int _arf_are_close(const arf_t x, const arf_t y, long prec)
{
fmpz_t xb, yb;
fmpz_t delta;
int result;
fmpz_init(xb);
fmpz_init(yb);
fmpz_init(delta);
arf_bot(xb, x);
arf_bot(yb, y);
if (fmpz_cmp(ARF_EXPREF(x), ARF_EXPREF(y)) >= 0)
fmpz_sub(delta, xb, ARF_EXPREF(y));
else
fmpz_sub(delta, yb, ARF_EXPREF(x));
fmpz_sub_ui(delta, delta, 64);
result = (fmpz_cmp_ui(delta, prec) < 0);
fmpz_clear(xb);
fmpz_clear(yb);
fmpz_clear(delta);
return result;
}
void
fmpr_divappr_abs_ubound(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec)
{
if (fmpr_is_special(x) || fmpr_is_special(y) || fmpz_is_pm1(fmpr_manref(y)))
{
fmpr_div(z, x, y, prec, FMPR_RND_UP);
fmpr_abs(z, z);
}
else
{
fmpz_t t, u;
slong xbits, ybits, tbits, ubits, shift;
xbits = fmpz_bits(fmpr_manref(x));
ybits = fmpz_bits(fmpr_manref(y));
fmpz_init(t);
fmpz_init(u);
ubits = FLINT_MIN(ybits, prec);
tbits = prec + ubits + 1;
/* upper bound for |x|, shifted */
if (xbits <= tbits)
{
fmpz_mul_2exp(t, fmpr_manref(x), tbits - xbits);
fmpz_abs(t, t);
}
else if (fmpz_sgn(fmpr_manref(x)) > 0)
{
fmpz_cdiv_q_2exp(t, fmpr_manref(x), xbits - tbits);
}
else
{
fmpz_fdiv_q_2exp(t, fmpr_manref(x), xbits - tbits);
fmpz_neg(t, t);
}
/* lower bound for |y|, shifted */
if (ybits <= ubits)
fmpz_mul_2exp(u, fmpr_manref(y), ubits - ybits);
else
fmpz_tdiv_q_2exp(u, fmpr_manref(y), ybits - ubits);
fmpz_abs(u, u);
fmpz_cdiv_q(fmpr_manref(z), t, u);
shift = (ubits - ybits) - (tbits - xbits);
fmpz_sub(fmpr_expref(z), fmpr_expref(x), fmpr_expref(y));
if (shift >= 0)
fmpz_add_ui(fmpr_expref(z), fmpr_expref(z), shift);
else
fmpz_sub_ui(fmpr_expref(z), fmpr_expref(z), -shift);
_fmpr_normalise(fmpr_manref(z), fmpr_expref(z), prec, FMPR_RND_UP);
fmpz_clear(t);
fmpz_clear(u);
}
}
void
fmpr_randtest_not_zero(fmpr_t x, flint_rand_t state, slong bits, slong mag_bits)
{
fmpz_randtest_not_zero(fmpr_manref(x), state, bits);
fmpz_randtest(fmpr_expref(x), state, mag_bits);
fmpz_sub_ui(fmpr_expref(x), fmpr_expref(x), fmpz_bits(fmpr_manref(x)));
_fmpr_normalise(fmpr_manref(x), fmpr_expref(x), bits, FMPR_RND_DOWN);
}
void
_fmprb_get_rand_fmpq(fmpz_t num, fmpz_t den, flint_rand_t state,
const fmpz_t den_mult, const fmprb_t x)
{
fmpz_t a, b, exp;
fmpz_init(a);
fmpz_init(b);
fmpz_init(exp);
fmprb_get_interval_fmpz_2exp(a, b, exp, x);
if (COEFF_IS_MPZ(*exp))
{
printf("exception: fmprb_get_rand_fmpq: too large exponent\n");
abort();
}
if (*exp >= 0)
{
fmpz_mul_2exp(a, a, *exp);
fmpz_mul_2exp(b, b, *exp);
}
/* generate random integer in [a*den, b*den] */
fmpz_mul(a, a, den_mult);
fmpz_mul(b, b, den_mult);
fmpz_add_ui(b, b, 1UL);
fmpz_sub(b, b, a);
/* return one endpoint with high probability (used for stress
testing rounding) */
if (n_randint(state, 6) == 0)
{
if (n_randint(state, 2))
fmpz_zero(num);
else
fmpz_sub_ui(num, b, 1UL);
}
else
{
fmpz_randtest_mod(num, state, b);
}
fmpz_add(num, num, a);
fmpz_set(den, den_mult);
if (*exp < 0)
fmpz_mul_2exp(den, den, -(*exp));
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(exp);
}
int padic_log_balanced(padic_t rop, const padic_t op, const padic_ctx_t ctx)
{
if (padic_val(op) < 0)
{
return 0;
}
else
{
fmpz_t x;
int ans;
