static cl_fixnum
count_bits(cl_object x)
{
cl_fixnum count;
switch (ecl_t_of(x)) {
case t_fixnum: {
cl_fixnum i = ecl_fixnum(x);
cl_fixnum j = (i < 0) ? ~i : i;
for (count=0 ; j ; j >>= 1)
if (j & 1) count++;
break;
}
case t_bignum:
if (_ecl_big_sign(x) >= 0)
count = mpz_popcount(x->big.big_num);
else {
cl_object z = _ecl_big_register0();
mpz_com(z->big.big_num, x->big.big_num);
count = mpz_popcount(z->big.big_num);
_ecl_big_register_free(z);
}
break;
default:
FEwrong_type_only_arg(ecl_make_fixnum(/*LOGCOUNT*/496), x, ecl_make_fixnum(/*INTEGER*/437));
}
return count;
}
static int
mpz_bitcount(__mpz_struct *x)
{
if (mpz_sgn(x) >= 0) {
return mpz_popcount(x);
} else {
object u = new_bignum();
mpz_com(MP(u),x);
return mpz_popcount(MP(u));
}
}
static Variant HHVM_FUNCTION(gmp_popcount,
const Variant& data) {
mpz_t gmpData;
if (!variantToGMPData(cs_GMP_FUNC_NAME_GMP_POPCOUNT, gmpData, data)) {
return false;
}
int64_t population = mpz_popcount(gmpData);
mpz_clear(gmpData);
return population;
}
static void d_pairing_pp_clear(pairing_pp_t p) {
// TODO: Better to store a sentinel value in p->data?
mpz_ptr q = p->pairing->r;
mp_bitcnt_t m = (mp_bitcnt_t)mpz_sizeinbase(q, 2) + mpz_popcount(q);
m = (m > 3 ? m - 3 : 0);
mp_bitcnt_t i;
pp_coeff_t *coeff = (pp_coeff_t *) p->data;
pp_coeff_ptr pp;
for (i=0; i<m; i++) {
pp = coeff[i];
element_clear(pp->a);
element_clear(pp->b);
element_clear(pp->c);
}
pbc_free(p->data);
}
static PyObject *
GMPy_MPZ_popcount(PyObject *self, PyObject *other)
{
mp_bitcnt_t n;
MPZ_Object *tempx;
if ((tempx = GMPy_MPZ_From_Integer(other, NULL))) {
n = mpz_popcount(tempx->z);
Py_DECREF((PyObject*)tempx);
if (n == (mp_bitcnt_t)(-1))
return PyLong_FromLong(-1);
else
return PyIntOrLong_FromMpBitCnt(n);
}
else {
TYPE_ERROR("popcount() requires 'mpz' argument");
return NULL;
}
}
void
check_data (void)
{
static const struct {
const char *n;
unsigned long want;
} data[] = {
{ "-1", ~ (unsigned long) 0 },
{ "-12345678", ~ (unsigned long) 0 },
{ "0", 0 },
{ "1", 1 },
{ "3", 2 },
{ "5", 2 },
{ "0xFFFF", 16 },
{ "0xFFFFFFFF", 32 },
{ "0xFFFFFFFFFFFFFFFF", 64 },
{ "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", 128 },
};
unsigned long got;
int i;
mpz_t n;
mpz_init (n);
for (i = 0; i < numberof (data); i++)
{
mpz_set_str_or_abort (n, data[i].n, 0);
got = mpz_popcount (n);
if (got != data[i].want)
{
printf ("mpz_popcount wrong at data[%d]\n", i);
printf (" n \"%s\"\n", data[i].n);
printf (" "); mpz_out_str (stdout, 10, n); printf ("\n");
printf (" 0x"); mpz_out_str (stdout, 16, n); printf ("\n");
printf (" got %lu\n", got);
printf (" want %lu\n", data[i].want);
abort ();
}
}
mpz_clear (n);
}
void
check_random (void)
{
gmp_randstate_t rands;
mpz_t bs;
mpz_t arg;
unsigned long arg_size, size_range;
unsigned long got, ref;
int i;
gmp_randinit_default(rands);
mpz_init (bs);
mpz_init (arg);
for (i = 0; i < 10000; i++)
{
mpz_urandomb (bs, rands, 32);
size_range = mpz_get_ui (bs) % 11 + 2; /* 0..4096 bit operands */
mpz_urandomb (bs, rands, size_range);
