Contributed to the GNU project by Niels Möller
-Copyright 1991-1997, 1999-2019 Free Software Foundation, Inc.
+Copyright 1991-1997, 1999-2018 Free Software Foundation, Inc.
This file is part of the GNU MP Library.
/* Macros */
#define GMP_LIMB_BITS (sizeof(mp_limb_t) * CHAR_BIT)
-#define GMP_LIMB_MAX (~ (mp_limb_t) 0)
+#define GMP_LIMB_MAX ((mp_limb_t) ~ (mp_limb_t) 0)
#define GMP_LIMB_HIGHBIT ((mp_limb_t) 1 << (GMP_LIMB_BITS - 1))
#define GMP_HLIMB_BIT ((mp_limb_t) 1 << (GMP_LIMB_BITS / 2))
#define gmp_umul_ppmm(w1, w0, u, v) \
do { \
+ int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS; \
+ if (sizeof(unsigned int) * CHAR_BIT >= 2 * GMP_LIMB_BITS) \
+ { \
+ unsigned int __ww = (unsigned int) (u) * (v); \
+ w0 = (mp_limb_t) __ww; \
+ w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS); \
+ } \
+ else if (GMP_ULONG_BITS >= 2 * GMP_LIMB_BITS) \
+ { \
+ unsigned long int __ww = (unsigned long int) (u) * (v); \
+ w0 = (mp_limb_t) __ww; \
+ w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS); \
+ } \
+ else { \
mp_limb_t __x0, __x1, __x2, __x3; \
unsigned __ul, __vl, __uh, __vh; \
mp_limb_t __u = (u), __v = (v); \
\
(w1) = __x3 + (__x1 >> (GMP_LIMB_BITS / 2)); \
(w0) = (__x1 << (GMP_LIMB_BITS / 2)) + (__x0 & GMP_LLIMB_MASK); \
+ } \
} while (0)
#define gmp_udiv_qrnnd_preinv(q, r, nh, nl, d, di) \
mp_limb_t
mpn_invert_3by2 (mp_limb_t u1, mp_limb_t u0)
{
+ int GMP_LIMB_BITS_MUL_3 = GMP_LIMB_BITS * 3;
+ if (sizeof (unsigned) * CHAR_BIT > GMP_LIMB_BITS * 3)
+ {
+ return (((unsigned) 1 << GMP_LIMB_BITS_MUL_3) - 1) /
+ (((unsigned) u1 << GMP_LIMB_BITS_MUL_3 / 3) + u0);
+ }
+ else if (GMP_ULONG_BITS > GMP_LIMB_BITS * 3)
+ {
+ return (((unsigned long) 1 << GMP_LIMB_BITS_MUL_3) - 1) /
+ (((unsigned long) u1 << GMP_LIMB_BITS_MUL_3 / 3) + u0);
+ }
+ else {
mp_limb_t r, p, m, ql;
unsigned ul, uh, qh;
r -= u1;
}
- /* Now m is the 2/1 invers of u1. If u0 > 0, adjust it to become a
+ /* Now m is the 2/1 inverse of u1. If u0 > 0, adjust it to become a
3/2 inverse. */
if (u0 > 0)
{
}
return m;
+ }
}
struct gmp_div_inverse
return r >> inv->shift;
}
-static mp_limb_t
-mpn_div_qr_1 (mp_ptr qp, mp_srcptr np, mp_size_t nn, mp_limb_t d)
-{
- assert (d > 0);
-
- /* Special case for powers of two. */
- if ((d & (d-1)) == 0)
- {
- mp_limb_t r = np[0] & (d-1);
- if (qp)
- {
- if (d <= 1)
- mpn_copyi (qp, np, nn);
- else
- {
- unsigned shift;
- gmp_ctz (shift, d);
- mpn_rshift (qp, np, nn, shift);
- }
- }
- return r;
- }
- else
- {
- struct gmp_div_inverse inv;
- mpn_div_qr_1_invert (&inv, d);
- return mpn_div_qr_1_preinv (qp, np, nn, &inv);
- }
-}
-
static void
mpn_div_qr_2_preinv (mp_ptr qp, mp_ptr np, mp_size_t nn,
const struct gmp_div_inverse *inv)
if (shift > 0)
{
- assert ((r0 << (GMP_LIMB_BITS - shift)) == 0);
+ assert ((r0 & (GMP_LIMB_MAX >> (GMP_LIMB_BITS - shift))) == 0);
r0 = (r0 >> shift) | (r1 << (GMP_LIMB_BITS - shift));
r1 >>= shift;
}
l = w << binv->shift;
gmp_udiv_qrnnd_preinv (w, r, h, l, binv->d1, binv->di);
- assert ( (r << (GMP_LIMB_BITS - binv->shift)) == 0);
+ assert ((r & (GMP_LIMB_MAX >> (GMP_LIMB_BITS - binv->shift))) == 0);
r >>= binv->shift;
sp[i] = r;
void
mpz_init (mpz_t r)
{
- static const mp_limb_t dummy_limb = 0xc1a0;
+ static const mp_limb_t dummy_limb = GMP_LIMB_MAX & 0xc1a0;
r->_mp_alloc = 0;
r->_mp_size = 0;
if (x >= 0)
mpz_set_ui (r, x);
else /* (x < 0) */
+ if (GMP_LIMB_BITS < GMP_ULONG_BITS)
