I've got a fix for the --tag issue, but I can't commit it because
aclocal, autoconf, automake return a whole pile of errors. Seems like
the whole build system has gotten screwed up.
I'll commit the fix for the --tag issue, but it won't take effect
until someone can successfully run aclocal, autoconf, automake and
commit the diff.
Bill.
2008/12/24 <ja...@njkfrudils.plus.com>:
>
> On Wednesday 24 December 2008 01:15:08 Bill Hart wrote:
>> Are you sure it is not in there? It is in the version I checked out.
>>
>
> Yeah , sorry it is there , just not right permissions so on a color term I
> miss it
>
>> Bill.
>>
>> 2008/12/24 <ja...@njkfrudils.plus.com>:
>> > On Wednesday 24 December 2008 00:51:20 ja...@njkfrudils.plus.com wrote:
>> >> On Wednesday 24 December 2008 00:31:50 Bill Hart wrote:
>> >> > On sage.math:
>> >> >
>> >> > cd tune
>> >> > make tune
>> >> >
>> >> > ./.libs/libspeed.a(gcd_bin.o): In function `__gmpn_ngcd_matrix_init':
>> >> > gcd_bin.c:(.text+0x0): multiple definition of
>> >> > `__gmpn_ngcd_matrix_init' gcd.o:gcd.c:(.text+0x0): first defined here
>> >> > ./.libs/libspeed.a(gcd_bin.o): In function `__gmpn_nhgcd_itch':
>> >> > gcd_bin.c:(.text+0x80): multiple definition of `__gmpn_nhgcd_itch'
>> >> > gcd.o:gcd.c:(.text+0x80): first defined here
>> >> > ./.libs/libspeed.a(gcd_bin.o): In function `__gmpn_nhgcd':
>> >> > gcd_bin.c:(.text+0xc4): multiple definition of `__gmpn_nhgcd'
>> >> > gcd.o:gcd.c:(.text+0xc4): first defined here
>> >> > ./.libs/libspeed.a(gcd_bin.o): In function `mpn_basic_gcd':
>> >> > gcd_bin.c:(.text+0x2ed): multiple definition of `mpn_basic_gcd'
>> >> > gcd.o:gcd.c:(.text+0x2ed): first defined here
>> >>
>> >> On my K8-linux same problem with make speed and tune
>> >>
>> >> ./configure && make && make check passes OK , and I got bored running
>> >> ./try mpn_gcd :)
>> >>
>> >> get this warning from the build though
>> >>
>> >> ngcd.c: In function 'mpn_ngcd':
>> >> ngcd.c:75: warning: implicit declaration of function 'mpn_basic_gcd'
>> >>
>> >>
>> >> gcc -std=gnu99 -DHAVE_CONFIG_H -I. -I.. -D__GMP_WITHIN_GMP -I.. -O2 -m64
>> >> -march=k8 -mtune=k8 -c gcd.c -fPIC -DPIC -o .libs/gcd.o
>> >> gcd.c: In function 'mpz_rgcd':
>> >> gcd.c:167: warning: implicit declaration of function 'mpn_rgcd'
>> >> gcd.c: In function 'mpz_bgcd':
>> >> gcd.c:171: warning: implicit declaration of function 'mpn_bgcd'
>> >> gcd.c: In function 'mpz_sgcd':
>> >> gcd.c:175: warning: implicit declaration of function 'mpn_sgcd'
>> >> gcd.c: In function 'mpz_ngcd':
>> >> gcd.c:179: warning: implicit declaration of function 'mpn_ngcd'
>> >>
>> >>
>> >> ./configure --enable-alloca=debug --enable-assert && make && make check
>> >> passes OK
>> >>
>> >> but
>> >>
>> >> ./configure --enable-alloca=debug --enable-assert --enable-nails=2 &&
>> >> make && make check
>> >>
>> >> PASS: t-mul_i
>> >> PASS: t-tdiv
>> >> PASS: t-tdiv_ui
>> >> PASS: t-fdiv
>> >> PASS: t-fdiv_ui
>> >> PASS: t-cdiv_ui
>> >> nhgcd2.c:206: GNU MP assertion failed: h0 == h1
>> >> /bin/sh: line 4: 31599 Aborted ${dir}$tst
>> >> FAIL: t-gcd
>> >> PASS: t-gcd_ui
>> >> nhgcd2.c:206: GNU MP assertion failed: h0 == h1
>> >> /bin/sh: line 4: 31647 Aborted ${dir}$tst
>> >> FAIL: t-lcm
>> >> PASS: dive
>> >> PASS: dive_ui
>> >> PASS: t-sqrtrem
>> >> PASS: convert
>> >> PASS: io
>> >
>> > ./configure --enable-cxx --build=none && make && make check passes
>> > but
>> > ./configure --enable-cxx && make && make check Fails to build
>> >
>> > this again on K8-linux
>> >
>> > make[4]: Leaving directory `/root/mpir/mpir/mpir/trunk/yasm'
>> > make[3]: Leaving directory `/root/mpir/mpir/mpir/trunk/yasm'
>> > make[2]: Leaving directory `/root/mpir/mpir/mpir/trunk/yasmbuild'
>> > Making all in mpn
>> > make[2]: Entering directory `/root/mpir/mpir/mpir/trunk/mpn'
>> > /bin/sh ../libtool --tag=CC --mode=compile
>> > gcc -std=gnu99 -DHAVE_CONFIG_H -I. -I.. -D__GMP_WITHIN_GMP -I..
>> > -DOPERATION_`echo fib_table | sed 's/_$//'` -O2 -m64 -march=k8
>> > -mtune=k8 -c -o fib_table.lo fib_table.c
>> > mkdir .libs
>> >
>> > gcc -std=gnu99 -DHAVE_CONFIG_H -I. -I.. -D__GMP_WITHIN_GMP -I..
>> > -DOPERATION_fib_table -O2 -m64 -march=k8 -mtune=k8 -c fib_table.c -fPIC
>> > -DPIC -o .libs/fib_table.o
>> >
>> > gcc -std=gnu99 -DHAVE_CONFIG_H -I. -I.. -D__GMP_WITHIN_GMP -I..
>> > -DOPERATION_fib_table -O2 -m64 -march=k8 -mtune=k8 -c fib_table.c -o
>> > fib_table.o >/dev/null 2>&1
>> > /bin/sh ../libtool --tag=CC --mode=compile
>> > gcc -std=gnu99 -DHAVE_CONFIG_H -I. -I.. -D__GMP_WITHIN_GMP -I..
>> > -DOPERATION_`echo mp_bases | sed 's/_$//'` -O2 -m64 -march=k8
>> > -mtune=k8 -c -o mp_bases.lo mp_bases.c
>> >
>> > gcc -std=gnu99 -DHAVE_CONFIG_H -I. -I.. -D__GMP_WITHIN_GMP -I..
