static void
special_overflow (void)
{
mpfr_t x, y;
mpfr_exp_t emin, emax;
emin = mpfr_get_emin ();
emax = mpfr_get_emax ();
set_emin (-125);
set_emax (128);
mpfr_init2 (x, 24);
mpfr_init2 (y, 48);
mpfr_set_str_binary (x, "0.101100100000000000110100E0");
mpfr_acos (y, x, MPFR_RNDN);
if (mpfr_cmp_str (y, "0.110011010100101111000100111010111011010000001001E0",
2, MPFR_RNDN))
{
printf("Special Overflow error.\n");
mpfr_dump (y);
exit (1);
}
mpfr_clear (y);
mpfr_clear (x);
set_emin (emin);
set_emax (emax);
}
decimal r_acos(const decimal& a,bool round)
{
#ifdef USE_CGAL
CGAL::Gmpfr m;
CGAL::Gmpfr n=to_gmpfr(a);
mpfr_acos(m.fr(),n.fr(),MPFR_RNDN);
return r_round_preference(decimal(m),round);
#else
return r_round_preference(acos(a),round);
#endif
}
static void
special (void)
{
mpfr_t x, y;
int inex1, inex2;
mpfr_init2 (x, 32);
mpfr_init2 (y, 32);
mpfr_set_str_binary (x, "0.10001000001001011000100001E-6");
mpfr_acos (y, x, MPFR_RNDN);
mpfr_set_str_binary (x, "1.10001111111111110001110110001");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_acos (1)\n");
exit (1);
}
mpfr_set_str_binary (x, "-0.01101011110111100111010011001011");
mpfr_acos (y, x, MPFR_RNDZ);
mpfr_set_str_binary (x, "10.0000000101111000011101000101");
if (mpfr_cmp (x, y))
{
printf ("Error in mpfr_acos (2)\n");
mpfr_print_binary (y); printf ("\n");
exit (1);
}
mpfr_set_prec (x, 2);
mpfr_set_ui (x, 0, MPFR_RNDN);
inex1 = mpfr_acos (x, x, MPFR_RNDN); /* Pi/2 */
inex2 = mpfr_const_pi (x, MPFR_RNDN);
if (inex1 != inex2)
{
printf ("Error in mpfr_acos (3) for prec=2\n");
exit (1);
}
mpfr_clear (y);
mpfr_clear (x);
}
/// @brief acos keyword implementation
///
void program::rpn_acos(void) {
MIN_ARGUMENTS(1);
if (_stack->get_type(0) == cmd_number) {
floating_t* left = &((number*)_stack->get_obj(0))->_value;
CHECK_MPFR(mpfr_acos(left->mpfr, left->mpfr, floating_t::s_mpfr_rnd));
} else if (_stack->get_type(0) == cmd_complex) {
// acos(z)=pi/2-asin(z)
rpn_asin();
rpn_pi();
number* num = (number*)_stack->allocate_back(number::calc_size(), cmd_number);
CHECK_MPFR(mpfr_set_d(num->_value.mpfr, 2.0, floating_t::s_mpfr_rnd));
rpn_div();
rpn_minus();
rpn_neg();
} else
ERR_CONTEXT(ret_bad_operand_type);
}
static PyObject *
_GMPy_MPFR_Acos(PyObject *x, CTXT_Object *context)
{
MPFR_Object *result;
if (!mpfr_nan_p(MPFR(x)) &&
(mpfr_cmp_si(MPFR(x), 1) > 0 || mpfr_cmp_si(MPFR(x), -1) < 0) &&
context->ctx.allow_complex
) {
return GMPy_Complex_Acos(x, context);
}
if (!(result = GMPy_MPFR_New(0, context))) {
return NULL;
}
mpfr_clear_flags();
result->rc = mpfr_acos(result->f, MPFR(x), GET_MPFR_ROUND(context));
_GMPy_MPFR_Cleanup(&result, context);
return (PyObject*)result;
}
REAL _acos(REAL a, REAL, QByteArray &)
{
mpfr_t tmp1; mpfr_init2(tmp1, NUMBITS);
mpfr_t result; mpfr_init2(result, NUMBITS);
try
{
// mpfr_init_set_f(tmp1, a.get_mpf_t(), MPFR_RNDN);
mpfr_set_str(tmp1, getString(a).data(), 10, MPFR_RNDN);
mpfr_acos(result, tmp1, MPFR_RNDN);
mpfr_get_f(a.get_mpf_t(), result, MPFR_RNDN);
}
catch(...)
