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Use values for all Float methods #82

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merged 2 commits into from Jun 13, 2020
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Use values for all Float methods #82

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3564494
Use values for all Float methods
cuviper Jun 13, 2020
59624e8
cargo fmt
cuviper Jun 13, 2020
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8 changes: 6 additions & 2 deletions src/cast.rs
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Expand Up @@ -5,9 +5,13 @@ macro_rules! impl_to_primitive {
($ty:ty, $to:ident) => {
#[inline]
fn $to(&self) -> Option<$ty> {
if self.im.is_zero() { self.re.$to() } else { None }
if self.im.is_zero() {
self.re.$to()
} else {
None
}
}
}
};
} // impl_to_primitive

// Returns None if Complex part is non-zero
Expand Down
94 changes: 47 additions & 47 deletions src/lib.rs
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Expand Up @@ -160,35 +160,35 @@ impl<T: Clone + Signed> Complex<T> {
}

#[cfg(any(feature = "std", feature = "libm"))]
impl<T: Clone + Float> Complex<T> {
impl<T: Float> Complex<T> {
/// Calculate |self|
#[inline]
pub fn norm(&self) -> T {
pub fn norm(self) -> T {
self.re.hypot(self.im)
}
/// Calculate the principal Arg of self.
#[inline]
pub fn arg(&self) -> T {
pub fn arg(self) -> T {
self.im.atan2(self.re)
}
/// Convert to polar form (r, theta), such that
/// `self = r * exp(i * theta)`
#[inline]
pub fn to_polar(&self) -> (T, T) {
pub fn to_polar(self) -> (T, T) {
(self.norm(), self.arg())
}
/// Convert a polar representation into a complex number.
#[inline]
pub fn from_polar(r: &T, theta: &T) -> Self {
Self::new(*r * theta.cos(), *r * theta.sin())
pub fn from_polar(r: T, theta: T) -> Self {
Self::new(r * theta.cos(), r * theta.sin())
}

/// Computes `e^(self)`, where `e` is the base of the natural logarithm.
#[inline]
pub fn exp(&self) -> Self {
pub fn exp(self) -> Self {
// formula: e^(a + bi) = e^a (cos(b) + i*sin(b))
// = from_polar(e^a, b)
Self::from_polar(&self.re.exp(), &self.im)
Self::from_polar(self.re.exp(), self.im)
}

/// Computes the principal value of natural logarithm of `self`.
Expand All @@ -199,7 +199,7 @@ impl<T: Clone + Float> Complex<T> {
///
/// The branch satisfies `-π ≤ arg(ln(z)) ≤ π`.
#[inline]
pub fn ln(&self) -> Self {
pub fn ln(self) -> Self {
// formula: ln(z) = ln|z| + i*arg(z)
let (r, theta) = self.to_polar();
Self::new(r.ln(), theta)
Expand All @@ -213,7 +213,7 @@ impl<T: Clone + Float> Complex<T> {
///
/// The branch satisfies `-π/2 ≤ arg(sqrt(z)) ≤ π/2`.
#[inline]
pub fn sqrt(&self) -> Self {
pub fn sqrt(self) -> Self {
if self.im.is_zero() {
if self.re.is_sign_positive() {
// simple positive real √r, and copy `im` for its sign
Expand Down Expand Up @@ -245,7 +245,7 @@ impl<T: Clone + Float> Complex<T> {
let one = T::one();
let two = one + one;
let (r, theta) = self.to_polar();
Self::from_polar(&(r.sqrt()), &(theta / two))
Self::from_polar(r.sqrt(), theta / two)
}
}

