diff --git a/compiler/rustc_const_eval/src/interpret/intrinsics.rs b/compiler/rustc_const_eval/src/interpret/intrinsics.rs
index bf4152d4b8cd5..64467a9013696 100644
--- a/compiler/rustc_const_eval/src/interpret/intrinsics.rs
+++ b/compiler/rustc_const_eval/src/interpret/intrinsics.rs
@@ -518,6 +518,103 @@ impl<'tcx, M: Machine<'tcx>> InterpCx<'tcx, M> {
             sym::fabsf64 => self.float_abs_intrinsic::<Double>(args, dest)?,
             sym::fabsf128 => self.float_abs_intrinsic::<Quad>(args, dest)?,
 
+            sym::floorf16 => self.float_round_intrinsic::<Half>(
+                args,
+                dest,
+                rustc_apfloat::Round::TowardNegative,
+            )?,
+            sym::floorf32 => self.float_round_intrinsic::<Single>(
+                args,
+                dest,
+                rustc_apfloat::Round::TowardNegative,
+            )?,
+            sym::floorf64 => self.float_round_intrinsic::<Double>(
+                args,
+                dest,
+                rustc_apfloat::Round::TowardNegative,
+            )?,
+            sym::floorf128 => self.float_round_intrinsic::<Quad>(
+                args,
+                dest,
+                rustc_apfloat::Round::TowardNegative,
+            )?,
+
+            sym::ceilf16 => self.float_round_intrinsic::<Half>(
+                args,
+                dest,
+                rustc_apfloat::Round::TowardPositive,
+            )?,
+            sym::ceilf32 => self.float_round_intrinsic::<Single>(
+                args,
+                dest,
+                rustc_apfloat::Round::TowardPositive,
+            )?,
+            sym::ceilf64 => self.float_round_intrinsic::<Double>(
+                args,
+                dest,
+                rustc_apfloat::Round::TowardPositive,
+            )?,
+            sym::ceilf128 => self.float_round_intrinsic::<Quad>(
+                args,
+                dest,
+                rustc_apfloat::Round::TowardPositive,
+            )?,
+
+            sym::truncf16 => {
+                self.float_round_intrinsic::<Half>(args, dest, rustc_apfloat::Round::TowardZero)?
+            }
+            sym::truncf32 => {
+                self.float_round_intrinsic::<Single>(args, dest, rustc_apfloat::Round::TowardZero)?
+            }
+            sym::truncf64 => {
+                self.float_round_intrinsic::<Double>(args, dest, rustc_apfloat::Round::TowardZero)?
+            }
+            sym::truncf128 => {
+                self.float_round_intrinsic::<Quad>(args, dest, rustc_apfloat::Round::TowardZero)?
+            }
+
+            sym::roundf16 => self.float_round_intrinsic::<Half>(
+                args,
+                dest,
+                rustc_apfloat::Round::NearestTiesToAway,
+            )?,
+            sym::roundf32 => self.float_round_intrinsic::<Single>(
+                args,
+                dest,
+                rustc_apfloat::Round::NearestTiesToAway,
+            )?,
+            sym::roundf64 => self.float_round_intrinsic::<Double>(
+                args,
+                dest,
+                rustc_apfloat::Round::NearestTiesToAway,
+            )?,
+            sym::roundf128 => self.float_round_intrinsic::<Quad>(
+                args,
+                dest,
+                rustc_apfloat::Round::NearestTiesToAway,
+            )?,
+
+            sym::round_ties_even_f16 => self.float_round_intrinsic::<Half>(
+                args,
+                dest,
+                rustc_apfloat::Round::NearestTiesToEven,
+            )?,
+            sym::round_ties_even_f32 => self.float_round_intrinsic::<Single>(
+                args,
+                dest,
+                rustc_apfloat::Round::NearestTiesToEven,
+            )?,
+            sym::round_ties_even_f64 => self.float_round_intrinsic::<Double>(
+                args,
+                dest,
+                rustc_apfloat::Round::NearestTiesToEven,
+            )?,
+            sym::round_ties_even_f128 => self.float_round_intrinsic::<Quad>(
+                args,
+                dest,
+                rustc_apfloat::Round::NearestTiesToEven,
+            )?,
+
             // Unsupported intrinsic: skip the return_to_block below.
             _ => return interp_ok(false),
         }
@@ -900,4 +997,20 @@ impl<'tcx, M: Machine<'tcx>> InterpCx<'tcx, M> {
         self.write_scalar(x.abs(), dest)?;
         interp_ok(())
     }
+
+    fn float_round_intrinsic<F>(
+        &mut self,
+        args: &[OpTy<'tcx, M::Provenance>],
+        dest: &PlaceTy<'tcx, M::Provenance>,
+        mode: rustc_apfloat::Round,
+    ) -> InterpResult<'tcx, ()>
+    where
+        F: rustc_apfloat::Float + rustc_apfloat::FloatConvert<F> + Into<Scalar<M::Provenance>>,
+    {
+        let x: F = self.read_scalar(&args[0])?.to_float()?;
+        let res = x.round_to_integral(mode).value;
+        let res = self.adjust_nan(res, &[x]);
+        self.write_scalar(res, dest)?;
+        interp_ok(())
+    }
 }
diff --git a/library/core/src/intrinsics/mod.rs b/library/core/src/intrinsics/mod.rs
index f89baef76f093..bb3e870389c70 100644
--- a/library/core/src/intrinsics/mod.rs
+++ b/library/core/src/intrinsics/mod.rs
@@ -2212,28 +2212,28 @@ pub unsafe fn fmuladdf128(a: f128, b: f128, c: f128) -> f128;
 /// [`f16::floor`](../../std/primitive.f16.html#method.floor)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub unsafe fn floorf16(x: f16) -> f16;
+pub const unsafe fn floorf16(x: f16) -> f16;
 /// Returns the largest integer less than or equal to an `f32`.
 ///
 /// The stabilized version of this intrinsic is
 /// [`f32::floor`](../../std/primitive.f32.html#method.floor)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub unsafe fn floorf32(x: f32) -> f32;
+pub const unsafe fn floorf32(x: f32) -> f32;
 /// Returns the largest integer less than or equal to an `f64`.
 ///
 /// The stabilized version of this intrinsic is
 /// [`f64::floor`](../../std/primitive.f64.html#method.floor)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub unsafe fn floorf64(x: f64) -> f64;
+pub const unsafe fn floorf64(x: f64) -> f64;
 /// Returns the largest integer less than or equal to an `f128`.
 ///
 /// The stabilized version of this intrinsic is
 /// [`f128::floor`](../../std/primitive.f128.html#method.floor)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub unsafe fn floorf128(x: f128) -> f128;
+pub const unsafe fn floorf128(x: f128) -> f128;
 
