fix: harden fast-math reassociation barriers

- Add zero-cost register constraints for all supported architectures:
  x86 "+x", ARM NEON/SVE "+w", PPC VSX "+wa", RISC-V scalar "+f",
  RISC-V RVV "+vr" (GCC 15+ / Clang 20+).
- Replace old "r"(&x):"memory" fallback with "+m" guarded by new
  XSIMD_REASSOCIATIVE_MATH macro so unknown targets only spill when
  the compiler can actually reassociate.
- Add XSIMD_REASSOCIATIVE_MATH config macro, auto-detected from
  __FAST_MATH__ / __ASSOCIATIVE_MATH__, user-overridable for Clang
  with standalone -fassociative-math.
- Add std::array overload so emulated batches get per-element
  barriers instead of spilling the whole array.
- Add missing barriers in exp/exp2/exp10 range reduction (float and
  double) after nearbyint() to prevent compensated subtraction
  reordering.
- Add missing barriers in log2 (float and double) after to_float(k)
  to protect Kahan compensated summation.

Author: DiamonDinoia

include/xsimd/arch/common/xsimd_common_details.hpp

@@ -111,6 +111,72 @@ namespace xsimd
 
         namespace detail
         {
+            // Prevent -ffast-math from reassociating floating-point
+            // arithmetic across this point.  The reason string
+            // documents *why* at each call site; unused at runtime.
+            //
+            // Zero-cost register constraints per target:
+            //   x86  "+x"  (XMM/YMM/ZMM, also scalar float/double)
+            //   ARM  "+w"  (V-reg / SVE Z-reg, also scalar float/double)
+            //   PPC  "+wa" (VS register, also scalar float/double)
+            //   RISC-V "+f" (F/D register, scalar float/double)
+            //   RISC-V RVV "+vr" (V register; GCC 15+ / Clang 20+)
+            //
+            // On unknown targets the "+m" fallback spills; it is
+            // guarded by XSIMD_REASSOCIATIVE_MATH so it is only
+            // emitted when the compiler can actually reassociate.
+            template <class T>
+            XSIMD_INLINE void reassociation_barrier(T& x, const char*) noexcept
+            {
+#if XSIMD_WITH_INLINE_ASM && !defined(__EMSCRIPTEN__)
+#if XSIMD_WITH_SSE2
+                __asm__ volatile("" : "+x"(x));
+#elif XSIMD_WITH_NEON || XSIMD_WITH_SVE
+                __asm__ volatile("" : "+w"(x));
+#elif XSIMD_WITH_VSX
+                __asm__ volatile("" : "+wa"(x));
+#elif XSIMD_REASSOCIATIVE_MATH
+                __asm__ volatile("" : "+m"(x));
+#else
+                (void)x;
+#endif
+#else
+                (void)x;
+#endif
+            }
+
+            // RISC-V scalar float/double: use F/D registers instead of
+            // spilling through "+m".  These overloads also serve
+            // emulated batches on RISC-V via the std::array overload.
+#if XSIMD_WITH_INLINE_ASM && defined(__riscv)
+            XSIMD_INLINE void reassociation_barrier(float& x, const char*) noexcept
+            {
+                __asm__ volatile("" : "+f"(x));
+            }
+            XSIMD_INLINE void reassociation_barrier(double& x, const char*) noexcept
+            {
+                __asm__ volatile("" : "+f"(x));
+            }
+#endif
+
+            template <class T, size_t N>
+            XSIMD_INLINE void reassociation_barrier(std::array<T, N>& arr, const char* reason) noexcept
+            {
+                for (auto& v : arr)
+                    reassociation_barrier(v, reason);
+            }
+
+            template <class T, class A>
+            XSIMD_INLINE void reassociation_barrier(batch<T, A>& b, const char* reason) noexcept
+            {
+#if XSIMD_WITH_RVV && XSIMD_WITH_INLINE_ASM && ((__GNUC__ >= 15) || (__clang_major__ >= 20))
+                __asm__ volatile("" : "+vr"(b.data.value.value));
+                (void)reason;
+#else
+                reassociation_barrier(b.data, reason);
+#endif
+            }
+
             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

