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-rw-r--r--library/core/src/intrinsics/mod.rs10
-rw-r--r--library/core/src/num/f128.rs50
-rw-r--r--library/core/src/num/f16.rs50
-rw-r--r--library/core/src/num/f32.rs50
-rw-r--r--library/core/src/num/f64.rs50
-rw-r--r--library/core/src/primitive_docs.rs45
-rw-r--r--library/std/src/lib.rs1
-rw-r--r--library/std/tests/floats/f128.rs19
-rw-r--r--library/std/tests/floats/f16.rs21
-rw-r--r--library/std/tests/floats/f32.rs21
-rw-r--r--library/std/tests/floats/f64.rs19
-rw-r--r--library/std/tests/floats/lib.rs4
-rw-r--r--src/tools/miri/src/intrinsics/mod.rs8
-rw-r--r--tests/codegen/float/algebraic.rs149
-rw-r--r--tests/codegen/float_math.rs71
15 files changed, 544 insertions, 24 deletions
diff --git a/library/core/src/intrinsics/mod.rs b/library/core/src/intrinsics/mod.rs
index 81e59a1f349..afd6192d7c4 100644
--- a/library/core/src/intrinsics/mod.rs
+++ b/library/core/src/intrinsics/mod.rs
@@ -2475,35 +2475,35 @@ pub unsafe fn float_to_int_unchecked<Float: Copy, Int: Copy>(value: Float) -> In
 
 /// Float addition that allows optimizations based on algebraic rules.
 ///
-/// This intrinsic does not have a stable counterpart.
+/// Stabilized as [`f16::algebraic_add`], [`f32::algebraic_add`], [`f64::algebraic_add`] and [`f128::algebraic_add`].
 #[rustc_nounwind]
 #[rustc_intrinsic]
 pub fn fadd_algebraic<T: Copy>(a: T, b: T) -> T;
 
 /// Float subtraction that allows optimizations based on algebraic rules.
 ///
-/// This intrinsic does not have a stable counterpart.
+/// Stabilized as [`f16::algebraic_sub`], [`f32::algebraic_sub`], [`f64::algebraic_sub`] and [`f128::algebraic_sub`].
 #[rustc_nounwind]
 #[rustc_intrinsic]
 pub fn fsub_algebraic<T: Copy>(a: T, b: T) -> T;
 
 /// Float multiplication that allows optimizations based on algebraic rules.
 ///
-/// This intrinsic does not have a stable counterpart.
+/// Stabilized as [`f16::algebraic_mul`], [`f32::algebraic_mul`], [`f64::algebraic_mul`] and [`f128::algebraic_mul`].
 #[rustc_nounwind]
 #[rustc_intrinsic]
 pub fn fmul_algebraic<T: Copy>(a: T, b: T) -> T;
 
 /// Float division that allows optimizations based on algebraic rules.
 ///
-/// This intrinsic does not have a stable counterpart.
+/// Stabilized as [`f16::algebraic_div`], [`f32::algebraic_div`], [`f64::algebraic_div`] and [`f128::algebraic_div`].
 #[rustc_nounwind]
 #[rustc_intrinsic]
 pub fn fdiv_algebraic<T: Copy>(a: T, b: T) -> T;
 
