diff options
Diffstat (limited to 'src/libstd/num/mod.rs')
| -rw-r--r-- | src/libstd/num/mod.rs | 819 |
1 files changed, 777 insertions, 42 deletions
diff --git a/src/libstd/num/mod.rs b/src/libstd/num/mod.rs index 29532cb9b02..4582dcd2b03 100644 --- a/src/libstd/num/mod.rs +++ b/src/libstd/num/mod.rs @@ -51,71 +51,143 @@ pub trait Float + Rem<Output=Self> { // inlined methods from `num::Float` - /// Returns the NaN value. + /// Returns the `NaN` value. + /// + /// ``` + /// use std::num::Float; + /// + /// let nan: f32 = Float::nan(); + /// + /// assert!(nan.is_nan()); + /// ``` #[unstable(feature = "std_misc", reason = "unsure about its place in the world")] fn nan() -> Self; /// Returns the infinite value. + /// + /// ``` + /// use std::num::Float; + /// use std::f32; + /// + /// let infinity: f32 = Float::infinity(); + /// + /// assert!(infinity.is_infinite()); + /// assert!(!infinity.is_finite()); + /// assert!(infinity > f32::MAX); + /// ``` #[unstable(feature = "std_misc", reason = "unsure about its place in the world")] fn infinity() -> Self; /// Returns the negative infinite value. + /// + /// ``` + /// use std::num::Float; + /// use std::f32; + /// + /// let neg_infinity: f32 = Float::neg_infinity(); + /// + /// assert!(neg_infinity.is_infinite()); + /// assert!(!neg_infinity.is_finite()); + /// assert!(neg_infinity < f32::MIN); + /// ``` #[unstable(feature = "std_misc", reason = "unsure about its place in the world")] fn neg_infinity() -> Self; - /// Returns the `0` value. + /// Returns `0.0`. + /// + /// ``` + /// use std::num::Float; + /// + /// let inf: f32 = Float::infinity(); + /// let zero: f32 = Float::zero(); + /// let neg_zero: f32 = Float::neg_zero(); + /// + /// assert_eq!(zero, neg_zero); + /// assert_eq!(7.0f32/inf, zero); + /// assert_eq!(zero * 10.0, zero); + /// ``` #[unstable(feature = "std_misc", reason = "unsure about its place in the world")] fn zero() -> Self; - /// Returns -0.0. + /// Returns `-0.0`. + /// + /// ``` + /// use std::num::Float; + /// + /// let inf: f32 = Float::infinity(); + /// let zero: f32 = Float::zero(); + /// let neg_zero: f32 = Float::neg_zero(); + /// + /// assert_eq!(zero, neg_zero); + /// assert_eq!(7.0f32/inf, zero); + /// assert_eq!(zero * 10.0, zero); + /// ``` #[unstable(feature = "std_misc", reason = "unsure about its place in the world")] fn neg_zero() -> Self; - /// Returns the `1` value. + /// Returns `1.0`. + /// + /// ``` + /// use std::num::Float; + /// + /// let one: f32 = Float::one(); + /// + /// assert_eq!(one, 1.0f32); + /// ``` #[unstable(feature = "std_misc", reason = "unsure about its place in the world")] fn one() -> Self; // FIXME (#5527): These should be associated constants - /// Returns the number of binary digits of mantissa that this type supports. + /// Deprecated: use `std::f32::MANTISSA_DIGITS` or `std::f64::MANTISSA_DIGITS` + /// instead. #[unstable(feature = "std_misc")] #[deprecated(since = "1.0.0", reason = "use `std::f32::MANTISSA_DIGITS` or \ `std::f64::MANTISSA_DIGITS` as appropriate")] fn mantissa_digits(unused_self: Option<Self>) -> uint; - /// Returns the number of base-10 digits of precision that this type supports. + /// Deprecated: use `std::f32::DIGITS` or `std::f64::DIGITS` instead. #[unstable(feature = "std_misc")] #[deprecated(since = "1.0.0", reason = "use `std::f32::DIGITS` or `std::f64::DIGITS` as appropriate")] fn digits(unused_self: Option<Self>) -> uint; - /// Returns the difference between 1.0 and the smallest representable number larger than 1.0. + /// Deprecated: use `std::f32::EPSILON` or `std::f64::EPSILON` instead. #[unstable(feature = "std_misc")] #[deprecated(since = "1.0.0", reason = "use `std::f32::EPSILON` or `std::f64::EPSILON` as appropriate")] fn epsilon() -> Self; - /// Returns the minimum binary exponent that this type can represent. + /// Deprecated: