fix: harden reassociation barriers for fast-math

.github/workflows/windows.yml

@@ -92,6 +92,70 @@ jobs:
         run: |
           cd _build && ./test/test_xsimd
 
+  build-windows-clang-cl:
+    name: 'clang-cl x64 AVX2'
+    defaults:
+      run:
+        shell: bash {0}
+    runs-on: windows-2025
+    steps:
+    - name: Setup compiler
+      uses: ilammy/msvc-dev-cmd@v1
+      with:
+        arch: amd64
+    - name: Check clang-cl
+      run: |
+        command -v clang-cl
+        clang-cl --version
+    - name: Setup Ninja
+      run: |
+        python3 -m pip install --upgrade pip setuptools wheel
+        python3 -m pip install ninja
+    - name: Checkout xsimd
+      uses: actions/checkout@v3
+    - name: Setup
+      run: |
+        mkdir _build
+        cd _build && cmake .. -DBUILD_TESTS=ON -DDOWNLOAD_DOCTEST=ON -DBUILD_BENCHMARK=ON -DBUILD_EXAMPLES=ON -DCMAKE_BUILD_TYPE=Release -DCMAKE_C_COMPILER=clang-cl -DCMAKE_CXX_COMPILER=clang-cl -DCMAKE_CXX_FLAGS="/arch:AVX2" -G Ninja
+    - name: Build
+      run: |
+        cd _build && cmake --build .
+    - name: Testing xsimd
+      run: |
+        cd _build && ./test/test_xsimd
+
+  build-windows-clang-cl-fast-math:
+    name: 'clang-cl x64 /fp:fast'
+    defaults:
+      run:
+        shell: bash {0}
+    runs-on: windows-2025
+    steps:
+    - name: Setup compiler
+      uses: ilammy/msvc-dev-cmd@v1
+      with:
+        arch: amd64
+    - name: Check clang-cl
+      run: |
+        command -v clang-cl
+        clang-cl --version
+    - name: Setup Ninja
+      run: |
+        python3 -m pip install --upgrade pip setuptools wheel
+        python3 -m pip install ninja
+    - name: Checkout xsimd
+      uses: actions/checkout@v3
+    - name: Setup
+      run: |
+        mkdir _build
+        cd _build && cmake .. -DBUILD_TESTS=ON -DDOWNLOAD_DOCTEST=ON -DBUILD_BENCHMARK=OFF -DBUILD_EXAMPLES=OFF -DCMAKE_BUILD_TYPE=Release -DCMAKE_C_COMPILER=clang-cl -DCMAKE_CXX_COMPILER=clang-cl -DCMAKE_CXX_FLAGS="/fp:fast" -G Ninja
+    - name: Build
+      run: |
+        cd _build && cmake --build .
+    - name: Testing xsimd
+      run: |
+        cd _build && ./test/test_xsimd
+
   build-windows-arm64:
     name: 'MSVC arm64'
     defaults:

include/xsimd/arch/common/xsimd_common_details.hpp

@@ -111,6 +111,22 @@ namespace xsimd
 
         namespace detail
         {
+            template <class T>
+            XSIMD_INLINE void reassociation_barrier(T& x, memory_barrier_tag) noexcept
+            {
+#if XSIMD_WITH_INLINE_ASM
+                __asm__ volatile("" : : "r"(&x) : "memory");
+#else
+                (void)x;
+#endif
+            }
+
+            template <class T, class A>
+            XSIMD_INLINE void reassociation_barrier(T& x, A const&) noexcept
+            {
+                detail::reassociation_barrier(x, memory_barrier_tag {});
+            }
+
             template <class F, class A, class T, class... Batches>
             XSIMD_INLINE batch<T, A> apply(F&& func, batch<T, A> const& self, batch<T, A> const& other) noexcept
             {

include/xsimd/arch/common/xsimd_common_math.hpp

@@ -878,6 +878,8 @@ namespace xsimd
                 {
                     batch_type k = nearbyint(a);
                     x = (a - k) * constants::log_2<batch_type>();
+                    // Keep the reduced exponent offset from being reassociated before finalize().
+                    detail::reassociation_barrier(x, A {});
                     return k;
                 }
 