>> > -DOPERATION_mp_bases -O2 -m64 -march=k8 -mtune=k8 -c mp_bases.c -fPIC
>> > -DPIC -o .libs/mp_bases.o
>> >
>> > gcc -std=gnu99 -DHAVE_CONFIG_H -I. -I.. -D__GMP_WITHIN_GMP -I..
>> > -DOPERATION_mp_bases -O2 -m64 -march=k8 -mtune=k8 -c mp_bases.c -o
>> > mp_bases.o >/dev/null 2>&1
>> > /bin/sh ../libtool --tag=CC --mode=compile
>> > gcc -std=gnu99 -DHAVE_CONFIG_H -I. -I.. -D__GMP_WITHIN_GMP -I..
>> > -DOPERATION_`echo add | sed 's/_$//'` -O2 -m64 -march=k8 -mtune=k8 -c
>> > -o add.lo add.c
>> >
>> > gcc -std=gnu99 -DHAVE_CONFIG_H -I. -I.. -D__GMP_WITHIN_GMP -I..
>> > -DOPERATION_add -O2 -m64 -march=k8 -mtune=k8 -c add.c -fPIC -DPIC -o
>> > .libs/add.o
>> >
>> > gcc -std=gnu99 -DHAVE_CONFIG_H -I. -I.. -D__GMP_WITHIN_GMP -I..
>> > -DOPERATION_add -O2 -m64 -march=k8 -mtune=k8 -c add.c -o add.o >/dev/null
>> > 2>&1
>> > /bin/sh ../libtool --tag=CC --mode=compile
>> > gcc -std=gnu99 -DHAVE_CONFIG_H -I. -I.. -D__GMP_WITHIN_GMP -I..
>> > -DOPERATION_`echo add_1 | sed 's/_$//'` -O2 -m64 -march=k8 -mtune=k8
>> > -c -o add_1.lo add_1.c
>> >
>> > gcc -std=gnu99 -DHAVE_CONFIG_H -I. -I.. -D__GMP_WITHIN_GMP -I..
>> > -DOPERATION_add_1 -O2 -m64 -march=k8 -mtune=k8 -c add_1.c -fPIC -DPIC -o
>> > .libs/add_1.o
>> >
>> > gcc -std=gnu99 -DHAVE_CONFIG_H -I. -I.. -D__GMP_WITHIN_GMP -I..
>> > -DOPERATION_add_1 -O2 -m64 -march=k8 -mtune=k8 -c add_1.c -o add_1.o
>> > >/dev/null 2>&1
>> > /bin/sh ../libtool --mode=compile ../strip_fPIC.sh ../yasm/yasm -f elf64
>> > -o add_n.lo `test -f 'add_n.as' || echo './'`add_n.as
>> > libtool: compile: unable to infer tagged configuration
>> > libtool: compile: specify a tag with `--tag'
>> > make[2]: *** [add_n.lo] Error 1
>> > make[2]: Leaving directory `/root/mpir/mpir/mpir/trunk/mpn'
>> > make[1]: *** [all-recursive] Error 1
>> > make[1]: Leaving directory `/root/mpir/mpir/mpir/trunk'
>> > make: *** [all] Error 2
>> >
>> > config.guess from gmp is athlon64-unknown-linux-gnu
>> > note config.guess not in mpir , is it supposed to be ?
>> >
>> >> > Bill.
>> >> >
>> >> > 2008/12/23 Jason Martin <jason.worth.mar...@gmail.com>:
>> >> > > Attached are some edited versions of
>> >> > >
>> >> > > mpn/generic/gcd.c
>> >> > >
>> >> > > and
>> >> > >
>> >> > > mpn/generic/ngcd.c
>> >> > >
>> >> > > Drop them in, test them for correctness and speed. Let me know what
>> >> > > breaks. When everyone is happy, I'll check them in to svn
>> >> > >
>> >> > > --jason
>> >> > >
>> >> > > Jason Worth Martin
>> >> > > Asst. Professor of Mathematics
>> >> > > http://www.math.jmu.edu/~martin
>> >> > >
>> >> > >
>> >> > >
>> >> > > /* Schönhage's 1987 algorithm, reorganized into hgcd form */
>> >> > >
>> >> > > #include <stdio.h> /* for NULL */
>> >> > >
>> >> > > #include "gmp.h"
>> >> > > #include "gmp-impl.h"
>> >> > > #include "longlong.h"
>> >> > >
>> >> > >
>> >> > > /*
>> >> > > ****************************************************************** *
>> >> > > Here we are including the original GMP version of mpn_gcd *
>> >> > > but we rename it as mpn_basic_gcd. It needs to be available *
>> >> > > for the ngcd algorithm to call in the base case.
>> >> > > *
>> >> > > * Preconditions [U = (up, usize) and V = (vp, vsize)]:
>> >> > > *
>> >> > > * 1. V is odd.
>> >> > > * 2. numbits(U) >= numbits(V).
>> >> > > *
>> >> > > * Both U and V are destroyed by the operation. The result is
>> >> > > left at vp, * and its size is returned.
>> >> > > *
>> >> > > * Ken Weber (kwe...@mat.ufrgs.br, kwe...@mcs.kent.edu)
>> >> > > *
>> >> > > * Funding for this work has been partially provided by Conselho
>> >> > > * Nacional de Desenvolvimento Cienti'fico e Tecnolo'gico (CNPq)
>> >> > > do * Brazil, Grant 301314194-2, and was done while I was a
>> >> > > visiting * reseacher in the Instituto de Matema'tica at
>> >> > > Universidade Federal * do Rio Grande do Sul (UFRGS).
>> >> > > *
>> >> > > * Refer to K. Weber, The accelerated integer GCD algorithm, ACM
>> >> > > * Transactions on Mathematical Software, v. 21 (March), 1995,
>> >> > > * pp. 111-122.
>> >> > > *
>> >> > > *
>> >> > > *****************************************************************/
>> >> > >
>> >> > >
>> >> > >
>> >> > > /* If MIN (usize, vsize) >= GCD_ACCEL_THRESHOLD, then the
>> >> > > accelerated algorithm is used, otherwise the binary algorithm is
>> >> > > used. This may be adjusted for different architectures. */
>> >> > > #ifndef GCD_ACCEL_THRESHOLD
>> >> > > #define GCD_ACCEL_THRESHOLD 5
>> >> > > #endif
>> >> > >
>> >> > > /* When U and V differ in size by more than BMOD_THRESHOLD, the
>> >> > > accelerated algorithm reduces using the bmod operation. Otherwise,
>> >> > > the k-ary reduction is used. 0 <= BMOD_THRESHOLD < GMP_NUMB_BITS.