arg_size = mpz_get_ui (bs);
mpz_rrandomb (arg, rands, arg_size);
got = mpz_popcount (arg);
ref = refmpz_popcount (arg);
if (got != ref)
{
printf ("mpz_popcount wrong on random\n");
printf (" "); mpz_out_str (stdout, 10, arg); printf ("\n");
printf (" 0x"); mpz_out_str (stdout, 16, arg); printf ("\n");
printf (" got %lu\n", got);
printf (" want %lu\n", ref);
abort();
abort ();
}
}
mpz_clear (arg);
mpz_clear (bs);
gmp_randclear(rands);
}
void
check_onebit (void)
{
mpz_t n;
unsigned long i, got;
mpz_init (n);
for (i = 0; i < 5 * GMP_LIMB_BITS; i++)
{
mpz_setbit (n, i);
got = mpz_popcount (n);
if (got != 1)
{
printf ("mpz_popcount wrong on single bit at %lu\n", i);
printf (" got %lu, want 1\n", got);
abort();
}
mpz_clrbit (n, i);
}
mpz_clear (n);
}
void
generate_sq_res_0x100 (int limb_bits)
{
int i, res;
nsq_res_0x100 = (0x100 + limb_bits - 1) / limb_bits;
sq_res_0x100 = xmalloc (nsq_res_0x100 * sizeof (*sq_res_0x100));
for (i = 0; i < nsq_res_0x100; i++)
mpz_init_set_ui (sq_res_0x100[i], 0L);
for (i = 0; i < 0x100; i++)
{
res = (i * i) % 0x100;
mpz_setbit (sq_res_0x100[res / limb_bits],
(unsigned long) (res % limb_bits));
}
sq_res_0x100_num = 0;
for (i = 0; i < nsq_res_0x100; i++)
sq_res_0x100_num += mpz_popcount (sq_res_0x100[i]);
sq_res_0x100_fraction = (double) sq_res_0x100_num / 256.0;
}
int GMPISCount(iset_t s)
{
return (mpz_popcount(*s));
}
/* returns 0 on success */
int
gen_consts (int numb, int nail, int limb)
{
mpz_t x, mask, y, last;
unsigned long a, b;
unsigned long ofl, ofe;
printf ("/* This file is automatically generated by gen-fac.c */\n\n");
printf ("#if GMP_NUMB_BITS != %d\n", numb);
printf ("Error , error this data is for %d GMP_NUMB_BITS only\n", numb);
printf ("#endif\n");
#if 0
printf ("#if GMP_LIMB_BITS != %d\n", limb);
printf ("Error , error this data is for %d GMP_LIMB_BITS only\n", limb);
printf ("#endif\n");
#endif
printf
("/* This table is 0!,1!,2!,3!,...,n! where n! has <= GMP_NUMB_BITS bits */\n");
printf
("#define ONE_LIMB_FACTORIAL_TABLE CNST_LIMB(0x1),CNST_LIMB(0x1");
mpz_init_set_ui (x, 1);
mpz_init (last);
for (b = 2;; b++)
{
mpz_mul_ui (x, x, b); /* so b!=a */
if (mpz_sizeinbase (x, 2) > numb)
break;
printf ("),CNST_LIMB(0x");
mpz_out_str (stdout, 16, x);
}
printf (")\n");
printf
("\n/* This table is 0!,1!,2!/2,3!/2,...,n!/2^sn where n!/2^sn is an */\n");
printf
("/* odd integer for each n, and n!/2^sn has <= GMP_NUMB_BITS bits */\n");
printf
("#define ONE_LIMB_ODD_FACTORIAL_TABLE CNST_LIMB(0x1),CNST_LIMB(0x1),CNST_LIMB(0x1");
mpz_set_ui (x, 1);
for (b = 3;; b++)
{
for (a = b; (a & 1) == 0; a >>= 1);
mpz_swap (last, x);
mpz_mul_ui (x, last, a);
if (mpz_sizeinbase (x, 2) > numb)
break;
printf ("),CNST_LIMB(0x");
mpz_out_str (stdout, 16, x);
}
printf (")\n");
printf
("#define ODD_FACTORIAL_TABLE_MAX CNST_LIMB(0x");
mpz_out_str (stdout, 16, last);
printf (")\n");
ofl = b - 1;
printf
("#define ODD_FACTORIAL_TABLE_LIMIT (%lu)\n", ofl);
mpz_init2 (mask, numb + 1);
mpz_setbit (mask, numb);