@@ -937,7 +939,11 @@ namespace xsimd
         template <class A, class T>
         XSIMD_INLINE batch<T, A> exp10(batch<T, A> const& self, requires_arch<common>) noexcept
         {
-            return detail::exp<detail::exp10_tag>(self);
+            using batch_type = batch<T, A>;
+            batch_type out = detail::exp<detail::exp10_tag>(self);
+            // Prevent -ffast-math from folding the whole exp10 batch path for literal inputs.
+            detail::reassociation_barrier(out, A {});
+            return out;
         }
 
         // exp2
@@ -1494,6 +1500,8 @@ namespace xsimd
             batch_type R = t2 + t1;
             batch_type hfsq = batch_type(0.5) * f * f;
             batch_type dk = to_float(k);
+            // Keep the compensated k -> float conversion intact before scaling by split log(2).
+            detail::reassociation_barrier(dk, A {});
             batch_type r = fma(dk, constants::log_2hi<batch_type>(), fma(s, (hfsq + R), dk * constants::log_2lo<batch_type>()) - hfsq + f);
 #ifdef __FAST_MATH__
             return r;
@@ -1525,6 +1533,8 @@ namespace xsimd
             hx += 0x3ff00000 - 0x3fe6a09e;
             k += (hx >> 20) - 0x3ff;
             batch_type dk = to_float(k);
+            // Keep the compensated k -> double conversion intact before scaling by split log(2).
+            detail::reassociation_barrier(dk, A {});
             hx = (hx & i_type(0x000fffff)) + 0x3fe6a09e;
             x = ::xsimd::bitwise_cast<double>(hx << 32 | (i_type(0xffffffff) & ::xsimd::bitwise_cast<int_type>(x)));
 
@@ -1705,6 +1715,8 @@ namespace xsimd
             batch_type t2 = z * detail::horner<batch_type, 0x3f2aaaaa, 0x3e91e9ee>(w);
             batch_type R = t2 + t1;
             batch_type dk = to_float(k);
+            // Prevent fast-math from distributing later multiplies through the compensated exponent conversion.
+            detail::reassociation_barrier(dk, A {});
             batch_type hfsq = batch_type(0.5) * f * f;
             batch_type hibits = f - hfsq;
             hibits &= ::xsimd::bitwise_cast<float>(i_type(0xfffff000));
@@ -1752,10 +1764,12 @@ namespace xsimd
 #endif
             hx += 0x3ff00000 - 0x3fe6a09e;
             k += (hx >> 20) - 0x3ff;
+            batch_type dk = to_float(k);
+            // Prevent fast-math from distributing later multiplies through the compensated exponent conversion.
+            detail::reassociation_barrier(dk, A {});
             hx = (hx & i_type(0x000fffff)) + 0x3fe6a09e;
             x = ::xsimd::bitwise_cast<double>(hx << 32 | (i_type(0xffffffff) & ::xsimd::bitwise_cast<int_type>(x)));
             batch_type f = --x;
-            batch_type dk = to_float(k);
             batch_type s = f / (batch_type(2.) + f);
             batch_type z = s * s;
             batch_type w = z * z;
@@ -1818,6 +1832,8 @@ namespace xsimd
             batch_type R = t2 + t1;
             batch_type hfsq = batch_type(0.5) * f * f;
             batch_type dk = to_float(k);
+            // Prevent fast-math from distributing later multiplies through the compensated exponent conversion.
+            detail::reassociation_barrier(dk, A {});
             /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
             batch_type c = select(batch_bool_cast<float>(k >= i_type(2)), batch_type(1.) - (uf - self), self - (uf - batch_type(1.))) / uf;
             batch_type r = fma(dk, constants::log_2hi<batch_type>(), fma(s, (hfsq + R), dk * constants::log_2lo<batch_type>() + c) - hfsq + f);
@@ -1853,6 +1869,8 @@ namespace xsimd
             batch_type t2 = z * detail::horner<batch_type, 0x3fe5555555555593ll, 0x3fd2492494229359ll, 0x3fc7466496cb03dell, 0x3fc2f112df3e5244ll>(w);
             batch_type R = t2 + t1;
             batch_type dk = to_float(k);
+            // Prevent fast-math from distributing later multiplies through the compensated exponent conversion.
+            detail::reassociation_barrier(dk, A {});
             batch_type r = fma(dk, constants::log_2hi<batch_type>(), fma(s, hfsq + R, dk * constants::log_2lo<batch_type>() + c) - hfsq + f);
 #ifdef __FAST_MATH__
             return r;
@@ -1900,17 +1918,10 @@ namespace xsimd
                 batch_type s = bitofsign(self);
                 batch_type v = self ^ s;
                 batch_type t2n = constants::twotonmb<batch_type>();
-                // Under fast-math, reordering is possible and the compiler optimizes d
-                // to v. That's not what we want, so prevent compiler optimization here.
-                // FIXME: it may be better to emit a memory barrier here (?).
-#ifdef __FAST_MATH__
                 batch_type d0 = v + t2n;
-                asm volatile("" ::"r"(&d0) : "memory");
+                // Prevent fast-math from collapsing (v + 2^n) - 2^n back to v.
+                detail::reassociation_barrier(d0.data, A {});
                 batch_type d = d0 - t2n;
-#else
-                batch_type d0 = v + t2n;
-                batch_type d = d0 - t2n;
-#endif
                 return s ^ select(v < t2n, d, v);
             }
         }
@@ -2192,12 +2203,18 @@ namespace xsimd
         template <class A>
         XSIMD_INLINE batch<float, A> remainder(batch<float, A> const& self, batch<float, A> const& other, requires_arch<common>) noexcept
         {
-            return fnma(nearbyint(self / other), other, self);
+            batch<float, A> q = nearbyint(self / other);
+            // Prevent fast-math from pulling the later multiply back through the rounded quotient.
+            detail::reassociation_barrier(q, A {});
+            return fnma(q, other, self);
         }
         template <class A>
         XSIMD_INLINE batch<double, A> remainder(batch<double, A> const& self, batch<double, A> const& other, requires_arch<common>) noexcept
         {
-            return fnma(nearbyint(self / other), other, self);
+            batch<double, A> q = nearbyint(self / other);
+            // Prevent fast-math from pulling the later multiply back through the rounded quotient.
+            detail::reassociation_barrier(q, A {});
+            return fnma(q, other, self);
         }
         template <class A, class T, class = std::enable_if_t<std::is_integral<T>::value>>
         XSIMD_INLINE batch<T, A> remainder(batch<T, A> const& self, batch<T, A> const& other, requires_arch<common>) noexcept

