diff --git a/library/coretests/tests/num/floats.rs b/library/coretests/tests/num/floats.rs
index d87f850944503..d6f6a7c4a4122 100644
--- a/library/coretests/tests/num/floats.rs
+++ b/library/coretests/tests/num/floats.rs
@@ -1699,6 +1699,8 @@ float_test! {
         assert!(nan.asinh().is_nan());
         assert!(flt(-0.0).asinh().is_sign_negative());
 
+        assert_ne!(Float::MAX.asinh(), inf);
+
         // issue 63271
         assert_approx_eq!(flt(2.0).asinh(), 1.443635475178810342493276740273105, Float::ASINH_APPROX);
         assert_approx_eq!(flt(-2.0).asinh(), -1.443635475178810342493276740273105, Float::ASINH_APPROX);
@@ -1732,6 +1734,7 @@ float_test! {
         assert!(nan.acosh().is_nan());
         assert_approx_eq!(flt(2.0).acosh(), 1.31695789692481670862504634730796844, Float::ACOSH_APPROX);
         assert_approx_eq!(flt(3.0).acosh(), 1.76274717403908605046521864995958461, Float::ACOSH_APPROX);
+        assert_ne!(Float::MAX.acosh(), inf);
 
         #[allow(overflowing_literals)]
         if Float::MAX > flt(66000.0) {
diff --git a/library/std/src/num/f128.rs b/library/std/src/num/f128.rs
index 2c8898a6aa86a..9af94c90c0028 100644
--- a/library/std/src/num/f128.rs
+++ b/library/std/src/num/f128.rs
@@ -868,6 +868,10 @@ impl f128 {
     #[must_use = "method returns a new number and does not mutate the original value"]
     pub fn asinh(self) -> f128 {
         let ax = self.abs();
+        if ax >= (1u128 << f128::MANTISSA_DIGITS / 2) as f128 {
+            return (ax.ln() + consts::LN_2).copysign(self);
+        }
+
         let ix = 1.0 / ax;
         (ax + (ax / (Self::hypot(1.0, ix) + ix))).ln_1p().copysign(self)
     }
@@ -902,6 +906,8 @@ impl f128 {
     pub fn acosh(self) -> f128 {
         if self < 1.0 {
             Self::NAN
+        } else if self >= (1u128 << f128::MANTISSA_DIGITS / 2) as f128 {
+            self.ln() + consts::LN_2
         } else {
             (self + ((self - 1.0).sqrt() * (self + 1.0).sqrt())).ln()
         }
diff --git a/library/std/src/num/f16.rs b/library/std/src/num/f16.rs
index 7ca266c8a5f60..ef610eacb05d7 100644
--- a/library/std/src/num/f16.rs
+++ b/library/std/src/num/f16.rs
@@ -832,9 +832,7 @@ impl f16 {
     #[unstable(feature = "f16", issue = "116909")]
     #[must_use = "method returns a new number and does not mutate the original value"]
     pub fn asinh(self) -> f16 {
-        let ax = self.abs();
-        let ix = 1.0 / ax;
-        (ax + (ax / (Self::hypot(1.0, ix) + ix))).ln_1p().copysign(self)
+        cmath::asinhf(self as f32) as f16
     }
 
     /// Inverse hyperbolic cosine function.
@@ -865,11 +863,7 @@ impl f16 {
     #[unstable(feature = "f16", issue = "116909")]
     #[must_use = "method returns a new number and does not mutate the original value"]
     pub fn acosh(self) -> f16 {
-        if self < 1.0 {
-            Self::NAN
-        } else {
-            (self + ((self - 1.0).sqrt() * (self + 1.0).sqrt())).ln()
-        }
+        cmath::acoshf(self as f32) as f16
     }
 
