summaryrefslogtreecommitdiff
path: root/mpn/generic
diff options
context:
space:
mode:
Diffstat (limited to 'mpn/generic')
-rw-r--r--mpn/generic/hgcd2_jacobi.c356
-rw-r--r--mpn/generic/hgcd_jacobi.c235
-rw-r--r--mpn/generic/jacobi_2.c342
3 files changed, 933 insertions, 0 deletions
diff --git a/mpn/generic/hgcd2_jacobi.c b/mpn/generic/hgcd2_jacobi.c
new file mode 100644
index 000000000..c888deb1d
--- /dev/null
+++ b/mpn/generic/hgcd2_jacobi.c
@@ -0,0 +1,356 @@
+/* hgcd2_jacobi.c
+
+ THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
+ SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
+ GUARANTEED THAT THEY'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
+
+Copyright 1996, 1998, 2000, 2001, 2002, 2003, 2004, 2008, 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 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.
+
+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. If not, see http://www.gnu.org/licenses/. */
+
+#include "gmp.h"
+#include "gmp-impl.h"
+#include "longlong.h"
+
+#if GMP_NAIL_BITS > 0
+#error Nails not supported.
+#endif
+
+/* FIXME: Duplicated in hgcd2.c. Should move to gmp-impl.h, and
+ possibly be renamed. */
+static inline mp_limb_t
+div1 (mp_ptr rp,
+ mp_limb_t n0,
+ mp_limb_t d0)
+{
+ mp_limb_t q = 0;
+
+ if ((mp_limb_signed_t) n0 < 0)
+ {
+ int cnt;
+ for (cnt = 1; (mp_limb_signed_t) d0 >= 0; cnt++)
+ {
+ d0 = d0 << 1;
+ }
+
+ q = 0;
+ while (cnt)
+ {
+ q <<= 1;
+ if (n0 >= d0)
+ {
+ n0 = n0 - d0;
+ q |= 1;
+ }
+ d0 = d0 >> 1;
+ cnt--;
+ }
+ }
+ else
+ {
+ int cnt;
+ for (cnt = 0; n0 >= d0; cnt++)
+ {
+ d0 = d0 << 1;
+ }
+
+ q = 0;
+ while (cnt)
+ {
+ d0 = d0 >> 1;
+ q <<= 1;
+ if (n0 >= d0)
+ {
+ n0 = n0 - d0;
+ q |= 1;
+ }
+ cnt--;
+ }
+ }
+ *rp = n0;
+ return q;
+}
+
+/* Two-limb division optimized for small quotients. */
+static inline mp_limb_t
+div2 (mp_ptr rp,
+ mp_limb_t nh, mp_limb_t nl,
+ mp_limb_t dh, mp_limb_t dl)
+{
+ mp_limb_t q = 0;
+
+ if ((mp_limb_signed_t) nh < 0)
+ {
+ int cnt;
+ for (cnt = 1; (mp_limb_signed_t) dh >= 0; cnt++)
+ {
+ dh = (dh << 1) | (dl >> (GMP_LIMB_BITS - 1));
+ dl = dl << 1;
+ }
+
+ while (cnt)
+ {
+ q <<= 1;
+ if (nh > dh || (nh == dh && nl >= dl))
+ {
+ sub_ddmmss (nh, nl, nh, nl, dh, dl);
+ q |= 1;
+ }
+ dl = (dh << (GMP_LIMB_BITS - 1)) | (dl >> 1);
+ dh = dh >> 1;
+ cnt--;
+ }
+ }
+ else
+ {
+ int cnt;
+ for (cnt = 0; nh > dh || (nh == dh && nl >= dl); cnt++)
+ {
+ dh = (dh << 1) | (dl >> (GMP_LIMB_BITS - 1));
+ dl = dl << 1;
+ }
+
+ while (cnt)
+ {
+ dl = (dh << (GMP_LIMB_BITS - 1)) | (dl >> 1);
+ dh = dh >> 1;
+ q <<= 1;
+ if (nh > dh || (nh == dh && nl >= dl))
+ {
+ sub_ddmmss (nh, nl, nh, nl, dh, dl);
+ q |= 1;
+ }
+ cnt--;
+ }
+ }
+
+ rp[0] = nl;
+ rp[1] = nh;
+
+ return q;
+}
+
+int
+mpn_hgcd2_jacobi (mp_limb_t ah, mp_limb_t al, mp_limb_t bh, mp_limb_t bl,
