src/atan.c: compute special values and pure real/ pure imaginary arguments.

src/atanh.c: fix inversions in rounding mode and nonary value.
tests/atan.dat: Fix special values, add tests with pure real and pure imaginary argument.
tests/atanh.dat: Fix undetermined signs of zero, add tests with pure real and pure imaginary argument.


git-svn-id: svn://scm.gforge.inria.fr/svn/mpc/branches/feature-inverse-trigo@642 211d60ee-9f03-0410-a15a-8952a2c7a4e4

4 files changed, 277 insertions, 38 deletions

diff --git a/src/atan.c b/src/atan.c
index 60d6c6c..b394b28 100644
--- a/src/atan.c
+++ b/src/atan.c
@@ -21,10 +21,193 @@ MA 02111-1307, USA. */
 
 #include "mpc-impl.h"
 
+/* set rop to
+   -pi/2 if s < 0
+   +pi/2 else
+   rounded in the direction rnd
+*/
+static int
+set_pi_over_2 (mpfr_ptr rop, int s, mpfr_rnd_t rnd)
+{
+  int inex;
+
+  inex = mpfr_const_pi (rop, s ? INV_RND (rnd) : rnd);
+  mpfr_div_2ui (rop, rop, 1, GMP_RNDN);
+  if (s)
+    {
+      inex = -inex;
+      mpfr_neg (rop, rop, GMP_RNDN);
+    }
+
+  return inex;
+}
+
 int
 mpc_atan (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
 {
+  int s_re;
+  int s_im;
+
+  s_re = mpfr_signbit (MPC_RE (op));
+  s_im = mpfr_signbit (MPC_IM (op));
+
+  /* special values */
+  if (mpfr_nan_p (MPC_RE (op)) || mpfr_nan_p (MPC_IM (op)))
+    {
+      int inex_re;
+      inex_re = 0;
+
+      if (mpfr_nan_p (MPC_RE (op)))
+        {
+          mpfr_set_nan (MPC_RE (rop));
+          if (mpfr_zero_p (MPC_IM (op)) || mpfr_inf_p (MPC_IM (op)))
+            {
+              mpfr_set_ui (MPC_IM (rop), 0, GMP_RNDN);
+              if (s_im)
+                mpc_conj (rop, rop, MPC_RNDNN);
+            }
+          else
+            mpfr_set_nan (MPC_IM (rop));
+        }
+      else
+        {
+          if (mpfr_inf_p (MPC_RE (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);
+            }
+          else
+            {
+              mpfr_set_nan (MPC_RE (rop));
+              mpfr_set_nan (MPC_IM (rop));
+            }
+        }
+      return MPC_INEX (inex_re, 0);
+    }
+
+  if (mpfr_inf_p (MPC_RE (op)) || mpfr_inf_p (MPC_IM (op)))
+    {
+      int inex_re;
+      inex_re = set_pi_over_2 (MPC_RE (rop), s_re, MPC_RND_RE (rnd));
+
+      mpfr_set_ui (MPC_IM (rop), 0, GMP_RNDN);
+      if (s_im)
+        mpc_conj (rop, rop, GMP_RNDN);
+
+      return MPC_INEX (inex_re, 0);
+    }
+
+  /* pure real argument */
+  if (mpfr_zero_p (MPC_IM (op)))
+    {
+      int inex_re;
+
+      inex_re = mpfr_atan (MPC_RE (rop), MPC_RE (op), MPC_RND_RE (rnd));
+      
+      mpfr_set_ui (MPC_IM (rop), 0, GMP_RNDN);
+      if (s_im)
+        mpc_conj (rop, rop, GMP_RNDN);
+
+      return MPC_INEX (inex_re, 0);
+    }
+
+  /* pure imaginary argument */
