mirror of
https://git.savannah.gnu.org/git/emacs.git
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Update from GMP
* admin/update-copyright (updatable_files): Don’t update copyright year on files copied from GMP, so that they’re identical to upstream. * src/mini-gmp.c, src/mini-gmp.h: Copy from GMP development versions as of 2019-01-01 20:15:39 UTC.
This commit is contained in:
Paul Eggert
parent
4d97e1a9ea
commit
9469d58ebe
@ -50,6 +50,7 @@ repo_files=$(git ls-files) &&
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# Do not update the copyright of files that have one or more of the
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# following problems:
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# . They are license files, maintained by the FSF, with their own dates.
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# . They are GMP files, maintained by the GMP project, with their own dates.
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# . Their format cannot withstand changing the contents of copyright strings.
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updatable_files=$(find $repo_files \
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@ -70,6 +71,7 @@ updatable_files=$(find $repo_files \
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! -name hand.cur \
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! -name key.pub \
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! -name key.sec \
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! -name 'mini-gmp.[ch]' \
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-print) &&
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build-aux/update-copyright $updatable_files
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563
src/mini-gmp.c
563
src/mini-gmp.c
@ -2,7 +2,7 @@
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Contributed to the GNU project by Niels Möller
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Copyright 1991-1997, 1999-2019 Free Software Foundation, Inc.
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Copyright 1991-1997, 1999-2018 Free Software Foundation, Inc.
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This file is part of the GNU MP Library.
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@ -58,7 +58,7 @@ see https://www.gnu.org/licenses/. */
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/* Macros */
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#define GMP_LIMB_BITS (sizeof(mp_limb_t) * CHAR_BIT)
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#define GMP_LIMB_MAX (~ (mp_limb_t) 0)
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#define GMP_LIMB_MAX ((mp_limb_t) ~ (mp_limb_t) 0)
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#define GMP_LIMB_HIGHBIT ((mp_limb_t) 1 << (GMP_LIMB_BITS - 1))
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#define GMP_HLIMB_BIT ((mp_limb_t) 1 << (GMP_LIMB_BITS / 2))
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@ -129,6 +129,20 @@ see https://www.gnu.org/licenses/. */
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#define gmp_umul_ppmm(w1, w0, u, v) \
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do { \
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int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS; \
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if (sizeof(unsigned int) * CHAR_BIT >= 2 * GMP_LIMB_BITS) \
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{ \
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unsigned int __ww = (unsigned int) (u) * (v); \
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w0 = (mp_limb_t) __ww; \
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w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS); \
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} \
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else if (GMP_ULONG_BITS >= 2 * GMP_LIMB_BITS) \
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{ \
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unsigned long int __ww = (unsigned long int) (u) * (v); \
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w0 = (mp_limb_t) __ww; \
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w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS); \
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} \
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else { \
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mp_limb_t __x0, __x1, __x2, __x3; \
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unsigned __ul, __vl, __uh, __vh; \
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mp_limb_t __u = (u), __v = (v); \
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@ -150,6 +164,7 @@ see https://www.gnu.org/licenses/. */
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\
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(w1) = __x3 + (__x1 >> (GMP_LIMB_BITS / 2)); \
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(w0) = (__x1 << (GMP_LIMB_BITS / 2)) + (__x0 & GMP_LLIMB_MASK); \
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} \
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} while (0)
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#define gmp_udiv_qrnnd_preinv(q, r, nh, nl, d, di) \
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@ -753,6 +768,18 @@ mpn_neg (mp_ptr rp, mp_srcptr up, mp_size_t n)
