| // 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 `f32` floating point data type. |
| //! |
| //! Mathematically significant numbers are provided in the `consts` sub-module. |
| //! |
| //! *[See also the `f32` primitive type](../../std/primitive.f32.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::f32::{RADIX, MANTISSA_DIGITS, DIGITS, EPSILON}; |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub use core::f32::{MIN_EXP, MAX_EXP, MIN_10_EXP}; |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub use core::f32::{MAX_10_EXP, NAN, INFINITY, NEG_INFINITY}; |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub use core::f32::{MIN, MIN_POSITIVE, MAX}; |
| #[stable(feature = "rust1", since = "1.0.0")] |
| pub use core::f32::consts; |
| |
| #[cfg(not(test))] |
| #[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()); |
| /// ``` |
| #[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::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()); |
| /// ``` |
| #[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::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()); |
| /// ``` |
| #[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::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 |
| #[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::f32; |
| /// |
| /// let num = 12.4_f32; |
| /// let inf = f32::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_f32; |
| /// let g = 3.0_f32; |
| /// |
| /// assert_eq!(f.floor(), 3.0); |
| /// assert_eq!(g.floor(), 3.0); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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()); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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()); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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()); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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()); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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()); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "f32_deg_rad_conversions", since="1.7.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "f32_deg_rad_conversions", since="1.7.0")] |
| #[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. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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. |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[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 `fdimf` in C). If you truly need the positive \ |
| difference, consider using that expression or the C function \ |
| `fdimf`, depending on how you wish to handle NaN (please consider \ |
| filing an issue describing your use-case too).")] |
| 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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[inline] |
| pub fn atan(self) -> f32 { |
| unsafe { cmath::atanf(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::f32; |
| /// |
| /// let pi = f32::consts::PI; |
| /// // All angles from horizontal right (+x) |
| /// // 45 deg counter-clockwise |
| /// let x1 = 3.0f32; |
| /// let y1 = -3.0f32; |
| /// |
| /// // 135 deg 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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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); |
