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complex: forward ops to val-val 

Since the Num constraint only requires val-val ops, we ended up cloning
everything in Complex ops when they were forwarded to ref-ref.  By using
val-val, we can reduce how often clones are needed.
This commit is contained in:
Josh Stone 2015-11-16 10:10:59 -08:00
parent b4026b9fec
commit c310e5da8e
1 changed files with 38 additions and 36 deletions
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74
src/complex.rs
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@ -79,12 +79,12 @@ impl<T: Clone + Float> Complex<T> {
/// Calculate |self| /// Calculate |self|
#[inline] #[inline]
pub fn norm(&self) -> T { pub fn norm(&self) -> T {
self.re.clone().hypot(self.im.clone()) self.re.hypot(self.im)
} }
/// Calculate the principal Arg of self. /// Calculate the principal Arg of self.
#[inline] #[inline]
pub fn arg(&self) -> T { pub fn arg(&self) -> T {
self.im.clone().atan2(self.re.clone()) self.im.atan2(self.re)
} }
/// Convert to polar form (r, theta), such that `self = r * exp(i /// Convert to polar form (r, theta), such that `self = r * exp(i
/// * theta)` /// * theta)`
@ -102,7 +102,7 @@ impl<T: Clone + Float> Complex<T> {
#[inline] #[inline]
pub fn exp(&self) -> Complex<T> { pub fn exp(&self) -> Complex<T> {
// formula: e^(a + bi) = e^a (cos(b) + i*sin(b)) // formula: e^(a + bi) = e^a (cos(b) + i*sin(b))
Complex::new(self.im.clone().cos(), self.im.clone().sin()).scale(self.re.clone().exp()) Complex::new(self.im.cos(), self.im.sin()).scale(self.re.exp())
} }
/// Computes the principal value of natural logarithm of `self`. /// Computes the principal value of natural logarithm of `self`.
@ -137,22 +137,22 @@ impl<T: Clone + Float> Complex<T> {
#[inline] #[inline]
pub fn sin(&self) -> Complex<T> { pub fn sin(&self) -> Complex<T> {
// formula: sin(a + bi) = sin(a)cosh(b) + i*cos(a)sinh(b) // formula: sin(a + bi) = sin(a)cosh(b) + i*cos(a)sinh(b)
Complex::new(self.re.clone().sin() * self.im.clone().cosh(), self.re.clone().cos() * self.im.clone().sinh()) Complex::new(self.re.sin() * self.im.cosh(), self.re.cos() * self.im.sinh())
} }
/// Computes the cosine of `self`. /// Computes the cosine of `self`.
#[inline] #[inline]
pub fn cos(&self) -> Complex<T> { pub fn cos(&self) -> Complex<T> {
// formula: cos(a + bi) = cos(a)cosh(b) - i*sin(a)sinh(b) // formula: cos(a + bi) = cos(a)cosh(b) - i*sin(a)sinh(b)
Complex::new(self.re.clone().cos() * self.im.clone().cosh(), -self.re.clone().sin() * self.im.clone().sinh()) Complex::new(self.re.cos() * self.im.cosh(), -self.re.sin() * self.im.sinh())
} }
/// Computes the tangent of `self`. /// Computes the tangent of `self`.
#[inline] #[inline]
pub fn tan(&self) -> Complex<T> { pub fn tan(&self) -> Complex<T> {
// formula: tan(a + bi) = (sin(2a) + i*sinh(2b))/(cos(2a) + cosh(2b)) // formula: tan(a + bi) = (sin(2a) + i*sinh(2b))/(cos(2a) + cosh(2b))
let (two_re, two_im) = (self.re.clone() + self.re.clone(), self.im.clone() + self.im.clone()); let (two_re, two_im) = (self.re + self.re, self.im + self.im);
Complex::new(two_re.clone().sin(), two_im.clone().sinh()).unscale(two_re.cos() + two_im.cosh()) Complex::new(two_re.sin(), two_im.sinh()).unscale(two_re.cos() + two_im.cosh())
} }
/// Computes the principal value of the inverse sine of `self`. /// Computes the principal value of the inverse sine of `self`.
