void
check_random ()
{
gmp_randstate_ptr rands;
mpz_t bs;
unsigned long arg_size, size_range;
mpq_t q, r;
int i;
mp_bitcnt_t shift;
int reps = 10000;
rands = RANDS;
mpz_init (bs);
mpq_init (q);
mpq_init (r);
for (i = 0; i < reps; 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 (mpq_numref (q), rands, arg_size);
do
{
mpz_urandomb (bs, rands, size_range);
arg_size = mpz_get_ui (bs);
mpz_rrandomb (mpq_denref (q), rands, arg_size);
}
while (mpz_sgn (mpq_denref (q)) == 0);
/* We now have a random rational in q, albeit an unnormalised one. The
lack of normalisation should not matter here, so let's save the time a
gcd would require. */
mpz_urandomb (bs, rands, 32);
shift = mpz_get_ui (bs) % 4096;
mpq_mul_2exp (r, q, shift);
if (mpq_cmp (r, q) < 0)
{
printf ("mpq_mul_2exp wrong on random\n");
abort ();
}
mpq_div_2exp (r, r, shift);
if (mpq_cmp (r, q) != 0)
{
printf ("mpq_mul_2exp or mpq_div_2exp wrong on random\n");
abort ();
}
}
mpq_clear (q);
mpq_clear (r);
mpz_clear (bs);
}
/* Check various values 2^n and 1/2^n. */
void
check_onebit (void)
{
static const long data[] = {
-3*GMP_NUMB_BITS-1, -3*GMP_NUMB_BITS, -3*GMP_NUMB_BITS+1,
-2*GMP_NUMB_BITS-1, -2*GMP_NUMB_BITS, -2*GMP_NUMB_BITS+1,
-GMP_NUMB_BITS-1, -GMP_NUMB_BITS, -GMP_NUMB_BITS+1,
-5, -2, -1, 0, 1, 2, 5,
GMP_NUMB_BITS-1, GMP_NUMB_BITS, GMP_NUMB_BITS+1,
2*GMP_NUMB_BITS-1, 2*GMP_NUMB_BITS, 2*GMP_NUMB_BITS+1,
3*GMP_NUMB_BITS-1, 3*GMP_NUMB_BITS, 3*GMP_NUMB_BITS+1,
};
int i, neg;
long exp, l;
mpq_t q;
double got, want;
mpq_init (q);
for (i = 0; i < numberof (data); i++)
{
exp = data[i];
mpq_set_ui (q, 1L, 1L);
if (exp >= 0)
mpq_mul_2exp (q, q, exp);
else
mpq_div_2exp (q, q, -exp);
want = 1.0;
for (l = 0; l < exp; l++)
want *= 2.0;
for (l = 0; l > exp; l--)
want /= 2.0;
for (neg = 0; neg <= 1; neg++)
{
if (neg)
{
mpq_neg (q, q);
want = -want;
}
got = mpq_get_d (q);
if (got != want)
{
printf ("mpq_get_d wrong on %s2**%ld\n", neg ? "-" : "", exp);
mpq_trace (" q ", q);
d_trace (" want ", want);
d_trace (" got ", got);
abort();
}
}
}
mpq_clear (q);
}
/* put in rop the value of exp(2*i*pi*k/n) rounded according to rnd */
int
mpc_rootofunity (mpc_ptr rop, unsigned long n, unsigned long k, mpc_rnd_t rnd)
{
unsigned long g;
mpq_t kn;
mpfr_t t, s, c;
mpfr_prec_t prec;
int inex_re, inex_im;
mpfr_rnd_t rnd_re, rnd_im;
if (n == 0) {
/* Compute exp (0 + i*inf). */
mpfr_set_nan (mpc_realref (rop));
mpfr_set_nan (mpc_imagref (rop));
return MPC_INEX (0, 0);
}
/* Eliminate common denominator. */
k %= n;
g = gcd (k, n);
k /= g;
n /= g;
/* Now 0 <= k < n and gcd(k,n)=1. */
/* We assume that only n=1, 2, 3, 4, 6 and 12 may yield exact results
and treat them separately; n=8 is also treated here for efficiency
reasons. */
if (n == 1)
{
/* necessarily k=0 thus we want exp(0)=1 */
MPC_ASSERT (k == 0);
return mpc_set_ui_ui (rop, 1, 0, rnd);
}
else if (n == 2)
{
/* since gcd(k,n)=1, necessarily k=1, thus we want exp(i*pi)=-1 */
MPC_ASSERT (k == 1);
return mpc_set_si_si (rop, -1, 0, rnd);
}
else if (n == 4)
{
/* since gcd(k,n)=1, necessarily k=1 or k=3, thus we want
exp(2*i*pi/4)=i or exp(2*i*pi*3/4)=-i */
MPC_ASSERT (k == 1 || k == 3);
if (k == 1)
return mpc_set_ui_ui (rop, 0, 1, rnd);
else