Expand All @@ -261,7 +261,7 @@ impl<T: Clone + Float> Complex<T> {
/// negative real numbers. For example, the real cube root of `-8` is `-2`,
/// but the principal complex cube root of `-8` is `1 + i√3`.
#[inline]
pub fn cbrt(&self) -> Self {
pub fn cbrt(self) -> Self {
if self.im.is_zero() {
if self.re.is_sign_positive() {
// simple positive real ∛r, and copy `im` for its sign
Expand Down Expand Up @@ -298,22 +298,22 @@ impl<T: Clone + Float> Complex<T> {
let one = T::one();
let three = one + one + one;
let (r, theta) = self.to_polar();
Self::from_polar(&(r.cbrt()), &(theta / three))
Self::from_polar(r.cbrt(), theta / three)
}
}

/// Raises `self` to a floating point power.
#[inline]
pub fn powf(&self, exp: T) -> Self {
pub fn powf(self, exp: T) -> Self {
// formula: x^y = (ρ e^(i θ))^y = ρ^y e^(i θ y)
// = from_polar(ρ^y, θ y)
let (r, theta) = self.to_polar();
Self::from_polar(&r.powf(exp), &(theta * exp))
Self::from_polar(r.powf(exp), theta * exp)
}

/// Returns the logarithm of `self` with respect to an arbitrary base.
#[inline]
pub fn log(&self, base: T) -> Self {
pub fn log(self, base: T) -> Self {
// formula: log_y(x) = log_y(ρ e^(i θ))
// = log_y(ρ) + log_y(e^(i θ)) = log_y(ρ) + ln(e^(i θ)) / ln(y)
// = log_y(ρ) + i θ / ln(y)
Expand All @@ -323,7 +323,7 @@ impl<T: Clone + Float> Complex<T> {

/// Raises `self` to a complex power.
#[inline]
pub fn powc(&self, exp: Self) -> Self {
pub fn powc(self, exp: Self) -> Self {
// formula: x^y = (a + i b)^(c + i d)
// = (ρ e^(i θ))^c (ρ e^(i θ))^(i d)
// where ρ=|x| and θ=arg(x)
Expand All @@ -337,22 +337,22 @@ impl<T: Clone + Float> Complex<T> {
// = from_polar(p^c e^(−d θ), c θ + d ln(ρ))
let (r, theta) = self.to_polar();
Self::from_polar(
&(r.powf(exp.re) * (-exp.im * theta).exp()),
&(exp.re * theta + exp.im * r.ln()),
r.powf(exp.re) * (-exp.im * theta).exp(),
exp.re * theta + exp.im * r.ln(),
)
}

/// Raises a floating point number to the complex power `self`.
#[inline]
pub fn expf(&self, base: T) -> Self {
pub fn expf(self, base: T) -> Self {
// formula: x^(a+bi) = x^a x^bi = x^a e^(b ln(x) i)
// = from_polar(x^a, b ln(x))
Self::from_polar(&base.powf(self.re), &(self.im * base.ln()))
Self::from_polar(base.powf(self.re), self.im * base.ln())
}

/// Computes the sine of `self`.
#[inline]
pub fn sin(&self) -> Self {
pub fn sin(self) -> Self {
// formula: sin(a + bi) = sin(a)cosh(b) + i*cos(a)sinh(b)
Self::new(
self.re.sin() * self.im.cosh(),
Expand All @@ -362,7 +362,7 @@ impl<T: Clone + Float> Complex<T> {

/// Computes the cosine of `self`.
#[inline]
pub fn cos(&self) -> Self {
pub fn cos(self) -> Self {
// formula: cos(a + bi) = cos(a)cosh(b) - i*sin(a)sinh(b)
Self::new(
self.re.cos() * self.im.cosh(),
Expand All @@ -372,7 +372,7 @@ impl<T: Clone + Float> Complex<T> {