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mp_limb_t
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mpn_invert_3by2 (mp_limb_t u1, mp_limb_t u0)
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{
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int GMP_LIMB_BITS_MUL_3 = GMP_LIMB_BITS * 3;
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if (sizeof (unsigned) * CHAR_BIT > GMP_LIMB_BITS * 3)
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{
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return (((unsigned) 1 << GMP_LIMB_BITS_MUL_3) - 1) /
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(((unsigned) u1 << GMP_LIMB_BITS_MUL_3 / 3) + u0);
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}
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else if (GMP_ULONG_BITS > GMP_LIMB_BITS * 3)
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{
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return (((unsigned long) 1 << GMP_LIMB_BITS_MUL_3) - 1) /
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(((unsigned long) u1 << GMP_LIMB_BITS_MUL_3 / 3) + u0);
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}
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else {
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mp_limb_t r, p, m, ql;
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unsigned ul, uh, qh;
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@ -827,7 +854,7 @@ mpn_invert_3by2 (mp_limb_t u1, mp_limb_t u0)
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r -= u1;
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}
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/* Now m is the 2/1 invers of u1. If u0 > 0, adjust it to become a
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/* Now m is the 2/1 inverse of u1. If u0 > 0, adjust it to become a
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3/2 inverse. */
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if (u0 > 0)
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{
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@ -854,6 +881,7 @@ mpn_invert_3by2 (mp_limb_t u1, mp_limb_t u0)
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}
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return m;
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}
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}
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struct gmp_div_inverse
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@ -964,36 +992,6 @@ mpn_div_qr_1_preinv (mp_ptr qp, mp_srcptr np, mp_size_t nn,
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return r >> inv->shift;
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}
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static mp_limb_t
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mpn_div_qr_1 (mp_ptr qp, mp_srcptr np, mp_size_t nn, mp_limb_t d)
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{
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assert (d > 0);
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/* Special case for powers of two. */
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if ((d & (d-1)) == 0)
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{
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mp_limb_t r = np[0] & (d-1);
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if (qp)
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{
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if (d <= 1)
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mpn_copyi (qp, np, nn);
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else
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{
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unsigned shift;
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gmp_ctz (shift, d);
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mpn_rshift (qp, np, nn, shift);
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}
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}
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return r;
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}
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else
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{
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struct gmp_div_inverse inv;
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mpn_div_qr_1_invert (&inv, d);
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return mpn_div_qr_1_preinv (qp, np, nn, &inv);
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}
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}
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static void
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mpn_div_qr_2_preinv (mp_ptr qp, mp_ptr np, mp_size_t nn,
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const struct gmp_div_inverse *inv)
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@ -1029,7 +1027,7 @@ mpn_div_qr_2_preinv (mp_ptr qp, mp_ptr np, mp_size_t nn,
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if (shift > 0)
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{
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assert ((r0 << (GMP_LIMB_BITS - shift)) == 0);
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assert ((r0 & (GMP_LIMB_MAX >> (GMP_LIMB_BITS - shift))) == 0);
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r0 = (r0 >> shift) | (r1 << (GMP_LIMB_BITS - shift));
