_infinite()); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn is_infinite(self) -> bool { num::Float::is_infinite(self) } |
| |
| /// Returns `true` if this number is neither infinite nor `NaN`. |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let f = 7.0f64; |
| /// let inf: f64 = f64::INFINITY; |
| /// let neg_inf: f64 = f64::NEG_INFINITY; |
| /// let nan: f64 = f64::NAN; |
| /// |
| /// assert!(f.is_finite()); |
| /// |
| /// assert!(!nan.is_finite()); |
| /// assert!(!inf.is_finite()); |
| /// assert!(!neg_inf.is_finite()); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn is_finite(self) -> bool { num::Float::is_finite(self) } |
| |
| /// Returns `true` if the number is neither zero, infinite, |
| /// [subnormal][subnormal], or `NaN`. |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308f64 |
| /// let max = f64::MAX; |
| /// let lower_than_min = 1.0e-308_f64; |
| /// let zero = 0.0f64; |
| /// |
| /// assert!(min.is_normal()); |
| /// assert!(max.is_normal()); |
| /// |
| /// assert!(!zero.is_normal()); |
| /// assert!(!f64::NAN.is_normal()); |
| /// assert!(!f64::INFINITY.is_normal()); |
| /// // Values between `0` and `min` are Subnormal. |
| /// assert!(!lower_than_min.is_normal()); |
| /// ``` |
| /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn is_normal(self) -> bool { num::Float::is_normal(self) } |
| |
| /// Returns the floating point category of the number. If only one property |
| /// is going to be tested, it is generally faster to use the specific |
| /// predicate instead. |
| /// |
| /// ``` |
| /// use std::num::FpCategory; |
| /// use std::f64; |
| /// |
| /// let num = 12.4_f64; |
| /// let inf = f64::INFINITY; |
| /// |
| /// assert_eq!(num.classify(), FpCategory::Normal); |
| /// assert_eq!(inf.classify(), FpCategory::Infinite); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn classify(self) -> FpCategory { num::Float::classify(self) } |
| |
| /// Returns the largest integer less than or equal to a number. |
| /// |
| /// ``` |
| /// let f = 3.99_f64; |
| /// let g = 3.0_f64; |
| /// |
| /// assert_eq!(f.floor(), 3.0); |
| /// assert_eq!(g.floor(), 3.0); |
| /// ``` |
| #[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. |
| /// |
| /// ``` |
| /// let f = 3.01_f64; |
| /// let g = 4.0_f64; |
| /// |
| /// assert_eq!(f.ceil(), 4.0); |
| /// assert_eq!(g.ceil(), 4.0); |
| /// ``` |
| #[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`. |
| /// |
| /// ``` |
| /// let f = 3.3_f64; |
| /// let g = -3.3_f64; |
| /// |
| /// assert_eq!(f.round(), 3.0); |
| /// assert_eq!(g.round(), -3.0); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn round(self) -> f64 { |
| unsafe { intrinsics::roundf64(self) } |
| } |
| |
| /// Returns the integer part of a number. |
| /// |
| /// ``` |
| /// let f = 3.3_f64; |
| /// let g = -3.7_f64; |
| /// |
| /// assert_eq!(f.trunc(), 3.0); |
| /// assert_eq!(g.trunc(), -3.0); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn trunc(self) -> f64 { |
| unsafe { intrinsics::truncf64(self) } |
| } |
| |
| /// Returns the fractional part of a number. |
| /// |
| /// ``` |
| /// let x = 3.5_f64; |
| /// let y = -3.5_f64; |
| /// let abs_difference_x = (x.fract() - 0.5).abs(); |
| /// let abs_difference_y = (y.fract() - (-0.5)).abs(); |
| /// |
| /// assert!(abs_difference_x < 1e-10); |
| /// assert!(abs_difference_y < 1e-10); |
| /// ``` |
| #[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`. |
| /// |
| /// ``` |
| /// 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()); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn abs(self) -> f64 { num::Float::abs(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` |
| /// |
| /// ``` |
| /// 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()); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn signum(self) -> f64 { num::Float::signum(self) } |
| |
| /// Returns `true` if and only if `self` has a positive sign, including `+0.0`, `NaN`s with |
| /// positive sign bit and positive infinity. |
| /// |
| /// ``` |
| /// let f = 7.0_f64; |
| /// let g = -7.0_f64; |
| /// |
| /// assert!(f.is_sign_positive()); |
| /// assert!(!g.is_sign_positive()); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn is_sign_positive(self) -> bool { num::Float::is_sign_positive(self) } |
| |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[rustc_deprecated(since = "1.0.0", reason = "renamed to is_sign_positive")] |
| #[inline] |
| pub fn is_positive(self) -> bool { num::Float::is_sign_positive(self) } |
| |
| /// Returns `true` if and only if `self` has a negative sign, including `-0.0`, `NaN`s with |
