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Diffstat (limited to 'std/src/num/f64.rs')
| -rw-r--r-- | std/src/num/f64.rs | 1712 |
1 files changed, 1712 insertions, 0 deletions
diff --git a/std/src/num/f64.rs b/std/src/num/f64.rs new file mode 100644 index 0000000..2f23dbe --- /dev/null +++ b/std/src/num/f64.rs @@ -0,0 +1,1712 @@ +// 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 or the MIT license +// , at your +// option. This file may not be copied, modified, or distributed +// except according to those terms. + +//! The 64-bit floating point type. +//! +//! *[See also the `f64` primitive type](../primitive.f64.html).* + +#![allow(missing_docs)] + +#[cfg(not(test))] +use core::num; +#[cfg(not(test))] +use core::intrinsics; +#[cfg(not(test))] +use libctru::libc::c_int; +#[cfg(not(test))] +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 libctru::libc::{c_double, c_int}; + + #[link_name = "m"] + extern "C" { + 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 fmax(a: c_double, b: c_double) -> c_double; + pub fn fmin(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; + + #[cfg_attr(all(windows, target_env = "msvc"), link_name = "__lgamma_r")] + pub fn lgamma_r(n: c_double, sign: &mut c_int) -> c_double; + + #[cfg_attr(all(windows, target_env = "msvc"), link_name = "_hypot")] + pub fn hypot(x: c_double, y: c_double) -> c_double; + } +} + +#[cfg(not(test))] +#[lang = "f64"] +impl f64 { + /// Returns `true` if this value is `NaN` and false otherwise. + /// + /// ``` + /// use std::f64; + /// + /// let nan = f64::NAN; + /// let f = 7.0_f64; + /// + /// assert!(nan.is_nan()); + /// assert!(!f.is_nan()); + /// ``` + #[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 mantissa, base 2 exponent, and sign as integers, respectively. + /// The original number can be recovered by `sign * mantissa * 2 ^ exponent`. + /// The floating point encoding is documented in the [Reference][floating-point]. + /// + /// ``` + /// #![feature(float_extras)] + /// + /// let num = 2.0f64; + /// + /// // (8388608, -22, 1) + /// let (mantissa, exponent, sign) = num.integer_decode(); + /// let sign_f = sign as f64; + /// let mantissa_f = mantissa as f64; + /// let exponent_f = num.powf(exponent as f64); + /// + /// // 1 * 8388608 * 2^(-22) == 2 + /// let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + /// [floating-point]: ../reference.html#machine-types + #[inline] + #[allow(deprecated)] + pub fn integer_decode(self) -> (u64, i16, i8) { + num::Float::integer_decode(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 `self`'s sign bit is positive, including + /// `+0.0` and `INFINITY`. + /// + /// ``` + /// use std::f64; + /// + /// let nan: f64 = f64::NAN; + /// + /// let f = 7.0_f64; + /// let g = -7.0_f64; + /// + /// assert!(f.is_sign_positive()); + /// assert!(!g.is_sign_positive()); + /// // Requires both tests to determine if is `NaN` + /// assert!