+ struct hgcd_matrix1 *M, unsigned *bitsp)
+{
+ mp_limb_t u00, u01, u10, u11;
+ unsigned bits = *bitsp;
+
+ if (ah < 2 || bh < 2)
+ return 0;
+
+ if (ah > bh || (ah == bh && al > bl))
+ {
+ sub_ddmmss (ah, al, ah, al, bh, bl);
+ if (ah < 2)
+ return 0;
+
+ u00 = u01 = u11 = 1;
+ u10 = 0;
+ bits = mpn_jacobi_update (bits, 1, 1);
+ }
+ else
+ {
+ sub_ddmmss (bh, bl, bh, bl, ah, al);
+ if (bh < 2)
+ return 0;
+
+ u00 = u10 = u11 = 1;
+ u01 = 0;
+ bits = mpn_jacobi_update (bits, 0, 1);
+ }
+
+ if (ah < bh)
+ goto subtract_a;
+
+ for (;;)
+ {
+ ASSERT (ah >= bh);
+ if (ah == bh)
+ goto done;
+
+ if (ah < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2)))
+ {
+ ah = (ah << (GMP_LIMB_BITS / 2) ) + (al >> (GMP_LIMB_BITS / 2));
+ bh = (bh << (GMP_LIMB_BITS / 2) ) + (bl >> (GMP_LIMB_BITS / 2));
+
+ break;
+ }
+
+ /* Subtract a -= q b, and multiply M from the right by (1 q ; 0
+ 1), affecting the second column of M. */
+ ASSERT (ah > bh);
+ sub_ddmmss (ah, al, ah, al, bh, bl);
+
+ if (ah < 2)
+ goto done;
+
+ if (ah <= bh)
+ {
+ /* Use q = 1 */
+ u01 += u00;
+ u11 += u10;
+ bits = mpn_jacobi_update (bits, 1, 1);
+ }
+ else
+ {
+ mp_limb_t r[2];
+ mp_limb_t q = div2 (r, ah, al, bh, bl);
+ al = r[0]; ah = r[1];
+ if (ah < 2)
+ {
+ /* A is too small, but q is correct. */
+ u01 += q * u00;
+ u11 += q * u10;
+ bits = mpn_jacobi_update (bits, 1, q & 3);
+ goto done;
+ }
+ q++;
+ u01 += q * u00;
+ u11 += q * u10;
+ bits = mpn_jacobi_update (bits, 1, q & 3);
+ }
+ subtract_a:
+ ASSERT (bh >= ah);
+ if (ah == bh)
+ goto done;
+
+ if (bh < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2)))
+ {
+ ah = (ah << (GMP_LIMB_BITS / 2) ) + (al >> (GMP_LIMB_BITS / 2));
+ bh = (bh << (GMP_LIMB_BITS / 2) ) + (bl >> (GMP_LIMB_BITS / 2));
+
+ goto subtract_a1;
+ }
+
+ /* Subtract b -= q a, and multiply M from the right by (1 0 ; q
+ 1), affecting the first column of M. */
+ sub_ddmmss (bh, bl, bh, bl, ah, al);
+
+ if (bh < 2)
+ goto done;
+
+ if (bh <= ah)
+ {
+ /* Use q = 1 */
+ u00 += u01;
+ u10 += u11;
+ bits = mpn_jacobi_update (bits, 0, 1);
+ }
+ else
+ {
+ mp_limb_t r[2];
+ mp_limb_t q = div2 (r, bh, bl, ah, al);
+ bl = r[0]; bh = r[1];
+ if (bh < 2)
+ {
+ /* B is too small, but q is correct. */
+ u00 += q * u01;
+ u10 += q * u11;
+ bits = mpn_jacobi_update (bits, 0, q & 3);
+ goto done;
+ }
+ q++;
+ u00 += q * u01;
+ u10 += q * u11;
+ bits = mpn_jacobi_update (bits, 0, q & 3);
+ }
+ }
+
+ /* NOTE: Since we discard the least significant half limb, we don't
+ get a truly maximal M (corresponding to |a - b| <
+ 2^{GMP_LIMB_BITS +1}). */
+ /* Single precision loop */
+ for (;;)
+ {
+ ASSERT (ah >= bh);
+ if (ah == bh)
+ break;
+
+ ah -= bh;
+ if (ah < (CNST_LIMB (1) << (GMP_LIMB_BITS / 2 + 1)))
+ break;
+
+ if (ah <= bh)
+ {
+ /* Use q = 1 */
+ u01 += u00;
+ u11 += u10;
