diff --git a/CMakeLists.txt b/CMakeLists.txt
index 9daec5f1e6..dab5632bc9 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -41,6 +41,8 @@ option(DYNAMIC_OLDER "Include specific support for older x86 cpu models (Penryn,
 
 option(BUILD_RELAPACK "Build with ReLAPACK (recursive implementation of several LAPACK functions on top of standard LAPACK)" OFF)
 
+option(WASM_RELAXED_SIMD "WASM: emit relaxed SIMD opcodes (not portable to engines without the feature, including shipping Safari)" OFF)
+
 option(USE_LOCKING "Use locks even in single-threaded builds to make them callable from multiple threads" OFF)
 
 option(USE_PERL "Use the older PERL scripts for build preparation instead of universal shell scripts" OFF)
diff --git a/Makefile.rule b/Makefile.rule
index 664a3d8036..5c843cfedd 100644
--- a/Makefile.rule
+++ b/Makefile.rule
@@ -311,6 +311,14 @@ COMMON_PROF = -pg
 # If you want to enable the experimental HFLOAT16 support
 # BUILD_HFLOAT16 = 1
 
+# WASM only: emit WebAssembly relaxed SIMD (for example f32x4.relaxed_madd)
+# in kernels that support it. Off by default because a module that contains
+# those opcodes will not instantiate on engines without the relaxed-simd
+# feature, including shipping Safari. See docs/install.md#webassembly and
+# https://webassembly.org/features/
+# WASM_RELAXED_SIMD = 1
+
+
 # Set the thread number threshold beyond which the job array for the threaded level3 BLAS
 # will be allocated on the heap rather than the stack. (This array alone requires 
 # NUM_THREADS*NUM_THREADS*128 bytes of memory so should not pose a problem at low cpu
diff --git a/Makefile.wasm b/Makefile.wasm
index feca75ed4c..fa144e8a37 100644
--- a/Makefile.wasm
+++ b/Makefile.wasm
@@ -1 +1,9 @@
-CCOMMON_OPT += -msimd128 -mrelaxed-simd
+# Portable WASM SIMD128. Do not pass -mrelaxed-simd by default: the resulting
+# module contains opcodes that engines without the relaxed-simd feature reject
+# at instantiate time (shipping Safari / JavaScriptCore among them). Engine
+# support is tracked at https://webassembly.org/features/
+# Opt in with WASM_RELAXED_SIMD=1 (see Makefile.rule and docs/install.md).
+CCOMMON_OPT += -msimd128
+ifeq ($(WASM_RELAXED_SIMD), 1)
+CCOMMON_OPT += -mrelaxed-simd
+endif
diff --git a/README.md b/README.md
index 31c2bd0b4f..d651c42b36 100644
--- a/README.md
+++ b/README.md
@@ -258,6 +258,9 @@ e.g.:
 
 - **WASM128_GENERIC**: Optimized SGEMM,DGEMM, DAXPY, SSUM/DSUM, SDOT/DDOT and SROT/DROT
 
+  Builds target [WASM SIMD128](https://github.com/WebAssembly/simd) (`-msimd128`) by default. Relaxed SIMD is **not** enabled globally: a module that contains those opcodes fails to instantiate on engines that do not implement the proposal (notably shipping Safari / JavaScriptCore). Engine support is listed at [webassembly.org/features](https://webassembly.org/features/). Pass `WASM_RELAXED_SIMD=1` (or `-DWASM_RELAXED_SIMD=ON` with CMake) to opt in. Details: [docs/install.md](docs/install.md#webassembly).
+
+
 
 ### Support for multiple targets in a single library
 
diff --git a/cmake/arch.cmake b/cmake/arch.cmake
index b902937a05..12d7de54e7 100644
--- a/cmake/arch.cmake
+++ b/cmake/arch.cmake
@@ -175,3 +175,11 @@ if (RISCV64)
   set(BINARY_DEFINED 1)
 endif ()
 
