| // Copyright (C) 2017-2018 Baidu, Inc. All Rights Reserved. |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions |
| // are met: |
| // |
| // * Redistributions of source code must retain the above copyright |
| // notice, this list of conditions and the following disclaimer. |
| // * Redistributions in binary form must reproduce the above copyright |
| // notice, this list of conditions and the following disclaimer in |
| // the documentation and/or other materials provided with the |
| // distribution. |
| // * Neither the name of Baidu, Inc., nor the names of its |
| // contributors may be used to endorse or promote products derived |
| // from this software without specific prior written permission. |
| // |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
| // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
| // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
| // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT |
| // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT |
| // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
| // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
| // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
| // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| |
| //! This module provides constants which are specific to the implementation |
| //! of the `f32` floating point data type. |
| //! |
| //! Mathematically significant numbers are provided in the `consts` sub-module. |
| //! |
| |
| #![allow(missing_docs)] |
| |
| use core::num; |
| use core::intrinsics; |
| use core::num::FpCategory; |
| use sys::cmath; |
| |
| pub use core::f32::{RADIX, MANTISSA_DIGITS, DIGITS, EPSILON}; |
| pub use core::f32::{MIN_EXP, MAX_EXP, MIN_10_EXP}; |
| pub use core::f32::{MAX_10_EXP, NAN, INFINITY, NEG_INFINITY}; |
| pub use core::f32::{MIN, MIN_POSITIVE, MAX}; |
| pub use core::f32::consts; |
| |
| #[lang = "f32"] |
| impl f32 { |
| /// Returns `true` if this value is `NaN` and false otherwise. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let nan = f32::NAN; |
| /// let f = 7.0_f32; |
| /// |
| /// assert!(nan.is_nan()); |
| /// assert!(!f.is_nan()); |
| /// ``` |
| #[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::f32; |
| /// |
| /// let f = 7.0f32; |
| /// let inf = f32::INFINITY; |
| /// let neg_inf = f32::NEG_INFINITY; |
| /// let nan = f32::NAN; |
| /// |
| /// assert!(!f.is_infinite()); |
| /// assert!(!nan.is_infinite()); |
| /// |
| /// assert!(inf.is_infinite()); |
| /// assert!(neg_inf.is_infinite()); |
| /// ``` |
| #[inline] |
| pub fn is_infinite(self) -> bool { num::Float::is_infinite(self) } |
| |
| /// Returns `true` if this number is neither infinite nor `NaN`. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let f = 7.0f32; |
| /// let inf = f32::INFINITY; |
| /// let neg_inf = f32::NEG_INFINITY; |
| /// let nan = f32::NAN; |
| /// |
| /// assert!(f.is_finite()); |
| /// |
| /// assert!(!nan.is_finite()); |
| /// assert!(!inf.is_finite()); |
| /// assert!(!neg_inf.is_finite()); |
| /// ``` |
| #[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::f32; |
| /// |
| /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32 |
| /// let max = f32::MAX; |
| /// let lower_than_min = 1.0e-40_f32; |
| /// let zero = 0.0_f32; |
| /// |
| /// assert!(min.is_normal()); |
| /// assert!(max.is_normal()); |
| /// |
| /// assert!(!zero.is_normal()); |
| /// assert!(!f32::NAN.is_normal()); |
| /// assert!(!f32::INFINITY.is_normal()); |
| /// // Values between `0` and `min` are Subnormal. |
| /// assert!(!lower_than_min.is_normal()); |
| /// ``` |
| /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number |
| #[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::f32; |
| /// |
| /// let num = 12.4_f32; |
| /// let inf = f32::INFINITY; |
| /// |
| /// assert_eq!(num.classify(), FpCategory::Normal); |
| /// assert_eq!(inf.classify(), FpCategory::Infinite); |
| /// ``` |
| #[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_f32; |
| /// let g = 3.0_f32; |
| /// |
| /// assert_eq!(f.floor(), 3.0); |
| /// assert_eq!(g.floor(), 3.0); |
| /// ``` |
| #[inline] |
| pub fn floor(self) -> f32 { |
| // On MSVC LLVM will lower many math intrinsics to a call to the |
| // corresponding function. On MSVC, however, many of these functions |
| // aren't actually available as symbols to call, but rather they are all |