+ bits = mpn_jacobi_update (bits, 1, 1);
+ }
+ else
+ {
+ mp_limb_t r;
+ mp_limb_t q = div1 (&r, ah, bh);
+ ah = r;
+ if (ah < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2 + 1)))
+ {
+ /* A is too small, but q is correct. */
+ u01 += q * u00;
+ u11 += q * u10;
+ bits = mpn_jacobi_update (bits, 1, q & 3);
+ break;
+ }
+ q++;
+ u01 += q * u00;
+ u11 += q * u10;
+ bits = mpn_jacobi_update (bits, 1, q & 3);
+ }
+ subtract_a1:
+ ASSERT (bh >= ah);
+ if (ah == bh)
+ break;
+
+ bh -= ah;
+ if (bh < (CNST_LIMB (1) << (GMP_LIMB_BITS / 2 + 1)))
+ break;
+
+ if (bh <= ah)
+ {
+ /* Use q = 1 */
+ u00 += u01;
+ u10 += u11;
+ bits = mpn_jacobi_update (bits, 0, 1);
+ }
+ else
+ {
+ mp_limb_t r;
+ mp_limb_t q = div1 (&r, bh, ah);
+ bh = r;
+ if (bh < (CNST_LIMB(1) << (GMP_LIMB_BITS / 2 + 1)))
+ {
+ /* B is too small, but q is correct. */
+ u00 += q * u01;
+ u10 += q * u11;
+ bits = mpn_jacobi_update (bits, 0, q & 3);
+ break;
+ }
+ q++;
+ u00 += q * u01;
+ u10 += q * u11;
+ bits = mpn_jacobi_update (bits, 0, q & 3);
+ }
+ }
+
+ done:
+ M->u[0][0] = u00; M->u[0][1] = u01;
+ M->u[1][0] = u10; M->u[1][1] = u11;
+ *bitsp = bits;
+
+ return 1;
+}
diff --git a/mpn/generic/hgcd_jacobi.c b/mpn/generic/hgcd_jacobi.c
new file mode 100644
index 000000000..2dce43b99
--- /dev/null
+++ b/mpn/generic/hgcd_jacobi.c
@@ -0,0 +1,235 @@
+/* hgcd_jacobi.c.
+
+ THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
+ SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
+ GUARANTEED THAT THEY'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
+
+Copyright 2003, 2004, 2005, 2008, 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 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.
+
+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. If not, see http://www.gnu.org/licenses/. */
+
+#include "gmp.h"
+#include "gmp-impl.h"
+#include "longlong.h"
+
+/* This file is almost a copy of hgcd.c, with some added calls to
+ mpn_jacobi_update */
+
+struct hgcd_jacobi_ctx
+{
+ struct hgcd_matrix *M;
+ unsigned *bitsp;
+};
+
+static void
+hgcd_jacobi_hook (void *p, mp_srcptr gp, mp_size_t gn,
+ mp_srcptr qp, mp_size_t qn, int d)
+{
+ ASSERT (!gp);
+ ASSERT (d >= 0);
+
+ MPN_NORMALIZE (qp, qn);
+ if (qn > 0)
+ {
+ struct hgcd_jacobi_ctx *ctx = (struct hgcd_jacobi_ctx *) p;
+ /* NOTES: This is a bit ugly. A tp area is passed to
+ gcd_subdiv_step, which stores q at the start of that area. We
+ now use the rest. */
+ mp_ptr tp = (mp_ptr) qp + qn;
+
+ mpn_hgcd_matrix_update_q (ctx->M, qp, qn, d, tp);
+ *ctx->bitsp = mpn_jacobi_update (*ctx->bitsp, d, qp[0] & 3);
+ }
+}
+
+/* Perform a few steps, using some of mpn_hgcd2, subtraction and
+ division. Reduces the size by almost one limb or more, but never
+ below the given size s. Return new size for a and b, or 0 if no
+ more steps are possible.