{
mpfr_clear(tmp1);
mpfr_clear(result);
return ZERO;
}
mpfr_clear(tmp1);
mpfr_clear(result);
return a;
}
//------------------------------------------------------------------------------
// Name:
//------------------------------------------------------------------------------s
knumber_base *knumber_float::acos() {
if(mpf_cmp_d(mpf_, 1.0) > 0 || mpf_cmp_d(mpf_, -1.0) < 0) {
delete this;
return new knumber_error(knumber_error::ERROR_UNDEFINED);
}
#ifdef KNUMBER_USE_MPFR
mpfr_t mpfr;
mpfr_init_set_f(mpfr, mpf_, rounding_mode);
mpfr_acos(mpfr, mpfr, rounding_mode);
mpfr_get_f(mpf_, mpfr, rounding_mode);
mpfr_clear(mpfr);
return this;
#else
const double x = mpf_get_d(mpf_);
if(isinf(x)) {
delete this;
return new knumber_error(knumber_error::ERROR_POS_INFINITY);
} else {
return execute_libc_func< ::acos>(x);
}
#endif
}
int main()
{
long iter;
flint_rand_t state;
printf("acos....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
arb_t a, b;
fmpq_t q;
mpfr_t t;
long prec = 2 + n_randint(state, 200);
arb_init(a);
arb_init(b);
fmpq_init(q);
mpfr_init2(t, prec + 100);
arb_randtest(a, state, 1 + n_randint(state, 200), 3);
arb_randtest(b, state, 1 + n_randint(state, 200), 3);
arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200));
fmpq_get_mpfr(t, q, MPFR_RNDN);
mpfr_acos(t, t, MPFR_RNDN);
arb_acos(b, a, prec);
if (!arb_contains_mpfr(b, t))
{
printf("FAIL: containment\n\n");
printf("a = "); arb_printd(a, 100); printf("\n\n");
printf("b = "); arb_printd(b, 100); printf("\n\n");
abort();
}
arb_acos(a, a, prec);
if (!arb_equal(a, b))
{
printf("FAIL: aliasing\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
fmpq_clear(q);
mpfr_clear(t);
}
/* check large arguments */
for (iter = 0; iter < 10000; iter++)
{
arb_t a, b, c;
long prec1, prec2;
prec1 = 2 + n_randint(state, 1000);
prec2 = prec1 + 30;
arb_init(a);
arb_init(b);
arb_init(c);
arb_randtest_precise(a, state, 1 + n_randint(state, 1000), 100);
arb_acos(b, a, prec1);
arb_acos(c, a, prec2);
if (!arb_overlaps(b, c))
{
printf("FAIL: overlap\n\n");
printf("a = "); arb_print(a); printf("\n\n");
printf("b = "); arb_print(b); printf("\n\n");
printf("c = "); arb_print(c); printf("\n\n");
abort();
}
/* check sin(asin(x)) = x */
arb_cos(c, b, prec1);
if (!arb_contains(c, a))
{
printf("FAIL: functional equation\n\n");
printf("a = "); arb_print(a); printf("\n\n");
printf("b = "); arb_print(b); printf("\n\n");
printf("c = "); arb_print(c); printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int
main (int argc, char *argv[])