| // `static inline` functions in header files. This means that from a C |
| // perspective it's "compatible", but not so much from an ABI |
| // perspective (which we're worried about). |
| // |
| // The inline header functions always just cast to a f64 and do their |
| // operation, so we do that here as well, but only for MSVC targets. |
| // |
| // Note that there are many MSVC-specific float operations which |
| // redirect to this comment, so `floorf` is just one case of a missing |
| // function on MSVC, but there are many others elsewhere. |
| #[cfg(target_env = "msvc")] |
| return (self as f64).floor() as f32; |
| #[cfg(not(target_env = "msvc"))] |
| return unsafe { intrinsics::floorf32(self) }; |
| } |
| |
| /// Returns the smallest integer greater than or equal to a number. |
| /// |
| /// ``` |
| /// let f = 3.01_f32; |
| /// let g = 4.0_f32; |
| /// |
| /// assert_eq!(f.ceil(), 4.0); |
| /// assert_eq!(g.ceil(), 4.0); |
| /// ``` |
| #[inline] |
| pub fn ceil(self) -> f32 { |
| // see notes above in `floor` |
| #[cfg(target_env = "msvc")] |
| return (self as f64).ceil() as f32; |
| #[cfg(not(target_env = "msvc"))] |
| return unsafe { intrinsics::ceilf32(self) }; |
| } |
| |
| /// Returns the nearest integer to a number. Round half-way cases away from |
| /// `0.0`. |
| /// |
| /// ``` |
| /// let f = 3.3_f32; |
| /// let g = -3.3_f32; |
| /// |
| /// assert_eq!(f.round(), 3.0); |
| /// assert_eq!(g.round(), -3.0); |
| /// ``` |
| #[inline] |
| pub fn round(self) -> f32 { |
| unsafe { intrinsics::roundf32(self) } |
| } |
| |
| /// Returns the integer part of a number. |
| /// |
| /// ``` |
| /// let f = 3.3_f32; |
| /// let g = -3.7_f32; |
| /// |
| /// assert_eq!(f.trunc(), 3.0); |
| /// assert_eq!(g.trunc(), -3.0); |
| /// ``` |
| #[inline] |
| pub fn trunc(self) -> f32 { |
| unsafe { intrinsics::truncf32(self) } |
| } |
| |
| /// Returns the fractional part of a number. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let x = 3.5_f32; |
| /// let y = -3.5_f32; |
| /// let abs_difference_x = (x.fract() - 0.5).abs(); |
| /// let abs_difference_y = (y.fract() - (-0.5)).abs(); |
| /// |
| /// assert!(abs_difference_x <= f32::EPSILON); |
| /// assert!(abs_difference_y <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn fract(self) -> f32 { self - self.trunc() } |
| |
| /// Computes the absolute value of `self`. Returns `NAN` if the |
| /// number is `NAN`. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let x = 3.5_f32; |
| /// let y = -3.5_f32; |
| /// |
| /// let abs_difference_x = (x.abs() - x).abs(); |
| /// let abs_difference_y = (y.abs() - (-y)).abs(); |
| /// |
| /// assert!(abs_difference_x <= f32::EPSILON); |
| /// assert!(abs_difference_y <= f32::EPSILON); |
| /// |
| /// assert!(f32::NAN.abs().is_nan()); |
| /// ``` |
| #[inline] |
| pub fn abs(self) -> f32 { 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::f32; |
| /// |
| /// let f = 3.5_f32; |
| /// |
| /// assert_eq!(f.signum(), 1.0); |
| /// assert_eq!(f32::NEG_INFINITY.signum(), -1.0); |
| /// |
| /// assert!(f32::NAN.signum().is_nan()); |
| /// ``` |
| #[inline] |
| pub fn signum(self) -> f32 { 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_f32; |
| /// let g = -7.0_f32; |
| /// |
| /// assert!(f.is_sign_positive()); |
| /// assert!(!g.is_sign_positive()); |
| /// ``` |
| #[inline] |
| pub fn is_sign_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 = 7.0f32; |
| /// let g = -7.0f32; |
| /// |
| /// assert!(!f.is_sign_negative()); |
| /// assert!(g.is_sign_negative()); |
| /// ``` |
| #[inline] |
| pub fn is_sign_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. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let m = 10.0_f32; |
| /// let x = 4.0_f32; |
| /// let b = 60.0_f32; |
| /// |
| /// // 100.0 |
| /// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn mul_add(self, a: f32, b: f32) -> f32 { |
| unsafe { intrinsics::fmaf32(self, a, b) } |
| } |
| |
| /// Takes the reciprocal (inverse) of a number, `1/x`. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let x = 2.0_f32; |
| /// let abs_difference = (x.recip() - (1.0/x)).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn recip(self) -> f32 { num::Float::recip(self) } |
| |
| /// Raises a number to an integer power. |
| /// |
| /// Using this function is generally faster than using `powf` |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let x = 2.0_f32; |
