//------------------------------------------------------------------------------
// Name:
//------------------------------------------------------------------------------
knumber_base *knumber_float::asinh() {
#ifdef KNUMBER_USE_MPFR
mpfr_t mpfr;
mpfr_init_set_f(mpfr, mpf_, rounding_mode);
mpfr_asinh(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< ::asinh>(x);
#endif
}
int
mpc_asin (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
{
mpfr_prec_t p, p_re, p_im, incr_p = 0;
mpfr_rnd_t rnd_re, rnd_im;
mpc_t z1;
int inex;
/* 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_nan (mpc_realref (rop));
mpfr_set_inf (mpc_imagref (rop), mpfr_signbit (mpc_imagref (op)) ? -1 : +1);
}
else if (mpfr_zero_p (mpc_realref (op)))
{
mpfr_set (mpc_realref (rop), mpc_realref (op), GMP_RNDN);
mpfr_set_nan (mpc_imagref (rop));
}
else
{
mpfr_set_nan (mpc_realref (rop));
mpfr_set_nan (mpc_imagref (rop));
}
return 0;
}
if (mpfr_inf_p (mpc_realref (op)) || mpfr_inf_p (mpc_imagref (op)))
{
int inex_re;
if (mpfr_inf_p (mpc_realref (op)))
{
int inf_im = mpfr_inf_p (mpc_imagref (op));
inex_re = set_pi_over_2 (mpc_realref (rop),
(mpfr_signbit (mpc_realref (op)) ? -1 : 1), MPC_RND_RE (rnd));
mpfr_set_inf (mpc_imagref (rop), (mpfr_signbit (mpc_imagref (op)) ? -1 : 1));
if (inf_im)
mpfr_div_2ui (mpc_realref (rop), mpc_realref (rop), 1, GMP_RNDN);
}
else
{
mpfr_set_zero (mpc_realref (rop), (mpfr_signbit (mpc_realref (op)) ? -1 : 1));
inex_re = 0;
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 inex_re;
int inex_im;
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),
INV_RND (MPC_RND_IM (rnd)));
else
inex_im = mpfr_acosh (mpc_imagref (rop), mpc_realref (op),
MPC_RND_IM (rnd));
inex_re = set_pi_over_2 (mpc_realref (rop),
(mpfr_signbit (mpc_realref (op)) ? -1 : 1), MPC_RND_RE (rnd));
if (s_im)
mpc_conj (rop, rop, MPC_RNDNN);
}
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,
INV_RND (MPC_RND_IM (rnd)));
else
inex_im = mpfr_acosh (mpc_imagref (rop), minus_op_re,
MPC_RND_IM (rnd));
inex_re = set_pi_over_2 (mpc_realref (rop),
(mpfr_signbit (mpc_realref (op)) ? -1 : 1), MPC_RND_RE (rnd));
if (s_im)
mpc_conj (rop, rop, MPC_RNDNN);
}
else
{
inex_im = mpfr_set_ui (mpc_imagref (rop), 0, MPC_RND_IM (rnd));
if (s_im)
mpfr_neg (mpc_imagref (rop), mpc_imagref (rop), GMP_RNDN);
inex_re = mpfr_asin (mpc_realref (rop), mpc_realref (op), MPC_RND_RE (rnd));
}
return MPC_INEX (inex_re, inex_im);
}
/* pure imaginary argument */
if (mpfr_zero_p (mpc_realref (op)))
{
int inex_im;
int s;
s = mpfr_signbit (mpc_realref (op));
mpfr_set_ui (mpc_realref (rop), 0, GMP_RNDN);
if (s)
mpfr_neg (mpc_realref (rop), mpc_realref (rop), GMP_RNDN);
inex_im = mpfr_asinh (mpc_imagref (rop), mpc_imagref (op), MPC_RND_IM (rnd));
return MPC_INEX (0, inex_im);
}
/* regular complex: asin(z) = -i*log(i*z+sqrt(1-z^2)) */
p_re = mpfr_get_prec (mpc_realref(rop));
p_im = mpfr_get_prec (mpc_imagref(rop));
rnd_re = MPC_RND_RE(rnd);
rnd_im = MPC_RND_IM(rnd);