mpz_sub_ui (mask, mask, 1);
printf
("\n/* Previous table, continued, values modulo 2^GMP_NUMB_BITS */\n");
printf
("#define ONE_LIMB_ODD_FACTORIAL_EXTTABLE CNST_LIMB(0x");
mpz_and (x, x, mask);
mpz_out_str (stdout, 16, x);
mpz_init (y);
mpz_bin_uiui (y, b, b/2);
b++;
for (;; b++)
{
for (a = b; (a & 1) == 0; a >>= 1);
if (a == b) {
mpz_divexact_ui (y, y, a/2+1);
mpz_mul_ui (y, y, a);
} else
mpz_mul_2exp (y, y, 1);
if (mpz_sizeinbase (y, 2) > numb)
break;
mpz_mul_ui (x, x, a);
mpz_and (x, x, mask);
printf ("),CNST_LIMB(0x");
mpz_out_str (stdout, 16, x);
}
printf (")\n");
ofe = b - 1;
printf
("#define ODD_FACTORIAL_EXTTABLE_LIMIT (%lu)\n", ofe);
printf
("\n/* This table is 1!!,3!!,...,(2n+1)!! where (2n+1)!! has <= GMP_NUMB_BITS bits */\n");
printf
("#define ONE_LIMB_ODD_DOUBLEFACTORIAL_TABLE CNST_LIMB(0x1");
mpz_set_ui (x, 1);
for (b = 3;; b+=2)
{
mpz_swap (last, x);
mpz_mul_ui (x, last, b);
if (mpz_sizeinbase (x, 2) > numb)
break;
printf ("),CNST_LIMB(0x");
mpz_out_str (stdout, 16, x);
}
printf (")\n");
printf
("#define ODD_DOUBLEFACTORIAL_TABLE_MAX CNST_LIMB(0x");
mpz_out_str (stdout, 16, last);
printf (")\n");
printf
("#define ODD_DOUBLEFACTORIAL_TABLE_LIMIT (%lu)\n", b - 2);
printf
("\n/* This table x_1, x_2,... contains values s.t. x_n^n has <= GMP_NUMB_BITS bits */\n");
printf
("#define NTH_ROOT_NUMB_MASK_TABLE (GMP_NUMB_MASK");
for (b = 2;b <= 8; b++)
{
mpz_root (x, mask, b);
printf ("),CNST_LIMB(0x");
mpz_out_str (stdout, 16, x);
}
printf (")\n");
mpz_add_ui (mask, mask, 1);
printf
("\n/* This table contains inverses of odd factorials, modulo 2^GMP_NUMB_BITS */\n");
printf
("\n/* It begins with (2!/2)^-1=1 */\n");
printf
("#define ONE_LIMB_ODD_FACTORIAL_INVERSES_TABLE CNST_LIMB(0x1");
mpz_set_ui (x, 1);
for (b = 3;b <= ofe - 2; b++)
{
for (a = b; (a & 1) == 0; a >>= 1);
mpz_mul_ui (x, x, a);
mpz_invert (y, x, mask);
printf ("),CNST_LIMB(0x");
mpz_out_str (stdout, 16, y);
}
printf (")\n");
ofe = (ofe / 16 + 1) * 16;
printf
("\n/* This table contains 2n-popc(2n) for small n */\n");
printf
("\n/* It begins with 2-1=1 (n=1) */\n");
printf
("#define TABLE_2N_MINUS_POPC_2N 1");
for (b = 4; b <= ofe; b += 2)
{
mpz_set_ui (x, b);
printf (",%lu",b - mpz_popcount (x));
}
printf ("\n");
printf
("#define TABLE_LIMIT_2N_MINUS_POPC_2N %lu\n", ofe + 1);
ofl = (ofl + 1) / 2;
printf
("#define ODD_CENTRAL_BINOMIAL_OFFSET (%lu)\n", ofl);
printf
("\n/* This table contains binomial(2k,k)/2^t */\n");
printf
("\n/* It begins with ODD_CENTRAL_BINOMIAL_TABLE_MIN */\n");
printf
("#define ONE_LIMB_ODD_CENTRAL_BINOMIAL_TABLE ");
for (b = ofl;; b++)
{
mpz_bin_uiui (x, 2 * b, b);
mpz_remove_twos (x);
if (mpz_sizeinbase (x, 2) > numb)
break;
if (b != ofl)
printf ("),");
printf("CNST_LIMB(0x");
mpz_out_str (stdout, 16, x);
}
printf (")\n");
ofe = b - 1;
printf
("#define ODD_CENTRAL_BINOMIAL_TABLE_LIMIT (%lu)\n", ofe);
printf
("\n/* This table contains the inverses of elements in the previous table. */\n");
printf
("#define ONE_LIMB_ODD_CENTRAL_BINOMIAL_INVERSE_TABLE CNST_LIMB(0x");