| /// negative sign bit and negative infinity. |
| /// |
| /// ``` |
| /// let f = 7.0_f64; |
| /// let g = -7.0_f64; |
| /// |
| /// assert!(!f.is_sign_negative()); |
| /// assert!(g.is_sign_negative()); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn is_sign_negative(self) -> bool { num::Float::is_sign_negative(self) } |
| |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[rustc_deprecated(since = "1.0.0", reason = "renamed to is_sign_negative")] |
| #[inline] |
| pub fn is_negative(self) -> bool { num::Float::is_sign_negative(self) } |
| |
| /// Fused multiply-add. Computes `(self * a) + b` with only one rounding |
| /// error. This produces a more accurate result with better performance than |
| /// a separate multiplication operation followed by an add. |
| /// |
| /// ``` |
| /// 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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn mul_add(self, a: f64, b: f64) -> f64 { |
| unsafe { intrinsics::fmaf64(self, a, b) } |
| } |
| |
| /// Takes the reciprocal (inverse) of a number, `1/x`. |
| /// |
| /// ``` |
| /// let x = 2.0_f64; |
| /// let abs_difference = (x.recip() - (1.0/x)).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn recip(self) -> f64 { num::Float::recip(self) } |
| |
| /// Raises a number to an integer power. |
| /// |
| /// Using this function is generally faster than using `powf` |
| /// |
| /// ``` |
| /// let x = 2.0_f64; |
| /// let abs_difference = (x.powi(2) - x*x).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn powi(self, n: i32) -> f64 { num::Float::powi(self, n) } |
| |
| /// Raises a number to a floating point power. |
| /// |
| /// ``` |
| /// let x = 2.0_f64; |
| /// let abs_difference = (x.powf(2.0) - x*x).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn powf(self, n: f64) -> f64 { |
| unsafe { intrinsics::powf64(self, n) } |
| } |
| |
| /// Takes the square root of a number. |
| /// |
| /// Returns NaN if `self` is a negative number. |
| /// |
| /// ``` |
| /// 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()); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn sqrt(self) -> f64 { |
| if self < 0.0 { |
| NAN |
| } else { |
| unsafe { intrinsics::sqrtf64(self) } |
| } |
| } |
| |
| /// Returns `e^(self)`, (the exponential function). |
| /// |
| /// ``` |
| /// 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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn exp(self) -> f64 { |
| unsafe { intrinsics::expf64(self) } |
| } |
| |
| /// Returns `2^(self)`. |
| /// |
| /// ``` |
| /// let f = 2.0_f64; |
| /// |
| /// // 2^2 - 4 == 0 |
| /// let abs_difference = (f.exp2() - 4.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn exp2(self) -> f64 { |
| unsafe { intrinsics::exp2f64(self) } |
| } |
| |
| /// Returns the natural logarithm of the number. |
| /// |
| /// ``` |
| /// 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); |
| /// ``` |
| #[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. |
| /// |
| /// ``` |
| /// let ten = 10.0_f64; |
| /// let two = 2.0_f64; |
| /// |
| /// // log10(10) - 1 == 0 |
| /// let abs_difference_10 = (ten.log(10.0) - 1.0).abs(); |
| /// |
| /// // log2(2) - 1 == 0 |
| /// let abs_difference_2 = (two.log(2.0) - 1.0).abs(); |
| /// |
| /// assert!(abs_difference_10 < 1e-10); |
| /// assert!(abs_difference_2 < 1e-10); |
| /// ``` |
| #[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. |
| /// |
| /// ``` |
| /// let two = 2.0_f64; |
| /// |
| /// // log2(2) - 1 == 0 |
| /// let abs_difference = (two.log2() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn log2(self) -> f64 { |
| self.log_wrapper(|n| { |
| #[cfg(target_os = "android")] |
| return ::sys::android::log2f64(n); |
| #[cfg(not(target_os = "android"))] |
| return unsafe { intrinsics::log2f64(n) }; |
| }) |
| } |
| |
| /// Returns the base 10 logarithm of the number. |
| /// |
| /// ``` |
| /// let ten = 10.0_f64; |
| /// |
| /// // log10(10) - 1 == 0 |
| /// let abs_difference = (ten.log10() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn log10(self) -> f64 { |
| self.log_wrapper(|n| { unsafe { intrinsics::log10f64(n) } }) |
| } |
| |
| /// Converts radians to degrees. |
| /// |
| /// ``` |
| /// use std::f64::consts; |
| /// |
| /// let angle = consts::PI; |
| /// |
| /// let abs_difference = (angle.to_degrees() - 180.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn to_degrees(self) -> f64 { num::Float::to_degrees(self) } |
| |
| /// Converts degrees to radians. |
| /// |
| /// ``` |
| /// use std::f64::consts; |
| /// |
| /// let angle = 180.0_f64; |
| /// |