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r1 >>= shift;
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}
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@ -1252,7 +1250,7 @@ mpn_limb_get_str (unsigned char *sp, mp_limb_t w,
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l = w << binv->shift;
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gmp_udiv_qrnnd_preinv (w, r, h, l, binv->d1, binv->di);
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assert ( (r << (GMP_LIMB_BITS - binv->shift)) == 0);
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assert ((r & (GMP_LIMB_MAX >> (GMP_LIMB_BITS - binv->shift))) == 0);
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r >>= binv->shift;
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sp[i] = r;
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@ -1420,7 +1418,7 @@ mpn_set_str (mp_ptr rp, const unsigned char *sp, size_t sn, int base)
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void
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mpz_init (mpz_t r)
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{
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static const mp_limb_t dummy_limb = 0xc1a0;
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static const mp_limb_t dummy_limb = GMP_LIMB_MAX & 0xc1a0;
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r->_mp_alloc = 0;
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r->_mp_size = 0;
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@ -1478,6 +1476,12 @@ mpz_set_si (mpz_t r, signed long int x)
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if (x >= 0)
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mpz_set_ui (r, x);
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else /* (x < 0) */
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if (GMP_LIMB_BITS < GMP_ULONG_BITS)
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{
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mpz_set_ui (r, GMP_NEG_CAST (unsigned long int, x));
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mpz_neg (r, r);
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}
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else
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{
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r->_mp_size = -1;
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MPZ_REALLOC (r, 1)[0] = GMP_NEG_CAST (unsigned long int, x);
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@ -1491,6 +1495,15 @@ mpz_set_ui (mpz_t r, unsigned long int x)
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{
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r->_mp_size = 1;
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MPZ_REALLOC (r, 1)[0] = x;
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if (GMP_LIMB_BITS < GMP_ULONG_BITS)
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{
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int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS;
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while (x >>= LOCAL_GMP_LIMB_BITS)
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{
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++ r->_mp_size;
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MPZ_REALLOC (r, r->_mp_size)[r->_mp_size - 1] = x;
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}
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}
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}
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else
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r->_mp_size = 0;
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@ -1537,14 +1550,20 @@ mpz_init_set (mpz_t r, const mpz_t x)
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int
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mpz_fits_slong_p (const mpz_t u)
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{
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mp_size_t us = u->_mp_size;
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return (LONG_MAX + LONG_MIN == 0 || mpz_cmp_ui (u, LONG_MAX) <= 0) &&
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mpz_cmpabs_ui (u, GMP_NEG_CAST (unsigned long int, LONG_MIN)) <= 0;
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}
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if (us == 1)
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return u->_mp_d[0] < GMP_LIMB_HIGHBIT;
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else if (us == -1)
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return u->_mp_d[0] <= GMP_LIMB_HIGHBIT;
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else
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return (us == 0);
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static int
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mpn_absfits_ulong_p (mp_srcptr up, mp_size_t un)
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{
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int ulongsize = GMP_ULONG_BITS / GMP_LIMB_BITS;
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mp_limb_t ulongrem = 0;
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if (GMP_ULONG_BITS % GMP_LIMB_BITS != 0)
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ulongrem = (mp_limb_t) (ULONG_MAX >> GMP_LIMB_BITS * ulongsize) + 1;