{
int n, prec, st, st2, N, i;
mpfr_t x, y, z;
if (argc != 2 && argc != 3)
{
fprintf(stderr, "Usage: timing digits \n");
exit(1);
}
printf ("Using MPFR-%s with GMP-%s\n", mpfr_version, gmp_version);
n = atoi(argv[1]);
prec = (int) ( n * log(10.0) / log(2.0) + 1.0 );
printf("[precision is %u bits]\n", prec);
mpfr_init2(x, prec); mpfr_init2(y, prec); mpfr_init2(z, prec);
mpfr_set_d(x, 3.0, GMP_RNDN); mpfr_sqrt(x, x, GMP_RNDN); mpfr_sub_ui (x, x, 1, GMP_RNDN);
mpfr_set_d(y, 5.0, GMP_RNDN); mpfr_sqrt(y, y, GMP_RNDN);
mpfr_log (z, x, GMP_RNDN);
N=1; st = cputime();
do {
for (i=0;i<N;i++) mpfr_mul(z, x, y, GMP_RNDN);
N=2*N;
st2=cputime();
} while (st2-st<1000);
printf("x*y took %f ms (%d eval in %d ms)\n",
(double)(st2-st)/(N-1),N-1,st2-st);
N=1; st = cputime();
do {
for (i=0;i<N;i++) mpfr_mul(z, x, x, GMP_RNDN);
N=2*N;
st2=cputime();
} while (st2-st<1000);
printf("x*x took %f ms (%d eval in %d ms)\n",
(double)(st2-st)/(N-1),N-1,st2-st);
N=1; st = cputime();
do {
for (i=0;i<N;i++) mpfr_div(z, x, y, GMP_RNDN);
N=2*N;
st2=cputime();
} while (st2-st<1000);
printf("x/y took %f ms (%d eval in %d ms)\n",
(double)(st2-st)/(N-1),N-1,st2-st);
N=1; st = cputime();
do {
for (i=0;i<N;i++) mpfr_sqrt(z, x, GMP_RNDN);
N=2*N;
st2=cputime();
} while (st2-st<1000);
printf("sqrt(x) took %f ms (%d eval in %d ms)\n",
(double)(st2-st)/(N-1),N-1,st2-st);
N=1; st = cputime();
do {
for (i=0;i<N;i++) mpfr_exp(z, x, GMP_RNDN);
N=2*N;
st2=cputime();
} while (st2-st<1000);
printf("exp(x) took %f ms (%d eval in %d ms)\n",
(double)(st2-st)/(N-1),N-1,st2-st);
N=1; st = cputime();
do {
for (i=0;i<N;i++) mpfr_log(z, x, GMP_RNDN);
N=2*N;
st2=cputime();
} while (st2-st<1000);
printf("log(x) took %f ms (%d eval in %d ms)\n",
(double)(st2-st)/(N-1),N-1,st2-st);
N=1; st = cputime();
do {
for (i=0;i<N;i++) mpfr_sin(z, x, GMP_RNDN);
N=2*N;
st2=cputime();
} while (st2-st<1000);
printf("sin(x) took %f ms (%d eval in %d ms)\n",
(double)(st2-st)/(N-1),N-1,st2-st);
N=1; st = cputime();
do {
for (i=0;i<N;i++) mpfr_cos(z, x, GMP_RNDN);
N=2*N;
st2=cputime();
} while (st2-st<1000);
printf("cos(x) took %f ms (%d eval in %d ms)\n",
(double)(st2-st)/(N-1),N-1,st2-st);
N=1; st = cputime();
do {
for (i=0;i<N;i++) mpfr_acos(z, x, GMP_RNDN);
N=2*N;
st2=cputime();
} while (st2-st<1000);
printf("arccos(x) took %f ms (%d eval in %d ms)\n",
(double)(st2-st)/(N-1),N-1,st2-st);
N=1; st = cputime();
do {
for (i=0;i<N;i++) mpfr_atan(z, x, GMP_RNDN);
N=2*N;
st2=cputime();
} while (st2-st<1000);