@ -212,22 +212,22 @@ impl<T: Clone + Float> Complex<T> {
#[inline] #[inline]
pub fn sinh(&self) -> Complex<T> { pub fn sinh(&self) -> Complex<T> {
// formula: sinh(a + bi) = sinh(a)cos(b) + i*cosh(a)sin(b) // formula: sinh(a + bi) = sinh(a)cos(b) + i*cosh(a)sin(b)
Complex::new(self.re.clone().sinh() * self.im.clone().cos(), self.re.clone().cosh() * self.im.clone().sin()) Complex::new(self.re.sinh() * self.im.cos(), self.re.cosh() * self.im.sin())
} }
/// Computes the hyperbolic cosine of `self`. /// Computes the hyperbolic cosine of `self`.
#[inline] #[inline]
pub fn cosh(&self) -> Complex<T> { pub fn cosh(&self) -> Complex<T> {
// formula: cosh(a + bi) = cosh(a)cos(b) + i*sinh(a)sin(b) // formula: cosh(a + bi) = cosh(a)cos(b) + i*sinh(a)sin(b)
Complex::new(self.re.clone().cosh() * self.im.clone().cos(), self.re.clone().sinh() * self.im.clone().sin()) Complex::new(self.re.cosh() * self.im.cos(), self.re.sinh() * self.im.sin())
} }
/// Computes the hyperbolic tangent of `self`. /// Computes the hyperbolic tangent of `self`.
#[inline] #[inline]
pub fn tanh(&self) -> Complex<T> { pub fn tanh(&self) -> Complex<T> {
// formula: tanh(a + bi) = (sinh(2a) + i*sin(2b))/(cosh(2a) + cos(2b)) // formula: tanh(a + bi) = (sinh(2a) + i*sin(2b))/(cosh(2a) + cos(2b))
let (two_re, two_im) = (self.re.clone() + self.re.clone(), self.im.clone() + self.im.clone()); let (two_re, two_im) = (self.re + self.re, self.im + self.im);
Complex::new(two_re.clone().sinh(), two_im.clone().sin()).unscale(two_re.cosh() + two_im.cos()) Complex::new(two_re.sinh(), two_im.sin()).unscale(two_re.cosh() + two_im.cos())
} }
/// Computes the principal value of inverse hyperbolic sine of `self`. /// Computes the principal value of inverse hyperbolic sine of `self`.
@ -321,14 +321,14 @@ impl<'a, T: Clone + Num> From<&'a T> for Complex<T> {
} }
} }
macro_rules! forward_val_val_binop { macro_rules! forward_ref_ref_binop {
(impl $imp:ident, $method:ident) => { (impl $imp:ident, $method:ident) => {
impl<T: Clone + Num> $imp<Complex<T>> for Complex<T> { impl<'a, 'b, T: Clone + Num> $imp<&'b Complex<T>> for &'a Complex<T> {
type Output = Complex<T>; type Output = Complex<T>;
#[inline] #[inline]
fn $method(self, other: Complex<T>) -> Complex<T> { fn $method(self, other: &Complex<T>) -> Complex<T> {
(&self).$method(&other) self.clone().$method(other.clone())
} }
} }
} }
@ -341,7 +341,7 @@ macro_rules! forward_ref_val_binop {
#[inline] #[inline]
fn $method(self, other: Complex<T>) -> Complex<T> { fn $method(self, other: Complex<T>) -> Complex<T> {
self.$method(&other) self.clone().$method(other)
} }
} }
} }
@ -354,7 +354,7 @@ macro_rules! forward_val_ref_binop {
#[inline] #[inline]
fn $method(self, other: &Complex<T>) -> Complex<T> { fn $method(self, other: &Complex<T>) -> Complex<T> {
(&self).$method(other) self.$method(other.clone())
} }
} }
} }
@ -362,7 +362,7 @@ macro_rules! forward_val_ref_binop {
macro_rules! forward_all_binop { macro_rules! forward_all_binop {
(impl $imp:ident, $method:ident) => { (impl $imp:ident, $method:ident) => {
forward_val_val_binop!(impl $imp, $method); forward_ref_ref_binop!(impl $imp, $method);
forward_ref_val_binop!(impl $imp, $method); forward_ref_val_binop!(impl $imp, $method);
forward_val_ref_binop!(impl $imp, $method); forward_val_ref_binop!(impl $imp, $method);
}; };
@ -372,39 +372,38 @@ macro_rules! forward_all_binop {
forward_all_binop!(impl Add, add); forward_all_binop!(impl Add, add);
// (a + i b) + (c + i d) == (a + c) + i (b + d) // (a + i b) + (c + i d) == (a + c) + i (b + d)