+ {
+ mpz_set_ui (r, GMP_NEG_CAST (unsigned long int, x));
+ mpz_neg (r, r);
+ }
+ else
{
r->_mp_size = -1;
MPZ_REALLOC (r, 1)[0] = GMP_NEG_CAST (unsigned long int, x);
{
r->_mp_size = 1;
MPZ_REALLOC (r, 1)[0] = x;
+ if (GMP_LIMB_BITS < GMP_ULONG_BITS)
+ {
+ int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS;
+ while (x >>= LOCAL_GMP_LIMB_BITS)
+ {
+ ++ r->_mp_size;
+ MPZ_REALLOC (r, r->_mp_size)[r->_mp_size - 1] = x;
+ }
+ }
}
else
r->_mp_size = 0;
int
mpz_fits_slong_p (const mpz_t u)
{
- mp_size_t us = u->_mp_size;
+ return (LONG_MAX + LONG_MIN == 0 || mpz_cmp_ui (u, LONG_MAX) <= 0) &&
+ mpz_cmpabs_ui (u, GMP_NEG_CAST (unsigned long int, LONG_MIN)) <= 0;
+}
- if (us == 1)
- return u->_mp_d[0] < GMP_LIMB_HIGHBIT;
- else if (us == -1)
- return u->_mp_d[0] <= GMP_LIMB_HIGHBIT;
- else
- return (us == 0);
+static int
+mpn_absfits_ulong_p (mp_srcptr up, mp_size_t un)
+{
+ int ulongsize = GMP_ULONG_BITS / GMP_LIMB_BITS;
+ mp_limb_t ulongrem = 0;
+
+ if (GMP_ULONG_BITS % GMP_LIMB_BITS != 0)
+ ulongrem = (mp_limb_t) (ULONG_MAX >> GMP_LIMB_BITS * ulongsize) + 1;
+
+ return un <= ulongsize || (up[ulongsize] < ulongrem && un == ulongsize + 1);
}
int
{
mp_size_t us = u->_mp_size;
- return (us == (us > 0));
+ return us >= 0 && mpn_absfits_ulong_p (u->_mp_d, us);
}
long int
mpz_get_si (const mpz_t u)
{
+ unsigned long r = mpz_get_ui (u);
+ unsigned long c = -LONG_MAX - LONG_MIN;
+
if (u->_mp_size < 0)
- /* This expression is necessary to properly handle 0x80000000 */
- return -1 - (long) ((u->_mp_d[0] - 1) & ~GMP_LIMB_HIGHBIT);
+ /* This expression is necessary to properly handle -LONG_MIN */
+ return -(long) c - (long) ((r - c) & LONG_MAX);
else
- return (long) (mpz_get_ui (u) & ~GMP_LIMB_HIGHBIT);
+ return (long) (r & LONG_MAX);
}
unsigned long int
mpz_get_ui (const mpz_t u)
{
+ if (GMP_LIMB_BITS < GMP_ULONG_BITS)
+ {
+ int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS;
+ unsigned long r = 0;
+ mp_size_t n = GMP_ABS (u->_mp_size);
+ n = GMP_MIN (n, 1 + (GMP_ULONG_BITS - 1) / GMP_LIMB_BITS);
+ while (--n >= 0)
+ r = (r << LOCAL_GMP_LIMB_BITS) + u->_mp_d[n];
+ return r;
+ }
+
return u->_mp_size == 0 ? 0 : u->_mp_d[0];
}
r->_mp_size = 0;
return;
}
- B = 2.0 * (double) GMP_LIMB_HIGHBIT;
+ B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
Bi = 1.0 / B;
for (rn = 1; x >= B; rn++)
x *= Bi;
mp_limb_t l;
mp_size_t un;
double x;
- double B = 2.0 * (double) GMP_LIMB_HIGHBIT;
+ double B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
un = GMP_ABS (u->_mp_size);
{
xn = GMP_ABS (xn);
- B = 2.0 * (double) GMP_LIMB_HIGHBIT;
+ B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
Bi = 1.0 / B;
/* Scale d so it can be compared with the top limb. */
{
mp_size_t usize = u->_mp_size;
- if (usize < -1)
- return -1;
- else if (v >= 0)
+ if (v >= 0)
return mpz_cmp_ui (u, v);
else if (usize >= 0)
return 1;
- else /* usize == -1 */
- return GMP_CMP (GMP_NEG_CAST (mp_limb_t, v), u->_mp_d[0]);
+ else
+ return - mpz_cmpabs_ui (u, GMP_NEG_CAST (unsigned long int, v));
}
int
{
mp_size_t usize = u->_mp_size;
- if (usize > 1)
- return 1;
- else if (usize < 0)
+ if (usize < 0)
return -1;
else
- return GMP_CMP (mpz_get_ui (u), v);
+ return mpz_cmpabs_ui (u, v);
}
int
int
mpz_cmpabs_ui (const mpz_t u, unsigned long v)
{
- if (GMP_ABS (u->_mp_size) > 1)
+ mp_size_t un = GMP_ABS (u->_mp_size);
+
+ if (! mpn_absfits_ulong_p (u->_mp_d, un))
