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Rollup merge of #104553 - mwillsey:asinh-acosh-accuracy, r=thomcc
Improve accuracy of asinh and acosh This PR addresses the inaccuracy of `asinh` and `acosh` identified by the [Herbie](http://herbie.uwplse.org/) tool, `@pavpanchekha,` `@finnbear` in #104548. It also adds a couple tests that failed in the existing implementations and now pass. Closes #104548 r? rust-lang/libs
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45bfb1cdf1
@ -880,7 +880,9 @@ impl f32 {
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn asinh(self) -> f32 {
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(self.abs() + ((self * self) + 1.0).sqrt()).ln().copysign(self)
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let ax = self.abs();
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let ix = 1.0 / ax;
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(ax + (ax / (Self::hypot(1.0, ix) + ix))).ln_1p().copysign(self)
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}
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/// Inverse hyperbolic cosine function.
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@ -900,7 +902,11 @@ impl f32 {
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn acosh(self) -> f32 {
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if self < 1.0 { Self::NAN } else { (self + ((self * self) - 1.0).sqrt()).ln() }
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if self < 1.0 {
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Self::NAN
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} else {
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(self + ((self - 1.0).sqrt() * (self + 1.0).sqrt())).ln()
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}
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}
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/// Inverse hyperbolic tangent function.
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@ -587,6 +587,11 @@ fn test_asinh() {
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assert_approx_eq!((-2.0f32).asinh(), -1.443635475178810342493276740273105f32);
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// regression test for the catastrophic cancellation fixed in 72486
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assert_approx_eq!((-3000.0f32).asinh(), -8.699514775987968673236893537700647f32);
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// test for low accuracy from issue 104548
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assert_approx_eq!(60.0f32, 60.0f32.sinh().asinh());
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// mul needed for approximate comparison to be meaningful
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assert_approx_eq!(1.0f32, 1e-15f32.sinh().asinh() * 1e15f32);
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}
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#[test]
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@ -602,6 +607,9 @@ fn test_acosh() {
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assert!(nan.acosh().is_nan());
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assert_approx_eq!(2.0f32.acosh(), 1.31695789692481670862504634730796844f32);
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assert_approx_eq!(3.0f32.acosh(), 1.76274717403908605046521864995958461f32);
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// test for low accuracy from issue 104548
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assert_approx_eq!(60.0f32, 60.0f32.cosh().acosh());
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}
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#[test]
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@ -882,7 +882,9 @@ impl f64 {
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn asinh(self) -> f64 {
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(self.abs() + ((self * self) + 1.0).sqrt()).ln().copysign(self)
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let ax = self.abs();
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let ix = 1.0 / ax;
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(ax + (ax / (Self::hypot(1.0, ix) + ix))).ln_1p().copysign(self)
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}
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/// Inverse hyperbolic cosine function.
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@ -902,7 +904,11 @@ impl f64 {
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn acosh(self) -> f64 {
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if self < 1.0 { Self::NAN } else { (self + ((self * self) - 1.0).sqrt()).ln() }
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if self < 1.0 {
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Self::NAN
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} else {
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(self + ((self - 1.0).sqrt() * (self + 1.0).sqrt())).ln()
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}
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}
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/// Inverse hyperbolic tangent function.
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@ -575,6 +575,11 @@ fn test_asinh() {
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assert_approx_eq!((-2.0f64).asinh(), -1.443635475178810342493276740273105f64);
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// regression test for the catastrophic cancellation fixed in 72486
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assert_approx_eq!((-67452098.07139316f64).asinh(), -18.72007542627454439398548429400083);
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// test for low accuracy from issue 104548
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assert_approx_eq!(60.0f64, 60.0f64.sinh().asinh());
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// mul needed for approximate comparison to be meaningful
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assert_approx_eq!(1.0f64, 1e-15f64.sinh().asinh() * 1e15f64);
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}
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#[test]
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@ -590,6 +595,9 @@ fn test_acosh() {
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assert!(nan.acosh().is_nan());
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assert_approx_eq!(2.0f64.acosh(), 1.31695789692481670862504634730796844f64);
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assert_approx_eq!(3.0f64.acosh(), 1.76274717403908605046521864995958461f64);
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// test for low accuracy from issue 104548
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assert_approx_eq!(60.0f64, 60.0f64.cosh().acosh());
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}
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#[test]
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