return mpc_set_si_si (rop, 0, -1, rnd);
}
else if (n == 3 || n == 6)
{
MPC_ASSERT ((n == 3 && (k == 1 || k == 2)) ||
(n == 6 && (k == 1 || k == 5)));
/* for n=3, necessarily k=1 or k=2: -1/2+/-1/2*sqrt(3)*i;
for n=6, necessarily k=1 or k=5: 1/2+/-1/2*sqrt(3)*i */
inex_re = mpfr_set_si (mpc_realref (rop), (n == 3 ? -1 : 1),
MPC_RND_RE (rnd));
/* inverse the rounding mode for -sqrt(3)/2 for zeta_3^2 and zeta_6^5 */
rnd_im = MPC_RND_IM (rnd);
if (k != 1)
rnd_im = INV_RND (rnd_im);
inex_im = mpfr_sqrt_ui (mpc_imagref (rop), 3, rnd_im);
mpc_div_2ui (rop, rop, 1, MPC_RNDNN);
if (k != 1)
{
mpfr_neg (mpc_imagref (rop), mpc_imagref (rop), MPFR_RNDN);
inex_im = -inex_im;
}
return MPC_INEX (inex_re, inex_im);
}
else if (n == 12)
{
/* necessarily k=1, 5, 7, 11:
k=1: 1/2*sqrt(3) + 1/2*I
k=5: -1/2*sqrt(3) + 1/2*I
k=7: -1/2*sqrt(3) - 1/2*I
k=11: 1/2*sqrt(3) - 1/2*I */
MPC_ASSERT (k == 1 || k == 5 || k == 7 || k == 11);
/* inverse the rounding mode for -sqrt(3)/2 for zeta_12^5 and zeta_12^7 */
rnd_re = MPC_RND_RE (rnd);
if (k == 5 || k == 7)
rnd_re = INV_RND (rnd_re);
inex_re = mpfr_sqrt_ui (mpc_realref (rop), 3, rnd_re);
inex_im = mpfr_set_si (mpc_imagref (rop), k < 6 ? 1 : -1,
MPC_RND_IM (rnd));
mpc_div_2ui (rop, rop, 1, MPC_RNDNN);
if (k == 5 || k == 7)
{
mpfr_neg (mpc_realref (rop), mpc_realref (rop), MPFR_RNDN);
inex_re = -inex_re;
}
return MPC_INEX (inex_re, inex_im);
}
else if (n == 8)
{
/* k=1, 3, 5 or 7:
k=1: (1/2*I + 1/2)*sqrt(2)
k=3: (1/2*I - 1/2)*sqrt(2)
k=5: -(1/2*I + 1/2)*sqrt(2)
k=7: -(1/2*I - 1/2)*sqrt(2) */
MPC_ASSERT (k == 1 || k == 3 || k == 5 || k == 7);
rnd_re = MPC_RND_RE (rnd);
if (k == 3 || k == 5)
rnd_re = INV_RND (rnd_re);
rnd_im = MPC_RND_IM (rnd);
if (k > 4)
rnd_im = INV_RND (rnd_im);
inex_re = mpfr_sqrt_ui (mpc_realref (rop), 2, rnd_re);
inex_im = mpfr_sqrt_ui (mpc_imagref (rop), 2, rnd_im);
mpc_div_2ui (rop, rop, 1, MPC_RNDNN);
if (k == 3 || k == 5)
{
mpfr_neg (mpc_realref (rop), mpc_realref (rop), MPFR_RNDN);
inex_re = -inex_re;
}
if (k > 4)
{
mpfr_neg (mpc_imagref (rop), mpc_imagref (rop), MPFR_RNDN);
inex_im = -inex_im;
}
return MPC_INEX (inex_re, inex_im);
}
prec = MPC_MAX_PREC(rop);
/* For the error analysis justifying the following algorithm,
see algorithms.tex. */
mpfr_init2 (t, 67);
mpfr_init2 (s, 67);
mpfr_init2 (c, 67);
mpq_init (kn);
mpq_set_ui (kn, k, n);
mpq_mul_2exp (kn, kn, 1); /* kn=2*k/n < 2 */
do {
prec += mpc_ceil_log2 (prec) + 5; /* prec >= 6 */
mpfr_set_prec (t, prec);
mpfr_set_prec (s, prec);
mpfr_set_prec (c, prec);
mpfr_const_pi (t, MPFR_RNDN);
mpfr_mul_q (t, t, kn, MPFR_RNDN);
mpfr_sin_cos (s, c, t, MPFR_RNDN);
}
while ( !mpfr_can_round (c, prec - (4 - mpfr_get_exp (c)),
MPFR_RNDN, MPFR_RNDZ,
MPC_PREC_RE(rop) + (MPC_RND_RE(rnd) == MPFR_RNDN))
|| !mpfr_can_round (s, prec - (4 - mpfr_get_exp (s)),
MPFR_RNDN, MPFR_RNDZ,
MPC_PREC_IM(rop) + (MPC_RND_IM(rnd) == MPFR_RNDN)));
inex_re = mpfr_set (mpc_realref(rop), c, MPC_RND_RE(rnd));
inex_im = mpfr_set (mpc_imagref(rop), s, MPC_RND_IM(rnd));
mpfr_clear (t);
mpfr_clear (s);
mpfr_clear (c);
mpq_clear (kn);
return MPC_INEX(inex_re, inex_im);
}
void Lib_Mpq_Mul_2exp(MpqPtr x, MpqPtr y, uint32_t e)
{
mpq_mul_2exp( (mpq_ptr) x, (mpq_ptr) y, e);
}