>> >> > > */ enum
>> >> > > {
>> >> > > BMOD_THRESHOLD = GMP_NUMB_BITS/2
>> >> > > };
>> >> > >
>> >> > >
>> >> > > /* Use binary algorithm to compute V <-- GCD (V, U) for usize, vsize
>> >> > > == 2. Both U and V must be odd. */
>> >> > > static inline mp_size_t
>> >> > > gcd_2 (mp_ptr vp, mp_srcptr up)
>> >> > > {
>> >> > > mp_limb_t u0, u1, v0, v1;
>> >> > > mp_size_t vsize;
>> >> > >
>> >> > > u0 = up[0];
>> >> > > u1 = up[1];
>> >> > > v0 = vp[0];
>> >> > > v1 = vp[1];
>> >> > >
>> >> > > while (u1 != v1 && u0 != v0)
>> >> > > {
>> >> > > unsigned long int r;
>> >> > > if (u1 > v1)
>> >> > > {
>> >> > > u1 -= v1 + (u0 < v0);
>> >> > > u0 = (u0 - v0) & GMP_NUMB_MASK;
>> >> > > count_trailing_zeros (r, u0);
>> >> > > u0 = ((u1 << (GMP_NUMB_BITS - r)) & GMP_NUMB_MASK) | (u0 >>
>> >> > > r); u1 >>= r;
>> >> > > }
>> >> > > else /* u1 < v1. */
>> >> > > {
>> >> > > v1 -= u1 + (v0 < u0);
>> >> > > v0 = (v0 - u0) & GMP_NUMB_MASK;
>> >> > > count_trailing_zeros (r, v0);
>> >> > > v0 = ((v1 << (GMP_NUMB_BITS - r)) & GMP_NUMB_MASK) | (v0 >>
>> >> > > r); v1 >>= r;
>> >> > > }
>> >> > > }
>> >> > >
>> >> > > vp[0] = v0, vp[1] = v1, vsize = 1 + (v1 != 0);
>> >> > >
>> >> > > /* If U == V == GCD, done. Otherwise, compute GCD (V, |U - V|).
>> >> > > */ if (u1 == v1 && u0 == v0)
>> >> > > return vsize;
>> >> > >
>> >> > > v0 = (u0 == v0) ? (u1 > v1) ? u1-v1 : v1-u1 : (u0 > v0) ? u0-v0 :
>> >> > > v0-u0; vp[0] = mpn_gcd_1 (vp, vsize, v0);
>> >> > >
>> >> > > return 1;
>> >> > > }
>> >> > >
>> >> > > /* The function find_a finds 0 < N < 2^GMP_NUMB_BITS such that there
>> >> > > exists 0 < |D| < 2^GMP_NUMB_BITS, and N == D * C mod
>> >> > > 2^(2*GMP_NUMB_BITS). In the reference article, D was computed along
>> >> > > with N, but it is better to compute D separately as D <-- N / C mod
>> >> > > 2^(GMP_NUMB_BITS + 1), treating the result as a twos' complement
>> >> > > signed integer.
>> >> > >
>> >> > > Initialize N1 to C mod 2^(2*GMP_NUMB_BITS). According to the
>> >> > > reference article, N2 should be initialized to 2^(2*GMP_NUMB_BITS),
>> >> > > but we use 2^(2*GMP_NUMB_BITS) - N1 to start the calculations within
>> >> > > double precision. If N2 > N1 initially, the first iteration of the
>> >> > > while loop will swap them. In all other situations, N1 >= N2 is
>> >> > > maintained. */
>> >> > >
>> >> > > #if HAVE_NATIVE_mpn_gcd_finda
>> >> > > #define find_a(cp) mpn_gcd_finda (cp)
>> >> > >
>> >> > > #else
>> >> > > static
>> >> > > #if ! defined (__i386__)
>> >> > > inline /* don't inline this for the x86 */
>> >> > > #endif
>> >> > > mp_limb_t
>> >> > > find_a (mp_srcptr cp)
>> >> > > {
>> >> > > unsigned long int leading_zero_bits = 0;
>> >> > >
>> >> > > mp_limb_t n1_l = cp[0]; /* N1 == n1_h * 2^GMP_NUMB_BITS +
>> >> > > n1_l. */ mp_limb_t n1_h = cp[1];
>> >> > >
>> >> > > mp_limb_t n2_l = (-n1_l & GMP_NUMB_MASK); /* N2 == n2_h *
>> >> > > 2^GMP_NUMB_BITS + n2_l. */ mp_limb_t n2_h = (~n1_h &
>> >> > > GMP_NUMB_MASK);
>> >> > >
>> >> > > /* Main loop. */
>> >> > > while (n2_h != 0) /* While N2 >= 2^GMP_NUMB_BITS. */
>> >> > > {
>> >> > > /* N1 <-- N1 % N2. */
>> >> > > if (((GMP_NUMB_HIGHBIT >> leading_zero_bits) & n2_h) == 0)
>> >> > > {
>> >> > > unsigned long int i;
>> >> > > count_leading_zeros (i, n2_h);
>> >> > > i -= GMP_NAIL_BITS;
>> >> > > i -= leading_zero_bits;
>> >> > > leading_zero_bits += i;
>> >> > > n2_h = ((n2_h << i) & GMP_NUMB_MASK) | (n2_l >>
>> >> > > (GMP_NUMB_BITS - i)); n2_l = (n2_l << i) & GMP_NUMB_MASK;
>> >> > > do
>> >> > > {
>> >> > > if (n1_h > n2_h || (n1_h == n2_h && n1_l >= n2_l))
>> >> > > {
>> >> > > n1_h -= n2_h + (n1_l < n2_l);
>> >> > > n1_l = (n1_l - n2_l) & GMP_NUMB_MASK;
>> >> > > }
>> >> > > n2_l = (n2_l >> 1) | ((n2_h << (GMP_NUMB_BITS - 1)) &
>> >> > > GMP_NUMB_MASK); n2_h >>= 1;
>> >> > > i -= 1;
>> >> > > }
>> >> > > while (i != 0);
>> >> > > }
>> >> > > if (n1_h > n2_h || (n1_h == n2_h && n1_l >= n2_l))
>> >> > > {
>> >> > > n1_h -= n2_h + (n1_l < n2_l);
>> >> > > n1_l = (n1_l - n2_l) & GMP_NUMB_MASK;
>> >> > > }
>> >> > >
>> >> > > MP_LIMB_T_SWAP (n1_h, n2_h);
>> >> > > MP_LIMB_T_SWAP (n1_l, n2_l);
>> >> > > }
>> >> > >
>> >> > > return n2_l;
>> >> > > }
>> >> > > #endif
>> >> > >
>> >> > >
>> >> > > mp_size_t
>> >> > > mpn_basic_gcd (mp_ptr gp, mp_ptr up, mp_size_t usize, mp_ptr vp,
>> >> > > mp_size_t vsize) {
>> >> > > mp_ptr orig_vp = vp;
>> >> > > mp_size_t orig_vsize = vsize;
>> >> > > int binary_gcd_ctr; /* Number of times binary gcd will
>> >> > > execute. */ mp_size_t scratch;
>> >> > > mp_ptr tp;
>> >> > > TMP_DECL;
>> >> > >
>> >> > > ASSERT (usize >= 1);
>> >> > > ASSERT (vsize >= 1);
>> >> > > ASSERT (usize >= vsize);
>> >> > > ASSERT (vp[0] & 1);
>> >> > > ASSERT (up[usize - 1] != 0);
>> >> > > ASSERT (vp[vsize - 1] != 0);
>> >> > > #if WANT_ASSERT
>> >> > > if (usize == vsize)
>> >> > > {
>> >> > > int uzeros, vzeros;
>> >> > > count_leading_zeros (uzeros, up[usize - 1]);
>> >> > > count_leading_zeros (vzeros, vp[vsize - 1]);
>> >> > > ASSERT (uzeros <= vzeros);
>> >> > > }
>> >> > > #endif
>> >> > > ASSERT (! MPN_OVERLAP_P (up, usize, vp, vsize));
>> >> > > ASSERT (MPN_SAME_OR_SEPARATE2_P (gp, vsize, up, usize));
>> >> > > ASSERT (MPN_SAME_OR_SEPARATE2_P (gp, vsize, vp, vsize));
>> >> > >
>> >> > > TMP_MARK;
>> >> > >
>> >> > > /* Use accelerated algorithm if vsize is over GCD_ACCEL_THRESHOLD.
