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auto merge of #14167 : cmr/rust/cmplx, r=alexcrichton

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bors 2014-05-13 04:06:50 -07:00
commit 463436ffeb
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106
src/libnum/complex.rs
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@ -23,21 +23,21 @@ use std::num::{Zero,One,ToStrRadix};
/// A complex number in Cartesian form.
#[deriving(Eq,Clone)]
pub struct Cmplx<T> {
pub struct Complex<T> {
/// Real portion of the complex number
pub re: T,
/// Imaginary portion of the complex number
pub im: T
}
pub type Complex32 = Cmplx<f32>;
pub type Complex64 = Cmplx<f64>;
pub type Complex32 = Complex<f32>;
pub type Complex64 = Complex<f64>;
impl<T: Clone + Num> Cmplx<T> {
/// Create a new Cmplx
impl<T: Clone + Num> Complex<T> {
/// Create a new Complex
#[inline]
pub fn new(re: T, im: T) -> Cmplx<T> {
Cmplx { re: re, im: im }
pub fn new(re: T, im: T) -> Complex<T> {
Complex { re: re, im: im }
}
/**
@ -52,33 +52,33 @@ impl<T: Clone + Num> Cmplx<T> {
/// Returns the complex conjugate. i.e. `re - i im`
#[inline]
pub fn conj(&self) -> Cmplx<T> {
Cmplx::new(self.re.clone(), -self.im)
pub fn conj(&self) -> Complex<T> {
Complex::new(self.re.clone(), -self.im)
}
/// Multiplies `self` by the scalar `t`.
#[inline]
pub fn scale(&self, t: T) -> Cmplx<T> {
Cmplx::new(self.re * t, self.im * t)
pub fn scale(&self, t: T) -> Complex<T> {
Complex::new(self.re * t, self.im * t)
}
/// Divides `self` by the scalar `t`.
#[inline]
pub fn unscale(&self, t: T) -> Cmplx<T> {
Cmplx::new(self.re / t, self.im / t)
pub fn unscale(&self, t: T) -> Complex<T> {
Complex::new(self.re / t, self.im / t)
}
/// Returns `1/self`
#[inline]
pub fn inv(&self) -> Cmplx<T> {
pub fn inv(&self) -> Complex<T> {
let norm_sqr = self.norm_sqr();
Cmplx::new(self.re / norm_sqr,
Complex::new(self.re / norm_sqr,
-self.im / norm_sqr)
}
}
impl<T: Clone + Float> Cmplx<T> {
impl<T: Clone + Float> Complex<T> {
/// Calculate |self|
#[inline]
pub fn norm(&self) -> T {
@ -86,7 +86,7 @@ impl<T: Clone + Float> Cmplx<T> {
}
}
impl<T: Clone + Float> Cmplx<T> {
impl<T: Clone + Float> Complex<T> {
/// Calculate the principal Arg of self.
#[inline]
pub fn arg(&self) -> T {
@ -100,58 +100,58 @@ impl<T: Clone + Float> Cmplx<T> {
}
/// Convert a polar representation into a complex number.
#[inline]
pub fn from_polar(r: &T, theta: &T) -> Cmplx<T> {
Cmplx::new(*r * theta.cos(), *r * theta.sin())
pub fn from_polar(r: &T, theta: &T) -> Complex<T> {
Complex::new(*r * theta.cos(), *r * theta.sin())
}
}
/* arithmetic */
// (a + i b) + (c + i d) == (a + c) + i (b + d)
impl<T: Clone + Num> Add<Cmplx<T>, Cmplx<T>> for Cmplx<T> {
impl<T: Clone + Num> Add<Complex<T>, Complex<T>> for Complex<T> {
#[inline]
fn add(&self, other: &Cmplx<T>) -> Cmplx<T> {
Cmplx::new(self.re + other.re, self.im + other.im)
fn add(&self, other: &Complex<T>) -> Complex<T> {
Complex::new(self.re + other.re, self.im + other.im)
}
}
// (a + i b) - (c + i d) == (a - c) + i (b - d)
impl<T: Clone + Num> Sub<Cmplx<T>, Cmplx<T>> for Cmplx<T> {
impl<T: Clone + Num> Sub<Complex<T>, Complex<T>> for Complex<T> {
#[inline]
fn sub(&self, other: &Cmplx<T>) -> Cmplx<T> {
Cmplx::new(self.re - other.re, self.im - other.im)
fn sub(&self, other: &Complex<T>) -> Complex<T> {
Complex::new(self.re - other.re, self.im - other.im)
}
}
// (a + i b) * (c + i d) == (a*c - b*d) + i (a*d + b*c)
impl<T: Clone + Num> Mul<Cmplx<T>, Cmplx<T>> for Cmplx<T> {
impl<T: Clone + Num> Mul<Complex<T>, Complex<T>> for Complex<T> {
#[inline]
fn mul(&self, other: &Cmplx<T>) -> Cmplx<T> {
Cmplx::new(self.re*other.re - self.im*other.im,
fn mul(&self, other: &Complex<T>) -> Complex<T> {
Complex::new(self.re*other.re - self.im*other.im,
self.re*other.im + self.im*other.re)
