// Copyright 2012-2014 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. //! Numeric traits and functions for generic mathematics //! //! These are implemented for the primitive numeric types in `std::{u8, u16, //! u32, u64, usize, i8, i16, i32, i64, isize, f32, f64}`. #![stable(feature = "rust1", since = "1.0.0")] #![allow(missing_docs)] #![allow(deprecated)] #[cfg(test)] use fmt::Debug; use ops::{Add, Sub, Mul, Div, Rem, Neg}; use marker::Copy; use clone::Clone; use cmp::{PartialOrd, PartialEq}; pub use core::num::{Int, SignedInt, Zero, One}; pub use core::num::{cast, FromPrimitive, NumCast, ToPrimitive}; pub use core::num::{from_int, from_i8, from_i16, from_i32, from_i64}; pub use core::num::{from_uint, from_u8, from_u16, from_u32, from_u64}; pub use core::num::{from_f32, from_f64}; pub use core::num::{FromStrRadix, from_str_radix}; pub use core::num::{FpCategory, ParseIntError, ParseFloatError}; pub use core::num::{wrapping, Wrapping}; use option::Option; #[unstable(feature = "std_misc", reason = "likely to be removed")] pub mod strconv; /// Mathematical operations on primitive floating point numbers. #[stable(feature = "rust1", since = "1.0.0")] #[deprecated(since = "1.0.0", reason = "replaced by inherent methods; use rust-lang/num for generics")] pub trait Float : Copy + Clone + NumCast + PartialOrd + PartialEq + Neg + Add + Sub + Mul + Div + Rem { // inlined methods from `num::Float` /// Returns the `NaN` value. /// /// ``` /// # #![feature(std_misc)] /// 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. /// /// ``` /// # #![feature(std_misc)] /// 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. /// /// ``` /// # #![feature(std_misc)] /// 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 `0.0`. /// /// ``` /// # #![feature(std_misc)] /// 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`. /// /// ``` /// # #![feature(std_misc)] /// 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 `1.0`. /// /// ``` /// # #![feature(std_misc)] /// 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 /// 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) -> usize; /// 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) -> usize; /// 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; /// 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) -> isize; /// 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) -> isize; /// 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) -> isize; /// 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) -> isize; /// Returns the smallest finite value that this type can represent. /// /// ``` /// # #![feature(std_misc)] /// 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; /// Returns the smallest normalized positive number that this type can represent. #[unstable(feature = "std_misc", reason = "unsure about its place in the world")] fn min_pos_value(unused_self: Option) -> Self; /// Returns the largest finite value that this type can represent. /// /// ``` /// # #![feature(std_misc)] /// 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. /// /// ``` /// # #![feature(std_misc)] /// 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 /// false otherwise. /// /// ``` /// # #![feature(std_misc)] /// 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`. /// /// ``` /// # #![feature(std_misc)] /// 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 the number is neither zero, infinite, /// [subnormal][subnormal], or `NaN`. /// /// ``` /// # #![feature(std_misc)] /// 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 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. /// /// ``` /// # #![feature(core)] /// 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, 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(std_misc)] /// use std::num::Float; /// /// let num = 2.0f32; /// /// // (8388608, -22, 1) /// 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); /// 