>> >> > > Two EXTRA limbs for U and V are required for kary reduction. */
>> >> > > if (vsize >= GCD_ACCEL_THRESHOLD)
>> >> > > {
>> >> > > unsigned long int vbitsize, d;
>> >> > > mp_ptr orig_up = up;
>> >> > > mp_size_t orig_usize = usize;
>> >> > > mp_ptr anchor_up = (mp_ptr) TMP_ALLOC ((usize + 2) *
>> >> > > BYTES_PER_MP_LIMB);
>> >> > >
>> >> > > MPN_COPY (anchor_up, orig_up, usize);
>> >> > > up = anchor_up;
>> >> > >
>> >> > > count_leading_zeros (d, up[usize - 1]);
>> >> > > d -= GMP_NAIL_BITS;
>> >> > > d = usize * GMP_NUMB_BITS - d;
>> >> > > count_leading_zeros (vbitsize, vp[vsize - 1]);
>> >> > > vbitsize -= GMP_NAIL_BITS;
>> >> > > vbitsize = vsize * GMP_NUMB_BITS - vbitsize;
>> >> > > ASSERT (d >= vbitsize);
>> >> > > d = d - vbitsize + 1;
>> >> > >
>> >> > > /* Use bmod reduction to quickly discover whether V divides U.
>> >> > > */ up[usize++] = 0; /* Insert leading zero.
>> >> > > */ mpn_bdivmod (up, up, usize, vp, vsize, d);
>> >> > >
>> >> > > /* Now skip U/V mod 2^d and any low zero limbs. */
>> >> > > d /= GMP_NUMB_BITS, up += d, usize -= d;
>> >> > > while (usize != 0 && up[0] == 0)
>> >> > > up++, usize--;
>> >> > >
>> >> > > if (usize == 0) /* GCD == ORIG_V. */
>> >> > > goto done;
>> >> > >
>> >> > > vp = (mp_ptr) TMP_ALLOC ((vsize + 2) * BYTES_PER_MP_LIMB);
>> >> > > MPN_COPY (vp, orig_vp, vsize);
>> >> > >
>> >> > > do /* Main loop. */
>> >> > > {
>> >> > > /* mpn_com_n can't be used here because anchor_up and up
>> >> > > may partially overlap */
>> >> > > if ((up[usize - 1] & GMP_NUMB_HIGHBIT) != 0) /* U < 0;
>> >> > > take twos' compl. */ {
>> >> > > mp_size_t i;
>> >> > > anchor_up[0] = -up[0] & GMP_NUMB_MASK;
>> >> > > for (i = 1; i < usize; i++)
>> >> > > anchor_up[i] = (~up[i] & GMP_NUMB_MASK);
>> >> > > up = anchor_up;
>> >> > > }
>> >> > >
>> >> > > MPN_NORMALIZE_NOT_ZERO (up, usize);
>> >> > >
>> >> > > if ((up[0] & 1) == 0) /* Result even;
>> >> > > remove twos. */ {
>> >> > > unsigned int r;
>> >> > > count_trailing_zeros (r, up[0]);
>> >> > > mpn_rshift (anchor_up, up, usize, r);
>> >> > > usize -= (anchor_up[usize - 1] == 0);
>> >> > > }
>> >> > > else if (anchor_up != up)
>> >> > > MPN_COPY_INCR (anchor_up, up, usize);
>> >> > >
>> >> > > MPN_PTR_SWAP (anchor_up,usize, vp,vsize);
>> >> > > up = anchor_up;
>> >> > >
>> >> > > if (vsize <= 2) /* Kary can't handle < 2
>> >> > > limbs and */ break; /* isn't efficient for == 2
>> >> > > limbs. */
>> >> > >
>> >> > > d = vbitsize;
>> >> > > count_leading_zeros (vbitsize, vp[vsize - 1]);
>> >> > > vbitsize -= GMP_NAIL_BITS;
>> >> > > vbitsize = vsize * GMP_NUMB_BITS - vbitsize;
>> >> > > d = d - vbitsize + 1;
>> >> > >
>> >> > > if (d > BMOD_THRESHOLD) /* Bmod reduction. */
>> >> > > {
>> >> > > up[usize++] = 0;
>> >> > > mpn_bdivmod (up, up, usize, vp, vsize, d);
>> >> > > d /= GMP_NUMB_BITS, up += d, usize -= d;
>> >> > > }
>> >> > > else /* Kary reduction. */
>> >> > > {
>> >> > > mp_limb_t bp[2], cp[2];
>> >> > >
>> >> > > /* C <-- V/U mod 2^(2*GMP_NUMB_BITS). */
>> >> > > {
>> >> > > mp_limb_t u_inv, hi, lo;
>> >> > > modlimb_invert (u_inv, up[0]);
>> >> > > cp[0] = (vp[0] * u_inv) & GMP_NUMB_MASK;
>> >> > > umul_ppmm (hi, lo, cp[0], up[0] << GMP_NAIL_BITS);
>> >> > > lo >>= GMP_NAIL_BITS;
>> >> > > cp[1] = (vp[1] - hi - cp[0] * up[1]) * u_inv &
>> >> > > GMP_NUMB_MASK; }
>> >> > >
>> >> > > /* U <-- find_a (C) * U. */
>> >> > > up[usize] = mpn_mul_1 (up, up, usize, find_a (cp));
>> >> > > usize++;
>> >> > >
>> >> > > /* B <-- A/C == U/V mod 2^(GMP_NUMB_BITS + 1).
