decimal r_tan(const decimal& a,bool round)
{
#ifdef USE_CGAL
CGAL::Gmpfr m;
CGAL::Gmpfr n=to_gmpfr(a);
mpfr_tan(m.fr(),n.fr(),MPFR_RNDN);
return r_round_preference(decimal(m),round);
#else
return r_round_preference(tan(a),round);
#endif
}
//------------------------------------------------------------------------------
// Name:
//------------------------------------------------------------------------------
knumber_base *knumber_float::tan() {
#ifdef KNUMBER_USE_MPFR
mpfr_t mpfr;
mpfr_init_set_f(mpfr, mpf_, rounding_mode);
mpfr_tan(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< ::tan>(x);
}
#endif
}
REAL _tan(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_tan(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;
}
/// @brief tan keyword implementation
///
void program::rpn_tan(void) {
MIN_ARGUMENTS(1);
if (_stack->get_type(0) == cmd_number) {
floating_t* left = &((number*)_stack->get_obj(0))->_value;
CHECK_MPFR(mpfr_tan(left->mpfr, left->mpfr, floating_t::s_mpfr_rnd));
} else if (_stack->get_type(0) == cmd_complex) {
// tan(x+iy) = (sin(2x)+isinh(2y)) / cosh(2y)+cos(2x)
stack::copy_and_push_back(*_stack, _stack->size() - 1, _calc_stack);
floating_t* tmp = &((number*)_calc_stack.allocate_back(number::calc_size(), cmd_number))->_value;
floating_t* x = ((complex*)_calc_stack.get_obj(1))->re();
floating_t* y = ((complex*)_calc_stack.get_obj(1))->im();
floating_t* re = ((complex*)_stack->get_obj(0))->re();
floating_t* im = ((complex*)_stack->get_obj(0))->im();
// x->2x
CHECK_MPFR(mpfr_mul_si(x->mpfr, x->mpfr, 2, floating_t::s_mpfr_rnd));
// y->2y
CHECK_MPFR(mpfr_mul_si(y->mpfr, y->mpfr, 2, floating_t::s_mpfr_rnd));
// sin(2x)+sinh(2y)
CHECK_MPFR(mpfr_sin(re->mpfr, x->mpfr, floating_t::s_mpfr_rnd));
CHECK_MPFR(mpfr_sinh(im->mpfr, y->mpfr, floating_t::s_mpfr_rnd));
// cosh(2y)+cos(2x)
CHECK_MPFR(mpfr_cosh(tmp->mpfr, y->mpfr, floating_t::s_mpfr_rnd));
CHECK_MPFR(mpfr_cos(x->mpfr, x->mpfr, floating_t::s_mpfr_rnd));
CHECK_MPFR(mpfr_add(tmp->mpfr, tmp->mpfr, x->mpfr, floating_t::s_mpfr_rnd));
// sin(2x)+sinh(2y) / (cosh(2y)+cos(2x))
CHECK_MPFR(mpfr_div(re->mpfr, re->mpfr, tmp->mpfr, floating_t::s_mpfr_rnd));
CHECK_MPFR(mpfr_div(im->mpfr, im->mpfr, tmp->mpfr, floating_t::s_mpfr_rnd));
_calc_stack.pop_back(2);
} else
ERR_CONTEXT(ret_bad_operand_type);
}
int
mpc_tan (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
{
mpc_t x, y;
mpfr_prec_t prec;
mpfr_exp_t err;
int ok = 0;
int inex;
/* special values */
if (!mpc_fin_p (op))
{
if (mpfr_nan_p (mpc_realref (op)))
{
if (mpfr_inf_p (mpc_imagref (op)))
/* tan(NaN -i*Inf) = +/-0 -i */
/* tan(NaN +i*Inf) = +/-0 +i */
{
/* exact unless 1 is not in exponent range */
inex = mpc_set_si_si (rop, 0,
(MPFR_SIGN (mpc_imagref (op)) < 0) ? -1 : +1,
rnd);
}
else
/* tan(NaN +i*y) = NaN +i*NaN, when y is finite */
/* tan(NaN +i*NaN) = NaN +i*NaN */
{
mpfr_set_nan (mpc_realref (rop));
mpfr_set_nan (mpc_imagref (rop));