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; /// 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; /// 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; /// 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()`. /// /// ``` /// # #![feature(std_misc)] /// 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`. /// /// - `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()` /// /// ``` /// # #![feature(std_misc)] /// 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. /// /// ``` /// # #![feature(std_misc)] /// 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`. /// /// ``` /// # #![feature(std_misc)] /// 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; /// 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. /// /// ``` /// # #![feature(std_misc)] /// 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)`. /// /// ``` /// # #![feature(std_misc)] /// 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^(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. /// /// ``` /// # #![feature(std_misc, core)] /// 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. /// /// ``` /// # #![feature(std_misc, core)] /// 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 of `x*2^exp`. /// /// ``` /// # #![feature(std_misc)] /// 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(self, exp: isize) -> Self; /// Breaks the number into a normalized fraction and a base-2 exponent, /// satisfying: /// /// * `self = x * 2^exp` /// * `0.5 <= abs(x) < 1.0` /// /// ``` /// # #![feature(std_misc)] /// 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, isize); /// Returns the next representable floating-point value in the direction of /// `other`. /// /// ``` /// # #![feature(std_misc)] /// 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. /// /// * If `self <= other`: `0:0` /// * Else: `self - other` /// /// ``` /// # #![feature(std_misc)] /// 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. /// /// ``` /// # #![feature(std_misc)] /// 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`. /// /// ``` /// # #![feature(std_misc)] /// 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). /// /// ``` /// # #![feature(core)] /// 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). /// /// ``` /// # #![feature(core)] /// 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). /// /// ``` /// # #![feature(core)] /// 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]. /// /// ``` /// # #![feature(core)] /// 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]. /// /// ``` /// # #![feature(core)] /// 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 `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)` /// /// ``` /// # #![feature(core)] /// 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))`. /// /// ``` /// # #![feature(core)] /// 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 `e^(self) - 1` in a way that is accurate even if the /// number is close to zero. /// /// ``` /// # #![feature(std_misc)] /// 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 `ln(1+n)` (natural logarithm) more accurately than if /// the operations were performed separately. /// /// ``` /// # #![feature(std_misc, core)] /// 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. /// /// ``` /// # #![feature(core)] /// 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. /// /// ``` /// # #![feature(core)] /// 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. /// /// ``` /// # #![feature(core)] /// 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. /// /// ``` /// # #![feature(core)] /// 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; } /// Helper function for testing numeric operations #[cfg(test)] pub fn test_num(ten: T, two: T) where T: PartialEq + NumCast + Add + Sub + Mul + Div + Rem + Debug + Copy { assert_eq!(ten.add(two), cast(12).unwrap()); assert_eq!