printf("arctan(x) took %f ms (%d eval in %d ms)\n",
(double)(st2-st)/(N-1),N-1,st2-st);
mpfr_clear(x); mpfr_clear(y); mpfr_clear(z);
return 0;
}
MpfrFloat MpfrFloat::acos(const MpfrFloat& value)
{
MpfrFloat retval(MpfrFloat::kNoInitialization);
mpfr_acos(retval.mData->mFloat, value.mData->mFloat, GMP_RNDN);
return retval;
}
int
main (void)
{
mpfr_t x, y;
int r;
tests_start_mpfr ();
special_overflow ();
special ();
mpfr_init (x);
mpfr_init (y);
MPFR_SET_NAN(x);
mpfr_acos (y, x, MPFR_RNDN);
if (mpfr_nan_p(y) == 0)
{
printf ("Error: acos(NaN) != NaN\n");
exit (1);
}
mpfr_set_ui (x, 2, MPFR_RNDN);
mpfr_acos (y, x, MPFR_RNDN);
if (mpfr_nan_p(y) == 0)
{
printf ("Error: acos(2) != NaN\n");
exit (1);
}
mpfr_set_si (x, -2, MPFR_RNDN);
mpfr_acos (y, x, MPFR_RNDN);
if (mpfr_nan_p(y) == 0)
{
printf ("Error: acos(-2) != NaN\n");
exit (1);
}
/* acos (1) = 0 */
mpfr_set_ui (x, 1, MPFR_RNDN);
mpfr_acos (y, x, MPFR_RNDN);
if (mpfr_cmp_ui (y, 0) || mpfr_sgn (y) < 0)
{
printf ("Error: acos(1) != +0.0\n");
exit (1);
}
/* acos (0) = Pi/2 */
for (r = 0; r < MPFR_RND_MAX; r++)
{
mpfr_set_ui (x, 0, MPFR_RNDN); /* exact */
mpfr_acos (y, x, (mpfr_rnd_t) r);
mpfr_const_pi (x, (mpfr_rnd_t) r);
mpfr_div_2exp (x, x, 1, MPFR_RNDN); /* exact */
if (mpfr_cmp (x, y))
{
printf ("Error: acos(0) != Pi/2 for rnd=%s\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) r));
exit (1);
}
}
/* acos (-1) = Pi */
for (r = 0; r < MPFR_RND_MAX; r++)
{
mpfr_set_si (x, -1, MPFR_RNDN); /* exact */
mpfr_acos (y, x, (mpfr_rnd_t) r);
mpfr_const_pi (x, (mpfr_rnd_t) r);
if (mpfr_cmp (x, y))
{
printf ("Error: acos(1) != Pi for rnd=%s\n",
mpfr_print_rnd_mode ((mpfr_rnd_t) r));
exit (1);
}
}
test_generic (2, 100, 7);
mpfr_clear (x);
mpfr_clear (y);
data_check ("data/acos", mpfr_acos, "mpfr_acos");
bad_cases (mpfr_acos, mpfr_cos, "mpfr_acos", 0, -40, 2, 4, 128, 800, 30);
tests_end_mpfr ();
return 0;
}
int
mpc_acos (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
{
int inex_re, inex_im, inex;
mpfr_prec_t p_re, p_im, p;
mpc_t z1;
mpfr_t pi_over_2;
mpfr_exp_t e1, e2;
mpfr_rnd_t rnd_im;
mpc_rnd_t rnd1;
inex_re = 0;
inex_im = 0;
/* special values */
if (mpfr_nan_p (mpc_realref (op)) || mpfr_nan_p (mpc_imagref (op)))
{
if (mpfr_inf_p (mpc_realref (op)) || mpfr_inf_p (mpc_imagref (op)))
{
mpfr_set_inf (mpc_imagref (rop), mpfr_signbit (mpc_imagref (op)) ? +1 : -1);
mpfr_set_nan (mpc_realref (rop));
}
else if (mpfr_zero_p (mpc_realref (op)))
{
inex_re = set_pi_over_2 (mpc_realref (rop), +1, MPC_RND_RE (rnd));
mpfr_set_nan (mpc_imagref (rop));
