static void
special (void)
{
mpfr_t x;
int i;
mpfr_init (x);
mpfr_set_nan (x);
mpfr_sinh (x, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_nan_p (x));
mpfr_set_inf (x, 1);
mpfr_sinh (x, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
mpfr_set_inf (x, -1);
mpfr_sinh (x, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) < 0);
mpfr_set_prec (x, 10);
mpfr_set_str_binary (x, "-0.1001011001");
mpfr_sinh (x, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_si_2exp (x, -159, -8) == 0);
/* corner case */
mpfr_set_prec (x, 2);
mpfr_set_str_binary (x, "1E-6");
mpfr_sinh (x, x, MPFR_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui_2exp (x, 1, -6) == 0);
mpfr_clear_flags ();
mpfr_set_str_binary (x, "1E1000000000");
i = mpfr_sinh (x, x, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_INF (x) && MPFR_SIGN (x) > 0);
MPFR_ASSERTN (mpfr_overflow_p ());
MPFR_ASSERTN (i == 1);
mpfr_clear_flags ();
mpfr_set_str_binary (x, "-1E1000000000");
i = mpfr_sinh (x, x, MPFR_RNDN);
MPFR_ASSERTN (MPFR_IS_INF (x) && MPFR_SIGN (x) < 0);
MPFR_ASSERTN (mpfr_overflow_p () && !mpfr_underflow_p ());
MPFR_ASSERTN (i == -1);
mpfr_clear_flags ();
mpfr_set_str_binary (x, "-1E1000000000");
i = mpfr_sinh (x, x, MPFR_RNDD);
MPFR_ASSERTN (MPFR_IS_INF (x) && MPFR_SIGN (x) < 0);
MPFR_ASSERTN (mpfr_overflow_p () && !mpfr_underflow_p ());
MPFR_ASSERTN (i == -1);
mpfr_clear_flags ();
mpfr_set_str_binary (x, "-1E1000000000");
i = mpfr_sinh (x, x, MPFR_RNDU);
MPFR_ASSERTN (!MPFR_IS_INF (x) && MPFR_SIGN (x) < 0);
MPFR_ASSERTN (mpfr_overflow_p () && !mpfr_underflow_p ());
MPFR_ASSERTN (i == 1);
mpfr_clear (x);
}
/// @brief sin keyword implementation
///
void program::rpn_sin(void) {
MIN_ARGUMENTS(1);
if (_stack->get_type(0) == cmd_number) {
floating_t* left = &((number*)_stack->get_obj(0))->_value;
CHECK_MPFR(mpfr_sin(left->mpfr, left->mpfr, floating_t::s_mpfr_rnd));
} else if (_stack->get_type(0) == cmd_complex) {
// sin(x+iy)=sin(x)cosh(y)+icos(x)sinh(y)
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();
CHECK_MPFR(mpfr_sin(re->mpfr, x->mpfr, floating_t::s_mpfr_rnd));
CHECK_MPFR(mpfr_cosh(tmp->mpfr, y->mpfr, floating_t::s_mpfr_rnd));
CHECK_MPFR(mpfr_mul(re->mpfr, re->mpfr, tmp->mpfr, floating_t::s_mpfr_rnd));
CHECK_MPFR(mpfr_cos(im->mpfr, x->mpfr, floating_t::s_mpfr_rnd));
CHECK_MPFR(mpfr_sinh(tmp->mpfr, y->mpfr, floating_t::s_mpfr_rnd));
CHECK_MPFR(mpfr_mul(im->mpfr, im->mpfr, tmp->mpfr, floating_t::s_mpfr_rnd));
_calc_stack.pop_back(2);
} else
ERR_CONTEXT(ret_bad_operand_type);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("sinh....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
arb_t a, b;
fmpq_t q;
mpfr_t t;
slong 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_sinh(t, t, MPFR_RNDN);
arb_sinh(b, a, prec);
if (!arb_contains_mpfr(b, t))
{
flint_printf("FAIL: containment\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_abort();