for (b = ofl; b <= ofe; b++)
{
mpz_bin_uiui (x, 2 * b, b);
mpz_remove_twos (x);
mpz_invert (x, x, mask);
mpz_out_str (stdout, 16, x);
if (b != ofe)
printf ("),CNST_LIMB(0x");
}
printf (")\n");
printf
("\n/* This table contains the values t in the formula binomial(2k,k)/2^t */\n");
printf
("#define CENTRAL_BINOMIAL_2FAC_TABLE ");
for (b = ofl; b <= ofe; b++)
{
mpz_bin_uiui (x, 2 * b, b);
printf ("%d", mpz_remove_twos (x));
if (b != ofe)
printf (",");
}
printf ("\n");
return 0;
}
/* Evaluate the expression E and put the result in R. */
void
mpz_eval_expr (mpz_ptr r, expr_t e)
{
mpz_t lhs, rhs;
switch (e->op)
{
case LIT:
mpz_set (r, e->operands.val);
return;
case PLUS:
mpz_init (lhs); mpz_init (rhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
mpz_eval_expr (rhs, e->operands.ops.rhs);
mpz_add (r, lhs, rhs);
mpz_clear (lhs); mpz_clear (rhs);
return;
case MINUS:
mpz_init (lhs); mpz_init (rhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
mpz_eval_expr (rhs, e->operands.ops.rhs);
mpz_sub (r, lhs, rhs);
mpz_clear (lhs); mpz_clear (rhs);
return;
case MULT:
mpz_init (lhs); mpz_init (rhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
mpz_eval_expr (rhs, e->operands.ops.rhs);
mpz_mul (r, lhs, rhs);
mpz_clear (lhs); mpz_clear (rhs);
return;
case DIV:
mpz_init (lhs); mpz_init (rhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
mpz_eval_expr (rhs, e->operands.ops.rhs);
mpz_fdiv_q (r, lhs, rhs);
mpz_clear (lhs); mpz_clear (rhs);
return;
case MOD:
mpz_init (rhs);
mpz_eval_expr (rhs, e->operands.ops.rhs);
mpz_abs (rhs, rhs);
mpz_eval_mod_expr (r, e->operands.ops.lhs, rhs);
mpz_clear (rhs);
return;
case REM:
/* Check if lhs operand is POW expression and optimize for that case. */
if (e->operands.ops.lhs->op == POW)
{
mpz_t powlhs, powrhs;
mpz_init (powlhs);
mpz_init (powrhs);
mpz_init (rhs);
mpz_eval_expr (powlhs, e->operands.ops.lhs->operands.ops.lhs);
mpz_eval_expr (powrhs, e->operands.ops.lhs->operands.ops.rhs);
mpz_eval_expr (rhs, e->operands.ops.rhs);
mpz_powm (r, powlhs, powrhs, rhs);
if (mpz_cmp_si (rhs, 0L) < 0)
mpz_neg (r, r);
mpz_clear (powlhs);
mpz_clear (powrhs);
mpz_clear (rhs);
return;
}
mpz_init (lhs); mpz_init (rhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
mpz_eval_expr (rhs, e->operands.ops.rhs);
mpz_fdiv_r (r, lhs, rhs);
mpz_clear (lhs); mpz_clear (rhs);
return;
#if __GNU_MP_VERSION >= 2
case INVMOD:
mpz_init (lhs); mpz_init (rhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
mpz_eval_expr (rhs, e->operands.ops.rhs);
mpz_invert (r, lhs, rhs);
mpz_clear (lhs); mpz_clear (rhs);
return;
#endif
case POW:
mpz_init (lhs); mpz_init (rhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
if (mpz_cmpabs_ui (lhs, 1) <= 0)
{
/* For 0^rhs and 1^rhs, we just need to verify that
rhs is well-defined. For (-1)^rhs we need to
determine (rhs mod 2). For simplicity, compute
(rhs mod 2) for all three cases. */
expr_t two, et;
two = malloc (sizeof (struct expr));
two -> op = LIT;
mpz_init_set_ui (two->operands.val, 2L);