(ten.sub(two), cast(8).unwrap()); assert_eq!(ten.mul(two), cast(20).unwrap()); assert_eq!(ten.div(two), cast(5).unwrap()); assert_eq!(ten.rem(two), cast(0).unwrap()); assert_eq!(ten.add(two), ten + two); assert_eq!(ten.sub(two), ten - two); assert_eq!(ten.mul(two), ten * two); assert_eq!(ten.div(two), ten / two); assert_eq!(ten.rem(two), ten % two); } #[cfg(test)] mod tests { use core::prelude::*; use super::*; use i8; use i16; use i32; use i64; use isize; use u8; use u16; use u32; use u64; use usize; use string::ToString; macro_rules! test_cast_20 { ($_20:expr) => ({ let _20 = $_20; assert_eq!(20usize, _20.to_uint().unwrap()); assert_eq!(20u8, _20.to_u8().unwrap()); assert_eq!(20u16, _20.to_u16().unwrap()); assert_eq!(20u32, _20.to_u32().unwrap()); assert_eq!(20u64, _20.to_u64().unwrap()); assert_eq!(20, _20.to_int().unwrap()); assert_eq!(20i8, _20.to_i8().unwrap()); assert_eq!(20i16, _20.to_i16().unwrap()); assert_eq!(20i32, _20.to_i32().unwrap()); assert_eq!(20i64, _20.to_i64().unwrap()); assert_eq!(20f32, _20.to_f32().unwrap()); assert_eq!(20f64, _20.to_f64().unwrap()); assert_eq!(_20, NumCast::from(20usize).unwrap()); assert_eq!(_20, NumCast::from(20u8).unwrap()); assert_eq!(_20, NumCast::from(20u16).unwrap()); assert_eq!(_20, NumCast::from(20u32).unwrap()); assert_eq!(_20, NumCast::from(20u64).unwrap()); assert_eq!(_20, NumCast::from(20).unwrap()); assert_eq!(_20, NumCast::from(20i8).unwrap()); assert_eq!(_20, NumCast::from(20i16).unwrap()); assert_eq!(_20, NumCast::from(20i32).unwrap()); assert_eq!(_20, NumCast::from(20i64).unwrap()); assert_eq!(_20, NumCast::from(20f32).unwrap()); assert_eq!(_20, NumCast::from(20f64).unwrap()); assert_eq!(_20, cast(20usize).unwrap()); assert_eq!(_20, cast(20u8).unwrap()); assert_eq!(_20, cast(20u16).unwrap()); assert_eq!(_20, cast(20u32).unwrap()); assert_eq!(_20, cast(20u64).unwrap()); assert_eq!(_20, cast(20).unwrap()); assert_eq!(_20, cast(20i8).unwrap()); assert_eq!(_20, cast(20i16).unwrap()); assert_eq!(_20, cast(20i32).unwrap()); assert_eq!(_20, cast(20i64).unwrap()); assert_eq!(_20, cast(20f32).unwrap()); assert_eq!(_20, cast(20f64).unwrap()); }) } #[test] fn test_u8_cast() { test_cast_20!(20u8) } #[test] fn test_u16_cast() { test_cast_20!(20u16) } #[test] fn test_u32_cast() { test_cast_20!(20u32) } #[test] fn test_u64_cast() { test_cast_20!(20u64) } #[test] fn test_uint_cast() { test_cast_20!(20usize) } #[test] fn test_i8_cast() { test_cast_20!(20i8) } #[test] fn test_i16_cast() { test_cast_20!(20i16) } #[test] fn test_i32_cast() { test_cast_20!(20i32) } #[test] fn test_i64_cast() { test_cast_20!(20i64) } #[test] fn test_int_cast() { test_cast_20!(20) } #[test] fn test_f32_cast() { test_cast_20!(20f32) } #[test] fn test_f64_cast() { test_cast_20!(20f64) } #[test] fn test_cast_range_int_min() { assert_eq!(isize::MIN.to_int(), Some(isize::MIN as isize)); assert_eq!(isize::MIN.to_i8(), None); assert_eq!(isize::MIN.to_i16(), None); // isize::MIN.to_i32() is word-size specific assert_eq!(isize::MIN.to_i64(), Some(isize::MIN as i64)); assert_eq!(isize::MIN.to_uint(), None); assert_eq!(isize::MIN.to_u8(), None); assert_eq!(isize::MIN.to_u16(), None); assert_eq!(isize::MIN.to_u32(), None); assert_eq!(isize::MIN.to_u64(), None); #[cfg(target_pointer_width = "32")] fn check_word_size() { assert_eq!(isize::MIN.to_i32(), Some(isize::MIN as i32)); } #[cfg(target_pointer_width = "64")] fn check_word_size() { assert_eq!(isize::MIN.to_i32(), None); } check_word_size(); } #[test] fn test_cast_range_i8_min() { assert_eq!(i8::MIN.to_int(), Some(i8::MIN as isize)); assert_eq!(i8::MIN.to_i8(), Some(i8::MIN as i8)); assert_eq!(i8::MIN.to_i16(), Some(i8::MIN as i16)); assert_eq!(i8::MIN.to_i32(), Some(i8::MIN as i32)); assert_eq!(i8::MIN.to_i64(), Some(i8::MIN as i64)); assert_eq!(i8::MIN.to_uint(), None); assert_eq!(i8::MIN.to_u8(), None); assert_eq!(i8::MIN.to_u16(), None); assert_eq!(i8::MIN.to_u32(), None); assert_eq!