| /// let abs_difference = (x.powi(2) - x*x).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn powi(self, n: i32) -> f32 { num::Float::powi(self, n) } |
| |
| /// Raises a number to a floating point power. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let x = 2.0_f32; |
| /// let abs_difference = (x.powf(2.0) - x*x).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn powf(self, n: f32) -> f32 { |
| // see notes above in `floor` |
| #[cfg(target_env = "msvc")] |
| return (self as f64).powf(n as f64) as f32; |
| #[cfg(not(target_env = "msvc"))] |
| return unsafe { intrinsics::powf32(self, n) }; |
| } |
| |
| /// Takes the square root of a number. |
| /// |
| /// Returns NaN if `self` is a negative number. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let positive = 4.0_f32; |
| /// let negative = -4.0_f32; |
| /// |
| /// let abs_difference = (positive.sqrt() - 2.0).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// assert!(negative.sqrt().is_nan()); |
| /// ``` |
| #[inline] |
| pub fn sqrt(self) -> f32 { |
| if self < 0.0 { |
| NAN |
| } else { |
| unsafe { intrinsics::sqrtf32(self) } |
| } |
| } |
| |
| /// Returns `e^(self)`, (the exponential function). |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let one = 1.0f32; |
| /// // e^1 |
| /// let e = one.exp(); |
| /// |
| /// // ln(e) - 1 == 0 |
| /// let abs_difference = (e.ln() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn exp(self) -> f32 { |
| // see notes above in `floor` |
| #[cfg(target_env = "msvc")] |
| return (self as f64).exp() as f32; |
| #[cfg(not(target_env = "msvc"))] |
| return unsafe { intrinsics::expf32(self) }; |
| } |
| |
| /// Returns `2^(self)`. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let f = 2.0f32; |
| /// |
| /// // 2^2 - 4 == 0 |
| /// let abs_difference = (f.exp2() - 4.0).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn exp2(self) -> f32 { |
| unsafe { intrinsics::exp2f32(self) } |
| } |
| |
| /// Returns the natural logarithm of the number. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let one = 1.0f32; |
| /// // e^1 |
| /// let e = one.exp(); |
| /// |
| /// // ln(e) - 1 == 0 |
| /// let abs_difference = (e.ln() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn ln(self) -> f32 { |
| // see notes above in `floor` |
| #[cfg(target_env = "msvc")] |
| return (self as f64).ln() as f32; |
| #[cfg(not(target_env = "msvc"))] |
| return unsafe { intrinsics::logf32(self) }; |
| } |
| |
| /// 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. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let five = 5.0f32; |
| /// |
| /// // log5(5) - 1 == 0 |
| /// let abs_difference = (five.log(5.0) - 1.0).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn log(self, base: f32) -> f32 { self.ln() / base.ln() } |
| |
| /// Returns the base 2 logarithm of the number. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let two = 2.0f32; |
| /// |
| /// // log2(2) - 1 == 0 |
| /// let abs_difference = (two.log2() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn log2(self) -> f32 { |
| #[cfg(target_os = "android")] |
| return ::sys::android::log2f32(self); |
| #[cfg(not(target_os = "android"))] |
| return unsafe { intrinsics::log2f32(self) }; |
| } |
| |
| /// Returns the base 10 logarithm of the number. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let ten = 10.0f32; |
| /// |
| /// // log10(10) - 1 == 0 |
| /// let abs_difference = (ten.log10() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn log10(self) -> f32 { |
| // see notes above in `floor` |
| #[cfg(target_env = "msvc")] |
| return (self as f64).log10() as f32; |
| #[cfg(not(target_env = "msvc"))] |
| return unsafe { intrinsics::log10f32(self) }; |
| } |
| |
| /// Converts radians to degrees. |
| /// |
| /// ``` |
| /// use std::f32::{self, consts}; |
| /// |
| /// let angle = consts::PI; |
| /// |
| /// let abs_difference = (angle.to_degrees() - 180.0).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn to_degrees(self) -> f32 { num::Float::to_degrees(self) } |
| |
| /// Converts degrees to radians. |
| /// |
| /// ``` |
| /// use std::f32::{self, consts}; |
| /// |
| /// let angle = 180.0f32; |
| /// |
| /// let abs_difference = (angle.to_radians() - consts::PI).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn to_radians(self) -> f32 { num::Float::to_radians(self) } |
| |
| /// Returns the maximum of the two numbers. |