| /// ``` |
| #[stable(feature = "rust1", since = "1.0.0")] |
| #[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. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// assert_ne!((1f32).to_bits(), 1f32 as u32); // to_bits() is not casting! |
| /// assert_eq!((12.5f32).to_bits(), 0x41480000); |
| /// |
| /// ``` |
| #[stable(feature = "float_bits_conv", since = "1.20.0")] |
| #[inline] |
| pub fn to_bits(self) -> u32 { |
| unsafe { ::mem::transmute(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 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::f32; |
| /// let v = f32::from_bits(0x41480000); |
| /// 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: u32) -> Self { |
| // It turns out the safety issues with sNaN were overblown! Hooray! |
| unsafe { ::mem::transmute(v) } |
| } |
| } |
| |
| #[cfg(test)] |
| mod tests { |
| use f32; |
| use f32::*; |
| use num::*; |
| use num::FpCategory as Fp; |
| |
| #[test] |
| fn test_num_f32() { |
| test_num(10f32, 2f32); |
| } |
| |
| #[test] |
| fn test_min_nan() { |
| assert_eq!(NAN.min(2.0), 2.0); |
| assert_eq!(2.0f32.min(NAN), 2.0); |
| } |
| |
| #[test] |
| fn test_max_nan() { |
| assert_eq!(NAN.max(2.0), 2.0); |
| assert_eq!(2.0f32.max(NAN), 2.0); |
| } |
| |
| #[test] |
| fn test_nan() { |
| let nan: f32 = f32::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: f32 = f32::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: f32 = f32::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: f32 = 0.0f32; |
| 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: f32 = -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()); |
| } |
| |
| #[test] |
| fn test_one() { |
| let one: f32 = 1.0f32; |
| 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: f32 = f32::NAN; |
| let inf: f32 = f32::INFINITY; |
| let neg_inf: f32 = f32::NEG_INFINITY; |
| assert!(nan.is_nan()); |
| assert!(!0.0f32.is_nan()); |
| assert!(!5.3f32.is_nan()); |
| assert!(!(-10.732f32).is_nan()); |
| assert!(!inf.is_nan()); |
| assert!(!neg_inf.is_nan()); |
| } |
| |
| #[test] |
| fn test_is_infinite() { |
| let nan: f32 = f32::NAN; |
| let inf: f32 = f32::INFINITY; |
| let neg_inf: f32 = f32::NEG_INFINITY; |
| assert!(!nan.is_infinite()); |
| assert!(inf.is_infinite()); |
| assert!(neg_inf.is_infinite()); |
| assert!(!0.0f32.is_infinite()); |
| assert!(!42.8f32.is_infinite()); |
| assert!(!(-109.2f32).is_infinite()); |
| } |
| |
| #[test] |
| fn test_is_finite() { |
| let nan: f32 = f32::NAN; |
| let inf: f32 = f32::INFINITY; |
| let neg_inf: f32 = f32::NEG_INFINITY; |
| assert!(!nan.is_finite()); |
| assert!(!inf.is_finite()); |
| assert!(!neg_inf.is_finite()); |
| assert!(0.0f32.is_finite()); |
| assert!(42.8f32.is_finite()); |
| assert!((-109.2f32).is_finite()); |
| } |
| |
| #[test] |
| fn test_is_normal() { |
| let nan: f32 = f32::NAN; |
| let inf: f32 = f32::INFINITY; |
| let neg_inf: f32 = f32::NEG_INFINITY; |
| let zero: f32 = 0.0f32; |
| let neg_zero: f32 = -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!(1f32.is_normal()); |
| assert!(1e-37f32.is_normal()); |
| assert!(!1e-38f32.is_normal()); |
| } |
| |
| #[test] |
| fn test_classify() { |
| let nan: f32 = f32::NAN; |
| let inf: f32 = f32::INFINITY; |
| let neg_inf: f32 = f32::NEG_INFINITY; |
| let zero: f32 = 0.0f32; |