@@ -743,7 +743,9 @@ namespace xsimd
                 static XSIMD_INLINE batch_type reduce(const batch_type& a, batch_type& x) noexcept
                 {
                     batch_type k = nearbyint(constants::invlog_2<batch_type>() * a);
+                    detail::reassociation_barrier(k, "compensated exp range reduction");
                     x = fnma(k, constants::log_2hi<batch_type>(), a);
+                    detail::reassociation_barrier(x, "compensated exp range reduction");
                     x = fnma(k, constants::log_2lo<batch_type>(), x);
                     return k;
                 }
@@ -769,7 +771,9 @@ namespace xsimd
                 static XSIMD_INLINE batch_type reduce(const batch_type& a, batch_type& x) noexcept
                 {
                     batch_type k = nearbyint(constants::invlog10_2<batch_type>() * a);
+                    detail::reassociation_barrier(k, "compensated exp10 range reduction");
                     x = fnma(k, constants::log10_2hi<batch_type>(), a);
+                    detail::reassociation_barrier(x, "compensated exp10 range reduction");
                     x -= k * constants::log10_2lo<batch_type>();
                     return k;
                 }
@@ -794,6 +798,7 @@ namespace xsimd
                 static XSIMD_INLINE batch_type reduce(const batch_type& a, batch_type& x) noexcept
                 {
                     batch_type k = nearbyint(a);
+                    detail::reassociation_barrier(k, "compensated exp2 range reduction");
                     x = (a - k);
                     return k;
                 }
@@ -819,7 +824,9 @@ namespace xsimd
                 static XSIMD_INLINE batch_type reduce(const batch_type& a, batch_type& hi, batch_type& lo, batch_type& x) noexcept
                 {
                     batch_type k = nearbyint(constants::invlog_2<batch_type>() * a);
+                    detail::reassociation_barrier(k, "compensated exp range reduction");
                     hi = fnma(k, constants::log_2hi<batch_type>(), a);
+                    detail::reassociation_barrier(hi, "compensated exp range reduction");
                     lo = k * constants::log_2lo<batch_type>();
                     x = hi - lo;
                     return k;
@@ -846,7 +853,9 @@ namespace xsimd
                 static XSIMD_INLINE batch_type reduce(const batch_type& a, batch_type&, batch_type&, batch_type& x) noexcept
                 {
                     batch_type k = nearbyint(constants::invlog10_2<batch_type>() * a);
+                    detail::reassociation_barrier(k, "compensated exp10 range reduction");
                     x = fnma(k, constants::log10_2hi<batch_type>(), a);
+                    detail::reassociation_barrier(x, "compensated exp10 range reduction");
                     x = fnma(k, constants::log10_2lo<batch_type>(), x);
                     return k;
                 }
@@ -878,6 +887,7 @@ namespace xsimd
                 {
                     batch_type k = nearbyint(a);
                     x = (a - k) * constants::log_2<batch_type>();
+                    detail::reassociation_barrier(x, "keep reduced exponent ordered before finalize");
                     return k;
                 }
 
@@ -937,7 +947,10 @@ 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);
+            detail::reassociation_barrier(out, "prevent folding exp10 for literal inputs");
+            return out;
         }
 
         // exp2
@@ -1494,6 +1507,7 @@ namespace xsimd
             batch_type R = t2 + t1;
             batch_type hfsq = batch_type(0.5) * f * f;
             batch_type dk = to_float(k);
+            detail::reassociation_barrier(dk, "keep compensated k conversion before split log(2) scaling");
             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 +1539,7 @@ namespace xsimd
             hx += 0x3ff00000 - 0x3fe6a09e;
             k += (hx >> 20) - 0x3ff;
             batch_type dk = to_float(k);
+            detail::reassociation_barrier(dk, "keep compensated k conversion before split log(2) scaling");
             hx = (hx & i_type(0x000fffff)) + 0x3fe6a09e;
             x = ::xsimd::bitwise_cast<double>(hx << 32 | (i_type(0xffffffff) & ::xsimd::bitwise_cast<int_type>(x)));
 
@@ -1584,6 +1599,7 @@ namespace xsimd
             batch_type R = t1 + t2;
             batch_type hfsq = batch_type(0.5) * f * f;
             batch_type dk = to_float(k);
+            detail::reassociation_barrier(dk, "prevent distributing multiplies through compensated exponent conversion");
             batch_type r = fma(fms(s, hfsq + R, hfsq) + f, constants::invlog_2<batch_type>(), dk);
 #ifdef __FAST_MATH__
             return r;
@@ -1629,7 +1645,9 @@ namespace xsimd
             batch_type val_hi = hi * constants::invlog_2hi<batch_type>();
             batch_type val_lo = fma(lo + hi, constants::invlog_2lo<batch_type>(), lo * constants::invlog_2hi<batch_type>());
             batch_type dk = to_float(k);
+            detail::reassociation_barrier(dk, "Kahan compensated log2 summation");
             batch_type w1 = dk + val_hi;
+            detail::reassociation_barrier(w1, "Kahan compensated log2 summation");
             val_lo += (dk - w1) + val_hi;
             val_hi = w1;
             batch_type r = val_lo + val_hi;
@@ -1705,6 +1723,7 @@ namespace xsimd
             batch_type t2 = z * detail::horner<batch_type, 0x3f2aaaaa, 0x3e91e9ee>(w);
             batch_type R = t2 + t1;
             batch_type dk = to_float(k);
+            detail::reassociation_barrier(dk, "prevent distributing multiplies through compensated exponent conversion");
             batch_type hfsq = batch_type(0.5) * f * f;
             batch_type hibits = f - hfsq;
             hibits &= ::xsimd::bitwise_cast<float>(i_type(0xfffff000));
@@ -1752,10 +1771,11 @@ namespace xsimd
 #endif
             hx += 0x3ff00000 - 0x3fe6a09e;
             k += (hx >> 20) - 0x3ff;
+            batch_type dk = to_float(k);
+            detail::reassociation_barrier(dk, "prevent distributing multiplies through compensated exponent conversion");
             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 +1838,7 @@ namespace xsimd
             batch_type R = t2 + t1;
             batch_type hfsq = batch_type(0.5) * f * f;
             batch_type dk = to_float(k);
+            detail::reassociation_barrier(dk, "prevent distributing multiplies through compensated exponent conversion");
             /* 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 +1874,7 @@ 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);
+            detail::reassociation_barrier(dk, "prevent distributing multiplies through compensated exponent conversion");
             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 +1922,9 @@ 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");
+                detail::reassociation_barrier(d0, "prevent collapsing (v + 2^n) - 2^n back to v");
                 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 +2206,16 @@ 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);
+            detail::reassociation_barrier(q, "prevent pulling multiply back through rounded quotient");
+            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);
+            detail::reassociation_barrier(q, "prevent pulling multiply back through rounded quotient");
+            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