p = p_re >= p_im ? p_re : p_im;
mpc_init2 (z1, p);
while (1)
{
mpfr_exp_t ex, ey, err;
p += mpc_ceil_log2 (p) + 3 + incr_p; /* incr_p is zero initially */
incr_p = p / 2;
mpfr_set_prec (mpc_realref(z1), p);
mpfr_set_prec (mpc_imagref(z1), p);
/* z1 <- z^2 */
mpc_sqr (z1, op, MPC_RNDNN);
/* err(x) <= 1/2 ulp(x), err(y) <= 1/2 ulp(y) */
/* z1 <- 1-z1 */
ex = mpfr_get_exp (mpc_realref(z1));
mpfr_ui_sub (mpc_realref(z1), 1, mpc_realref(z1), GMP_RNDN);
mpfr_neg (mpc_imagref(z1), mpc_imagref(z1), GMP_RNDN);
ex = ex - mpfr_get_exp (mpc_realref(z1));
ex = (ex <= 0) ? 0 : ex;
/* err(x) <= 2^ex * ulp(x) */
ex = ex + mpfr_get_exp (mpc_realref(z1)) - p;
/* err(x) <= 2^ex */
ey = mpfr_get_exp (mpc_imagref(z1)) - p - 1;
/* err(y) <= 2^ey */
ex = (ex >= ey) ? ex : ey; /* err(x), err(y) <= 2^ex, i.e., the norm
of the error is bounded by |h|<=2^(ex+1/2) */
/* z1 <- sqrt(z1): if z1 = z + h, then sqrt(z1) = sqrt(z) + h/2/sqrt(t) */
ey = mpfr_get_exp (mpc_realref(z1)) >= mpfr_get_exp (mpc_imagref(z1))
? mpfr_get_exp (mpc_realref(z1)) : mpfr_get_exp (mpc_imagref(z1));
/* we have |z1| >= 2^(ey-1) thus 1/|z1| <= 2^(1-ey) */
mpc_sqrt (z1, z1, MPC_RNDNN);
ex = (2 * ex + 1) - 2 - (ey - 1); /* |h^2/4/|t| <= 2^ex */
ex = (ex + 1) / 2; /* ceil(ex/2) */
/* express ex in terms of ulp(z1) */
ey = mpfr_get_exp (mpc_realref(z1)) <= mpfr_get_exp (mpc_imagref(z1))
? mpfr_get_exp (mpc_realref(z1)) : mpfr_get_exp (mpc_imagref(z1));
ex = ex - ey + p;
/* take into account the rounding error in the mpc_sqrt call */
err = (ex <= 0) ? 1 : ex + 1;
/* err(x) <= 2^err * ulp(x), err(y) <= 2^err * ulp(y) */
/* z1 <- i*z + z1 */
ex = mpfr_get_exp (mpc_realref(z1));
ey = mpfr_get_exp (mpc_imagref(z1));
mpfr_sub (mpc_realref(z1), mpc_realref(z1), mpc_imagref(op), GMP_RNDN);
mpfr_add (mpc_imagref(z1), mpc_imagref(z1), mpc_realref(op), GMP_RNDN);
if (mpfr_cmp_ui (mpc_realref(z1), 0) == 0 || mpfr_cmp_ui (mpc_imagref(z1), 0) == 0)
continue;
ex -= mpfr_get_exp (mpc_realref(z1)); /* cancellation in x */
ey -= mpfr_get_exp (mpc_imagref(z1)); /* cancellation in y */
ex = (ex >= ey) ? ex : ey; /* maximum cancellation */
err += ex;
err = (err <= 0) ? 1 : err + 1; /* rounding error in sub/add */
/* z1 <- log(z1): if z1 = z + h, then log(z1) = log(z) + h/t with
|t| >= min(|z1|,|z|) */
ex = mpfr_get_exp (mpc_realref(z1));
ey = mpfr_get_exp (mpc_imagref(z1));
ex = (ex >= ey) ? ex : ey;
err += ex - p; /* revert to absolute error <= 2^err */
mpc_log (z1, z1, GMP_RNDN);
err -= ex - 1; /* 1/|t| <= 1/|z| <= 2^(1-ex) */
/* express err in terms of ulp(z1) */
ey = mpfr_get_exp (mpc_realref(z1)) <= mpfr_get_exp (mpc_imagref(z1))
? mpfr_get_exp (mpc_realref(z1)) : mpfr_get_exp (mpc_imagref(z1));
err = err - ey + p;
/* take into account the rounding error in the mpc_log call */
err = (err <= 0) ? 1 : err + 1;
/* z1 <- -i*z1 */
mpfr_swap (mpc_realref(z1), mpc_imagref(z1));
mpfr_neg (mpc_imagref(z1), mpc_imagref(z1), GMP_RNDN);
if (mpfr_can_round (mpc_realref(z1), p - err, GMP_RNDN, GMP_RNDZ,