makeexp (&et, MOD, e->operands.ops.rhs, two);
e->operands.ops.rhs = et;
}
mpz_eval_expr (rhs, e->operands.ops.rhs);
if (mpz_cmp_si (rhs, 0L) == 0)
/* x^0 is 1 */
mpz_set_ui (r, 1L);
else if (mpz_cmp_si (lhs, 0L) == 0)
/* 0^y (where y != 0) is 0 */
mpz_set_ui (r, 0L);
else if (mpz_cmp_ui (lhs, 1L) == 0)
/* 1^y is 1 */
mpz_set_ui (r, 1L);
else if (mpz_cmp_si (lhs, -1L) == 0)
/* (-1)^y just depends on whether y is even or odd */
mpz_set_si (r, (mpz_get_ui (rhs) & 1) ? -1L : 1L);
else if (mpz_cmp_si (rhs, 0L) < 0)
/* x^(-n) is 0 */
mpz_set_ui (r, 0L);
else
{
unsigned long int cnt;
unsigned long int y;
/* error if exponent does not fit into an unsigned long int. */
if (mpz_cmp_ui (rhs, ~(unsigned long int) 0) > 0)
goto pow_err;
y = mpz_get_ui (rhs);
/* x^y == (x/(2^c))^y * 2^(c*y) */
#if __GNU_MP_VERSION >= 2
cnt = mpz_scan1 (lhs, 0);
#else
cnt = 0;
#endif
if (cnt != 0)
{
if (y * cnt / cnt != y)
goto pow_err;
mpz_tdiv_q_2exp (lhs, lhs, cnt);
mpz_pow_ui (r, lhs, y);
mpz_mul_2exp (r, r, y * cnt);
}
else
mpz_pow_ui (r, lhs, y);
}
mpz_clear (lhs); mpz_clear (rhs);
return;
pow_err:
error = "result of `pow' operator too large";
mpz_clear (lhs); mpz_clear (rhs);
longjmp (errjmpbuf, 1);
case GCD:
mpz_init (lhs); mpz_init (rhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
mpz_eval_expr (rhs, e->operands.ops.rhs);
mpz_gcd (r, lhs, rhs);
mpz_clear (lhs); mpz_clear (rhs);
return;
#if __GNU_MP_VERSION > 2 || __GNU_MP_VERSION_MINOR >= 1
case LCM:
mpz_init (lhs); mpz_init (rhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
mpz_eval_expr (rhs, e->operands.ops.rhs);
mpz_lcm (r, lhs, rhs);
mpz_clear (lhs); mpz_clear (rhs);
return;
#endif
case AND:
mpz_init (lhs); mpz_init (rhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
mpz_eval_expr (rhs, e->operands.ops.rhs);
mpz_and (r, lhs, rhs);
mpz_clear (lhs); mpz_clear (rhs);
return;
case IOR:
mpz_init (lhs); mpz_init (rhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
mpz_eval_expr (rhs, e->operands.ops.rhs);
mpz_ior (r, lhs, rhs);
mpz_clear (lhs); mpz_clear (rhs);
return;
#if __GNU_MP_VERSION > 2 || __GNU_MP_VERSION_MINOR >= 1
case XOR:
mpz_init (lhs); mpz_init (rhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
mpz_eval_expr (rhs, e->operands.ops.rhs);
mpz_xor (r, lhs, rhs);
mpz_clear (lhs); mpz_clear (rhs);
return;
#endif
case NEG:
mpz_eval_expr (r, e->operands.ops.lhs);
mpz_neg (r, r);
return;
case NOT:
mpz_eval_expr (r, e->operands.ops.lhs);
mpz_com (r, r);
return;
case SQRT:
mpz_init (lhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
if (mpz_sgn (lhs) < 0)
{
error = "cannot take square root of negative numbers";
mpz_clear (lhs);
longjmp (errjmpbuf, 1);
}
mpz_sqrt (r, lhs);
return;
#if __GNU_MP_VERSION > 2 || __GNU_MP_VERSION_MINOR >= 1
case ROOT:
mpz_init (lhs); mpz_init (rhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
mpz_eval_expr (rhs, e->operands.ops.rhs);
if (mpz_sgn (rhs) <= 0)
{
error = "cannot take non-positive root orders";
mpz_clear (lhs); mpz_clear (rhs);