| let neg_zero: f32 = -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!(1f32.classify(), Fp::Normal); |
| assert_eq!(1e-37f32.classify(), Fp::Normal); |
| assert_eq!(1e-38f32.classify(), Fp::Subnormal); |
| } |
| |
| #[test] |
| fn test_floor() { |
| assert_approx_eq!(1.0f32.floor(), 1.0f32); |
| assert_approx_eq!(1.3f32.floor(), 1.0f32); |
| assert_approx_eq!(1.5f32.floor(), 1.0f32); |
| assert_approx_eq!(1.7f32.floor(), 1.0f32); |
| assert_approx_eq!(0.0f32.floor(), 0.0f32); |
| assert_approx_eq!((-0.0f32).floor(), -0.0f32); |
| assert_approx_eq!((-1.0f32).floor(), -1.0f32); |
| assert_approx_eq!((-1.3f32).floor(), -2.0f32); |
| assert_approx_eq!((-1.5f32).floor(), -2.0f32); |
| assert_approx_eq!((-1.7f32).floor(), -2.0f32); |
| } |
| |
| #[test] |
| fn test_ceil() { |
| assert_approx_eq!(1.0f32.ceil(), 1.0f32); |
| assert_approx_eq!(1.3f32.ceil(), 2.0f32); |
| assert_approx_eq!(1.5f32.ceil(), 2.0f32); |
| assert_approx_eq!(1.7f32.ceil(), 2.0f32); |
| assert_approx_eq!(0.0f32.ceil(), 0.0f32); |
| assert_approx_eq!((-0.0f32).ceil(), -0.0f32); |
| assert_approx_eq!((-1.0f32).ceil(), -1.0f32); |
| assert_approx_eq!((-1.3f32).ceil(), -1.0f32); |
| assert_approx_eq!((-1.5f32).ceil(), -1.0f32); |
| assert_approx_eq!((-1.7f32).ceil(), -1.0f32); |
| } |
| |
| #[test] |
| fn test_round() { |
| assert_approx_eq!(1.0f32.round(), 1.0f32); |
| assert_approx_eq!(1.3f32.round(), 1.0f32); |
| assert_approx_eq!(1.5f32.round(), 2.0f32); |
| assert_approx_eq!(1.7f32.round(), 2.0f32); |
| assert_approx_eq!(0.0f32.round(), 0.0f32); |
| assert_approx_eq!((-0.0f32).round(), -0.0f32); |
| assert_approx_eq!((-1.0f32).round(), -1.0f32); |
| assert_approx_eq!((-1.3f32).round(), -1.0f32); |
| assert_approx_eq!((-1.5f32).round(), -2.0f32); |
| assert_approx_eq!((-1.7f32).round(), -2.0f32); |
| } |
| |
| #[test] |
| fn test_trunc() { |
| assert_approx_eq!(1.0f32.trunc(), 1.0f32); |
| assert_approx_eq!(1.3f32.trunc(), 1.0f32); |
| assert_approx_eq!(1.5f32.trunc(), 1.0f32); |
| assert_approx_eq!(1.7f32.trunc(), 1.0f32); |
| assert_approx_eq!(0.0f32.trunc(), 0.0f32); |
| assert_approx_eq!((-0.0f32).trunc(), -0.0f32); |
| assert_approx_eq!((-1.0f32).trunc(), -1.0f32); |
| assert_approx_eq!((-1.3f32).trunc(), -1.0f32); |
| assert_approx_eq!((-1.5f32).trunc(), -1.0f32); |
| assert_approx_eq!((-1.7f32).trunc(), -1.0f32); |
| } |
| |
| #[test] |
| fn test_fract() { |
| assert_approx_eq!(1.0f32.fract(), 0.0f32); |
| assert_approx_eq!(1.3f32.fract(), 0.3f32); |
| assert_approx_eq!(1.5f32.fract(), 0.5f32); |
| assert_approx_eq!(1.7f32.fract(), 0.7f32); |
| assert_approx_eq!(0.0f32.fract(), 0.0f32); |
| assert_approx_eq!((-0.0f32).fract(), -0.0f32); |
| assert_approx_eq!((-1.0f32).fract(), -0.0f32); |
| assert_approx_eq!((-1.3f32).fract(), -0.3f32); |
| assert_approx_eq!((-1.5f32).fract(), -0.5f32); |
| assert_approx_eq!((-1.7f32).fract(), -0.7f32); |
| } |
| |
| #[test] |
| fn test_abs() { |
| assert_eq!(INFINITY.abs(), INFINITY); |
| assert_eq!(1f32.abs(), 1f32); |
| assert_eq!(0f32.abs(), 0f32); |
| assert_eq!((-0f32).abs(), 0f32); |
| assert_eq!((-1f32).abs(), 1f32); |
| assert_eq!(NEG_INFINITY.abs(), INFINITY); |
| assert_eq!((1f32/NEG_INFINITY).abs(), 0f32); |
| assert!(NAN.abs().is_nan()); |
| } |
| |
| #[test] |
| fn test_signum() { |
| assert_eq!(INFINITY.signum(), 1f32); |
| assert_eq!(1f32.signum(), 1f32); |