(i8::MIN.to_u64(), None); } #[test] fn test_cast_range_i16_min() { assert_eq!(i16::MIN.to_int(), Some(i16::MIN as isize)); assert_eq!(i16::MIN.to_i8(), None); assert_eq!(i16::MIN.to_i16(), Some(i16::MIN as i16)); assert_eq!(i16::MIN.to_i32(), Some(i16::MIN as i32)); assert_eq!(i16::MIN.to_i64(), Some(i16::MIN as i64)); assert_eq!(i16::MIN.to_uint(), None); assert_eq!(i16::MIN.to_u8(), None); assert_eq!(i16::MIN.to_u16(), None); assert_eq!(i16::MIN.to_u32(), None); assert_eq!(i16::MIN.to_u64(), None); } #[test] fn test_cast_range_i32_min() { assert_eq!(i32::MIN.to_int(), Some(i32::MIN as isize)); assert_eq!(i32::MIN.to_i8(), None); assert_eq!(i32::MIN.to_i16(), None); assert_eq!(i32::MIN.to_i32(), Some(i32::MIN as i32)); assert_eq!(i32::MIN.to_i64(), Some(i32::MIN as i64)); assert_eq!(i32::MIN.to_uint(), None); assert_eq!(i32::MIN.to_u8(), None); assert_eq!(i32::MIN.to_u16(), None); assert_eq!(i32::MIN.to_u32(), None); assert_eq!(i32::MIN.to_u64(), None); } #[test] fn test_cast_range_i64_min() { // i64::MIN.to_int() is word-size specific assert_eq!(i64::MIN.to_i8(), None); assert_eq!(i64::MIN.to_i16(), None); assert_eq!(i64::MIN.to_i32(), None); assert_eq!(i64::MIN.to_i64(), Some(i64::MIN as i64)); assert_eq!(i64::MIN.to_uint(), None); assert_eq!(i64::MIN.to_u8(), None); assert_eq!(i64::MIN.to_u16(), None); assert_eq!(i64::MIN.to_u32(), None); assert_eq!(i64::MIN.to_u64(), None); #[cfg(target_pointer_width = "32")] fn check_word_size() { assert_eq!(i64::MIN.to_int(), None); } #[cfg(target_pointer_width = "64")] fn check_word_size() { assert_eq!(i64::MIN.to_int(), Some(i64::MIN as isize)); } check_word_size(); } #[test] fn test_cast_range_int_max() { assert_eq!(isize::MAX.to_int(), Some(isize::MAX as isize)); assert_eq!(isize::MAX.to_i8(), None); assert_eq!(isize::MAX.to_i16(), None); // isize::MAX.to_i32() is word-size specific assert_eq!(isize::MAX.to_i64(), Some(isize::MAX as i64)); assert_eq!(isize::MAX.to_u8(), None); assert_eq!(isize::MAX.to_u16(), None); // isize::MAX.to_u32() is word-size specific assert_eq!(isize::MAX.to_u64(), Some(isize::MAX as u64)); #[cfg(target_pointer_width = "32")] fn check_word_size() { assert_eq!(isize::MAX.to_i32(), Some(isize::MAX as i32)); assert_eq!(isize::MAX.to_u32(), Some(isize::MAX as u32)); } #[cfg(target_pointer_width = "64")] fn check_word_size() { assert_eq!(isize::MAX.to_i32(), None); assert_eq!(isize::MAX.to_u32(), None); } check_word_size(); } #[test] fn test_cast_range_i8_max() { assert_eq!(i8::MAX.to_int(), Some(i8::MAX as isize)); assert_eq!(i8::MAX.to_i8(), Some(i8::MAX as i8)); assert_eq!(i8::MAX.to_i16(), Some(i8::MAX as i16)); assert_eq!(i8::MAX.to_i32(), Some(i8::MAX as i32)); assert_eq!(i8::MAX.to_i64(), Some(i8::MAX as i64)); assert_eq!(i8::MAX.to_uint(), Some(i8::MAX as usize)); assert_eq!(i8::MAX.to_u8(), Some(i8::MAX as u8)); assert_eq!(i8::MAX.to_u16(), Some(i8::MAX as u16)); assert_eq!(i8::MAX.to_u32(), Some(i8::MAX as u32)); assert_eq!(i8::MAX.to_u64(), Some(i8::MAX as u64)); } #[test] fn test_cast_range_i16_max() { assert_eq!(i16::MAX.to_int(), Some(i16::MAX as isize)); assert_eq!(i16::MAX.to_i8(), None); assert_eq!(i16::MAX.to_i16(), Some(i16::MAX as i16)); assert_eq!(i16::MAX.to_i32(), Some(i16::MAX as i32)); assert_eq!(i16::MAX.to_i64(), Some(i16::MAX as i64)); assert_eq!(i16::MAX.to_uint(), Some(i16::MAX as usize)); assert_eq!(i16::MAX.to_u8(), None); assert_eq!(i16::MAX.to_u16(), Some(i16::MAX as u16)); assert_eq!(i16::MAX.to_u32(), Some(i16::MAX as u32)); assert_eq!(i16::MAX.to_u64(), Some(i16::MAX as u64)); } #[test] fn test_cast_range_i32_max() { assert_eq!(i32::MAX.to_int(), Some(i32::MAX as isize)); assert_eq!(i32::MAX.to_i8(), None); assert_eq!(i32::MAX.to_i16(), None); assert_eq!(i32::MAX.to_i32(), Some(i32::MAX as i32)); assert_eq!(i32::MAX.to_i64(), Some(i32::MAX as i64)); assert_eq!(i32::MAX.to_uint(), Some(i32::MAX as usize)); assert_eq!(i32::MAX.to_u8(), None); assert_eq!