(!nan.is_sign_positive() && !nan.is_sign_negative()); + /// ``` + #[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 `self`'s sign is negative, including `-0.0` + /// and `NEG_INFINITY`. + /// + /// ``` + /// use std::f64; + /// + /// let nan = f64::NAN; + /// + /// let f = 7.0_f64; + /// let g = -7.0_f64; + /// + /// assert!(!f.is_sign_negative()); + /// assert!(g.is_sign_negative()); + /// // Requires both tests to determine if is `NaN`. + /// assert!(!nan.is_sign_positive() && !nan.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) + } + + /// Constructs a floating point number of `x*2^exp`. + /// + /// ``` + /// #![feature(float_extras)] + /// + /// // 3*2^2 - 12 == 0 + /// let abs_difference = (f64::ldexp(3.0, 2) - 12.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` + #[inline] + pub fn ldexp(x: f64, exp: isize) -> f64 { + unsafe { cmath::ldexp(x, exp as c_int) } + } + + /// Breaks the number into a normalized fraction and a base-2 exponent, + /// satisfying: + /// + /// * `self = x * 2^exp` + /// * `0.5 <= abs(x) < 1.0` + /// + /// ``` + /// #![feature(float_extras)] + /// + /// let x = 4.0_f64; + /// + /// // (1/2)*2^3 -> 1 * 8/2 -> 4.0 + /// let f = x.frexp(); + /// let abs_difference_0 = (f.0 - 0.5).abs(); + /// let abs_difference_1 = (f.1 as f64 - 3.0).abs(); + /// + /// assert!(abs_difference_0 < 1e-10); + /// assert!(abs_difference_1 < 1e-10); + /// ``` + #[inline] + pub fn frexp(self) -> (f64, isize) { + unsafe { + let mut exp = 0; + let x = cmath::frexp(self, &mut exp); + (x, exp as isize) + } + } + + /// Returns the next representable floating-point value in the direction of + /// `other`. + /// + /// ``` + /// #![feature(float_extras)] + /// + /// let x = 1.0f64; + /// + /// let abs_diff = (x.next_after(2.0) - 1.0000000000000002220446049250313_f64).abs(); + /// + /// assert!(abs_diff < 1e-10); + /// ``` + #[inline] + pub fn next_after(self, other: f64) -> f64 { + unsafe { cmath::nextafter(self, other) } + } + + /// 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 { + unsafe { cmath::fmax(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 { + unsafe { cmath::fmin(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 + } + } + } +} + +#[cfg(test)] +mod tests { + use f64; + use f64::*; + use num::*; + use num::FpCategory as Fp; + + #[test] + fn test_num_f64() { + test_num(10f64, 2f64); + } + + #[test] + fn test_min_nan() { + assert_eq!(NAN.min(2.0), 2.0); + assert_eq!(2.0f64.min(NAN), 2.0); + } + + #[test] + fn test_max_nan() { + assert_eq!(NAN.max(2.0), 2.0); + assert_eq!(2.0f64.max(NAN), 2.0); + } + + #[test] + fn test_nan() { + let nan: f64 = NAN; + assert!(nan.is_nan()); + assert!(!nan.is_infinite()); + assert!(!nan.is_finite()); + assert!(!nan.is_normal()); + assert!(!nan.is_sign_positive()); + assert!(!nan.is_sign_negative()); + assert_eq!(Fp::Nan, nan.classify()); + } + + #[test] + fn test_infinity() { + let inf: f64 = INFINITY; + assert!(inf.is_infinite()); + assert!(!inf.is_finite()); + assert!(inf.is_sign_positive()); + assert!(!inf.is_sign_negative()); + assert!