 /// Returns the smallest integer greater than or equal to an `f16`.
 ///
@@ -2241,28 +2241,28 @@ pub unsafe fn floorf128(x: f128) -> f128;
 /// [`f16::ceil`](../../std/primitive.f16.html#method.ceil)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub unsafe fn ceilf16(x: f16) -> f16;
+pub const unsafe fn ceilf16(x: f16) -> f16;
 /// Returns the smallest integer greater than or equal to an `f32`.
 ///
 /// The stabilized version of this intrinsic is
 /// [`f32::ceil`](../../std/primitive.f32.html#method.ceil)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub unsafe fn ceilf32(x: f32) -> f32;
+pub const unsafe fn ceilf32(x: f32) -> f32;
 /// Returns the smallest integer greater than or equal to an `f64`.
 ///
 /// The stabilized version of this intrinsic is
 /// [`f64::ceil`](../../std/primitive.f64.html#method.ceil)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub unsafe fn ceilf64(x: f64) -> f64;
+pub const unsafe fn ceilf64(x: f64) -> f64;
 /// Returns the smallest integer greater than or equal to an `f128`.
 ///
 /// The stabilized version of this intrinsic is
 /// [`f128::ceil`](../../std/primitive.f128.html#method.ceil)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub unsafe fn ceilf128(x: f128) -> f128;
+pub const unsafe fn ceilf128(x: f128) -> f128;
 
 /// Returns the integer part of an `f16`.
 ///
@@ -2270,28 +2270,28 @@ pub unsafe fn ceilf128(x: f128) -> f128;
 /// [`f16::trunc`](../../std/primitive.f16.html#method.trunc)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub unsafe fn truncf16(x: f16) -> f16;
+pub const unsafe fn truncf16(x: f16) -> f16;
 /// Returns the integer part of an `f32`.
 ///
 /// The stabilized version of this intrinsic is
 /// [`f32::trunc`](../../std/primitive.f32.html#method.trunc)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub unsafe fn truncf32(x: f32) -> f32;
+pub const unsafe fn truncf32(x: f32) -> f32;
 /// Returns the integer part of an `f64`.
 ///
 /// The stabilized version of this intrinsic is
 /// [`f64::trunc`](../../std/primitive.f64.html#method.trunc)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub unsafe fn truncf64(x: f64) -> f64;
+pub const unsafe fn truncf64(x: f64) -> f64;
 /// Returns the integer part of an `f128`.
 ///
 /// The stabilized version of this intrinsic is
 /// [`f128::trunc`](../../std/primitive.f128.html#method.trunc)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub unsafe fn truncf128(x: f128) -> f128;
+pub const unsafe fn truncf128(x: f128) -> f128;
 
 /// Returns the nearest integer to an `f16`. Rounds half-way cases to the number with an even
 /// least significant digit.
@@ -2300,7 +2300,7 @@ pub unsafe fn truncf128(x: f128) -> f128;
 /// [`f16::round_ties_even`](../../std/primitive.f16.html#method.round_ties_even)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub fn round_ties_even_f16(x: f16) -> f16;
+pub const fn round_ties_even_f16(x: f16) -> f16;
 
 /// Returns the nearest integer to an `f32`. Rounds half-way cases to the number with an even
 /// least significant digit.
@@ -2309,7 +2309,7 @@ pub fn round_ties_even_f16(x: f16) -> f16;
 /// [`f32::round_ties_even`](../../std/primitive.f32.html#method.round_ties_even)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub fn round_ties_even_f32(x: f32) -> f32;
+pub const fn round_ties_even_f32(x: f32) -> f32;
 
 /// Returns the nearest integer to an `f64`. Rounds half-way cases to the number with an even
 /// least significant digit.
@@ -2318,7 +2318,7 @@ pub fn round_ties_even_f32(x: f32) -> f32;
 /// [`f64::round_ties_even`](../../std/primitive.f64.html#method.round_ties_even)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub fn round_ties_even_f64(x: f64) -> f64;
+pub const fn round_ties_even_f64(x: f64) -> f64;
 