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return un <= ulongsize || (up[ulongsize] < ulongrem && un == ulongsize + 1);
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}
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int
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@ -1552,22 +1571,36 @@ mpz_fits_ulong_p (const mpz_t u)
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{
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mp_size_t us = u->_mp_size;
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return (us == (us > 0));
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return us >= 0 && mpn_absfits_ulong_p (u->_mp_d, us);
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}
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long int
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mpz_get_si (const mpz_t u)
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{
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unsigned long r = mpz_get_ui (u);
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unsigned long c = -LONG_MAX - LONG_MIN;
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if (u->_mp_size < 0)
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/* This expression is necessary to properly handle 0x80000000 */
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return -1 - (long) ((u->_mp_d[0] - 1) & ~GMP_LIMB_HIGHBIT);
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/* This expression is necessary to properly handle -LONG_MIN */
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return -(long) c - (long) ((r - c) & LONG_MAX);
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else
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return (long) (mpz_get_ui (u) & ~GMP_LIMB_HIGHBIT);
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return (long) (r & LONG_MAX);
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}
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unsigned long int
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mpz_get_ui (const mpz_t u)
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{
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if (GMP_LIMB_BITS < GMP_ULONG_BITS)
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{
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int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS;
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unsigned long r = 0;
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mp_size_t n = GMP_ABS (u->_mp_size);
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n = GMP_MIN (n, 1 + (GMP_ULONG_BITS - 1) / GMP_LIMB_BITS);
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while (--n >= 0)
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r = (r << LOCAL_GMP_LIMB_BITS) + u->_mp_d[n];
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return r;
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}
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return u->_mp_size == 0 ? 0 : u->_mp_d[0];
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}
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@ -1665,7 +1698,7 @@ mpz_set_d (mpz_t r, double x)
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r->_mp_size = 0;
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return;
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}
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B = 2.0 * (double) GMP_LIMB_HIGHBIT;
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B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
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Bi = 1.0 / B;
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for (rn = 1; x >= B; rn++)
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x *= Bi;
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@ -1703,7 +1736,7 @@ mpz_get_d (const mpz_t u)
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mp_limb_t l;
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mp_size_t un;
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double x;
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double B = 2.0 * (double) GMP_LIMB_HIGHBIT;
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double B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
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un = GMP_ABS (u->_mp_size);
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@ -1748,7 +1781,7 @@ mpz_cmpabs_d (const mpz_t x, double d)
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{
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xn = GMP_ABS (xn);
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B = 2.0 * (double) GMP_LIMB_HIGHBIT;
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B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
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Bi = 1.0 / B;
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/* Scale d so it can be compared with the top limb. */
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@ -1807,14 +1840,12 @@ mpz_cmp_si (const mpz_t u, long v)
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{
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mp_size_t usize = u->_mp_size;
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if (usize < -1)
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return -1;
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else if (v >= 0)
