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+/* mpn_sqr_basecase -- Internal routine to square a natural number
+ of length n.
+
+ THIS IS AN INTERNAL FUNCTION WITH A MUTABLE INTERFACE. IT IS ONLY
+ SAFE TO REACH THIS FUNCTION THROUGH DOCUMENTED INTERFACES.
+
+
+Copyright 1991-1994, 1996, 1997, 2000-2005, 2008, 2010, 2011 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 either:
+
+ * the GNU Lesser General Public License as published by the Free
+ Software Foundation; either version 3 of the License, or (at your
+ option) any later version.
+
+or
+
+ * the GNU General Public License as published by the Free Software
+ Foundation; either version 2 of the License, or (at your option) any
+ later version.
+
+or both in parallel, as here.
+
+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 General Public License
+for more details.
+
+You should have received copies of the GNU General Public License and the
+GNU Lesser General Public License along with the GNU MP Library. If not,
+see https://www.gnu.org/licenses/. */
+
+#include "gmp.h"
+#include "gmp-impl.h"
+#include "longlong.h"
+
+
+#if HAVE_NATIVE_mpn_sqr_diagonal
+#define MPN_SQR_DIAGONAL(rp, up, n) \
+ mpn_sqr_diagonal (rp, up, n)
+#else
+#define MPN_SQR_DIAGONAL(rp, up, n) \
+ do { \
+ mp_size_t _i; \
+ for (_i = 0; _i < (n); _i++) \
+ { \
+ mp_limb_t ul, lpl; \
+ ul = (up)[_i]; \
+ umul_ppmm ((rp)[2 * _i + 1], lpl, ul, ul << GMP_NAIL_BITS); \
+ (rp)[2 * _i] = lpl >> GMP_NAIL_BITS; \
+ } \
+ } while (0)
+#endif
+
+#if HAVE_NATIVE_mpn_sqr_diag_addlsh1
+#define MPN_SQR_DIAG_ADDLSH1(rp, tp, up, n) \
+ mpn_sqr_diag_addlsh1 (rp, tp, up, n)
+#else
+#if HAVE_NATIVE_mpn_addlsh1_n
+#define MPN_SQR_DIAG_ADDLSH1(rp, tp, up, n) \
+ do { \
+ mp_limb_t cy; \
+ MPN_SQR_DIAGONAL (rp, up, n); \
+ cy = mpn_addlsh1_n (rp + 1, rp + 1, tp, 2 * n - 2); \
+ rp[2 * n - 1] += cy; \
+ } while (0)
+#else
+#define MPN_SQR_DIAG_ADDLSH1(rp, tp, up, n) \
+ do { \
+ mp_limb_t cy; \
+ MPN_SQR_DIAGONAL (rp, up, n); \
+ cy = mpn_lshift (tp, tp, 2 * n - 2, 1); \
+ cy += mpn_add_n (rp + 1, rp + 1, tp, 2 * n - 2); \
+ rp[2 * n - 1] += cy; \
+ } while (0)
+#endif
+#endif
+
+
+#undef READY_WITH_mpn_sqr_basecase
+
+
+#if ! defined (READY_WITH_mpn_sqr_basecase) && HAVE_NATIVE_mpn_addmul_2s
+void
+mpn_sqr_basecase (mp_ptr rp, mp_srcptr up, mp_size_t n)
+{
+ mp_size_t i;
+ mp_limb_t tarr[2 * SQR_TOOM2_THRESHOLD];
+ mp_ptr tp = tarr;
+ mp_limb_t cy;
+