longjmp (errjmpbuf, 1);
}
if (mpz_sgn (lhs) < 0 && (mpz_get_ui (rhs) & 1) == 0)
{
error = "cannot take even root orders of negative numbers";
mpz_clear (lhs); mpz_clear (rhs);
longjmp (errjmpbuf, 1);
}
{
unsigned long int nth = mpz_get_ui (rhs);
if (mpz_cmp_ui (rhs, ~(unsigned long int) 0) > 0)
{
/* If we are asked to take an awfully large root order, cheat and
ask for the largest order we can pass to mpz_root. This saves
some error prone special cases. */
nth = ~(unsigned long int) 0;
}
mpz_root (r, lhs, nth);
}
mpz_clear (lhs); mpz_clear (rhs);
return;
#endif
case FAC:
mpz_eval_expr (r, e->operands.ops.lhs);
if (mpz_size (r) > 1)
{
error = "result of `!' operator too large";
longjmp (errjmpbuf, 1);
}
mpz_fac_ui (r, mpz_get_ui (r));
return;
#if __GNU_MP_VERSION >= 2
case POPCNT:
mpz_eval_expr (r, e->operands.ops.lhs);
{ long int cnt;
cnt = mpz_popcount (r);
mpz_set_si (r, cnt);
}
return;
case HAMDIST:
{ long int cnt;
mpz_init (lhs); mpz_init (rhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
mpz_eval_expr (rhs, e->operands.ops.rhs);
cnt = mpz_hamdist (lhs, rhs);
mpz_clear (lhs); mpz_clear (rhs);
mpz_set_si (r, cnt);
}
return;
#endif
case LOG2:
mpz_eval_expr (r, e->operands.ops.lhs);
{ unsigned long int cnt;
if (mpz_sgn (r) <= 0)
{
error = "logarithm of non-positive number";
longjmp (errjmpbuf, 1);
}
cnt = mpz_sizeinbase (r, 2);
mpz_set_ui (r, cnt - 1);
}
return;
case LOG:
{ unsigned long int cnt;
mpz_init (lhs); mpz_init (rhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
mpz_eval_expr (rhs, e->operands.ops.rhs);
if (mpz_sgn (lhs) <= 0)
{
error = "logarithm of non-positive number";
mpz_clear (lhs); mpz_clear (rhs);
longjmp (errjmpbuf, 1);
}
if (mpz_cmp_ui (rhs, 256) >= 0)
{
error = "logarithm base too large";
mpz_clear (lhs); mpz_clear (rhs);
longjmp (errjmpbuf, 1);
}
cnt = mpz_sizeinbase (lhs, mpz_get_ui (rhs));
mpz_set_ui (r, cnt - 1);
mpz_clear (lhs); mpz_clear (rhs);
}
return;
case FERMAT:
{
unsigned long int t;
mpz_init (lhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
t = (unsigned long int) 1 << mpz_get_ui (lhs);
if (mpz_cmp_ui (lhs, ~(unsigned long int) 0) > 0 || t == 0)
{
error = "too large Mersenne number index";
mpz_clear (lhs);
longjmp (errjmpbuf, 1);
}
mpz_set_ui (r, 1);
mpz_mul_2exp (r, r, t);
mpz_add_ui (r, r, 1);
mpz_clear (lhs);
}
return;
case MERSENNE:
mpz_init (lhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
if (mpz_cmp_ui (lhs, ~(unsigned long int) 0) > 0)
{
error = "too large Mersenne number index";
mpz_clear (lhs);
longjmp (errjmpbuf, 1);
}
mpz_set_ui (r, 1);
mpz_mul_2exp (r, r, mpz_get_ui (lhs));
mpz_sub_ui (r, r, 1);
mpz_clear (lhs);
return;
case FIBONACCI:
{ mpz_t t;
unsigned long int n, i;
mpz_init (lhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
if (mpz_sgn (lhs) <= 0 || mpz_cmp_si (lhs, 1000000000) > 0)
{
error = "Fibonacci index out of range";
mpz_clear (lhs);
longjmp (errjmpbuf, 1);
}
n = mpz_get_ui (lhs);
mpz_clear (lhs);
#if __GNU_MP_VERSION > 2 || __GNU_MP_VERSION_MINOR >= 1