 /// Float remainder that allows optimizations based on algebraic rules.
 ///
-/// This intrinsic does not have a stable counterpart.
+/// Stabilized as [`f16::algebraic_rem`], [`f32::algebraic_rem`], [`f64::algebraic_rem`] and [`f128::algebraic_rem`].
 #[rustc_nounwind]
 #[rustc_intrinsic]
 pub fn frem_algebraic<T: Copy>(a: T, b: T) -> T;
diff --git a/library/core/src/num/f128.rs b/library/core/src/num/f128.rs
index b17190971c3..08c34e852da 100644
--- a/library/core/src/num/f128.rs
+++ b/library/core/src/num/f128.rs
@@ -1362,4 +1362,54 @@ impl f128 {
         // SAFETY: this is actually a safe intrinsic
         unsafe { intrinsics::copysignf128(self, sign) }
     }
+
+    /// Float addition that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_add(self, rhs: f128) -> f128 {
+        intrinsics::fadd_algebraic(self, rhs)
+    }
+
+    /// Float subtraction that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_sub(self, rhs: f128) -> f128 {
+        intrinsics::fsub_algebraic(self, rhs)
+    }
+
+    /// Float multiplication that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_mul(self, rhs: f128) -> f128 {
+        intrinsics::fmul_algebraic(self, rhs)
+    }
+
+    /// Float division that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_div(self, rhs: f128) -> f128 {
+        intrinsics::fdiv_algebraic(self, rhs)
+    }
+
+    /// Float remainder that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_rem(self, rhs: f128) -> f128 {
+        intrinsics::frem_algebraic(self, rhs)
+    }
 }
diff --git a/library/core/src/num/f16.rs b/library/core/src/num/f16.rs
index d20677f43b4..a33e5f53014 100644
--- a/library/core/src/num/f16.rs
+++ b/library/core/src/num/f16.rs
@@ -1338,4 +1338,54 @@ impl f16 {
         // SAFETY: this is actually a safe intrinsic
         unsafe { intrinsics::copysignf16(self, sign) }
     }
+
+    /// Float addition that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_add(self, rhs: f16) -> f16 {
+        intrinsics::fadd_algebraic(self, rhs)
+    }
+
+    /// Float subtraction that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_sub(self, rhs: f16) -> f16 {
+        intrinsics::fsub_algebraic(self, rhs)
+    }
+
+    /// Float multiplication that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_mul(self, rhs: f16) -> f16 {
+        intrinsics::fmul_algebraic(self, rhs)
+    }
+
+    /// Float division that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_div(self, rhs: f16) -> f16 {
+        intrinsics::fdiv_algebraic(self, rhs)
+    }
+
+    /// Float remainder that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_rem(self, rhs: f16) -> f16 {
+        intrinsics::frem_algebraic(self, rhs)
+    }
 }
diff --git a/library/core/src/num/f32.rs b/library/core/src/num/f32.rs
index 53373584d55..e473fac0393 100644
--- a/library/core/src/num/f32.rs
+++ b/library/core/src/num/f32.rs
@@ -1504,4 +1504,54 @@ impl f32 {
         // SAFETY: this is actually a safe intrinsic
         unsafe { intrinsics::copysignf32(self, sign) }
     }
+
+    /// Float addition that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_add(self, rhs: f32) -> f32 {
+        intrinsics::fadd_algebraic(self, rhs)
+    }
+
+    /// Float subtraction that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_sub(self, rhs: f32) -> f32 {
+        intrinsics::fsub_algebraic(self, rhs)
+    }
+
+    /// Float multiplication that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_mul(self, rhs: f32) -> f32 {
+        intrinsics::fmul_algebraic(self, rhs)
+    }
+
+    /// Float division that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_div(self, rhs: f32) -> f32 {
+        intrinsics::fdiv_algebraic(self, rhs)
+    }
+
+    /// Float remainder that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_rem(self, rhs: f32) -> f32 {
+        intrinsics::frem_algebraic(self, rhs)