p_re + (rnd_re == GMP_RNDN)) &&
mpfr_can_round (mpc_imagref(z1), p - err, GMP_RNDN, GMP_RNDZ,
p_im + (rnd_im == GMP_RNDN)))
break;
}
inex = mpc_set (rop, z1, rnd);
mpc_clear (z1);
return inex;
}
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;
}
MpfrFloat MpfrFloat::asinh(const MpfrFloat& value)
{
MpfrFloat retval(MpfrFloat::kNoInitialization);
mpfr_asinh(retval.mData->mFloat, value.mData->mFloat, GMP_RNDN);
return retval;
}
static void
special (void)
{
mpfr_t x, y, z;
mpfr_init (x);
mpfr_init (y);
MPFR_SET_INF(x);
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_asinh (x, y, MPFR_RNDN);
if (MPFR_IS_INF(x) || MPFR_IS_NAN(x) )
{
printf ("Inf flag not clears in asinh!\n");
exit (1);
}
MPFR_SET_NAN(x);
mpfr_asinh (x, y, MPFR_RNDN);
if (MPFR_IS_NAN(x) || MPFR_IS_INF(x))
{
printf ("NAN flag not clears in asinh!\n");
exit (1);
}
/* asinh(+0) = +0, asinh(-0) = -0 */
mpfr_set_ui (x, 0, MPFR_RNDN);
mpfr_asinh (y, x, MPFR_RNDN);
if (mpfr_cmp_ui (y, 0) || mpfr_sgn (y) < 0)
{
printf ("Error: mpfr_asinh(+0) <> +0\n");
exit (1);
}
mpfr_neg (x, x, MPFR_RNDN);
mpfr_asinh (y, x, MPFR_RNDN);
if (mpfr_cmp_ui (y, 0) || mpfr_sgn (y) > 0)
{
printf ("Error: mpfr_asinh(-0) <> -0\n");
exit (1);
}
MPFR_SET_NAN(x);
mpfr_asinh (y, x, MPFR_RNDN);
if (!mpfr_nan_p (y))
{
printf ("Error: mpfr_asinh(NaN) <> NaN\n");
exit (1);
}
mpfr_set_inf (x, 1);
mpfr_asinh (y, x, MPFR_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0)
{
printf ("Error: mpfr_asinh(+Inf) <> +Inf\n");
exit (1);
}
mpfr_set_inf (x, -1);
mpfr_asinh (y, x, MPFR_RNDN);
if (!mpfr_inf_p (y) || mpfr_sgn (y) > 0)
{
printf ("Error: mpfr_asinh(-Inf) <> -Inf\n");
exit (1);
}
mpfr_set_prec (x, 32);
mpfr_set_prec (y, 32);
mpfr_set_str_binary (x, "0.1010100100111011001111100101E-1");
mpfr_asinh (x, x, MPFR_RNDN);
mpfr_set_str_binary (y, "0.10100110010010101101010011011101E-1");
if (!mpfr_equal_p (x, y))
{
printf ("Error: mpfr_asinh (1)\n");
exit (1);
}
mpfr_set_str_binary (x, "-.10110011011010111110010001100001");
mpfr_asinh (x, x, MPFR_RNDN);
mpfr_set_str_binary (y, "-.10100111010000111001011100110011");
if (!mpfr_equal_p (x, y))
{
printf ("Error: mpfr_asinh (2)\n");
exit (1);
}
mpfr_set_prec (x, 33);
mpfr_set_prec (y, 43);
mpfr_set_str_binary (x, "0.111001101100000110011001010000101");
mpfr_asinh (y, x, MPFR_RNDZ);
mpfr_init2 (z, 43);
mpfr_set_str_binary (z, "0.1100111101010101101010101110000001000111001");
if (!mpfr_equal_p (y, z))
{
printf ("Error: mpfr_asinh (3)\n");
exit (1);
}
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 2);
mpfr_set_str (x, "1.8000000000009@-6", 16, MPFR_RNDN);
mpfr_asinh (y, x, MPFR_RNDZ);
mpfr_set_prec (z, 2);
mpfr_set_str (z, "1.0@-6", 16, MPFR_RNDN);
if (!mpfr_equal_p (y, z))
{
printf ("Error: mpfr_asinh (4)\n");
exit (1);
}
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
}
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 ASinh &x) {
apply(result_, *(x.get_arg()));
mpfr_asinh(result_, result_, rnd_);
}