fmpz_init(x);
padic_get_fmpz(x, op, ctx);
fmpz_sub_ui(x, x, 1);
if (fmpz_is_zero(x))
{
padic_zero(rop);
ans = 1;
}
else
{
fmpz_t t;
long v;
fmpz_init(t);
v = fmpz_remove(t, x, ctx->p);
fmpz_clear(t);
if (v >= 2 || (*(ctx->p) != 2L && v >= 1))
{
if (v >= ctx->N)
{
padic_zero(rop);
}
else
{
_padic_log_balanced(padic_unit(rop), x, v, ctx->p, ctx->N);
padic_val(rop) = 0;
padic_reduce(rop, ctx);
}
ans = 1;
}
else
{
ans = 0;
}
}
fmpz_clear(x);
return ans;
}
}
int
main(void)
{
long i;
fmpz_t x;
printf("fits_si....");
fflush(stdout);
fmpz_init(x);
fmpz_set_si(x, COEFF_MIN);
check(x, 1);
fmpz_set_si(x, COEFF_MAX);
check(x, 1);
fmpz_set_si(x, LONG_MAX);
check(x, 1);
fmpz_set_si(x, LONG_MIN);
check(x, 1);
fmpz_set_ui(x, ULONG_MAX);
check(x, 0);
fmpz_set_ui(x, ULONG_MAX);
fmpz_neg(x, x);
check(x, 0);
fmpz_set_si(x, LONG_MAX);
fmpz_add_ui(x, x, 1);
check(x, 0);
fmpz_set_si(x, LONG_MIN);
fmpz_sub_ui(x, x, 1);
check(x, 0);
for (i = 0; i < 1000; i++)
{
fmpz_set_ui(x, 1);
fmpz_mul_2exp(x, x, i);
check(x, i < FLINT_BITS - 1);
fmpz_neg(x, x);
check(x, i < FLINT_BITS); /* LONG_MIN fits */
}
fmpz_clear(x);
_fmpz_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
void
fmpz_randtest_mod(fmpz_t f, flint_rand_t state, const fmpz_t m)
{
fmpz_t t;
fmpz_init(t);
fmpz_randtest_unsigned(t, state, fmpz_bits(m) + 2);
fmpz_mod(t, t, m);
if (n_randlimb(state) & UWORD(1))
{
fmpz_sub(t, m, t);
fmpz_sub_ui(t, t, UWORD(1));
}
fmpz_set(f, t);
fmpz_clear(t);
}
mpz_class renf_elem_class::ceil() const noexcept
{
fmpz_t tmp;
fmpz_init(tmp);
if (nf == nullptr)
{
fmpz_add(tmp, fmpq_numref(b), fmpq_denref(b));
fmpz_sub_ui(tmp, tmp, 1);
fmpz_fdiv_q(tmp, tmp, fmpq_denref(b));
}
else
renf_elem_ceil(tmp, a, nf->renf_t());
mpz_class z;
fmpz_get_mpz(z.get_mpz_t(), tmp);
fmpz_clear(tmp);
return z;
}
void
fmpz_mat_randajtai(fmpz_mat_t mat, flint_rand_t state, double alpha)
{
long r, c, i, j, d;
fmpz_t tmp;
r = mat->r;
c = mat->c;
d = r;
if (c != r)
{
printf("Exception: fmpz_mat_ajtai called on an ill-formed matrix\n");
abort();
}
fmpz_init(tmp);
for (i = 0; i < d; i++)
{
mp_bitcnt_t bits = (mp_bitcnt_t) pow((double) (2 * d - i), alpha);
fmpz_one(tmp);
fmpz_mul_2exp(tmp, tmp, bits);
fmpz_sub_ui(tmp, tmp, 1);
fmpz_randm(mat->rows[i] + i, state, tmp);
fmpz_add_ui(mat->rows[i] + i, mat->rows[i] + i, 2);
fmpz_fdiv_q_2exp(mat->rows[i] + i, mat->rows[i] + i, 1);
for (j = i + 1; j <= d; j++)
{
fmpz_randm(mat->rows[j] + i, state, tmp);
if (n_randint(state, 2))
fmpz_neg(mat->rows[j] + i, mat->rows[j] + i);
fmpz_zero(mat->rows[i] + j);
}
}
fmpz_clear(tmp);
}
void arith_euler_phi(fmpz_t res, const fmpz_t n)
{
fmpz_factor_t factors;
fmpz_t t;
ulong exp;
slong i;
if (fmpz_sgn(n) <= 0)
{
fmpz_zero(res);
return;
}
if (fmpz_abs_fits_ui(n))
{
fmpz_set_ui(res, n_euler_phi(fmpz_get_ui(n)));
return;
}
fmpz_factor_init(factors);
fmpz_factor(factors, n);
fmpz_one(res);
fmpz_init(t);
for (i = 0; i < factors->num; i++)
{
fmpz_sub_ui(t, factors->p + i, UWORD(1));
fmpz_mul(res, res, t);
exp = factors->exp[i];
if (exp != 1)
{
fmpz_pow_ui(t, factors->p + i, exp - UWORD(1));
fmpz_mul(res, res, t);
}
}
fmpz_clear(t);
fmpz_factor_clear(factors);
}