(i32::MAX.to_u16(), None); assert_eq!(i32::MAX.to_u32(), Some(i32::MAX as u32)); assert_eq!(i32::MAX.to_u64(), Some(i32::MAX as u64)); } #[test] fn test_cast_range_i64_max() { // i64::MAX.to_int() is word-size specific assert_eq!(i64::MAX.to_i8(), None); assert_eq!(i64::MAX.to_i16(), None); assert_eq!(i64::MAX.to_i32(), None); assert_eq!(i64::MAX.to_i64(), Some(i64::MAX as i64)); // i64::MAX.to_uint() is word-size specific assert_eq!(i64::MAX.to_u8(), None); assert_eq!(i64::MAX.to_u16(), None); assert_eq!(i64::MAX.to_u32(), None); assert_eq!(i64::MAX.to_u64(), Some(i64::MAX as u64)); #[cfg(target_pointer_width = "32")] fn check_word_size() { assert_eq!(i64::MAX.to_int(), None); assert_eq!(i64::MAX.to_uint(), None); } #[cfg(target_pointer_width = "64")] fn check_word_size() { assert_eq!(i64::MAX.to_int(), Some(i64::MAX as isize)); assert_eq!(i64::MAX.to_uint(), Some(i64::MAX as usize)); } check_word_size(); } #[test] fn test_cast_range_uint_min() { assert_eq!(usize::MIN.to_int(), Some(usize::MIN as isize)); assert_eq!(usize::MIN.to_i8(), Some(usize::MIN as i8)); assert_eq!(usize::MIN.to_i16(), Some(usize::MIN as i16)); assert_eq!(usize::MIN.to_i32(), Some(usize::MIN as i32)); assert_eq!(usize::MIN.to_i64(), Some(usize::MIN as i64)); assert_eq!(usize::MIN.to_uint(), Some(usize::MIN as usize)); assert_eq!(usize::MIN.to_u8(), Some(usize::MIN as u8)); assert_eq!(usize::MIN.to_u16(), Some(usize::MIN as u16)); assert_eq!(usize::MIN.to_u32(), Some(usize::MIN as u32)); assert_eq!(usize::MIN.to_u64(), Some(usize::MIN as u64)); } #[test] fn test_cast_range_u8_min() { assert_eq!(u8::MIN.to_int(), Some(u8::MIN as isize)); assert_eq!(u8::MIN.to_i8(), Some(u8::MIN as i8)); assert_eq!(u8::MIN.to_i16(), Some(u8::MIN as i16)); assert_eq!(u8::MIN.to_i32(), Some(u8::MIN as i32)); assert_eq!(u8::MIN.to_i64(), Some(u8::MIN as i64)); assert_eq!(u8::MIN.to_uint(), Some(u8::MIN as usize)); assert_eq!(u8::MIN.to_u8(), Some(u8::MIN as u8)); assert_eq!(u8::MIN.to_u16(), Some(u8::MIN as u16)); assert_eq!(u8::MIN.to_u32(), Some(u8::MIN as u32)); assert_eq!(u8::MIN.to_u64(), Some(u8::MIN as u64)); } #[test] fn test_cast_range_u16_min() { assert_eq!(u16::MIN.to_int(), Some(u16::MIN as isize)); assert_eq!(u16::MIN.to_i8(), Some(u16::MIN as i8)); assert_eq!(u16::MIN.to_i16(), Some(u16::MIN as i16)); assert_eq!(u16::MIN.to_i32(), Some(u16::MIN as i32)); assert_eq!(u16::MIN.to_i64(), Some(u16::MIN as i64)); assert_eq!(u16::MIN.to_uint(), Some(u16::MIN as usize)); assert_eq!(u16::MIN.to_u8(), Some(u16::MIN as u8)); assert_eq!(u16::MIN.to_u16(), Some(u16::MIN as u16)); assert_eq!(u16::MIN.to_u32(), Some(u16::MIN as u32)); assert_eq!(u16::MIN.to_u64(), Some(u16::MIN as u64)); } #[test] fn test_cast_range_u32_min() { assert_eq!(u32::MIN.to_int(), Some(u32::MIN as isize)); assert_eq!(u32::MIN.to_i8(), Some(u32::MIN as i8)); assert_eq!(u32::MIN.to_i16(), Some(u32::MIN as i16)); assert_eq!(u32::MIN.to_i32(), Some(u32::MIN as i32)); assert_eq!(u32::MIN.to_i64(), Some(u32::MIN as i64)); assert_eq!(u32::MIN.to_uint(), Some(u32::MIN as usize)); assert_eq!(u32::MIN.to_u8(), Some(u32::MIN as u8)); assert_eq!(u32::MIN.to_u16(), Some(u32::MIN as u16)); assert_eq!(u32::MIN.to_u32(), Some(u32::MIN as u32)); assert_eq!(u32::MIN.to_u64(), Some(u32::MIN as u64)); } #[test] fn test_cast_range_u64_min() { assert_eq!(u64::MIN.to_int(), Some(u64::MIN as isize)); assert_eq!(u64::MIN.to_i8(), Some(u64::MIN as i8)); assert_eq!(u64::MIN.to_i16(), Some(u64::MIN as i16)); assert_eq!(u64::MIN.to_i32(), Some(u64::MIN as i32)); assert_eq!(u64::MIN.to_i64(), Some(u64::MIN as i64)); assert_eq!(u64::MIN.to_uint(), Some(u64::MIN as usize)); assert_eq!(u64::MIN.to_u8(), Some(u64::MIN as u8)); assert_eq!(u64::MIN.to_u16(), Some(u64::MIN as u16)); assert_eq!(u64::MIN.to_u32(), Some(u64::MIN as u32)); assert_eq!(u64::MIN.to_u64(), Some(u64::MIN as u64)); } #[test] fn test_cast_range_uint_max() { assert_eq!