mpz_fib_ui (r, n);
#else
mpz_init_set_ui (t, 1);
mpz_set_ui (r, 1);
if (n <= 2)
mpz_set_ui (r, 1);
else
{
for (i = 3; i <= n; i++)
{
mpz_add (t, t, r);
mpz_swap (t, r);
}
}
mpz_clear (t);
#endif
}
return;
case RANDOM:
{
unsigned long int n;
mpz_init (lhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
if (mpz_sgn (lhs) <= 0 || mpz_cmp_si (lhs, 1000000000) > 0)
{
error = "random number size out of range";
mpz_clear (lhs);
longjmp (errjmpbuf, 1);
}
n = mpz_get_ui (lhs);
mpz_clear (lhs);
mpz_urandomb (r, rstate, n);
}
return;
case NEXTPRIME:
{
mpz_eval_expr (r, e->operands.ops.lhs);
mpz_nextprime (r, r);
}
return;
case BINOM:
mpz_init (lhs); mpz_init (rhs);
mpz_eval_expr (lhs, e->operands.ops.lhs);
mpz_eval_expr (rhs, e->operands.ops.rhs);
{
unsigned long int k;
if (mpz_cmp_ui (rhs, ~(unsigned long int) 0) > 0)
{
error = "k too large in (n over k) expression";
mpz_clear (lhs); mpz_clear (rhs);
longjmp (errjmpbuf, 1);
}
k = mpz_get_ui (rhs);
mpz_bin_ui (r, lhs, k);
}
mpz_clear (lhs); mpz_clear (rhs);
return;
case TIMING:
{
int t0;
t0 = cputime ();
mpz_eval_expr (r, e->operands.ops.lhs);
printf ("time: %d\n", cputime () - t0);
}
return;
default:
abort ();
}
}
void
generate_mod (int limb_bits, int nail_bits)
{
int numb_bits = limb_bits - nail_bits;
int i, divisor;
mpz_init_set_ui (pp, 0L);
mpz_init_set_ui (pp_norm, 0L);
mpz_init_set_ui (pp_inverted, 0L);
/* no more than limb_bits many factors in a one limb modulus (and of
course in reality nothing like that many) */
factor_alloc = limb_bits;
factor = xmalloc (factor_alloc * sizeof (*factor));
rawfactor = xmalloc (factor_alloc * sizeof (*rawfactor));
if (numb_bits % 4 != 0)
{
strcpy (mod34_excuse, "GMP_NUMB_BITS % 4 != 0");
goto use_pp;
}
max_divisor = 2*limb_bits;
max_divisor_bits = log2_ceil (max_divisor);
if (numb_bits / 4 < max_divisor_bits)
{
/* Wind back to one limb worth of max_divisor, if that will let us use
mpn_mod_34lsub1. */
max_divisor = limb_bits;
max_divisor_bits = log2_ceil (max_divisor);
if (numb_bits / 4 < max_divisor_bits)
{
strcpy (mod34_excuse, "GMP_NUMB_BITS / 4 too small");
goto use_pp;
}
}
{
/* Can use mpn_mod_34lsub1, find small factors of 2^mod34_bits-1. */
mpz_t m, q, r;
int multiplicity;
mod34_bits = (numb_bits / 4) * 3;
/* mpn_mod_34lsub1 returns a full limb value, PERFSQR_MOD_34 folds it at
the mod34_bits mark, adding the two halves for a remainder of at most
mod34_bits+1 many bits */
mod_bits = mod34_bits + 1;
mpz_init_set_ui (m, 1L);
mpz_mul_2exp (m, m, mod34_bits);
mpz_sub_ui (m, m, 1L);
mpz_init (q);
mpz_init (r);
for (i = 3; i <= max_divisor; i++)
{
if (! isprime (i))
continue;
mpz_tdiv_qr_ui (q, r, m, (unsigned long) i);
if (mpz_sgn (r) != 0)
continue;
/* if a repeated prime is found it's used as an i^n in one factor */
divisor = 1;
multiplicity = 0;
do
{
if (divisor > max_divisor / i)
break;
multiplicity++;
mpz_set (m, q);
mpz_tdiv_qr_ui (q, r, m, (unsigned long) i);
}
while (mpz_sgn (r) == 0);
assert (nrawfactor < factor_alloc);