+if (WASM)
+  set(CCOMMON_OPT "${CCOMMON_OPT} -msimd128")
+  if (WASM_RELAXED_SIMD)
+    set(CCOMMON_OPT "${CCOMMON_OPT} -mrelaxed-simd")
+  endif ()
+endif ()
+
+
diff --git a/docs/build_system.md b/docs/build_system.md
index ad0c77e89c..9b95a5e678 100644
--- a/docs/build_system.md
+++ b/docs/build_system.md
@@ -73,6 +73,10 @@ though - please read the linked Makefiles if you want to see all variables.
 - `FCOMMON_OPT`: flags to add to all invocations of the target Fortran compiler
   (overrides `FFLAGS`)
 - `LDFLAGS`: flags to add to all target linker invocations
+- `WASM_RELAXED_SIMD`: WASM only; if set to `1`, pass `-mrelaxed-simd` so
+  kernels can emit relaxed SIMD FMA. Off by default because the binary will
+  not load on engines without the feature (see
+  [install.md](install.md#webassembly)).
 - `AR`, `AS`, `LD`, `RANLIB`: `TARGET` toolchain helpers used for compilation
   (can be cross-toolchains).
 - `HOSTCC`: compiler of build machine, needed to create proper config files for
diff --git a/docs/install.md b/docs/install.md
index b842595494..edd539918f 100644
--- a/docs/install.md
+++ b/docs/install.md
@@ -847,6 +847,62 @@ riscv64-linux-gnu-objdump -d libopenblas*.a | \
 returns approximately 12,000-14,000 (GCC 14: ~12,691; GCC 15: ~14,355).
 
 
+### WebAssembly
+
+OpenBLAS can be cross-compiled with [Emscripten](https://emscripten.org/)
+(`TARGET=WASM128_GENERIC`). `Makefile.wasm` always passes `-msimd128` so
+kernels can use the portable [WASM SIMD128](https://github.com/WebAssembly/simd)
+instruction set (128-bit `v128` vectors).
+
+#### Relaxed SIMD
+
+[Relaxed SIMD](https://github.com/WebAssembly/relaxed-simd) is a follow-on
+proposal. It keeps the same 128-bit vectors but allows a few operations —
+in particular fused multiply-add (`f32x4.relaxed_madd` /
+`f64x2.relaxed_madd`) — to map to native hardware FMA. The result may use
+one rounding or two, depending on the CPU, so it is not bit-identical across
+engines.
+
+OpenBLAS kernels already select `relaxed_madd` when the compiler defines
+`__wasm_relaxed_simd__` (from `-mrelaxed-simd`), and fall back to a separate
+multiply then add otherwise. That compile-time split is not enough for a
+single portable binary: WebAssembly validates the whole module, so any
+relaxed-SIMD opcode causes instantiate to fail on an engine that does not
+implement the feature. There is no in-module runtime dispatch.
+
+Engine support is tracked at [webassembly.org/features](https://webassembly.org/features/).
+As of 2026, shipping Safari / JavaScriptCore still lacks relaxed SIMD
+(Safari Technology Preview has it; a page cannot enable the JSC flag
+`useWasmRelaxedSIMD` itself). Chrome/V8 and current Firefox do support it.
+
+For a library that must load in every current browser, leave relaxed SIMD
+**off** (the default). Opt in only when every target engine is known to
+support it, or when you ship a second binary and select it from JavaScript
+with [wasm-feature-detect](https://github.com/GoogleChromeLabs/wasm-feature-detect).
+
+```bash
+# Portable default (SIMD128 only)
+make TARGET=WASM128_GENERIC \
+  HOSTCC=gcc CC=emcc AR=emar RANLIB=emranlib \
+  USE_THREAD=0 NOFORTRAN=1
+
+# Relaxed SIMD (FMA); will not instantiate on engines without the feature
+make TARGET=WASM128_GENERIC WASM_RELAXED_SIMD=1 \
+  HOSTCC=gcc CC=emcc AR=emar RANLIB=emranlib \
+  USE_THREAD=0 NOFORTRAN=1
+```
+
+With CMake, pass `-DWASM_RELAXED_SIMD=ON`.
+
+After the tree is configured for WASM (`ARCH=wasm` in `Makefile.conf`), check
+that the default build stays SIMD128-only and that the opt-in path emits
+`relaxed_madd`:
+
+```bash
+./kernel/wasm/test_relaxed_simd.sh
+```
+
+
 ### FreeBSD
 