inex = MPC_INEX (0, 0); /* always exact */
}
}
else if (mpfr_nan_p (mpc_imagref (op)))
{
if (mpfr_cmp_ui (mpc_realref (op), 0) == 0)
/* tan(-0 +i*NaN) = -0 +i*NaN */
/* tan(+0 +i*NaN) = +0 +i*NaN */
{
mpc_set (rop, op, rnd);
inex = MPC_INEX (0, 0); /* always exact */
}
else
/* tan(x +i*NaN) = NaN +i*NaN, when x != 0 */
{
mpfr_set_nan (mpc_realref (rop));
mpfr_set_nan (mpc_imagref (rop));
inex = MPC_INEX (0, 0); /* always exact */
}
}
else if (mpfr_inf_p (mpc_realref (op)))
{
if (mpfr_inf_p (mpc_imagref (op)))
/* tan(-Inf -i*Inf) = -/+0 -i */
/* tan(-Inf +i*Inf) = -/+0 +i */
/* tan(+Inf -i*Inf) = +/-0 -i */
/* tan(+Inf +i*Inf) = +/-0 +i */
{
const int sign_re = mpfr_signbit (mpc_realref (op));
int inex_im;
mpfr_set_ui (mpc_realref (rop), 0, MPC_RND_RE (rnd));
mpfr_setsign (mpc_realref (rop), mpc_realref (rop), sign_re, MPFR_RNDN);
/* exact, unless 1 is not in exponent range */
inex_im = mpfr_set_si (mpc_imagref (rop),
mpfr_signbit (mpc_imagref (op)) ? -1 : +1,
MPC_RND_IM (rnd));
inex = MPC_INEX (0, inex_im);
}
else
/* tan(-Inf +i*y) = tan(+Inf +i*y) = NaN +i*NaN, when y is
finite */
{
mpfr_set_nan (mpc_realref (rop));
mpfr_set_nan (mpc_imagref (rop));
inex = MPC_INEX (0, 0); /* always exact */
}
}
else
/* tan(x -i*Inf) = +0*sin(x)*cos(x) -i, when x is finite */
/* tan(x +i*Inf) = +0*sin(x)*cos(x) +i, when x is finite */
{
mpfr_t c;
mpfr_t s;
int inex_im;
mpfr_init (c);
mpfr_init (s);
mpfr_sin_cos (s, c, mpc_realref (op), MPFR_RNDN);
mpfr_set_ui (mpc_realref (rop), 0, MPC_RND_RE (rnd));
mpfr_setsign (mpc_realref (rop), mpc_realref (rop),
mpfr_signbit (c) != mpfr_signbit (s), MPFR_RNDN);
/* exact, unless 1 is not in exponent range */
inex_im = mpfr_set_si (mpc_imagref (rop),
(mpfr_signbit (mpc_imagref (op)) ? -1 : +1),
MPC_RND_IM (rnd));
inex = MPC_INEX (0, inex_im);
mpfr_clear (s);
mpfr_clear (c);
}
return inex;
}
if (mpfr_zero_p (mpc_realref (op)))
/* tan(-0 -i*y) = -0 +i*tanh(y), when y is finite. */
/* tan(+0 +i*y) = +0 +i*tanh(y), when y is finite. */
{
int inex_im;
mpfr_set (mpc_realref (rop), mpc_realref (op), MPC_RND_RE (rnd));
inex_im = mpfr_tanh (mpc_imagref (rop), mpc_imagref (op), MPC_RND_IM (rnd));
return MPC_INEX (0, inex_im);
}
if (mpfr_zero_p (mpc_imagref (op)))
/* tan(x -i*0) = tan(x) -i*0, when x is finite. */
/* tan(x +i*0) = tan(x) +i*0, when x is finite. */
{
int inex_re;
inex_re = mpfr_tan (mpc_realref (rop), mpc_realref (op), MPC_RND_RE (rnd));
mpfr_set (mpc_imagref (rop), mpc_imagref (op), MPC_RND_IM (rnd));
return MPC_INEX (inex_re, 0);
}
/* ordinary (non-zero) numbers */
/* tan(op) = sin(op) / cos(op).
We use the following algorithm with rounding away from 0 for all
operations, and working precision w:
(1) x = A(sin(op))
(2) y = A(cos(op))
(3) z = A(x/y)
the error on Im(z) is at most 81 ulp,
the error on Re(z) is at most
7 ulp if k < 2,
8 ulp if k = 2,
else 5+k ulp, where
k = Exp(Re(x))+Exp(Re(y))-2min{Exp(Re(y)), Exp(Im(y))}-Exp(Re(x/y))
see proof in algorithms.tex.
