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44cb46f7bf
rust/src/libcore/num/num.rs
Brendan Zabarauskas 44cb46f7bf Add ldexp and frexp functions
2013-05-14 11:24:55 +10:00

495 lines
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Rust
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// Copyright 2012-2013 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
//! An interface for numeric types
use cmp::{Eq, ApproxEq, Ord};
use ops::{Add, Sub, Mul, Div, Rem, Neg};
use ops::{Not, BitAnd, BitOr, BitXor, Shl, Shr};
use option::Option;
use kinds::Copy;
pub mod strconv;
///
/// The base trait for numeric types
///
pub trait Num: Eq + Zero + One
+ Neg<Self>
+ Add<Self,Self>
+ Sub<Self,Self>
+ Mul<Self,Self>
+ Div<Self,Self>
+ Rem<Self,Self> {}
pub trait IntConvertible {
fn to_int(&self) -> int;
fn from_int(n: int) -> Self;
}
pub trait Orderable: Ord {
// These should be methods on `Ord`, with overridable default implementations. We don't want
// to encumber all implementors of Ord by requiring them to implement these functions, but at
// the same time we want to be able to take advantage of the speed of the specific numeric
// functions (like the `fmin` and `fmax` intrinsics).
fn min(&self, other: &Self) -> Self;
fn max(&self, other: &Self) -> Self;
fn clamp(&self, mn: &Self, mx: &Self) -> Self;
}
pub trait Zero {
fn zero() -> Self; // FIXME (#5527): This should be an associated constant
fn is_zero(&self) -> bool;
}
pub trait One {
fn one() -> Self; // FIXME (#5527): This should be an associated constant
}
pub trait Signed: Num
+ Neg<Self> {
fn abs(&self) -> Self;
fn abs_sub(&self, other: &Self) -> Self;
fn signum(&self) -> Self;
fn is_positive(&self) -> bool;
fn is_negative(&self) -> bool;
}
pub trait Unsigned: Num {}
// This should be moved into the default implementation for Signed::abs
pub fn abs<T:Ord + Zero + Neg<T>>(v: T) -> T {
if v < Zero::zero() { v.neg() } else { v }
}
pub trait Integer: Num
+ Orderable
+ Div<Self,Self>
+ Rem<Self,Self> {
fn div_rem(&self, other: &Self) -> (Self,Self);
fn div_floor(&self, other: &Self) -> Self;
fn mod_floor(&self, other: &Self) -> Self;
fn div_mod_floor(&self, other: &Self) -> (Self,Self);
fn gcd(&self, other: &Self) -> Self;
fn lcm(&self, other: &Self) -> Self;
fn is_multiple_of(&self, other: &Self) -> bool;
fn is_even(&self) -> bool;
fn is_odd(&self) -> bool;
}
pub trait Round {
fn floor(&self) -> Self;
fn ceil(&self) -> Self;
fn round(&self) -> Self;
fn trunc(&self) -> Self;
fn fract(&self) -> Self;
}
pub trait Fractional: Num
+ Orderable
+ Round
+ Div<Self,Self> {
fn recip(&self) -> Self;
}
pub trait Algebraic {
fn pow(&self, n: Self) -> Self;
fn sqrt(&self) -> Self;
fn rsqrt(&self) -> Self;
fn cbrt(&self) -> Self;
fn hypot(&self, other: Self) -> Self;
}
pub trait Trigonometric {
fn sin(&self) -> Self;
fn cos(&self) -> Self;
fn tan(&self) -> Self;
fn asin(&self) -> Self;
fn acos(&self) -> Self;
fn atan(&self) -> Self;
fn atan2(&self, other: Self) -> Self;
}
pub trait Exponential {
fn exp(&self) -> Self;
fn exp2(&self) -> Self;
fn ln(&self) -> Self;
fn log(&self, base: Self) -> Self;
fn log2(&self) -> Self;
fn log10(&self) -> Self;
}
pub trait Hyperbolic: Exponential {
fn sinh(&self) -> Self;
fn cosh(&self) -> Self;
fn tanh(&self) -> Self;
fn asinh(&self) -> Self;
fn acosh(&self) -> Self;
fn atanh(&self) -> Self;
}
///
/// Defines constants and methods common to real numbers
///
pub trait Real: Signed
+ Fractional
+ Algebraic
+ Trigonometric
+ Hyperbolic {
// Common Constants
// FIXME (#5527): These should be associated constants
fn pi() -> Self;
fn two_pi() -> Self;
fn frac_pi_2() -> Self;
fn frac_pi_3() -> Self;
fn frac_pi_4() -> Self;
fn frac_pi_6() -> Self;
fn frac_pi_8() -> Self;
fn frac_1_pi() -> Self;
fn frac_2_pi() -> Self;
fn frac_2_sqrtpi() -> Self;
fn sqrt2() -> Self;
fn frac_1_sqrt2() -> Self;
fn e() -> Self;
fn log2_e() -> Self;
fn log10_e() -> Self;
fn ln_2() -> Self;
fn ln_10() -> Self;
// Angular conversions
fn to_degrees(&self) -> Self;
fn to_radians(&self) -> Self;
}
///
/// Methods that are harder to implement and not commonly used.