 /// Returns the nearest integer to an `f128`. Rounds half-way cases to the number with an even
 /// least significant digit.
@@ -2327,7 +2327,7 @@ pub fn round_ties_even_f64(x: f64) -> f64;
 /// [`f128::round_ties_even`](../../std/primitive.f128.html#method.round_ties_even)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub fn round_ties_even_f128(x: f128) -> f128;
+pub const fn round_ties_even_f128(x: f128) -> f128;
 
 /// Returns the nearest integer to an `f16`. Rounds half-way cases away from zero.
 ///
@@ -2335,28 +2335,28 @@ pub fn round_ties_even_f128(x: f128) -> f128;
 /// [`f16::round`](../../std/primitive.f16.html#method.round)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub unsafe fn roundf16(x: f16) -> f16;
+pub const unsafe fn roundf16(x: f16) -> f16;
 /// Returns the nearest integer to an `f32`. Rounds half-way cases away from zero.
 ///
 /// The stabilized version of this intrinsic is
 /// [`f32::round`](../../std/primitive.f32.html#method.round)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub unsafe fn roundf32(x: f32) -> f32;
+pub const unsafe fn roundf32(x: f32) -> f32;
 /// Returns the nearest integer to an `f64`. Rounds half-way cases away from zero.
 ///
 /// The stabilized version of this intrinsic is
 /// [`f64::round`](../../std/primitive.f64.html#method.round)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub unsafe fn roundf64(x: f64) -> f64;
+pub const unsafe fn roundf64(x: f64) -> f64;
 /// Returns the nearest integer to an `f128`. Rounds half-way cases away from zero.
 ///
 /// The stabilized version of this intrinsic is
 /// [`f128::round`](../../std/primitive.f128.html#method.round)
 #[rustc_intrinsic]
 #[rustc_nounwind]
-pub unsafe fn roundf128(x: f128) -> f128;
+pub const unsafe fn roundf128(x: f128) -> f128;
 
 /// Float addition that allows optimizations based on algebraic rules.
 /// May assume inputs are finite.
diff --git a/library/core/src/num/f128.rs b/library/core/src/num/f128.rs
index 0c2c4155d66ce..6b9b2ba868911 100644
--- a/library/core/src/num/f128.rs
+++ b/library/core/src/num/f128.rs
@@ -1447,8 +1447,10 @@ impl f128 {
     #[inline]
     #[rustc_allow_incoherent_impl]
     #[unstable(feature = "f128", issue = "116909")]
+    #[rustc_const_unstable(feature = "f128", issue = "116909")]
+    // #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn floor(self) -> f128 {
+    pub const fn floor(self) -> f128 {
         // SAFETY: intrinsic with no preconditions
         unsafe { intrinsics::floorf128(self) }
     }
@@ -1477,8 +1479,10 @@ impl f128 {
     #[doc(alias = "ceiling")]
     #[rustc_allow_incoherent_impl]
     #[unstable(feature = "f128", issue = "116909")]
+    #[rustc_const_unstable(feature = "f128", issue = "116909")]
+    // #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn ceil(self) -> f128 {
+    pub const fn ceil(self) -> f128 {
         // SAFETY: intrinsic with no preconditions
         unsafe { intrinsics::ceilf128(self) }
     }
@@ -1513,8 +1517,10 @@ impl f128 {
     #[inline]
     #[rustc_allow_incoherent_impl]
     #[unstable(feature = "f128", issue = "116909")]
+    #[rustc_const_unstable(feature = "f128", issue = "116909")]
+    // #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn round(self) -> f128 {
+    pub const fn round(self) -> f128 {
         // SAFETY: intrinsic with no preconditions
         unsafe { intrinsics::roundf128(self) }
     }
@@ -1547,8 +1553,10 @@ impl f128 {
     #[inline]
     #[rustc_allow_incoherent_impl]
     #[unstable(feature = "f128", issue = "116909")]
+    #[rustc_const_unstable(feature = "f128", issue = "116909")]
+    // #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn round_ties_even(self) -> f128 {
+    pub const fn round_ties_even(self) -> f128 {
         intrinsics::round_ties_even_f128(self)
     }
 
@@ -1579,8 +1587,10 @@ impl f128 {
     #[doc(alias = "truncate")]
     #[rustc_allow_incoherent_impl]
     #[unstable(feature = "f128", issue = "116909")]
+    #[rustc_const_unstable(feature = "f128", issue = "116909")]
+    // #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn trunc(self) -> f128 {
+    pub const fn trunc(self) -> f128 {
         // SAFETY: intrinsic with no preconditions
         unsafe { intrinsics::truncf128(self) }
     }
@@ -1610,8 +1620,10 @@ impl f128 {
     #[inline]
     #[rustc_allow_incoherent_impl]
     #[unstable(feature = "f128", issue = "116909")]
+    #[rustc_const_unstable(feature = "f128", issue = "116909")]
+    // #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn fract(self) -> f128 {
+    pub const fn fract(self) -> f128 {
         self - self.trunc()
     }
 