+ /* must fit 2*n limbs in tarr */
+ ASSERT (n <= SQR_TOOM2_THRESHOLD);
+
+ if ((n & 1) != 0)
+ {
+ if (n == 1)
+ {
+ mp_limb_t ul, lpl;
+ ul = up[0];
+ umul_ppmm (rp[1], lpl, ul, ul << GMP_NAIL_BITS);
+ rp[0] = lpl >> GMP_NAIL_BITS;
+ return;
+ }
+
+ MPN_ZERO (tp, n);
+
+ for (i = 0; i <= n - 2; i += 2)
+ {
+ cy = mpn_addmul_2s (tp + 2 * i, up + i + 1, n - (i + 1), up + i);
+ tp[n + i] = cy;
+ }
+ }
+ else
+ {
+ if (n == 2)
+ {
+#if HAVE_NATIVE_mpn_mul_2
+ rp[3] = mpn_mul_2 (rp, up, 2, up);
+#else
+ rp[0] = 0;
+ rp[1] = 0;
+ rp[3] = mpn_addmul_2 (rp, up, 2, up);
+#endif
+ return;
+ }
+
+ MPN_ZERO (tp, n);
+
+ for (i = 0; i <= n - 4; i += 2)
+ {
+ cy = mpn_addmul_2s (tp + 2 * i, up + i + 1, n - (i + 1), up + i);
+ tp[n + i] = cy;
+ }
+ cy = mpn_addmul_1 (tp + 2 * n - 4, up + n - 1, 1, up[n - 2]);
+ tp[2 * n - 3] = cy;
+ }
+
+ MPN_SQR_DIAG_ADDLSH1 (rp, tp, up, n);
+}
+#define READY_WITH_mpn_sqr_basecase
+#endif
+
+
+#if ! defined (READY_WITH_mpn_sqr_basecase) && HAVE_NATIVE_mpn_addmul_2
+
+/* mpn_sqr_basecase using plain mpn_addmul_2.
+
+ This is tricky, since we have to let mpn_addmul_2 make some undesirable
+ multiplies, u[k]*u[k], that we would like to let mpn_sqr_diagonal handle.
+ This forces us to conditionally add or subtract the mpn_sqr_diagonal
+ results. Examples of the product we form:
+
+ n = 4 n = 5 n = 6
+ u1u0 * u3u2u1 u1u0 * u4u3u2u1 u1u0 * u5u4u3u2u1
+ u2 * u3 u3u2 * u4u3 u3u2 * u5u4u3
+ u4 * u5
+ add: u0 u2 u3 add: u0 u2 u4 add: u0 u2 u4 u5
+ sub: u1 sub: u1 u3 sub: u1 u3
+*/
+
+void
+mpn_sqr_basecase (mp_ptr rp, mp_srcptr up, mp_size_t n)
+{
+ mp_size_t i;
+ mp_limb_t tarr[2 * SQR_TOOM2_THRESHOLD];
+ mp_ptr tp = tarr;
+ mp_limb_t cy;
+
+ /* must fit 2*n limbs in tarr */
+ ASSERT (n <= SQR_TOOM2_THRESHOLD);
+
+ if ((n & 1) != 0)
+ {
+ mp_limb_t x0, x1;
+
+ if (n == 1)
+ {
+ mp_limb_t ul, lpl;
+ ul = up[0];
+ umul_ppmm (rp[1], lpl, ul, ul << GMP_NAIL_BITS);
+ rp[0] = lpl >> GMP_NAIL_BITS;
+ return;
+ }
+
+ /* The code below doesn't like unnormalized operands. Since such
+ operands are unusual, handle them with a dumb recursion. */
+ if (up[n - 1] == 0)
+ {
+ rp[2 * n - 2] = 0;
+ rp[2 * n - 1] = 0;
+ mpn_sqr_basecase (rp, up, n - 1);
+ return;
+ }
+
+ MPN_ZERO (tp, n);
+
+ for (i = 0; i <= n - 2; i += 2)
+ {
+ cy = mpn_addmul_2 (tp + 2 * i, up + i + 1, n - (i + 1), up + i);
+ tp[n + i] = cy;
+ }
+
+ MPN_SQR_DIAGONAL (rp, up, n);
+
+ for (i = 2;; i += 4)
+ {
+ x0 = rp[i + 0];