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if (v >= 0)
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return mpz_cmp_ui (u, v);
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else if (usize >= 0)
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return 1;
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else /* usize == -1 */
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return GMP_CMP (GMP_NEG_CAST (mp_limb_t, v), u->_mp_d[0]);
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else
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return - mpz_cmpabs_ui (u, GMP_NEG_CAST (unsigned long int, v));
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}
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int
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@ -1822,12 +1853,10 @@ mpz_cmp_ui (const mpz_t u, unsigned long v)
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{
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mp_size_t usize = u->_mp_size;
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if (usize > 1)
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return 1;
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else if (usize < 0)
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if (usize < 0)
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return -1;
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else
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return GMP_CMP (mpz_get_ui (u), v);
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return mpz_cmpabs_ui (u, v);
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}
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int
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@ -1847,10 +1876,15 @@ mpz_cmp (const mpz_t a, const mpz_t b)
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int
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mpz_cmpabs_ui (const mpz_t u, unsigned long v)
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{
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if (GMP_ABS (u->_mp_size) > 1)
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mp_size_t un = GMP_ABS (u->_mp_size);
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if (! mpn_absfits_ulong_p (u->_mp_d, un))
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return 1;
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else
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return GMP_CMP (mpz_get_ui (u), v);
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{
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unsigned long uu = mpz_get_ui (u);
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return GMP_CMP(uu, v);
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}
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}
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int
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@ -1885,81 +1919,28 @@ mpz_swap (mpz_t u, mpz_t v)
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/* MPZ addition and subtraction */
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/* Adds to the absolute value. Returns new size, but doesn't store it. */
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static mp_size_t
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mpz_abs_add_ui (mpz_t r, const mpz_t a, unsigned long b)
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{
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mp_size_t an;
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mp_ptr rp;
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mp_limb_t cy;
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an = GMP_ABS (a->_mp_size);
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if (an == 0)
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{
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MPZ_REALLOC (r, 1)[0] = b;
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return b > 0;
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}
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rp = MPZ_REALLOC (r, an + 1);
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cy = mpn_add_1 (rp, a->_mp_d, an, b);
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rp[an] = cy;
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an += cy;
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return an;
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}
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/* Subtract from the absolute value. Returns new size, (or -1 on underflow),
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but doesn't store it. */
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static mp_size_t
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mpz_abs_sub_ui (mpz_t r, const mpz_t a, unsigned long b)
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{
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mp_size_t an = GMP_ABS (a->_mp_size);
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mp_ptr rp;
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if (an == 0)
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{
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MPZ_REALLOC (r, 1)[0] = b;
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return -(b > 0);
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}
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rp = MPZ_REALLOC (r, an);