+
+ If hgcd2 succeds, needs temporary space for hgcd_matrix_mul_1, M->n
+ limbs, and hgcd_mul_matrix1_inverse_vector, n limbs. If hgcd2
+ fails, needs space for the quotient, qn <= n - s + 1 limbs, for and
+ hgcd_matrix_update_q, qn + (size of the appropriate column of M) <=
+ resulting size of M.
+
+ If N is the input size to the calling hgcd, then s = floor(N/2) +
+ 1, M->n < N, qn + matrix size <= n - s + 1 + n - s = 2 (n - s) + 1
+ < N, so N is sufficient.
+*/
+
+static mp_size_t
+hgcd_jacobi_step (mp_size_t n, mp_ptr ap, mp_ptr bp, mp_size_t s,
+ struct hgcd_matrix *M, unsigned *bitsp, mp_ptr tp)
+{
+ struct hgcd_matrix1 M1;
+ mp_limb_t mask;
+ mp_limb_t ah, al, bh, bl;
+ mp_size_t an, bn, qn;
+ int col;
+
+ ASSERT (n > s);
+
+ mask = ap[n-1] | bp[n-1];
+ ASSERT (mask > 0);
+
+ if (n == s + 1)
+ {
+ if (mask < 4)
+ goto subtract;
+
+ ah = ap[n-1]; al = ap[n-2];
+ bh = bp[n-1]; bl = bp[n-2];
+ }
+ else if (mask & GMP_NUMB_HIGHBIT)
+ {
+ ah = ap[n-1]; al = ap[n-2];
+ bh = bp[n-1]; bl = bp[n-2];
+ }
+ else
+ {
+ int shift;
+
+ count_leading_zeros (shift, mask);
+ ah = MPN_EXTRACT_NUMB (shift, ap[n-1], ap[n-2]);
+ al = MPN_EXTRACT_NUMB (shift, ap[n-2], ap[n-3]);
+ bh = MPN_EXTRACT_NUMB (shift, bp[n-1], bp[n-2]);
+ bl = MPN_EXTRACT_NUMB (shift, bp[n-2], bp[n-3]);
+ }
+
+ /* Try an mpn_hgcd2 step */
+ if (mpn_hgcd2_jacobi (ah, al, bh, bl, &M1, bitsp))
+ {
+ /* Multiply M <- M * M1 */
+ mpn_hgcd_matrix_mul_1 (M, &M1, tp);
+
+ /* Can't swap inputs, so we need to copy. */
+ MPN_COPY (tp, ap, n);
+ /* Multiply M1^{-1} (a;b) */
+ return mpn_matrix22_mul1_inverse_vector (&M1, ap, tp, bp, n);
+ }
+
+ subtract:
+ {
+ struct hgcd_jacobi_ctx ctx;
+ ctx.M = M;
+ ctx.bitsp = bitsp;
+
+ return mpn_gcd_subdiv_step (ap, bp, n, s, hgcd_jacobi_hook, &ctx, tp);
+ }
+}
+
+/* Reduces a,b until |a-b| fits in n/2 + 1 limbs. Constructs matrix M
+ with elements of size at most (n+1)/2 - 1. Returns new size of a,
+ b, or zero if no reduction is possible. */
+
+/* Same scratch requirements as for mpn_hgcd. */
+mp_size_t
+mpn_hgcd_jacobi (mp_ptr ap, mp_ptr bp, mp_size_t n,
+ struct hgcd_matrix *M, unsigned *bitsp, mp_ptr tp)
+{
+ mp_size_t s = n/2 + 1;
+
+ mp_size_t nn;
+ int success = 0;
+
+ if (n <= s)
+ /* Happens when n <= 2, a fairly uninteresting case but exercised
+ by the random inputs of the testsuite. */
+ return 0;
+
+ ASSERT ((ap[n-1] | bp[n-1]) > 0);
+
+ ASSERT ((n+1)/2 - 1 < M->alloc);
+
+ if (ABOVE_THRESHOLD (n, HGCD_THRESHOLD))
+ {
+ mp_size_t n2 = (3*n)/4 + 1;
+ mp_size_t p = n/2;
+
+ nn = mpn_hgcd_jacobi (ap + p, bp + p, n - p, M, bitsp, tp);
+ if (nn > 0)
+ {