}
else
{
mpfr_set_nan (mpc_realref (rop));
mpfr_set_nan (mpc_imagref (rop));
}
return MPC_INEX (inex_re, 0);
}
if (mpfr_inf_p (mpc_realref (op)) || mpfr_inf_p (mpc_imagref (op)))
{
if (mpfr_inf_p (mpc_realref (op)))
{
if (mpfr_inf_p (mpc_imagref (op)))
{
if (mpfr_sgn (mpc_realref (op)) > 0)
{
inex_re =
set_pi_over_2 (mpc_realref (rop), +1, MPC_RND_RE (rnd));
mpfr_div_2ui (mpc_realref (rop), mpc_realref (rop), 1, GMP_RNDN);
}
else
{
/* the real part of the result is 3*pi/4
a = o(pi) error(a) < 1 ulp(a)
b = o(3*a) error(b) < 2 ulp(b)
c = b/4 exact
thus 1 bit is lost */
mpfr_t x;
mpfr_prec_t prec;
int ok;
mpfr_init (x);
prec = mpfr_get_prec (mpc_realref (rop));
p = prec;
do
{
p += mpc_ceil_log2 (p);
mpfr_set_prec (x, p);
mpfr_const_pi (x, GMP_RNDD);
mpfr_mul_ui (x, x, 3, GMP_RNDD);
ok =
mpfr_can_round (x, p - 1, GMP_RNDD, MPC_RND_RE (rnd),
prec+(MPC_RND_RE (rnd) == GMP_RNDN));
} while (ok == 0);
inex_re =
mpfr_div_2ui (mpc_realref (rop), x, 2, MPC_RND_RE (rnd));
mpfr_clear (x);
}
}
else
{
if (mpfr_sgn (mpc_realref (op)) > 0)
mpfr_set_ui (mpc_realref (rop), 0, GMP_RNDN);
else
inex_re = mpfr_const_pi (mpc_realref (rop), MPC_RND_RE (rnd));
}
}
else
inex_re = set_pi_over_2 (mpc_realref (rop), +1, MPC_RND_RE (rnd));
mpfr_set_inf (mpc_imagref (rop), mpfr_signbit (mpc_imagref (op)) ? +1 : -1);
return MPC_INEX (inex_re, 0);
}
/* pure real argument */
if (mpfr_zero_p (mpc_imagref (op)))
{
int s_im;
s_im = mpfr_signbit (mpc_imagref (op));
if (mpfr_cmp_ui (mpc_realref (op), 1) > 0)
{
if (s_im)
inex_im = mpfr_acosh (mpc_imagref (rop), mpc_realref (op),
MPC_RND_IM (rnd));
else
inex_im = -mpfr_acosh (mpc_imagref (rop), mpc_realref (op),
INV_RND (MPC_RND_IM (rnd)));
mpfr_set_ui (mpc_realref (rop), 0, GMP_RNDN);
}
else if (mpfr_cmp_si (mpc_realref (op), -1) < 0)
{
mpfr_t minus_op_re;
minus_op_re[0] = mpc_realref (op)[0];
MPFR_CHANGE_SIGN (minus_op_re);
if (s_im)
inex_im = mpfr_acosh (mpc_imagref (rop), minus_op_re,
MPC_RND_IM (rnd));
else
inex_im = -mpfr_acosh (mpc_imagref (rop), minus_op_re,
INV_RND (MPC_RND_IM (rnd)));
inex_re = mpfr_const_pi (mpc_realref (rop), MPC_RND_RE (rnd));
}
else
{
inex_re = mpfr_acos (mpc_realref (rop), mpc_realref (op), MPC_RND_RE (rnd));
mpfr_set_ui (mpc_imagref (rop), 0, MPC_RND_IM (rnd));
}
if (!s_im)
mpc_conj (rop, rop, MPC_RNDNN);
return MPC_INEX (inex_re, inex_im);
}
/* pure imaginary argument */
if (mpfr_zero_p (mpc_realref (op)))
{
inex_re = set_pi_over_2 (mpc_realref (rop), +1, MPC_RND_RE (rnd));