(!inf.is_nan()); + assert!(!inf.is_normal()); + assert_eq!(Fp::Infinite, inf.classify()); + } + + #[test] + fn test_neg_infinity() { + let neg_inf: f64 = NEG_INFINITY; + assert!(neg_inf.is_infinite()); + assert!(!neg_inf.is_finite()); + assert!(!neg_inf.is_sign_positive()); + assert!(neg_inf.is_sign_negative()); + assert!(!neg_inf.is_nan()); + assert!(!neg_inf.is_normal()); + assert_eq!(Fp::Infinite, neg_inf.classify()); + } + + #[test] + fn test_zero() { + let zero: f64 = 0.0f64; + assert_eq!(0.0, zero); + assert!(!zero.is_infinite()); + assert!(zero.is_finite()); + assert!(zero.is_sign_positive()); + assert!(!zero.is_sign_negative()); + assert!(!zero.is_nan()); + assert!(!zero.is_normal()); + assert_eq!(Fp::Zero, zero.classify()); + } + + #[test] + fn test_neg_zero() { + let neg_zero: f64 = -0.0; + assert_eq!(0.0, neg_zero); + assert!(!neg_zero.is_infinite()); + assert!(neg_zero.is_finite()); + assert!(!neg_zero.is_sign_positive()); + assert!(neg_zero.is_sign_negative()); + assert!(!neg_zero.is_nan()); + assert!(!neg_zero.is_normal()); + assert_eq!(Fp::Zero, neg_zero.classify()); + } + + #[test] + fn test_one() { + let one: f64 = 1.0f64; + assert_eq!(1.0, one); + assert!(!one.is_infinite()); + assert!(one.is_finite()); + assert!(one.is_sign_positive()); + assert!(!one.is_sign_negative()); + assert!(!one.is_nan()); + assert!(one.is_normal()); + assert_eq!(Fp::Normal, one.classify()); + } + + #[test] + fn test_is_nan() { + let nan: f64 = NAN; + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + assert!(nan.is_nan()); + assert!(!0.0f64.is_nan()); + assert!(!5.3f64.is_nan()); + assert!(!(-10.732f64).is_nan()); + assert!(!inf.is_nan()); + assert!(!neg_inf.is_nan()); + } + + #[test] + fn test_is_infinite() { + let nan: f64 = NAN; + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + assert!(!nan.is_infinite()); + assert!(inf.is_infinite()); + assert!(neg_inf.is_infinite()); + assert!(!0.0f64.is_infinite()); + assert!(!42.8f64.is_infinite()); + assert!(!(-109.2f64).is_infinite()); + } + + #[test] + fn test_is_finite() { + let nan: f64 = NAN; + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + assert!(!nan.is_finite()); + assert!(!inf.is_finite()); + assert!(!neg_inf.is_finite()); + assert!(0.0f64.is_finite()); + assert!(42.8f64.is_finite()); + assert!((-109.2f64).is_finite()); + } + + #[test] + fn test_is_normal() { + let nan: f64 = NAN; + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + let zero: f64 = 0.0f64; + let neg_zero: f64 = -0.0; + assert!(!nan.is_normal()); + assert!(!inf.is_normal()); + assert!(!neg_inf.is_normal()); + assert!(!zero.is_normal()); + assert!(!neg_zero.is_normal()); + assert!(1f64.is_normal()); + assert!(1e-307f64.is_normal()); + assert!(!1e-308f64.is_normal()); + } + + #[test] + fn test_classify() { + let nan: f64 = NAN; + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + let zero: f64 = 0.0f64; + let neg_zero: f64 = -0.0; + assert_eq!(nan.classify(), Fp::Nan); + assert_eq!