include/xsimd/arch/common/xsimd_common_trigo.hpp

@@ -550,34 +550,49 @@ namespace xsimd
                     else if (all(x <= constants::pio2<B>()))
                     {
                         auto test = x > constants::pio4<B>();
+                        // Keep the compensated pio2 subtraction sequence ordered under -ffast-math.
                         xr = x - constants::pio2_1<B>();
+                        detail::reassociation_barrier(xr, typename B::arch_type {});
                         xr -= constants::pio2_2<B>();
+                        detail::reassociation_barrier(xr, typename B::arch_type {});
                         xr -= constants::pio2_3<B>();
+                        detail::reassociation_barrier(xr, typename B::arch_type {});
                         xr = select(test, xr, x);
                         return select(test, B(1.), B(0.));
                     }
                     else if (all(x <= constants::twentypi<B>()))
                     {
                         B xi = nearbyint(x * constants::twoopi<B>());
+                        // Preserve the quadrant selection and compensated range reduction under -ffast-math.
+                        detail::reassociation_barrier(xi, typename B::arch_type {});
                         xr = fnma(xi, constants::pio2_1<B>(), x);
+                        detail::reassociation_barrier(xr, typename B::arch_type {});
                         xr -= xi * constants::pio2_2<B>();
+                        detail::reassociation_barrier(xr, typename B::arch_type {});
                         xr -= xi * constants::pio2_3<B>();
+                        detail::reassociation_barrier(xr, typename B::arch_type {});
                         return quadrant(xi);
                     }
                     else if (all(x <= constants::mediumpi<B>()))
                     {
                         B fn = nearbyint(x * constants::twoopi<B>());
+                        // Keep the multi-term range reduction from being reassociated across correction terms.
+                        detail::reassociation_barrier(fn, typename B::arch_type {});
                         B r = x - fn * constants::pio2_1<B>();
+                        detail::reassociation_barrier(r, typename B::arch_type {});
                         B w = fn * constants::pio2_1t<B>();
                         B t = r;
                         w = fn * constants::pio2_2<B>();
                         r = t - w;
+                        detail::reassociation_barrier(r, typename B::arch_type {});
                         w = fn * constants::pio2_2t<B>() - ((t - r) - w);
                         t = r;
                         w = fn * constants::pio2_3<B>();
                         r = t - w;
+                        detail::reassociation_barrier(r, typename B::arch_type {});
                         w = fn * constants::pio2_3t<B>() - ((t - r) - w);
                         xr = r - w;
+                        detail::reassociation_barrier(xr, typename B::arch_type {});
                         return quadrant(fn);
                     }
                     else

