diff --git a/m4/ax_cache_size.m4 b/m4/ax_cache_size.m4
index 72754bb..a11344a 100644
--- a/m4/ax_cache_size.m4
+++ b/m4/ax_cache_size.m4
@@ -41,8 +41,9 @@ AC_DEFUN([AX_CACHE_SIZE],
 
     ax_l1_size=
     ax_l2_size=
+    ax_l3_size=
 
-    #Check if the variable is present
+    # Linux sysfs path
     if test -e /sys/devices/system/cpu/cpu0/cache/index0/size; then
         for idx in `seq 0 3`; do
             if test -e /sys/devices/system/cpu/cpu0/cache/index$idx/size ; then
@@ -57,63 +58,78 @@ AC_DEFUN([AX_CACHE_SIZE],
         ax_l3_size=$CPU0_L3_CACHE
 
     else
-      if test "x$ax_cv_cpu_vendor" != "xUnknown"; then
-        #Or use CPUID
-	AX_GCC_X86_CPUID(0x80000000)
-	cpu_exthigh=`echo $ax_cv_gcc_x86_cpuid_0x80000000 | cut -d ":" -f 1`
-	if test "x$cpu_exthi" \> "x80000004"; then
-          AX_GCC_X86_CPUID(0x80000005) # For L1 cache
-          l1_hexval=`echo $ax_cv_gcc_x86_cpuid_0x80000005 | cut -d ":" -f 4`
-          ax_l1_size=$((0x$l1_hexval >> 24))
-        fi
+        # Try CPUID (mostly for Linux without sysfs or during cross-compilation)
+        if test "x$ax_cv_cpu_vendor" != "xIntel"; then
+            AX_GCC_X86_CPUID(0x80000000)
+            cpu_exthigh=`echo $ax_cv_gcc_x86_cpuid_0x80000000 | cut -d ":" -f 1`
+            if test "x$cpu_exthigh" \> "x80000004"; then
+                AX_GCC_X86_CPUID(0x80000005)
+                l1_hexval=`echo $ax_cv_gcc_x86_cpuid_0x80000005 | cut -d ":" -f 4`
+                ax_l1_size=$((0x$l1_hexval >> 24))
+            fi
+
+            if test "x$cpu_exthigh" \> "x80000005"; then
+                AX_GCC_X86_CPUID(0x80000006)
+                l2_hexval=`echo $ax_cv_gcc_x86_cpuid_0x80000006 | cut -d ":" -f 3`
+                ax_l2_size=$((0x$l2_hexval >> 16))
 
-	if test "x$cpu_exthi" \> "x80000005"; then
-          AX_GCC_X86_CPUID(0x80000006) # For L2 cache
-          l2_hexval=`echo $ax_cv_gcc_x86_cpuid_0x80000006 | cut -d ":" -f 3`
-          ax_l2_size=$((0x$l2_hexval >> 16))
+                # L3 info in EDX (bits 31:18) → 512-byte blocks (AMD only)
+                l3_hexval=`echo $ax_cv_gcc_x86_cpuid_0x80000006 | cut -d ":" -f 4`
+                ax_l3_size=$(( (0x$l3_hexval >> 18) * 512 ))
+            fi
         fi
 
-	if test "x$cpu_exthi" \> "x80000005"; then
-          AX_GCC_X86_CPUID(0x80000006) # For L3 cache
-          l2_hexval=`echo $ax_cv_gcc_x86_cpuid_0x80000006 | cut -d ":" -f 4`
-          ax_l2_size=$((0x$l2_hexval >> 18))*512
+        # sysctl fallback
+        sysctl_exe=
+        if test -x /usr/sbin/sysctl; then
+            sysctl_exe=/usr/sbin/sysctl
+        elif test -x /sbin/sysctl; then
+            sysctl_exe=/sbin/sysctl
         fi
 