+ /* Needs 2*(p + M->n) <= 2*(floor(n/2) + ceil(n/2) - 1)
+ = 2 (n - 1) */
+ n = mpn_hgcd_matrix_adjust (M, p + nn, ap, bp, p, tp);
+ success = 1;
+ }
+ while (n > n2)
+ {
+ /* Needs n + 1 storage */
+ nn = hgcd_jacobi_step (n, ap, bp, s, M, bitsp, tp);
+ if (!nn)
+ return success ? n : 0;
+ n = nn;
+ success = 1;
+ }
+
+ if (n > s + 2)
+ {
+ struct hgcd_matrix M1;
+ mp_size_t scratch;
+
+ p = 2*s - n + 1;
+ scratch = MPN_HGCD_MATRIX_INIT_ITCH (n-p);
+
+ mpn_hgcd_matrix_init(&M1, n - p, tp);
+ nn = mpn_hgcd_jacobi (ap + p, bp + p, n - p, &M1, bitsp, tp + scratch);
+ if (nn > 0)
+ {
+ /* We always have max(M) > 2^{-(GMP_NUMB_BITS + 1)} max(M1) */
+ ASSERT (M->n + 2 >= M1.n);
+
+ /* Furthermore, assume M ends with a quotient (1, q; 0, 1),
+ then either q or q + 1 is a correct quotient, and M1 will
+ start with either (1, 0; 1, 1) or (2, 1; 1, 1). This
+ rules out the case that the size of M * M1 is much
+ smaller than the expected M->n + M1->n. */
+
+ ASSERT (M->n + M1.n < M->alloc);
+
+ /* Needs 2 (p + M->n) <= 2 (2*s - n2 + 1 + n2 - s - 1)
+ = 2*s <= 2*(floor(n/2) + 1) <= n + 2. */
+ n = mpn_hgcd_matrix_adjust (&M1, p + nn, ap, bp, p, tp + scratch);
+
+ /* We need a bound for of M->n + M1.n. Let n be the original
+ input size. Then
+
+ ceil(n/2) - 1 >= size of product >= M.n + M1.n - 2
+
+ and it follows that
+
+ M.n + M1.n <= ceil(n/2) + 1
+
+ Then 3*(M.n + M1.n) + 5 <= 3 * ceil(n/2) + 8 is the
+ amount of needed scratch space. */
+ mpn_hgcd_matrix_mul (M, &M1, tp + scratch);
+ success = 1;
+ }
+ }
+ }
+
+ for (;;)
+ {
+ /* Needs s+3 < n */
+ nn = hgcd_jacobi_step (n, ap, bp, s, M, bitsp, tp);
+ if (!nn)
+ return success ? n : 0;
+
+ n = nn;
+ success = 1;
+ }
+}
diff --git a/mpn/generic/jacobi_2.c b/mpn/generic/jacobi_2.c
new file mode 100644
index 000000000..9a8a2b551
--- /dev/null
+++ b/mpn/generic/jacobi_2.c
@@ -0,0 +1,342 @@
+/* jacobi_2.c
+
+ THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
+ SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
+ GUARANTEED THAT THEY'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
+
+Copyright 1996, 1998, 2000, 2001, 2002, 2003, 2004, 2008, 2010 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 3 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. If not, see http://www.gnu.org/licenses/. */
+
+#include "gmp.h"
+#include "gmp-impl.h"
+#include "longlong.h"
+
+#ifndef JACOBI_2_METHOD
+#define JACOBI_2_METHOD 2
+#endif
+
+/* Computes (a / b) where b is odd, and a and b are otherwise arbitrary
+ two-limb numbers. */
+#if JACOBI_2_METHOD == 1
+int
+mpn_jacobi_2 (mp_srcptr ap, mp_srcptr bp, unsigned bit)
+{
+ mp_limb_t ah, al, bh, bl;
+ int c;