(inf.classify(), Fp::Infinite); + assert_eq!(neg_inf.classify(), Fp::Infinite); + assert_eq!(zero.classify(), Fp::Zero); + assert_eq!(neg_zero.classify(), Fp::Zero); + assert_eq!(1e-307f64.classify(), Fp::Normal); + assert_eq!(1e-308f64.classify(), Fp::Subnormal); + } + + #[test] + #[allow(deprecated)] + fn test_integer_decode() { + assert_eq!(3.14159265359f64.integer_decode(), + (7074237752028906, -51, 1)); + assert_eq!((-8573.5918555f64).integer_decode(), + (4713381968463931, -39, -1)); + assert_eq!(2f64.powf(100.0).integer_decode(), (4503599627370496, 48, 1)); + assert_eq!(0f64.integer_decode(), (0, -1075, 1)); + assert_eq!((-0f64).integer_decode(), (0, -1075, -1)); + assert_eq!(INFINITY.integer_decode(), (4503599627370496, 972, 1)); + assert_eq!(NEG_INFINITY.integer_decode(), (4503599627370496, 972, -1)); + + // Ignore the "sign" (quiet / signalling flag) of NAN. + // It can vary between runtime operations and LLVM folding. + let (nan_m, nan_e, _nan_s) = NAN.integer_decode(); + assert_eq!((nan_m, nan_e), (6755399441055744, 972)); + } + + #[test] + fn test_floor() { + assert_approx_eq!(1.0f64.floor(), 1.0f64); + assert_approx_eq!(1.3f64.floor(), 1.0f64); + assert_approx_eq!(1.5f64.floor(), 1.0f64); + assert_approx_eq!(1.7f64.floor(), 1.0f64); + assert_approx_eq!(0.0f64.floor(), 0.0f64); + assert_approx_eq!((-0.0f64).floor(), -0.0f64); + assert_approx_eq!((-1.0f64).floor(), -1.0f64); + assert_approx_eq!((-1.3f64).floor(), -2.0f64); + assert_approx_eq!((-1.5f64).floor(), -2.0f64); + assert_approx_eq!((-1.7f64).floor(), -2.0f64); + } + + #[test] + fn test_ceil() { + assert_approx_eq!(1.0f64.ceil(), 1.0f64); + assert_approx_eq!(1.3f64.ceil(), 2.0f64); + assert_approx_eq!(1.5f64.ceil(), 2.0f64); + assert_approx_eq!(1.7f64.ceil(), 2.0f64); + assert_approx_eq!(0.0f64.ceil(), 0.0f64); + assert_approx_eq!((-0.0f64).ceil(), -0.0f64); + assert_approx_eq!((-1.0f64).ceil(), -1.0f64); + assert_approx_eq!((-1.3f64).ceil(), -1.0f64); + assert_approx_eq!((-1.5f64).ceil(), -1.0f64); + assert_approx_eq!((-1.7f64).ceil(), -1.0f64); + } + + #[test] + fn test_round() { + assert_approx_eq!(1.0f64.round(), 1.0f64); + assert_approx_eq!(1.3f64.round(), 1.0f64); + assert_approx_eq!(1.5f64.round(), 2.0f64); + assert_approx_eq!(1.7f64.round(), 2.0f64); + assert_approx_eq!(0.0f64.round(), 0.0f64); + assert_approx_eq!((-0.0f64).round(), -0.0f64); + assert_approx_eq!((-1.0f64).round(), -1.0f64); + assert_approx_eq!((-1.3f64).round(), -1.0f64); + assert_approx_eq!((-1.5f64).round(), -2.0f64); + assert_approx_eq!((-1.7f64).round(), -2.0f64); + } + + #[test] + fn test_trunc() { + assert_approx_eq!(1.0f64.trunc(), 1.0f64); + assert_approx_eq!(1.3f64.trunc(), 1.0f64); + assert_approx_eq!(1.5f64.trunc(), 1.0f64); + assert_approx_eq!(1.7f64.trunc(), 1.0f64); + assert_approx_eq!(0.0f64.trunc(), 0.0f64); + assert_approx_eq!((-0.0f64).trunc(), -0.0f64); + assert_approx_eq!((-1.0f64).trunc(), -1.0f64); + assert_approx_eq!((-1.3f64).trunc(), -1.0f64); + assert_approx_eq!