-      fi
-
-      #Or use sysctl
-      sysctl_exe=
-      if test -x /usr/sbin/sysctl ; then
-	sysctl_exe=/usr/sbin/sysctl
-      elif test -x /sbin/sysctl ; then
-	sysctl_exe=/sbin/sysctl
-      fi
-      if test -n "$sysctl_exe"; then
-	if test -z "$ax_l2_size" -o "$ax_l2_size" = "0"; then
-          sysctl_out=`$sysctl_exe -n hw.l2cachesize 2>/dev/null`;
-          if test ! -z "$sysctl_out"; then
-            ax_l2_size=$(($sysctl_out / 1024))
-          fi;
-
-	fi
-	if test -z "$ax_l1_size" -o "$ax_l1_size" = "0" ; then
-          sysctl_out=`$sysctl_exe -n hw.l1dcachesize 2>/dev/null`;
-          if test ! -z "$sysctl_out"; then
-  	    ax_l1_size=$(($sysctl_out / 1024))
-          fi;
-	fi
-	if test -z "$ax_l1_size" -o "ax_l1_size" = "0" ; then
-          sysctl_out=`$sysctl_exe -n hw.l1cachesize 2>/dev/null`;
-          if test ! -z "$sysctl_out"; then
-             ax_l1_size=$(($sysctl_out / 1024))
-          fi;
+        if test -n "$sysctl_exe"; then
+            # L1
+            if test -z "$ax_l1_size" -o "$ax_l1_size" = "0"; then
+                sysctl_out=`$sysctl_exe -n hw.l1dcachesize 2>/dev/null`
+                if test -n "$sysctl_out"; then
+                    ax_l1_size=$(($sysctl_out / 1024))
+                fi
+            fi
+            if test -z "$ax_l1_size" -o "$ax_l1_size" = "0"; then
+                sysctl_out=`$sysctl_exe -n hw.l1icachesize 2>/dev/null`
+                if test -n "$sysctl_out"; then
+                    ax_l1_size=$(($sysctl_out / 1024))
+                fi
+            fi
+            if test -z "$ax_l1_size" -o "$ax_l1_size" = "0"; then
+                sysctl_out=`$sysctl_exe -n hw.l1cachesize 2>/dev/null`
+                if test -n "$sysctl_out"; then
+                    ax_l1_size=$(($sysctl_out / 1024))
+                fi
+            fi
+
+            # L2
+            if test -z "$ax_l2_size" -o "$ax_l2_size" = "0"; then
+                sysctl_out=`$sysctl_exe -n hw.l2cachesize 2>/dev/null`
+                if test -n "$sysctl_out"; then
+                    ax_l2_size=$(($sysctl_out / 1024))
+                fi
+            fi
+
+            # L3
+            if test -z "$ax_l3_size" -o "$ax_l3_size" = "0"; then
+                sysctl_out=`$sysctl_exe -n hw.l3cachesize 2>/dev/null`
+                if test -n "$sysctl_out"; then
+                    ax_l3_size=$(($sysctl_out / 1024))
+                fi
+            fi
         fi
-      fi
     fi
 
+    # Final fallbacks
     test -z "$ax_l1_size" && ax_l1_size=0
     test -z "$ax_l2_size" && ax_l2_size=0
-    test -z "$ax_l3_size" && ax_l3_size=$ax_l2_size
+    test -z "$ax_l3_size" && ax_l3_size=0
 
     # Keep only digits if there is a unit (ie 1024K -> 1024) and convert in Bytes
     AC_MSG_CHECKING(the L1 cache size)
diff --git a/m4ri/misc.h b/m4ri/misc.h
index 99fd6bb..64c63bd 100644
--- a/m4ri/misc.h
+++ b/m4ri/misc.h
@@ -138,7 +138,7 @@ typedef uint64_t word;
  * \brief The number of bits in a word.
  */
 
-static int const m4ri_radix = 64;
+#define m4ri_radix 64
 
 /**
  * \brief The number one as a word.