rawfactor[nrawfactor].divisor = i;
rawfactor[nrawfactor].multiplicity = multiplicity;
nrawfactor++;
}
mpz_clear (m);
mpz_clear (q);
mpz_clear (r);
}
if (nrawfactor <= 2)
{
mpz_t new_pp;
sprintf (mod34_excuse, "only %d small factor%s",
nrawfactor, nrawfactor == 1 ? "" : "s");
use_pp:
/* reset to two limbs of max_divisor, in case the mpn_mod_34lsub1 code
tried with just one */
max_divisor = 2*limb_bits;
max_divisor_bits = log2_ceil (max_divisor);
mpz_init (new_pp);
nrawfactor = 0;
mod_bits = MIN (numb_bits, limb_bits - max_divisor_bits);
/* one copy of each small prime */
mpz_set_ui (pp, 1L);
for (i = 3; i <= max_divisor; i++)
{
if (! isprime (i))
continue;
mpz_mul_ui (new_pp, pp, (unsigned long) i);
if (mpz_sizeinbase (new_pp, 2) > mod_bits)
break;
mpz_set (pp, new_pp);
assert (nrawfactor < factor_alloc);
rawfactor[nrawfactor].divisor = i;
rawfactor[nrawfactor].multiplicity = 1;
nrawfactor++;
}
/* Plus an extra copy of one or more of the primes selected, if that
still fits in max_divisor and the total in mod_bits. Usually only
3 or 5 will be candidates */
for (i = nrawfactor-1; i >= 0; i--)
{
if (rawfactor[i].divisor > max_divisor / rawfactor[i].divisor)
continue;
mpz_mul_ui (new_pp, pp, (unsigned long) rawfactor[i].divisor);
if (mpz_sizeinbase (new_pp, 2) > mod_bits)
continue;
mpz_set (pp, new_pp);
rawfactor[i].multiplicity++;
}
mod_bits = mpz_sizeinbase (pp, 2);
mpz_set (pp_norm, pp);
while (mpz_sizeinbase (pp_norm, 2) < numb_bits)
mpz_add (pp_norm, pp_norm, pp_norm);
mpz_preinv_invert (pp_inverted, pp_norm, numb_bits);
mpz_clear (new_pp);
}
/* start the factor array */
for (i = 0; i < nrawfactor; i++)
{
int j;
assert (nfactor < factor_alloc);
factor[nfactor].divisor = 1;
for (j = 0; j < rawfactor[i].multiplicity; j++)
factor[nfactor].divisor *= rawfactor[i].divisor;
nfactor++;
}
combine:
/* Combine entries in the factor array. Combine the smallest entry with
the biggest one that will fit with it (ie. under max_divisor), then
repeat that with the new smallest entry. */
qsort (factor, nfactor, sizeof (factor[0]), f_cmp_divisor);
for (i = nfactor-1; i >= 1; i--)
{
if (factor[i].divisor <= max_divisor / factor[0].divisor)
{
factor[0].divisor *= factor[i].divisor;
COLLAPSE_ELEMENT (factor, i, nfactor);
goto combine;
}
}
total_fraction = 1.0;
for (i = 0; i < nfactor; i++)
{
mpz_init (factor[i].inverse);
mpz_invert_ui_2exp (factor[i].inverse,
(unsigned long) factor[i].divisor,
(unsigned long) mod_bits);
mpz_init (factor[i].mask);
square_mask (factor[i].mask, factor[i].divisor);
/* fraction of possible squares */
factor[i].fraction = (double) mpz_popcount (factor[i].mask)
/ factor[i].divisor;
/* total fraction of possible squares */
total_fraction *= factor[i].fraction;
}
/* best tests first (ie. smallest fraction) */
qsort (factor, nfactor, sizeof (factor[0]), f_cmp_fraction);
}
inline int Solver::popcount(BIGINT x){
return (int)mpz_popcount(x.get_mpz_t());
}
static void
e_mpz_popcount (mpz_ptr w, mpz_srcptr x)
{
mpz_set_ui (w, mpz_popcount (x));
}