void
test0(slong b)
{
fmpz_t M; fmpz_init_set_ui(M,1);
fmpz_mul_2exp(M,M,(ulong)b);
test1_ui(b,M,0);
test1_ui(b,M,1);
test1_ui(b,M,(mp_limb_t)-1);
test1(b,M,M); // M
fmpz_t n; fmpz_init_set(n,M);
fmpz_add_ui(n,M,1);
test1(b,M,n); // M+1
fmpz_sub_ui(n,M,1);
test1(b,M,n); // M-1
slong i;
fmpz_t m; fmpz_init(m);
fmpz_t Mhalf; fmpz_init(Mhalf);
fmpz_fdiv_q_2exp(Mhalf,M,1);
for(i=100;i--;)
{
fmpz_randm(m,rst,n); // m = random(M-1)
test1(b,M,m);
fmpz_add(m,m,Mhalf); // m+M/2
test1(b,M,m);
}
fmpz_mul_2exp(m,M,1);
test1(b,M,m); // M<<1
fmpz_mul_2exp(m,m,1);
test1(b,M,m); // M<<2
fmpz_mul_2exp(m,m,1);
test1(b,M,m); // M<<3
fmpz_mul(m,m,M);
test1(b,M,m); // M*(M<<3)
fmpz_clear(Mhalf);
fmpz_clear(m);
fmpz_clear(n);
fmpz_clear(M);
}
void
fmpz_mat_randajtai(fmpz_mat_t mat, flint_rand_t state, double alpha)
{
const slong c = mat->c, r = mat->r, d = r;
slong i, j;
fmpz_t tmp;
if (c != r)
{
flint_printf("Exception (fmpz_mat_ajtai): Non-square matrix.\n");
abort();
}
fmpz_init(tmp);
for (i = 0; i < d; i++)
{
mp_bitcnt_t bits = (mp_bitcnt_t) pow((double) (2 * d - i), alpha);
fmpz_one(tmp);
fmpz_mul_2exp(tmp, tmp, bits);
fmpz_sub_ui(tmp, tmp, 1);
fmpz_randm(mat->rows[i] + i, state, tmp);
fmpz_add_ui(mat->rows[i] + i, mat->rows[i] + i, 2);
fmpz_fdiv_q_2exp(mat->rows[i] + i, mat->rows[i] + i, 1);
for (j = i + 1; j <= d; j++)
{
fmpz_randm(mat->rows[j] + i, state, tmp);
if (n_randint(state, 2))
fmpz_neg(mat->rows[j] + i, mat->rows[j] + i);
fmpz_zero(mat->rows[i] + j);
}
}
fmpz_clear(tmp);
}
static __inline__ void
_arb_vec_get_fmpz_2exp_blocks(fmpz * coeffs, fmpz * exps,
slong * blocks, const fmpz_t scale, arb_srcptr x, slong len, slong prec)
{
fmpz_t top, bot, t, b, v, block_top, block_bot;
slong i, j, s, block, bits, maxheight;
int in_zero;
fmpz_init(top);
fmpz_init(bot);
fmpz_init(t);
fmpz_init(b);
fmpz_init(v);
fmpz_init(block_top);
fmpz_init(block_bot);
blocks[0] = 0;
block = 0;
in_zero = 1;
if (prec == ARF_PREC_EXACT)
maxheight = ARF_PREC_EXACT;
else
maxheight = ALPHA * prec + BETA;
for (i = 0; i < len; i++)
{
bits = arf_bits(arb_midref(x + i));
/* Skip (must be zero, since we assume there are no Infs/NaNs). */
if (bits == 0)
continue;
/* Bottom and top exponent of current number */
fmpz_set(top, ARF_EXPREF(arb_midref(x + i)));
fmpz_submul_ui(top, scale, i);
fmpz_sub_ui(bot, top, bits);
/* Extend current block. */
if (in_zero)
{
fmpz_swap(block_top, top);
fmpz_swap(block_bot, bot);
}
else
{
fmpz_max(t, top, block_top);
fmpz_min(b, bot, block_bot);
fmpz_sub(v, t, b);
/* extend current block */
if (fmpz_cmp_ui(v, maxheight) < 0)
{
fmpz_swap(block_top, t);
fmpz_swap(block_bot, b);
}
else /* start new block */
{
/* write exponent for previous block */
fmpz_set(exps + block, block_bot);
block++;
blocks[block] = i;
fmpz_swap(block_top, top);
fmpz_swap(block_bot, bot);
}
}
in_zero = 0;
}
/* write exponent for last block */
fmpz_set(exps + block, block_bot);
/* end marker */
blocks[block + 1] = len;
/* write the block data */
for (i = 0; blocks[i] != len; i++)
{
for (j = blocks[i]; j < blocks[i + 1]; j++)
{
if (arf_is_special(arb_midref(x + j)))
{
fmpz_zero(coeffs + j);
}
else
{