diff --git a/library/core/src/num/f16.rs b/library/core/src/num/f16.rs
index 1a859f2277ff3..eb7af993c60a0 100644
--- a/library/core/src/num/f16.rs
+++ b/library/core/src/num/f16.rs
@@ -1423,8 +1423,10 @@ impl f16 {
     #[inline]
     #[rustc_allow_incoherent_impl]
     #[unstable(feature = "f16", issue = "116909")]
+    #[rustc_const_unstable(feature = "f16", issue = "116909")]
+    // #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn floor(self) -> f16 {
+    pub const fn floor(self) -> f16 {
         // SAFETY: intrinsic with no preconditions
         unsafe { intrinsics::floorf16(self) }
     }
@@ -1453,8 +1455,10 @@ impl f16 {
     #[doc(alias = "ceiling")]
     #[rustc_allow_incoherent_impl]
     #[unstable(feature = "f16", issue = "116909")]
+    #[rustc_const_unstable(feature = "f16", issue = "116909")]
+    // #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn ceil(self) -> f16 {
+    pub const fn ceil(self) -> f16 {
         // SAFETY: intrinsic with no preconditions
         unsafe { intrinsics::ceilf16(self) }
     }
@@ -1489,8 +1493,10 @@ impl f16 {
     #[inline]
     #[rustc_allow_incoherent_impl]
     #[unstable(feature = "f16", issue = "116909")]
+    #[rustc_const_unstable(feature = "f16", issue = "116909")]
+    // #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn round(self) -> f16 {
+    pub const fn round(self) -> f16 {
         // SAFETY: intrinsic with no preconditions
         unsafe { intrinsics::roundf16(self) }
     }
@@ -1523,8 +1529,10 @@ impl f16 {
     #[inline]
     #[rustc_allow_incoherent_impl]
     #[unstable(feature = "f16", issue = "116909")]
+    #[rustc_const_unstable(feature = "f16", issue = "116909")]
+    // #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn round_ties_even(self) -> f16 {
+    pub const fn round_ties_even(self) -> f16 {
         intrinsics::round_ties_even_f16(self)
     }
 
@@ -1555,8 +1563,10 @@ impl f16 {
     #[doc(alias = "truncate")]
     #[rustc_allow_incoherent_impl]
     #[unstable(feature = "f16", issue = "116909")]
+    #[rustc_const_unstable(feature = "f16", issue = "116909")]
+    // #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn trunc(self) -> f16 {
+    pub const fn trunc(self) -> f16 {
         // SAFETY: intrinsic with no preconditions
         unsafe { intrinsics::truncf16(self) }
     }
@@ -1586,8 +1596,10 @@ impl f16 {
     #[inline]
     #[rustc_allow_incoherent_impl]
     #[unstable(feature = "f16", issue = "116909")]
+    #[rustc_const_unstable(feature = "f16", issue = "116909")]
+    // #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn fract(self) -> f16 {
+    pub const fn fract(self) -> f16 {
         self - self.trunc()
     }
 
diff --git a/library/core/src/num/f32.rs b/library/core/src/num/f32.rs
index 6636054a659b5..bf923d4070ad7 100644
--- a/library/core/src/num/f32.rs
+++ b/library/core/src/num/f32.rs
@@ -1591,8 +1591,9 @@ pub mod math {
     /// [`f32::floor`]: ../../../std/primitive.f32.html#method.floor
     #[inline]
     #[unstable(feature = "core_float_math", issue = "137578")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn floor(x: f32) -> f32 {
+    pub const fn floor(x: f32) -> f32 {
         // SAFETY: intrinsic with no preconditions
         unsafe { intrinsics::floorf32(x) }
     }
@@ -1621,7 +1622,8 @@ pub mod math {
     #[doc(alias = "ceiling")]
     #[must_use = "method returns a new number and does not mutate the original value"]
     #[unstable(feature = "core_float_math", issue = "137578")]
-    pub fn ceil(x: f32) -> f32 {
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
+    pub const fn ceil(x: f32) -> f32 {
         // SAFETY: intrinsic with no preconditions
         unsafe { intrinsics::ceilf32(x) }
     }
@@ -1655,7 +1657,8 @@ pub mod math {
     #[inline]
     #[unstable(feature = "core_float_math", issue = "137578")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn round(x: f32) -> f32 {
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
+    pub const fn round(x: f32) -> f32 {
         // SAFETY: intrinsic with no preconditions
         unsafe { intrinsics::roundf32(x) }
     }
@@ -1688,7 +1691,8 @@ pub mod math {
     #[inline]
     #[unstable(feature = "core_float_math", issue = "137578")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn round_ties_even(x: f32) -> f32 {
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
+    pub const fn round_ties_even(x: f32) -> f32 {
         intrinsics::round_ties_even_f32(x)
     }
 