include/xsimd/arch/xsimd_avx2.hpp

@@ -554,11 +554,8 @@ namespace xsimd
                 __m256d f = _mm256_sub_pd(_mm256_castsi256_pd(xH), _mm256_set1_pd(19342813118337666422669312.)); //  2^84 + 2^52
                 // With -ffast-math, the compiler may reassociate (xH-C)+xL into
                 // xH+(xL-C). Since xL<<C this causes catastrophic cancellation.
-                // The asm barrier forces f into a register before the add, blocking
-                // the reorder. It emits zero instructions.
-#if defined(__GNUC__)
-                __asm__ volatile("" : "+x"(f));
-#endif
+                // Barrier the intermediate before the final add.
+                detail::reassociation_barrier(f, A {});
                 return _mm256_add_pd(f, _mm256_castsi256_pd(xL));
             }
 
@@ -575,9 +572,7 @@ namespace xsimd
                 __m256i xL = _mm256_or_si256(_mm256_and_si256(mask, x), _mm256_andnot_si256(mask, _mm256_castpd_si256(_mm256_set1_pd(0x0010000000000000)))); //  2^52
                 __m256d f = _mm256_sub_pd(_mm256_castsi256_pd(xH), _mm256_set1_pd(442726361368656609280.)); //  3*2^67 + 2^52
                 // See above: prevent -ffast-math from reassociating (xH-C)+xL.
-#if defined(__GNUC__)
-                __asm__ volatile("" : "+x"(f));
-#endif
+                detail::reassociation_barrier(f, A {});
                 return _mm256_add_pd(f, _mm256_castsi256_pd(xL));
             }
         }

include/xsimd/arch/xsimd_common_fwd.hpp

@@ -23,6 +23,15 @@ namespace xsimd
     class batch;
     template <class T, class A>
     class batch_bool;
+    namespace kernel
+    {
+        namespace detail
+        {
+            struct memory_barrier_tag
+            {
+            };
+        }
+    }
     template <class T, class A, T... Vs>
     struct batch_constant;
     template <class T, class A, bool... Vs>
@@ -101,6 +110,12 @@ namespace xsimd
         // Forward declarations for pack-level helpers
         namespace detail
         {
+            template <class T>
+            XSIMD_INLINE void reassociation_barrier(T& x, memory_barrier_tag) noexcept;
+
+            template <class T, class A>
+            XSIMD_INLINE void reassociation_barrier(T& x, A const&) noexcept;
+
             template <typename T, T... Vs>
             XSIMD_INLINE constexpr bool is_identity() noexcept;
             template <typename T, class A, T... Vs>
@@ -115,7 +130,6 @@ namespace xsimd
             XSIMD_INLINE constexpr bool is_only_from_lo(batch_constant<T, A, Vs...>) noexcept;
             template <typename T, class A, T... Vs>
             XSIMD_INLINE constexpr bool is_only_from_hi(batch_constant<T, A, Vs...>) noexcept;
-
         }
     }
 }

include/xsimd/arch/xsimd_sse2.hpp

@@ -716,6 +716,8 @@ namespace xsimd
                 __m128i mask = _mm_setr_epi16(0xFFFF, 0xFFFF, 0x0000, 0x0000, 0xFFFF, 0xFFFF, 0x0000, 0x0000);
                 __m128i xL = _mm_or_si128(_mm_and_si128(mask, x), _mm_andnot_si128(mask, _mm_castpd_si128(_mm_set1_pd(0x0010000000000000)))); //  2^52
                 __m128d f = _mm_sub_pd(_mm_castsi128_pd(xH), _mm_set1_pd(19342813118337666422669312.)); //  2^84 + 2^52
+                // Prevent -ffast-math from reassociating (xH-C)+xL into xH+(xL-C).
+                detail::reassociation_barrier(f, A {});
                 return _mm_add_pd(f, _mm_castsi128_pd(xL));
             }
 