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if (an == 1 && a->_mp_d[0] < b)
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{
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rp[0] = b - a->_mp_d[0];
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return -1;
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}
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else
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{
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gmp_assert_nocarry (mpn_sub_1 (rp, a->_mp_d, an, b));
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return mpn_normalized_size (rp, an);
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}
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}
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void
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mpz_add_ui (mpz_t r, const mpz_t a, unsigned long b)
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{
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if (a->_mp_size >= 0)
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r->_mp_size = mpz_abs_add_ui (r, a, b);
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else
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r->_mp_size = -mpz_abs_sub_ui (r, a, b);
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mpz_t bb;
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mpz_init_set_ui (bb, b);
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mpz_add (r, a, bb);
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mpz_clear (bb);
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}
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void
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mpz_sub_ui (mpz_t r, const mpz_t a, unsigned long b)
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{
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if (a->_mp_size < 0)
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r->_mp_size = -mpz_abs_add_ui (r, a, b);
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else
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r->_mp_size = mpz_abs_sub_ui (r, a, b);
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mpz_ui_sub (r, b, a);
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mpz_neg (r, r);
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}
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void
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mpz_ui_sub (mpz_t r, unsigned long a, const mpz_t b)
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{
|
||||
if (b->_mp_size < 0)
|
||||
r->_mp_size = mpz_abs_add_ui (r, b, a);
|
||||
else
|
||||
r->_mp_size = -mpz_abs_sub_ui (r, b, a);
|
||||
mpz_neg (r, b);
|
||||
mpz_add_ui (r, r, a);
|
||||
}
|
||||
|
||||
static mp_size_t
|
||||
@ -2046,32 +2027,17 @@ mpz_mul_si (mpz_t r, const mpz_t u, long int v)
|
||||
mpz_neg (r, r);
|
||||
}
|
||||
else
|
||||
mpz_mul_ui (r, u, (unsigned long int) v);
|
||||
mpz_mul_ui (r, u, v);
|
||||
}
|
||||
|
||||
void
|
||||
mpz_mul_ui (mpz_t r, const mpz_t u, unsigned long int v)
|
||||
{
|
||||
mp_size_t un, us;
|
||||
mp_ptr tp;
|
||||
mp_limb_t cy;
|
||||
|
||||
us = u->_mp_size;
|
||||
|
||||
if (us == 0 || v == 0)
|
||||
{
|
||||
r->_mp_size = 0;
|
||||
return;
|
||||
}
|
||||
|
||||
un = GMP_ABS (us);
|
||||
|
||||
tp = MPZ_REALLOC (r, un + 1);
|
||||
cy = mpn_mul_1 (tp, u->_mp_d, un, v);
|
||||
tp[un] = cy;
|
||||
|
||||
un += (cy > 0);
|
||||
r->_mp_size = (us < 0) ? - un : un;
|
||||
mpz_t vv;
|
||||
mpz_init_set_ui (vv, v);
|
||||
mpz_mul (r, u, vv);
|
||||
mpz_clear (vv);
|
||||
return;
|
||||
}
|
||||
|
||||
void
|
||||
@ -2150,8 +2116,8 @@ void
|
||||
mpz_addmul_ui (mpz_t r, const mpz_t u, unsigned long int v)
|
||||
{
|
||||
mpz_t t;
|
||||
mpz_init (t);
|
||||
mpz_mul_ui (t, u, v);
|
||||
mpz_init_set_ui (t, v);
|
||||
mpz_mul (t, u, t);
|
||||
mpz_add (r, r, t);
|
||||
mpz_clear (t);
|
||||
}
|
||||
@ -2160,8 +2126,8 @@ void
|
||||
mpz_submul_ui (mpz_t r, const mpz_t u, unsigned long int v)
|
||||
{
|
||||
mpz_t t;
|
||||
mpz_init (t);
|
||||
mpz_mul_ui (t, u, v);
|
||||
mpz_init_set_ui (t, v);
|
||||
mpz_mul (t, u, t);
|
||||
mpz_sub (r, r, t);
|
||||
mpz_clear (t);
|
||||
}
|
||||
@ -2557,56 +2523,20 @@ static unsigned long
|
||||
mpz_div_qr_ui (mpz_t q, mpz_t r,
|
||||
const mpz_t n, unsigned long d, enum mpz_div_round_mode mode)
|
||||
{
|
||||
mp_size_t ns, qn;
|
||||
mp_ptr qp;
|
||||
mp_limb_t rl;
|
||||
mp_size_t rs;
|
||||
unsigned long ret;
|
||||
mpz_t rr, dd;
|
||||
|
||||
ns = n->_mp_size;
|
||||
if (ns == 0)
|
||||
{
|
||||
if (q)
|
||||
q->_mp_size = 0;
|
||||
if (r)
|
||||
r->_mp_size = 0;
|
||||
return 0;
|
||||
}
|
||||
|
||||
qn = GMP_ABS (ns);
|
||||
if (q)
|
||||
qp = MPZ_REALLOC (q, qn);
|
||||
else
|
||||
qp = NULL;
|
||||
|
||||
rl = mpn_div_qr_1 (qp, n->_mp_d, qn, d);
|
||||
assert (rl < d);
|
||||
|
||||
rs = rl > 0;
|
||||
rs = (ns < 0) ? -rs : rs;
|
||||
|
||||
if (rl > 0 && ( (mode == GMP_DIV_FLOOR && ns < 0)
|
||||
|| (mode == GMP_DIV_CEIL && ns >= 0)))
|
||||
{
|
||||
if (q)
|
||||
gmp_assert_nocarry (mpn_add_1 (qp, qp, qn, 1));
|
||||
rl = d - rl;
|
||||
rs = -rs;
|
||||
}
|
||||
mpz_init (rr);
|
||||
mpz_init_set_ui (dd, d);
|
||||
mpz_div_qr (q, rr, n, dd, mode);
|
||||
mpz_clear (dd);
|
||||
ret = mpz_get_ui (rr);
|
||||
|
||||
if (r)
|
||||
{
|
||||
MPZ_REALLOC (r, 1)[0] = rl;
|
||||