/* TODO: make this a single operation */
arf_get_fmpz_2exp(coeffs + j, bot, arb_midref(x + j));
fmpz_mul_ui(t, scale, j);
fmpz_sub(t, bot, t);
s = _fmpz_sub_small(t, exps + i);
if (s < 0) abort(); /* Bug catcher */
fmpz_mul_2exp(coeffs + j, coeffs + j, s);
}
}
}
fmpz_clear(top);
fmpz_clear(bot);
fmpz_clear(t);
fmpz_clear(b);
fmpz_clear(v);
fmpz_clear(block_top);
fmpz_clear(block_bot);
}
void
arb_mul_naive(arb_t z, const arb_t x, const arb_t y, slong prec)
{
arf_t zm_exact, zm_rounded, zr, t, u;
arf_init(zm_exact);
arf_init(zm_rounded);
arf_init(zr);
arf_init(t);
arf_init(u);
arf_mul(zm_exact, arb_midref(x), arb_midref(y), ARF_PREC_EXACT, ARF_RND_DOWN);
arf_set_round(zm_rounded, zm_exact, prec, ARB_RND);
/* rounding error */
if (arf_equal(zm_exact, zm_rounded))
{
arf_zero(zr);
}
else
{
fmpz_t e;
fmpz_init(e);
/* more accurate, but not what we are testing
arf_sub(zr, zm_exact, zm_rounded, MAG_BITS, ARF_RND_UP);
arf_abs(zr, zr); */
fmpz_sub_ui(e, ARF_EXPREF(zm_rounded), prec);
arf_one(zr);
arf_mul_2exp_fmpz(zr, zr, e);
fmpz_clear(e);
}
/* propagated error */
if (!arb_is_exact(x))
{
arf_set_mag(t, arb_radref(x));
arf_abs(u, arb_midref(y));
arf_addmul(zr, t, u, MAG_BITS, ARF_RND_UP);
}
if (!arb_is_exact(y))
{
arf_set_mag(t, arb_radref(y));
arf_abs(u, arb_midref(x));
arf_addmul(zr, t, u, MAG_BITS, ARF_RND_UP);
}
if (!arb_is_exact(x) && !arb_is_exact(y))
{
arf_set_mag(t, arb_radref(x));
arf_set_mag(u, arb_radref(y));
arf_addmul(zr, t, u, MAG_BITS, ARF_RND_UP);
}
arf_set(arb_midref(z), zm_rounded);
arf_get_mag(arb_radref(z), zr);
arf_clear(zm_exact);
arf_clear(zm_rounded);
arf_clear(zr);
arf_clear(t);
arf_clear(u);
}
void
fmpz_addmul_ui(fmpz_t f, const fmpz_t g, ulong x)
{
fmpz c1, r;
c1 = *g;
if ((x == 0) || (c1 == 0)) /* product is zero */
return;
r = *f;
if (r == 0)
{
fmpz_mul_ui(f, g, x); /* we are adding product to 0 */
return;
}
if (x == UWORD(1)) /* special case, adding g*1 to f */
{
fmpz_add(f, f, g);
return;
}
if (c1 == UWORD(1)) /* special case, adding 1*x to f */
{
fmpz_add_ui(f, f, x);
return;
}
if (!COEFF_IS_MPZ(c1)) /* c1 is small */
{
mp_limb_t prod[2];
ulong uc1 = FLINT_ABS(c1);
umul_ppmm(prod[1], prod[0], uc1, x); /* compute product */
if (prod[1] == 0) /* product fits in one limb */
{
if (c1 < WORD(0))
fmpz_sub_ui(f, f, prod[0]);
else
fmpz_add_ui(f, f, prod[0]);
return;
}
else if ((prod[1] == 1) && (!COEFF_IS_MPZ(r)) && ((r ^ c1) < WORD(0)))
{
/*
only chance at cancellation is if product is one bit past
a limb and res is small and opposite sign to this product
*/
ulong ur = FLINT_ABS(r);
if (ur > prod[0]) /* cancellation will occur */
{
fmpz_set_ui(f, prod[0] - ur);
if (r > WORD(0))
fmpz_neg(f, f);
return;
}
}
/*
in all remaining cases res is either big already,
or will be big in the end
*/
{
__mpz_struct * mpz_ptr = _fmpz_promote_val(f);
mpz_t temp; /* set up a temporary, cheap mpz_t to contain prod */
temp->_mp_d = prod;
temp->_mp_size = (c1 < WORD(0) ? -2 : 2);
mpz_add(mpz_ptr, mpz_ptr, temp);
_fmpz_demote_val(f); /* cancellation may have occurred */
}
}
else /* c1 is large */
{
__mpz_struct * mpz_ptr = _fmpz_promote_val(f);
flint_mpz_addmul_ui(mpz_ptr, COEFF_TO_PTR(c1), x);