impl<'a, 'b, T: Clone + Num> Add<&'b Complex<T>> for &'a Complex<T> { impl<T: Clone + Num> Add<Complex<T>> for Complex<T> {
type Output = Complex<T>; type Output = Complex<T>;
#[inline] #[inline]
fn add(self, other: &Complex<T>) -> Complex<T> { fn add(self, other: Complex<T>) -> Complex<T> {
Complex::new(self.re.clone() + other.re.clone(), Complex::new(self.re + other.re, self.im + other.im)
self.im.clone() + other.im.clone())
} }
} }
forward_all_binop!(impl Sub, sub); forward_all_binop!(impl Sub, sub);
// (a + i b) - (c + i d) == (a - c) + i (b - d) // (a + i b) - (c + i d) == (a - c) + i (b - d)
impl<'a, 'b, T: Clone + Num> Sub<&'b Complex<T>> for &'a Complex<T> { impl<T: Clone + Num> Sub<Complex<T>> for Complex<T> {
type Output = Complex<T>; type Output = Complex<T>;
#[inline] #[inline]
fn sub(self, other: &Complex<T>) -> Complex<T> { fn sub(self, other: Complex<T>) -> Complex<T> {
Complex::new(self.re.clone() - other.re.clone(), Complex::new(self.re - other.re, self.im - other.im)
self.im.clone() - other.im.clone())
} }
} }
forward_all_binop!(impl Mul, mul); forward_all_binop!(impl Mul, mul);
// (a + i b) * (c + i d) == (a*c - b*d) + i (a*d + b*c) // (a + i b) * (c + i d) == (a*c - b*d) + i (a*d + b*c)
impl<'a, 'b, T: Clone + Num> Mul<&'b Complex<T>> for &'a Complex<T> { impl<T: Clone + Num> Mul<Complex<T>> for Complex<T> {
type Output = Complex<T>; type Output = Complex<T>;
#[inline] #[inline]
fn mul(self, other: &Complex<T>) -> Complex<T> { fn mul(self, other: Complex<T>) -> Complex<T> {
Complex::new(self.re.clone() * other.re.clone() - self.im.clone() * other.im.clone(), let re = self.re.clone() * other.re.clone() - self.im.clone() * other.im.clone();
self.re.clone() * other.im.clone() + self.im.clone() * other.re.clone()) let im = self.re * other.im + self.im * other.re;
Complex::new(re, im)
} }
} }
@ -412,14 +411,15 @@ forward_all_binop!(impl Div, div);
// (a + i b) / (c + i d) == [(a + i b) * (c - i d)] / (c*c + d*d) // (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)] // == [(a*c + b*d) / (c*c + d*d)] + i [(b*c - a*d) / (c*c + d*d)]
impl<'a, 'b, T: Clone + Num> Div<&'b Complex<T>> for &'a Complex<T> { impl<T: Clone + Num> Div<Complex<T>> for Complex<T> {
type Output = Complex<T>; type Output = Complex<T>;
#[inline] #[inline]
fn div(self, other: &Complex<T>) -> Complex<T> { fn div(self, other: Complex<T>) -> Complex<T> {
let norm_sqr = other.norm_sqr(); let norm_sqr = other.norm_sqr();
Complex::new((self.re.clone() * other.re.clone() + self.im.clone() * other.im.clone()) / norm_sqr.clone(), let re = self.re.clone() * other.re.clone() + self.im.clone() * other.im.clone();
(self.im.clone() * other.re.clone() - self.re.clone() * other.im.clone()) / norm_sqr) let im = self.im * other.re - self.re * other.im;
Complex::new(re / norm_sqr.clone(), im / norm_sqr)
} }
} }
@ -427,7 +427,9 @@ impl<T: Clone + Num + Neg<Output = T>> Neg for Complex<T> {
type Output = Complex<T>; type Output = Complex<T>;
#[inline] #[inline]
fn neg(self) -> Complex<T> { -&self } fn neg(self) -> Complex<T> {
Complex::new(-self.re, -self.im)
}
} }
impl<'a, T: Clone + Num + Neg<Output = T>> Neg for &'a Complex<T> { impl<'a, T: Clone + Num + Neg<Output = T>> Neg for &'a Complex<T> {
@ -435,7 +437,7 @@ impl<'a, T: Clone + Num + Neg<Output = T>> Neg for &'a Complex<T> {
#[inline] #[inline]
fn neg(self) -> Complex<T> { fn neg(self) -> Complex<T> {
Complex::new(-self.re.clone(), -self.im.clone()) -self.clone()
} }
} }