r->_mp_size = rs;
|
||||
}
|
||||
if (q)
|
||||
{
|
||||
qn -= (qp[qn-1] == 0);
|
||||
assert (qn == 0 || qp[qn-1] > 0);
|
||||
mpz_swap (r, rr);
|
||||
mpz_clear (rr);
|
||||
|
||||
q->_mp_size = (ns < 0) ? - qn : qn;
|
||||
}
|
||||
|
||||
return rl;
|
||||
return ret;
|
||||
}
|
||||
|
||||
unsigned long
|
||||
@ -2745,22 +2675,16 @@ mpn_gcd_11 (mp_limb_t u, mp_limb_t v)
|
||||
unsigned long
|
||||
mpz_gcd_ui (mpz_t g, const mpz_t u, unsigned long v)
|
||||
{
|
||||
mp_size_t un;
|
||||
mpz_t t;
|
||||
mpz_init_set_ui(t, v);
|
||||
mpz_gcd (t, u, t);
|
||||
if (v > 0)
|
||||
v = mpz_get_ui (t);
|
||||
|
||||
if (v == 0)
|
||||
{
|
||||
if (g)
|
||||
mpz_abs (g, u);
|
||||
}
|
||||
else
|
||||
{
|
||||
un = GMP_ABS (u->_mp_size);
|
||||
if (un != 0)
|
||||
v = mpn_gcd_11 (mpn_div_qr_1 (NULL, u->_mp_d, un, v), v);
|
||||
if (g)
|
||||
mpz_swap (t, g);
|
||||
|
||||
if (g)
|
||||
mpz_set_ui (g, v);
|
||||
}
|
||||
mpz_clear (t);
|
||||
|
||||
return v;
|
||||
}
|
||||
@ -2854,7 +2778,7 @@ mpz_gcdext (mpz_t g, mpz_t s, mpz_t t, const mpz_t u, const mpz_t v)
|
||||
signed long sign = mpz_sgn (v);
|
||||
mpz_abs (g, v);
|
||||
if (s)
|
||||
mpz_set_ui (s, 0);
|
||||
s->_mp_size = 0;
|
||||
if (t)
|
||||
mpz_set_si (t, sign);
|
||||
return;
|
||||
@ -2868,7 +2792,7 @@ mpz_gcdext (mpz_t g, mpz_t s, mpz_t t, const mpz_t u, const mpz_t v)
|
||||
if (s)
|
||||
mpz_set_si (s, sign);
|
||||
if (t)
|
||||
mpz_set_ui (t, 0);
|
||||
t->_mp_size = 0;
|
||||
return;
|
||||
}
|
||||
|
||||
@ -2993,8 +2917,9 @@ mpz_gcdext (mpz_t g, mpz_t s, mpz_t t, const mpz_t u, const mpz_t v)
|
||||
mpz_sub (s0, s0, s1);
|
||||
mpz_add (t0, t0, t1);
|
||||
}
|
||||
mpz_divexact_ui (s0, s0, 2);
|
||||
mpz_divexact_ui (t0, t0, 2);
|
||||
assert (mpz_even_p (t0) && mpz_even_p (s0));
|
||||
mpz_tdiv_q_2exp (s0, s0, 1);
|
||||
mpz_tdiv_q_2exp (t0, t0, 1);
|
||||
}
|
||||
|
||||
/* Arrange so that |s| < |u| / 2g */
|
||||
@ -3119,7 +3044,10 @@ void
|
||||
mpz_ui_pow_ui (mpz_t r, unsigned long blimb, unsigned long e)
|
||||
{
|
||||
mpz_t b;
|
||||
mpz_pow_ui (r, mpz_roinit_normal_n (b, &blimb, blimb != 0), e);
|
||||
|
||||
mpz_init_set_ui (b, blimb);
|
||||
mpz_pow_ui (r, b, e);
|
||||
mpz_clear (b);
|
||||
}
|
||||
|
||||
void
|
||||
@ -3231,7 +3159,10 @@ void
|
||||
mpz_powm_ui (mpz_t r, const mpz_t b, unsigned long elimb, const mpz_t m)
|
||||
{
|
||||
mpz_t e;
|
||||
mpz_powm (r, b, mpz_roinit_normal_n (e, &elimb, elimb != 0), m);
|
||||
|
||||
mpz_init_set_ui (e, elimb);
|
||||
mpz_powm (r, b, e, m);
|
||||
mpz_clear (e);
|
||||
}
|
||||
|
||||
/* x=trunc(y^(1/z)), r=y-x^z */
|
||||
@ -3409,6 +3340,177 @@ mpz_bin_uiui (mpz_t r, unsigned long n, unsigned long k)
|
||||
|
||||
|
||||
/* Primality testing */
|
||||
|
||||
/* Computes Kronecker (a/b) with odd b, a!=0 and GCD(a,b) = 1 */
|
||||
/* Adapted from JACOBI_BASE_METHOD==4 in mpn/generic/jacbase.c */
|
||||
static int
|
||||
gmp_jacobi_coprime (mp_limb_t a, mp_limb_t b)
|
||||
{
|
||||
int c, bit = 0;
|
||||
|
||||
assert (b & 1);
|
||||
assert (a != 0);
|
||||
/* assert (mpn_gcd_11 (a, b) == 1); */
|
||||
|
||||
/* Below, we represent a and b shifted right so that the least
|
||||
significant one bit is implicit. */
|
||||
b >>= 1;
|
||||
|
||||
gmp_ctz(c, a);
|
||||
a >>= 1;
|
||||
|
||||
do
|
||||
{
|
||||
a >>= c;
|
||||
/* (2/b) = -1 if b = 3 or 5 mod 8 */
|
||||
bit ^= c & (b ^ (b >> 1));
|
||||
if (a < b)
|
||||
{
|
||||
bit ^= a & b;
|
||||
a = b - a;
|
||||
b -= a;
|
||||
}
|
||||
else
|
||||
{
|
||||
a -= b;
|
||||
assert (a != 0);
|
||||
}
|
||||
|
||||
gmp_ctz(c, a);
|
||||
++c;
|
||||
}
|
||||
while (b > 0);
|
||||
|
||||
return bit & 1 ? -1 : 1;
|
||||
}
|
||||
|
||||
static void
|
||||
gmp_lucas_step_k_2k (mpz_t V, mpz_t Qk, const mpz_t n)
|
||||
{
|
||||
mpz_mod (Qk, Qk, n);
|
||||
/* V_{2k} <- V_k ^ 2 - 2Q^k */
|
||||
mpz_mul (V, V, V);
|
||||
mpz_submul_ui (V, Qk, 2);
|
||||
mpz_tdiv_r (V, V, n);
|
||||
/* Q^{2k} = (Q^k)^2 */
|
||||
mpz_mul (Qk, Qk, Qk);
|
||||
}
|
||||
|
||||
/* Computes V_k, Q^k (mod n) for the Lucas' sequence */
|
||||
/* with P=1, Q=Q; k = (n>>b0)|1. */
|
||||
/* Requires an odd n > 4; b0 > 0; -2*Q must not overflow a long */
|
||||
/* Returns (U_k == 0) and sets V=V_k and Qk=Q^k. */
|
||||
static int
|
||||
gmp_lucas_mod (mpz_t V, mpz_t Qk, long Q,
|
||||
mp_bitcnt_t b0, const mpz_t n)
|
||||
{
|
||||
mp_bitcnt_t bs;
|
||||
mpz_t U;
|
||||
int res;
|
||||
|
||||
assert (b0 > 0);
|
||||
assert (Q <= - (LONG_MIN / 2));
|
||||
assert (Q >= - (LONG_MAX / 2));
|
||||
assert (mpz_cmp_ui (n, 4) > 0);
|
||||
assert (mpz_odd_p (n));
|
||||
|
||||
mpz_init_set_ui (U, 1); /* U1 = 1 */
|
||||
mpz_set_ui (V, 1); /* V1 = 1 */
|
||||
mpz_set_si (Qk, Q);
|
||||
|
||||
for (bs = mpz_sizeinbase (n, 2) - 1; --bs >= b0;)
|
||||
{
|
||||
/* U_{2k} <- U_k * V_k */
|
||||
mpz_mul (U, U, V);
|
||||
/* V_{2k} <- V_k ^ 2 - 2Q^k */
|
||||
/* Q^{2k} = (Q^k)^2 */
|
||||
gmp_lucas_step_k_2k (V, Qk, n);
|
||||
|
||||
/* A step k->k+1 is performed if the bit in $n$ is 1 */
|
||||
/* mpz_tstbit(n,bs) or the the bit is 0 in $n$ but */
|
||||
/* should be 1 in $n+1$ (bs == b0) */
|
||||
if (b0 == bs || mpz_tstbit (n, bs))
|
||||
{
|
||||
/* Q^{k+1} <- Q^k * Q */
|
||||
mpz_mul_si (Qk, Qk, Q);
|
||||
/* U_{k+1} <- (U_k + V_k) / 2 */
|
||||
mpz_swap (U, V); /* Keep in V the old value of U_k */
|
||||
mpz_add (U, U, V);
|
||||
/* We have to compute U/2, so we need an even value, */
|
||||
/* equivalent (mod n) */
|
||||