_fmpz_demote_val(f); /* cancellation may have occurred */
}
}
/* convert to an fmpz poly with a common exponent and coefficients
at most prec bits, also bounding input error plus rounding error */
void _fmprb_poly_get_fmpz_poly_2exp(fmpr_t error, fmpz_t exp, fmpz * coeffs,
fmprb_srcptr A, long lenA, long prec)
{
fmpz_t top_exp, bot_exp;
long shift;
long i;
int rounding;
fmpz_init(top_exp);
fmpz_init(bot_exp);
if (!_fmprb_poly_mid_get_hull(bot_exp, top_exp, A, lenA))
{
fmpz_zero(exp);
_fmpz_vec_zero(coeffs, lenA);
fmpr_zero(error);
for (i = 0; i < lenA; i++)
{
if (fmpr_cmp(fmprb_radref(A + i), error) > 0)
fmpr_set(error, fmprb_radref(A + i));
}
return; /* no need to clear fmpzs */
}
/* only take as much precision as necessary */
shift = _fmpz_sub_small(top_exp, bot_exp);
prec = FLINT_MIN(prec, shift);
fmpz_sub_ui(exp, top_exp, prec);
/* extract integer polynomial */
rounding = 0;
for (i = 0; i < lenA; i++)
rounding |= fmpr_get_fmpz_fixed_fmpz(coeffs + i,
fmprb_midref(A + i), exp);
fmpr_zero(error);
/* compute maximum of input errors */
for (i = 0; i < lenA; i++)
{
if (fmpr_cmp(fmprb_radref(A + i), error) > 0)
fmpr_set(error, fmprb_radref(A + i));
}
/* add rounding error */
if (rounding)
{
fmpr_t t;
fmpr_init(t);
fmpz_set_ui(fmpr_manref(t), 1UL);
fmpz_set(fmpr_expref(t), exp);
fmpr_add(error, error, t, FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_clear(t);
}
fmpz_clear(top_exp);
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("sub_ui....");
fflush(stdout);
for (i = 0; i < 10000 * flint_test_multiplier(); i++)
{
fmpz_t a, b;
mpz_t d, e, f;
ulong x;
fmpz_init(a);
fmpz_init(b);
mpz_init(d);
mpz_init(e);
mpz_init(f);
fmpz_randtest(a, state, 200);
fmpz_get_mpz(d, a);
x = n_randtest(state);
fmpz_sub_ui(b, a, x);
flint_mpz_sub_ui(e, d, x);
fmpz_get_mpz(f, b);
result = (mpz_cmp(e, f) == 0);
if (!result)
{
flint_printf("FAIL:\n");
gmp_printf("d = %Zd, e = %Zd, f = %Zd, x = %wu\n", d, e, f, x);
abort();
}
fmpz_clear(a);
fmpz_clear(b);
mpz_clear(d);
mpz_clear(e);
mpz_clear(f);
}
/* Check aliasing of a and b */
for (i = 0; i < 10000 * flint_test_multiplier(); i++)
{
fmpz_t a;
mpz_t d, e, f;
ulong x;
fmpz_init(a);
mpz_init(d);
mpz_init(e);
mpz_init(f);
fmpz_randtest(a, state, 200);
fmpz_get_mpz(d, a);
x = n_randtest(state);
fmpz_sub_ui(a, a, x);
flint_mpz_sub_ui(e, d, x);
fmpz_get_mpz(f, a);
result = (mpz_cmp(e, f) == 0);
if (!result)
{
flint_printf("FAIL:\n");
gmp_printf("d = %Zd, e = %Zd, f = %Zd, x = %wu\n", d, e, f, x);
abort();
}
fmpz_clear(a);
mpz_clear(d);
mpz_clear(e);
mpz_clear(f);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
void _padic_teichmuller(fmpz_t rop, const fmpz_t op, const fmpz_t p, slong N)
{
if (fmpz_equal_ui(p, 2))
{
fmpz_one(rop);
}
else if (N == 1)
{
fmpz_mod(rop, op, p);
}
else
{
slong *a, i, n;
fmpz *pow, *u;
fmpz_t s, t;
fmpz_t inv;
fmpz_t pm1;
a = _padic_lifts_exps(&n, N);
pow = _fmpz_vec_init(2 * n);
u = pow + n;
_padic_lifts_pows(pow, a, n, p);
fmpz_init(s);
fmpz_init(t);
fmpz_init(inv);
fmpz_init(pm1);
fmpz_sub_ui(pm1, p, 1);
/* Compute reduced units for (p-1) */
{
fmpz_mod(u + 0, pm1, pow + 0);
}
for (i = 1; i < n; i++)
{