| /// let abs_difference = (angle.to_radians() - consts::PI).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn to_radians(self) -> f64 { num::Float::to_radians(self) } |
| |
| /// Returns the maximum of the two numbers. |
| /// |
| /// ``` |
| /// let x = 1.0_f64; |
| /// let y = 2.0_f64; |
| /// |
| /// assert_eq!(x.max(y), y); |
| /// ``` |
| /// |
| /// If one of the arguments is NaN, then the other argument is returned. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn max(self, other: f64) -> f64 { |
| num::Float::max(self, other) |
| } |
| |
| /// Returns the minimum of the two numbers. |
| /// |
| /// ``` |
| /// let x = 1.0_f64; |
| /// let y = 2.0_f64; |
| /// |
| /// assert_eq!(x.min(y), x); |
| /// ``` |
| /// |
| /// If one of the arguments is NaN, then the other argument is returned. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn min(self, other: f64) -> f64 { |
| num::Float::min(self, other) |
| } |
| |
| /// The positive difference of two numbers. |
| /// |
| /// * If `self <= other`: `0:0` |
| /// * Else: `self - other` |
| /// |
| /// ``` |
| /// 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); |
| /// ``` |
| #[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)` (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) } |
| } |
| |
| /// Takes the cubic root of a number. |
| /// |
| /// ``` |
| /// let x = 8.0_f64; |
| /// |
| /// // x^(1/3) - 2 == 0 |
| /// let abs_difference = (x.cbrt() - 2.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[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`. |
| /// |
| /// ``` |
| /// 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); |
| /// ``` |
| #[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). |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let x = f64::consts::PI/2.0; |
| /// |
| /// let abs_difference = (x.sin() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[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). |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let x = 2.0*f64::consts::PI; |
| /// |
| /// let abs_difference = (x.cos() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[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). |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let x = f64::consts::PI/4.0; |
| /// let abs_difference = (x.tan() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-14); |
| /// ``` |
| #[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]. |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let f = f64::consts::PI / 2.0; |
| /// |
| /// // asin(sin(pi/2)) |
| /// let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[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]. |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let f = f64::consts::PI / 4.0; |
| /// |
| /// // acos(cos(pi/4)) |
| /// let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[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]; |
| /// |
| /// ``` |
| /// let f = 1.0_f64; |
| /// |
| /// // atan(tan(1)) |
| /// let abs_difference = (f.tan().atan() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[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`). |
| /// |
| /// * `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)` |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let pi = f64::consts::PI; |
| /// // All angles from horizontal right (+x) |
| /// // 45 deg counter-clockwise |
| /// let x1 = 3.0_f64; |
| /// let y1 = -3.0_f64; |
| /// |
| /// // 135 deg clockwise |
| /// let x2 = -3.0_f64; |
| /// let y2 = 3.0_f64; |
| /// |
| /// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs(); |
| /// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs(); |
| /// |
| /// assert!(abs_difference_1 < 1e-10); |
| /// assert!(abs_difference_2 < 1e-10); |
| /// ``` |
| #[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))`. |
| /// |
| /// ``` |
| /// use std::f64; |
| /// |
| /// let x = f64::consts::PI/4.0; |
| /// 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. |
| /// |
| /// ``` |
| /// let x = 7.0_f64; |
| /// |
| /// // e^(ln(7)) - 1 |
| /// let abs_difference = (x.ln().exp_m1() - 6.0).abs(); |
| /// |
| /// assert!(abs_difference < 1e-10); |
| /// ``` |
| #[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. |
| /// |
| /// ``` |
| /// 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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn ln_1p(self) -> f64 { |
| unsafe { cmath::log1p(self) } |
| } |
| |
| /// Hyperbolic sine function. |
| /// |
| /// ``` |
| /// 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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn sinh(self) -> f64 { |