}
arb_sinh(a, a, prec);
if (!arb_equal(a, b))
{
flint_printf("FAIL: aliasing\n\n");
flint_abort();
}
arb_clear(a);
arb_clear(b);
fmpq_clear(q);
mpfr_clear(t);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
decimal r_sinh(const decimal& a,bool round)
{
#ifdef USE_CGAL
CGAL::Gmpfr m;
CGAL::Gmpfr n=to_gmpfr(a);
mpfr_sinh(m.fr(),n.fr(),MPFR_RNDN);
return r_round_preference(decimal(m),round);
#else
return r_round_preference(sinh(a),round);
#endif
}
//------------------------------------------------------------------------------
// Name:
//------------------------------------------------------------------------------
knumber_base *knumber_float::sinh() {
#ifdef KNUMBER_USE_MPFR
mpfr_t mpfr;
mpfr_init_set_f(mpfr, mpf_, rounding_mode);
mpfr_sinh(mpfr, mpfr, rounding_mode);
mpfr_get_f(mpf_, mpfr, rounding_mode);
mpfr_clear(mpfr);
return this;
#else
const double x = mpf_get_d(mpf_);
return execute_libc_func< ::sinh>(x);
#endif
}
/* check against sinh, cosh */
static void
check (mpfr_t x, mpfr_rnd_t rnd)
{
mpfr_t s, c, sx, cx;
int isc, is, ic;
mpfr_inits2 (MPFR_PREC(x), s, c, sx, cx, (mpfr_ptr) 0);
isc = mpfr_sinh_cosh (sx, cx, x, rnd);
is = mpfr_sinh (s, x, rnd);
ic = mpfr_cosh (c, x, rnd);
if (!mpfr_equal_p (s, sx) || !mpfr_equal_p (c, cx))
failed (x, s, sx, c, cx);
MPFR_ASSERTN (isc = is || ic);
mpfr_clears (s, c, sx, cx, (mpfr_ptr) 0);
}
static int
mpc_sin_cos_imag (mpc_ptr rop_sin, mpc_ptr rop_cos, mpc_srcptr op,
mpc_rnd_t rnd_sin, mpc_rnd_t rnd_cos)
/* assumes that op is purely imaginary */
{
int inex_sin_im = 0, inex_cos_re = 0;
/* assume exact if not computed */
int overlap;
mpc_t op_loc;
overlap = (rop_sin == op || rop_cos == op);
if (overlap) {
mpc_init3 (op_loc, MPC_PREC_RE (op), MPC_PREC_IM (op));
mpc_set (op_loc, op, MPC_RNDNN);
}
else
op_loc [0] = op [0];
if (rop_sin != NULL) {
/* sin(+-O +i*y) = +-0 +i*sinh(y) */
mpfr_set (MPC_RE(rop_sin), MPC_RE(op_loc), GMP_RNDN);
inex_sin_im = mpfr_sinh (MPC_IM(rop_sin), MPC_IM(op_loc), MPC_RND_IM(rnd_sin));
}
if (rop_cos != NULL) {
/* cos(-0 - i * y) = cos(+0 + i * y) = cosh(y) - i * 0,
cos(-0 + i * y) = cos(+0 - i * y) = cosh(y) + i * 0,
where y >= 0 */
if (mpfr_zero_p (MPC_IM (op_loc)))
inex_cos_re = mpfr_set_ui (MPC_RE (rop_cos), 1ul, MPC_RND_RE (rnd_cos));
else
inex_cos_re = mpfr_cosh (MPC_RE (rop_cos), MPC_IM (op_loc), MPC_RND_RE (rnd_cos));
mpfr_set_ui (MPC_IM (rop_cos), 0ul, MPC_RND_IM (rnd_cos));
if (mpfr_signbit (MPC_RE (op_loc)) == mpfr_signbit (MPC_IM (op_loc)))
MPFR_CHANGE_SIGN (MPC_IM (rop_cos));
}
if (overlap)
mpc_clear (op_loc);
return MPC_INEX12 (MPC_INEX (0, inex_sin_im), MPC_INEX (inex_cos_re, 0));
}
static int
check_NAN (void)
{
mpfr_t t, ch,sh,th,ach,ash,ath;
int tester;
int fail = 0;
mpfr_init2(t,200);
mpfr_init2(ch,200);
mpfr_init2(sh,200);
mpfr_init2(th,200);
mpfr_init2(ach,200);
mpfr_init2(ash,200);
mpfr_init2(ath,200);