if (mpz_odd_p (U))
|
||||
mpz_add (U, U, n);
|
||||
mpz_tdiv_q_2exp (U, U, 1);
|
||||
/* V_{k+1} <-(D*U_k + V_k) / 2 =
|
||||
U_{k+1} + (D-1)/2*U_k = U_{k+1} - 2Q*U_k */
|
||||
mpz_mul_si (V, V, -2*Q);
|
||||
mpz_add (V, U, V);
|
||||
mpz_tdiv_r (V, V, n);
|
||||
}
|
||||
mpz_tdiv_r (U, U, n);
|
||||
}
|
||||
|
||||
res = U->_mp_size == 0;
|
||||
mpz_clear (U);
|
||||
return res;
|
||||
}
|
||||
|
||||
/* Performs strong Lucas' test on x, with parameters suggested */
|
||||
/* for the BPSW test. Qk is only passed to recycle a variable. */
|
||||
/* Requires GCD (x,6) = 1.*/
|
||||
static int
|
||||
gmp_stronglucas (const mpz_t x, mpz_t Qk)
|
||||
{
|
||||
mp_bitcnt_t b0;
|
||||
mpz_t V, n;
|
||||
mp_limb_t maxD, D; /* The absolute value is stored. */
|
||||
long Q;
|
||||
mp_limb_t tl;
|
||||
|
||||
/* Test on the absolute value. */
|
||||
mpz_roinit_normal_n (n, x->_mp_d, GMP_ABS (x->_mp_size));
|
||||
|
||||
assert (mpz_odd_p (n));
|
||||
/* assert (mpz_gcd_ui (NULL, n, 6) == 1); */
|
||||
if (mpz_root (Qk, n, 2))
|
||||
return 0; /* A square is composite. */
|
||||
|
||||
/* Check Ds up to square root (in case, n is prime)
|
||||
or avoid overflows */
|
||||
maxD = (Qk->_mp_size == 1) ? Qk->_mp_d [0] - 1 : GMP_LIMB_MAX;
|
||||
|
||||
D = 3;
|
||||
/* Search a D such that (D/n) = -1 in the sequence 5,-7,9,-11,.. */
|
||||
/* For those Ds we have (D/n) = (n/|D|) */
|
||||
do
|
||||
{
|
||||
if (D >= maxD)
|
||||
return 1 + (D != GMP_LIMB_MAX); /* (1 + ! ~ D) */
|
||||
D += 2;
|
||||
tl = mpz_tdiv_ui (n, D);
|
||||
if (tl == 0)
|
||||
return 0;
|
||||
}
|
||||
while (gmp_jacobi_coprime (tl, D) == 1);
|
||||
|
||||
mpz_init (V);
|
||||
|
||||
/* n-(D/n) = n+1 = d*2^{b0}, with d = (n>>b0) | 1 */
|
||||
b0 = mpz_scan0 (n, 0);
|
||||
|
||||
/* D= P^2 - 4Q; P = 1; Q = (1-D)/4 */
|
||||
Q = (D & 2) ? (D >> 2) + 1 : -(long) (D >> 2);
|
||||
|
||||
if (! gmp_lucas_mod (V, Qk, Q, b0, n)) /* If Ud != 0 */
|
||||
while (V->_mp_size != 0 && --b0 != 0) /* while Vk != 0 */
|
||||
/* V <- V ^ 2 - 2Q^k */
|
||||
/* Q^{2k} = (Q^k)^2 */
|
||||
gmp_lucas_step_k_2k (V, Qk, n);
|
||||
|
||||
mpz_clear (V);
|
||||
return (b0 != 0);
|
||||
}
|
||||
|
||||
static int
|
||||
gmp_millerrabin (const mpz_t n, const mpz_t nm1, mpz_t y,
|
||||
const mpz_t q, mp_bitcnt_t k)
|
||||
@ -3470,21 +3572,26 @@ mpz_probab_prime_p (const mpz_t n, int reps)
|
||||
if (mpz_cmpabs_ui (n, 31*31) < 0)
|
||||
return 2;
|
||||
|
||||
mpz_init (nm1);
|
||||
mpz_init (q);
|
||||
|
||||
/* Find q and k, where q is odd and n = 1 + 2**k * q. */
|
||||
mpz_abs (nm1, n);
|
||||
nm1->_mp_d[0] -= 1;
|
||||
k = mpz_scan1 (nm1, 0);
|
||||
mpz_tdiv_q_2exp (q, nm1, k);
|
||||
|
||||
/* BPSW test */
|
||||
mpz_init_set_ui (y, 2);
|
||||
is_prime = gmp_millerrabin (n, nm1, y, q, k) && gmp_stronglucas (n, y);
|
||||
reps -= 24; /* skip the first 24 repetitions */
|
||||
|
||||
/* Use Miller-Rabin, with a deterministic sequence of bases, a[j] =
|
||||
j^2 + j + 41 using Euler's polynomial. We potentially stop early,
|
||||
if a[j] >= n - 1. Since n >= 31*31, this can happen only if reps >
|
||||
30 (a[30] == 971 > 31*31 == 961). */
|
||||
|
||||
mpz_init (nm1);
|
||||
mpz_init (q);
|
||||
mpz_init (y);
|
||||
|
||||
/* Find q and k, where q is odd and n = 1 + 2**k * q. */
|
||||
nm1->_mp_size = mpz_abs_sub_ui (nm1, n, 1);
|
||||
k = mpz_scan1 (nm1, 0);
|
||||
mpz_tdiv_q_2exp (q, nm1, k);
|
||||
|
||||
for (j = 0, is_prime = 1; is_prime & (j < reps); j++)
|
||||
for (j = 0; is_prime & (j < reps); j++)
|
||||
{
|
||||
mpz_set_ui (y, (unsigned long) j*j+j+41);
|
||||
if (mpz_cmp (y, nm1) >= 0)
|
||||
@ -3552,7 +3659,7 @@ mpz_tstbit (const mpz_t d, mp_bitcnt_t bit_index)
|
||||
{
|
||||
/* d < 0. Check if any of the bits below is set: If so, our bit
|
||||
must be complemented. */
|
||||
if (shift > 0 && (w << (GMP_LIMB_BITS - shift)) > 0)
|
||||
if (shift > 0 && (mp_limb_t) (w << (GMP_LIMB_BITS - shift)) > 0)
|
||||
return bit ^ 1;
|
||||
while (--limb_index >= 0)
|
||||
if (d->_mp_d[limb_index] > 0)
|
||||
@ -3659,8 +3766,8 @@ mpz_combit (mpz_t d, mp_bitcnt_t bit_index)
|
||||
void
|
||||
mpz_com (mpz_t r, const mpz_t u)
|
||||
{
|
||||
mpz_neg (r, u);
|
||||
mpz_sub_ui (r, r, 1);
|
||||
mpz_add_ui (r, u, 1);
|
||||
mpz_neg (r, r);
|
||||
}
|
||||
|
||||
void
|
||||
@ -4000,7 +4107,7 @@ mpz_scan1 (const mpz_t u, mp_bitcnt_t starting_bit)
|
||||
}
|
||||
|
||||
/* Mask to 0 all bits before starting_bit, thus ignoring them. */
|
||||
limb &= (GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS));
|
||||
limb &= GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS);
|
||||
}
|
||||
|
||||
return mpn_common_scan (limb, i, up, un, ux);
|
||||
@ -4030,7 +4137,7 @@ mpz_scan0 (const mpz_t u, mp_bitcnt_t starting_bit)
|
||||
limb -= mpn_zero_p (up, i); /* limb = ~(~limb + zero_p) */
|
||||
|
||||
/* Mask all bits before starting_bit, thus ignoring them. */
|
||||
limb &= (GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS));
|
||||
limb &= GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS);
|
||||
|
||||
return mpn_common_scan (limb, i, up, un, ux);
|
||||
}
|
||||
|
||||
@ -1,6 +1,6 @@
|
||||
/* mini-gmp, a minimalistic implementation of a GNU GMP subset.
|
||||
|
||||
Copyright 2011-2015, 2017, 2019 Free Software Foundation, Inc.
|
||||
Copyright 2011-2015, 2017 Free Software Foundation, Inc.
|
||||
|
||||
This file is part of the GNU MP Library.
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user