((-1.5f64).trunc(), -1.0f64); + assert_approx_eq!((-1.7f64).trunc(), -1.0f64); + } + + #[test] + fn test_fract() { + assert_approx_eq!(1.0f64.fract(), 0.0f64); + assert_approx_eq!(1.3f64.fract(), 0.3f64); + assert_approx_eq!(1.5f64.fract(), 0.5f64); + assert_approx_eq!(1.7f64.fract(), 0.7f64); + assert_approx_eq!(0.0f64.fract(), 0.0f64); + assert_approx_eq!((-0.0f64).fract(), -0.0f64); + assert_approx_eq!((-1.0f64).fract(), -0.0f64); + assert_approx_eq!((-1.3f64).fract(), -0.3f64); + assert_approx_eq!((-1.5f64).fract(), -0.5f64); + assert_approx_eq!((-1.7f64).fract(), -0.7f64); + } + + #[test] + fn test_abs() { + assert_eq!(INFINITY.abs(), INFINITY); + assert_eq!(1f64.abs(), 1f64); + assert_eq!(0f64.abs(), 0f64); + assert_eq!((-0f64).abs(), 0f64); + assert_eq!((-1f64).abs(), 1f64); + assert_eq!(NEG_INFINITY.abs(), INFINITY); + assert_eq!((1f64 / NEG_INFINITY).abs(), 0f64); + assert!(NAN.abs().is_nan()); + } + + #[test] + fn test_signum() { + assert_eq!(INFINITY.signum(), 1f64); + assert_eq!(1f64.signum(), 1f64); + assert_eq!(0f64.signum(), 1f64); + assert_eq!((-0f64).signum(), -1f64); + assert_eq!((-1f64).signum(), -1f64); + assert_eq!(NEG_INFINITY.signum(), -1f64); + assert_eq!((1f64 / NEG_INFINITY).signum(), -1f64); + assert!(NAN.signum().is_nan()); + } + + #[test] + fn test_is_sign_positive() { + assert!(INFINITY.is_sign_positive()); + assert!(1f64.is_sign_positive()); + assert!(0f64.is_sign_positive()); + assert!(!(-0f64).is_sign_positive()); + assert!(!(-1f64).is_sign_positive()); + assert!(!NEG_INFINITY.is_sign_positive()); + assert!(!(1f64 / NEG_INFINITY).is_sign_positive()); + assert!(!NAN.is_sign_positive()); + } + + #[test] + fn test_is_sign_negative() { + assert!(!INFINITY.is_sign_negative()); + assert!(!1f64.is_sign_negative()); + assert!(!0f64.is_sign_negative()); + assert!((-0f64).is_sign_negative()); + assert!((-1f64).is_sign_negative()); + assert!(NEG_INFINITY.is_sign_negative()); + assert!((1f64 / NEG_INFINITY).is_sign_negative()); + assert!(!NAN.is_sign_negative()); + } + + #[test] + fn test_mul_add() { + let nan: f64 = NAN; + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + assert_approx_eq!(12.3f64.mul_add(4.5, 6.7), 62.05); + assert_approx_eq!((-12.3f64).mul_add(-4.5, -6.7), 48.65); + assert_approx_eq!(0.0f64.mul_add(8.9, 1.2), 1.2); + assert_approx_eq!(3.4f64.mul_add(-0.0, 5.6), 5.6); + assert!(nan.mul_add(7.8, 9.0).is_nan()); + assert_eq!(inf.mul_add(7.8, 9.0), inf); + assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf); + assert_eq!(8.9f64.mul_add(inf, 3.2), inf); + assert_eq!((-3.2f64).mul_add(2.4, neg_inf), neg_inf); + } + + #[test] + fn test_recip() { + let nan: f64 = NAN; + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + assert_eq!(1.0f64.recip(), 1.0); + assert_eq!(2.0f64.recip(), 0.5); + assert_eq!((-0.4f64).recip(), -2.5); + assert_eq!(0.0f64.recip(), inf); + assert!(nan.recip().is_nan()); + assert_eq!(inf.recip(), 0.0); + assert_eq!