>> >> > > bp[0] <-- U/V mod 2^GMP_NUMB_BITS and
>> >> > > bp[1] <-- ( (U - bp[0] * V)/2^GMP_NUMB_BITS ) / V
>> >> > > mod 2
>> >> > >
>> >> > > Like V/U above, but simplified because only the low
>> >> > > bit of bp[1] is wanted. */
>> >> > > {
>> >> > > mp_limb_t v_inv, hi, lo;
>> >> > > modlimb_invert (v_inv, vp[0]);
>> >> > > bp[0] = (up[0] * v_inv) & GMP_NUMB_MASK;
>> >> > > umul_ppmm (hi, lo, bp[0], vp[0] << GMP_NAIL_BITS);
>> >> > > lo >>= GMP_NAIL_BITS;
>> >> > > bp[1] = (up[1] + hi + (bp[0] & vp[1])) & 1;
>> >> > > }
>> >> > >
>> >> > > up[usize++] = 0;
>> >> > > if (bp[1] != 0) /* B < 0: U <-- U + (-B) * V. */
>> >> > > {
>> >> > > mp_limb_t c = mpn_addmul_1 (up, vp, vsize, -bp[0]
>> >> > > & GMP_NUMB_MASK); mpn_add_1 (up + vsize, up + vsize, usize - vsize,
>> >> > > c); } else /* B >= 0: U <-- U - B * V. */ {
>> >> > > mp_limb_t b = mpn_submul_1 (up, vp, vsize, bp[0]);
>> >> > > mpn_sub_1 (up + vsize, up + vsize, usize - vsize,
>> >> > > b); }
>> >> > >
>> >> > > up += 2, usize -= 2; /* At least two low limbs are
>> >> > > zero. */ }
>> >> > >
>> >> > > /* Must remove low zero limbs before complementing. */
>> >> > > while (usize != 0 && up[0] == 0)
>> >> > > up++, usize--;
>> >> > > }
>> >> > > while (usize != 0);
>> >> > >
>> >> > > /* Compute GCD (ORIG_V, GCD (ORIG_U, V)). Binary will execute
>> >> > > twice. */ up = orig_up, usize = orig_usize;
>> >> > > binary_gcd_ctr = 2;
>> >> > > }
>> >> > > else
>> >> > > binary_gcd_ctr = 1;
>> >> > >
>> >> > > scratch = MPN_NGCD_LEHMER_ITCH (vsize);
>> >> > > if (usize + 1 > scratch)
>> >> > > scratch = usize + 1;
>> >> > >
>> >> > > tp = TMP_ALLOC_LIMBS (scratch);
>> >> > >
>> >> > > /* Finish up with the binary algorithm. Executes once or twice.
>> >> > > */ for ( ; binary_gcd_ctr--; up = orig_vp, usize = orig_vsize) {
>> >> > > #if 1
>> >> > > if (usize > vsize)
>> >> > > {
>> >> > > /* FIXME: Could use mpn_bdivmod. */
>> >> > > mp_size_t rsize;
>> >> > >
>> >> > > mpn_tdiv_qr (tp + vsize, tp, 0, up, usize, vp, vsize);
>> >> > > rsize = vsize;
>> >> > > MPN_NORMALIZE (tp, rsize);
>> >> > > if (rsize == 0)
>> >> > > continue;
>> >> > >
>> >> > > MPN_COPY (up, tp, vsize);
>> >> > > }
>> >> > > vsize = mpn_ngcd_lehmer (vp, up, vp, vsize, tp);
>> >> > > #else
>> >> > > if (usize > 2) /* First make U close to V in size.
>> >> > > */ {
>> >> > > unsigned long int vbitsize, d;
>> >> > > count_leading_zeros (d, up[usize - 1]);
>> >> > > d -= GMP_NAIL_BITS;
>> >> > > d = usize * GMP_NUMB_BITS - d;
>> >> > > count_leading_zeros (vbitsize, vp[vsize - 1]);
>> >> > > vbitsize -= GMP_NAIL_BITS;
>> >> > > vbitsize = vsize * GMP_NUMB_BITS - vbitsize;
>> >> > > d = d - vbitsize - 1;
>> >> > > if (d != -(unsigned long int)1 && d > 2)
>> >> > > {
>> >> > > mpn_bdivmod (up, up, usize, vp, vsize, d); /* Result >
>> >> > > 0. */ d /= (unsigned long int)GMP_NUMB_BITS, up += d, usize -= d; }
>> >> > > }
>> >> > >
>> >> > > /* Start binary GCD. */
>> >> > > do
>> >> > > {
>> >> > > mp_size_t zeros;
>> >> > >
>> >> > > /* Make sure U is odd. */
>> >> > > MPN_NORMALIZE (up, usize);
>> >> > > while (up[0] == 0)
>> >> > > up += 1, usize -= 1;
>> >> > > if ((up[0] & 1) == 0)
>> >> > > {
>> >> > > unsigned int r;
>> >> > > count_trailing_zeros (r, up[0]);
>> >> > > mpn_rshift (up, up, usize, r);
>> >> > > usize -= (up[usize - 1] == 0);
>> >> > > }
>> >> > >
>> >> > > /* Keep usize >= vsize. */
>> >> > > if (usize < vsize)
>> >> > > MPN_PTR_SWAP (up, usize, vp, vsize);
>> >> > >
>> >> > > if (usize <= 2) /* Double
>> >> > > precision. */ {
>> >> > > if (vsize == 1)
>> >> > > vp[0] = mpn_gcd_1 (up, usize, vp[0]);
>> >> > > else
>> >> > > vsize = gcd_2 (vp, up);
>> >> > > break; /* Binary GCD
>> >> > > done. */ }
>> >> > >
>> >> > > /* Count number of low zero limbs of U - V. */
>> >> > > for (zeros = 0; up[zeros] == vp[zeros] && ++zeros != vsize;
>> >> > > ) continue;
>> >> > >
>> >> > > /* If U < V, swap U and V; in any case, subtract V from U.
>> >> > > */ if (zeros == vsize) /* Subtract done.
