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/mpn/generic/perfpow.c b/third_party/gmp/mpn/generic/perfpow.c
new file mode 100644
index 0000000..9d46477
--- /dev/null
+++ b/third_party/gmp/mpn/generic/perfpow.c
@@ -0,0 +1,342 @@
+/* mpn_perfect_power_p -- mpn perfect power detection.
+
+ Contributed to the GNU project by Martin Boij.
+
+Copyright 2009, 2010, 2012, 2014 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"
+#include "longlong.h"
+
+#define SMALL 20
+#define MEDIUM 100
+
+/* Return non-zero if {np,nn} == {xp,xn} ^ k.
+ Algorithm:
+ For s = 1, 2, 4, ..., s_max, compute the s least significant limbs of
+ {xp,xn}^k. Stop if they don't match the s least significant limbs of
+ {np,nn}.
+
+ FIXME: Low xn limbs can be expected to always match, if computed as a mod
+ B^{xn} root. So instead of using mpn_powlo, compute an approximation of the
+ most significant (normalized) limb of {xp,xn} ^ k (and an error bound), and
+ compare to {np, nn}. Or use an even cruder approximation based on fix-point
+ base 2 logarithm. */
+static int
+pow_equals (mp_srcptr np, mp_size_t n,
+ mp_srcptr xp,mp_size_t xn,
+ mp_limb_t k, mp_bitcnt_t f,
+ mp_ptr tp)
+{
+ mp_bitcnt_t y, z;
+ mp_size_t bn;
+ mp_limb_t h, l;
+
+ ASSERT (n > 1 || (n == 1 && np[0] > 1));
+ ASSERT (np[n - 1] > 0);
+ ASSERT (xn > 0);
+
+ if (xn == 1 && xp[0] == 1)
+ return 0;
+
+ z = 1 + (n >> 1);
+ for (bn = 1; bn < z; bn <<= 1)
+ {
+ mpn_powlo (tp, xp, &k, 1, bn, tp + bn);
+ if (mpn_cmp (tp, np, bn) != 0)
+ return 0;
+ }
+
+ /* Final check. Estimate the size of {xp,xn}^k before computing the power
+ with full precision. Optimization: It might pay off to make a more
+ accurate estimation of the logarithm of {xp,xn}, rather than using the
+ index of the MSB. */
+
+ MPN_SIZEINBASE_2EXP(y, xp, xn, 1);
+ y -= 1; /* msb_index (xp, xn) */
+
+ umul_ppmm (h, l, k, y);
+ h -= l == 0; --l; /* two-limb decrement */
+
+ z = f - 1; /* msb_index (np, n) */
+ if (h == 0 && l <= z)
+ {
+ mp_limb_t *tp2;
+ mp_size_t i;
+ int ans;
+ mp_limb_t size;
+ TMP_DECL;
+
+ size = l + k;
+ ASSERT_ALWAYS (size >= k);
+
+ TMP_MARK;
+ y = 2 + size / GMP_LIMB_BITS;
+ tp2 = TMP_ALLOC_LIMBS (y);
+
+ i = mpn_pow_1 (tp, xp, xn, k, tp2);
+ if (i == n && mpn_cmp (tp, np, n) == 0)
+ ans = 1;
+ else
+ ans = 0;
+ TMP_FREE;
+ return ans;
+ }
+
+ return 0;
+}
+
+
+/* Return non-zero if N = {np,n} is a kth power.
+ I = {ip,n} = N^(-1) mod B^n. */
+static int
+is_kth_power (mp_ptr rp, mp_srcptr np,
+ mp_limb_t k, mp_srcptr ip,
+ mp_size_t n, mp_bitcnt_t f,
+ mp_ptr tp)
+{
+ mp_bitcnt_t b;
+ mp_size_t rn, xn;
+
+ ASSERT (n > 0);
+ ASSERT ((k & 1) != 0 || k == 2);
+ ASSERT ((np[0] & 1) != 0);
+
+ if (k == 2)
+ {
+ b = (f + 1) >> 1;
+ rn = 1 + b / GMP_LIMB_BITS;
+ if (mpn_bsqrtinv (rp, ip, b, tp) != 0)
+ {
+ rp[rn - 1] &= (CNST_LIMB(1) << (b % GMP_LIMB_BITS)) - 1;
+ xn = rn;
+ MPN_NORMALIZE (rp, xn);
+ if (pow_equals (np, n, rp, xn, k, f, tp) != 0)
+ return 1;
+
+ /* Check if (2^b - r)^2 == n */
+ mpn_neg (rp, rp, rn);
+ rp[rn - 1] &= (CNST_LIMB(1) << (b % GMP_LIMB_BITS)) - 1;
+ MPN_NORMALIZE (rp, rn);
+ if (pow_equals (np, n, rp, rn, k, f, tp) != 0)
+ return 1;
+ }
+ }
+ else
+ {
+ b = 1 + (f - 1) / k;
+ rn = 1 + (b - 1) / GMP_LIMB_BITS;
+ mpn_brootinv (rp, ip, rn, k, tp);
+ if ((b % GMP_LIMB_BITS) != 0)
+ rp[rn - 1] &= (CNST_LIMB(1) << (b % GMP_LIMB_BITS)) - 1;
+ MPN_NORMALIZE (rp, rn);
+ if (pow_equals (np, n, rp, rn, k, f, tp) != 0)
+ return 1;
+ }
+ MPN_ZERO (rp, rn); /* Untrash rp */