(usize::MAX.to_int(), None); assert_eq!(usize::MAX.to_i8(), None); assert_eq!(usize::MAX.to_i16(), None); assert_eq!(usize::MAX.to_i32(), None); // usize::MAX.to_i64() is word-size specific assert_eq!(usize::MAX.to_u8(), None); assert_eq!(usize::MAX.to_u16(), None); // usize::MAX.to_u32() is word-size specific assert_eq!(usize::MAX.to_u64(), Some(usize::MAX as u64)); #[cfg(target_pointer_width = "32")] fn check_word_size() { assert_eq!(usize::MAX.to_u32(), Some(usize::MAX as u32)); assert_eq!(usize::MAX.to_i64(), Some(usize::MAX as i64)); } #[cfg(target_pointer_width = "64")] fn check_word_size() { assert_eq!(usize::MAX.to_u32(), None); assert_eq!(usize::MAX.to_i64(), None); } check_word_size(); } #[test] fn test_cast_range_u8_max() { assert_eq!(u8::MAX.to_int(), Some(u8::MAX as isize)); assert_eq!(u8::MAX.to_i8(), None); assert_eq!(u8::MAX.to_i16(), Some(u8::MAX as i16)); assert_eq!(u8::MAX.to_i32(), Some(u8::MAX as i32)); assert_eq!(u8::MAX.to_i64(), Some(u8::MAX as i64)); assert_eq!(u8::MAX.to_uint(), Some(u8::MAX as usize)); assert_eq!(u8::MAX.to_u8(), Some(u8::MAX as u8)); assert_eq!(u8::MAX.to_u16(), Some(u8::MAX as u16)); assert_eq!(u8::MAX.to_u32(), Some(u8::MAX as u32)); assert_eq!(u8::MAX.to_u64(), Some(u8::MAX as u64)); } #[test] fn test_cast_range_u16_max() { assert_eq!(u16::MAX.to_int(), Some(u16::MAX as isize)); assert_eq!(u16::MAX.to_i8(), None); assert_eq!(u16::MAX.to_i16(), None); assert_eq!(u16::MAX.to_i32(), Some(u16::MAX as i32)); assert_eq!(u16::MAX.to_i64(), Some(u16::MAX as i64)); assert_eq!(u16::MAX.to_uint(), Some(u16::MAX as usize)); assert_eq!(u16::MAX.to_u8(), None); assert_eq!(u16::MAX.to_u16(), Some(u16::MAX as u16)); assert_eq!(u16::MAX.to_u32(), Some(u16::MAX as u32)); assert_eq!(u16::MAX.to_u64(), Some(u16::MAX as u64)); } #[test] fn test_cast_range_u32_max() { // u32::MAX.to_int() is word-size specific assert_eq!(u32::MAX.to_i8(), None); assert_eq!(u32::MAX.to_i16(), None); assert_eq!(u32::MAX.to_i32(), None); assert_eq!(u32::MAX.to_i64(), Some(u32::MAX as i64)); assert_eq!(u32::MAX.to_uint(), Some(u32::MAX as usize)); assert_eq!(u32::MAX.to_u8(), None); assert_eq!(u32::MAX.to_u16(), None); assert_eq!(u32::MAX.to_u32(), Some(u32::MAX as u32)); assert_eq!(u32::MAX.to_u64(), Some(u32::MAX as u64)); #[cfg(target_pointer_width = "32")] fn check_word_size() { assert_eq!(u32::MAX.to_int(), None); } #[cfg(target_pointer_width = "64")] fn check_word_size() { assert_eq!(u32::MAX.to_int(), Some(u32::MAX as isize)); } check_word_size(); } #[test] fn test_cast_range_u64_max() { assert_eq!(u64::MAX.to_int(), None); assert_eq!(u64::MAX.to_i8(), None); assert_eq!(u64::MAX.to_i16(), None); assert_eq!(u64::MAX.to_i32(), None); assert_eq!(u64::MAX.to_i64(), None); // u64::MAX.to_uint() is word-size specific assert_eq!(u64::MAX.to_u8(), None); assert_eq!(u64::MAX.to_u16(), None); assert_eq!(u64::MAX.to_u32(), None); assert_eq!(u64::MAX.to_u64(), Some(u64::MAX as u64)); #[cfg(target_pointer_width = "32")] fn check_word_size() { assert_eq!(u64::MAX.to_uint(), None); } #[cfg(target_pointer_width = "64")] fn check_word_size() { assert_eq!(u64::MAX.to_uint(), Some(u64::MAX as usize)); } check_word_size(); } #[test] fn test_saturating_add_uint() { use usize::MAX; assert_eq!(3_usize.saturating_add(5_usize), 8_usize); assert_eq!(3_usize.saturating_add(MAX-1), MAX); assert_eq!(MAX.saturating_add(MAX), MAX); assert_eq!((MAX-2).saturating_add(1), MAX-1); } #[test] fn test_saturating_sub_uint() { use usize::MAX; assert_eq!(5_usize.saturating_sub(3_usize), 2_usize); assert_eq!(3_usize.saturating_sub(5_usize), 0_usize); assert_eq!(0_usize.saturating_sub(1_usize), 0_usize); assert_eq!((MAX-1).saturating_sub(MAX), 0); } #[test] fn test_saturating_add_int() { use isize::{MIN,MAX}; assert_eq!(3.saturating_add(5), 8); assert_eq!(3.saturating_add(MAX-1), MAX); assert_eq!(MAX.saturating_add(MAX), MAX); assert_eq!((MAX-2).saturating_add(1), MAX-1); assert_eq!