 You will need to install the following tools from the FreeBSD ports tree:
diff --git a/kernel/wasm/test_relaxed_simd.sh b/kernel/wasm/test_relaxed_simd.sh
new file mode 100755
index 0000000000..41fb732b3e
--- /dev/null
+++ b/kernel/wasm/test_relaxed_simd.sh
@@ -0,0 +1,238 @@
+#!/usr/bin/env bash
+# Verify WASM relaxed SIMD is opt-in:
+#   * the default compile does not pass -mrelaxed-simd and emits no relaxed_madd
+#   * WASM_RELAXED_SIMD=1 passes the flag and kernels use relaxed_madd
+#
+# Requires a WASM-configured tree (ARCH=wasm in Makefile.conf), emcc, and
+# wasm-dis (Binaryen, shipped with Emscripten). Node is used to instantiate
+# the default module when available.
+set -euo pipefail
+
+ROOT="$(cd "$(dirname "$0")/../.." && pwd)"
+JOBS="${JOBS:-$(nproc 2>/dev/null || echo 4)}"
+FAILS=0
+
+activate_emscripten() {
+  if command -v emcc >/dev/null 2>&1; then
+    return 0
+  fi
+  local prefix="${OPENBLAS_EM_PREFIX:-}"
+  if [[ -z "$prefix" && -n "${CONDA_PREFIX:-}" && -f "${CONDA_PREFIX}/bin/activate_emscripten.sh" ]]; then
+    prefix="$CONDA_PREFIX"
+  fi
+  if [[ -z "$prefix" && -n "${EMSDK:-}" && -x "${EMSDK}/upstream/emscripten/emcc" ]]; then
+    export PATH="${EMSDK}/upstream/emscripten:${EMSDK}/upstream/bin:${PATH}"
+    return 0
+  fi
+  if [[ -z "$prefix" && -f "$ROOT/.em-prefix/bin/activate_emscripten.sh" ]]; then
+    prefix="$ROOT/.em-prefix"
+  fi
+  if [[ -z "$prefix" || ! -f "$prefix/bin/activate_emscripten.sh" ]]; then
+    echo "emcc not found. Set OPENBLAS_EM_PREFIX to an Emscripten prefix." >&2
+    exit 1
+  fi
+  export CONDA_PREFIX="$prefix"
+  export PREFIX="${PREFIX:-$prefix}"
+  export PATH="$prefix/bin:$prefix/opt/emsdk/upstream/emscripten:$prefix/opt/emsdk/upstream/bin:$PATH"
+  # shellcheck disable=SC1091
+  source "$prefix/bin/activate_emscripten.sh"
+}
+
+count_op() {
+  # wasm-dis prints a warning on relocatable objects; keep stdout only.
+  local n
+  n="$(wasm-dis "$1" 2>/dev/null | grep -c "$2" || true)"
+  echo "${n:-0}"
+}
+
+expect() {
+  local name="$1" got="$2" pred="$3" want="$4"
+  if [[ "$pred" == "eq" && "$got" == "$want" ]]; then
+    echo "PASS  $name ($got)"
+    return 0
+  fi
+  if [[ "$pred" == "gt" && "$got" -gt "$want" ]]; then
+    echo "PASS  $name ($got > $want)"
+    return 0
+  fi
+  echo "FAIL  $name (got $got, expected $pred $want)" >&2
+  FAILS=$((FAILS + 1))
+}
+
+activate_emscripten
+cd "$ROOT"
+
+if ! command -v wasm-dis >/dev/null 2>&1; then
+  echo "wasm-dis not found (Binaryen). It is usually on PATH after activating Emscripten." >&2
+  exit 1
+fi
+
+if [[ ! -f Makefile.conf ]] || ! grep -q '^ARCH=wasm$' Makefile.conf; then