MPFR_SET_NAN(t);
/******cosh********/
tester=mpfr_cosh(ch,t,MPFR_RNDD);
if (!MPFR_IS_NAN(ch) || tester!=0)
{
printf("cosh NAN \n");
fail = 1;
goto clean_up;
}
/******sinh********/
tester=mpfr_sinh(sh,t,MPFR_RNDD);
if (!MPFR_IS_NAN(sh) || tester!=0)
{
printf("sinh NAN \n");
fail = 1;
goto clean_up;
}
/******tanh********/
tester=mpfr_tanh(th,t,MPFR_RNDD);
if (!MPFR_IS_NAN(th) || tester!=0)
{
printf("tanh NAN \n");
fail = 1;
goto clean_up;
}
/******acosh********/
tester=mpfr_acosh(ach,t,MPFR_RNDD);
if (!MPFR_IS_NAN(ach) || tester!=0)
{
printf("acosh NAN \n");
fail = 1;
goto clean_up;
}
/******asinh********/
tester=mpfr_asinh(ash,t,MPFR_RNDD);
if (!MPFR_IS_NAN(ash) || tester!=0)
{
printf("asinh NAN \n");
fail = 1;
goto clean_up;
}
/******atanh********/
tester=mpfr_atanh(ath,t,MPFR_RNDD);
if (!MPFR_IS_NAN(ath) || tester!=0)
{
printf("atanh NAN \n");
fail = 1;
goto clean_up;
}
clean_up:
mpfr_clear(t);
mpfr_clear(ch);
mpfr_clear(sh);
mpfr_clear(th);
mpfr_clear(ach);
mpfr_clear(ash);
mpfr_clear(ath);
return fail;
}
static int
check_INF (void)
{
mpfr_t t, ch, sh, th, ach, ash, ath;
int tester;
int fail = 0;
mpfr_init2 (t, 200);
mpfr_init2 (ch, 200);
mpfr_init2 (sh, 200);
mpfr_init2 (th, 200);
mpfr_init2 (ach, 200);
mpfr_init2 (ash, 200);
mpfr_init2 (ath, 200);
MPFR_SET_INF(t);
if(MPFR_IS_NEG (t))
MPFR_CHANGE_SIGN(t);
/******cosh********/
tester = mpfr_cosh(ch,t,MPFR_RNDD);
if (!MPFR_IS_INF(ch) || MPFR_IS_NEG (ch) || tester!=0)
{
printf("cosh(INF) \n");
fail = 1;
goto clean_up;
}
/******sinh********/
tester=mpfr_sinh(sh,t,MPFR_RNDD);
if (!MPFR_IS_INF(sh) || MPFR_IS_NEG (sh) || tester!=0)
{
printf("sinh(INF) \n");
fail = 1;
goto clean_up;
}
/******tanh********/
tester=mpfr_tanh(th,t,MPFR_RNDD);
if (mpfr_cmp_ui(th,1) != 0 || tester!=0)
{
printf("tanh(INF) \n");
fail = 1;
goto clean_up;
}
/******acosh********/
tester=mpfr_acosh(ach,t,MPFR_RNDD);
if (!MPFR_IS_INF(ach) || MPFR_IS_NEG (ach) || tester!=0)
{
printf("acosh(INF) \n");
fail = 1;
goto clean_up;
}
/******asinh********/
tester=mpfr_asinh(ash,t,MPFR_RNDD);
if (!MPFR_IS_INF(ash) || MPFR_IS_NEG (ash) || tester!=0)
{
printf("asinh(INF) \n");
fail = 1;
goto clean_up;
}
/******atanh********/
tester = mpfr_atanh (ath, t, MPFR_RNDD);
if (!MPFR_IS_NAN(ath) || tester != 0)
{
printf("atanh(INF) \n");
fail = 1;
goto clean_up;
}
MPFR_CHANGE_SIGN(t);
/******cosh********/
tester=mpfr_cosh(ch,t,MPFR_RNDD);
if (!MPFR_IS_INF(ch) || MPFR_IS_NEG (ch) || tester!=0)
{
printf("cosh(-INF) \n");
fail = 1;
goto clean_up;
}
/******sinh********/
tester=mpfr_sinh(sh,t,MPFR_RNDD);
if (!MPFR_IS_INF(sh) || MPFR_IS_POS (sh) || tester!=0)
{
printf("sinh(-INF) \n");
fail = 1;
goto clean_up;
}
/******tanh********/
tester=mpfr_tanh(th,t,MPFR_RNDD);
if (!mpfr_cmp_ui(th,-1) || tester!=0)
{
printf("tanh(-INF) \n");
fail = 1;
goto clean_up;
}
/******acosh********/
tester=mpfr_acosh(ach,t,MPFR_RNDD);