+ return 0;
+}
+
+static int
+perfpow (mp_srcptr np, mp_size_t n,
+ mp_limb_t ub, mp_limb_t g,
+ mp_bitcnt_t f, int neg)
+{
+ mp_ptr ip, tp, rp;
+ mp_limb_t k;
+ int ans;
+ mp_bitcnt_t b;
+ gmp_primesieve_t ps;
+ TMP_DECL;
+
+ ASSERT (n > 0);
+ ASSERT ((np[0] & 1) != 0);
+ ASSERT (ub > 0);
+
+ TMP_MARK;
+ gmp_init_primesieve (&ps);
+ b = (f + 3) >> 1;
+
+ TMP_ALLOC_LIMBS_3 (ip, n, rp, n, tp, 5 * n);
+
+ MPN_ZERO (rp, n);
+
+ /* FIXME: It seems the inverse in ninv is needed only to get non-inverted
+ roots. I.e., is_kth_power computes n^{1/2} as (n^{-1})^{-1/2} and
+ similarly for nth roots. It should be more efficient to compute n^{1/2} as
+ n * n^{-1/2}, with a mullo instead of a binvert. And we can do something
+ similar for kth roots if we switch to an iteration converging to n^{1/k -
+ 1}, and we can then eliminate this binvert call. */
+ mpn_binvert (ip, np, 1 + (b - 1) / GMP_LIMB_BITS, tp);
+ if (b % GMP_LIMB_BITS)
+ ip[(b - 1) / GMP_LIMB_BITS] &= (CNST_LIMB(1) << (b % GMP_LIMB_BITS)) - 1;
+
+ if (neg)
+ gmp_nextprime (&ps);
+
+ ans = 0;
+ if (g > 0)
+ {
+ ub = MIN (ub, g + 1);
+ while ((k = gmp_nextprime (&ps)) < ub)
+ {
+ if ((g % k) == 0)
+ {
+ if (is_kth_power (rp, np, k, ip, n, f, tp) != 0)
+ {
+ ans = 1;
+ goto ret;
+ }
+ }
+ }
+ }
+ else
+ {
+ while ((k = gmp_nextprime (&ps)) < ub)
+ {
+ if (is_kth_power (rp, np, k, ip, n, f, tp) != 0)
+ {
+ ans = 1;
+ goto ret;
+ }
+ }
+ }
+ ret:
+ TMP_FREE;
+ return ans;
+}
+
+static const unsigned short nrtrial[] = { 100, 500, 1000 };
+
+/* Table of (log_{p_i} 2) values, where p_i is the (nrtrial[i] + 1)'th prime
+ number. */
+static const double logs[] =
+ { 0.1099457228193620, 0.0847016403115322, 0.0772048195144415 };
+
+int
+mpn_perfect_power_p (mp_srcptr np, mp_size_t n)
+{
+ mp_limb_t *nc, factor, g;
+ mp_limb_t exp, d;
+ mp_bitcnt_t twos, count;
+ int ans, where, neg, trial;
+ TMP_DECL;
+
+ neg = n < 0;
+ if (neg)
+ {
+ n = -n;
+ }
+
+ if (n == 0 || (n == 1 && np[0] == 1)) /* Valgrind doesn't like
+ (n <= (np[0] == 1)) */
+ return 1;
+
+ TMP_MARK;
+
+ count = 0;
+
+ twos = mpn_scan1 (np, 0);
+ if (twos != 0)
+ {
+ mp_size_t s;
+ if (twos == 1)
+ {
+ return 0;
+ }
+ s = twos / GMP_LIMB_BITS;
+ if (s + 1 == n && POW2_P (np[s]))
+ {
+ return ! (neg && POW2_P (twos));
+ }
+ count = twos % GMP_LIMB_BITS;
+ n -= s;
+ np += s;
+ if (count > 0)
+ {
+ nc = TMP_ALLOC_LIMBS (n);
+ mpn_rshift (nc, np, n, count);
+ n -= (nc[n - 1] == 0);
+ np = nc;
+ }
+ }
+ g = twos;
+
+ trial = (n > SMALL) + (n > MEDIUM);
+
+ where = 0;
+ factor = mpn_trialdiv (np, n, nrtrial[trial], &where);
+
+ if (factor != 0)
+ {
+ if (count == 0) /* We did not allocate nc yet. */
+ {
+ nc = TMP_ALLOC_LIMBS (n);
+ }
+
+ /* Remove factors found by trialdiv. Optimization: If remove
+ define _itch, we can allocate its scratch just once */
+
+ do
+ {
+ binvert_limb (d, factor);
+
+ /* After the first round we always have nc == np */
+ exp = mpn_remove (nc, &n, np, n, &d, 1, ~(mp_bitcnt_t)0);
+
+ if (g == 0)
+ g = exp;
+ else
+ g = mpn_gcd_1 (&g, 1, exp);
+
+ if (g == 1)
+ {
+ ans = 0;
+ goto ret;
+ }
+
+ if ((n == 1) & (nc[0] == 1))
+ {
+ ans = ! (neg && POW2_P (g));
+ goto ret;
+ }
+
+ np = nc;
+ factor = mpn_trialdiv (np, n, nrtrial[trial], &where);
+ }
+ while (factor != 0);
+ }
+
+ MPN_SIZEINBASE_2EXP(count, np, n, 1); /* log (np) + 1 */
+ d = (mp_limb_t) (count * logs[trial] + 1e-9) + 1;
+ ans = perfpow (np, n, d, g, count, neg);
+
+ ret:
+ TMP_FREE;
+ return ans;
+}