///
pub trait RealExt: Real {
// FIXME (#5527): usages of `int` should be replaced with an associated
// integer type once these are implemented
// Gamma functions
fn lgamma(&self) -> (int, Self);
fn tgamma(&self) -> Self;
// Bessel functions
fn j0(&self) -> Self;
fn j1(&self) -> Self;
fn jn(&self, n: int) -> Self;
fn y0(&self) -> Self;
fn y1(&self) -> Self;
fn yn(&self, n: int) -> Self;
}
///
/// Collects the bitwise operators under one trait.
///
pub trait Bitwise: Not<Self>
+ BitAnd<Self,Self>
+ BitOr<Self,Self>
+ BitXor<Self,Self>
+ Shl<Self,Self>
+ Shr<Self,Self> {}
pub trait BitCount {
fn population_count(&self) -> Self;
fn leading_zeros(&self) -> Self;
fn trailing_zeros(&self) -> Self;
}
pub trait Bounded {
// FIXME (#5527): These should be associated constants
fn min_value() -> Self;
fn max_value() -> Self;
}
///
/// Specifies the available operations common to all of Rust's core numeric primitives.
/// These may not always make sense from a purely mathematical point of view, but
/// may be useful for systems programming.
///
pub trait Primitive: Num
+ NumCast
+ Bounded
+ Neg<Self>
+ Add<Self,Self>
+ Sub<Self,Self>
+ Mul<Self,Self>
+ Div<Self,Self>
+ Rem<Self,Self> {
// FIXME (#5527): These should be associated constants
fn bits() -> uint;
fn bytes() -> uint;
}
///
/// A collection of traits relevant to primitive signed and unsigned integers
///
pub trait Int: Integer
+ Primitive
+ Bitwise
+ BitCount {}
///
/// Used for representing the classification of floating point numbers
///
#[deriving(Eq)]
pub enum FPCategory {
/// "Not a Number", often obtained by dividing by zero
FPNaN,
/// Positive or negative infinity
FPInfinite ,
/// Positive or negative zero
FPZero,
/// De-normalized floating point representation (less precise than `FPNormal`)
FPSubnormal,
/// A regular floating point number
FPNormal,
}
///
/// Primitive floating point numbers
///
pub trait Float: Real
+ Signed
+ Primitive
+ ApproxEq<Self> {
// FIXME (#5527): These should be associated constants
fn NaN() -> Self;
fn infinity() -> Self;
fn neg_infinity() -> Self;
fn neg_zero() -> Self;
fn is_NaN(&self) -> bool;
fn is_infinite(&self) -> bool;
fn is_finite(&self) -> bool;
fn is_normal(&self) -> bool;
fn classify(&self) -> FPCategory;
fn mantissa_digits() -> uint;
fn digits() -> uint;
fn epsilon() -> Self;
fn min_exp() -> int;
fn max_exp() -> int;
fn min_10_exp() -> int;
fn max_10_exp() -> int;
fn ldexp(x: Self, exp: int) -> Self;
fn frexp(&self) -> (Self, int);
fn exp_m1(&self) -> Self;
fn ln_1p(&self) -> Self;
fn mul_add(&self, a: Self, b: Self) -> Self;
fn next_after(&self, other: Self) -> Self;
}
///
/// Cast from one machine scalar to another
///
/// # Example
///
/// ~~~
/// let twenty: f32 = num::cast(0x14);
/// assert_eq!(twenty, 20f32);
/// ~~~
///
#[inline(always)]
pub fn cast<T:NumCast,U:NumCast>(n: T) -> U {
NumCast::from(n)
}
///
/// An interface for casting between machine scalars
///
pub trait NumCast {
fn from<T:NumCast>(n: T) -> Self;
fn to_u8(&self) -> u8;
fn to_u16(&self) -> u16;
fn to_u32(&self) -> u32;
fn to_u64(&self) -> u64;
fn to_uint(&self) -> uint;
fn to_i8(&self) -> i8;
fn to_i16(&self) -> i16;
fn to_i32(&self) -> i32;
fn to_i64(&self) -> i64;
fn to_int(&self) -> int;
fn to_f32(&self) -> f32;
fn to_f64(&self) -> f64;
fn to_float(&self) -> float;
}
macro_rules! impl_num_cast(
($T:ty, $conv:ident) => (
impl NumCast for $T {
#[inline(always)]
fn from<N:NumCast>(n: N) -> $T {
// `$conv` could be generated using `concat_idents!`, but that
// macro seems to be broken at the moment
n.$conv()
}
#[inline(always)] fn to_u8(&self) -> u8 { *self as u8 }
#[inline(always)] fn to_u16(&self) -> u16 { *self as u16 }
#[inline(always)] fn to_u32(&self) -> u32 { *self as u32 }
#[inline(always)] fn to_u64(&self) -> u64 { *self as u64 }
#[inline(always)] fn to_uint(&self) -> uint { *self as uint }
#[inline(always)] fn to_i8(&self) -> i8 { *self as i8 }
#[inline(always)] fn to_i16(&self) -> i16 { *self as i16 }
#[inline(always)] fn to_i32(&self) -> i32 { *self as i32 }
#[inline(always)] fn to_i64(&self) -> i64 { *self as i64 }
#[inline(always)] fn to_int(&self) -> int { *self as int }
#[inline(always)] fn to_f32(&self) -> f32 { *self as f32 }
#[inline(always)] fn to_f64(&self) -> f64 { *self as f64 }
#[inline(always)] fn to_float(&self) -> float { *self as float }
}
)
)
impl_num_cast!(u8, to_u8)
impl_num_cast!(u16, to_u16)
impl_num_cast!(u32, to_u32)
impl_num_cast!(u64, to_u64)
impl_num_cast!(uint, to_uint)
impl_num_cast!(i8, to_i8)
impl_num_cast!(i16, to_i16)
impl_num_cast!(i32, to_i32)
impl_num_cast!(i64, to_i64)
impl_num_cast!(int, to_int)
impl_num_cast!(f32, to_f32)
impl_num_cast!(f64, to_f64)
impl_num_cast!(float, to_float)
pub trait ToStrRadix {
pub fn to_str_radix(&self, radix: uint) -> ~str;
}
pub trait FromStrRadix {
pub fn from_str_radix(str: &str, radix: uint) -> Option<Self>;
}
///
/// Calculates a power to a given radix, optimized for uint `pow` and `radix`.