>> >> > > */ up += zeros, usize -= zeros;
>> >> > > else if (usize == vsize)
>> >> > > {
>> >> > > mp_size_t size = vsize;
>> >> > > do
>> >> > > size--;
>> >> > > while (up[size] == vp[size]);
>> >> > > if (up[size] < vp[size]) /* usize ==
>> >> > > vsize. */ MP_PTR_SWAP (up, vp);
>> >> > > up += zeros, usize = size + 1 - zeros;
>> >> > > mpn_sub_n (up, up, vp + zeros, usize);
>> >> > > }
>> >> > > else
>> >> > > {
>> >> > > mp_size_t size = vsize - zeros;
>> >> > > up += zeros, usize -= zeros;
>> >> > > if (mpn_sub_n (up, up, vp + zeros, size))
>> >> > > {
>> >> > > while (up[size] == 0) /* Propagate
>> >> > > borrow. */ up[size++] = -(mp_limb_t)1;
>> >> > > up[size] -= 1;
>> >> > > }
>> >> > > }
>> >> > > }
>> >> > > while (usize); /* End binary
>> >> > > GCD. */ #endif
>> >> > > }
>> >> > >
>> >> > > done:
>> >> > > if (vp != gp)
>> >> > > MPN_COPY_INCR (gp, vp, vsize);
>> >> > > TMP_FREE;
>> >> > > return vsize;
>> >> > > }
>> >> > >
>> >> > >
>> >> > >
>> >> > > /*
>> >> > > ****************************************************************** *
>> >> > > END of original GMP mpn_gcd
>> >> > > *
>> >> > > *****************************************************************/
>> >> > >
>> >> > >
>> >> > >
>> >> > >
>> >> > >
>> >> > > /* For input of size n, matrix elements are of size at most
>> >> > > ceil(n/2) - 1, but we need one limb extra. */
>> >> > >
>> >> > > void
>> >> > > mpn_ngcd_matrix_init (struct ngcd_matrix *M, mp_size_t n, mp_ptr p)
>> >> > > {
>> >> > > mp_size_t s = (n+1)/2;
>> >> > > M->alloc = s;
>> >> > > M->n = 1;
>> >> > > MPN_ZERO (p, 4 * s);
>> >> > > M->p[0][0] = p;
>> >> > > M->p[0][1] = p + s;
>> >> > > M->p[1][0] = p + 2 * s;
>> >> > > M->p[1][1] = p + 3 * s;
>> >> > > M->tp = p + 4*s;
>> >> > >
>> >> > > M->p[0][0][0] = M->p[1][1][0] = 1;
>> >> > > }
>> >> > >
>> >> > > #define NHGCD_BASE_ITCH MPN_NGCD_STEP_ITCH
>> >> > >
>> >> > > /* 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. */
>> >> > > static mp_size_t
>> >> > > nhgcd_base (mp_ptr ap, mp_ptr bp, mp_size_t n,
>> >> > > struct ngcd_matrix *M, mp_ptr tp)
>> >> > > {
>> >> > > mp_size_t s = n/2 + 1;
>> >> > > mp_size_t nn;
>> >> > >
>> >> > > ASSERT (n > s);
>> >> > > ASSERT (ap[n-1] > 0 || bp[n-1] > 0);
>> >> > >
>> >> > > nn = mpn_ngcd_step (n, ap, bp, s, M, tp);
>> >> > > if (!nn)
>> >> > > return 0;
>> >> > >
>> >> > > for (;;)
>> >> > > {
>> >> > > n = nn;
>> >> > > ASSERT (n > s);
>> >> > > nn = mpn_ngcd_step (n, ap, bp, s, M, tp);
>> >> > > if (!nn )
>> >> > > return n;
>> >> > > }
>> >> > > }
>> >> > >
>> >> > > /* Size analysis for nhgcd:
>> >> > >
>> >> > > For the recursive calls, we have n1 <= ceil(n / 2). Then the
>> >> > > storage need is determined by the storage for the recursive call
>> >> > > computing M1, and ngcd_matrix_adjust and ngcd_matrix_mul calls
>> >> > > that use M1 (after this, the storage needed for M1 can be recycled).
>> >> > >
>> >> > > Let S(r) denote the required storage. For M1 we need 5 *
>> >> > > ceil(n1/2) = 5 * ceil(n/4), and for the ngcd_matrix_adjust call, we
>> >> > > need n + 2. In total, 5 * ceil(n/4) + n + 2 <= 9 ceil(n/4) + 2.
>> >> > >
>> >> > > For the recursive call, we need S(n1) = S(ceil(n/2)).
>> >> > >
>> >> > > S(n) <= 9*ceil(n/4) + 2 + S(ceil(n/2))
>> >> > > <= 9*(ceil(n/4) + ... + ceil(n/2^(1+k))) + 2k +
>> >> > > S(ceil(n/2^k)) <= 9*(2 ceil(n/4) + k) + 2k + S(n/2^k)
>> >> > > <= 18 ceil(n/4) + 11k + S(n/2^k)
>> >> > >
>> >> > > */
>> >> > >
>> >> > > mp_size_t
>> >> > > mpn_nhgcd_itch (mp_size_t n)
>> >> > > {
>> >> > > unsigned k;
>> >> > > mp_size_t nn;
>> >> > >
>> >> > > /* Inefficient way to almost compute
>> >> > > log_2(n/NHGCD_BASE_THRESHOLD) */
>> >> > > for (k = 0, nn = n;
>> >> > > ABOVE_THRESHOLD (nn, NHGCD_THRESHOLD);
>> >> > > nn = (nn + 1) / 2)
>> >> > > k++;
>> >> > >
>> >> > > if (k == 0)
>> >> > > return NHGCD_BASE_ITCH (n);
>> >> > >
>> >> > > return 18 * ((n+3) / 4) + 11 * k
>> >> > > + NHGCD_BASE_ITCH (NHGCD_THRESHOLD);
>> >> > > }
>> >> > >
>> >> > > /* 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. */
>> >> > >
>> >> > > mp_size_t
>> >> > > mpn_nhgcd (mp_ptr ap, mp_ptr bp, mp_size_t n,
>> >> > > struct ngcd_matrix *M, mp_ptr tp)
>> >> > > {
>> >> > > mp_size_t s = n/2 + 1;
>> >> > > mp_size_t n2 = (3*n)/4 + 1;
>> >> > >
>> >> > > mp_size_t p, nn;
>> >> > > unsigned count;
>> >> > > int success = 0;
>> >> > >
>> >> > > ASSERT (n > s);
>> >> > > ASSERT ((ap[n-1] | bp[n-1]) > 0);
>> >> > >
>> >> > > ASSERT ((n+1)/2 - 1 < M->alloc);
>> >> > >
>> >> > > if (BELOW_THRESHOLD (n, NHGCD_THRESHOLD))
>> >> > > return nhgcd_base (ap, bp, n, M, tp);
>> >> > >
>> >> > > p = n/2;
>> >> > > nn = mpn_nhgcd (ap + p, bp + p, n - p, M, tp);
>> >> > > if (nn > 0)
>> >> > > {
>> >> > > /* Needs 2*(p + M->n) <= 2*(floor(n/2) + ceil(n/2) - 1)
>> >> > > = 2 (n - 1) */
>> >> > > n = mpn_ngcd_matrix_adjust (M, p + nn, ap, bp, p, tp);
>> >> > > success = 1;
>> >> > > }
>> >> > > count = 0;
>> >> > > while (n > n2)
>> >> > > {
>> >> > > count++;
>> >> > > /* Needs n + 1 storage */
>> >> > > nn = mpn_ngcd_step (n, ap, bp, s, M, tp);
>> >> > > if (!nn)
>> >> > > return success ? n : 0;
>> >> > > n = nn;
>> >> > > success = 1;
>> >> > > }
>> >> > >
>> >> > > if (n > s + 2)
>> >> > > {
