Add basic support for rational and complex numbers

src/libstd/num/complex.rs

@@ -0,0 +1,315 @@
+// Copyright 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.
+
+
+//! Complex numbers.
+
+use core::num::{Zero,One,ToStrRadix};
+use core::prelude::*;
+
+// FIXME #1284: handle complex NaN & infinity etc. This
+// probably doesn't map to C's _Complex correctly.
+
+// FIXME #5734:: Need generic sin/cos for .to/from_polar().
+// FIXME #5735: Need generic sqrt to implement .norm().
+
+
+/// A complex number in Cartesian form.
+#[deriving(Eq,Clone)]
+pub struct Cmplx<T> {
+    re: T,
+    im: T
+}
+
+pub type Complex = Cmplx<float>;
+pub type Complex32 = Cmplx<f32>;
+pub type Complex64 = Cmplx<f64>;
+
+impl<T: Copy + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>>
+    Cmplx<T> {
+    /// Create a new Cmplx
+    #[inline]
+    pub fn new(re: T, im: T) -> Cmplx<T> {
+        Cmplx { re: re, im: im }
+    }
+
+    /**
+    Returns the square of the norm (since `T` doesn't necessarily
+    have a sqrt function), i.e. `re^2 + im^2`.
+    */
+    #[inline]
+    pub fn norm_sqr(&self) -> T {
+        self.re * self.re + self.im * self.im
+    }
+
+
+    /// Returns the complex conjugate. i.e. `re - i im`
+    #[inline]
+    pub fn conj(&self) -> Cmplx<T> {
+        Cmplx::new(self.re, -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)
+    }
+
+    /// Divides `self` by the scalar `t`.
+    #[inline]
+    pub fn unscale(&self, t: T) -> Cmplx<T> {
+        Cmplx::new(self.re / t, self.im / t)
+    }
+
+    /// Returns `1/self`
+    #[inline]
+    pub fn inv(&self) -> Cmplx<T> {
+        let norm_sqr = self.norm_sqr();
+        Cmplx::new(self.re / norm_sqr,
+                    -self.im / norm_sqr)
+    }
+}
+
+/* arithmetic */
+// (a + i b) + (c + i d) == (a + c) + i (b + d)
+impl<T: Copy + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>>
+    Add<Cmplx<T>, Cmplx<T>> for Cmplx<T> {
+    #[inline]
+    fn add(&self, other: &Cmplx<T>) -> Cmplx<T> {
+        Cmplx::new(self.re + other.re, self.im + other.im)
+    }
+}
+// (a + i b) - (c + i d) == (a - c) + i (b - d)
+impl<T: Copy + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>>
+    Sub<Cmplx<T>, Cmplx<T>> for Cmplx<T> {
+    #[inline]
+    fn sub(&self, other: &Cmplx<T>) -> Cmplx<T> {
+        Cmplx::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: Copy + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>>
+    Mul<Cmplx<T>, Cmplx<T>> for Cmplx<T> {
+    #[inline]
+    fn mul(&self, other: &Cmplx<T>) -> Cmplx<T> {
+        Cmplx::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: Copy + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>>
+    Div<Cmplx<T>, Cmplx<T>> for Cmplx<T> {
+    #[inline]
+    fn div(&self, other: &Cmplx<T>) -> Cmplx<T> {
+        let norm_sqr = other.norm_sqr();
+        Cmplx::new((self.re*other.re + self.im*other.im) / norm_sqr,
+                     (self.im*other.re - self.re*other.im) / norm_sqr)
+    }
+}
+
+impl<T: Copy + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>>
+    Neg<Cmplx<T>> for Cmplx<T> {
+    #[inline]
+    fn neg(&self) -> Cmplx<T> {
+        Cmplx::new(-self.re, -self.im)
+    }
+}
+
+/* constants */
+impl<T: Copy + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T> + Zero>
+    Zero for Cmplx<T> {
+    #[inline]
+    fn zero() -> Cmplx<T> {
+        Cmplx::new(Zero::zero(), Zero::zero())
+    }
+}
+
+impl<T: Copy + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T> + Zero + One>
+    One for Cmplx<T> {
+    #[inline]
+    fn one() -> Cmplx<T> {
+        Cmplx::new(One::one(), Zero::zero())
+    }
+}
+
+/* string conversions */
+impl<T: ToStr + Zero + Ord + Neg<T>> ToStr for Cmplx<T> {
+    fn to_str(&self) -> ~str {
+        if self.im < Zero::zero() {
+            fmt!("%s-%si", self.re.to_str(), (-self.im).to_str())
+        } else {
+            fmt!("%s+%si", self.re.to_str(), self.im.to_str())
+        }
+    }
+}
+
+impl<T: ToStrRadix + Zero + Ord + Neg<T>> ToStrRadix for Cmplx<T> {
+    fn to_str_radix(&self, radix: uint) -> ~str {
+        if self.im < Zero::zero() {
+            fmt!("%s-%si", self.re.to_str_radix(radix), (-self.im).to_str_radix(radix))
+        } else {
+            fmt!("%s+%si", self.re.to_str_radix(radix), self.im.to_str_radix(radix))