}
}
// (a + i b) / (c + i d) == [(a + i b) * (c - i d)] / (c*c + d*d)
// == [(a*c + b*d) / (c*c + d*d)] + i [(b*c - a*d) / (c*c + d*d)]
impl<T: Clone + Num> Div<Cmplx<T>, Cmplx<T>> for Cmplx<T> {
impl<T: Clone + Num> Div<Complex<T>, Complex<T>> for Complex<T> {
#[inline]
fn div(&self, other: &Cmplx<T>) -> Cmplx<T> {
fn div(&self, other: &Complex<T>) -> Complex<T> {
let norm_sqr = other.norm_sqr();
Cmplx::new((self.re*other.re + self.im*other.im) / norm_sqr,
Complex::new((self.re*other.re + self.im*other.im) / norm_sqr,
(self.im*other.re - self.re*other.im) / norm_sqr)
}
}
impl<T: Clone + Num> Neg<Cmplx<T>> for Cmplx<T> {
impl<T: Clone + Num> Neg<Complex<T>> for Complex<T> {
#[inline]
fn neg(&self) -> Cmplx<T> {
Cmplx::new(-self.re, -self.im)
fn neg(&self) -> Complex<T> {
Complex::new(-self.re, -self.im)
}
}
/* constants */
impl<T: Clone + Num> Zero for Cmplx<T> {
impl<T: Clone + Num> Zero for Complex<T> {
#[inline]
fn zero() -> Cmplx<T> {
Cmplx::new(Zero::zero(), Zero::zero())
fn zero() -> Complex<T> {
Complex::new(Zero::zero(), Zero::zero())
}
#[inline]
@ -160,15 +160,15 @@ impl<T: Clone + Num> Zero for Cmplx<T> {
}
}
impl<T: Clone + Num> One for Cmplx<T> {
impl<T: Clone + Num> One for Complex<T> {
#[inline]
fn one() -> Cmplx<T> {
Cmplx::new(One::one(), Zero::zero())
fn one() -> Complex<T> {
Complex::new(One::one(), Zero::zero())
}
}
/* string conversions */
impl<T: fmt::Show + Num + Ord> fmt::Show for Cmplx<T> {
impl<T: fmt::Show + Num + Ord> fmt::Show for Complex<T> {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
if self.im < Zero::zero() {
write!(f.buf, "{}-{}i", self.re, -self.im)
@ -178,7 +178,7 @@ impl<T: fmt::Show + Num + Ord> fmt::Show for Cmplx<T> {
}
}
impl<T: ToStrRadix + Num + Ord> ToStrRadix for Cmplx<T> {
impl<T: ToStrRadix + Num + Ord> ToStrRadix for Complex<T> {
fn to_str_radix(&self, radix: uint) -> ~str {
if self.im < Zero::zero() {
format!("{}-{}i", self.re.to_str_radix(radix), (-self.im).to_str_radix(radix))
@ -192,22 +192,22 @@ impl<T: ToStrRadix + Num + Ord> ToStrRadix for Cmplx<T> {
mod test {
#![allow(non_uppercase_statics)]
use super::{Complex64, Cmplx};
use super::{Complex64, Complex};
use std::num::{Zero,One,Float};
pub static _0_0i : Complex64 = Cmplx { re: 0.0, im: 0.0 };
pub static _1_0i : Complex64 = Cmplx { re: 1.0, im: 0.0 };
pub static _1_1i : Complex64 = Cmplx { re: 1.0, im: 1.0 };
pub static _0_1i : Complex64 = Cmplx { re: 0.0, im: 1.0 };
pub static _neg1_1i : Complex64 = Cmplx { re: -1.0, im: 1.0 };
pub static _05_05i : Complex64 = Cmplx { re: 0.5, im: 0.5 };
pub static _0_0i : Complex64 = Complex { re: 0.0, im: 0.0 };
pub static _1_0i : Complex64 = Complex { re: 1.0, im: 0.0 };
pub static _1_1i : Complex64 = Complex { re: 1.0, im: 1.0 };
pub static _0_1i : Complex64 = Complex { re: 0.0, im: 1.0 };
pub static _neg1_1i : Complex64 = Complex { re: -1.0, im: 1.0 };
pub static _05_05i : Complex64 = Complex { re: 0.5, im: 0.5 };
pub static all_consts : [Complex64, .. 5] = [_0_0i, _1_0i, _1_1i, _neg1_1i, _05_05i];
#[test]
fn test_consts() {
// check our constants are what Cmplx::new creates
// check our constants are what Complex::new creates
fn test(c : Complex64, r : f64, i: f64) {
assert_eq!(c, Cmplx::new(r,i));
assert_eq!(c, Complex::new(r,i));
}
test(_0_0i, 0.0, 0.0);
test(_1_0i, 1.0, 0.0);
@ -246,7 +246,7 @@ mod test {
#[test]
fn test_conj() {
for &c in all_consts.iter() {
assert_eq!(c.conj(), Cmplx::new(c.re, -c.im));
assert_eq!(c.conj(), Complex::new(c.re, -c.im));
assert_eq!(c.conj().conj(), c);
}
}
@ -280,7 +280,7 @@ mod test {
fn test_polar_conv() {
fn test(c: Complex64) {
let (r, theta) = c.to_polar();
assert!((c - Cmplx::from_polar(&r, &theta)).norm() < 1e-6);
assert!((c - Complex::from_polar(&r, &theta)).norm() < 1e-6);
}
for &c in all_consts.iter() { test(c); }
}