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authorenge <enge@211d60ee-9f03-0410-a15a-8952a2c7a4e4>2011-11-04 18:39:52 +0000
committerenge <enge@211d60ee-9f03-0410-a15a-8952a2c7a4e4>2011-11-04 18:39:52 +0000
commit5ad0bccecc2c0aafdc23571a491fccc31171c22c (patch)
treefbb979252a636e9fc3215e15e12be49ca6d35a95 /src/atan.c
parent18e9d42b59925987d8128096c4a7ea6d49721862 (diff)
downloadmpc-5ad0bccecc2c0aafdc23571a491fccc31171c22c.tar.gz
replaced MPC_RE by mpc_realref and MPC_IM by mpc_imagref everywhere
git-svn-id: svn://scm.gforge.inria.fr/svn/mpc/trunk@1112 211d60ee-9f03-0410-a15a-8952a2c7a4e4
Diffstat (limited to 'src/atan.c')
-rw-r--r--src/atan.c96
1 files changed, 48 insertions, 48 deletions
diff --git a/src/atan.c b/src/atan.c
index dea9d3f..fb0f067 100644
--- a/src/atan.c
+++ b/src/atan.c
@@ -52,45 +52,45 @@ mpc_atan (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
inex_re = 0;
inex_im = 0;
- s_re = mpfr_signbit (MPC_RE (op));
- s_im = mpfr_signbit (MPC_IM (op));
+ s_re = mpfr_signbit (mpc_realref (op));
+ s_im = mpfr_signbit (mpc_imagref (op));
/* special values */
- if (mpfr_nan_p (MPC_RE (op)) || mpfr_nan_p (MPC_IM (op)))
+ if (mpfr_nan_p (mpc_realref (op)) || mpfr_nan_p (mpc_imagref (op)))
{
- if (mpfr_nan_p (MPC_RE (op)))
+ if (mpfr_nan_p (mpc_realref (op)))
{
- mpfr_set_nan (MPC_RE (rop));
- if (mpfr_zero_p (MPC_IM (op)) || mpfr_inf_p (MPC_IM (op)))
+ mpfr_set_nan (mpc_realref (rop));
+ if (mpfr_zero_p (mpc_imagref (op)) || mpfr_inf_p (mpc_imagref (op)))
{
- mpfr_set_ui (MPC_IM (rop), 0, GMP_RNDN);
+ mpfr_set_ui (mpc_imagref (rop), 0, GMP_RNDN);
if (s_im)
mpc_conj (rop, rop, MPC_RNDNN);
}
else
- mpfr_set_nan (MPC_IM (rop));
+ mpfr_set_nan (mpc_imagref (rop));
}
else
{
- if (mpfr_inf_p (MPC_RE (op)))
+ if (mpfr_inf_p (mpc_realref (op)))
{
- inex_re = set_pi_over_2 (MPC_RE (rop), -s_re, MPC_RND_RE (rnd));
- mpfr_set_ui (MPC_IM (rop), 0, GMP_RNDN);
+ inex_re = set_pi_over_2 (mpc_realref (rop), -s_re, MPC_RND_RE (rnd));
+ mpfr_set_ui (mpc_imagref (rop), 0, GMP_RNDN);
}
else
{
- mpfr_set_nan (MPC_RE (rop));
- mpfr_set_nan (MPC_IM (rop));
+ mpfr_set_nan (mpc_realref (rop));
+ mpfr_set_nan (mpc_imagref (rop));
}
}
return MPC_INEX (inex_re, 0);
}
- if (mpfr_inf_p (MPC_RE (op)) || mpfr_inf_p (MPC_IM (op)))
+ if (mpfr_inf_p (mpc_realref (op)) || mpfr_inf_p (mpc_imagref (op)))
{
- inex_re = set_pi_over_2 (MPC_RE (rop), -s_re, MPC_RND_RE (rnd));
+ inex_re = set_pi_over_2 (mpc_realref (rop), -s_re, MPC_RND_RE (rnd));
- mpfr_set_ui (MPC_IM (rop), 0, GMP_RNDN);
+ mpfr_set_ui (mpc_imagref (rop), 0, GMP_RNDN);
if (s_im)
mpc_conj (rop, rop, GMP_RNDN);
@@ -98,11 +98,11 @@ mpc_atan (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
}
/* pure real argument */
- if (mpfr_zero_p (MPC_IM (op)))
+ if (mpfr_zero_p (mpc_imagref (op)))
{
- inex_re = mpfr_atan (MPC_RE (rop), MPC_RE (op), MPC_RND_RE (rnd));
+ inex_re = mpfr_atan (mpc_realref (rop), mpc_realref (op), MPC_RND_RE (rnd));
- mpfr_set_ui (MPC_IM (rop), 0, GMP_RNDN);
+ mpfr_set_ui (mpc_imagref (rop), 0, GMP_RNDN);
if (s_im)
mpc_conj (rop, rop, GMP_RNDN);
