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Fix tests and acosh zero sign #147

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Fix tests and acosh zero sign #147

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24 changes: 14 additions & 10 deletions src/lib.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -481,13 +481,12 @@ impl<T: Float> Complex<T> {
// 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 {
return Self::new(T::zero(), T::infinity());
} else if self == -i {
return Self::new(T::zero(), -T::infinity());
}
((one + i * self).ln() - (one - i * self).ln()) / (two * i)
((one + i * self).ln() - (one - i * self).ln()) / (i + i)
}

/// Computes the hyperbolic sine of `self`.
Expand Down Expand Up @@ -544,8 +543,8 @@ impl<T: Float> Complex<T> {
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;
two * (((self + one) / two).sqrt() + ((self - one) / two).sqrt()).ln()
let two = T::one() + T::one();
(((self + one) / two).sqrt() + ((self - one) / two).sqrt()).ln() * two
}

/// Computes the principal value of inverse hyperbolic tangent of `self`.
Expand All @@ -560,7 +559,7 @@ impl<T: Float> Complex<T> {
pub fn atanh(self) -> Self {
// formula: arctanh(z) = (ln(1+z) - ln(1-z))/2
let one = Self::one();
let two = one + one;
let two = T::one() + T::one();
if self == one {
return Self::new(T::infinity(), T::zero());
} else if self == -one {
Expand Down Expand Up @@ -2274,7 +2273,7 @@ pub(crate) mod test {
assert!(close(_0_1i.tanh(), _0_1i.scale(1.0.tan())));
for &c in all_consts.iter() {
// tanh(conj(z)) = conj(tanh(z))
assert!(close(c.conj().tanh(), c.conj().tanh()));
assert!(close(c.conj().tanh(), c.tanh().conj()));
// tanh(-z) = -tanh(z)
assert!(close(c.scale(-1.0).tanh(), c.tanh().scale(-1.0)));
}
Expand All @@ -2291,7 +2290,7 @@ pub(crate) mod test {
));
for &c in all_consts.iter() {
// asinh(conj(z)) = conj(asinh(z))
assert!(close(c.conj().asinh(), c.conj().asinh()));
assert!(close(c.conj().asinh(), c.asinh().conj()));
// asinh(-z) = -asinh(z)
assert!(close(c.scale(-1.0).asinh(), c.asinh().scale(-1.0)));
// for this branch, -pi/2 <= asinh(z).im <= pi/2
Expand All @@ -2305,13 +2304,18 @@ pub(crate) mod test {
fn test_acosh() {
assert!(close(_0_0i.acosh(), _0_1i.scale(f64::consts::PI / 2.0)));
assert!(close(_1_0i.acosh(), _0_0i));
// zero sign on imaginary part is used!
assert!(close(
_1_0i.scale(-1.0).acosh(),
Complex::new(-1., 0.).acosh(),
_0_1i.scale(f64::consts::PI)
));
assert!(close(
_1_0i.scale(-1.0).acosh(),
_0_1i.scale(-f64::consts::PI)
));
for &c in all_consts.iter() {
// acosh(conj(z)) = conj(acosh(z))
assert!(close(c.conj().acosh(), c.conj().acosh()));
assert!(close(c.conj().acosh(), c.acosh().conj()));
// for this branch, -pi <= acosh(z).im <= pi and 0 <= acosh(z).re
assert!(
-f64::consts::PI <= c.acosh().im
Expand All @@ -2328,7 +2332,7 @@ pub(crate) mod test {
assert!(close(_1_0i.atanh(), Complex::new(f64::infinity(), 0.0)));
for &c in all_consts.iter() {
// atanh(conj(z)) = conj(atanh(z))
assert!(close(c.conj().atanh(), c.conj().atanh()));
assert!(close(c.conj().atanh(), c.atanh().conj()));
// atanh(-z) = -atanh(z)
assert!(close(c.scale(-1.0).atanh(), c.atanh().scale(-1.0)));
// for this branch, -pi/2 <= atanh(z).im <= pi/2
Expand Down