+
+ al = ap[0];
+ ah = ap[1];
+ bl = bp[0];
+ bh = bp[1];
+
+ ASSERT (bl & 1);
+
+ bl = ((bh << (GMP_NUMB_BITS - 1)) & GMP_NUMB_MASK) | (bl >> 1);
+ bh >>= 1;
+
+ if ( (bh | bl) == 0)
+ return 1 - 2*(bit & 1);
+
+ if ( (ah | al) == 0)
+ return 0;
+
+ if (al == 0)
+ {
+ al = ah;
+ ah = 0;
+ bit ^= GMP_NUMB_BITS & (bl ^ (bl >> 1));
+ }
+ count_trailing_zeros (c, al);
+ bit ^= c & (bl ^ (bl >> 1));
+
+ c++;
+ if (UNLIKELY (c == GMP_NUMB_BITS))
+ {
+ al = ah;
+ ah = 0;
+ }
+ else
+ {
+ al = ((ah << (GMP_NUMB_BITS - c)) & GMP_NUMB_MASK) | (al >> c);
+ ah >>= c;
+ }
+ while ( (ah | bh) > 0)
+ {
+ mp_limb_t th, tl;
+ mp_limb_t bgta;
+
+ sub_ddmmss (th, tl, ah, al, bh, bl);
+ if ( (tl | th) == 0)
+ return 0;
+
+ bgta = LIMB_HIGHBIT_TO_MASK (th);
+
+ /* If b > a, invoke reciprocity */
+ bit ^= (bgta & al & bl);
+
+ /* b <-- min (a, b) */
+ add_ssaaaa (bh, bl, bh, bl, th & bgta, tl & bgta);
+
+ if ( (bh | bl) == 0)
+ return 1 - 2*(bit & 1);
+
+ /* a <-- |a - b| */
+ al = (bgta ^ tl) - bgta;
+ ah = (bgta ^ th);
+
+ if (UNLIKELY (al == 0))
+ {
+ /* If b > a, al == 0 implies that we have a carry to
+ propagate. */
+ al = ah - bgta;
+ ah = 0;
+ bit ^= GMP_NUMB_BITS & (bl ^ (bl >> 1));
+ }
+ count_trailing_zeros (c, al);
+ c++;
+ bit ^= c & (bl ^ (bl >> 1));
+
+ if (UNLIKELY (c == GMP_NUMB_BITS))
+ {
+ al = ah;
+ ah = 0;
+ }
+ else
+ {
+ al = ((ah << (GMP_NUMB_BITS - c)) & GMP_NUMB_MASK) | (al >> c);
+ ah >>= c;
+ }
+ }
+
+ ASSERT (bl > 0);
+
+ while ( (al | bl) & GMP_LIMB_HIGHBIT)
+ {
+ /* Need an extra comparison to get the mask. */
+ mp_limb_t t = al - bl;
+ mp_limb_t bgta = - (bl > al);
+
+ if (t == 0)
+ return 0;
+
+ /* If b > a, invoke reciprocity */
+ bit ^= (bgta & al & bl);
+
+ /* b <-- min (a, b) */
+ bl += (bgta & t);
+
+ /* a <-- |a - b| */
+ al = (t ^ bgta) - bgta;
+
+ /* Number of trailing zeros is the same no matter if we look at
+ * t or a, but using t gives more parallelism. */
+ count_trailing_zeros (c, t);
+ c ++;
+ /* (2/b) = -1 if b = 3 or 5 mod 8 */
+ bit ^= c & (bl ^ (bl >> 1));
+
+ if (UNLIKELY (c == GMP_NUMB_BITS))
+ return 1 - 2*(bit & 1);
+
+ al >>= c;
+ }
+
+ /* Here we have a little impedance mismatch. Better to inline it? */
+ return mpn_jacobi_base (2*al+1, 2*bl+1, bit << 1);
+}
+#elif JACOBI_2_METHOD == 2
+int
+mpn_jacobi_2 (mp_srcptr ap, mp_srcptr bp, unsigned bit)
+{
+ mp_limb_t ah, al, bh, bl;
+ int c;
+
+ al = ap[0];
+ ah = ap[1];
+ bl = bp[0];
+ bh = bp[1];
+
+ ASSERT (bl & 1);
+
+ /* Use bit 1. */
+ bit <<= 1;
+
+ if (bh == 0 && bl == 1)
+ /* (a|1) = 1 */
+ return 1 - (bit & 2);
+
+ if (al == 0)
+ {
+ if (ah == 0)
+ /* (0|b) = 0, b > 1 */
+ return 0;