>> >> > > struct ngcd_matrix M1;
>> >> > > mp_size_t scratch;
>> >> > >
>> >> > > p = 2*s - n + 1;
>> >> > > scratch = MPN_NGCD_MATRIX_INIT_ITCH (n-p);
>> >> > >
>> >> > > mpn_ngcd_matrix_init(&M1, n - p, tp);
>> >> > > nn = mpn_nhgcd (ap + p, bp + p, n - p, &M1, tp + scratch);
>> >> > > if (nn > 0)
>> >> > > {
>> >> > > /* Needs 2 (p + M->n) <= 2 (2*s - n2 + 1 + n2 - s - 1)
>> >> > > = 2*s <= 2*(floor(n/2) + 1) <= n + 2. */
>> >> > > n = mpn_ngcd_matrix_adjust (&M1, p + nn, ap, bp, p, tp +
>> >> > > scratch); /* Needs M->n <= n2 - s - 1 < n/4 */
>> >> > > mpn_ngcd_matrix_mul (M, &M1, tp + scratch);
>> >> > > success = 1;
>> >> > > }
>> >> > > }
>> >> > >
>> >> > > /* FIXME: This really is the base case */
>> >> > > for (count = 0;; count++)
>> >> > > {
>> >> > > /* Needs s+3 < n */
>> >> > > nn = mpn_ngcd_step (n, ap, bp, s, M, tp);
>> >> > > if (!nn)
>> >> > > return success ? n : 0;
>> >> > >
>> >> > > n = nn;
>> >> > > success = 1;
>> >> > > }
>> >> > > }
>> >> > >
>> >> > > #define EVEN_P(x) (((x) & 1) == 0)
>> >> > >
>> >> > > mp_size_t
>> >> > > mpn_gcd (mp_ptr gp, mp_ptr ap, mp_size_t an, mp_ptr bp, mp_size_t n)
>> >> > > {
>> >> > > mp_size_t init_scratch;
>> >> > > mp_size_t scratch;
>> >> > > mp_ptr tp;
>> >> > > TMP_DECL;
>> >> > >
>> >> > > ASSERT (an >= n);
>> >> > >
>> >> > > if (BELOW_THRESHOLD (n, NGCD_THRESHOLD))
>> >> > > return mpn_basic_gcd (gp, ap, an, bp, n);
>> >> > >
>> >> > > init_scratch = MPN_NGCD_MATRIX_INIT_ITCH ((n+1)/2);
>> >> > > scratch = mpn_nhgcd_itch ((n+1)/2);
>> >> > >
>> >> > > /* Space needed for mpn_ngcd_matrix_adjust */
>> >> > > if (scratch < 2*n)
>> >> > > scratch = 2*n;
>> >> > >
>> >> > > TMP_MARK;
>> >> > >
>> >> > > if (an + 1 > init_scratch + scratch)
>> >> > > tp = TMP_ALLOC_LIMBS (an + 1);
>> >> > > else
>> >> > > tp = TMP_ALLOC_LIMBS (init_scratch + scratch);
>> >> > >
>> >> > > if (an > n)
>> >> > > {
>> >> > > mp_ptr rp = tp;
>> >> > > mp_ptr qp = rp + n;
>> >> > >
>> >> > > mpn_tdiv_qr (qp, rp, 0, ap, an, bp, n);
>> >> > > MPN_COPY (ap, rp, n);
>> >> > > an = n;
>> >> > > MPN_NORMALIZE (ap, an);
>> >> > > if (an == 0)
>> >> > > {
>> >> > > MPN_COPY (gp, bp, n);
>> >> > > TMP_FREE;
>> >> > > return n;
>> >> > > }
>> >> > > }
>> >> > >
>> >> > > while (ABOVE_THRESHOLD (n, NGCD_THRESHOLD))
>> >> > > {
>> >> > > struct ngcd_matrix M;
>> >> > > mp_size_t p = n/2;
>> >> > > mp_size_t nn;
>> >> > >
>> >> > > mpn_ngcd_matrix_init (&M, n - p, tp);
>> >> > > nn = mpn_nhgcd (ap + p, bp + p, n - p, &M, tp + init_scratch);
>> >> > > if (nn > 0)
>> >> > > /* Needs 2*(p + M->n) <= 2*(floor(n/2) + ceil(n/2) - 1)
>> >> > > = 2(n-1) */
>> >> > > n = mpn_ngcd_matrix_adjust (&M, p + nn, ap, bp, p, tp +
>> >> > > init_scratch);
>> >> > >
>> >> > > else
>> >> > > {
>> >> > > mp_size_t gn;
>> >> > > n = mpn_ngcd_subdiv_step (gp, &gn, ap, bp, n, tp);
>> >> > > if (n == 0)
>> >> > > {
>> >> > > TMP_FREE;
>> >> > > return gn;
>> >> > > }
>> >> > > }
>> >> > > }
>> >> > >
>> >> > > ASSERT (ap[n-1] > 0 || bp[n-1] > 0);
>> >> > > #if 0
>> >> > > /* FIXME: We may want to use lehmer on some systems. */
>> >> > > n = mpn_ngcd_lehmer (gp, ap, bp, n, tp);
>> >> > >
>> >> > > TMP_FREE;
>> >> > > return n;
>> >> > > #endif
>> >> > >
>> >> > > if (ap[n-1] < bp[n-1])
>> >> > > MP_PTR_SWAP (ap, bp);
>> >> > >
>> >> > > an = n;
>> >> > > MPN_NORMALIZE (bp, n);
>> >> > >
>> >> > > if (n == 0)
>> >> > > {
>> >> > > MPN_COPY (gp, ap, an);
>> >> > > TMP_FREE;
>> >> > > return an;
>> >> > > }
>> >> > >
>> >> > > if (EVEN_P (bp[0]))
>> >> > > {
>> >> > > /* Then a must be odd (since the calling convention implies
>> >> > > that there's no common factor of 2) */
>> >> > > ASSERT (!EVEN_P (ap[0]));
>> >> > >
>> >> > > while (bp[0] == 0)
>> >> > > {
>> >> > > bp++;
>> >> > > n--;
>> >> > > }
>> >> > >
>> >> > > if (EVEN_P(bp[0]))
>> >> > > {
>> >> > > int count;
>> >> > > count_trailing_zeros (count, bp[0]);
>> >> > > ASSERT_NOCARRY (mpn_rshift (bp, bp, n, count));
>> >> > > n -= (bp[n-1] == 0);
>> >> > > }
>> >> > > }
>> >> > >
>> >> > > TMP_FREE;
>> >> > > return mpn_basic_gcd (gp, ap, an, bp, n);
>> >> > > }
>> >> > >
>> >> > > /* Schönhage's 1987 algorithm, reorganized into hgcd form */
>> >> > >
>> >> > > #include <stdio.h> /* for NULL */
>> >> > >
>> >> > > #include "gmp.h"
>> >> > > #include "gmp-impl.h"
>> >> > > #include "longlong.h"
>> >> > >
>> >> > >
>> >> > >
>> >> > >
>> >> > >
>> >> > >
>> >> > > /* For input of size n, matrix elements are of size at most
>> >> > > ceil(n/2) - 1, but we need one limb extra. */
>> >> > >
>> >> > > void
>> >> > > mpn_ngcd_matrix_init (struct ngcd_matrix *M, mp_size_t n, mp_ptr p);
>> >> > >
>> >> > > #define NHGCD_BASE_ITCH MPN_NGCD_STEP_ITCH
>> >> > >
>> >> > > /* 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. */
>> >> > > static mp_size_t
>> >> > > nhgcd_base (mp_ptr ap, mp_ptr bp, mp_size_t n,
>> >> > > struct ngcd_matrix *M, mp_ptr tp);
>> >> > >
>> >> > > /* Size analysis for nhgcd:
>> >> > >
>> >> > > For the recursive calls, we have n1 <= ceil(n / 2). Then the
>> >> > > storage need is determined by the storage for the recursive call
>> >> > > computing M1, and ngcd_matrix_adjust and ngcd_matrix_mul calls
>> >> > > that use M1 (after this, the storage needed for M1 can be recycled).