+    }
 }
diff --git a/library/core/src/num/f64.rs b/library/core/src/num/f64.rs
index ca28b40bb3a..6522a80b0b7 100644
--- a/library/core/src/num/f64.rs
+++ b/library/core/src/num/f64.rs
@@ -1503,4 +1503,54 @@ impl f64 {
         // SAFETY: this is actually a safe intrinsic
         unsafe { intrinsics::copysignf64(self, sign) }
     }
+
+    /// Float addition that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_add(self, rhs: f64) -> f64 {
+        intrinsics::fadd_algebraic(self, rhs)
+    }
+
+    /// Float subtraction that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_sub(self, rhs: f64) -> f64 {
+        intrinsics::fsub_algebraic(self, rhs)
+    }
+
+    /// Float multiplication that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_mul(self, rhs: f64) -> f64 {
+        intrinsics::fmul_algebraic(self, rhs)
+    }
+
+    /// Float division that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_div(self, rhs: f64) -> f64 {
+        intrinsics::fdiv_algebraic(self, rhs)
+    }
+
+    /// Float remainder that allows optimizations based on algebraic rules.
+    ///
+    /// See [algebraic operators](primitive@f32#algebraic-operators) for more info.
+    #[must_use = "method returns a new number and does not mutate the original value"]
+    #[unstable(feature = "float_algebraic", issue = "136469")]
+    #[inline]
+    pub fn algebraic_rem(self, rhs: f64) -> f64 {
+        intrinsics::frem_algebraic(self, rhs)
+    }
 }
diff --git a/library/core/src/primitive_docs.rs b/library/core/src/primitive_docs.rs
index ba4c849837e..369bf18c2b9 100644
--- a/library/core/src/primitive_docs.rs
+++ b/library/core/src/primitive_docs.rs
@@ -1313,6 +1313,51 @@ mod prim_f16 {}
 /// | `wasm32`, `wasm64` | If all input NaNs are quiet with all-zero payload: None.<br> Otherwise: all possible payloads. |
 ///
 /// For targets not in this table, all payloads are possible.
+///
+/// # Algebraic operators
+///
+/// Algebraic operators of the form `a.algebraic_*(b)` allow the compiler to optimize
+/// floating point operations using all the usual algebraic properties of real numbers --
+/// despite the fact that those properties do *not* hold on floating point numbers.
+/// This can give a great performance boost since it may unlock vectorization.
+///
+/// The exact set of optimizations is unspecified but typically allows combining operations,
+/// rearranging series of operations based on mathematical properties, converting between division
+/// and reciprocal multiplication, and disregarding the sign of zero. This means that the results of
+/// elementary operations may have undefined precision, and "non-mathematical" values
+/// such as NaN, +/-Inf, or -0.0 may behave in unexpected ways, but these operations
+/// will never cause undefined behavior.
+///
+/// Because of the unpredictable nature of compiler optimizations, the same inputs may produce
+/// different results even within a single program run. **Unsafe code must not rely on any property
+/// of the return value for soundness.** However, implementations will generally do their best to
+/// pick a reasonable tradeoff between performance and accuracy of the result.
+///
+/// For example:
+///
+/// ```
+/// # #![feature(float_algebraic)]
+/// # #![allow(unused_assignments)]
+/// # let mut x: f32 = 0.0;
+/// # let a: f32 = 1.0;
+/// # let b: f32 = 2.0;
+/// # let c: f32 = 3.0;
+/// # let d: f32 = 4.0;
+/// x = a.algebraic_add(b).algebraic_add(c).algebraic_add(d);
+/// ```
+///
+/// May be rewritten as:
+///
+/// ```
+/// # #![allow(unused_assignments)]
+/// # let mut x: f32 = 0.0;
+/// # let a: f32 = 1.0;
+/// # let b: f32 = 2.0;
+/// # let c: f32 = 3.0;
+/// # let d: f32 = 4.0;
+/// x = a + b + c + d; // As written
+/// x = (a + c) + (b + d); // Reordered to shorten critical path and enable vectorization
+/// ```
 