fmpz_mod(u + i, u + (i - 1), pow + i);
}
/* Run Newton iteration */
i = n - 1;
{
fmpz_mod(rop, op, pow + i);
fmpz_set(inv, pm1);
}
for (i--; i >= 0; i--)
{
/* Lift rop */
fmpz_powm(s, rop, p, pow + i);
fmpz_sub(s, s, rop);
fmpz_mul(t, s, inv);
fmpz_sub(rop, rop, t);
fmpz_mod(rop, rop, pow + i);
/* Lift inv */
if (i > 0)
{
fmpz_mul(s, inv, inv);
fmpz_mul(t, u + i, s);
fmpz_mul_2exp(inv, inv, 1);
fmpz_sub(inv, inv, t);
fmpz_mod(inv, inv, pow + i);
}
}
fmpz_clear(s);
fmpz_clear(t);
fmpz_clear(inv);
fmpz_clear(pm1);
_fmpz_vec_clear(pow, 2 * n);
flint_free(a);
}
}
int
main(void)
{
long iter;
int result;
flint_rand_t state;
printf("abs_ubound_ui_2exp....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000; iter++)
{
fmpz_t x, y;
long bits, yexp;
long exp;
mp_limb_t man;
fmpz_init(x);
fmpz_init(y);
fmpz_randtest_not_zero(x, state, 1 + n_randint(state, 400));
bits = 1 + n_randint(state, FLINT_BITS - 1);
/* compute an exactly rounded mantissa */
fmpz_abs(y, x);
if (fmpz_is_zero(y))
{
yexp = 0;
}
else
{
yexp = fmpz_bits(y) - bits;
if (yexp >= 0)
{
fmpz_cdiv_q_2exp(y, y, yexp);
if (fmpz_bits(y) == bits + 1)
{
fmpz_tdiv_q_2exp(y, y, 1);
yexp--;
}
}
else
{
fmpz_mul_2exp(y, y, -yexp);
}
}
man = fmpz_abs_ubound_ui_2exp(&exp, x, bits);
if (FLINT_BIT_COUNT(man) != bits)
{
printf("wrong number of bits!\n");
printf("bits = %ld, count = %u\n\n", bits, FLINT_BIT_COUNT(man));
printf("x = "); fmpz_print(x); printf("\n\n");
printf("bits(x) = %ld\n\n", fmpz_bits(x));
printf("y = "); fmpz_print(y); printf("\n\n");
printf("yexp = %ld\n\n", yexp);
printf("man = %lu, exp = %ld\n", man, exp);
abort();
}
/* ok if equal */
result = (fmpz_cmp_ui(y, man) == 0);
/* ok if mantissa is 1 larger */
if (!result)
{
result = ((exp == yexp) && (fmpz_cmp_ui(y, man - 1) == 0));
}
/* ok if the exact mantissa is 2^r-1 and overflow to 2^r happened */
if (!result)
{
fmpz_t t;
fmpz_init(t);
fmpz_set_ui(t, man);
fmpz_mul_ui(t, t, 2);
fmpz_sub_ui(t, t, 1);
result = (exp == yexp + 1) && fmpz_equal(t, y);
fmpz_clear(t);
}
if (!result)
{
printf("different from exact ceiling division\n");
printf("bits = %ld\n\n", bits);
printf("x = "); fmpz_print(x); printf("\n\n");
printf("bits(x) = %ld\n\n", fmpz_bits(x));
printf("y = "); fmpz_print(y); printf(", yexp = %ld\n\n", yexp);
printf("man = %lu, exp = %ld\n", man, exp);
abort();
}
fmpz_clear(x);
fmpz_clear(y);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
void eis_series(fmpz_poly_t *eis, ulong k, ulong prec)
{
ulong i, p, ee, p_pow, ind;
fmpz_t last, last_m1, mult, fp, t_coeff, term, term_m1;
long bern_fac[15] = {0, 0, 0, 0, 240, 0, -504, 0, 480, 0, -264, 0, 0, 0, -24};
// Now, we compute the eisenstein series
// First, compute primes by sieving.
// allocate memory for the array.
/*
char *primes;
primes = calloc(prec + 1, sizeof(char));
for(i = 0; i <= prec; i++) {
primes[i] = 1;
}
primes[0] = 0;
primes[1] = 0;
p = 2;
while(p*p <= prec) {
j = p*p;
while(j <= prec) {
primes[j] = 0;
j += p;
}
p += 1;
while(primes[p] != 1)
p += 1;
}
*/
// Now, create the eisenstein series.
// We build up each coefficient using the multiplicative properties of the
// divisor sum function.