+        }
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use core::prelude::*;
+    use super::*;
+    use core::num::{Zero,One};
+
+    pub static _0_0i : Complex = Cmplx { re: 0f, im: 0f };
+    pub static _1_0i : Complex = Cmplx { re: 1f, im: 0f };
+    pub static _1_1i : Complex = Cmplx { re: 1f, im: 1f };
+    pub static _0_1i : Complex = Cmplx { re: 0f, im: 1f };
+    pub static _neg1_1i : Complex = Cmplx { re: -1f, im: 1f };
+    pub static _05_05i : Complex = Cmplx { re: 0.5f, im: 0.5f };
+    pub static all_consts : [Complex, .. 5] = [_0_0i, _1_0i, _1_1i, _neg1_1i, _05_05i];
+
+    #[test]
+    fn test_consts() {
+        // check our constants are what Cmplx::new creates
+        fn test(c : Complex, r : float, i: float) {
+            assert_eq!(c, Cmplx::new(r,i));
+        }
+        test(_0_0i, 0f, 0f);
+        test(_1_0i, 1f, 0f);
+        test(_1_1i, 1f, 1f);
+        test(_neg1_1i, -1f, 1f);
+        test(_05_05i, 0.5f, 0.5f);
+
+        assert_eq!(_0_0i, Zero::zero());
+        assert_eq!(_1_0i, One::one());
+    }
+
+    #[test]
+    fn test_norm_sqr() {
+        fn test(c: Complex, ns: float) {
+            assert_eq!(c.norm_sqr(), ns);
+        }
+        test(_0_0i, 0f);
+        test(_1_0i, 1f);
+        test(_1_1i, 2f);
+        test(_neg1_1i, 2f);
+        test(_05_05i, 0.5f);
+    }
+
+    #[test]
+    fn test_scale_unscale() {
+        assert_eq!(_05_05i.scale(2f), _1_1i);
+        assert_eq!(_1_1i.unscale(2f), _05_05i);
+        for all_consts.each |&c| {
+            assert_eq!(c.scale(2f).unscale(2f), c);
+        }
+    }
+
+    #[test]
+    fn test_conj() {
+        for all_consts.each |&c| {
+            assert_eq!(c.conj(), Cmplx::new(c.re, -c.im));
+            assert_eq!(c.conj().conj(), c);
+        }
+    }
+
+    #[test]
+    fn test_inv() {
+        assert_eq!(_1_1i.inv(), _05_05i.conj());
+        assert_eq!(_1_0i.inv(), _1_0i.inv());
+    }
+
+    #[test]
+    #[should_fail]
+    #[ignore]
+    fn test_inv_zero() {
+        // FIXME #5736: should this really fail, or just NaN?
+        _0_0i.inv();
+    }
+
+
+    mod arith {
+        use super::*;
+        use super::super::*;
+        use core::num::Zero;
+
+        #[test]
+        fn test_add() {
+            assert_eq!(_05_05i + _05_05i, _1_1i);
+            assert_eq!(_0_1i + _1_0i, _1_1i);
+            assert_eq!(_1_0i + _neg1_1i, _0_1i);
+
+            for all_consts.each |&c| {
+                assert_eq!(_0_0i + c, c);
+                assert_eq!(c + _0_0i, c);
+            }
+        }
+
+        #[test]
+        fn test_sub() {
+            assert_eq!(_05_05i - _05_05i, _0_0i);
+            assert_eq!(_0_1i - _1_0i, _neg1_1i);
+            assert_eq!(_0_1i - _neg1_1i, _1_0i);
+
+            for all_consts.each |&c| {
+                assert_eq!(c - _0_0i, c);
+                assert_eq!(c - c, _0_0i);
+            }
+        }
+
+        #[test]
+        fn test_mul() {
+            assert_eq!(_05_05i * _05_05i, _0_1i.unscale(2f));
+            assert_eq!(_1_1i * _0_1i, _neg1_1i);
+
+            // i^2 & i^4
+            assert_eq!(_0_1i * _0_1i, -_1_0i);
+            assert_eq!(_0_1i * _0_1i * _0_1i * _0_1i, _1_0i);
+
+            for all_consts.each |&c| {
+                assert_eq!(c * _1_0i, c);
+                assert_eq!(_1_0i * c, c);
+            }
+        }
+        #[test]
+        fn test_div() {
+            assert_eq!(_neg1_1i / _0_1i, _1_1i);
+            for all_consts.each |&c| {
+                if c != Zero::zero() {
+                    assert_eq!(c / c, _1_0i);
+                }
+            }
+        }
+        #[test]
+        fn test_neg() {
+            assert_eq!(-_1_0i + _0_1i, _neg1_1i);
+            assert_eq!((-_0_1i) * _0_1i, _1_0i);
+            for all_consts.each |&c| {
+                assert_eq!(-(-c), c);
+            }
+        }
+    }
+
+    #[test]
+    fn test_to_str() {
+        fn test(c : Complex, s: ~str) {
+            assert_eq!(c.to_str(), s);
+        }
+        test(_0_0i, ~"0+0i");
+        test(_1_0i, ~"1+0i");
+        test(_0_1i, ~"0+1i");
+        test(_1_1i, ~"1+1i");
+        test(_neg1_1i, ~"-1+1i");
+        test(-_neg1_1i, ~"1-1i");
+        test(_05_05i, ~"0.5+0.5i");
+    }
+}