@@ -1718,7 +1722,8 @@ pub mod math {
     #[doc(alias = "truncate")]
     #[must_use = "method returns a new number and does not mutate the original value"]
     #[unstable(feature = "core_float_math", issue = "137578")]
-    pub fn trunc(x: f32) -> f32 {
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
+    pub const fn trunc(x: f32) -> f32 {
         // SAFETY: intrinsic with no preconditions
         unsafe { intrinsics::truncf32(x) }
     }
@@ -1747,8 +1752,9 @@ pub mod math {
     /// [`f32::fract`]: ../../../std/primitive.f32.html#method.fract
     #[inline]
     #[unstable(feature = "core_float_math", issue = "137578")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn fract(x: f32) -> f32 {
+    pub const fn fract(x: f32) -> f32 {
         x - trunc(x)
     }
 
diff --git a/library/core/src/num/f64.rs b/library/core/src/num/f64.rs
index 8fbf2cffbaf4e..0a63ed828aedf 100644
--- a/library/core/src/num/f64.rs
+++ b/library/core/src/num/f64.rs
@@ -1589,8 +1589,9 @@ pub mod math {
     /// [`f64::floor`]: ../../../std/primitive.f64.html#method.floor
     #[inline]
     #[unstable(feature = "core_float_math", issue = "137578")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn floor(x: f64) -> f64 {
+    pub const fn floor(x: f64) -> f64 {
         // SAFETY: intrinsic with no preconditions
         unsafe { intrinsics::floorf64(x) }
     }
@@ -1618,8 +1619,9 @@ pub mod math {
     #[inline]
     #[doc(alias = "ceiling")]
     #[unstable(feature = "core_float_math", issue = "137578")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn ceil(x: f64) -> f64 {
+    pub const fn ceil(x: f64) -> f64 {
         // SAFETY: intrinsic with no preconditions
         unsafe { intrinsics::ceilf64(x) }
     }
@@ -1652,8 +1654,9 @@ pub mod math {
     /// [`f64::round`]: ../../../std/primitive.f64.html#method.round
     #[inline]
     #[unstable(feature = "core_float_math", issue = "137578")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn round(x: f64) -> f64 {
+    pub const fn round(x: f64) -> f64 {
         // SAFETY: intrinsic with no preconditions
         unsafe { intrinsics::roundf64(x) }
     }
@@ -1685,8 +1688,9 @@ pub mod math {
     /// [`f64::round_ties_even`]: ../../../std/primitive.f64.html#method.round_ties_even
     #[inline]
     #[unstable(feature = "core_float_math", issue = "137578")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn round_ties_even(x: f64) -> f64 {
+    pub const fn round_ties_even(x: f64) -> f64 {
         intrinsics::round_ties_even_f64(x)
     }
 
@@ -1715,8 +1719,9 @@ pub mod math {
     #[inline]
     #[doc(alias = "truncate")]
     #[unstable(feature = "core_float_math", issue = "137578")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn trunc(x: f64) -> f64 {
+    pub const fn trunc(x: f64) -> f64 {
         // SAFETY: intrinsic with no preconditions
         unsafe { intrinsics::truncf64(x) }
     }
@@ -1745,8 +1750,9 @@ pub mod math {
     /// [`f64::fract`]: ../../../std/primitive.f64.html#method.fract
     #[inline]
     #[unstable(feature = "core_float_math", issue = "137578")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[must_use = "method returns a new number and does not mutate the original value"]
-    pub fn fract(x: f64) -> f64 {
+    pub const fn fract(x: f64) -> f64 {
         x - trunc(x)
     }
 
diff --git a/library/coretests/tests/lib.rs b/library/coretests/tests/lib.rs
index 693b14ef76209..dd7cdd79c0d60 100644
--- a/library/coretests/tests/lib.rs
+++ b/library/coretests/tests/lib.rs
@@ -16,6 +16,7 @@
 #![feature(char_max_len)]
 #![feature(clone_to_uninit)]
 #![feature(const_eval_select)]
+#![feature(const_float_round_methods)]
 #![feature(const_trait_impl)]
 #![feature(core_float_math)]
 #![feature(core_intrinsics)]
diff --git a/library/coretests/tests/num/mod.rs b/library/coretests/tests/num/mod.rs
index 1212d36a1b15c..fa05bbdd9b774 100644
--- a/library/coretests/tests/num/mod.rs
+++ b/library/coretests/tests/num/mod.rs
@@ -731,6 +731,9 @@ assume_usize_width! {
     }
 }
 