return 1;
else
- return GMP_CMP (mpz_get_ui (u), v);
+ {
+ unsigned long uu = mpz_get_ui (u);
+ return GMP_CMP(uu, v);
+ }
}
int
\f
/* MPZ addition and subtraction */
-/* Adds to the absolute value. Returns new size, but doesn't store it. */
-static mp_size_t
-mpz_abs_add_ui (mpz_t r, const mpz_t a, unsigned long b)
-{
- mp_size_t an;
- mp_ptr rp;
- mp_limb_t cy;
-
- an = GMP_ABS (a->_mp_size);
- if (an == 0)
- {
- MPZ_REALLOC (r, 1)[0] = b;
- return b > 0;
- }
-
- rp = MPZ_REALLOC (r, an + 1);
-
- cy = mpn_add_1 (rp, a->_mp_d, an, b);
- rp[an] = cy;
- an += cy;
-
- return an;
-}
-
-/* Subtract from the absolute value. Returns new size, (or -1 on underflow),
- but doesn't store it. */
-static mp_size_t
-mpz_abs_sub_ui (mpz_t r, const mpz_t a, unsigned long b)
-{
- mp_size_t an = GMP_ABS (a->_mp_size);
- mp_ptr rp;
-
- if (an == 0)
- {
- MPZ_REALLOC (r, 1)[0] = b;
- return -(b > 0);
- }
- rp = MPZ_REALLOC (r, an);
- if (an == 1 && a->_mp_d[0] < b)
- {
- rp[0] = b - a->_mp_d[0];
- return -1;
- }
- else
- {
- gmp_assert_nocarry (mpn_sub_1 (rp, a->_mp_d, an, b));
- return mpn_normalized_size (rp, an);
- }
-}
void
mpz_add_ui (mpz_t r, const mpz_t a, unsigned long b)
{
- if (a->_mp_size >= 0)
- r->_mp_size = mpz_abs_add_ui (r, a, b);
- else
- r->_mp_size = -mpz_abs_sub_ui (r, a, b);
+ mpz_t bb;
+ mpz_init_set_ui (bb, b);
+ mpz_add (r, a, bb);
+ mpz_clear (bb);
}
void
mpz_sub_ui (mpz_t r, const mpz_t a, unsigned long b)
{
- if (a->_mp_size < 0)
- r->_mp_size = -mpz_abs_add_ui (r, a, b);
- else
- r->_mp_size = mpz_abs_sub_ui (r, a, b);
+ mpz_ui_sub (r, b, a);
+ mpz_neg (r, r);
}
void
mpz_ui_sub (mpz_t r, unsigned long a, const mpz_t b)
{
- 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
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
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);
}
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);
}
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;
-
- 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;
+ unsigned long ret;
+ mpz_t rr, dd;
- 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);
-
- q->_mp_size = (ns < 0) ? - qn : qn;
- }
+ mpz_swap (r, rr);
+ mpz_clear (rr);
- return rl;
+ return ret;
}
unsigned long
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;
}
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;
if (s)
mpz_set_si (s, sign);
if (t)
- mpz_set_ui (t, 0);
+ t->_mp_size = 0;
return;
}
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 */
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
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 */
\f
/* 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)
if (mpz_cmpabs_ui (n, 31*31) < 0)
return 2;
- /* 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);
+ mpz_abs (nm1, n);
+ nm1->_mp_d[0] -= 1;
k = mpz_scan1 (nm1, 0);
mpz_tdiv_q_2exp (q, nm1, k);
- for (j = 0, is_prime = 1; is_prime & (j < reps); j++)
+ /* 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). */
+
+ for (j = 0; is_prime & (j < reps); j++)
{
mpz_set_ui (y, (unsigned long) j*j+j+41);
if (mpz_cmp (y, nm1) >= 0)
{
/* 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)
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
}
/* 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);
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);
}
projects / emacs.git / commitdiff