>> >> > >
>> >> > > Let S(r) denote the required storage. For M1 we need 5 *
>> >> > > ceil(n1/2) = 5 * ceil(n/4), and for the ngcd_matrix_adjust call, we
>> >> > > need n + 2. In total, 5 * ceil(n/4) + n + 2 <= 9 ceil(n/4) + 2.
>> >> > >
>> >> > > For the recursive call, we need S(n1) = S(ceil(n/2)).
>> >> > >
>> >> > > S(n) <= 9*ceil(n/4) + 2 + S(ceil(n/2))
>> >> > > <= 9*(ceil(n/4) + ... + ceil(n/2^(1+k))) + 2k +
>> >> > > S(ceil(n/2^k)) <= 9*(2 ceil(n/4) + k) + 2k + S(n/2^k)
>> >> > > <= 18 ceil(n/4) + 11k + S(n/2^k)
>> >> > >
>> >> > > */
>> >> > >
>> >> > > mp_size_t
>> >> > > mpn_nhgcd_itch (mp_size_t n);
>> >> > >
>> >> > >
>> >> > > /* 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. */
>> >> > >
>> >> > > mp_size_t
>> >> > > mpn_nhgcd (mp_ptr ap, mp_ptr bp, mp_size_t n,
>> >> > > struct ngcd_matrix *M, mp_ptr tp);
>> >> > >
>> >> > >
>> >> > > #define EVEN_P(x) (((x) & 1) == 0)
>> >> > >
>> >> > > mp_size_t
>> >> > > mpn_ngcd (mp_ptr gp, mp_ptr ap, mp_size_t an, mp_ptr bp, mp_size_t
>> >> > > n) {
>> >> > > mp_size_t init_scratch;
>> >> > > mp_size_t scratch;
>> >> > > mp_ptr tp;
>> >> > > TMP_DECL;
>> >> > >
>> >> > > ASSERT (an >= n);
>> >> > >
>> >> > > if (BELOW_THRESHOLD (n, NGCD_THRESHOLD))
>> >> > > return mpn_basic_gcd (gp, ap, an, bp, n);
>> >> > >
>> >> > > init_scratch = MPN_NGCD_MATRIX_INIT_ITCH ((n+1)/2);
>> >> > > scratch = mpn_nhgcd_itch ((n+1)/2);
>> >> > >
>> >> > > /* Space needed for mpn_ngcd_matrix_adjust */
>> >> > > if (scratch < 2*n)
>> >> > > scratch = 2*n;
>> >> > >
>> >> > > TMP_MARK;
>> >> > >
>> >> > > if (an + 1 > init_scratch + scratch)
>> >> > > tp = TMP_ALLOC_LIMBS (an + 1);
>> >> > > else
>> >> > > tp = TMP_ALLOC_LIMBS (init_scratch + scratch);
>> >> > >
>> >> > > if (an > n)
>> >> > > {
>> >> > > mp_ptr rp = tp;
>> >> > > mp_ptr qp = rp + n;
>> >> > >
>> >> > > mpn_tdiv_qr (qp, rp, 0, ap, an, bp, n);
>> >> > > MPN_COPY (ap, rp, n);
>> >> > > an = n;
>> >> > > MPN_NORMALIZE (ap, an);
>> >> > > if (an == 0)
>> >> > > {
>> >> > > MPN_COPY (gp, bp, n);
>> >> > > TMP_FREE;
>> >> > > return n;
>> >> > > }
>> >> > > }
>> >> > >
>> >> > > while (ABOVE_THRESHOLD (n, NGCD_THRESHOLD))
>> >> > > {
>> >> > > struct ngcd_matrix M;
>> >> > > mp_size_t p = n/2;
>> >> > > mp_size_t nn;
>> >> > >
>> >> > > mpn_ngcd_matrix_init (&M, n - p, tp);
>> >> > > nn = mpn_nhgcd (ap + p, bp + p, n - p, &M, tp + init_scratch);
>> >> > > if (nn > 0)
>> >> > > /* Needs 2*(p + M->n) <= 2*(floor(n/2) + ceil(n/2) - 1)
>> >> > > = 2(n-1) */
>> >> > > n = mpn_ngcd_matrix_adjust (&M, p + nn, ap, bp, p, tp +
>> >> > > init_scratch);
>> >> > >
>> >> > > else
>> >> > > {
>> >> > > mp_size_t gn;
>> >> > > n = mpn_ngcd_subdiv_step (gp, &gn, ap, bp, n, tp);
>> >> > > if (n == 0)
>> >> > > {
>> >> > > TMP_FREE;
>> >> > > return gn;
>> >> > > }
>> >> > > }
>> >> > > }
>> >> > >
>> >> > > ASSERT (ap[n-1] > 0 || bp[n-1] > 0);
>> >> > > #if 0
>> >> > > /* FIXME: We may want to use lehmer on some systems. */
>> >> > > n = mpn_ngcd_lehmer (gp, ap, bp, n, tp);
>> >> > >
>> >> > > TMP_FREE;
>> >> > > return n;
>> >> > > #endif
>> >> > >
>> >> > > if (ap[n-1] < bp[n-1])
>> >> > > MP_PTR_SWAP (ap, bp);
>> >> > >
>> >> > > an = n;
>> >> > > MPN_NORMALIZE (bp, n);
>> >> > >
>> >> > > if (n == 0)
>> >> > > {
>> >> > > MPN_COPY (gp, ap, an);
>> >> > > TMP_FREE;
>> >> > > return an;
>> >> > > }
>> >> > >
>> >> > > if (EVEN_P (bp[0]))
>> >> > > {
>> >> > > /* Then a must be odd (since the calling convention implies
>> >> > > that there's no common factor of 2) */
>> >> > > ASSERT (!EVEN_P (ap[0]));
>> >> > >
>> >> > > while (bp[0] == 0)
>> >> > > {
>> >> > > bp++;
>> >> > > n--;
>> >> > > }
>> >> > >
>> >> > > if (EVEN_P(bp[0]))
>> >> > > {
>> >> > > int count;
>> >> > > count_trailing_zeros (count, bp[0]);
>> >> > > ASSERT_NOCARRY (mpn_rshift (bp, bp, n, count));
>> >> > > n -= (bp[n-1] == 0);
>> >> > > }
>> >> > > }
>> >> > >
>> >> > > TMP_FREE;
>> >> > > return mpn_basic_gcd (gp, ap, an, bp, n);
>> >> > > }
>>
>>
>
>
> >
>
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