*/
prec = MPC_MAX_PREC(rop);
mpc_init2 (x, 2);
mpc_init2 (y, 2);
err = 7;
do
{
mpfr_exp_t k, exr, eyr, eyi, ezr;
ok = 0;
/* FIXME: prevent addition overflow */
prec += mpc_ceil_log2 (prec) + err;
mpc_set_prec (x, prec);
mpc_set_prec (y, prec);
/* rounding away from zero: except in the cases x=0 or y=0 (processed
above), sin x and cos y are never exact, so rounding away from 0 is
rounding towards 0 and adding one ulp to the absolute value */
mpc_sin_cos (x, y, op, MPC_RNDZZ, MPC_RNDZZ);
MPFR_ADD_ONE_ULP (mpc_realref (x));
MPFR_ADD_ONE_ULP (mpc_imagref (x));
MPFR_ADD_ONE_ULP (mpc_realref (y));
MPFR_ADD_ONE_ULP (mpc_imagref (y));
MPC_ASSERT (mpfr_zero_p (mpc_realref (x)) == 0);
if ( mpfr_inf_p (mpc_realref (x)) || mpfr_inf_p (mpc_imagref (x))
|| mpfr_inf_p (mpc_realref (y)) || mpfr_inf_p (mpc_imagref (y))) {
/* If the real or imaginary part of x is infinite, it means that
Im(op) was large, in which case the result is
sign(tan(Re(op)))*0 + sign(Im(op))*I,
where sign(tan(Re(op))) = sign(Re(x))*sign(Re(y)). */
int inex_re, inex_im;
mpfr_set_ui (mpc_realref (rop), 0, MPFR_RNDN);
if (mpfr_sgn (mpc_realref (x)) * mpfr_sgn (mpc_realref (y)) < 0)
{
mpfr_neg (mpc_realref (rop), mpc_realref (rop), MPFR_RNDN);
inex_re = 1;
}
else
inex_re = -1; /* +0 is rounded down */
if (mpfr_sgn (mpc_imagref (op)) > 0)
{
mpfr_set_ui (mpc_imagref (rop), 1, MPFR_RNDN);
inex_im = 1;
}
else
{
mpfr_set_si (mpc_imagref (rop), -1, MPFR_RNDN);
inex_im = -1;
}
inex = MPC_INEX(inex_re, inex_im);
goto end;
}
exr = mpfr_get_exp (mpc_realref (x));
eyr = mpfr_get_exp (mpc_realref (y));
eyi = mpfr_get_exp (mpc_imagref (y));
/* some parts of the quotient may be exact */
inex = mpc_div (x, x, y, MPC_RNDZZ);
/* OP is no pure real nor pure imaginary, so in theory the real and
imaginary parts of its tangent cannot be null. However due to
rouding errors this might happen. Consider for example
tan(1+14*I) = 1.26e-10 + 1.00*I. For small precision sin(op) and
cos(op) differ only by a factor I, thus after mpc_div x = I and
its real part is zero. */
if (mpfr_zero_p (mpc_realref (x)) || mpfr_zero_p (mpc_imagref (x)))
{
err = prec; /* double precision */
continue;
}
if (MPC_INEX_RE (inex))
MPFR_ADD_ONE_ULP (mpc_realref (x));
if (MPC_INEX_IM (inex))
MPFR_ADD_ONE_ULP (mpc_imagref (x));
MPC_ASSERT (mpfr_zero_p (mpc_realref (x)) == 0);
ezr = mpfr_get_exp (mpc_realref (x));
/* FIXME: compute
k = Exp(Re(x))+Exp(Re(y))-2min{Exp(Re(y)), Exp(Im(y))}-Exp(Re(x/y))
avoiding overflow */
k = exr - ezr + MPC_MAX(-eyr, eyr - 2 * eyi);
err = k < 2 ? 7 : (k == 2 ? 8 : (5 + k));
/* Can the real part be rounded? */
ok = (!mpfr_number_p (mpc_realref (x)))
|| mpfr_can_round (mpc_realref(x), prec - err, MPFR_RNDN, MPFR_RNDZ,
MPC_PREC_RE(rop) + (MPC_RND_RE(rnd) == MPFR_RNDN));
if (ok)
{
/* Can the imaginary part be rounded? */
ok = (!mpfr_number_p (mpc_imagref (x)))
|| mpfr_can_round (mpc_imagref(x), prec - 6, MPFR_RNDN, MPFR_RNDZ,
MPC_PREC_IM(rop) + (MPC_RND_IM(rnd) == MPFR_RNDN));
}
}
while (ok == 0);
inex = mpc_set (rop, x, rnd);
end:
mpc_clear (x);