 #[stable(feature = "rust1", since = "1.0.0")]
 mod prim_f32 {}
diff --git a/library/std/src/lib.rs b/library/std/src/lib.rs
index 9dcedaa13f6..5c381181218 100644
--- a/library/std/src/lib.rs
+++ b/library/std/src/lib.rs
@@ -341,6 +341,7 @@
 #![feature(exact_size_is_empty)]
 #![feature(exclusive_wrapper)]
 #![feature(extend_one)]
+#![feature(float_algebraic)]
 #![feature(float_gamma)]
 #![feature(float_minimum_maximum)]
 #![feature(fmt_internals)]
diff --git a/library/std/tests/floats/f128.rs b/library/std/tests/floats/f128.rs
index b4a6c672bf0..df28e8129dd 100644
--- a/library/std/tests/floats/f128.rs
+++ b/library/std/tests/floats/f128.rs
@@ -985,6 +985,25 @@ fn test_total_cmp() {
 }
 
 #[test]
+fn test_algebraic() {
+    let a: f128 = 123.0;
+    let b: f128 = 456.0;
+
+    // Check that individual operations match their primitive counterparts.
+    //
+    // This is a check of current implementations and does NOT imply any form of
+    // guarantee about future behavior. The compiler reserves the right to make
+    // these operations inexact matches in the future.
+    let eps = if cfg!(miri) { 1e-6 } else { 0.0 };
+
+    assert_approx_eq!(a.algebraic_add(b), a + b, eps);
+    assert_approx_eq!(a.algebraic_sub(b), a - b, eps);
+    assert_approx_eq!(a.algebraic_mul(b), a * b, eps);
+    assert_approx_eq!(a.algebraic_div(b), a / b, eps);
+    assert_approx_eq!(a.algebraic_rem(b), a % b, eps);
+}
+
+#[test]
 fn test_from() {
     assert_eq!(f128::from(false), 0.0);
     assert_eq!(f128::from(true), 1.0);
diff --git a/library/std/tests/floats/f16.rs b/library/std/tests/floats/f16.rs
index ca0b8efbe83..1a90f00aecc 100644
--- a/library/std/tests/floats/f16.rs
+++ b/library/std/tests/floats/f16.rs
@@ -955,6 +955,27 @@ fn test_total_cmp() {
 }
 
 #[test]
+fn test_algebraic() {
+    let a: f16 = 123.0;
+    let b: f16 = 456.0;
+
+    // Check that individual operations match their primitive counterparts.
+    //
+    // This is a check of current implementations and does NOT imply any form of
+    // guarantee about future behavior. The compiler reserves the right to make
+    // these operations inexact matches in the future.
+    let eps_add = if cfg!(miri) { 1e1 } else { 0.0 };
+    let eps_mul = if cfg!(miri) { 1e3 } else { 0.0 };
+    let eps_div = if cfg!(miri) { 1e0 } else { 0.0 };
+
+    assert_approx_eq!(a.algebraic_add(b), a + b, eps_add);
+    assert_approx_eq!(a.algebraic_sub(b), a - b, eps_add);
+    assert_approx_eq!(a.algebraic_mul(b), a * b, eps_mul);
+    assert_approx_eq!(a.algebraic_div(b), a / b, eps_div);
+    assert_approx_eq!(a.algebraic_rem(b), a % b, eps_div);
+}
+
+#[test]
 fn test_from() {
     assert_eq!(f16::from(false), 0.0);
     assert_eq!(f16::from(true), 1.0);
diff --git a/library/std/tests/floats/f32.rs b/library/std/tests/floats/f32.rs
index bf7641986ad..d99b03cb255 100644
--- a/library/std/tests/floats/f32.rs
+++ b/library/std/tests/floats/f32.rs
@@ -915,3 +915,24 @@ fn test_total_cmp() {
     assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&f32::INFINITY));
     assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&s_nan()));
 }
+
+#[test]
+fn test_algebraic() {
+    let a: f32 = 123.0;
+    let b: f32 = 456.0;
+
+    // Check that individual operations match their primitive counterparts.
+    //
+    // This is a check of current implementations and does NOT imply any form of
+    // guarantee about future behavior. The compiler reserves the right to make
+    // these operations inexact matches in the future.
+    let eps_add = if cfg!(miri) { 1e-3 } else { 0.0 };
+    let eps_mul = if cfg!(miri) { 1e-1 } else { 0.0 };
+    let eps_div = if cfg!(miri) { 1e-4 } else { 0.0 };
+
+    assert_approx_eq!(a.algebraic_add(b), a + b, eps_add);
+    assert_approx_eq!(a.algebraic_sub(b), a - b, eps_add);
+    assert_approx_eq!(a.algebraic_mul(b), a * b, eps_mul);
+    assert_approx_eq!(a.algebraic_div(b), a / b, eps_div);
+    assert_approx_eq!(a.algebraic_rem(b), a % b, eps_div);
+}
diff --git a/library/std/tests/floats/f64.rs b/library/std/tests/floats/f64.rs
index cbbfcd15efd..611670751bb 100644
--- a/library/std/tests/floats/f64.rs
+++ b/library/std/tests/floats/f64.rs
@@ -894,3 +894,22 @@ fn test_total_cmp() {
     assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&f64::INFINITY));
     assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&s_nan()));
 }
+
+#[test]
+fn test_algebraic() {
+    let a: f64 = 123.0;
+    let b: f64 = 456.0;
+
+    // Check that individual operations match their primitive counterparts.
+    //
+    // This is a check of current implementations and does NOT imply any form of
+    // guarantee about future behavior. The compiler reserves the right to make
+    // these operations inexact matches in the future.
+    let eps = if cfg!(miri) { 1e-6 } else { 0.0 };
+
+    assert_approx_eq!(a.algebraic_add(b), a + b, eps);
+    assert_approx_eq!(a.algebraic_sub(b), a - b, eps);
+    assert_approx_eq!(a.algebraic_mul(b), a * b, eps);
+    assert_approx_eq!(a.algebraic_div(b), a / b, eps);
+    assert_approx_eq!(a.algebraic_rem(b), a % b, eps);
+}
diff --git a/library/std/tests/floats/lib.rs b/library/std/tests/floats/lib.rs
index ad82f1a44e7..de5a3cdbd0f 100644
--- a/library/std/tests/floats/lib.rs
+++ b/library/std/tests/floats/lib.rs
@@ -1,4 +1,4 @@
-#![feature(f16, f128, float_gamma, float_minimum_maximum)]
+#![feature(f16, f128, float_algebraic, float_gamma, float_minimum_maximum)]
 