| assert_eq!(0f32.signum(), 1f32); |
| assert_eq!((-0f32).signum(), -1f32); |
| assert_eq!((-1f32).signum(), -1f32); |
| assert_eq!(NEG_INFINITY.signum(), -1f32); |
| assert_eq!((1f32/NEG_INFINITY).signum(), -1f32); |
| assert!(NAN.signum().is_nan()); |
| } |
| |
| #[test] |
| fn test_is_sign_positive() { |
| assert!(INFINITY.is_sign_positive()); |
| assert!(1f32.is_sign_positive()); |
| assert!(0f32.is_sign_positive()); |
| assert!(!(-0f32).is_sign_positive()); |
| assert!(!(-1f32).is_sign_positive()); |
| assert!(!NEG_INFINITY.is_sign_positive()); |
| assert!(!(1f32/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!(!1f32.is_sign_negative()); |
| assert!(!0f32.is_sign_negative()); |
| assert!((-0f32).is_sign_negative()); |
| assert!((-1f32).is_sign_negative()); |
| assert!(NEG_INFINITY.is_sign_negative()); |
| assert!((1f32/NEG_INFINITY).is_sign_negative()); |
| assert!(!NAN.is_sign_negative()); |
| assert!((-NAN).is_sign_negative()); |
| } |
| |
| #[test] |
| fn test_mul_add() { |
| let nan: f32 = f32::NAN; |
| let inf: f32 = f32::INFINITY; |
| let neg_inf: f32 = f32::NEG_INFINITY; |
| assert_approx_eq!(12.3f32.mul_add(4.5, 6.7), 62.05); |
| assert_approx_eq!((-12.3f32).mul_add(-4.5, -6.7), 48.65); |
| assert_approx_eq!(0.0f32.mul_add(8.9, 1.2), 1.2); |
| assert_approx_eq!(3.4f32.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!(8.9f32.mul_add(inf, 3.2), inf); |
| assert_eq!((-3.2f32).mul_add(2.4, neg_inf), neg_inf); |
| } |
| |
| #[test] |
| fn test_recip() { |
| let nan: f32 = f32::NAN; |
| let inf: f32 = f32::INFINITY; |
| let neg_inf: f32 = f32::NEG_INFINITY; |
| assert_eq!(1.0f32.recip(), 1.0); |
| assert_eq!(2.0f32.recip(), 0.5); |
| assert_eq!((-0.4f32).recip(), -2.5); |
| assert_eq!(0.0f32.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: f32 = f32::NAN; |
| let inf: f32 = f32::INFINITY; |
| let neg_inf: f32 = f32::NEG_INFINITY; |
| assert_eq!(1.0f32.powi(1), 1.0); |
| assert_approx_eq!((-3.1f32).powi(2), 9.61); |
| assert_approx_eq!(5.9f32.powi(-2), 0.028727); |
| assert_eq!(8.3f32.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: f32 = f32::NAN; |
| let inf: f32 = f32::INFINITY; |
| let neg_inf: f32 = f32::NEG_INFINITY; |
| assert_eq!(1.0f32.powf(1.0), 1.0); |
| assert_approx_eq!(3.4f32.powf(4.5), 246.408218); |
| assert_approx_eq!(2.7f32.powf(-3.2), 0.041652); |
| assert_approx_eq!((-3.1f32).powf(2.0), 9.61); |
| assert_approx_eq!(5.9f32.powf(-2.0), 0.028727); |
| assert_eq!(8.3f32.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!((-1.0f32).sqrt().is_nan()); |
| assert_eq!((-0.0f32).sqrt(), -0.0); |
| assert_eq!(0.0f32.sqrt(), 0.0); |
| assert_eq!(1.0f32.sqrt(), 1.0); |
| assert_eq!(INFINITY.sqrt(), INFINITY); |
| } |
| |
| #[test] |
| fn test_exp() { |
| assert_eq!(1.0, 0.0f32.exp()); |
| assert_approx_eq!(2.718282, 1.0f32.exp()); |
| assert_approx_eq!(148.413162, 5.0f32.exp()); |
| |
| let inf: f32 = f32::INFINITY; |
| let neg_inf: f32 = f32::NEG_INFINITY; |
| let nan: f32 = f32::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, 5.0f32.exp2()); |
| assert_eq!(1.0, 0.0f32.exp2()); |
| |
| let inf: f32 = f32::INFINITY; |
| let neg_inf: f32 = f32::NEG_INFINITY; |
| let nan: f32 = f32::NAN; |
| assert_eq!(inf, inf.exp2()); |
| assert_eq!(0.0, neg_inf.exp2()); |
| assert!(nan.exp2().is_nan()); |
| } |
| |
| #[test] |
| fn test_ln() { |