+  if (mpfr_zero_p (MPC_RE (op)))
+    {
+      int inex_re;
+      int inex_im;
+      int cmp_1;
+
+      inex_re = 0;
+      inex_im = 0;
+
+      if (s_im)
+        cmp_1 = -mpfr_cmp_si (MPC_IM (op), -1);
+      else
+        cmp_1 = mpfr_cmp_ui (MPC_IM (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);
+          if (s_re)
+            mpfr_neg (MPC_RE (rop), MPC_RE (rop), GMP_RNDN);
+
+          inex_im = mpfr_atanh (MPC_IM (rop), MPC_IM (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);
+        }
+      else
+        {
+          /* atan(+0+iy) = +pi/2 +i*atanh(1/y), if |y| > 1
+             atan(-0+iy) = -pi/2 +i*atanh(1/y), if |y| > 1 */
+          mp_rnd_t rnd_im;
+          mpfr_t y;
+          mp_prec_t p, p_im;
+          mp_prec_t err;
+          int ok;
+          int cmp_2;
+
+          rnd_im = MPC_RND_IM (rnd);
+          mpfr_init (y);
+          p_im = mpfr_get_prec (MPC_IM (op));
+          p = p_im;
+
+          /* a = o(1/y)      with error(a) < 1 ulp(a)
+             b = o(atanh(a)) with error(b) < (1+2^{1+Exp(a)-Exp(b)}) ulp(b)
+
+             * if 1 < |y| <= 2 then Exp(a) = 0 and Exp(b) >= 0, so, at most, 2
+               bits of precision are lost.
+             * if |y| > 2, no simplification. */
+          if (s_im)
+            cmp_2 = -mpfr_cmp_si (MPC_IM (op), -2);
+          else
+            cmp_2 = mpfr_cmp_ui (MPC_IM (op), +2);
+          
+          err = 2;
+
+          do
+            {
+              p += mpc_ceil_log2 (p) + err;
+              mpfr_set_prec (y, p);
+              inex_im = mpfr_ui_div (y, 1, MPC_IM (op), GMP_RNDZ);
+              if (mpfr_zero_p (y))
+                break; /* underflow. */
+              /* 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 ? */
+              if (cmp_2 > 0)
+                err = 2 + (mp_prec_t)MPC_MAX (MPFR_EXP (y), 0);
+
+              /* atanh cannot underflow: |atanh(x)| > |x| for |x| < 1 */
+              inex_im |= mpfr_atanh (y, y, GMP_RNDZ);
+              if (cmp_2 > 0)
+                err += MPC_MAX (SAFE_ABS (mp_prec_t, MPFR_EXP (y)), 0);
+
+              ok = inex_im == 0 
+                || mpfr_can_round (y, p-err, GMP_RNDZ, rnd_im,
+                                   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);
+          mpfr_clear (y);
+        }
+      return MPC_INEX (inex_re, inex_im);
+    }
+
+  /* regular number argument */
+
+  /* TODO */
   mpfr_set_nan (MPC_RE (rop));
-  mpfr_set_nan (MPC_RE (rop));
+  mpfr_set_nan (MPC_IM (rop));
+
   return 0;
 }
diff --git a/src/atanh.c b/src/atanh.c
index 057462a..bb2ad1e 100644
--- a/src/atanh.c
+++ b/src/atanh.c
@@ -34,7 +34,7 @@ mpc_atanh (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
   MPFR_CHANGE_SIGN (MPC_RE (z));
 
