| // Copyright (c) 2017 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. |
| |
| #![allow(missing_docs)] |
| |
| use core::num; |
| use core::intrinsics; |
| use core::num::FpCategory; |
| |
| pub use core::f64::{RADIX, MANTISSA_DIGITS, DIGITS, EPSILON}; |
| pub use core::f64::{MIN_EXP, MAX_EXP, MIN_10_EXP}; |
| pub use core::f64::{MAX_10_EXP, NAN, INFINITY, NEG_INFINITY}; |
| pub use core::f64::{MIN, MIN_POSITIVE, MAX}; |
| pub use core::f64::consts; |
| |
| #[allow(dead_code)] |
| mod cmath { |
| use sgx_types::{c_double, c_int}; |
| |
| #[link_name = "sgx_tstdc"] |
| extern { |
| pub fn acos(n: c_double) -> c_double; |
| pub fn asin(n: c_double) -> c_double; |
| pub fn atan(n: c_double) -> c_double; |
| pub fn atan2(a: c_double, b: c_double) -> c_double; |
| pub fn cbrt(n: c_double) -> c_double; |
| pub fn cosh(n: c_double) -> c_double; |
| pub fn erf(n: c_double) -> c_double; |
| pub fn erfc(n: c_double) -> c_double; |
| pub fn expm1(n: c_double) -> c_double; |
| pub fn fdim(a: c_double, b: c_double) -> c_double; |
| pub fn fmod(a: c_double, b: c_double) -> c_double; |
| pub fn frexp(n: c_double, value: &mut c_int) -> c_double; |
| pub fn ilogb(n: c_double) -> c_int; |
| pub fn ldexp(x: c_double, n: c_int) -> c_double; |
| pub fn logb(n: c_double) -> c_double; |
| pub fn log1p(n: c_double) -> c_double; |
| pub fn nextafter(x: c_double, y: c_double) -> c_double; |
| pub fn modf(n: c_double, iptr: &mut c_double) -> c_double; |
| pub fn sinh(n: c_double) -> c_double; |
| pub fn tan(n: c_double) -> c_double; |
| pub fn tanh(n: c_double) -> c_double; |
| pub fn tgamma(n: c_double) -> c_double; |
| |
| // These are commonly only available for doubles |
| |
| pub fn j0(n: c_double) -> c_double; |
| pub fn j1(n: c_double) -> c_double; |
| pub fn jn(i: c_int, n: c_double) -> c_double; |
| |
| pub fn y0(n: c_double) -> c_double; |
| pub fn y1(n: c_double) -> c_double; |
| pub fn yn(i: c_int, n: c_double) -> c_double; |
| |
| pub fn lgamma_r(n: c_double, sign: &mut c_int) -> c_double; |
| pub fn hypot(x: c_double, y: c_double) -> c_double; |
| } |
| } |
| |
| #[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()); |
| /// ``` |
| #[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()); |
| /// ``` |
| #[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()); |
| /// ``` |
| #[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 |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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()); |
| /// ``` |
| #[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()); |
| /// ``` |
| #[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()); |
| /// ``` |
| #[inline] |
| pub fn is_sign_positive(self) -> bool { num::Float::is_sign_positive(self) } |
| |
| #[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()); |
| /// ``` |
| #[inline] |
| pub fn is_sign_negative(self) -> bool { num::Float::is_sign_negative(self) } |
| |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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()); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[inline] |
| pub fn log2(self) -> f64 { |
| self.log_wrapper(|n| { |
| 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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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. |
| #[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. |
| #[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); |
| /// ``` |
| #[inline] |
| 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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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); |
| /// ``` |
| #[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`. |
| /// |
| /// Converts the `f64` into its raw memory representation, |
| /// similar to the `transmute` function. |
| /// |
| /// Note that this function is distinct from casting. |
| /// |
| #[inline] |
| pub fn to_bits(self) -> u64 { |
| unsafe { ::mem::transmute(self) } |
| } |
| |
| /// Raw transmutation from `u64`. |
| /// |
| /// Converts the given `u64` containing the float's raw memory |
| /// representation into the `f64` type, similar to the |
| /// `transmute` function. |
| /// |
| /// There is only one difference to a bare `transmute`: |
| /// Due to the implications onto Rust's safety promises being |
| /// uncertain, if the representation of a signaling NaN "sNaN" float |
| /// is passed to the function, the implementation is allowed to |
| /// return a quiet NaN instead. |
| /// |
| /// Note that this function is distinct from casting. |
| /// |
| #[inline] |
| pub fn from_bits(mut v: u64) -> Self { |
| const EXP_MASK: u64 = 0x7FF0000000000000; |
| const FRACT_MASK: u64 = 0x000FFFFFFFFFFFFF; |
| if v & EXP_MASK == EXP_MASK && v & FRACT_MASK != 0 { |
| // While IEEE 754-2008 specifies encodings for quiet NaNs |
| // and signaling ones, certain MIPS and PA-RISC |
| // CPUs treat signaling NaNs differently. |
| // Therefore to be safe, we pass a known quiet NaN |
| // if v is any kind of NaN. |
| // The check above only assumes IEEE 754-1985 to be |
| // valid. |
| v = unsafe { ::mem::transmute(NAN) }; |
| } |
| unsafe { ::mem::transmute(v) } |
| } |
| } |