| let nan: f32 = f32::NAN; |
| let inf: f32 = f32::INFINITY; |
| let neg_inf: f32 = f32::NEG_INFINITY; |
| assert_approx_eq!(1.0f32.exp().ln(), 1.0); |
| assert!(nan.ln().is_nan()); |
| assert_eq!(inf.ln(), inf); |
| assert!(neg_inf.ln().is_nan()); |
| assert!((-2.3f32).ln().is_nan()); |
| assert_eq!((-0.0f32).ln(), neg_inf); |
| assert_eq!(0.0f32.ln(), neg_inf); |
| assert_approx_eq!(4.0f32.ln(), 1.386294); |
| } |
| |
| #[test] |
| fn test_log() { |
| let nan: f32 = f32::NAN; |
| let inf: f32 = f32::INFINITY; |
| let neg_inf: f32 = f32::NEG_INFINITY; |
| assert_eq!(10.0f32.log(10.0), 1.0); |
| assert_approx_eq!(2.3f32.log(3.5), 0.664858); |
| assert_eq!(1.0f32.exp().log(1.0f32.exp()), 1.0); |
| assert!(1.0f32.log(1.0).is_nan()); |
| assert!(1.0f32.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!((-2.3f32).log(0.1).is_nan()); |
| assert_eq!((-0.0f32).log(2.0), neg_inf); |
| assert_eq!(0.0f32.log(7.0), neg_inf); |
| } |
| |
| #[test] |
| fn test_log2() { |
| let nan: f32 = f32::NAN; |
| let inf: f32 = f32::INFINITY; |
| let neg_inf: f32 = f32::NEG_INFINITY; |
| assert_approx_eq!(10.0f32.log2(), 3.321928); |
| assert_approx_eq!(2.3f32.log2(), 1.201634); |
| assert_approx_eq!(1.0f32.exp().log2(), 1.442695); |
| assert!(nan.log2().is_nan()); |
| assert_eq!(inf.log2(), inf); |
| assert!(neg_inf.log2().is_nan()); |
| assert!((-2.3f32).log2().is_nan()); |
| assert_eq!((-0.0f32).log2(), neg_inf); |
| assert_eq!(0.0f32.log2(), neg_inf); |
| } |
| |
| #[test] |
| fn test_log10() { |
| let nan: f32 = f32::NAN; |
| let inf: f32 = f32::INFINITY; |
| let neg_inf: f32 = f32::NEG_INFINITY; |
| assert_eq!(10.0f32.log10(), 1.0); |
| assert_approx_eq!(2.3f32.log10(), 0.361728); |
| assert_approx_eq!(1.0f32.exp().log10(), 0.434294); |
| assert_eq!(1.0f32.log10(), 0.0); |
| assert!(nan.log10().is_nan()); |
| assert_eq!(inf.log10(), inf); |
| assert!(neg_inf.log10().is_nan()); |
| assert!((-2.3f32).log10().is_nan()); |
| assert_eq!((-0.0f32).log10(), neg_inf); |
| assert_eq!(0.0f32.log10(), neg_inf); |
| } |
| |
| #[test] |
| fn test_to_degrees() { |
| let pi: f32 = consts::PI; |
| let nan: f32 = f32::NAN; |
| let inf: f32 = f32::INFINITY; |
| let neg_inf: f32 = f32::NEG_INFINITY; |
| assert_eq!(0.0f32.to_degrees(), 0.0); |
| assert_approx_eq!((-5.8f32).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: f32 = consts::PI; |
| let nan: f32 = f32::NAN; |
| let inf: f32 = f32::INFINITY; |
| let neg_inf: f32 = f32::NEG_INFINITY; |
| assert_eq!(0.0f32.to_radians(), 0.0); |
| assert_approx_eq!(154.6f32.to_radians(), 2.698279); |
| assert_approx_eq!((-332.31f32).to_radians(), -5.799903); |
| assert_eq!(180.0f32.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!(0.0f32.asinh(), 0.0f32); |
| assert_eq!((-0.0f32).asinh(), -0.0f32); |
| |
| let inf: f32 = f32::INFINITY; |
| let neg_inf: f32 = f32::NEG_INFINITY; |
| let nan: f32 = f32::NAN; |
| assert_eq!(inf.asinh(), inf); |
| assert_eq!(neg_inf.asinh(), neg_inf); |
| assert!(nan.asinh().is_nan()); |
| assert_approx_eq!(2.0f32.asinh(), 1.443635475178810342493276740273105f32); |
| assert_approx_eq!((-2.0f32).asinh(), -1.443635475178810342493276740273105f32); |
| } |
| |
| #[test] |
| fn test_acosh() { |
| assert_eq!(1.0f32.acosh(), 0.0f32); |
| assert!(0.999f32.acosh().is_nan()); |
| |
| let inf: f32 = f32::INFINITY; |
| let neg_inf: f32 = f32::NEG_INFINITY; |