/// Computes the tangent of `self`.
#[inline]
pub fn tan(&self) -> Self {
pub fn tan(self) -> Self {
// formula: tan(a + bi) = (sin(2a) + i*sinh(2b))/(cos(2a) + cosh(2b))
let (two_re, two_im) = (self.re + self.re, self.im + self.im);
Self::new(two_re.sin(), two_im.sinh()).unscale(two_re.cos() + two_im.cosh())
Expand All @@ -387,7 +387,7 @@ impl<T: Clone + Float> Complex<T> {
///
/// The branch satisfies `-π/2 ≤ Re(asin(z)) ≤ π/2`.
#[inline]
pub fn asin(&self) -> Self {
pub fn asin(self) -> Self {
// formula: arcsin(z) = -i ln(sqrt(1-z^2) + iz)
let i = Self::i();
-i * ((Self::one() - self * self).sqrt() + i * self).ln()
Expand All @@ -402,7 +402,7 @@ impl<T: Clone + Float> Complex<T> {
///
/// The branch satisfies `0 ≤ Re(acos(z)) ≤ π`.
#[inline]
pub fn acos(&self) -> Self {
pub fn acos(self) -> Self {
// formula: arccos(z) = -i ln(i sqrt(1-z^2) + z)
let i = Self::i();
-i * (i * (Self::one() - self * self).sqrt() + self).ln()
Expand All @@ -417,22 +417,22 @@ impl<T: Clone + Float> Complex<T> {
///
/// The branch satisfies `-π/2 ≤ Re(atan(z)) ≤ π/2`.
#[inline]
pub fn atan(&self) -> Self {
pub fn atan(self) -> Self {
// formula: arctan(z) = (ln(1+iz) - ln(1-iz))/(2i)
let i = Self::i();
let one = Self::one();
let two = one + one;
if *self == i {
if self == i {
return Self::new(T::zero(), T::infinity());
} else if *self == -i {
} else if self == -i {
return Self::new(T::zero(), -T::infinity());
}
((one + i * self).ln() - (one - i * self).ln()) / (two * i)
}

/// Computes the hyperbolic sine of `self`.
#[inline]
pub fn sinh(&self) -> Self {
pub fn sinh(self) -> Self {
// formula: sinh(a + bi) = sinh(a)cos(b) + i*cosh(a)sin(b)
Self::new(
self.re.sinh() * self.im.cos(),
Expand All @@ -442,7 +442,7 @@ impl<T: Clone + Float> Complex<T> {

/// Computes the hyperbolic cosine of `self`.
#[inline]
pub fn cosh(&self) -> Self {
pub fn cosh(self) -> Self {
// formula: cosh(a + bi) = cosh(a)cos(b) + i*sinh(a)sin(b)
Self::new(
self.re.cosh() * self.im.cos(),
Expand All @@ -452,7 +452,7 @@ impl<T: Clone + Float> Complex<T> {