+  echo "Makefile.conf is not a WASM config (need ARCH=wasm)." >&2
+  echo "Configure first, for example:" >&2
+  echo "  make TARGET=WASM128_GENERIC HOSTCC=gcc CC=emcc AR=emar RANLIB=emranlib USE_THREAD=0 NOFORTRAN=1 NO_LAPACK=1" >&2
+  exit 1
+fi
+
+MAKE_COMMON=(
+  HOSTCC=gcc
+  CC=emcc
+  AR=emar
+  RANLIB=emranlib
+  TARGET=WASM128_GENERIC
+  USE_THREAD=0
+  NOFORTRAN=1
+  NO_LAPACK=1
+  COLORCODE=0
+)
+
+# Kernels that emit madd when __wasm_relaxed_simd__ is set.
+OBJS=(
+  sgemm_kernel.o
+  dgemm_kernel.o
+  cgemm_kernel_n.o
+  zgemm_kernel_n.o
+  sdot_k.o
+  ddot_k.o
+  dsdot_k.o
+  srot_k.o
+  dtrmm_kernel_LN.o
+)
+
+EXPORTS=_sgemm_kernel,_dgemm_kernel,_cgemm_kernel_n,_zgemm_kernel_n,_sdot_k,_ddot_k,_dsdot_k,_srot_k,_dtrmm_kernel_LN
+
+MAKE_BIN="${MAKE:-make}"
+
+sgemm_line() {
+  local extra=("$@")
+  rm -f kernel/sgemm_kernel.o
+  # GNU make -n prints the compile line only when the target is out of date.
+  "$MAKE_BIN" -C kernel -n sgemm_kernel.o "${MAKE_COMMON[@]}" "${extra[@]}" 2>/dev/null \
+    | grep -E '(^|[[:space:]])emcc[[:space:]]' | tail -1 || true
+}
+
+echo "==> compile-line flags"
+DEFAULT_LINE="$(sgemm_line)"
+RELAXED_LINE="$(sgemm_line WASM_RELAXED_SIMD=1)"
+echo "  default: $DEFAULT_LINE"
+echo "  relaxed: $RELAXED_LINE"
+if [[ -z "$DEFAULT_LINE" || -z "$RELAXED_LINE" ]]; then
+  echo "FAIL  could not extract an emcc compile line from make -n" >&2
+  exit 1
+fi
+
+case "$DEFAULT_LINE" in
+  *-msimd128*) expect "default passes -msimd128" 1 eq 1 ;;
+  *) expect "default passes -msimd128" 0 eq 1 ;;
+esac
+case "$DEFAULT_LINE" in
+  *-mrelaxed-simd*) expect "default omits -mrelaxed-simd" 1 eq 0 ;;
+  *) expect "default omits -mrelaxed-simd" 0 eq 0 ;;
+esac
+case "$RELAXED_LINE" in
+  *-mrelaxed-simd*) expect "WASM_RELAXED_SIMD=1 passes -mrelaxed-simd" 1 eq 1 ;;
+  *) expect "WASM_RELAXED_SIMD=1 passes -mrelaxed-simd" 0 eq 1 ;;
+esac
+
+OUT="$(mktemp -d "${TMPDIR:-/tmp}/openblas-relaxed-simd.XXXXXX")"
+trap 'rm -rf "$OUT"' EXIT
+
+build_variant() {
+  local dest="$1"
+  shift
+  rm -f "${OBJS[@]/#/kernel/}"
+  "$MAKE_BIN" -C kernel -j"$JOBS" "${OBJS[@]}" "${MAKE_COMMON[@]}" "$@"
+  mkdir -p "$dest"
+  local o
+  for o in "${OBJS[@]}"; do
+    cp "kernel/$o" "$dest/"
+  done
+}
+
+echo "==> compile default kernels"
+build_variant "$OUT/default"
+
+echo "==> compile WASM_RELAXED_SIMD=1 kernels"
+build_variant "$OUT/relaxed" WASM_RELAXED_SIMD=1
+
+sum_op() {
+  local dir="$1" op="$2" total=0 n
+  local o
+  for o in "$dir"/*.o; do
+    n="$(count_op "$o" "$op")"
+    total=$((total + n))
+  done
+  echo "$total"