 use std::fmt;
 use std::ops::{Add, Div, Mul, Rem, Sub};
@@ -10,7 +10,7 @@ macro_rules! assert_approx_eq {
         let (a, b) = (&$a, &$b);
         let diff = (*a - *b).abs();
         assert!(
-            diff < $lim,
+            diff <= $lim,
             "{a:?} is not approximately equal to {b:?} (threshold {lim:?}, difference {diff:?})",
             lim = $lim
         );
diff --git a/src/tools/miri/src/intrinsics/mod.rs b/src/tools/miri/src/intrinsics/mod.rs
index 85fb280a9a9..a3525dcc77a 100644
--- a/src/tools/miri/src/intrinsics/mod.rs
+++ b/src/tools/miri/src/intrinsics/mod.rs
@@ -411,9 +411,9 @@ pub trait EvalContextExt<'tcx>: crate::MiriInterpCxExt<'tcx> {
                 };
                 let res = this.binary_op(op, &a, &b)?;
                 // `binary_op` already called `generate_nan` if needed.
-                // Apply a relative error of 16ULP to simulate non-deterministic precision loss
+                // Apply a relative error of 4ULP to simulate non-deterministic precision loss
                 // due to optimizations.
-                let res = apply_random_float_error_to_imm(this, res, 4 /* log2(16) */)?;
+                let res = apply_random_float_error_to_imm(this, res, 2 /* log2(4) */)?;
                 this.write_immediate(*res, dest)?;
             }
 