/// Computes the hyperbolic tangent of `self`.
#[inline]
pub fn tanh(&self) -> Self {
pub fn tanh(self) -> Self {
// formula: tanh(a + bi) = (sinh(2a) + i*sin(2b))/(cosh(2a) + cos(2b))
let (two_re, two_im) = (self.re + self.re, self.im + self.im);
Self::new(two_re.sinh(), two_im.sin()).unscale(two_re.cosh() + two_im.cos())
Expand All @@ -467,7 +467,7 @@ impl<T: Clone + Float> Complex<T> {
///
/// The branch satisfies `-π/2 ≤ Im(asinh(z)) ≤ π/2`.
#[inline]
pub fn asinh(&self) -> Self {
pub fn asinh(self) -> Self {
// formula: arcsinh(z) = ln(z + sqrt(1+z^2))
let one = Self::one();
(self + (one + self * self).sqrt()).ln()
Expand All @@ -481,7 +481,7 @@ impl<T: Clone + Float> Complex<T> {
///
/// The branch satisfies `-π ≤ Im(acosh(z)) ≤ π` and `0 ≤ Re(acosh(z)) < ∞`.
#[inline]
pub fn acosh(&self) -> Self {
pub fn acosh(self) -> Self {
// formula: arccosh(z) = 2 ln(sqrt((z+1)/2) + sqrt((z-1)/2))
let one = Self::one();
let two = one + one;
Expand All @@ -497,13 +497,13 @@ impl<T: Clone + Float> Complex<T> {
///
/// The branch satisfies `-π/2 ≤ Im(atanh(z)) ≤ π/2`.
#[inline]
pub fn atanh(&self) -> Self {
pub fn atanh(self) -> Self {
// formula: arctanh(z) = (ln(1+z) - ln(1-z))/2
let one = Self::one();
let two = one + one;
if *self == one {
if self == one {
return Self::new(T::infinity(), T::zero());
} else if *self == -one {
} else if self == -one {
return Self::new(-T::infinity(), T::zero());
}
((one + self).ln() - (one - self).ln()) / two
Expand Down Expand Up @@ -532,7 +532,7 @@ impl<T: Clone + Float> Complex<T> {
/// assert!((inv - expected).norm() < 1e-315);
/// ```
#[inline]
pub fn finv(&self) -> Complex<T> {
pub fn finv(self) -> Complex<T> {
let norm = self.norm();
self.conj() / norm / norm
}
Expand Down Expand Up @@ -561,12 +561,12 @@ impl<T: Clone + Float> Complex<T> {
/// assert!((quotient - expected).norm() < 1e-315);
/// ```
#[inline]
pub fn fdiv(&self, other: Complex<T>) -> Complex<T> {
pub fn fdiv(self, other: Complex<T>) -> Complex<T> {
self * other.finv()
}
}

impl<T: Clone + FloatCore> Complex<T> {
impl<T: FloatCore> Complex<T> {
/// Checks if the given complex number is NaN
#[inline]
pub fn is_nan(self) -> bool {
Expand Down Expand Up @@ -1632,7 +1632,7 @@ mod test {
fn test_polar_conv() {
fn test(c: Complex64) {
let (r, theta) = c.to_polar();
assert!((c - Complex::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);
Expand Down Expand Up @@ -1775,12 +1775,12 @@ mod test {
let n2 = n * n;
assert!(close(
Complex64::new(0.0, n2).sqrt(),
Complex64::from_polar(&n, &(f64::consts::FRAC_PI_4))
Complex64::from_polar(n, f64::consts::FRAC_PI_4)
));
// √(0 - n²i) = n e^(-iπ/4)
assert!(close(
Complex64::new(0.0, -n2).sqrt(),
Complex64::from_polar(&n, &(-f64::consts::FRAC_PI_4))
Complex64::from_polar(n, -f64::consts::FRAC_PI_4)
));
}
}
Expand Down Expand Up @@ -1824,12 +1824,12 @@ mod test {
// ∛(-n³ + 0i) = n e^(iπ/3)
assert!(close(
Complex64::new(-n3, 0.0).cbrt(),
Complex64::from_polar(&n, &(f64::consts::FRAC_PI_3))
Complex64::from_polar(n, f64::consts::FRAC_PI_3)
));
// ∛(-n³ - 0i) = n e^(-iπ/3)
assert!(close(
Complex64::new(-n3, -0.0).cbrt(),
Complex64::from_polar(&n, &(-f64::consts::FRAC_PI_3))
Complex64::from_polar(n, -f64::consts::FRAC_PI_3)
));
}
}
Expand All @@ -1841,12 +1841,12 @@ mod test {
let n3 = n * n * n;
assert!(close(
Complex64::new(0.0, n3).cbrt(),
Complex64::from_polar(&n, &(f64::consts::FRAC_PI_6))
Complex64::from_polar(n, f64::consts::FRAC_PI_6)
));
// ∛(0 - n³i) = n e^(-iπ/6)
assert!(close(
Complex64::new(0.0, -n3).cbrt(),
Complex64::from_polar(&n, &(-f64::consts::FRAC_PI_6))
Complex64::from_polar(n, -f64::consts::FRAC_PI_6)
));
}
}
Expand Down