Add libgmp 6.2.0 to third_party
Don't build it yet. That will come in the next review.
Change-Id: Idf3266558165e5ab45f4a41c98cc8c838c8244d5
diff --git a/third_party/gmp/mpz/bin_ui.c b/third_party/gmp/mpz/bin_ui.c
new file mode 100644
index 0000000..bab3e07
--- /dev/null
+++ b/third_party/gmp/mpz/bin_ui.c
@@ -0,0 +1,459 @@
+/* mpz_bin_ui(RESULT, N, K) -- Set RESULT to N over K.
+
+Copyright 1998-2002, 2012, 2013, 2015, 2017-2018 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-impl.h"
+
+/* How many special cases? Minimum is 2: 0 and 1;
+ * also 3 {0,1,2} and 5 {0,1,2,3,4} are implemented.
+ */
+#define APARTAJ_KALKULOJ 2
+
+/* Whether to use (1) or not (0) the function mpz_bin_uiui whenever
+ * the operands fit.
+ */
+#define UZU_BIN_UIUI 0
+
+/* Whether to use a shortcut to precompute the product of four
+ * elements (1), or precompute only the product of a couple (0).
+ *
+ * In both cases the precomputed product is then updated with some
+ * linear operations to obtain the product of the next four (1)
+ * [or two (0)] operands.
+ */
+#define KVAROPE 1
+
+static void
+posmpz_init (mpz_ptr r)
+{
+ mp_ptr rp;
+ ASSERT (SIZ (r) > 0);
+ rp = SIZ (r) + MPZ_REALLOC (r, SIZ (r) + 2);
+ *rp = 0;
+ *++rp = 0;
+}
+
+/* Equivalent to mpz_add_ui (r, r, in), but faster when
+ 0 < SIZ (r) < ALLOC (r) and limbs above SIZ (r) contain 0. */
+static void
+posmpz_inc_ui (mpz_ptr r, unsigned long in)
+{
+#if BITS_PER_ULONG > GMP_NUMB_BITS
+ mpz_add_ui (r, r, in);
+#else
+ ASSERT (SIZ (r) > 0);
+ MPN_INCR_U (PTR (r), SIZ (r) + 1, in);
+ SIZ (r) += (PTR (r)[SIZ (r)] != 0);
+#endif
+}
+
+/* Equivalent to mpz_sub_ui (r, r, in), but faster when
+ 0 < SIZ (r) and we know in advance that the result is positive. */
+static void
+posmpz_dec_ui (mpz_ptr r, unsigned long in)
+{
+#if BITS_PER_ULONG > GMP_NUMB_BITS
+ mpz_sub_ui (r, r, in);
+#else
+ ASSERT (mpz_cmp_ui (r, in) >= 0);
+ MPN_DECR_U (PTR (r), SIZ (r), in);
+ SIZ (r) -= (PTR (r)[SIZ (r)-1] == 0);
+#endif
+}
+
+/* Equivalent to mpz_tdiv_q_2exp (r, r, 1), but faster when
+ 0 < SIZ (r) and we know in advance that the result is positive. */
+static void
+posmpz_rsh1 (mpz_ptr r)
+{
+ mp_ptr rp;
+ mp_size_t rn;
+
+ rn = SIZ (r);
+ rp = PTR (r);
+ ASSERT (rn > 0);
+ mpn_rshift (rp, rp, rn, 1);
+ SIZ (r) -= rp[rn - 1] == 0;
+}
+
+/* Computes r = n(n+(2*k-1))/2
+ It uses a sqare instead of a product, computing
+ r = ((n+k-1)^2 + n - (k-1)^2)/2
+ As a side effect, sets t = n+k-1