if (!MPFR_IS_NAN(ach) || tester!=0)
{
printf("acosh(-INF) \n");
fail = 1;
goto clean_up;
}
/******asinh********/
tester=mpfr_asinh(ash,t,MPFR_RNDD);
if (!MPFR_IS_INF(ash) || MPFR_IS_POS (ash) || tester!=0)
{
printf("asinh(-INF) \n");
fail = 1;
goto clean_up;
}
/******atanh********/
tester = mpfr_atanh (ath, t, MPFR_RNDD);
if (!MPFR_IS_NAN(ath) || tester != 0)
{
printf("atanh(-INF) \n");
fail = 1;
goto clean_up;
}
clean_up:
mpfr_clear(t);
mpfr_clear(ch);
mpfr_clear(sh);
mpfr_clear(th);
mpfr_clear(ach);
mpfr_clear(ash);
mpfr_clear(ath);
return fail;
}
static int
check_zero (void)
{
mpfr_t t, ch,sh,th,ach,ash,ath;
int tester;
int fail = 0;
mpfr_init2(t,200);
mpfr_init2(ch,200);
mpfr_init2(sh,200);
mpfr_init2(th,200);
mpfr_init2(ach,200);
mpfr_init2(ash,200);
mpfr_init2(ath,200);
mpfr_set_ui(t,0,MPFR_RNDD);
/******cosh********/
tester = mpfr_cosh (ch, t, MPFR_RNDD);
if (mpfr_cmp_ui(ch, 1) || tester)
{
printf("cosh(0) \n");
fail = 1;
goto clean_up;
}
/******sinh********/
tester = mpfr_sinh (sh, t, MPFR_RNDD);
if (!MPFR_IS_ZERO(sh) || tester)
{
printf("sinh(0) \n");
fail = 1;
goto clean_up;
}
/******tanh********/
tester = mpfr_tanh (th, t, MPFR_RNDD);
if (!MPFR_IS_ZERO(th) || tester)
{
printf("tanh(0) \n");
fail = 1;
goto clean_up;
}
/******acosh********/
tester=mpfr_acosh(ach,t,MPFR_RNDD);
if (!MPFR_IS_NAN(ach) || tester)
{
printf("acosh(0) \n");
fail = 1;
goto clean_up;
}
/******asinh********/
tester=mpfr_asinh(ash,t,MPFR_RNDD);
if (!MPFR_IS_ZERO(ash) || tester)
{
printf("asinh(0) \n");
fail = 1;
goto clean_up;
}
/******atanh********/
tester=mpfr_atanh(ath,t,MPFR_RNDD);
if (!MPFR_IS_ZERO(ath) || tester)
{
printf("atanh(0) \n");
fail = 1;
goto clean_up;
}
clean_up:
mpfr_clear(t);
mpfr_clear(ch);
mpfr_clear(sh);
mpfr_clear(th);
mpfr_clear(ach);
mpfr_clear(ash);
mpfr_clear(ath);
return fail;
}
int
mpfr_sinh (mpfr_ptr y, mpfr_srcptr xt, mpfr_rnd_t rnd_mode)
{
mpfr_t x;
int inexact;
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode),
("y[%Pu]=%.*Rg inexact=%d",
mpfr_get_prec (y), mpfr_log_prec, y, inexact));
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt)))
{
if (MPFR_IS_NAN (xt))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (xt))
{
MPFR_SET_INF (y);
MPFR_SET_SAME_SIGN (y, xt);
MPFR_RET (0);
}
else /* xt is zero */
{
MPFR_ASSERTD (MPFR_IS_ZERO (xt));
MPFR_SET_ZERO (y); /* sinh(0) = 0 */
MPFR_SET_SAME_SIGN (y, xt);
MPFR_RET (0);
}
}
/* sinh(x) = x + x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */
MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, xt, -2 * MPFR_GET_EXP(xt), 2, 1,
rnd_mode, {});
MPFR_TMP_INIT_ABS (x, xt);
{
mpfr_t t, ti;
mpfr_exp_t d;
mpfr_prec_t Nt; /* Precision of the intermediary variable */
long int err; /* Precision of error */
MPFR_ZIV_DECL (loop);
MPFR_SAVE_EXPO_DECL (expo);
MPFR_GROUP_DECL (group);
MPFR_SAVE_EXPO_MARK (expo);
/* compute the precision of intermediary variable */