(3.saturating_add(-5), -2); assert_eq!(MIN.saturating_add(-1), MIN); assert_eq!((-2).saturating_add(-MAX), MIN); } #[test] fn test_saturating_sub_int() { use isize::{MIN,MAX}; assert_eq!(3.saturating_sub(5), -2); assert_eq!(MIN.saturating_sub(1), MIN); assert_eq!((-2).saturating_sub(MAX), MIN); assert_eq!(3.saturating_sub(-5), 8); assert_eq!(3.saturating_sub(-(MAX-1)), MAX); assert_eq!(MAX.saturating_sub(-MAX), MAX); assert_eq!((MAX-2).saturating_sub(-1), MAX-1); } #[test] fn test_checked_add() { let five_less = usize::MAX - 5; assert_eq!(five_less.checked_add(0), Some(usize::MAX - 5)); assert_eq!(five_less.checked_add(1), Some(usize::MAX - 4)); assert_eq!(five_less.checked_add(2), Some(usize::MAX - 3)); assert_eq!(five_less.checked_add(3), Some(usize::MAX - 2)); assert_eq!(five_less.checked_add(4), Some(usize::MAX - 1)); assert_eq!(five_less.checked_add(5), Some(usize::MAX)); assert_eq!(five_less.checked_add(6), None); assert_eq!(five_less.checked_add(7), None); } #[test] fn test_checked_sub() { assert_eq!(5_usize.checked_sub(0), Some(5)); assert_eq!(5_usize.checked_sub(1), Some(4)); assert_eq!(5_usize.checked_sub(2), Some(3)); assert_eq!(5_usize.checked_sub(3), Some(2)); assert_eq!(5_usize.checked_sub(4), Some(1)); assert_eq!(5_usize.checked_sub(5), Some(0)); assert_eq!(5_usize.checked_sub(6), None); assert_eq!(5_usize.checked_sub(7), None); } #[test] fn test_checked_mul() { let third = usize::MAX / 3; assert_eq!(third.checked_mul(0), Some(0)); assert_eq!(third.checked_mul(1), Some(third)); assert_eq!(third.checked_mul(2), Some(third * 2)); assert_eq!(third.checked_mul(3), Some(third * 3)); assert_eq!(third.checked_mul(4), None); } macro_rules! test_is_power_of_two { ($test_name:ident, $T:ident) => ( fn $test_name() { #![test] assert_eq!((0 as $T).is_power_of_two(), false); assert_eq!((1 as $T).is_power_of_two(), true); assert_eq!((2 as $T).is_power_of_two(), true); assert_eq!((3 as $T).is_power_of_two(), false); assert_eq!((4 as $T).is_power_of_two(), true); assert_eq!((5 as $T).is_power_of_two(), false); assert_eq!(($T::MAX / 2 + 1).is_power_of_two(), true); } ) } test_is_power_of_two!{ test_is_power_of_two_u8, u8 } test_is_power_of_two!{ test_is_power_of_two_u16, u16 } test_is_power_of_two!{ test_is_power_of_two_u32, u32 } test_is_power_of_two!{ test_is_power_of_two_u64, u64 } test_is_power_of_two!{ test_is_power_of_two_uint, usize } macro_rules! test_next_power_of_two { ($test_name:ident, $T:ident) => ( fn $test_name() { #![test] assert_eq!((0 as $T).next_power_of_two(), 1); let mut next_power = 1; for i in 1 as $T..40 { assert_eq!(i.next_power_of_two(), next_power); if i == next_power { next_power *= 2 } } } ) } test_next_power_of_two! { test_next_power_of_two_u8, u8 } test_next_power_of_two! { test_next_power_of_two_u16, u16 } test_next_power_of_two! { test_next_power_of_two_u32, u32 } test_next_power_of_two! { test_next_power_of_two_u64, u64 } test_next_power_of_two! { test_next_power_of_two_uint, usize } macro_rules! test_checked_next_power_of_two { ($test_name:ident, $T:ident) => ( fn $test_name() { #![test] assert_eq!((0 as $T).checked_next_power_of_two(), Some(1)); assert!(($T::MAX / 2).checked_next_power_of_two().is_some()); assert_eq!(($T::MAX - 1).checked_next_power_of_two(), None); assert_eq!($T::MAX.checked_next_power_of_two(), None); let mut next_power = 1; for i in 1 as $T..40 { assert_eq!(i.checked_next_power_of_two(), Some(next_power)); if i == next_power { next_power *= 2 } } } ) } test_checked_next_power_of_two! { test_checked_next_power_of_two_u8, u8 } test_checked_next_power_of_two! { test_checked_next_power_of_two_u16, u16 } test_checked_next_power_of_two! { test_checked_next_power_of_two_u32, u32 } test_checked_next_power_of_two! { test_checked_next_power_of_two_u64, u64 } test_checked_next_power_of_two! { test_checked_next_power_of_two_uint, usize } #[derive(PartialEq, Debug)] struct Value { x: isize } impl ToPrimitive for Value { fn to_i64(&self) -> Option { self.x.to_i64() } fn to_u64(&self) -> Option { self.x.to_u64() } } impl FromPrimitive for Value { fn from_i64(n: i64) -> Option { Some(Value { x: n as isize }) } fn from_u64(n: u64) -> Option { Some(Value { x: n as isize }) } } #[test] fn test_to_primitive() { let value = Value { x: 5 }; assert_eq!