diff --git a/ap/libc/glibc/glibc-2.23/stdlib/mul.c b/ap/libc/glibc/glibc-2.23/stdlib/mul.c
new file mode 100644
index 0000000..de2663e
--- /dev/null
+++ b/ap/libc/glibc/glibc-2.23/stdlib/mul.c
@@ -0,0 +1,142 @@
+/* mpn_mul -- Multiply two natural numbers.
+
+Copyright (C) 1991-2016 Free Software Foundation, Inc.
+
+This file is part of the GNU MP Library.
+
+The GNU MP Library is free software; you can redistribute it and/or modify
+it under the terms of the GNU Lesser General Public License as published by
+the Free Software Foundation; either version 2.1 of the License, or (at your
+option) any later version.
+
+The GNU MP Library is distributed in the hope that it will be useful, but
+WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
+License for more details.
+
+You should have received a copy of the GNU Lesser General Public License
+along with the GNU MP Library; see the file COPYING.LIB.  If not, see
+<http://www.gnu.org/licenses/>.  */
+
+#include <gmp.h>
+#include "gmp-impl.h"
+
+/* Multiply the natural numbers u (pointed to by UP, with USIZE limbs)
+   and v (pointed to by VP, with VSIZE limbs), and store the result at
+   PRODP.  USIZE + VSIZE limbs are always stored, but if the input
+   operands are normalized.  Return the most significant limb of the
+   result.
+
+   NOTE: The space pointed to by PRODP is overwritten before finished
+   with U and V, so overlap is an error.
+
+   Argument constraints:
+   1. USIZE >= VSIZE.
+   2. PRODP != UP and PRODP != VP, i.e. the destination
+      must be distinct from the multiplier and the multiplicand.  */
+
+/* If KARATSUBA_THRESHOLD is not already defined, define it to a
+   value which is good on most machines.  */
+#ifndef KARATSUBA_THRESHOLD
+#define KARATSUBA_THRESHOLD 32
+#endif
+
+mp_limb_t
+mpn_mul (mp_ptr prodp,
+	 mp_srcptr up, mp_size_t usize,
+	 mp_srcptr vp, mp_size_t vsize)
+{
+  mp_ptr prod_endp = prodp + usize + vsize - 1;
+  mp_limb_t cy;
+  mp_ptr tspace;
+  TMP_DECL (marker);
+
+  if (vsize < KARATSUBA_THRESHOLD)
+    {
+      /* Handle simple cases with traditional multiplication.
+
+	 This is the most critical code of the entire function.  All
+	 multiplies rely on this, both small and huge.  Small ones arrive
+	 here immediately.  Huge ones arrive here as this is the base case
+	 for Karatsuba's recursive algorithm below.  */
+      mp_size_t i;
+      mp_limb_t cy_limb;
+      mp_limb_t v_limb;
+
+      if (vsize == 0)
+	return 0;
+
+      /* Multiply by the first limb in V separately, as the result can be
+	 stored (not added) to PROD.  We also avoid a loop for zeroing.  */
+      v_limb = vp[0];
+      if (v_limb <= 1)
+	{
+	  if (v_limb == 1)
+	    MPN_COPY (prodp, up, usize);
+	  else
+	    MPN_ZERO (prodp, usize);
+	  cy_limb = 0;
+	}
+      else
+	cy_limb = mpn_mul_1 (prodp, up, usize, v_limb);
+
+      prodp[usize] = cy_limb;
+      prodp++;
+
+      /* For each iteration in the outer loop, multiply one limb from
+	 U with one limb from V, and add it to PROD.  */
+      for (i = 1; i < vsize; i++)
+	{
+	  v_limb = vp[i];
+	  if (v_limb <= 1)
+	    {
+	      cy_limb = 0;
+	      if (v_limb == 1)
+		cy_limb = mpn_add_n (prodp, prodp, up, usize);
+	    }
+	  else
+	    cy_limb = mpn_addmul_1 (prodp, up, usize, v_limb);
+
+	  prodp[usize] = cy_limb;
+	  prodp++;
+	}
+      return cy_limb;
+    }
+
+  TMP_MARK (marker);
+
+  tspace = (mp_ptr) TMP_ALLOC (2 * vsize * BYTES_PER_MP_LIMB);
+  MPN_MUL_N_RECURSE (prodp, up, vp, vsize, tspace);
+
+  prodp += vsize;
+  up += vsize;
+  usize -= vsize;
+  if (usize >= vsize)
+    {
+      mp_ptr tp = (mp_ptr) TMP_ALLOC (2 * vsize * BYTES_PER_MP_LIMB);
+      do
+	{
+	  MPN_MUL_N_RECURSE (tp, up, vp, vsize, tspace);
+	  cy = mpn_add_n (prodp, prodp, tp, vsize);
+	  mpn_add_1 (prodp + vsize, tp + vsize, vsize, cy);
+	  prodp += vsize;
+	  up += vsize;
+	  usize -= vsize;
+	}
+      while (usize >= vsize);
+    }
+
+  /* True: usize < vsize.  */
+
+  /* Make life simple: Recurse.  */
+
+  if (usize != 0)
+    {
+      mpn_mul (tspace, vp, vsize, up, usize);
+      cy = mpn_add_n (prodp, prodp, tspace, vsize);
+      mpn_add_1 (prodp + vsize, tspace + vsize, usize, cy);
+    }
+
+  TMP_FREE (marker);
+  return *prod_endp;
+}