(neg_inf.recip(), 0.0); + } + + #[test] + fn test_powi() { + let nan: f64 = NAN; + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + assert_eq!(1.0f64.powi(1), 1.0); + assert_approx_eq!((-3.1f64).powi(2), 9.61); + assert_approx_eq!(5.9f64.powi(-2), 0.028727); + assert_eq!(8.3f64.powi(0), 1.0); + assert!(nan.powi(2).is_nan()); + assert_eq!(inf.powi(3), inf); + assert_eq!(neg_inf.powi(2), inf); + } + + #[test] + fn test_powf() { + let nan: f64 = NAN; + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + assert_eq!(1.0f64.powf(1.0), 1.0); + assert_approx_eq!(3.4f64.powf(4.5), 246.408183); + assert_approx_eq!(2.7f64.powf(-3.2), 0.041652); + assert_approx_eq!((-3.1f64).powf(2.0), 9.61); + assert_approx_eq!(5.9f64.powf(-2.0), 0.028727); + assert_eq!(8.3f64.powf(0.0), 1.0); + assert!(nan.powf(2.0).is_nan()); + assert_eq!(inf.powf(2.0), inf); + assert_eq!(neg_inf.powf(3.0), neg_inf); + } + + #[test] + fn test_sqrt_domain() { + assert!(NAN.sqrt().is_nan()); + assert!(NEG_INFINITY.sqrt().is_nan()); + assert!((-1.0f64).sqrt().is_nan()); + assert_eq!((-0.0f64).sqrt(), -0.0); + assert_eq!(0.0f64.sqrt(), 0.0); + assert_eq!(1.0f64.sqrt(), 1.0); + assert_eq!(INFINITY.sqrt(), INFINITY); + } + + #[test] + fn test_exp() { + assert_eq!(1.0, 0.0f64.exp()); + assert_approx_eq!(2.718282, 1.0f64.exp()); + assert_approx_eq!(148.413159, 5.0f64.exp()); + + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + let nan: f64 = NAN; + assert_eq!(inf, inf.exp()); + assert_eq!(0.0, neg_inf.exp()); + assert!(nan.exp().is_nan()); + } + + #[test] + fn test_exp2() { + assert_eq!(32.0, 5.0f64.exp2()); + assert_eq!(1.0, 0.0f64.exp2()); + + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + let nan: f64 = NAN; + assert_eq!(inf, inf.exp2()); + assert_eq!(0.0, neg_inf.exp2()); + assert!(nan.exp2().is_nan()); + } + + #[test] + fn test_ln() { + let nan: f64 = NAN; + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + assert_approx_eq!(1.0f64.exp().ln(), 1.0); + assert!(nan.ln().is_nan()); + assert_eq!(inf.ln(), inf); + assert!(neg_inf.ln().is_nan()); + assert!((-2.3f64).ln().is_nan()); + assert_eq!((-0.0f64).ln(), neg_inf); + assert_eq!(0.0f64.ln(), neg_inf); + assert_approx_eq!(4.0f64.ln(), 1.386294); + } + + #[test] + fn test_log() { + let nan: f64 = NAN; + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + assert_eq!(10.0f64.log(10.0), 1.0); + assert_approx_eq!(2.3f64.log(3.5), 0.664858); + assert_eq!(1.0f64.exp().log(1.0f64.exp()), 1.0); + assert!(1.0f64.log(1.0).is_nan()); + assert!(1.0f64.log(-13.9).is_nan()); + assert!(nan.log(2.3).is_nan()); + assert_eq!(inf.log(10.0), inf); + assert!(neg_inf.log(8.8).is_nan()); + assert!((-2.3f64).log(0.1).is_nan()); + assert_eq!((-0.0f64).log(2.0), neg_inf); + assert_eq!(0.0f64.log(7.0), neg_inf); + } + + #[test] + fn test_log2() { + let nan: f64 = NAN; + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + assert_approx_eq!(10.0f64.log2(), 3.321928); + assert_approx_eq!(2.3f64.log2(), 1.201634); + assert_approx_eq!(1.0f64.exp().log2(), 1.442695); + assert!