+// FIXME(141726): there is a lot of duplication between the following tests and
+// the tests in `coretests/tests/floats/f*.rs`
+// See issue https://github.com/rust-lang/rust/issues/141726 for more details.
 macro_rules! test_float {
     ($modname: ident, $fassert: ident, $fty: ty) => {
         mod $modname {
@@ -947,6 +950,117 @@ macro_rules! test_float {
                 assert!(<$fty>::INFINITY.div_euclid(<$fty>::NAN).is_nan());
                 assert!(<$fty>::NAN.div_euclid(<$fty>::INFINITY).is_nan());
             }
+            #[test]
+            #[cfg(not(bootstrap))]
+            fn floor() {
+                $fassert!((0.0 as $fty).floor(), 0.0);
+                $fassert!((0.0 as $fty).floor().is_sign_positive());
+                $fassert!((-0.0 as $fty).floor(), -0.0);
+                $fassert!((-0.0 as $fty).floor().is_sign_negative());
+                $fassert!((0.5 as $fty).floor(), 0.0);
+                $fassert!((-0.5 as $fty).floor(), -1.0);
+                $fassert!((1.5 as $fty).floor(), 1.0);
+                $fassert!(<$fty>::MAX.floor(), <$fty>::MAX);
+                $fassert!(<$fty>::MIN.floor(), <$fty>::MIN);
+                $fassert!(<$fty>::MIN_POSITIVE.floor(), 0.0);
+                $fassert!((-<$fty>::MIN_POSITIVE).floor(), -1.0);
+                $fassert!(<$fty>::NAN.floor().is_nan());
+                $fassert!(<$fty>::INFINITY.floor(), <$fty>::INFINITY);
+                $fassert!(<$fty>::NEG_INFINITY.floor(), <$fty>::NEG_INFINITY);
+            }
+            #[test]
+            #[cfg(not(bootstrap))]
+            fn ceil() {
+                $fassert!((0.0 as $fty).ceil(), 0.0);
+                $fassert!((0.0 as $fty).ceil().is_sign_positive());
+                $fassert!((-0.0 as $fty).ceil(), 0.0);
+                $fassert!((-0.0 as $fty).ceil().is_sign_negative());
+                $fassert!((0.5 as $fty).ceil(), 1.0);
+                $fassert!((-0.5 as $fty).ceil(), 0.0);
+                $fassert!(<$fty>::MAX.ceil(), <$fty>::MAX);
+                $fassert!(<$fty>::MIN.ceil(), <$fty>::MIN);
+                $fassert!(<$fty>::MIN_POSITIVE.ceil(), 1.0);
+                $fassert!((-<$fty>::MIN_POSITIVE).ceil(), 0.0);
+                $fassert!(<$fty>::NAN.ceil().is_nan());
+                $fassert!(<$fty>::INFINITY.ceil(), <$fty>::INFINITY);
+                $fassert!(<$fty>::NEG_INFINITY.ceil(), <$fty>::NEG_INFINITY);
+            }
+            #[test]
+            #[cfg(not(bootstrap))]
+            fn round() {
+                $fassert!((0.0 as $fty).round(), 0.0);
+                $fassert!((0.0 as $fty).round().is_sign_positive());
+                $fassert!((-0.0 as $fty).round(), -0.0);
+                $fassert!((-0.0 as $fty).round().is_sign_negative());
+                $fassert!((0.5 as $fty).round(), 1.0);
+                $fassert!((-0.5 as $fty).round(), -1.0);
+                $fassert!(<$fty>::MAX.round(), <$fty>::MAX);
+                $fassert!(<$fty>::MIN.round(), <$fty>::MIN);
+                $fassert!(<$fty>::MIN_POSITIVE.round(), 0.0);
+                $fassert!((-<$fty>::MIN_POSITIVE).round(), 0.0);
+                $fassert!(<$fty>::NAN.round().is_nan());
+                $fassert!(<$fty>::INFINITY.round(), <$fty>::INFINITY);
+                $fassert!(<$fty>::NEG_INFINITY.round(), <$fty>::NEG_INFINITY);
+            }
+            #[test]
+            #[cfg(not(bootstrap))]
+            fn round_ties_even() {
+                $fassert!((0.0 as $fty).round_ties_even(), 0.0);
+                $fassert!((0.0 as $fty).round_ties_even().is_sign_positive());
+                $fassert!((-0.0 as $fty).round_ties_even(), -0.0);
+                $fassert!((-0.0 as $fty).round_ties_even().is_sign_negative());
+                $fassert!((0.5 as $fty).round_ties_even(), 0.0);
+                $fassert!((0.5 as $fty).round_ties_even().is_sign_positive());
+                $fassert!((-0.5 as $fty).round_ties_even(), -0.0);
+                $fassert!((-0.5 as $fty).round_ties_even().is_sign_negative());
+                $fassert!(<$fty>::MAX.round_ties_even(), <$fty>::MAX);
+                $fassert!(<$fty>::MIN.round_ties_even(), <$fty>::MIN);
+                $fassert!(<$fty>::MIN_POSITIVE.round_ties_even(), 0.0);
+                $fassert!((-<$fty>::MIN_POSITIVE).round_ties_even(), 0.0);
+                $fassert!(<$fty>::NAN.round_ties_even().is_nan());
+                $fassert!(<$fty>::INFINITY.round_ties_even(), <$fty>::INFINITY);
+                $fassert!(<$fty>::NEG_INFINITY.round_ties_even(), <$fty>::NEG_INFINITY);
+            }
+            #[test]
+            #[cfg(not(bootstrap))]
+            fn trunc() {
+                $fassert!((0.0 as $fty).trunc(), 0.0);
+                $fassert!((0.0 as $fty).trunc().is_sign_positive());
+                $fassert!((-0.0 as $fty).trunc(), -0.0);
+                $fassert!((-0.0 as $fty).trunc().is_sign_negative());
+                $fassert!((0.5 as $fty).trunc(), 0.0);
+                $fassert!((0.5 as $fty).trunc().is_sign_positive());
+                $fassert!((-0.5 as $fty).trunc(), -0.0);
+                $fassert!((-0.5 as $fty).trunc().is_sign_negative());
+                $fassert!(<$fty>::MAX.trunc(), <$fty>::MAX);
+                $fassert!(<$fty>::MIN.trunc(), <$fty>::MIN);
+                $fassert!(<$fty>::MIN_POSITIVE.trunc(), 0.0);
+                $fassert!((-<$fty>::MIN_POSITIVE).trunc(), 0.0);
+                $fassert!(<$fty>::NAN.trunc().is_nan());
+                $fassert!(<$fty>::INFINITY.trunc(), <$fty>::INFINITY);
+                $fassert!(<$fty>::NEG_INFINITY.trunc(), <$fty>::NEG_INFINITY);
+            }
+            #[test]
+            #[cfg(not(bootstrap))]
+            fn fract() {
+                $fassert!((0.0 as $fty).fract(), 0.0);
+                $fassert!((0.0 as $fty).fract().is_sign_positive());
+                $fassert!((-0.0 as $fty).fract(), 0.0);
+                $fassert!((-0.0 as $fty).fract().is_sign_positive());
+                $fassert!((0.5 as $fty).fract(), 0.5);
+                $fassert!((0.5 as $fty).fract().is_sign_positive());
+                $fassert!((-0.5 as $fty).fract(), -0.5);
+                $fassert!((-0.5 as $fty).fract().is_sign_negative());
+                $fassert!(<$fty>::MAX.fract(), 0.0);
+                $fassert!(<$fty>::MIN.fract(), 0.0);
+                $fassert!(<$fty>::MIN_POSITIVE.fract(), <$fty>::MIN_POSITIVE);
+                $fassert!(<$fty>::MIN_POSITIVE.fract().is_sign_positive());
+                $fassert!((-<$fty>::MIN_POSITIVE).fract(), -<$fty>::MIN_POSITIVE);
+                $fassert!((-<$fty>::MIN_POSITIVE).fract().is_sign_negative());
+                $fassert!(<$fty>::NAN.fract().is_nan());
+                $fassert!(<$fty>::INFINITY.fract().is_nan());
+                $fassert!(<$fty>::NEG_INFINITY.fract().is_nan());
+            }
         }
     };
 }
diff --git a/library/std/src/lib.rs b/library/std/src/lib.rs
index a3f0f3cc55a19..74a3433986020 100644
--- a/library/std/src/lib.rs
+++ b/library/std/src/lib.rs
@@ -335,6 +335,7 @@
 #![feature(bstr_internals)]
 #![feature(char_internals)]
 #![feature(clone_to_uninit)]
+#![feature(const_float_round_methods)]
 #![feature(core_intrinsics)]
 #![feature(core_io_borrowed_buf)]
 #![feature(duration_constants)]
diff --git a/library/std/src/num/f32.rs b/library/std/src/num/f32.rs
index 5210e75ec4531..b7f6529ac4027 100644
--- a/library/std/src/num/f32.rs
+++ b/library/std/src/num/f32.rs
@@ -44,8 +44,9 @@ impl f32 {
     #[rustc_allow_incoherent_impl]
     #[must_use = "method returns a new number and does not mutate the original value"]
     #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[inline]
-    pub fn floor(self) -> f32 {
+    pub const fn floor(self) -> f32 {
         core::f32::math::floor(self)
     }
 