use `std::f32::MIN_EXP` or `std::f64::MIN_EXP` instead. #[unstable(feature = "std_misc")] #[deprecated(since = "1.0.0", reason = "use `std::f32::MIN_EXP` or `std::f64::MIN_EXP` as appropriate")] fn min_exp(unused_self: Option<Self>) -> int; - /// Returns the maximum binary exponent that this type can represent. + /// Deprecated: use `std::f32::MAX_EXP` or `std::f64::MAX_EXP` instead. #[unstable(feature = "std_misc")] #[deprecated(since = "1.0.0", reason = "use `std::f32::MAX_EXP` or `std::f64::MAX_EXP` as appropriate")] fn max_exp(unused_self: Option<Self>) -> int; - /// Returns the minimum base-10 exponent that this type can represent. + /// Deprecated: use `std::f32::MIN_10_EXP` or `std::f64::MIN_10_EXP` instead. #[unstable(feature = "std_misc")] #[deprecated(since = "1.0.0", reason = "use `std::f32::MIN_10_EXP` or `std::f64::MIN_10_EXP` as appropriate")] fn min_10_exp(unused_self: Option<Self>) -> int; - /// Returns the maximum base-10 exponent that this type can represent. + /// Deprecated: use `std::f32::MAX_10_EXP` or `std::f64::MAX_10_EXP` instead. #[unstable(feature = "std_misc")] #[deprecated(since = "1.0.0", reason = "use `std::f32::MAX_10_EXP` or `std::f64::MAX_10_EXP` as appropriate")] fn max_10_exp(unused_self: Option<Self>) -> int; /// Returns the smallest finite value that this type can represent. + /// + /// ``` + /// use std::num::Float; + /// use std::f64; + /// + /// let x: f64 = Float::min_value(); + /// + /// assert_eq!(x, f64::MIN); + /// ``` #[unstable(feature = "std_misc", reason = "unsure about its place in the world")] fn min_value() -> Self; @@ -124,50 +196,222 @@ pub trait Float reason = "unsure about its place in the world")] fn min_pos_value(unused_self: Option<Self>) -> Self; /// Returns the largest finite value that this type can represent. + /// + /// ``` + /// use std::num::Float; + /// use std::f64; + /// + /// let x: f64 = Float::max_value(); + /// assert_eq!(x, f64::MAX); + /// ``` #[unstable(feature = "std_misc", reason = "unsure about its place in the world")] fn max_value() -> Self; - - /// Returns true if this value is NaN and false otherwise. + /// Returns `true` if this value is `NaN` and false otherwise. + /// + /// ``` + /// use std::num::Float; + /// use std::f64; + /// + /// let nan = f64::NAN; + /// let f = 7.0; + /// + /// assert!(nan.is_nan()); + /// assert!(!f.is_nan()); + /// ``` #[unstable(feature = "std_misc", reason = "position is undecided")] fn is_nan(self) -> bool; - /// Returns true if this value is positive infinity or negative infinity and + /// Returns `true` if this value is positive infinity or negative infinity and /// false otherwise. + /// + /// ``` + /// use std::num::Float; + /// use std::f32; + /// + /// let f = 7.0f32; + /// let inf: f32 = Float::infinity(); + /// let neg_inf: f32 = Float::neg_infinity(); + /// let nan: f32 = f32::NAN; + /// + /// assert!(!f.is_infinite()); + /// assert!(!nan.is_infinite()); + /// + /// assert!(inf.is_infinite()); + /// assert!(neg_inf.is_infinite()); + /// ``` #[unstable(feature = "std_misc", reason = "position is undecided")] fn is_infinite(self) -> bool; - /// Returns true if this number is neither infinite nor NaN. + /// Returns `true` if this number is neither infinite nor `NaN`. + /// + /// ``` + /// use std::num::Float; + /// use std::f32; + /// + /// let f = 7.0f32; + /// let inf: f32 = Float::infinity(); + /// let neg_inf: f32 = Float::neg_infinity(); + /// let nan: f32 = f32::NAN; + /// + /// assert!(f.is_finite()); + /// + /// assert!(!nan.is_finite()); + /// assert!(!inf.is_finite()); + /// assert!