+ */
+static void
+mpz_hmul_nbnpk (mpz_ptr r, mpz_srcptr n, unsigned long int k, mpz_ptr t)
+{
+ ASSERT (k > 0 && SIZ(n) > 0);
+ --k;
+ mpz_add_ui (t, n, k);
+ mpz_mul (r, t, t);
+ mpz_add (r, r, n);
+ posmpz_rsh1 (r);
+ if (LIKELY (k <= (1UL << (BITS_PER_ULONG / 2))))
+ posmpz_dec_ui (r, (k + (k & 1))*(k >> 1));
+ else
+ {
+ mpz_t tmp;
+ mpz_init_set_ui (tmp, (k + (k & 1)));
+ mpz_mul_ui (tmp, tmp, k >> 1);
+ mpz_sub (r, r, tmp);
+ mpz_clear (tmp);
+ }
+}
+
+#if KVAROPE
+static void
+rek_raising_fac4 (mpz_ptr r, mpz_ptr p, mpz_ptr P, unsigned long int k, unsigned long int lk, mpz_ptr t)
+{
+ if (k - lk < 5)
+ {
+ do {
+ posmpz_inc_ui (p, 4*k+2);
+ mpz_addmul_ui (P, p, 4*k);
+ posmpz_dec_ui (P, k);
+ mpz_mul (r, r, P);
+ } while (--k > lk);
+ }
+ else
+ {
+ mpz_t lt;
+ unsigned long int m;
+
+ m = ((k + lk) >> 1) + 1;
+ rek_raising_fac4 (r, p, P, k, m, t);
+
+ posmpz_inc_ui (p, 4*m+2);
+ mpz_addmul_ui (P, p, 4*m);
+ posmpz_dec_ui (P, m);
+ if (t == NULL)
+ {
+ mpz_init_set (lt, P);
+ t = lt;
+ }
+ else
+ {
+ ALLOC (lt) = 0;
+ mpz_set (t, P);
+ }
+ rek_raising_fac4 (t, p, P, m - 1, lk, NULL);
+
+ mpz_mul (r, r, t);
+ mpz_clear (lt);
+ }
+}
+
+/* Computes (n+1)(n+2)...(n+k)/2^(k/2 +k/4) using the helper function
+ rek_raising_fac4, and exploiting an idea inspired by a piece of
+ code that Fredrik Johansson wrote and by a comment by Niels Möller.
+
+ Assume k = 4i then compute:
+ p = (n+1)(n+4i)/2 - i
+ (n+1+1)(n+4i)/2 = p + i + (n+4i)/2
+ (n+1+1)(n+4i-1)/2 = p + i + ((n+4i)-(n+1+1))/2 = p + i + (n-n+4i-2)/2 = p + 3i-1
+ P = (p + i)*(p+3i-1)/2 = (n+1)(n+2)(n+4i-1)(n+4i)/8
+ n' = n + 2
+ i' = i - 1
+ (n'-1)(n')(n'+4i'+1)(n'+4i'+2)/8 = P
+ (n'-1)(n'+4i'+2)/2 - i' - 1 = p
+ (n'-1+2)(n'+4i'+2)/2 - i' - 1 = p + (n'+4i'+2)
+ (n'-1+2)(n'+4i'+2-2)/2 - i' - 1 = p + (n'+4i'+2) - (n'-1+2) = p + 4i' + 1
+ (n'-1+2)(n'+4i'+2-2)/2 - i' = p + 4i' + 2
+ p' = p + 4i' + 2 = (n'+1)(n'+4i')/2 - i'
+ p' - 4i' - 2 = p
+ (p' - 4i' - 2 + i)*(p' - 4i' - 2+3i-1)/2 = P
+ (p' - 4i' - 2 + i' + 1)*(p' - 4i' - 2 + 3i' + 3 - 1)/2 = P
+ (p' - 3i' - 1)*(p' - i')/2 = P
+ (p' - 3i' - 1 + 4i' + 1)*(p' - i' + 4i' - 1)/2 = P + (4i' + 1)*(p' - i')/2 + (p' - 3i' - 1 + 4i' + 1)*(4i' - 1)/2
+ (p' + i')*(p' + 3i' - 1)/2 = P + (4i')*(p' + p')/2 + (p' - i' - (p' + i'))/2
+ (p' + i')*(p' + 3i' - 1)/2 = P + 4i'p' + (p' - i' - p' - i')/2
+ (p' + i')*(p' + 3i' - 1)/2 = P + 4i'p' - i'
+ P' = P + 4i'p' - i'
+
+ And compute the product P * P' * P" ...