@@ -464,9 +464,9 @@ pub trait EvalContextExt<'tcx>: crate::MiriInterpCxExt<'tcx> {
                 if !float_finite(&res)? {
                     throw_ub_format!("`{intrinsic_name}` intrinsic produced non-finite value as result");
                 }
-                // Apply a relative error of 16ULP to simulate non-deterministic precision loss
+                // Apply a relative error of 4ULP to simulate non-deterministic precision loss
                 // due to optimizations.
-                let res = apply_random_float_error_to_imm(this, res, 4 /* log2(16) */)?;
+                let res = apply_random_float_error_to_imm(this, res, 2 /* log2(4) */)?;
                 this.write_immediate(*res, dest)?;
             }
 
diff --git a/tests/codegen/float/algebraic.rs b/tests/codegen/float/algebraic.rs
new file mode 100644
index 00000000000..818a4bcdfe3
--- /dev/null
+++ b/tests/codegen/float/algebraic.rs
@@ -0,0 +1,149 @@
+// Verify that algebraic intrinsics generate the correct LLVM calls
+
+// Ensure operations get inlined
+//@ compile-flags: -Copt-level=1
+
+#![crate_type = "lib"]
+#![feature(f16)]
+#![feature(f128)]
+#![feature(float_algebraic)]
+
+// CHECK-LABEL: @f16_algebraic_add
+#[no_mangle]
+pub fn f16_algebraic_add(a: f16, b: f16) -> f16 {
+    // CHECK: fadd reassoc nsz arcp contract half %{{.+}}, %{{.+}}
+    a.algebraic_add(b)
+}
+
+// CHECK-LABEL: @f16_algebraic_sub
+#[no_mangle]
+pub fn f16_algebraic_sub(a: f16, b: f16) -> f16 {
+    // CHECK: fsub reassoc nsz arcp contract half %{{.+}}, %{{.+}}
+    a.algebraic_sub(b)
+}
+
+// CHECK-LABEL: @f16_algebraic_mul
+#[no_mangle]
+pub fn f16_algebraic_mul(a: f16, b: f16) -> f16 {
+    // CHECK: fmul reassoc nsz arcp contract half %{{.+}}, %{{.+}}
+    a.algebraic_mul(b)
+}
+
+// CHECK-LABEL: @f16_algebraic_div
+#[no_mangle]
+pub fn f16_algebraic_div(a: f16, b: f16) -> f16 {
+    // CHECK: fdiv reassoc nsz arcp contract half %{{.+}}, %{{.+}}
+    a.algebraic_div(b)
+}
+
+// CHECK-LABEL: @f16_algebraic_rem
+#[no_mangle]
+pub fn f16_algebraic_rem(a: f16, b: f16) -> f16 {
+    // CHECK: frem reassoc nsz arcp contract half %{{.+}}, %{{.+}}
+    a.algebraic_rem(b)
+}
+
+// CHECK-LABEL: @f32_algebraic_add
+#[no_mangle]
+pub fn f32_algebraic_add(a: f32, b: f32) -> f32 {
+    // CHECK: fadd reassoc nsz arcp contract float %{{.+}}, %{{.+}}
+    a.algebraic_add(b)
+}
+
+// CHECK-LABEL: @f32_algebraic_sub
+#[no_mangle]
+pub fn f32_algebraic_sub(a: f32, b: f32) -> f32 {
+    // CHECK: fsub reassoc nsz arcp contract float %{{.+}}, %{{.+}}
+    a.algebraic_sub(b)
+}
+
+// CHECK-LABEL: @f32_algebraic_mul
+#[no_mangle]
+pub fn f32_algebraic_mul(a: f32, b: f32) -> f32 {
+    // CHECK: fmul reassoc nsz arcp contract float %{{.+}}, %{{.+}}