(!neg_inf.is_finite()); + /// ``` #[unstable(feature = "std_misc", reason = "position is undecided")] fn is_finite(self) -> bool; - /// Returns true if this number is neither zero, infinite, denormal, or NaN. + /// Returns `true` if the number is neither zero, infinite, + /// [subnormal][subnormal], or `NaN`. + /// + /// ``` + /// use std::num::Float; + /// 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 = 0.0f32; + /// + /// 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]: http://en.wikipedia.org/wiki/Denormal_number #[unstable(feature = "std_misc", reason = "position is undecided")] fn is_normal(self) -> bool; - /// Returns the category that this number falls into. + + /// 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::{Float, FpCategory}; + /// use std::f32; + /// + /// let num = 12.4f32; + /// let inf = f32::INFINITY; + /// + /// assert_eq!(num.classify(), FpCategory::Normal); + /// assert_eq!(inf.classify(), FpCategory::Infinite); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn classify(self) -> FpCategory; - /// Returns the mantissa, exponent and sign as integers, respectively. + /// 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]. + /// + /// ``` + /// use std::num::Float; + /// + /// let num = 2.0f32; + /// + /// // (8388608u64, -22i16, 1i8) + /// let (mantissa, exponent, sign) = num.integer_decode(); + /// let sign_f = sign as f32; + /// let mantissa_f = mantissa as f32; + /// let exponent_f = num.powf(exponent as f32); + /// + /// // 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 #[unstable(feature = "std_misc", reason = "signature is undecided")] fn integer_decode(self) -> (u64, i16, i8); - /// Return the largest integer less than or equal to a number. + /// Returns the largest integer less than or equal to a number. + /// + /// ``` + /// use std::num::Float; + /// + /// let f = 3.99; + /// let g = 3.0; + /// + /// assert_eq!(f.floor(), 3.0); + /// assert_eq!(g.floor(), 3.0); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn floor(self) -> Self; - /// Return the smallest integer greater than or equal to a number. + /// Returns the smallest integer greater than or equal to a number. + /// + /// ``` + /// use std::num::Float; + /// + /// let f = 3.01; + /// let g = 4.0; + /// + /// assert_eq!(f.ceil(), 4.0); + /// assert_eq!(g.ceil(), 4.0); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn ceil(self) -> Self; - /// Return the nearest integer to a number. Round half-way cases away from + /// Returns the nearest integer to a number. Round half-way cases away from /// `0.0`. + /// + /// ``` + /// use std::num::Float; + /// + /// let f = 3.3; + /// let g = -3.3; + /// + /// assert_eq!(f.round(), 3.0); + /// assert_eq!(g.round(), -3.0); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn round(self) -> Self; /// Return the integer part of a number. + /// + /// ``` + /// use std::num::Float; + /// + /// let f = 3.3; + /// let g = -3.7; + /// + /// assert_eq!(f.trunc(), 3.0); + /// assert_eq!(g.trunc(), -3.0); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn trunc(self) -> Self; - /// Return the fractional part of a number. + /// Returns the fractional part of a number. + /// + /// ``` + /// use std::num::Float; + /// + /// let x = 3.5; + /// let y = -3.5; + /// let abs_difference_x = (x.fract() - 0.5).abs(); + /// let abs_difference_y = (y.fract() - (-0.5)).abs(); + /// + /// assert!(abs_difference_x < 1e-10); + /// assert!(abs_difference_y < 1e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn fract(self) -> Self; - /// Computes the absolute value of `self`. Returns `Float::nan()` if the /// number is `Float::nan()`. + /// + /// ``` + /// use std::num::Float; + /// use std::f64; + /// + /// let x = 3.5; + /// let y = -3.5; + /// + /// let abs_difference_x = (x.abs() - x).abs(); + /// let abs_difference_y = (y.abs() - (-y)).abs(); + /// + /// assert!(abs_difference_x < 1e-10); + /// assert!(abs_difference_y < 1e-10); + /// + /// assert!