@@ -66,8 +67,9 @@ impl f32 {
     #[rustc_allow_incoherent_impl]
     #[must_use = "method returns a new number and does not mutate the original value"]
     #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[inline]
-    pub fn ceil(self) -> f32 {
+    pub const fn ceil(self) -> f32 {
         core::f32::math::ceil(self)
     }
 
@@ -94,8 +96,9 @@ impl f32 {
     #[rustc_allow_incoherent_impl]
     #[must_use = "method returns a new number and does not mutate the original value"]
     #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[inline]
-    pub fn round(self) -> f32 {
+    pub const fn round(self) -> f32 {
         core::f32::math::round(self)
     }
 
@@ -120,8 +123,9 @@ impl f32 {
     #[rustc_allow_incoherent_impl]
     #[must_use = "method returns a new number and does not mutate the original value"]
     #[stable(feature = "round_ties_even", since = "1.77.0")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[inline]
-    pub fn round_ties_even(self) -> f32 {
+    pub const fn round_ties_even(self) -> f32 {
         core::f32::math::round_ties_even(self)
     }
 
@@ -145,8 +149,9 @@ impl f32 {
     #[rustc_allow_incoherent_impl]
     #[must_use = "method returns a new number and does not mutate the original value"]
     #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[inline]
-    pub fn trunc(self) -> f32 {
+    pub const fn trunc(self) -> f32 {
         core::f32::math::trunc(self)
     }
 
@@ -168,8 +173,9 @@ impl f32 {
     #[rustc_allow_incoherent_impl]
     #[must_use = "method returns a new number and does not mutate the original value"]
     #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[inline]
-    pub fn fract(self) -> f32 {
+    pub const fn fract(self) -> f32 {
         core::f32::math::fract(self)
     }
 
diff --git a/library/std/src/num/f64.rs b/library/std/src/num/f64.rs
index f837800d66342..75e35a8db3354 100644
--- a/library/std/src/num/f64.rs
+++ b/library/std/src/num/f64.rs
@@ -44,8 +44,9 @@ impl f64 {
     #[rustc_allow_incoherent_impl]
     #[must_use = "method returns a new number and does not mutate the original value"]
     #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[inline]
-    pub fn floor(self) -> f64 {
+    pub const fn floor(self) -> f64 {
         core::f64::math::floor(self)
     }
 
@@ -66,8 +67,9 @@ impl f64 {
     #[rustc_allow_incoherent_impl]
     #[must_use = "method returns a new number and does not mutate the original value"]
     #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[inline]
-    pub fn ceil(self) -> f64 {
+    pub const fn ceil(self) -> f64 {
         core::f64::math::ceil(self)
     }
 