+    a.algebraic_mul(b)
+}
+
+// CHECK-LABEL: @f32_algebraic_div
+#[no_mangle]
+pub fn f32_algebraic_div(a: f32, b: f32) -> f32 {
+    // CHECK: fdiv reassoc nsz arcp contract float %{{.+}}, %{{.+}}
+    a.algebraic_div(b)
+}
+
+// CHECK-LABEL: @f32_algebraic_rem
+#[no_mangle]
+pub fn f32_algebraic_rem(a: f32, b: f32) -> f32 {
+    // CHECK: frem reassoc nsz arcp contract float %{{.+}}, %{{.+}}
+    a.algebraic_rem(b)
+}
+
+// CHECK-LABEL: @f64_algebraic_add
+#[no_mangle]
+pub fn f64_algebraic_add(a: f64, b: f64) -> f64 {
+    // CHECK: fadd reassoc nsz arcp contract double %{{.+}}, %{{.+}}
+    a.algebraic_add(b)
+}
+
+// CHECK-LABEL: @f64_algebraic_sub
+#[no_mangle]
+pub fn f64_algebraic_sub(a: f64, b: f64) -> f64 {
+    // CHECK: fsub reassoc nsz arcp contract double %{{.+}}, %{{.+}}
+    a.algebraic_sub(b)
+}
+
+// CHECK-LABEL: @f64_algebraic_mul
+#[no_mangle]
+pub fn f64_algebraic_mul(a: f64, b: f64) -> f64 {
+    // CHECK: fmul reassoc nsz arcp contract double %{{.+}}, %{{.+}}
+    a.algebraic_mul(b)
+}
+
+// CHECK-LABEL: @f64_algebraic_div
+#[no_mangle]
+pub fn f64_algebraic_div(a: f64, b: f64) -> f64 {
+    // CHECK: fdiv reassoc nsz arcp contract double %{{.+}}, %{{.+}}
+    a.algebraic_div(b)
+}
+
+// CHECK-LABEL: @f64_algebraic_rem
+#[no_mangle]
+pub fn f64_algebraic_rem(a: f64, b: f64) -> f64 {
+    // CHECK: frem reassoc nsz arcp contract double %{{.+}}, %{{.+}}
+    a.algebraic_rem(b)
+}
+
+// CHECK-LABEL: @f128_algebraic_add
+#[no_mangle]
+pub fn f128_algebraic_add(a: f128, b: f128) -> f128 {
+    // CHECK: fadd reassoc nsz arcp contract fp128 %{{.+}}, %{{.+}}
+    a.algebraic_add(b)
+}
+
+// CHECK-LABEL: @f128_algebraic_sub
+#[no_mangle]
+pub fn f128_algebraic_sub(a: f128, b: f128) -> f128 {
+    // CHECK: fsub reassoc nsz arcp contract fp128 %{{.+}}, %{{.+}}
+    a.algebraic_sub(b)
+}
+
+// CHECK-LABEL: @f128_algebraic_mul
+#[no_mangle]
+pub fn f128_algebraic_mul(a: f128, b: f128) -> f128 {
+    // CHECK: fmul reassoc nsz arcp contract fp128 %{{.+}}, %{{.+}}
+    a.algebraic_mul(b)
+}
+
+// CHECK-LABEL: @f128_algebraic_div
+#[no_mangle]
+pub fn f128_algebraic_div(a: f128, b: f128) -> f128 {
+    // CHECK: fdiv reassoc nsz arcp contract fp128 %{{.+}}, %{{.+}}
+    a.algebraic_div(b)
+}
+
+// CHECK-LABEL: @f128_algebraic_rem
+#[no_mangle]
+pub fn f128_algebraic_rem(a: f128, b: f128) -> f128 {
+    // CHECK: frem reassoc nsz arcp contract fp128 %{{.+}}, %{{.+}}
+    a.algebraic_rem(b)
+}
diff --git a/tests/codegen/float_math.rs b/tests/codegen/float_math.rs
index 31387ec82b9..9a1e0b4d2d0 100644
--- a/tests/codegen/float_math.rs
+++ b/tests/codegen/float_math.rs
@@ -3,7 +3,10 @@
 #![crate_type = "lib"]
 #![feature(core_intrinsics)]
 