     /// Inverse hyperbolic tangent function.
diff --git a/library/std/src/num/f32.rs b/library/std/src/num/f32.rs
index 77e6824784605..771a0cae6dcd8 100644
--- a/library/std/src/num/f32.rs
+++ b/library/std/src/num/f32.rs
@@ -1091,9 +1091,7 @@ impl f32 {
     #[stable(feature = "rust1", since = "1.0.0")]
     #[inline]
     pub fn asinh(self) -> f32 {
-        let ax = self.abs();
-        let ix = 1.0 / ax;
-        (ax + (ax / (Self::hypot(1.0, ix) + ix))).ln_1p().copysign(self)
+        cmath::asinhf(self)
     }
 
     /// Inverse hyperbolic cosine function.
@@ -1119,11 +1117,7 @@ impl f32 {
     #[stable(feature = "rust1", since = "1.0.0")]
     #[inline]
     pub fn acosh(self) -> f32 {
-        if self < 1.0 {
-            Self::NAN
-        } else {
-            (self + ((self - 1.0).sqrt() * (self + 1.0).sqrt())).ln()
-        }
+        cmath::acoshf(self)
     }
 
     /// Inverse hyperbolic tangent function.
diff --git a/library/std/src/num/f64.rs b/library/std/src/num/f64.rs
index e0b9948a924db..59ef39a382b27 100644
--- a/library/std/src/num/f64.rs
+++ b/library/std/src/num/f64.rs
@@ -1091,9 +1091,7 @@ impl f64 {
     #[stable(feature = "rust1", since = "1.0.0")]
     #[inline]
     pub fn asinh(self) -> f64 {
-        let ax = self.abs();
-        let ix = 1.0 / ax;
-        (ax + (ax / (Self::hypot(1.0, ix) + ix))).ln_1p().copysign(self)
+        cmath::asinh(self)
     }
 
     /// Inverse hyperbolic cosine function.
@@ -1119,11 +1117,7 @@ impl f64 {
     #[stable(feature = "rust1", since = "1.0.0")]
     #[inline]
     pub fn acosh(self) -> f64 {
-        if self < 1.0 {
-            Self::NAN
-        } else {
-            (self + ((self - 1.0).sqrt() * (self + 1.0).sqrt())).ln()
-        }
+        cmath::acosh(self)
     }
 
     /// Inverse hyperbolic tangent function.
diff --git a/library/std/src/sys/cmath.rs b/library/std/src/sys/cmath.rs
index 1592218ead8b0..1d5c825710caf 100644
--- a/library/std/src/sys/cmath.rs
+++ b/library/std/src/sys/cmath.rs
@@ -4,7 +4,9 @@
 // or by `compiler-builtins` on unsupported platforms.
 unsafe extern "C" {
     pub safe fn acos(n: f64) -> f64;
+    pub safe fn acosh(n: f64) -> f64;
     pub safe fn asin(n: f64) -> f64;
+    pub safe fn asinh(n: f64) -> f64;
     pub safe fn atan(n: f64) -> f64;
     pub safe fn atan2(a: f64, b: f64) -> f64;
     pub safe fn cosh(n: f64) -> f64;
@@ -57,6 +59,16 @@ cfg_select! {
             f64::acos(n as f64) as f32
         }
 
+        #[inline]
+        pub fn acoshf(n: f32) -> f32 {
+            f64::acosh(n as f64) as f32
+        }
+
+        #[inline]
+        pub fn asinhf(n: f32) -> f32 {
+            f64::asinh(n as f64) as f32
+        }
+
         #[inline]
         pub fn asinf(n: f32) -> f32 {
             f64::asin(n as f64) as f32
@@ -95,7 +107,9 @@ cfg_select! {
     _ => {
         unsafe extern "C" {
             pub safe fn acosf(n: f32) -> f32;
+            pub safe fn acoshf(n: f32) -> f32;
             pub safe fn asinf(n: f32) -> f32;
+            pub safe fn asinhf(n: f32) -> f32;
             pub safe fn atan2f(a: f32, b: f32) -> f32;
             pub safe fn atanf(n: f32) -> f32;
             pub safe fn coshf(n: f32) -> f32;