(f64::NAN.abs().is_nan()); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn abs(self) -> Self; /// Returns a number that represents the sign of `self`. @@ -175,24 +419,88 @@ pub trait Float /// - `1.0` if the number is positive, `+0.0` or `Float::infinity()` /// - `-1.0` if the number is negative, `-0.0` or `Float::neg_infinity()` /// - `Float::nan()` if the number is `Float::nan()` + /// + /// ``` + /// use std::num::Float; + /// use std::f64; + /// + /// let f = 3.5; + /// + /// assert_eq!(f.signum(), 1.0); + /// assert_eq!(f64::NEG_INFINITY.signum(), -1.0); + /// + /// assert!(f64::NAN.signum().is_nan()); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn signum(self) -> Self; /// Returns `true` if `self` is positive, including `+0.0` and /// `Float::infinity()`. + /// + /// ``` + /// use std::num::Float; + /// use std::f64; + /// + /// let nan: f64 = f64::NAN; + /// + /// let f = 7.0; + /// let g = -7.0; + /// + /// assert!(f.is_positive()); + /// assert!(!g.is_positive()); + /// // Requires both tests to determine if is `NaN` + /// assert!(!nan.is_positive() && !nan.is_negative()); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn is_positive(self) -> bool; /// Returns `true` if `self` is negative, including `-0.0` and /// `Float::neg_infinity()`. + /// + /// ``` + /// use std::num::Float; + /// use std::f64; + /// + /// let nan = f64::NAN; + /// + /// let f = 7.0; + /// let g = -7.0; + /// + /// assert!(!f.is_negative()); + /// assert!(g.is_negative()); + /// // Requires both tests to determine if is `NaN`. + /// assert!(!nan.is_positive() && !nan.is_negative()); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn is_negative(self) -> bool; /// 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::num::Float; + /// + /// let m = 10.0; + /// let x = 4.0; + /// let b = 60.0; + /// + /// // 100.0 + /// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[unstable(feature = "std_misc", reason = "unsure about its place in the world")] fn mul_add(self, a: Self, b: Self) -> Self; /// Take the reciprocal (inverse) of a number, `1/x`. + /// + /// ``` + /// use std::num::Float; + /// + /// let x = 2.0; + /// let abs_difference = (x.recip() - (1.0/x)).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[unstable(feature = "std_misc", reason = "unsure about its place in the world")] fn recip(self) -> Self; @@ -200,149 +508,576 @@ pub trait Float /// Raise a number to an integer power. /// /// Using this function is generally faster than using `powf` + /// + /// ``` + /// use std::num::Float; + /// + /// let x = 2.0; + /// let abs_difference = (x.powi(2) - x*x).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn powi(self, n: i32) -> Self; /// Raise a number to a floating point power. + /// + /// ``` + /// use std::num::Float; + /// + /// let x = 2.0; + /// let abs_difference = (x.powf(2.0) - x*x).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn powf(self, n: Self) -> Self; - /// Take the square root of a number. /// /// Returns NaN if `self` is a negative number. + /// + /// ``` + /// use std::num::Float; + /// + /// let positive = 4.0; + /// let negative = -4.0; + /// + /// let abs_difference = (positive.sqrt() - 2.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// assert!(negative.sqrt().is_nan()); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn sqrt(self) -> Self; + /// Take the reciprocal (inverse) square root of a number, `1/sqrt(x)`. + /// + /// ``` + /// use std::num::Float; + /// + /// let f = 4.0; + /// + /// let abs_difference = (f.rsqrt() - 0.5).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[unstable(feature = "std_misc", reason = "unsure about its place in the world")] fn rsqrt(self) -> Self; /// Returns `e^(self)`, (the exponential function). + /// + /// ``` + /// use std::num::Float; + /// + /// let one = 1.0; + /// // e^1 + /// let e = one.exp(); + /// + /// // ln(e) - 1 == 0 + /// let abs_difference = (e.ln() - 1.