Nt = MAX (MPFR_PREC (x), MPFR_PREC (y));
/* the optimal number of bits : see algorithms.ps */
Nt = Nt + MPFR_INT_CEIL_LOG2 (Nt) + 4;
/* If x is near 0, exp(x) - 1/exp(x) = 2*x+x^3/3+O(x^5) */
if (MPFR_GET_EXP (x) < 0)
Nt -= 2*MPFR_GET_EXP (x);
/* initialise of intermediary variables */
MPFR_GROUP_INIT_2 (group, Nt, t, ti);
/* First computation of sinh */
MPFR_ZIV_INIT (loop, Nt);
for (;;)
{
MPFR_BLOCK_DECL (flags);
/* compute sinh */
MPFR_BLOCK (flags, mpfr_exp (t, x, MPFR_RNDD));
if (MPFR_OVERFLOW (flags))
/* exp(x) does overflow */
{
/* sinh(x) = 2 * sinh(x/2) * cosh(x/2) */
mpfr_div_2ui (ti, x, 1, MPFR_RNDD); /* exact */
/* t <- cosh(x/2): error(t) <= 1 ulp(t) */
MPFR_BLOCK (flags, mpfr_cosh (t, ti, MPFR_RNDD));
if (MPFR_OVERFLOW (flags))
/* when x>1 we have |sinh(x)| >= cosh(x/2), so sinh(x)
overflows too */
{
inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN (xt));
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
break;
}
/* ti <- sinh(x/2): , error(ti) <= 1 ulp(ti)
cannot overflow because 0 < sinh(x) < cosh(x) when x > 0 */
mpfr_sinh (ti, ti, MPFR_RNDD);
/* multiplication below, error(t) <= 5 ulp(t) */
MPFR_BLOCK (flags, mpfr_mul (t, t, ti, MPFR_RNDD));
if (MPFR_OVERFLOW (flags))
{
inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN (xt));
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
break;
}
/* doubling below, exact */
MPFR_BLOCK (flags, mpfr_mul_2ui (t, t, 1, MPFR_RNDN));
if (MPFR_OVERFLOW (flags))
{
inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN (xt));
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
break;
}
/* we have lost at most 3 bits of precision */
err = Nt - 3;
if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, MPFR_PREC (y),
rnd_mode)))
{
inexact = mpfr_set4 (y, t, rnd_mode, MPFR_SIGN (xt));
break;
}
err = Nt; /* double the precision */
}
else
{
d = MPFR_GET_EXP (t);
mpfr_ui_div (ti, 1, t, MPFR_RNDU); /* 1/exp(x) */
mpfr_sub (t, t, ti, MPFR_RNDN); /* exp(x) - 1/exp(x) */
mpfr_div_2ui (t, t, 1, MPFR_RNDN); /* 1/2(exp(x) - 1/exp(x)) */
/* it may be that t is zero (in fact, it can only occur when te=1,
and thus ti=1 too) */
if (MPFR_IS_ZERO (t))
err = Nt; /* double the precision */
else
{
/* calculation of the error */
d = d - MPFR_GET_EXP (t) + 2;
/* error estimate: err = Nt-(__gmpfr_ceil_log2(1+pow(2,d)));*/
err = Nt - (MAX (d, 0) + 1);
if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, MPFR_PREC (y),
rnd_mode)))
{
inexact = mpfr_set4 (y, t, rnd_mode, MPFR_SIGN (xt));
break;
}
}
}
/* actualisation of the precision */
Nt += err;
MPFR_ZIV_NEXT (loop, Nt);
MPFR_GROUP_REPREC_2 (group, Nt, t, ti);
}
MPFR_ZIV_FREE (loop);
MPFR_GROUP_CLEAR (group);
MPFR_SAVE_EXPO_FREE (expo);
}
return mpfr_check_range (y, inexact, rnd_mode);
}
int
mpfr_sinh_cosh (mpfr_ptr sh, mpfr_ptr ch, mpfr_srcptr xt, mpfr_rnd_t rnd_mode)
{
mpfr_t x;
int inexact_sh, inexact_ch;
MPFR_ASSERTN (sh != ch);