+ */
+
+static void
+mpz_raising_fac4 (mpz_ptr r, mpz_ptr n, unsigned long int k, mpz_ptr t, mpz_ptr p)
+{
+ ASSERT ((k >= APARTAJ_KALKULOJ) && (APARTAJ_KALKULOJ > 0));
+ posmpz_init (n);
+ posmpz_inc_ui (n, 1);
+ SIZ (r) = 0;
+ if (k & 1)
+ {
+ mpz_set (r, n);
+ posmpz_inc_ui (n, 1);
+ }
+ k >>= 1;
+ if (APARTAJ_KALKULOJ < 2 && k == 0)
+ return;
+
+ mpz_hmul_nbnpk (p, n, k, t);
+ posmpz_init (p);
+
+ if (k & 1)
+ {
+ if (SIZ (r))
+ mpz_mul (r, r, p);
+ else
+ mpz_set (r, p);
+ posmpz_inc_ui (p, k - 1);
+ }
+ k >>= 1;
+ if (APARTAJ_KALKULOJ < 4 && k == 0)
+ return;
+
+ mpz_hmul_nbnpk (t, p, k, n);
+ if (SIZ (r))
+ mpz_mul (r, r, t);
+ else
+ mpz_set (r, t);
+
+ if (APARTAJ_KALKULOJ > 8 || k > 1)
+ {
+ posmpz_dec_ui (p, k);
+ rek_raising_fac4 (r, p, t, k - 1, 0, n);
+ }
+}
+
+#else /* KVAROPE */
+
+static void
+rek_raising_fac (mpz_ptr r, mpz_ptr n, unsigned long int k, unsigned long int lk, mpz_ptr t1, mpz_ptr t2)
+{
+ /* Should the threshold depend on SIZ (n) ? */
+ if (k - lk < 10)
+ {
+ do {
+ posmpz_inc_ui (n, k);
+ mpz_mul (r, r, n);
+ --k;
+ } while (k > lk);
+ }
+ else
+ {
+ mpz_t t3;
+ unsigned long int m;
+
+ m = ((k + lk) >> 1) + 1;
+ rek_raising_fac (r, n, k, m, t1, t2);
+
+ posmpz_inc_ui (n, m);
+ if (t1 == NULL)
+ {
+ mpz_init_set (t3, n);
+ t1 = t3;
+ }
+ else
+ {
+ ALLOC (t3) = 0;
+ mpz_set (t1, n);
+ }
+ rek_raising_fac (t1, n, m - 1, lk, t2, NULL);
+
+ mpz_mul (r, r, t1);
+ mpz_clear (t3);
+ }
+}
+
+/* Computes (n+1)(n+2)...(n+k)/2^(k/2) using the helper function
+ rek_raising_fac, and exploiting an idea inspired by a piece of
+ code that Fredrik Johansson wrote.
+
+ Force an even k = 2i then compute:
+ p = (n+1)(n+2i)/2
+ i' = i - 1
+ p == (n+1)(n+2i'+2)/2
+ p' = p + i' == (n+2)(n+2i'+1)/2
+ n' = n + 1
+ p'== (n'+1)(n'+2i')/2 == (n+1 +1)(n+2i -1)/2
+
+ And compute the product p * p' * p" ...
+*/
+
+static void
+mpz_raising_fac (mpz_ptr r, mpz_ptr n, unsigned long int k, mpz_ptr t, mpz_ptr p)
+{
+ unsigned long int hk;
+ ASSERT ((k >= APARTAJ_KALKULOJ) && (APARTAJ_KALKULOJ > 1));
+ mpz_add_ui (n, n, 1);
+ hk = k >> 1;
+ mpz_hmul_nbnpk (p, n, hk, t);
+
+ if ((k & 1) != 0)
+ {
+ mpz_add_ui (t, t, hk + 1);
+ mpz_mul (r, t, p);
+ }
+ else
+ {
+ mpz_set (r, p);
+ }
+
+ if ((APARTAJ_KALKULOJ > 3) || (hk > 1))
+ {
+ posmpz_init (p);
+ rek_raising_fac (r, p, hk - 1, 0, t, n);
+ }
+}
+#endif /* KVAROPE */
+
+/* This is a poor implementation. Look at bin_uiui.c for improvement ideas.
+ In fact consider calling mpz_bin_uiui() when the arguments fit, leaving
+ the code here only for big n.