inex_im = -mpfr_asinh (mpc_imagref (rop), mpc_imagref (op),
INV_RND (MPC_RND_IM (rnd)));
mpc_conj (rop,rop, MPC_RNDNN);
return MPC_INEX (inex_re, inex_im);
}
/* regular complex argument: acos(z) = Pi/2 - asin(z) */
p_re = mpfr_get_prec (mpc_realref(rop));
p_im = mpfr_get_prec (mpc_imagref(rop));
p = p_re;
mpc_init3 (z1, p, p_im); /* we round directly the imaginary part to p_im,
with rounding mode opposite to rnd_im */
rnd_im = MPC_RND_IM(rnd);
/* the imaginary part of asin(z) has the same sign as Im(z), thus if
Im(z) > 0 and rnd_im = RNDZ, we want to round the Im(asin(z)) to -Inf
so that -Im(asin(z)) is rounded to zero */
if (rnd_im == GMP_RNDZ)
rnd_im = mpfr_sgn (mpc_imagref(op)) > 0 ? GMP_RNDD : GMP_RNDU;
else
rnd_im = rnd_im == GMP_RNDU ? GMP_RNDD
: rnd_im == GMP_RNDD ? GMP_RNDU
: rnd_im; /* both RNDZ and RNDA map to themselves for -asin(z) */
rnd1 = MPC_RND (GMP_RNDN, rnd_im);
mpfr_init2 (pi_over_2, p);
for (;;)
{
p += mpc_ceil_log2 (p) + 3;
mpfr_set_prec (mpc_realref(z1), p);
mpfr_set_prec (pi_over_2, p);
set_pi_over_2 (pi_over_2, +1, GMP_RNDN);
e1 = 1; /* Exp(pi_over_2) */
inex = mpc_asin (z1, op, rnd1); /* asin(z) */
MPC_ASSERT (mpfr_sgn (mpc_imagref(z1)) * mpfr_sgn (mpc_imagref(op)) > 0);
inex_im = MPC_INEX_IM(inex); /* inex_im is in {-1, 0, 1} */
e2 = mpfr_get_exp (mpc_realref(z1));
mpfr_sub (mpc_realref(z1), pi_over_2, mpc_realref(z1), GMP_RNDN);
if (!mpfr_zero_p (mpc_realref(z1)))
{
/* the error on x=Re(z1) is bounded by 1/2 ulp(x) + 2^(e1-p-1) +
2^(e2-p-1) */
e1 = e1 >= e2 ? e1 + 1 : e2 + 1;
/* the error on x is bounded by 1/2 ulp(x) + 2^(e1-p-1) */
e1 -= mpfr_get_exp (mpc_realref(z1));
/* the error on x is bounded by 1/2 ulp(x) [1 + 2^e1] */
e1 = e1 <= 0 ? 0 : e1;
/* the error on x is bounded by 2^e1 * ulp(x) */
mpfr_neg (mpc_imagref(z1), mpc_imagref(z1), GMP_RNDN); /* exact */
inex_im = -inex_im;
if (mpfr_can_round (mpc_realref(z1), p - e1, GMP_RNDN, GMP_RNDZ,
p_re + (MPC_RND_RE(rnd) == GMP_RNDN)))
break;
}
}
inex = mpc_set (rop, z1, rnd);
inex_re = MPC_INEX_RE(inex);
mpc_clear (z1);
mpfr_clear (pi_over_2);
return MPC_INEX(inex_re, inex_im);
}
void bvisit(const ACsc &x) {
apply(result_, *(x.get_arg()));
mpfr_ui_div(result_, 1, result_, rnd_);
mpfr_acos(result_, result_, rnd_);
}
void bvisit(const ACos &x) {
apply(result_, *(x.get_arg()));
mpfr_acos(result_, result_, rnd_);
}
CGAL::Gmpfr acos(const CGAL::Gmpfr &x)
{
CGAL::Gmpfr result(0, gmp_result_precision(x));
mpfr_acos(result.fr(), x.fr(), gmp_rounding_mode(CGAL::Gmpfr::get_default_rndmode()));
return result;
}