fmpz_poly_set_coeff_si(*eis, 0, 1);
for(i = 1; i <= prec; i++)
fmpz_poly_set_coeff_si(*eis, i, bern_fac[k]);
fmpz_init(last);
fmpz_init(last_m1);
fmpz_init(mult);
fmpz_init(fp);
fmpz_init(t_coeff);
fmpz_init(term);
fmpz_init(term_m1);
ee = k - 1;
p = 2;
while(p <= prec) {
p_pow = p;
fmpz_set_ui(fp, p);
fmpz_pow_ui(mult, fp, ee);
fmpz_pow_ui(term, mult, 2);
fmpz_set(last, mult);
while(p_pow <= prec) {
ind = p_pow;
fmpz_sub_ui(term_m1, term, 1);
fmpz_sub_ui(last_m1, last, 1);
while(ind <= prec) {
fmpz_poly_get_coeff_fmpz(t_coeff, *eis, ind);
fmpz_mul(t_coeff, t_coeff, term_m1);
fmpz_divexact(t_coeff, t_coeff, last_m1);
fmpz_poly_set_coeff_fmpz(*eis, ind, t_coeff);
ind += p_pow;
}
p_pow *= p;
fmpz_set(last, term);
fmpz_mul(term, term, mult);
}
p = n_nextprime(p, 1);
}
fmpz_clear(last);
fmpz_clear(last_m1);
fmpz_clear(mult);
fmpz_clear(fp);
fmpz_clear(t_coeff);
fmpz_clear(term);
fmpz_clear(term_m1);
}
static __inline__ void
_mag_vec_get_fmpz_2exp_blocks(fmpz * coeffs,
double * dblcoeffs, fmpz * exps, slong * blocks, const fmpz_t scale,
arb_srcptr x, mag_srcptr xm, slong len)
{
fmpz_t top, bot, t, b, v, block_top, block_bot;
slong i, j, s, block, bits, maxheight;
int in_zero;
mag_srcptr cur;
fmpz_init(top);
fmpz_init(bot);
fmpz_init(t);
fmpz_init(b);
fmpz_init(v);
fmpz_init(block_top);
fmpz_init(block_bot);
blocks[0] = 0;
block = 0;
in_zero = 1;
maxheight = ALPHA * MAG_BITS + BETA;
if (maxheight > DOUBLE_BLOCK_MAX_HEIGHT)
abort();
for (i = 0; i < len; i++)
{
cur = (x == NULL) ? (xm + i) : arb_radref(x + i);
/* Skip (must be zero, since we assume there are no Infs/NaNs). */
if (mag_is_special(cur))
continue;
/* Bottom and top exponent of current number */
bits = MAG_BITS;
fmpz_set(top, MAG_EXPREF(cur));
fmpz_submul_ui(top, scale, i);
fmpz_sub_ui(bot, top, bits);
/* Extend current block. */
if (in_zero)
{
fmpz_swap(block_top, top);
fmpz_swap(block_bot, bot);
}
else
{
fmpz_max(t, top, block_top);
fmpz_min(b, bot, block_bot);
fmpz_sub(v, t, b);
/* extend current block */
if (fmpz_cmp_ui(v, maxheight) < 0)
{
fmpz_swap(block_top, t);
fmpz_swap(block_bot, b);
}
else /* start new block */
{
/* write exponent for previous block */
fmpz_set(exps + block, block_bot);
block++;
blocks[block] = i;
fmpz_swap(block_top, top);
fmpz_swap(block_bot, bot);
}
}
in_zero = 0;
}
/* write exponent for last block */
fmpz_set(exps + block, block_bot);
/* end marker */
blocks[block + 1] = len;
/* write the block data */
for (i = 0; blocks[i] != len; i++)
{
for (j = blocks[i]; j < blocks[i + 1]; j++)
{
cur = (x == NULL) ? (xm + j) : arb_radref(x + j);
if (mag_is_special(cur))
{
fmpz_zero(coeffs + j);
dblcoeffs[j] = 0.0;
}
else
{
mp_limb_t man;
double c;
man = MAG_MAN(cur);
/* TODO: only write and use doubles when block is short? */
/* Divide by 2^(scale * j) */
fmpz_mul_ui(t, scale, j);
fmpz_sub(t, MAG_EXPREF(cur), t);
fmpz_sub_ui(t, t, MAG_BITS); /* bottom exponent */
s = _fmpz_sub_small(t, exps + i);
if (s < 0) abort(); /* Bug catcher */
fmpz_set_ui(coeffs + j, man);
fmpz_mul_2exp(coeffs + j, coeffs + j, s);
c = man;
c = ldexp(c, s - DOUBLE_BLOCK_SHIFT);
if (c < 1e-150 || c > 1e150) /* Bug catcher */
abort();
dblcoeffs[j] = c;
}
}
}
fmpz_clear(top);
fmpz_clear(bot);
fmpz_clear(t);
fmpz_clear(b);
fmpz_clear(v);
fmpz_clear(block_top);
fmpz_clear(block_bot);
}
void
arf_get_fmpz(fmpz_t z, const arf_t x, arf_rnd_t rnd)
{
if (arf_is_special(x))
{
if (arf_is_zero(x))