(nan.log2().is_nan()); + assert_eq!(inf.log2(), inf); + assert!(neg_inf.log2().is_nan()); + assert!((-2.3f64).log2().is_nan()); + assert_eq!((-0.0f64).log2(), neg_inf); + assert_eq!(0.0f64.log2(), neg_inf); + } + + #[test] + fn test_log10() { + let nan: f64 = NAN; + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + assert_eq!(10.0f64.log10(), 1.0); + assert_approx_eq!(2.3f64.log10(), 0.361728); + assert_approx_eq!(1.0f64.exp().log10(), 0.434294); + assert_eq!(1.0f64.log10(), 0.0); + assert!(nan.log10().is_nan()); + assert_eq!(inf.log10(), inf); + assert!(neg_inf.log10().is_nan()); + assert!((-2.3f64).log10().is_nan()); + assert_eq!((-0.0f64).log10(), neg_inf); + assert_eq!(0.0f64.log10(), neg_inf); + } + + #[test] + fn test_to_degrees() { + let pi: f64 = consts::PI; + let nan: f64 = NAN; + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + assert_eq!(0.0f64.to_degrees(), 0.0); + assert_approx_eq!((-5.8f64).to_degrees(), -332.315521); + assert_eq!(pi.to_degrees(), 180.0); + assert!(nan.to_degrees().is_nan()); + assert_eq!(inf.to_degrees(), inf); + assert_eq!(neg_inf.to_degrees(), neg_inf); + } + + #[test] + fn test_to_radians() { + let pi: f64 = consts::PI; + let nan: f64 = NAN; + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + assert_eq!(0.0f64.to_radians(), 0.0); + assert_approx_eq!(154.6f64.to_radians(), 2.698279); + assert_approx_eq!((-332.31f64).to_radians(), -5.799903); + assert_eq!(180.0f64.to_radians(), pi); + assert!(nan.to_radians().is_nan()); + assert_eq!(inf.to_radians(), inf); + assert_eq!(neg_inf.to_radians(), neg_inf); + } + + #[test] + #[allow(deprecated)] + fn test_ldexp() { + let f1 = 2.0f64.powi(-123); + let f2 = 2.0f64.powi(-111); + let f3 = 1.75 * 2.0f64.powi(-12); + assert_eq!(f64::ldexp(1f64, -123), f1); + assert_eq!(f64::ldexp(1f64, -111), f2); + assert_eq!(f64::ldexp(1.75f64, -12), f3); + + assert_eq!(f64::ldexp(0f64, -123), 0f64); + assert_eq!(f64::ldexp(-0f64, -123), -0f64); + + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + let nan: f64 = NAN; + assert_eq!(f64::ldexp(inf, -123), inf); + assert_eq!(f64::ldexp(neg_inf, -123), neg_inf); + assert!(f64::ldexp(nan, -123).is_nan()); + } + + #[test] + #[allow(deprecated)] + fn test_frexp() { + let f1 = 2.0f64.powi(-123); + let f2 = 2.0f64.powi(-111); + let f3 = 1.75 * 2.0f64.powi(-123); + let (x1, exp1) = f1.frexp(); + let (x2, exp2) = f2.frexp(); + let (x3, exp3) = f3.frexp(); + assert_eq!((x1, exp1), (0.5f64, -122)); + assert_eq!((x2, exp2), (0.5f64, -110)); + assert_eq!((x3, exp3), (0.875f64, -122)); + assert_eq!(f64::ldexp(x1, exp1), f1); + assert_eq!(f64::ldexp(x2, exp2), f2); + assert_eq!(f64::ldexp(x3, exp3), f3); + + assert_eq!(0f64.frexp(), (0f64, 0)); + assert_eq!((-0f64).frexp(), (-0f64, 0)); + } + + #[test] + #[cfg_attr(windows, ignore)] + // FIXME #8755 + #[allow(deprecated)] + fn test_frexp_nowin() { + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + let nan: f64 = NAN; + assert_eq!(match inf.frexp() { + (x, _) => x, + }, + inf); + assert_eq!