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg rnd=%d",
mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode),
("sh[%Pu]=%.*Rg ch[%Pu]=%.*Rg",
mpfr_get_prec (sh), mpfr_log_prec, sh,
mpfr_get_prec (ch), mpfr_log_prec, ch));
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt)))
{
if (MPFR_IS_NAN (xt))
{
MPFR_SET_NAN (ch);
MPFR_SET_NAN (sh);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (xt))
{
MPFR_SET_INF (sh);
MPFR_SET_SAME_SIGN (sh, xt);
MPFR_SET_INF (ch);
MPFR_SET_POS (ch);
MPFR_RET (0);
}
else /* xt is zero */
{
MPFR_ASSERTD (MPFR_IS_ZERO (xt));
MPFR_SET_ZERO (sh); /* sinh(0) = 0 */
MPFR_SET_SAME_SIGN (sh, xt);
inexact_sh = 0;
inexact_ch = mpfr_set_ui (ch, 1, rnd_mode); /* cosh(0) = 1 */
return INEX(inexact_sh,inexact_ch);
}
}
/* Warning: if we use MPFR_FAST_COMPUTE_IF_SMALL_INPUT here, make sure
that the code also works in case of overlap (see sin_cos.c) */
MPFR_TMP_INIT_ABS (x, xt);
{
mpfr_t s, c, ti;
mpfr_exp_t d;
mpfr_prec_t N; /* Precision of the intermediary variables */
long int err; /* Precision of error */
MPFR_ZIV_DECL (loop);
MPFR_SAVE_EXPO_DECL (expo);
MPFR_GROUP_DECL (group);
MPFR_SAVE_EXPO_MARK (expo);
/* compute the precision of intermediary variable */
N = MPFR_PREC (ch);
N = MAX (N, MPFR_PREC (sh));
/* the optimal number of bits : see algorithms.ps */
N = N + MPFR_INT_CEIL_LOG2 (N) + 4;
/* initialise of intermediary variables */
MPFR_GROUP_INIT_3 (group, N, s, c, ti);
/* First computation of sinh_cosh */
MPFR_ZIV_INIT (loop, N);
for (;;)
{
MPFR_BLOCK_DECL (flags);
/* compute sinh_cosh */
MPFR_BLOCK (flags, mpfr_exp (s, x, MPFR_RNDD));
if (MPFR_OVERFLOW (flags))
/* exp(x) does overflow */
{
/* since cosh(x) >= exp(x), cosh(x) overflows too */
inexact_ch = mpfr_overflow (ch, rnd_mode, MPFR_SIGN_POS);
/* sinh(x) may be representable */
inexact_sh = mpfr_sinh (sh, xt, rnd_mode);
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
break;
}
d = MPFR_GET_EXP (s);
mpfr_ui_div (ti, 1, s, MPFR_RNDU); /* 1/exp(x) */
mpfr_add (c, s, ti, MPFR_RNDU); /* exp(x) + 1/exp(x) */
mpfr_sub (s, s, ti, MPFR_RNDN); /* exp(x) - 1/exp(x) */
mpfr_div_2ui (c, c, 1, MPFR_RNDN); /* 1/2(exp(x) + 1/exp(x)) */
mpfr_div_2ui (s, s, 1, MPFR_RNDN); /* 1/2(exp(x) - 1/exp(x)) */
/* it may be that s is zero (in fact, it can only occur when exp(x)=1,
and thus ti=1 too) */
if (MPFR_IS_ZERO (s))
err = N; /* double the precision */
else
{
/* calculation of the error */
d = d - MPFR_GET_EXP (s) + 2;
/* error estimate: err = N-(__gmpfr_ceil_log2(1+pow(2,d)));*/
err = N - (MAX (d, 0) + 1);
if (MPFR_LIKELY (MPFR_CAN_ROUND (s, err, MPFR_PREC (sh),
rnd_mode) && \
MPFR_CAN_ROUND (c, err, MPFR_PREC (ch),
rnd_mode)))
{
inexact_sh = mpfr_set4 (sh, s, rnd_mode, MPFR_SIGN (xt));
inexact_ch = mpfr_set (ch, c, rnd_mode);
break;
}
}
/* actualisation of the precision */
N += err;
MPFR_ZIV_NEXT (loop, N);