-use std::intrinsics::{fadd_fast, fdiv_fast, fmul_fast, frem_fast, fsub_fast};
+use std::intrinsics::{
+    fadd_algebraic, fadd_fast, fdiv_algebraic, fdiv_fast, fmul_algebraic, fmul_fast,
+    frem_algebraic, frem_fast, fsub_algebraic, fsub_fast,
+};
 
 // CHECK-LABEL: @add
 #[no_mangle]
@@ -13,30 +16,72 @@ pub fn add(x: f32, y: f32) -> f32 {
     x + y
 }
 
-// CHECK-LABEL: @addition
+// CHECK-LABEL: @test_fadd_algebraic
 #[no_mangle]
-pub fn addition(x: f32, y: f32) -> f32 {
-    // CHECK: fadd fast float
+pub fn test_fadd_algebraic(x: f32, y: f32) -> f32 {
+    // CHECK: fadd reassoc nsz arcp contract float %x, %y
+    fadd_algebraic(x, y)
+}
+
+// CHECK-LABEL: @test_fsub_algebraic
+#[no_mangle]
+pub fn test_fsub_algebraic(x: f32, y: f32) -> f32 {
+    // CHECK: fsub reassoc nsz arcp contract float %x, %y
+    fsub_algebraic(x, y)
+}
+
+// CHECK-LABEL: @test_fmul_algebraic
+#[no_mangle]
+pub fn test_fmul_algebraic(x: f32, y: f32) -> f32 {
+    // CHECK: fmul reassoc nsz arcp contract float %x, %y
+    fmul_algebraic(x, y)
+}
+
+// CHECK-LABEL: @test_fdiv_algebraic
+#[no_mangle]
+pub fn test_fdiv_algebraic(x: f32, y: f32) -> f32 {
+    // CHECK: fdiv reassoc nsz arcp contract float %x, %y
+    fdiv_algebraic(x, y)
+}
+
+// CHECK-LABEL: @test_frem_algebraic
+#[no_mangle]
+pub fn test_frem_algebraic(x: f32, y: f32) -> f32 {
+    // CHECK: frem reassoc nsz arcp contract float %x, %y
+    frem_algebraic(x, y)
+}
+
+// CHECK-LABEL: @test_fadd_fast
+#[no_mangle]
+pub fn test_fadd_fast(x: f32, y: f32) -> f32 {
+    // CHECK: fadd fast float %x, %y
     unsafe { fadd_fast(x, y) }
 }
 
-// CHECK-LABEL: @subtraction
+// CHECK-LABEL: @test_fsub_fast
 #[no_mangle]
-pub fn subtraction(x: f32, y: f32) -> f32 {
-    // CHECK: fsub fast float
+pub fn test_fsub_fast(x: f32, y: f32) -> f32 {
+    // CHECK: fsub fast float %x, %y
     unsafe { fsub_fast(x, y) }
 }
 
-// CHECK-LABEL: @multiplication
+// CHECK-LABEL: @test_fmul_fast
 #[no_mangle]
-pub fn multiplication(x: f32, y: f32) -> f32 {
-    // CHECK: fmul fast float
+pub fn test_fmul_fast(x: f32, y: f32) -> f32 {
+    // CHECK: fmul fast float %x, %y
     unsafe { fmul_fast(x, y) }
 }
 
-// CHECK-LABEL: @division
+// CHECK-LABEL: @test_fdiv_fast
 #[no_mangle]
-pub fn division(x: f32, y: f32) -> f32 {
-    // CHECK: fdiv fast float
+pub fn test_fdiv_fast(x: f32, y: f32) -> f32 {
+    // CHECK: fdiv fast float %x, %y
     unsafe { fdiv_fast(x, y) }
 }
+
+// CHECK-LABEL: @test_frem_fast
+#[no_mangle]
+pub fn test_frem_fast(x: f32, y: f32) -> f32 {
+    // CHECK: frem fast float %x, %y
+    unsafe { frem_fast(x, y) }
+}
generated by cgit-pink 1.4.1-3-g733a5 (git 2.37.1) at 2026-04-24 04:49:54 +0000