| /// |
| /// ``` |
| /// let x = 1.0f32; |
| /// let y = 2.0f32; |
| /// |
| /// assert_eq!(x.max(y), y); |
| /// ``` |
| /// |
| /// If one of the arguments is NaN, then the other argument is returned. |
| |
| #[inline] |
| pub fn max(self, other: f32) -> f32 { |
| num::Float::max(self, other) |
| } |
| |
| /// Returns the minimum of the two numbers. |
| /// |
| /// ``` |
| /// let x = 1.0f32; |
| /// let y = 2.0f32; |
| /// |
| /// assert_eq!(x.min(y), x); |
| /// ``` |
| /// |
| /// If one of the arguments is NaN, then the other argument is returned. |
| #[inline] |
| pub fn min(self, other: f32) -> f32 { |
| num::Float::min(self, other) |
| } |
| |
| /// The positive difference of two numbers. |
| /// |
| /// * If `self <= other`: `0:0` |
| /// * Else: `self - other` |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let x = 3.0f32; |
| /// let y = -3.0f32; |
| /// |
| /// 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 <= f32::EPSILON); |
| /// assert!(abs_difference_y <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn abs_sub(self, other: f32) -> f32 { |
| unsafe { cmath::fdimf(self, other) } |
| } |
| |
| /// Takes the cubic root of a number. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let x = 8.0f32; |
| /// |
| /// // x^(1/3) - 2 == 0 |
| /// let abs_difference = (x.cbrt() - 2.0).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn cbrt(self) -> f32 { |
| unsafe { cmath::cbrtf(self) } |
| } |
| |
| /// Calculates the length of the hypotenuse of a right-angle triangle given |
| /// legs of length `x` and `y`. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let x = 2.0f32; |
| /// let y = 3.0f32; |
| /// |
| /// // sqrt(x^2 + y^2) |
| /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn hypot(self, other: f32) -> f32 { |
| unsafe { cmath::hypotf(self, other) } |
| } |
| |
| /// Computes the sine of a number (in radians). |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let x = f32::consts::PI/2.0; |
| /// |
| /// let abs_difference = (x.sin() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn sin(self) -> f32 { |
| // see notes in `core::f32::Float::floor` |
| #[cfg(target_env = "msvc")] |
| return (self as f64).sin() as f32; |
| #[cfg(not(target_env = "msvc"))] |
| return unsafe { intrinsics::sinf32(self) }; |
| } |
| |
| /// Computes the cosine of a number (in radians). |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let x = 2.0*f32::consts::PI; |
| /// |
| /// let abs_difference = (x.cos() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn cos(self) -> f32 { |
| // see notes in `core::f32::Float::floor` |
| #[cfg(target_env = "msvc")] |
| return (self as f64).cos() as f32; |
| #[cfg(not(target_env = "msvc"))] |
| return unsafe { intrinsics::cosf32(self) }; |
| } |
| |
| /// Computes the tangent of a number (in radians). |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let x = f32::consts::PI / 4.0; |
| /// let abs_difference = (x.tan() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn tan(self) -> f32 { |
| unsafe { cmath::tanf(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::f32; |
| /// |
| /// let f = f32::consts::PI / 2.0; |
| /// |
| /// // asin(sin(pi/2)) |
| /// let abs_difference = (f.sin().asin() - f32::consts::PI / 2.0).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn asin(self) -> f32 { |
| unsafe { cmath::asinf(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::f32; |
| /// |
| /// let f = f32::consts::PI / 4.0; |
| /// |
| /// // acos(cos(pi/4)) |
| /// let abs_difference = (f.cos().acos() - f32::consts::PI / 4.0).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn acos(self) -> f32 { |
| unsafe { cmath::acosf(self) } |
| } |
| |
| /// Computes the arctangent of a number. Return value is in radians in the |
| /// range [-pi/2, pi/2]; |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let f = 1.0f32; |
| /// |
| /// // atan(tan(1)) |
| /// let abs_difference = (f.tan().atan() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn atan(self) -> f32 { |
| unsafe { cmath::atanf(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)` |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let pi = f32::consts::PI; |
| /// // Positive angles measured counter-clockwise |
| /// // from positive x axis |
| /// // -pi/4 radians (45 deg clockwise) |
| /// let x1 = 3.0f32; |
| /// let y1 = -3.0f32; |
| /// |