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn exp(self) -> Self; - /// Returns 2 raised to the power of the number, `2^(self)`. + /// Returns `2^(self)`. + /// + /// ``` + /// use std::num::Float; + /// + /// let f = 2.0; + /// + /// // 2^2 - 4 == 0 + /// let abs_difference = (f.exp2() - 4.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn exp2(self) -> Self; /// Returns the natural logarithm of the number. + /// + /// ``` + /// use std::num::Float; + /// + /// let one = 1.0; + /// // e^1 + /// let e = one.exp(); + /// + /// // ln(e) - 1 == 0 + /// let abs_difference = (e.ln() - 1.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn ln(self) -> Self; /// Returns the logarithm of the number with respect to an arbitrary base. + /// + /// ``` + /// use std::num::Float; + /// + /// let ten = 10.0; + /// let two = 2.0; + /// + /// // log10(10) - 1 == 0 + /// let abs_difference_10 = (ten.log(10.0) - 1.0).abs(); + /// + /// // log2(2) - 1 == 0 + /// let abs_difference_2 = (two.log(2.0) - 1.0).abs(); + /// + /// assert!(abs_difference_10 < 1e-10); + /// assert!(abs_difference_2 < 1e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn log(self, base: Self) -> Self; /// Returns the base 2 logarithm of the number. + /// + /// ``` + /// use std::num::Float; + /// + /// let two = 2.0; + /// + /// // log2(2) - 1 == 0 + /// let abs_difference = (two.log2() - 1.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn log2(self) -> Self; /// Returns the base 10 logarithm of the number. + /// + /// ``` + /// use std::num::Float; + /// + /// let ten = 10.0; + /// + /// // log10(10) - 1 == 0 + /// let abs_difference = (ten.log10() - 1.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn log10(self) -> Self; /// Convert radians to degrees. + /// + /// ``` + /// use std::num::Float; + /// use std::f64::consts; + /// + /// let angle = consts::PI; + /// + /// let abs_difference = (angle.to_degrees() - 180.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[unstable(feature = "std_misc", reason = "desirability is unclear")] fn to_degrees(self) -> Self; /// Convert degrees to radians. + /// + /// ``` + /// use std::num::Float; + /// use std::f64::consts; + /// + /// let angle = 180.0; + /// + /// let abs_difference = (angle.to_radians() - consts::PI).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[unstable(feature = "std_misc", reason = "desirability is unclear")] fn to_radians(self) -> Self; - - /// Constructs a floating point number created by multiplying `x` by 2 - /// raised to the power of `exp`. + /// Constructs a floating point number of `x*2^exp`. + /// + /// ``` + /// use std::num::Float; + /// + /// // 3*2^2 - 12 == 0 + /// let abs_difference = (Float::ldexp(3.0, 2) - 12.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[unstable(feature = "std_misc", reason = "pending integer conventions")] fn ldexp(x: Self, exp: int) -> Self; /// Breaks the number into a normalized fraction and a base-2 exponent, /// satisfying: /// - /// * `self = x * pow(2, exp)` - /// + /// * `self = x * 2^exp` /// * `0.5 <= abs(x) < 1.0` + /// + /// ``` + /// use std::num::Float; + /// + /// let x = 4.0; + /// + /// // (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); + /// ``` #[unstable(feature = "std_misc", reason = "pending integer conventions")] fn frexp(self) -> (Self, int); - /// Returns the next representable floating-point value in the direction of /// `other`. + /// + /// ``` + /// use std::num::Float; + /// + /// let x = 1.0f32; + /// + /// let abs_diff = (x.next_after(2.0) - 1.00000011920928955078125_f32).abs(); + /// + /// assert!(abs_diff < 1e-10); + /// ``` #[unstable(feature = "std_misc", reason = "unsure about its place in the world")] fn next_after(self, other: Self) -> Self; /// Returns the maximum of the two numbers. + /// + /// ``` + /// use std::num::Float; + /// + /// let x = 1.0; + /// let y = 2.0; + /// + /// assert_eq!