@@ -551,33 +551,45 @@ namespace xsimd
                     {
                         auto test = x > constants::pio4<B>();
                         xr = x - constants::pio2_1<B>();
+                        detail::reassociation_barrier(xr, "ordered pio2 subtraction");
                         xr -= constants::pio2_2<B>();
+                        detail::reassociation_barrier(xr, "ordered pio2 subtraction");
                         xr -= constants::pio2_3<B>();
+                        detail::reassociation_barrier(xr, "ordered pio2 subtraction");
                         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>());
+                        detail::reassociation_barrier(xi, "preserve quadrant selection");
                         xr = fnma(xi, constants::pio2_1<B>(), x);
+                        detail::reassociation_barrier(xr, "compensated range reduction");
                         xr -= xi * constants::pio2_2<B>();
+                        detail::reassociation_barrier(xr, "compensated range reduction");
                         xr -= xi * constants::pio2_3<B>();
+                        detail::reassociation_barrier(xr, "compensated range reduction");
                         return quadrant(xi);
                     }
                     else if (all(x <= constants::mediumpi<B>()))
                     {
                         B fn = nearbyint(x * constants::twoopi<B>());
+                        detail::reassociation_barrier(fn, "multi-term range reduction");
                         B r = x - fn * constants::pio2_1<B>();
+                        detail::reassociation_barrier(r, "multi-term range reduction");
                         B w = fn * constants::pio2_1t<B>();
                         B t = r;
                         w = fn * constants::pio2_2<B>();
                         r = t - w;
+                        detail::reassociation_barrier(r, "multi-term range reduction");
                         w = fn * constants::pio2_2t<B>() - ((t - r) - w);
                         t = r;
                         w = fn * constants::pio2_3<B>();
                         r = t - w;
+                        detail::reassociation_barrier(r, "multi-term range reduction");
                         w = fn * constants::pio2_3t<B>() - ((t - r) - w);
                         xr = r - w;
+                        detail::reassociation_barrier(xr, "multi-term range reduction");
                         return quadrant(fn);
                     }
                     else

include/xsimd/arch/xsimd_avx2.hpp

@@ -552,13 +552,7 @@ namespace xsimd
                                                  0xFFFF, 0xFFFF, 0x0000, 0x0000, 0xFFFF, 0xFFFF, 0x0000, 0x0000);
                 __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(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
+                detail::reassociation_barrier(f, "prevent (xH-C)+xL -> xH+(xL-C)");
                 return _mm256_add_pd(f, _mm256_castsi256_pd(xL));
             }
 
@@ -574,10 +568,7 @@ namespace xsimd
                                                  0xFFFF, 0xFFFF, 0xFFFF, 0x0000, 0xFFFF, 0xFFFF, 0xFFFF, 0x0000);
                 __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, "prevent (xH-C)+xL -> xH+(xL-C)");
                 return _mm256_add_pd(f, _mm256_castsi256_pd(xL));
             }
         }

include/xsimd/arch/xsimd_common_fwd.hpp

@@ -101,6 +101,11 @@ namespace xsimd
         // Forward declarations for pack-level helpers
         namespace detail
         {
+            template <class T>
+            XSIMD_INLINE void reassociation_barrier(T& x, const char*) noexcept;
+            template <class T, class A>
+            XSIMD_INLINE void reassociation_barrier(batch<T, A>& b, const char* reason) noexcept;
+
             template <typename T, T... Vs>
             XSIMD_INLINE constexpr bool is_identity() noexcept;
             template <typename T, class A, T... Vs>
@@ -115,7 +120,6 @@ 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 +716,7 @@ 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
+                detail::reassociation_barrier(f, "prevent (xH-C)+xL -> xH+(xL-C)");
                 return _mm_add_pd(f, _mm_castsi128_pd(xL));
             }
 
@@ -730,6 +731,7 @@ 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
+                detail::reassociation_barrier(f, "prevent (xH-C)+xL -> xH+(xL-C)");
                 return _mm_add_pd(f, _mm_castsi128_pd(xL));
             }