| /// // 3pi/4 radians (135 deg counter-clockwise) |
| /// let x2 = -3.0f32; |
| /// let y2 = 3.0f32; |
| /// |
| /// 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 <= f32::EPSILON); |
| /// assert!(abs_difference_2 <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn atan2(self, other: f32) -> f32 { |
| unsafe { cmath::atan2f(self, other) } |
| } |
| |
| /// Simultaneously computes the sine and cosine of the number, `x`. Returns |
| /// `(sin(x), cos(x))`. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let x = f32::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 <= f32::EPSILON); |
| /// assert!(abs_difference_1 <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn sin_cos(self) -> (f32, f32) { |
| (self.sin(), self.cos()) |
| } |
| |
| /// Returns `e^(self) - 1` in a way that is accurate even if the |
| /// number is close to zero. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let x = 6.0f32; |
| /// |
| /// // e^(ln(6)) - 1 |
| /// let abs_difference = (x.ln().exp_m1() - 5.0).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn exp_m1(self) -> f32 { |
| unsafe { cmath::expm1f(self) } |
| } |
| |
| /// Returns `ln(1+n)` (natural logarithm) more accurately than if |
| /// the operations were performed separately. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let x = f32::consts::E - 1.0; |
| /// |
| /// // ln(1 + (e - 1)) == ln(e) == 1 |
| /// let abs_difference = (x.ln_1p() - 1.0).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn ln_1p(self) -> f32 { |
| unsafe { cmath::log1pf(self) } |
| } |
| |
| /// Hyperbolic sine function. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let e = f32::consts::E; |
| /// let x = 1.0f32; |
| /// |
| /// 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 <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn sinh(self) -> f32 { |
| unsafe { cmath::sinhf(self) } |
| } |
| |
| /// Hyperbolic cosine function. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let e = f32::consts::E; |
| /// let x = 1.0f32; |
| /// 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 <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn cosh(self) -> f32 { |
| unsafe { cmath::coshf(self) } |
| } |
| |
| /// Hyperbolic tangent function. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let e = f32::consts::E; |
| /// let x = 1.0f32; |
| /// |
| /// 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 <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn tanh(self) -> f32 { |
| unsafe { cmath::tanhf(self) } |
| } |
| |
| /// Inverse hyperbolic sine function. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let x = 1.0f32; |
| /// let f = x.sinh().asinh(); |
| /// |
| /// let abs_difference = (f - x).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn asinh(self) -> f32 { |
| if self == NEG_INFINITY { |
| NEG_INFINITY |
| } else { |
| (self + ((self * self) + 1.0).sqrt()).ln() |
| } |
| } |
| |
| /// Inverse hyperbolic cosine function. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let x = 1.0f32; |
| /// let f = x.cosh().acosh(); |
| /// |
| /// let abs_difference = (f - x).abs(); |
| /// |
| /// assert!(abs_difference <= f32::EPSILON); |
| /// ``` |
| #[inline] |
| pub fn acosh(self) -> f32 { |
| match self { |
| x if x < 1.0 => ::f32::NAN, |
| x => (x + ((x * x) - 1.0).sqrt()).ln(), |
| } |
| } |
| |
| /// Inverse hyperbolic tangent function. |
| /// |
| /// ``` |
| /// use std::f32; |
| /// |
| /// let e = f32::consts::E; |
| /// let f = e.tanh().atanh(); |
| /// |
| /// let abs_difference = (f - e).abs(); |
| /// |
| /// assert!(abs_difference <= 1e-5); |
| /// ``` |
| #[inline] |
| pub fn atanh(self) -> f32 { |
| 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p() |
| } |
| |
| /// Raw transmutation to `u32`. |
| /// |
| /// This is currently identical to `transmute::<f32, u32>(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. |
| /// |
| #[inline] |
| pub fn to_bits(self) -> u32 { |
| num::Float::to_bits(self) |
| } |
| |
| /// Raw transmutation from `u32`. |
| /// |
| /// This is currently identical to `transmute::<u32, f32>(v)` on all platforms. |
| /// It turns out this is incredibly portable, for two reasons: |
| /// |
| /// * Floats and Ints have the same endianness 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. |
| /// |
| #[inline] |
| pub fn from_bits(v: u32) -> Self { |
| num::Float::from_bits(v) |
| } |
| } |