+ rp[i + 0] = (-x0) & GMP_NUMB_MASK;
+ x1 = rp[i + 1];
+ rp[i + 1] = (-x1 - (x0 != 0)) & GMP_NUMB_MASK;
+ __GMPN_SUB_1 (cy, rp + i + 2, rp + i + 2, 2, (x1 | x0) != 0);
+ if (i + 4 >= 2 * n)
+ break;
+ mpn_incr_u (rp + i + 4, cy);
+ }
+ }
+ else
+ {
+ mp_limb_t x0, x1;
+
+ if (n == 2)
+ {
+#if HAVE_NATIVE_mpn_mul_2
+ rp[3] = mpn_mul_2 (rp, up, 2, up);
+#else
+ rp[0] = 0;
+ rp[1] = 0;
+ rp[3] = mpn_addmul_2 (rp, up, 2, up);
+#endif
+ return;
+ }
+
+ /* The code below doesn't like unnormalized operands. Since such
+ operands are unusual, handle them with a dumb recursion. */
+ if (up[n - 1] == 0)
+ {
+ rp[2 * n - 2] = 0;
+ rp[2 * n - 1] = 0;
+ mpn_sqr_basecase (rp, up, n - 1);
+ return;
+ }
+
+ MPN_ZERO (tp, n);
+
+ for (i = 0; i <= n - 4; i += 2)
+ {
+ cy = mpn_addmul_2 (tp + 2 * i, up + i + 1, n - (i + 1), up + i);
+ tp[n + i] = cy;
+ }
+ cy = mpn_addmul_1 (tp + 2 * n - 4, up + n - 1, 1, up[n - 2]);
+ tp[2 * n - 3] = cy;
+
+ MPN_SQR_DIAGONAL (rp, up, n);
+
+ for (i = 2;; i += 4)
+ {
+ x0 = rp[i + 0];
+ rp[i + 0] = (-x0) & GMP_NUMB_MASK;
+ x1 = rp[i + 1];
+ rp[i + 1] = (-x1 - (x0 != 0)) & GMP_NUMB_MASK;
+ if (i + 6 >= 2 * n)
+ break;
+ __GMPN_SUB_1 (cy, rp + i + 2, rp + i + 2, 2, (x1 | x0) != 0);
+ mpn_incr_u (rp + i + 4, cy);
+ }
+ mpn_decr_u (rp + i + 2, (x1 | x0) != 0);
+ }
+
+#if HAVE_NATIVE_mpn_addlsh1_n
+ cy = mpn_addlsh1_n (rp + 1, rp + 1, tp, 2 * n - 2);
+#else
+ cy = mpn_lshift (tp, tp, 2 * n - 2, 1);
+ cy += mpn_add_n (rp + 1, rp + 1, tp, 2 * n - 2);
+#endif
+ rp[2 * n - 1] += cy;
+}
+#define READY_WITH_mpn_sqr_basecase
+#endif
+
+
+#if ! defined (READY_WITH_mpn_sqr_basecase)
+
+/* Default mpn_sqr_basecase using mpn_addmul_1. */
+
+void
+mpn_sqr_basecase (mp_ptr rp, mp_srcptr up, mp_size_t n)
+{
+ mp_size_t i;
+
+ ASSERT (n >= 1);
+ ASSERT (! MPN_OVERLAP_P (rp, 2*n, up, n));
+
+ {
+ mp_limb_t ul, lpl;
+ ul = up[0];
+ umul_ppmm (rp[1], lpl, ul, ul << GMP_NAIL_BITS);
+ rp[0] = lpl >> GMP_NAIL_BITS;
+ }
+ if (n > 1)
+ {
+ mp_limb_t tarr[2 * SQR_TOOM2_THRESHOLD];
+ mp_ptr tp = tarr;
+ mp_limb_t cy;
+
+ /* must fit 2*n limbs in tarr */
+ ASSERT (n <= SQR_TOOM2_THRESHOLD);
+
+ cy = mpn_mul_1 (tp, up + 1, n - 1, up[0]);
+ tp[n - 1] = cy;
+ for (i = 2; i < n; i++)
+ {
+ mp_limb_t cy;
+ cy = mpn_addmul_1 (tp + 2 * i - 2, up + i, n - i, up[i - 1]);
+ tp[n + i - 2] = cy;
+ }
+
+ MPN_SQR_DIAG_ADDLSH1 (rp, tp, up, n);
+ }
+}
+#endif
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