(match neg_inf.frexp() { + (x, _) => x, + }, + neg_inf); + assert!(match nan.frexp() { + (x, _) => x.is_nan(), + }) + } + + #[test] + fn test_asinh() { + assert_eq!(0.0f64.asinh(), 0.0f64); + assert_eq!((-0.0f64).asinh(), -0.0f64); + + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + let nan: f64 = NAN; + assert_eq!(inf.asinh(), inf); + assert_eq!(neg_inf.asinh(), neg_inf); + assert!(nan.asinh().is_nan()); + assert_approx_eq!(2.0f64.asinh(), 1.443635475178810342493276740273105f64); + assert_approx_eq!((-2.0f64).asinh(), -1.443635475178810342493276740273105f64); + } + + #[test] + fn test_acosh() { + assert_eq!(1.0f64.acosh(), 0.0f64); + assert!(0.999f64.acosh().is_nan()); + + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + let nan: f64 = NAN; + assert_eq!(inf.acosh(), inf); + assert!(neg_inf.acosh().is_nan()); + assert!(nan.acosh().is_nan()); + assert_approx_eq!(2.0f64.acosh(), 1.31695789692481670862504634730796844f64); + assert_approx_eq!(3.0f64.acosh(), 1.76274717403908605046521864995958461f64); + } + + #[test] + fn test_atanh() { + assert_eq!(0.0f64.atanh(), 0.0f64); + assert_eq!((-0.0f64).atanh(), -0.0f64); + + let inf: f64 = INFINITY; + let neg_inf: f64 = NEG_INFINITY; + let nan: f64 = NAN; + assert_eq!(1.0f64.atanh(), inf); + assert_eq!((-1.0f64).atanh(), neg_inf); + assert!(2f64.atanh().atanh().is_nan()); + assert!((-2f64).atanh().atanh().is_nan()); + assert!(inf.atanh().is_nan()); + assert!(neg_inf.atanh().is_nan()); + assert!(nan.atanh().is_nan()); + assert_approx_eq!(0.5f64.atanh(), 0.54930614433405484569762261846126285f64); + assert_approx_eq!((-0.5f64).atanh(), -0.54930614433405484569762261846126285f64); + } + + #[test] + fn test_real_consts() { + use super::consts; + let pi: f64 = consts::PI; + let frac_pi_2: f64 = consts::FRAC_PI_2; + let frac_pi_3: f64 = consts::FRAC_PI_3; + let frac_pi_4: f64 = consts::FRAC_PI_4; + let frac_pi_6: f64 = consts::FRAC_PI_6; + let frac_pi_8: f64 = consts::FRAC_PI_8; + let frac_1_pi: f64 = consts::FRAC_1_PI; + let frac_2_pi: f64 = consts::FRAC_2_PI; + let frac_2_sqrtpi: f64 = consts::FRAC_2_SQRT_PI; + let sqrt2: f64 = consts::SQRT_2; + let frac_1_sqrt2: f64 = consts::FRAC_1_SQRT_2; + let e: f64 = consts::E; + let log2_e: f64 = consts::LOG2_E; + let log10_e: f64 = consts::LOG10_E; + let ln_2: f64 = consts::LN_2; + let ln_10: f64 = consts::LN_10; + + assert_approx_eq!(frac_pi_2, pi / 2f64); + assert_approx_eq!(frac_pi_3, pi / 3f64); + assert_approx_eq!(frac_pi_4, pi / 4f64); + assert_approx_eq!(frac_pi_6, pi / 6f64); + assert_approx_eq!(frac_pi_8, pi / 8f64); + assert_approx_eq!(frac_1_pi, 1f64 / pi); + assert_approx_eq!(frac_2_pi, 2f64 / pi); + assert_approx_eq!(frac_2_sqrtpi, 2f64 / pi.sqrt()); + assert_approx_eq!(sqrt2, 2f64.sqrt()); + assert_approx_eq!(frac_1_sqrt2, 1f64 / 2f64.sqrt()); + assert_approx_eq!(log2_e, e.log2()); + assert_approx_eq!(log10_e, e.log10()); + assert_approx_eq!(ln_2, 2f64.ln()); + assert_approx_eq!(ln_10, 10f64.ln()); + } +} |