MPFR_GROUP_REPREC_3 (group, N, s, c, ti);
}
MPFR_ZIV_FREE (loop);
MPFR_GROUP_CLEAR (group);
MPFR_SAVE_EXPO_FREE (expo);
}
/* now, let's raise the flags if needed */
inexact_sh = mpfr_check_range (sh, inexact_sh, rnd_mode);
inexact_ch = mpfr_check_range (ch, inexact_ch, rnd_mode);
return INEX(inexact_sh,inexact_ch);
}
MpfrFloat MpfrFloat::sinh(const MpfrFloat& value)
{
MpfrFloat retval(MpfrFloat::kNoInitialization);
mpfr_sinh(retval.mData->mFloat, value.mData->mFloat, GMP_RNDN);
return retval;
}
void bvisit(const Sinh &x) {
apply(result_, *(x.get_arg()));
mpfr_sinh(result_, result_, rnd_);
}
int
mpc_cos (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
{
mpfr_t x, y, z;
mp_prec_t prec;
int ok = 0;
int inex_re, inex_im;
/* special values */
if (!mpfr_number_p (MPC_RE (op)) || !mpfr_number_p (MPC_IM (op)))
{
if (mpfr_nan_p (MPC_RE (op)))
{
/* cos(NaN + i * NaN) = NaN + i * NaN */
/* cos(NaN - i * Inf) = +Inf + i * NaN */
/* cos(NaN + i * Inf) = +Inf + i * NaN */
/* cos(NaN - i * 0) = NaN - i * 0 */
/* cos(NaN + i * 0) = NaN + i * 0 */
/* cos(NaN + i * y) = NaN + i * NaN, when y != 0 */
if (mpfr_inf_p (MPC_IM (op)))
mpfr_set_inf (MPC_RE (rop), +1);
else
mpfr_set_nan (MPC_RE (rop));
if (mpfr_zero_p (MPC_IM (op)))
mpfr_set (MPC_IM (rop), MPC_IM (op), MPC_RND_IM (rnd));
else
mpfr_set_nan (MPC_IM (rop));
}
else if (mpfr_nan_p (MPC_IM (op)))
{
/* cos(-Inf + i * NaN) = NaN + i * NaN */
/* cos(+Inf + i * NaN) = NaN + i * NaN */
/* cos(-0 + i * NaN) = NaN - i * 0 */
/* cos(+0 + i * NaN) = NaN + i * 0 */
/* cos(x + i * NaN) = NaN + i * NaN, when x != 0 */
if (mpfr_zero_p (MPC_RE (op)))
mpfr_set (MPC_IM (rop), MPC_RE (op), MPC_RND_IM (rnd));
else
mpfr_set_nan (MPC_IM (rop));
mpfr_set_nan (MPC_RE (rop));
}
else if (mpfr_inf_p (MPC_RE (op)))
{
/* cos(-Inf -i*Inf) = cos(+Inf +i*Inf) = -Inf +i*NaN */
/* cos(-Inf +i*Inf) = cos(+Inf -i*Inf) = +Inf +i*NaN */
/* cos(-Inf -i*0) = cos(+Inf +i*0) = NaN -i*0 */
/* cos(-Inf +i*0) = cos(+Inf -i*0) = NaN +i*0 */
/* cos(-Inf +i*y) = cos(+Inf +i*y) = NaN +i*NaN, when y != 0 */
/* SAME_SIGN is useful only if op == (+/-)Inf + i * (+/-)0, but, as
MPC_RE(OP) might be erased (when ROP == OP), we compute it now */
const int same_sign =
mpfr_signbit (MPC_RE (op)) == mpfr_signbit (MPC_IM (op));
if (mpfr_inf_p (MPC_IM (op)))
mpfr_set_inf (MPC_RE (rop), (same_sign ? -1 : +1));
else
mpfr_set_nan (MPC_RE (rop));
if (mpfr_zero_p (MPC_IM (op)))
mpfr_setsign (MPC_IM (rop), MPC_IM (op), same_sign,
MPC_RND_IM(rnd));
else
mpfr_set_nan (MPC_IM (rop));
}
else if (mpfr_zero_p (MPC_RE (op)))
{
/* cos(-0 -i*Inf) = cos(+0 +i*Inf) = +Inf -i*0 */
/* cos(-0 +i*Inf) = cos(+0 -i*Inf) = +Inf +i*0 */
const int same_sign =
mpfr_signbit (MPC_RE (op)) == mpfr_signbit (MPC_IM (op));
mpfr_setsign (MPC_IM (rop), MPC_RE (op), same_sign,
MPC_RND_IM (rnd));
mpfr_set_inf (MPC_RE (rop), +1);
}
else
{
/* cos(x -i*Inf) = +Inf*cos(x) +i*Inf*sin(x), when x != 0 */