@@ -94,8 +96,9 @@ impl f64 {
     #[rustc_allow_incoherent_impl]
     #[must_use = "method returns a new number and does not mutate the original value"]
     #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[inline]
-    pub fn round(self) -> f64 {
+    pub const fn round(self) -> f64 {
         core::f64::math::round(self)
     }
 
@@ -120,8 +123,9 @@ impl f64 {
     #[rustc_allow_incoherent_impl]
     #[must_use = "method returns a new number and does not mutate the original value"]
     #[stable(feature = "round_ties_even", since = "1.77.0")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[inline]
-    pub fn round_ties_even(self) -> f64 {
+    pub const fn round_ties_even(self) -> f64 {
         core::f64::math::round_ties_even(self)
     }
 
@@ -145,8 +149,9 @@ impl f64 {
     #[rustc_allow_incoherent_impl]
     #[must_use = "method returns a new number and does not mutate the original value"]
     #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[inline]
-    pub fn trunc(self) -> f64 {
+    pub const fn trunc(self) -> f64 {
         core::f64::math::trunc(self)
     }
 
@@ -168,8 +173,9 @@ impl f64 {
     #[rustc_allow_incoherent_impl]
     #[must_use = "method returns a new number and does not mutate the original value"]
     #[stable(feature = "rust1", since = "1.0.0")]
+    #[rustc_const_unstable(feature = "const_float_round_methods", issue = "141555")]
     #[inline]
-    pub fn fract(self) -> f64 {
+    pub const fn fract(self) -> f64 {
         core::f64::math::fract(self)
     }
 
diff --git a/src/tools/miri/src/intrinsics/mod.rs b/src/tools/miri/src/intrinsics/mod.rs
index 581005bc9a1ed..a4882a201481c 100644
--- a/src/tools/miri/src/intrinsics/mod.rs
+++ b/src/tools/miri/src/intrinsics/mod.rs
@@ -159,67 +159,6 @@ pub trait EvalContextExt<'tcx>: crate::MiriInterpCxExt<'tcx> {
                 this.write_scalar(Scalar::from_bool(branch), dest)?;
             }
 
-            "floorf16" | "ceilf16" | "truncf16" | "roundf16" | "round_ties_even_f16" => {
-                let [f] = check_intrinsic_arg_count(args)?;
-                let f = this.read_scalar(f)?.to_f16()?;
-                let mode = match intrinsic_name {
-                    "floorf16" => Round::TowardNegative,
-                    "ceilf16" => Round::TowardPositive,
-                    "truncf16" => Round::TowardZero,
-                    "roundf16" => Round::NearestTiesToAway,
-                    "round_ties_even_f16" => Round::NearestTiesToEven,
-                    _ => bug!(),
-                };
-                let res = f.round_to_integral(mode).value;
-                let res = this.adjust_nan(res, &[f]);
-                this.write_scalar(res, dest)?;
-            }
-            "floorf32" | "ceilf32" | "truncf32" | "roundf32" | "round_ties_even_f32" => {
-                let [f] = check_intrinsic_arg_count(args)?;
-                let f = this.read_scalar(f)?.to_f32()?;
-                let mode = match intrinsic_name {
-                    "floorf32" => Round::TowardNegative,
-                    "ceilf32" => Round::TowardPositive,
-                    "truncf32" => Round::TowardZero,
-                    "roundf32" => Round::NearestTiesToAway,
-                    "round_ties_even_f32" => Round::NearestTiesToEven,
-                    _ => bug!(),
-                };
-                let res = f.round_to_integral(mode).value;
-                let res = this.adjust_nan(res, &[f]);
-                this.write_scalar(res, dest)?;
-            }
-            "floorf64" | "ceilf64" | "truncf64" | "roundf64" | "round_ties_even_f64" => {
-                let [f] = check_intrinsic_arg_count(args)?;
-                let f = this.read_scalar(f)?.to_f64()?;
-                let mode = match intrinsic_name {
-                    "floorf64" => Round::TowardNegative,
-                    "ceilf64" => Round::TowardPositive,
-                    "truncf64" => Round::TowardZero,
-                    "roundf64" => Round::NearestTiesToAway,
-                    "round_ties_even_f64" => Round::NearestTiesToEven,
-                    _ => bug!(),
-                };
-                let res = f.round_to_integral(mode).value;
-                let res = this.adjust_nan(res, &[f]);
-                this.write_scalar(res, dest)?;
-            }
-            "floorf128" | "ceilf128" | "truncf128" | "roundf128" | "round_ties_even_f128" => {
-                let [f] = check_intrinsic_arg_count(args)?;
-                let f = this.read_scalar(f)?.to_f128()?;
-                let mode = match intrinsic_name {
-                    "floorf128" => Round::TowardNegative,
-                    "ceilf128" => Round::TowardPositive,
-                    "truncf128" => Round::TowardZero,
-                    "roundf128" => Round::NearestTiesToAway,
-                    "round_ties_even_f128" => Round::NearestTiesToEven,
-                    _ => bug!(),
-                };
-                let res = f.round_to_integral(mode).value;
-                let res = this.adjust_nan(res, &[f]);
-                this.write_scalar(res, dest)?;
-            }
-
             "sqrtf32" => {
                 let [f] = check_intrinsic_arg_count(args)?;
                 let f = this.read_scalar(f)?.to_f32()?;