| unsafe { cmath::sinh(self) } |
| } |
| |
| /// Hyperbolic cosine function. |
| /// |
| /// ``` |
| /// 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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn cosh(self) -> f64 { |
| unsafe { cmath::cosh(self) } |
| } |
| |
| /// Hyperbolic tangent function. |
| /// |
| /// ``` |
| /// 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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn tanh(self) -> f64 { |
| unsafe { cmath::tanh(self) } |
| } |
| |
| /// Inverse hyperbolic sine function. |
| /// |
| /// ``` |
| /// let x = 1.0_f64; |
| /// let f = x.sinh().asinh(); |
| /// |
| /// let abs_difference = (f - x).abs(); |
| /// |
| /// assert!(abs_difference < 1.0e-10); |
| /// ``` |
| #[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() |
| } |
| } |
| |
| /// Inverse hyperbolic cosine function. |
| /// |
| /// ``` |
| /// let x = 1.0_f64; |
| /// let f = x.cosh().acosh(); |
| /// |
| /// let abs_difference = (f - x).abs(); |
| /// |
| /// assert!(abs_difference < 1.0e-10); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn acosh(self) -> f64 { |
| match self { |
| x if x < 1.0 => NAN, |
| x => (x + ((x * x) - 1.0).sqrt()).ln(), |
| } |
| } |
| |
| /// Inverse hyperbolic tangent function. |
| /// |
| /// ``` |
| /// 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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn atanh(self) -> f64 { |
| 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p() |
| } |
| |
| // 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 |
| } |
| } |
| } |
| |
| /// Raw transmutation to `u64`. |
| /// |
| /// This is currently identical to `transmute::<f64, u64>(self)` on all platforms. |
| /// |
| /// See `from_bits` for some discussion of the portability of this operation |
| /// (there are almost no issues). |
| /// |
| /// Note that this function is distinct from `as` casting, which attempts to |
| /// preserve the *numeric* value, and not the bitwise value. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// assert!((1f64).to_bits() != 1f64 as u64); // to_bits() is not casting! |
| /// assert_eq!((12.5f64).to_bits(), 0x4029000000000000); |
| /// |
| /// ``` |
| #[stable(feature = "float_bits_conv", since = "1.20.0")] |
| #[inline] |
| pub fn to_bits(self) -> u64 { |
| unsafe { ::mem::transmute(self) } |
| } |
| |
| /// Raw transmutation from `u64`. |
| /// |
| /// This is currently identical to `transmute::<u64, f64>(v)` on all platforms. |
| /// It turns out this is incredibly portable, for two reasons: |
| /// |
| /// * Floats and Ints have the same endianess on all supported platforms. |
| /// * IEEE-754 very precisely specifies the bit layout of floats. |
| /// |
| /// However there is one caveat: prior to the 2008 version of IEEE-754, how |
| /// to interpret the NaN signaling bit wasn't actually specified. Most platforms |
| /// (notably x86 and ARM) picked the interpretation that was ultimately |
| /// standardized in 2008, but some didn't (notably MIPS). As a result, all |
| /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa. |
| /// |
| /// Rather than trying to preserve signaling-ness cross-platform, this |
| /// implementation favours preserving the exact bits. This means that |
| /// any payloads encoded in NaNs will be preserved even if the result of |
| /// this method is sent over the network from an x86 machine to a MIPS one. |
| /// |
| /// If the results of this method are only manipulated by the same |
| /// architecture that produced them, then there is no portability concern. |
| /// |
| /// If the input isn't NaN, then there is no portability concern. |
| /// |
| /// If you don't care about signalingness (very likely), then there is no |
| /// portability concern. |
| /// |
| /// Note that this function is distinct from `as` casting, which attempts to |
| /// preserve the *numeric* value, and not the bitwise value. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use std::f64; |
| /// let v = f64::from_bits(0x4029000000000000); |
| /// let difference = (v - 12.5).abs(); |
| /// assert!(difference <= 1e-5); |
| /// ``` |
| #[stable(feature = "float_bits_conv", since = "1.20.0")] |
| #[inline] |
| pub fn from_bits(v: u64) -> Self { |
| // It turns out the safety issues with sNaN were overblown! Hooray! |
| unsafe { ::mem::transmute(v) } |
| } |
| } |
| |
| #[cfg(test)] |
| mod tests { |
| use f64; |
| use f64::*; |
| use num::*; |
| use num::FpCategory as Fp; |
| |
| #[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_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); |
| } |
| } |