| let nan: f32 = f32::NAN; |
| assert_eq!(inf.acosh(), inf); |
| assert!(neg_inf.acosh().is_nan()); |
| assert!(nan.acosh().is_nan()); |
| assert_approx_eq!(2.0f32.acosh(), 1.31695789692481670862504634730796844f32); |
| assert_approx_eq!(3.0f32.acosh(), 1.76274717403908605046521864995958461f32); |
| } |
| |
| #[test] |
| fn test_atanh() { |
| assert_eq!(0.0f32.atanh(), 0.0f32); |
| assert_eq!((-0.0f32).atanh(), -0.0f32); |
| |
| let inf32: f32 = f32::INFINITY; |
| let neg_inf32: f32 = f32::NEG_INFINITY; |
| assert_eq!(1.0f32.atanh(), inf32); |
| assert_eq!((-1.0f32).atanh(), neg_inf32); |
| |
| assert!(2f64.atanh().atanh().is_nan()); |
| assert!((-2f64).atanh().atanh().is_nan()); |
| |
| let inf64: f32 = f32::INFINITY; |
| let neg_inf64: f32 = f32::NEG_INFINITY; |
| let nan32: f32 = f32::NAN; |
| assert!(inf64.atanh().is_nan()); |
| assert!(neg_inf64.atanh().is_nan()); |
| assert!(nan32.atanh().is_nan()); |
| |
| assert_approx_eq!(0.5f32.atanh(), 0.54930614433405484569762261846126285f32); |
| assert_approx_eq!((-0.5f32).atanh(), -0.54930614433405484569762261846126285f32); |
| } |
| |
| #[test] |
| fn test_real_consts() { |
| use super::consts; |
| |
| let pi: f32 = consts::PI; |
| let frac_pi_2: f32 = consts::FRAC_PI_2; |
| let frac_pi_3: f32 = consts::FRAC_PI_3; |
| let frac_pi_4: f32 = consts::FRAC_PI_4; |
| let frac_pi_6: f32 = consts::FRAC_PI_6; |
| let frac_pi_8: f32 = consts::FRAC_PI_8; |
| let frac_1_pi: f32 = consts::FRAC_1_PI; |
| let frac_2_pi: f32 = consts::FRAC_2_PI; |
| let frac_2_sqrtpi: f32 = consts::FRAC_2_SQRT_PI; |
| let sqrt2: f32 = consts::SQRT_2; |
| let frac_1_sqrt2: f32 = consts::FRAC_1_SQRT_2; |
| let e: f32 = consts::E; |
| let log2_e: f32 = consts::LOG2_E; |
| let log10_e: f32 = consts::LOG10_E; |
| let ln_2: f32 = consts::LN_2; |
| let ln_10: f32 = consts::LN_10; |
| |
| assert_approx_eq!(frac_pi_2, pi / 2f32); |
| assert_approx_eq!(frac_pi_3, pi / 3f32); |
| assert_approx_eq!(frac_pi_4, pi / 4f32); |
| assert_approx_eq!(frac_pi_6, pi / 6f32); |
| assert_approx_eq!(frac_pi_8, pi / 8f32); |
| assert_approx_eq!(frac_1_pi, 1f32 / pi); |
| assert_approx_eq!(frac_2_pi, 2f32 / pi); |
| assert_approx_eq!(frac_2_sqrtpi, 2f32 / pi.sqrt()); |
| assert_approx_eq!(sqrt2, 2f32.sqrt()); |
| assert_approx_eq!(frac_1_sqrt2, 1f32 / 2f32.sqrt()); |
| assert_approx_eq!(log2_e, e.log2()); |
| assert_approx_eq!(log10_e, e.log10()); |
| assert_approx_eq!(ln_2, 2f32.ln()); |
| assert_approx_eq!(ln_10, 10f32.ln()); |
| } |
| |
| #[test] |
| fn test_float_bits_conv() { |
| assert_eq!((1f32).to_bits(), 0x3f800000); |
| assert_eq!((12.5f32).to_bits(), 0x41480000); |
| assert_eq!((1337f32).to_bits(), 0x44a72000); |
| assert_eq!((-14.25f32).to_bits(), 0xc1640000); |
| assert_approx_eq!(f32::from_bits(0x3f800000), 1.0); |
| assert_approx_eq!(f32::from_bits(0x41480000), 12.5); |
| assert_approx_eq!(f32::from_bits(0x44a72000), 1337.0); |
| assert_approx_eq!(f32::from_bits(0xc1640000), -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 = f32::NAN.to_bits() ^ 0x002A_AAAA; |
| let masked_nan2 = f32::NAN.to_bits() ^ 0x0055_5555; |
| assert!(f32::from_bits(masked_nan1).is_nan()); |
| assert!(f32::from_bits(masked_nan2).is_nan()); |
| |
| assert_eq!(f32::from_bits(masked_nan1).to_bits(), masked_nan1); |
| assert_eq!(f32::from_bits(masked_nan2).to_bits(), masked_nan2); |
| } |
| } |