+
+ count_trailing_zeros (c, ah);
+ bit ^= ((GMP_NUMB_BITS + c) << 1) & (bl ^ (bl >> 1));
+
+ al = bl;
+ bl = ah >> c;
+
+ if (bl == 1)
+ /* (1|b) = 1 */
+ return 1 - (bit & 2);
+
+ ah = bh;
+
+ bit ^= al & bl;
+
+ goto b_reduced;
+ }
+ if ( (al & 1) == 0)
+ {
+ count_trailing_zeros (c, al);
+
+ al = ((ah << (GMP_NUMB_BITS - c)) & GMP_NUMB_MASK) | (al >> c);
+ ah >>= c;
+ bit ^= (c << 1) & (bl ^ (bl >> 1));
+ }
+ if (ah == 0)
+ {
+ if (bh > 0)
+ {
+ bit ^= al & bl;
+ MP_LIMB_T_SWAP (al, bl);
+ ah = bh;
+ goto b_reduced;
+ }
+ goto ab_reduced;
+ }
+
+ while (bh > 0)
+ {
+ /* Compute (a|b) */
+ while (ah > bh)
+ {
+ sub_ddmmss (ah, al, ah, al, bh, bl);
+ if (al == 0)
+ {
+ count_trailing_zeros (c, ah);
+ bit ^= ((GMP_NUMB_BITS + c) << 1) & (bl ^ (bl >> 1));
+
+ al = bl;
+ bl = ah >> c;
+ ah = bh;
+
+ bit ^= al & bl;
+ goto b_reduced;
+ }
+ count_trailing_zeros (c, al);
+ bit ^= (c << 1) & (bl ^ (bl >> 1));
+ al = ((ah << (GMP_NUMB_BITS - c)) & GMP_NUMB_MASK) | (al >> c);
+ ah >>= c;
+ }
+ if (ah == bh)
+ goto cancel_hi;
+
+ if (ah == 0)
+ {
+ bit ^= al & bl;
+ MP_LIMB_T_SWAP (al, bl);
+ ah = bh;
+ break;
+ }
+
+ bit ^= al & bl;
+
+ /* Compute (b|a) */
+ while (bh > ah)
+ {
+ sub_ddmmss (bh, bl, bh, bl, ah, al);
+ if (bl == 0)
+ {
+ count_trailing_zeros (c, bh);
+ bit ^= ((GMP_NUMB_BITS + c) << 1) & (al ^ (al >> 1));
+
+ bl = bh >> c;
+ bit ^= al & bl;
+ goto b_reduced;
+ }
+ count_trailing_zeros (c, bl);
+ bit ^= (c << 1) & (al ^ (al >> 1));
+ bl = ((bh << (GMP_NUMB_BITS - c)) & GMP_NUMB_MASK) | (bl >> c);
+ bh >>= c;
+ }
+ bit ^= al & bl;
+
+ /* Compute (a|b) */
+ if (ah == bh)
+ {
+ cancel_hi:
+ if (al < bl)
+ {
+ MP_LIMB_T_SWAP (al, bl);
+ bit ^= al & bl;
+ }
+ al -= bl;
+ if (al == 0)
+ return 0;
+
+ count_trailing_zeros (c, al);
+ bit ^= (c << 1) & (bl ^ (bl >> 1));
+ al >>= c;
+
+ if (al == 1)
+ return 1 - (bit & 2);
+
+ MP_LIMB_T_SWAP (al, bl);
+ bit ^= al & bl;
+ break;
+ }
+ }
+
+ b_reduced:
+ /* Compute (a|b), with b a single limb. */
+ ASSERT (bl & 1);
+
+ if (bl == 1)
+ /* (a|1) = 1 */
+ return 1 - (bit & 2);
+
+ while (ah > 0)
+ {
+ ah -= (al < bl);
+ al -= bl;
+ if (al == 0)
+ {
+ if (ah == 0)
+ return 0;
+ count_trailing_zeros (c, ah);
+ bit ^= ((GMP_NUMB_BITS + c) << 1) & (bl ^ (bl >> 1));
+ al = ah >> c;
+ goto ab_reduced;
+ }
+ count_trailing_zeros (c, al);
+
+ al = ((ah << (GMP_NUMB_BITS - c)) & GMP_NUMB_MASK) | (al >> c);
+ ah >>= c;
+ bit ^= (c << 1) & (bl ^ (bl >> 1));
+ }
+ ab_reduced:
+ ASSERT (bl & 1);
+ ASSERT (bl > 1);
+
+ return mpn_jacobi_base (al, bl, bit);
+}
+#else
+#error Unsupported value for JACOBI_2_METHOD
+#endif
View Lorry Controller Status