+
+ The identity bin(n,k) = (-1)^k * bin(-n+k-1,k) can be found in Knuth vol
+ 1 section 1.2.6 part G. */
+
+void
+mpz_bin_ui (mpz_ptr r, mpz_srcptr n, unsigned long int k)
+{
+ mpz_t ni;
+ mp_size_t negate;
+
+ if (SIZ (n) < 0)
+ {
+ /* bin(n,k) = (-1)^k * bin(-n+k-1,k), and set ni = -n+k-1 - k = -n-1 */
+ mpz_init (ni);
+ mpz_add_ui (ni, n, 1L);
+ mpz_neg (ni, ni);
+ negate = (k & 1); /* (-1)^k */
+ }
+ else
+ {
+ /* bin(n,k) == 0 if k>n
+ (no test for this under the n<0 case, since -n+k-1 >= k there) */
+ if (mpz_cmp_ui (n, k) < 0)
+ {
+ SIZ (r) = 0;
+ return;
+ }
+
+ /* set ni = n-k */
+ mpz_init (ni);
+ mpz_sub_ui (ni, n, k);
+ negate = 0;
+ }
+
+ /* Now wanting bin(ni+k,k), with ni positive, and "negate" is the sign (0
+ for positive, 1 for negative). */
+
+ /* Rewrite bin(n,k) as bin(n,n-k) if that is smaller. In this case it's
+ whether ni+k-k < k meaning ni<k, and if so change to denominator ni+k-k
+ = ni, and new ni of ni+k-ni = k. */
+ if (mpz_cmp_ui (ni, k) < 0)
+ {
+ unsigned long tmp;
+ tmp = k;
+ k = mpz_get_ui (ni);
+ mpz_set_ui (ni, tmp);
+ }
+
+ if (k < APARTAJ_KALKULOJ)
+ {
+ if (k == 0)
+ {
+ SIZ (r) = 1;
+ MPZ_NEWALLOC (r, 1)[0] = 1;
+ }
+#if APARTAJ_KALKULOJ > 2
+ else if (k == 2)
+ {
+ mpz_add_ui (ni, ni, 1);
+ mpz_mul (r, ni, ni);
+ mpz_add (r, r, ni);
+ posmpz_rsh1 (r);
+ }
+#endif
+#if APARTAJ_KALKULOJ > 3
+ else if (k > 2)
+ { /* k = 3, 4 */
+ mpz_add_ui (ni, ni, 2); /* n+1 */
+ mpz_mul (r, ni, ni); /* (n+1)^2 */
+ mpz_sub_ui (r, r, 1); /* (n+1)^2-1 */
+ if (k == 3)
+ {
+ mpz_mul (r, r, ni); /* ((n+1)^2-1)(n+1) = n(n+1)(n+2) */
+ /* mpz_divexact_ui (r, r, 6); /\* 6=3<<1; div_by3 ? *\/ */
+ mpn_pi1_bdiv_q_1 (PTR(r), PTR(r), SIZ(r), 3, GMP_NUMB_MASK/3*2+1, 1);
+ MPN_NORMALIZE_NOT_ZERO (PTR(r), SIZ(r));
+ }
+ else /* k = 4 */
+ {
+ mpz_add (ni, ni, r); /* (n+1)^2+n */
+ mpz_mul (r, ni, ni); /* ((n+1)^2+n)^2 */
+ mpz_sub_ui (r, r, 1); /* ((n+1)^2+n)^2-1 = n(n+1)(n+2)(n+3) */
+ /* mpz_divexact_ui (r, r, 24); /\* 24=3<<3; div_by3 ? *\/ */
+ mpn_pi1_bdiv_q_1 (PTR(r), PTR(r), SIZ(r), 3, GMP_NUMB_MASK/3*2+1, 3);
+ MPN_NORMALIZE_NOT_ZERO (PTR(r), SIZ(r));
+ }
+ }
+#endif
+ else
+ { /* k = 1 */
+ mpz_add_ui (r, ni, 1);
+ }
+ }
+#if UZU_BIN_UIUI
+ else if (mpz_cmp_ui (ni, ULONG_MAX - k) <= 0)
+ {
+ mpz_bin_uiui (r, mpz_get_ui (ni) + k, k);
+ }
+#endif
+ else
+ {
+ mp_limb_t count;
+ mpz_t num, den;
+
+ mpz_init (num);
+ mpz_init (den);
+
+#if KVAROPE
+ mpz_raising_fac4 (num, ni, k, den, r);
+ popc_limb (count, k);
+ ASSERT (k - (k >> 1) - (k >> 2) - count >= 0);
+ mpz_tdiv_q_2exp (num, num, k - (k >> 1) - (k >> 2) - count);
+#else
+ mpz_raising_fac (num, ni, k, den, r);
+ popc_limb (count, k);
+ ASSERT (k - (k >> 1) - count >= 0);
+ mpz_tdiv_q_2exp (num, num, k - (k >> 1) - count);
+#endif
+
+ mpz_oddfac_1(den, k, 0);
+
+ mpz_divexact(r, num, den);
+ mpz_clear (num);
+ mpz_clear (den);
+ }
+ mpz_clear (ni);
+
+ SIZ(r) = (SIZ(r) ^ -negate) + negate;
+}