/* cos(x +i*Inf) = +Inf*cos(x) -i*Inf*sin(x), when x != 0 */
mpfr_t c;
mpfr_t s;
mpfr_init (c);
mpfr_init (s);
mpfr_sin_cos (s, c, MPC_RE (op), GMP_RNDN);
mpfr_set_inf (MPC_RE (rop), mpfr_sgn (c));
mpfr_set_inf (MPC_IM (rop),
(mpfr_sgn (MPC_IM (op)) == mpfr_sgn (s) ? -1 : +1));
mpfr_clear (s);
mpfr_clear (c);
}
return MPC_INEX (0, 0); /* always exact */
}
if (mpfr_zero_p (MPC_RE (op)))
{
/* cos(-0 - i * y) = cos(+0 + i * y) = cosh(y) - i * 0
cos(-0 + i * y) = cos(+0 - i * y) = cosh(y) + i * 0,
when y >= 0 */
/* When ROP == OP, the sign of 0 will be erased, so use it now */
const int imag_sign =
mpfr_signbit (MPC_RE (op)) == mpfr_signbit (MPC_IM (op));
if (mpfr_zero_p (MPC_IM (op)))
inex_re = mpfr_set_ui (MPC_RE (rop), 1, MPC_RND_RE (rnd));
else
inex_re = mpfr_cosh (MPC_RE (rop), MPC_IM (op), MPC_RND_RE (rnd));
mpfr_set_ui (MPC_IM (rop), 0, MPC_RND_IM (rnd));
mpfr_setsign (MPC_IM (rop), MPC_IM (rop), imag_sign, MPC_RND_IM (rnd));
return MPC_INEX (inex_re, 0);
}
if (mpfr_zero_p (MPC_IM (op)))
{
/* cos(x +i*0) = cos(x) -i*0*sign(sin(x)) */
/* cos(x -i*0) = cos(x) +i*0*sign(sin(x)) */
mpfr_t sign;
mpfr_init2 (sign, 2);
mpfr_sin (sign, MPC_RE (op), GMP_RNDN);
if (!mpfr_signbit (MPC_IM (op)))
MPFR_CHANGE_SIGN (sign);
inex_re = mpfr_cos (MPC_RE (rop), MPC_RE (op), MPC_RND_RE (rnd));
mpfr_set_ui (MPC_IM (rop), 0ul, GMP_RNDN);
if (mpfr_signbit (sign))
MPFR_CHANGE_SIGN (MPC_IM (rop));
mpfr_clear (sign);
return MPC_INEX (inex_re, 0);
}
/* ordinary (non-zero) numbers */
/* let op = a + i*b, then cos(op) = cos(a)*cosh(b) - i*sin(a)*sinh(b).
We use the following algorithm (same for the imaginary part),
with rounding to nearest for all operations, and working precision w:
(1) x = o(cos(a))
(2) y = o(cosh(b))
(3) r = o(x*y)
then the error on r is at most 4 ulps, since we can write
r = cos(a)*cosh(b)*(1+t)^3 with |t| <= 2^(-w),
thus for w >= 2, r = cos(a)*cosh(b)*(1+4*t) with |t| <= 2^(-w),
thus the relative error is bounded by 4*2^(-w) <= 4*ulp(r).
*/
prec = MPC_MAX_PREC(rop);
mpfr_init2 (x, 2);
mpfr_init2 (y, 2);
mpfr_init2 (z, 2);
do
{
prec += mpc_ceil_log2 (prec) + 5;
mpfr_set_prec (x, prec);
mpfr_set_prec (y, prec);
mpfr_set_prec (z, prec);
mpfr_sin_cos (y, x, MPC_RE(op), GMP_RNDN);
mpfr_cosh (z, MPC_IM(op), GMP_RNDN);
mpfr_mul (x, x, z, GMP_RNDN);
ok = mpfr_can_round (x, prec - 2, GMP_RNDN, GMP_RNDZ,
MPFR_PREC(MPC_RE(rop)) + (MPC_RND_RE(rnd) == GMP_RNDN));
if (ok) /* compute imaginary part */
{
mpfr_sinh (z, MPC_IM(op), GMP_RNDN);
mpfr_mul (y, y, z, GMP_RNDN);
mpfr_neg (y, y, GMP_RNDN);
ok = mpfr_can_round (y, prec - 2, GMP_RNDN, GMP_RNDZ,
MPFR_PREC(MPC_IM(rop)) + (MPC_RND_IM(rnd) == GMP_RNDN));
}
}
while (ok == 0);
inex_re = mpfr_set (MPC_RE(rop), x, MPC_RND_RE(rnd));
inex_im = mpfr_set (MPC_IM(rop), y, MPC_RND_IM(rnd));
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
return MPC_INEX (inex_re, inex_im);
}