(x.max(y), y); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn max(self, other: Self) -> Self; /// Returns the minimum of the two numbers. + /// + /// ``` + /// use std::num::Float; + /// + /// let x = 1.0; + /// let y = 2.0; + /// + /// assert_eq!(x.min(y), x); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn min(self, other: Self) -> Self; - /// The positive difference of two numbers. Returns `0.0` if the number is - /// less than or equal to `other`, otherwise the difference between`self` - /// and `other` is returned. + /// The positive difference of two numbers. + /// + /// * If `self <= other`: `0:0` + /// * Else: `self - other` + /// + /// ``` + /// use std::num::Float; + /// + /// let x = 3.0; + /// let y = -3.0; + /// + /// 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); + /// ``` #[unstable(feature = "std_misc", reason = "may be renamed")] fn abs_sub(self, other: Self) -> Self; - /// Take the cubic root of a number. + /// + /// ``` + /// use std::num::Float; + /// + /// let x = 8.0; + /// + /// // x^(1/3) - 2 == 0 + /// let abs_difference = (x.cbrt() - 2.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[unstable(feature = "std_misc", reason = "may be renamed")] fn cbrt(self) -> Self; /// Calculate the length of the hypotenuse of a right-angle triangle given /// legs of length `x` and `y`. + /// + /// ``` + /// use std::num::Float; + /// + /// let x = 2.0; + /// let y = 3.0; + /// + /// // sqrt(x^2 + y^2) + /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[unstable(feature = "std_misc", reason = "unsure about its place in the world")] fn hypot(self, other: Self) -> Self; /// Computes the sine of a number (in radians). + /// + /// ``` + /// use std::num::Float; + /// use std::f64; + /// + /// let x = f64::consts::PI/2.0; + /// + /// let abs_difference = (x.sin() - 1.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn sin(self) -> Self; /// Computes the cosine of a number (in radians). + /// + /// ``` + /// use std::num::Float; + /// use std::f64; + /// + /// let x = 2.0*f64::consts::PI; + /// + /// let abs_difference = (x.cos() - 1.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn cos(self) -> Self; /// Computes the tangent of a number (in radians). + /// + /// ``` + /// use std::num::Float; + /// use std::f64; + /// + /// let x = f64::consts::PI/4.0; + /// let abs_difference = (x.tan() - 1.0).abs(); + /// + /// assert!(abs_difference < 1e-14); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn tan(self) -> 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::num::Float; + /// use std::f64; + /// + /// let f = f64::consts::PI / 2.0; + /// + /// // asin(sin(pi/2)) + /// let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn asin(self) -> 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::num::Float; + /// use std::f64; + /// + /// let f = f64::consts::PI / 4.0; + /// + /// // acos(cos(pi/4)) + /// let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn acos(self) -> Self; /// Computes the arctangent of a number. Return value is in radians in the /// range [-pi/2, pi/2]; + /// + /// ``` + /// use std::num::Float; + /// + /// let f = 1.0; + /// + /// // atan(tan(1)) + /// let abs_difference = (f.tan().atan() - 1.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn atan(self) -> Self; - /// Computes the four quadrant arctangent of a number, `y`, and another - /// number `x`. Return value is in radians in the range [-pi, pi]. + /// 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::num::Float; + /// use std::f64; + /// + /// let pi = f64::consts::PI; + /// // All angles from horizontal right (+x) + /// // 45 deg counter-clockwise + /// let x1 = 3.0; + /// let y1 = -3.0; + /// + /// // 135 deg clockwise + /// let x2 = -3.0; + /// let y2 = 3.0; + /// + /// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs(); + /// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs(); + /// + /// assert!