@@ -110,32 +110,32 @@ mpc_atan (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
}
/* pure imaginary argument */
- if (mpfr_zero_p (MPC_RE (op)))
+ if (mpfr_zero_p (mpc_realref (op)))
{
int cmp_1;
if (s_im)
- cmp_1 = -mpfr_cmp_si (MPC_IM (op), -1);
+ cmp_1 = -mpfr_cmp_si (mpc_imagref (op), -1);
else
- cmp_1 = mpfr_cmp_ui (MPC_IM (op), +1);
+ cmp_1 = mpfr_cmp_ui (mpc_imagref (op), +1);
if (cmp_1 < 0)
{
/* atan(+0+iy) = +0 +i*atanh(y), if |y| < 1
atan(-0+iy) = -0 +i*atanh(y), if |y| < 1 */
- mpfr_set_ui (MPC_RE (rop), 0, GMP_RNDN);
+ mpfr_set_ui (mpc_realref (rop), 0, GMP_RNDN);
if (s_re)
- mpfr_neg (MPC_RE (rop), MPC_RE (rop), GMP_RNDN);
+ mpfr_neg (mpc_realref (rop), mpc_realref (rop), GMP_RNDN);
- inex_im = mpfr_atanh (MPC_IM (rop), MPC_IM (op), MPC_RND_IM (rnd));
+ inex_im = mpfr_atanh (mpc_imagref (rop), mpc_imagref (op), MPC_RND_IM (rnd));
}
else if (cmp_1 == 0)
{
/* atan(+/-0+i) = NaN +i*inf
atan(+/-0-i) = NaN -i*inf */
- mpfr_set_nan (MPC_RE (rop));
- mpfr_set_inf (MPC_IM (rop), s_im ? -1 : +1);
+ mpfr_set_nan (mpc_realref (rop));
+ mpfr_set_inf (mpc_imagref (rop), s_im ? -1 : +1);
}
else
{
@@ -148,7 +148,7 @@ mpc_atan (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
rnd_im = MPC_RND_IM (rnd);
mpfr_init (y);
- p_im = mpfr_get_prec (MPC_IM (rop));
+ p_im = mpfr_get_prec (mpc_imagref (rop));
p = p_im;
/* a = o(1/y) with error(a) < 1 ulp(a)
@@ -164,7 +164,7 @@ mpc_atan (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
p += mpc_ceil_log2 (p) + 2;
mpfr_set_prec (y, p);
rnd_away = s_im == 0 ? GMP_RNDU : GMP_RNDD;
- inex_im = mpfr_ui_div (y, 1, MPC_IM (op), rnd_away);
+ inex_im = mpfr_ui_div (y, 1, mpc_imagref (op), rnd_away);
/* FIXME: should we consider the case with unreasonably huge
precision prec(y)>3*exp_min, where atanh(1/Im(op)) could be
representable while 1/Im(op) underflows ?
@@ -179,8 +179,8 @@ mpc_atan (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
p_im + (rnd_im == GMP_RNDN));
} while (ok == 0);
- inex_re = set_pi_over_2 (MPC_RE (rop), -s_re, MPC_RND_RE (rnd));
- inex_im = mpfr_set (MPC_IM (rop), y, rnd_im);
+ inex_re = set_pi_over_2 (mpc_realref (rop), -s_re, MPC_RND_RE (rnd));
+ inex_im = mpfr_set (mpc_imagref (rop), y, rnd_im);
mpfr_clear (y);
}
return MPC_INEX (inex_re, inex_im);
@@ -199,12 +199,12 @@ mpc_atan (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
mpfr_inits2 (MPFR_PREC_MIN, a, b, x, y, (mpfr_ptr) 0);
/* real part: Re(arctan(x+i*y)) = [arctan2(x,1-y) - arctan2(-x,1+y)]/2 */
- minus_op_re[0] = MPC_RE (op)[0];
+ minus_op_re[0] = mpc_realref (op)[0];
MPFR_CHANGE_SIGN (minus_op_re);
- op_re_exp = mpfr_get_exp (MPC_RE (op));
- op_im_exp = mpfr_get_exp (MPC_IM (op));
+ op_re_exp = mpfr_get_exp (mpc_realref (op));
+ op_im_exp = mpfr_get_exp (mpc_imagref (op));
- prec = mpfr_get_prec (MPC_RE (rop)); /* result precision */
+ prec = mpfr_get_prec (mpc_realref (rop)); /* result precision */
/* a = o(1-y) error(a) < 1 ulp(a)
b = o(atan2(x,a)) error(b) < [1+2^{3+Exp(x)-Exp(a)-Exp(b)}] ulp(b)
@@ -225,8 +225,8 @@ mpc_atan (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
/* p: working precision */