{
fmpz_zero(z);
}
else
{
flint_printf("arf_get_fmpz: cannot convert infinity or nan to integer\n");
abort();
}
}
else if (COEFF_IS_MPZ(*ARF_EXPREF(x)))
{
/* tiny */
if (fmpz_sgn(ARF_EXPREF(x)) < 0)
{
int negative = ARF_SGNBIT(x);
if (rnd == ARF_RND_NEAR
|| rnd == ARF_RND_DOWN
|| (rnd == ARF_RND_FLOOR && !negative)
|| (rnd == ARF_RND_CEIL && negative))
{
fmpz_zero(z);
}
else
{
fmpz_set_si(z, negative ? -1 : 1);
}
}
else
{
flint_printf("arf_get_fmpz: number too large to convert to integer\n");
abort();
}
}
else
{
slong exp;
int negative, inexact;
mp_size_t xn, zn;
mp_srcptr xp;
__mpz_struct * zz;
/* TBD: implement efficiently */
if (rnd == ARF_RND_NEAR)
{
fmpr_t t;
fmpr_init(t);
arf_get_fmpr(t, x);
fmpr_get_fmpz(z, t, rnd);
fmpr_clear(t);
return;
}
exp = ARF_EXP(x);
negative = ARF_SGNBIT(x);
/* |x| < 1 */
if (exp <= 0)
{
if (rnd == ARF_RND_DOWN ||
(rnd == ARF_RND_FLOOR && !negative) ||
(rnd == ARF_RND_CEIL && negative))
{
fmpz_zero(z);
}
else
{
fmpz_set_si(z, negative ? -1 : 1);
}
return;
}
ARF_GET_MPN_READONLY(xp, xn, x);
/* |x| < 2^31 or 2^63 (must save 1 bit for rounding up!) */
if (exp < FLINT_BITS)
{
mp_limb_t v, v2;
v = xp[xn - 1];
v2 = v >> (FLINT_BITS - exp);
inexact = (xn > 1) || ((v2 << (FLINT_BITS - exp)) != v);
if (inexact && rnd != ARF_RND_DOWN)
{
if (negative && (rnd == ARF_RND_UP || rnd == ARF_RND_FLOOR))
v2++;
if (!negative && (rnd == ARF_RND_UP || rnd == ARF_RND_CEIL))
v2++;
}
if (negative)
fmpz_neg_ui(z, v2);
else
fmpz_set_ui(z, v2);
return;
}
/* |x| >= 1 */
zn = (exp + FLINT_BITS - 1) / FLINT_BITS;
zz = _fmpz_promote(z);
if (zz->_mp_alloc < zn)
mpz_realloc2(zz, zn * FLINT_BITS);
inexact = _arf_get_integer_mpn(zz->_mp_d, xp, xn, exp);
zz->_mp_size = negative ? -zn : zn;
_fmpz_demote_val(z);
if (inexact && rnd != ARF_RND_DOWN)
{
if (negative && (rnd == ARF_RND_UP || rnd == ARF_RND_FLOOR))
fmpz_sub_ui(z, z, 1);
if (!negative && (rnd == ARF_RND_UP || rnd == ARF_RND_CEIL))
fmpz_add_ui(z, z, 1);
}
}
slong
fmpr_div(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd)
{
if (fmpr_is_special(x) || fmpr_is_special(y))
{
_fmpr_div_special(z, x, y);
return FMPR_RESULT_EXACT;
}
/* division by power of two <=> shift exponents */
if (fmpz_is_pm1(fmpr_manref(y)))
{
if (fmpz_is_one(fmpr_manref(y)))
fmpz_set(fmpr_manref(z), fmpr_manref(x));
else
fmpz_neg(fmpr_manref(z), fmpr_manref(x));
fmpz_sub(fmpr_expref(z), fmpr_expref(x), fmpr_expref(y));
return _fmpr_normalise(fmpr_manref(z), fmpr_expref(z), prec, rnd);
}
else
{
slong xbits, ybits, extra, extra_pad, extra_control;
int negative;
fmpz_t t, u;
/* todo: work out exact needed shift */
xbits = fmpz_bits(fmpr_manref(x));
ybits = fmpz_bits(fmpr_manref(y));
extra = prec - xbits + ybits;
extra = FLINT_MAX(extra, 0);
extra_pad = 32;
extra_control = 24;
extra += extra_pad;
fmpz_init(t);
fmpz_init(u);
fmpz_mul_2exp(t, fmpr_manref(x), extra);
fmpz_tdiv_q(u, t, fmpr_manref(y));
if (low_bits_are_zero(u, extra_control))
{
fmpz_t v;
fmpz_init(v);
fmpz_mul(v, u, fmpr_manref(y));
negative = fmpz_sgn(fmpr_manref(x)) != fmpz_sgn(fmpr_manref(y));
if (!fmpz_equal(t, v))
{
if (negative)
fmpz_sub_ui(u, u, 1);
else
fmpz_add_ui(u, u, 1);
}
fmpz_clear(v);
}
fmpz_swap(fmpr_manref(z), u);
fmpz_clear(t);
fmpz_clear(u);
fmpz_sub(fmpr_expref(z), fmpr_expref(x), fmpr_expref(y));
fmpz_sub_ui(fmpr_expref(z), fmpr_expref(z), extra);
return _fmpr_normalise(fmpr_manref(z), fmpr_expref(z), prec, rnd);
}
}