(abs_difference_1 < 1e-10); + /// assert!(abs_difference_2 < 1e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn atan2(self, other: Self) -> Self; /// Simultaneously computes the sine and cosine of the number, `x`. Returns /// `(sin(x), cos(x))`. + /// + /// ``` + /// use std::num::Float; + /// 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_0 < 1e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn sin_cos(self) -> (Self, Self); - /// Returns the exponential of the number, minus 1, in a way that is - /// accurate even if the number is close to zero. + /// Returns `e^(self) - 1` in a way that is accurate even if the + /// number is close to zero. + /// + /// ``` + /// use std::num::Float; + /// + /// let x = 7.0; + /// + /// // e^(ln(7)) - 1 + /// let abs_difference = (x.ln().exp_m1() - 6.0).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[unstable(feature = "std_misc", reason = "may be renamed")] fn exp_m1(self) -> Self; - /// Returns the natural logarithm of the number plus 1 (`ln(1+n)`) more - /// accurately than if the operations were performed separately. + /// Returns `ln(1+n)` (natural logarithm) more accurately than if + /// the operations were performed separately. + /// + /// ``` + /// use std::num::Float; + /// 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); + /// ``` #[unstable(feature = "std_misc", reason = "may be renamed")] fn ln_1p(self) -> Self; /// Hyperbolic sine function. + /// + /// ``` + /// use std::num::Float; + /// use std::f64; + /// + /// let e = f64::consts::E; + /// let x = 1.0; + /// + /// let f = x.sinh(); + /// // Solving sinh() at 1 gives `(e^2-1)/(2e)` + /// let g = (e*e - 1.0)/(2.0*e); + /// let abs_difference = (f - g).abs(); + /// + /// assert!(abs_difference < 1e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn sinh(self) -> Self; /// Hyperbolic cosine function. + /// + /// ``` + /// use std::num::Float; + /// use std::f64; + /// + /// let e = f64::consts::E; + /// let x = 1.0; + /// let f = x.cosh(); + /// // Solving cosh() at 1 gives this result + /// let g = (e*e + 1.0)/(2.0*e); + /// let abs_difference = (f - g).abs(); + /// + /// // Same result + /// assert!(abs_difference < 1.0e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn cosh(self) -> Self; /// Hyperbolic tangent function. + /// + /// ``` + /// use std::num::Float; + /// use std::f64; + /// + /// let e = f64::consts::E; + /// let x = 1.0; + /// + /// let f = x.tanh(); + /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))` + /// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2)); + /// let abs_difference = (f - g).abs(); + /// + /// assert!(abs_difference < 1.0e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn tanh(self) -> Self; /// Inverse hyperbolic sine function. + /// + /// ``` + /// use std::num::Float; + /// + /// let x = 1.0; + /// let f = x.sinh().asinh(); + /// + /// let abs_difference = (f - x).abs(); + /// + /// assert!(abs_difference < 1.0e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn asinh(self) -> Self; /// Inverse hyperbolic cosine function. + /// + /// ``` + /// use std::num::Float; + /// + /// let x = 1.0; + /// let f = x.cosh().acosh(); + /// + /// let abs_difference = (f - x).abs(); + /// + /// assert!(abs_difference < 1.0e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn acosh(self) -> Self; /// Inverse hyperbolic tangent function. + /// + /// ``` + /// use std::num::Float; + /// use std::f64; + /// + /// let e = f64::consts::E; + /// let f = e.tanh().atanh(); + /// + /// let abs_difference = (f - e).abs(); + /// + /// assert!(abs_difference < 1.0e-10); + /// ``` #[stable(feature = "rust1", since = "1.0.0")] fn atanh(self) -> Self; } |