p = (op_im_exp > 0 || prec > SAFE_ABS (mpfr_prec_t, op_im_exp)) ? prec
: (prec - op_im_exp);
- rnd1 = mpfr_sgn (MPC_RE (op)) > 0 ? GMP_RNDD : GMP_RNDU;
- rnd2 = mpfr_sgn (MPC_RE (op)) < 0 ? GMP_RNDU : GMP_RNDD;
+ rnd1 = mpfr_sgn (mpc_realref (op)) > 0 ? GMP_RNDD : GMP_RNDU;
+ rnd2 = mpfr_sgn (mpc_realref (op)) < 0 ? GMP_RNDU : GMP_RNDD;
do
{
@@ -238,27 +238,27 @@ mpc_atan (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
/* x = upper bound for atan (x/(1-y)). Since atan is increasing, we
need an upper bound on x/(1-y), i.e., a lower bound on 1-y for
x positive, and an upper bound on 1-y for x negative */
- mpfr_ui_sub (a, 1, MPC_IM (op), rnd1);
+ mpfr_ui_sub (a, 1, mpc_imagref (op), rnd1);
if (mpfr_sgn (a) == 0) /* y is near 1, thus 1+y is near 2, and
expo will be 1 or 2 below */
{
- if (mpfr_cmp_ui (MPC_IM(op), 1) != 0)
+ if (mpfr_cmp_ui (mpc_imagref(op), 1) != 0)
continue;
err = 2; /* ensures err will be expo below */
}
else
err = mpfr_get_exp (a); /* err = Exp(a) with the notations above */
- mpfr_atan2 (x, MPC_RE (op), a, GMP_RNDU);
+ mpfr_atan2 (x, mpc_realref (op), a, GMP_RNDU);
/* b = lower bound for atan (-x/(1+y)): for x negative, we need a
lower bound on -x/(1+y), i.e., an upper bound on 1+y */
- mpfr_add_ui (a, MPC_IM(op), 1, rnd2);
+ mpfr_add_ui (a, mpc_imagref(op), 1, rnd2);
/* if a is zero but inexact, try again with a larger precision
if a is exactly zero, i.e., Im(op) = -1, then the error on a is 0,
and we can simply ignore the terms involving Exp(a) in the error */
if (mpfr_sgn (a) == 0)
{
- if (mpfr_cmp_si (MPC_IM(op), -1) != 0)
+ if (mpfr_cmp_si (mpc_imagref(op), -1) != 0)
continue;
expo = err; /* will leave err unchanged below */
}
@@ -283,7 +283,7 @@ mpc_atan (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
/* Imaginary part
Im(atan(x+I*y)) = 1/4 * [log(x^2+(1+y)^2) - log (x^2 +(1-y)^2)] */
- prec = mpfr_get_prec (MPC_IM (rop)); /* result precision */
+ prec = mpfr_get_prec (mpc_imagref (rop)); /* result precision */
/* a = o(1+y) error(a) < 1 ulp(a)
b = o(a^2) error(b) < 5 ulp(b)
@@ -304,7 +304,7 @@ mpc_atan (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
*/
err = 2;
p = prec; /* working precision */
- rnd1 = mpfr_cmp_si (MPC_IM (op), -1) > 0 ? GMP_RNDU : GMP_RNDD;
+ rnd1 = mpfr_cmp_si (mpc_imagref (op), -1) > 0 ? GMP_RNDU : GMP_RNDD;
do
{
@@ -314,16 +314,16 @@ mpc_atan (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
mpfr_set_prec (y, p);
/* a = upper bound for log(x^2 + (1+y)^2) */
- mpfr_add_ui (a, MPC_IM (op), 1, rnd1);
+ mpfr_add_ui (a, mpc_imagref (op), 1, rnd1);
mpfr_sqr (a, a, GMP_RNDU);
- mpfr_sqr (y, MPC_RE (op), GMP_RNDU);
+ mpfr_sqr (y, mpc_realref (op), GMP_RNDU);
mpfr_add (a, a, y, GMP_RNDU);
mpfr_log (a, a, GMP_RNDU);
/* b = lower bound for log(x^2 + (1-y)^2) */
- mpfr_ui_sub (b, 1, MPC_IM (op), GMP_RNDZ);
+ mpfr_ui_sub (b, 1, mpc_imagref (op), GMP_RNDZ);
mpfr_sqr (b, b, GMP_RNDU);
- /* mpfr_sqr (y, MPC_RE (op), GMP_RNDZ); */
+ /* mpfr_sqr (y, mpc_realref (op), GMP_RNDZ); */
mpfr_nextbelow (y);
mpfr_add (b, b, y, GMP_RNDZ);
mpfr_log (b, b, GMP_RNDZ);