mpc_clear (y);
return inex;
}
MpfrFloat MpfrFloat::tan(const MpfrFloat& value)
{
MpfrFloat retval(MpfrFloat::kNoInitialization);
mpfr_tan(retval.mData->mFloat, value.mData->mFloat, GMP_RNDN);
return retval;
}
int
main (int argc, char *argv[])
{
mpfr_t x;
unsigned int i;
unsigned int prec[10] = {14, 15, 19, 22, 23, 24, 25, 40, 41, 52};
unsigned int prec2[10] = {4, 5, 6, 19, 70, 95, 100, 106, 107, 108};
tests_start_mpfr ();
check_nans ();
mpfr_init (x);
mpfr_set_prec (x, 2);
mpfr_set_str (x, "0.5", 10, MPFR_RNDN);
mpfr_tan (x, x, MPFR_RNDD);
if (mpfr_cmp_ui_2exp(x, 1, -1))
{
printf ("mpfr_tan(0.5, MPFR_RNDD) failed\n"
"expected 0.5, got");
mpfr_print_binary(x);
putchar('\n');
exit (1);
}
/* check that tan(3*Pi/4) ~ -1 */
for (i=0; i<10; i++)
{
mpfr_set_prec (x, prec[i]);
mpfr_const_pi (x, MPFR_RNDN);
mpfr_mul_ui (x, x, 3, MPFR_RNDN);
mpfr_div_ui (x, x, 4, MPFR_RNDN);
mpfr_tan (x, x, MPFR_RNDN);
if (mpfr_cmp_si (x, -1))
{
printf ("tan(3*Pi/4) fails for prec=%u\n", prec[i]);
exit (1);
}
}
/* check that tan(7*Pi/4) ~ -1 */
for (i=0; i<10; i++)
{
mpfr_set_prec (x, prec2[i]);
mpfr_const_pi (x, MPFR_RNDN);
mpfr_mul_ui (x, x, 7, MPFR_RNDN);
mpfr_div_ui (x, x, 4, MPFR_RNDN);
mpfr_tan (x, x, MPFR_RNDN);
if (mpfr_cmp_si (x, -1))
{
printf ("tan(3*Pi/4) fails for prec=%u\n", prec2[i]);
exit (1);
}
}
mpfr_clear (x);
test_generic (2, 100, 10);
data_check ("data/tan", mpfr_tan, "mpfr_tan");
bad_cases (mpfr_tan, mpfr_atan, "mpfr_tan", 256, -256, 255, 4, 128, 800, 40);
tests_end_mpfr ();
return 0;
}
static void
check_nans (void)
{
mpfr_t x, y;
mpfr_init2 (x, 123L);
mpfr_init2 (y, 123L);
mpfr_set_nan (x);
mpfr_tan (y, x, MPFR_RNDN);
if (! mpfr_nan_p (y))
{
printf ("Error: tan(NaN) != NaN\n");
exit (1);
}
mpfr_set_inf (x, 1);
mpfr_tan (y, x, MPFR_RNDN);
if (! mpfr_nan_p (y))
{
printf ("Error: tan(Inf) != NaN\n");
exit (1);
}
mpfr_set_inf (x, -1);
mpfr_tan (y, x, MPFR_RNDN);
if (! mpfr_nan_p (y))
{
printf ("Error: tan(-Inf) != NaN\n");
exit (1);
}
/* exercise recomputation */
mpfr_set_prec (x, 14);
mpfr_set_str_binary (x, "0.10100000101010E0");
mpfr_set_prec (y, 24);
mpfr_tan (y, x, MPFR_RNDU);
mpfr_set_prec (x, 24);
mpfr_set_str_binary (x, "101110011011001100100001E-24");
MPFR_ASSERTN(mpfr_cmp (x, y) == 0);
/* Compute ~Pi/2 to check overflow */
mpfr_set_prec (x, 20000);
mpfr_const_pi (x, MPFR_RNDD);
mpfr_div_2ui (x, x, 1, MPFR_RNDN);
mpfr_set_prec (y, 24);
mpfr_tan (y, x, MPFR_RNDN);
if (mpfr_cmp_str (y, "0.100011101101011000100011E20001", 2, MPFR_RNDN))
{
printf("Error computing tan(~Pi/2)\n");
mpfr_dump (y);
exit (1);
}
/* bug found by Kaveh Ghazi on 13 Jul 2007 */
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
mpfr_set_str_binary (x, "0.10011100110111000001000010110100101000000000000000000E34");
mpfr_tan (y, x, MPFR_RNDN);
mpfr_set_str_binary (x, "0.1000010011001010001000010100000110100111000011010101E41");
MPFR_ASSERTN(mpfr_cmp (x, y) == 0);
mpfr_clear (x);
mpfr_clear (y);
}
void bvisit(const Tan &x) {
apply(result_, *(x.get_arg()));
mpfr_tan(result_, result_, rnd_);
}