(value.to_int(), Some(5)); assert_eq!(value.to_i8(), Some(5)); assert_eq!(value.to_i16(), Some(5)); assert_eq!(value.to_i32(), Some(5)); assert_eq!(value.to_i64(), Some(5)); assert_eq!(value.to_uint(), Some(5)); assert_eq!(value.to_u8(), Some(5)); assert_eq!(value.to_u16(), Some(5)); assert_eq!(value.to_u32(), Some(5)); assert_eq!(value.to_u64(), Some(5)); assert_eq!(value.to_f32(), Some(5f32)); assert_eq!(value.to_f64(), Some(5f64)); } #[test] fn test_from_primitive() { assert_eq!(from_int(5), Some(Value { x: 5 })); assert_eq!(from_i8(5), Some(Value { x: 5 })); assert_eq!(from_i16(5), Some(Value { x: 5 })); assert_eq!(from_i32(5), Some(Value { x: 5 })); assert_eq!(from_i64(5), Some(Value { x: 5 })); assert_eq!(from_uint(5), Some(Value { x: 5 })); assert_eq!(from_u8(5), Some(Value { x: 5 })); assert_eq!(from_u16(5), Some(Value { x: 5 })); assert_eq!(from_u32(5), Some(Value { x: 5 })); assert_eq!(from_u64(5), Some(Value { x: 5 })); assert_eq!(from_f32(5f32), Some(Value { x: 5 })); assert_eq!(from_f64(5f64), Some(Value { x: 5 })); } #[test] fn test_pow() { fn naive_pow(base: T, exp: usize) -> T { let one: T = Int::one(); (0..exp).fold(one, |acc, _| acc * base) } macro_rules! assert_pow { (($num:expr, $exp:expr) => $expected:expr) => {{ let result = $num.pow($exp); assert_eq!(result, $expected); assert_eq!(result, naive_pow($num, $exp)); }} } assert_pow!((3, 0 ) => 1); assert_pow!((5, 1 ) => 5); assert_pow!((-4, 2 ) => 16); assert_pow!((8, 3 ) => 512); assert_pow!((2u64, 50) => 1125899906842624); } #[test] fn test_uint_to_str_overflow() { let mut u8_val: u8 = 255; assert_eq!(u8_val.to_string(), "255"); u8_val = u8_val.wrapping_add(1); assert_eq!(u8_val.to_string(), "0"); let mut u16_val: u16 = 65_535; assert_eq!(u16_val.to_string(), "65535"); u16_val = u16_val.wrapping_add(1); assert_eq!(u16_val.to_string(), "0"); let mut u32_val: u32 = 4_294_967_295; assert_eq!(u32_val.to_string(), "4294967295"); u32_val = u32_val.wrapping_add(1); assert_eq!(u32_val.to_string(), "0"); let mut u64_val: u64 = 18_446_744_073_709_551_615; assert_eq!(u64_val.to_string(), "18446744073709551615"); u64_val = u64_val.wrapping_add(1); assert_eq!(u64_val.to_string(), "0"); } fn from_str(t: &str) -> Option { ::str::FromStr::from_str(t).ok() } #[test] fn test_uint_from_str_overflow() { let mut u8_val: u8 = 255; assert_eq!(from_str::("255"), Some(u8_val)); assert_eq!(from_str::("256"), None); u8_val = u8_val.wrapping_add(1); assert_eq!(from_str::("0"), Some(u8_val)); assert_eq!(from_str::("-1"), None); let mut u16_val: u16 = 65_535; assert_eq!(from_str::("65535"), Some(u16_val)); assert_eq!(from_str::("65536"), None); u16_val = u16_val.wrapping_add(1); assert_eq!(from_str::("0"), Some(u16_val)); assert_eq!(from_str::("-1"), None); let mut u32_val: u32 = 4_294_967_295; assert_eq!(from_str::("4294967295"), Some(u32_val)); assert_eq!(from_str::("4294967296"), None); u32_val = u32_val.wrapping_add(1); assert_eq!(from_str::("0"), Some(u32_val)); assert_eq!(from_str::("-1"), None); let mut u64_val: u64 = 18_446_744_073_709_551_615; assert_eq!(from_str::("18446744073709551615"), Some(u64_val)); assert_eq!(from_str::("18446744073709551616"), None); u64_val = u64_val.wrapping_add(1); assert_eq!(from_str::("0"), Some(u64_val)); assert_eq!(from_str::("-1"), None); } } #[cfg(test)] mod bench { extern crate test; use self::test::Bencher; use num::Int; use prelude::v1::*; #[bench] fn bench_pow_function(b: &mut Bencher) { let v = (0..1024).collect::>(); b.iter(|| {v.iter().fold(0, |old, new| old.pow(*new as u32));}); } }