///
/// Returns `radix^pow` as `T`.
///
/// Note:
/// Also returns `1` for `0^0`, despite that technically being an
/// undefined number. The reason for this is twofold:
/// - If code written to use this function cares about that special case, it's
/// probably going to catch it before making the call.
/// - If code written to use this function doesn't care about it, it's
/// probably assuming that `x^0` always equals `1`.
///
pub fn pow_with_uint<T:NumCast+One+Zero+Copy+Div<T,T>+Mul<T,T>>(
radix: uint, pow: uint) -> T {
let _0: T = Zero::zero();
let _1: T = One::one();
if pow == 0u { return _1; }
if radix == 0u { return _0; }
let mut my_pow = pow;
let mut total = _1;
let mut multiplier = cast(radix as int);
while (my_pow > 0u) {
if my_pow % 2u == 1u {
total *= multiplier;
}
my_pow /= 2u;
multiplier *= multiplier;
}
total
}
/// Helper function for testing numeric operations
#[cfg(test)]
pub fn test_num<T:Num + NumCast>(ten: T, two: T) {
assert_eq!(ten.add(&two), cast(12));
assert_eq!(ten.sub(&two), cast(8));
assert_eq!(ten.mul(&two), cast(20));
assert_eq!(ten.div(&two), cast(5));
assert_eq!(ten.rem(&two), cast(0));
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);
}
macro_rules! test_cast_20(
($_20:expr) => ({
let _20 = $_20;
assert_eq!(20u, _20.to_uint());
assert_eq!(20u8, _20.to_u8());
assert_eq!(20u16, _20.to_u16());
assert_eq!(20u32, _20.to_u32());
assert_eq!(20u64, _20.to_u64());
assert_eq!(20i, _20.to_int());
assert_eq!(20i8, _20.to_i8());
assert_eq!(20i16, _20.to_i16());
assert_eq!(20i32, _20.to_i32());
assert_eq!(20i64, _20.to_i64());
assert_eq!(20f, _20.to_float());
assert_eq!(20f32, _20.to_f32());
assert_eq!(20f64, _20.to_f64());
assert_eq!(_20, NumCast::from(20u));
assert_eq!(_20, NumCast::from(20u8));
assert_eq!(_20, NumCast::from(20u16));
assert_eq!(_20, NumCast::from(20u32));
assert_eq!(_20, NumCast::from(20u64));
assert_eq!(_20, NumCast::from(20i));
assert_eq!(_20, NumCast::from(20i8));
assert_eq!(_20, NumCast::from(20i16));
assert_eq!(_20, NumCast::from(20i32));
assert_eq!(_20, NumCast::from(20i64));
assert_eq!(_20, NumCast::from(20f));
assert_eq!(_20, NumCast::from(20f32));
assert_eq!(_20, NumCast::from(20f64));
assert_eq!(_20, cast(20u));
assert_eq!(_20, cast(20u8));
assert_eq!(_20, cast(20u16));
assert_eq!(_20, cast(20u32));
assert_eq!(_20, cast(20u64));
assert_eq!(_20, cast(20i));
assert_eq!(_20, cast(20i8));
assert_eq!(_20, cast(20i16));
assert_eq!(_20, cast(20i32));
assert_eq!(_20, cast(20i64));
assert_eq!(_20, cast(20f));
assert_eq!(_20, cast(20f32));
assert_eq!(_20, cast(20f64));
})
)
#[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!(20u) }
#[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!(20i) }
#[test] fn test_f32_cast() { test_cast_20!(20f32) }
#[test] fn test_f64_cast() { test_cast_20!(20f64) }
#[test] fn test_float_cast() { test_cast_20!(20f) }
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