@@ -730,6 +732,8 @@ namespace xsimd
                 __m128i mask = _mm_setr_epi16(0xFFFF, 0xFFFF, 0xFFFF, 0x0000, 0xFFFF, 0xFFFF, 0xFFFF, 0x0000);
                 __m128i xL = _mm_or_si128(_mm_and_si128(mask, x), _mm_andnot_si128(mask, _mm_castpd_si128(_mm_set1_pd(0x0010000000000000)))); //  2^52
                 __m128d f = _mm_sub_pd(_mm_castsi128_pd(xH), _mm_set1_pd(442726361368656609280.)); //  3*2^67 + 2^52
+                // Prevent -ffast-math from reassociating (xH-C)+xL into xH+(xL-C).
+                detail::reassociation_barrier(f, A {});
                 return _mm_add_pd(f, _mm_castsi128_pd(xL));
             }
 

include/xsimd/arch/xsimd_sse4_1.hpp

@@ -64,11 +64,8 @@ namespace xsimd
                 __m128d f = _mm_sub_pd(_mm_castsi128_pd(xH), _mm_set1_pd(442726361368656609280.)); //  3*2^67 + 2^52
                 // With -ffast-math, the compiler may reassociate (xH-C)+xL into
                 // xH+(xL-C). Since xL<<C this causes catastrophic cancellation.
-                // The asm barrier forces f into a register before the add, blocking
-                // the reorder. It emits zero instructions.
-#if defined(__GNUC__)
-                __asm__ volatile("" : "+x"(f));
-#endif
+                // Barrier the intermediate before the final add.
+                detail::reassociation_barrier(f, A {});
                 return _mm_add_pd(f, _mm_castsi128_pd(xL));
             }
 
@@ -81,9 +78,7 @@ namespace xsimd
                 __m128i xL = _mm_blend_epi16(x, _mm_castpd_si128(_mm_set1_pd(0x0010000000000000)), 0xcc); //  2^52
                 __m128d f = _mm_sub_pd(_mm_castsi128_pd(xH), _mm_set1_pd(19342813118337666422669312.)); //  2^84 + 2^52
                 // See above: prevent -ffast-math from reassociating (xH-C)+xL.
-#if defined(__GNUC__)
-                __asm__ volatile("" : "+x"(f));
-#endif
+                detail::reassociation_barrier(f, A {});
                 return _mm_add_pd(f, _mm_castsi128_pd(xL));
             }
         }

include/xsimd/config/xsimd_config.hpp

@@ -44,6 +44,27 @@
 #define XSIMD_TARGET_X86 0
 #endif
 
+/**
+ * @ingroup xsimd_config_macro
+ *
+ * Set to 1 if GNU-style inline assembly is available, to 0 otherwise.
+ */
+/* Use __clang__ || __GNUC__ for GNU-style inline asm. clang-cl runs in
+ * MSVC-compatibility mode and does not define __GNUC__ by default, but it
+ * still defines __clang__. Clang documents __asm__/__asm__ support and broad
+ * GCC-extension compatibility:
+ * https://clang.llvm.org/docs/LanguageExtensions.html
+ * Clang only emits __GNUC__ when GNUCVersion != 0:
+ * https://raw.githubusercontent.com/llvm/llvm-project/main/clang/lib/Frontend/InitPreprocessor.cpp
+ * and GNUCVersion defaults to 0:
+ * https://raw.githubusercontent.com/llvm/llvm-project/main/clang/include/clang/Basic/LangOptions.def
+ */
+#if defined(__clang__) || defined(__GNUC__)
+#define XSIMD_WITH_INLINE_ASM 1
+#else
+#define XSIMD_WITH_INLINE_ASM 0
+#endif
+
 /**
  * @ingroup xsimd_config_macro
  *