+}
+
+DEFAULT_MADD="$(sum_op "$OUT/default" 'relaxed_madd')"
+RELAXED_MADD="$(sum_op "$OUT/relaxed" 'relaxed_madd')"
+DEFAULT_MUL="$(sum_op "$OUT/default" 'f32x4.mul')"
+RELAXED_MUL="$(sum_op "$OUT/relaxed" 'f32x4.mul')"
+
+echo "==> opcode counts (wasm-dis)"
+echo "  default  relaxed_madd=$DEFAULT_MADD  f32x4.mul=$DEFAULT_MUL"
+echo "  relaxed  relaxed_madd=$RELAXED_MADD  f32x4.mul=$RELAXED_MUL"
+
+expect "default objects have no relaxed_madd" "$DEFAULT_MADD" eq 0
+expect "WASM_RELAXED_SIMD=1 objects use relaxed_madd" "$RELAXED_MADD" gt 0
+expect "default objects still use f32x4.mul" "$DEFAULT_MUL" gt 0
+
+link_wasm() {
+  local dir="$1"
+  local extra=()
+  if [[ "${2:-}" == "relaxed" ]]; then
+    extra+=(-mrelaxed-simd)
+  fi
+  emcc -O2 -msimd128 "${extra[@]}" --no-entry \
+    -sEXPORTED_FUNCTIONS="$EXPORTS" \
+    -sERROR_ON_UNDEFINED_SYMBOLS=0 \
+    -sSTANDALONE_WASM=1 \
+    "$dir"/*.o -o "$dir/kernels.wasm"
+}
+
+echo "==> link and instantiate"
+link_wasm "$OUT/default"
+link_wasm "$OUT/relaxed" relaxed
+
+LINKED_DEFAULT_MADD="$(count_op "$OUT/default/kernels.wasm" 'relaxed_madd')"
+LINKED_RELAXED_MADD="$(count_op "$OUT/relaxed/kernels.wasm" 'relaxed_madd')"
+expect "linked default module has no relaxed_madd" "$LINKED_DEFAULT_MADD" eq 0
+expect "linked WASM_RELAXED_SIMD=1 module has relaxed_madd" "$LINKED_RELAXED_MADD" gt 0
+
+if command -v node >/dev/null 2>&1; then
+  node -e '
+const fs = require("fs");
+const defb = fs.readFileSync(process.argv[1]);
+const relb = fs.readFileSync(process.argv[2]);
+if (!WebAssembly.validate(defb)) {
+  console.error("FAIL  default module failed WebAssembly.validate");
+  process.exit(1);
+}
+WebAssembly.instantiate(defb).then(function () {
+  console.log("PASS  default module instantiates (SIMD128 only)");
+  if (!WebAssembly.validate(relb)) {
+    console.log("SKIP  WASM_RELAXED_SIMD=1 module does not validate on this engine (expected without relaxed SIMD)");
+    return;
+  }
+  return WebAssembly.instantiate(relb).then(function () {
+    console.log("PASS  WASM_RELAXED_SIMD=1 module instantiates on this engine");
+  });
+}).catch(function (err) {
+  console.error(err);
+  process.exit(1);
+});
+' "$OUT/default/kernels.wasm" "$OUT/relaxed/kernels.wasm"
+else
+  echo "SKIP  node not found; opcode checks still apply"
+fi
+
+# Rebuild default objects so a following 'make libs' is not mixed.
+rm -f "${OBJS[@]/#/kernel/}"
+"$MAKE_BIN" -C kernel -j"$JOBS" "${OBJS[@]}" "${MAKE_COMMON[@]}"
+
+if [[ "$FAILS" -ne 0 ]]; then
+  echo "$FAILS check(s) failed" >&2
+  exit 1
+fi
+echo "relaxed-SIMD opt-in checks passed"