   inex = mpc_atan (rop, z,
-                   RNDC (MPC_RND_IM (rnd), INV_RND (MPC_RND_RE (rnd))));
+                   RNDC (INV_RND (MPC_RND_IM (rnd)), MPC_RND_RE (rnd)));
 
   /* change rop to -i*rop */
   tmp[0] = MPC_RE (rop)[0];
@@ -42,5 +42,5 @@ mpc_atanh (mpc_ptr rop, mpc_srcptr op, mpc_rnd_t rnd)
   MPC_IM (rop)[0] = tmp[0];
   MPFR_CHANGE_SIGN (MPC_IM (rop));
 
-  return MPC_INEX (-MPC_INEX_IM (inex), MPC_INEX_RE (inex));
+  return MPC_INEX (MPC_INEX_IM (inex), -MPC_INEX_RE (inex));
 }
diff --git a/tests/atan.dat b/tests/atan.dat
index c0029b3..bffec72 100644
--- a/tests/atan.dat
+++ b/tests/atan.dat
@@ -50,47 +50,87 @@
 # The sign of the result is checked with "+inf", "-inf", "-0", or "+0".
 
 # special values (following ISO C99 standard)
-+ 0 53 -0x1921FB54442D18p-52 53 -inf    53 -inf 53 -inf N N
-+ 0 53 -0x1921FB54442D18p-52 53 -inf    53 -inf 53   -1 N N
-+ 0 53 -0x1921FB54442D18p-52 53 -inf    53 -inf 53   -0 N N
-+ 0 53 -0x1921FB54442D18p-52 53 +inf    53 -inf 53   +0 N N
-+ 0 53 -0x1921FB54442D18p-52 53 +inf    53 -inf 53   +1 N N
-+ 0 53 -0x1921FB54442D18p-52 53 +inf    53 -inf 53 +inf N N
-+ 0 53 -0x1921FB54442D18p-52 53  inf    53 -inf 53  nan N N
++ 0 53 -0x1921FB54442D18p-52 53   -0    53 -inf 53 -inf N N
++ 0 53 -0x1921FB54442D18p-52 53   -0    53 -inf 53   -1 N N
++ 0 53 -0x1921FB54442D18p-52 53   -0    53 -inf 53   -0 N N
++ 0 53 -0x1921FB54442D18p-52 53   +0    53 -inf 53   +0 N N
++ 0 53 -0x1921FB54442D18p-52 53   +0    53 -inf 53   +1 N N
++ 0 53 -0x1921FB54442D18p-52 53   +0    53 -inf 53 +inf N N
++ 0 53 -0x1921FB54442D18p-52 53    0    53 -inf 53  nan N N
 + 0 53 -0x1921FB54442D18p-52 53   -0    53   -6 53 -inf N N
 + 0 53 -0x1921FB54442D18p-52 53   +0    53   -6 53 +inf N N
 0 0 53                   nan 53  nan    53   -6 53  nan N N
 + 0 53 -0x1921FB54442D18p-52 53   -0    53   -0 53 -inf N N
-+ 0 53 -0x1921FB54442D18p-52 53   -0    53   -0 53   -0 N N
-+ 0 53 -0x1921FB54442D18p-52 53   +0    53   -0 53   +0 N N
+0 0 53                    -0 53   -0    53   -0 53   -0 N N
+0 0 53                    -0 53   +0    53   -0 53   +0 N N
 + 0 53 -0x1921FB54442D18p-52 53   +0    53   -0 53 +inf N N
 0 0 53                   nan 53  nan    53   -0 53  nan N N
-+ 0 53 +0x1921FB54442D18p-52 53   -0    53   +0 53 -inf N N
-+ 0 53 +0x1921FB54442D18p-52 53   -0    53   +0 53   -0 N N
-+ 0 53 +0x1921FB54442D18p-52 53   +0    53   +0 53   +0 N N
-+ 0 53 +0x1921FB54442D18p-52 53   +0    53   +0 53 +inf N N
+- 0 53 +0x1921FB54442D18p-52 53   -0    53   +0 53 -inf N N
+0 0 53                    +0 53   -0    53   +0 53   -0 N N
+0 0 53                    +0 53   +0    53   +0 53   +0 N N
+- 0 53 +0x1921FB54442D18p-52 53   +0    53   +0 53 +inf N N
 0 0 53                   nan 53  nan    53   +0 53  nan N N
-+ 0 53 +0x1921FB54442D18p-52 53   -0    53   +6 53 -inf N N
-+ 0 53 +0x1921FB54442D18p-52 53   +0    53   +6 53 +inf N N
+- 0 53 +0x1921FB54442D18p-52 53   -0    53   +6 53 -inf N N
+- 0 53 +0x1921FB54442D18p-52 53   +0    53   +6 53 +inf N N
 0 0 53                   nan 53  nan    53   +6 53  nan N N
-+ 0 53 +0x1921FB54442D18p-52 53   -0    53 +inf 53 -inf N N
-+ 0 53 +0x1921FB54442D18p-52 53   -0    53 +inf 53   -1 N N
-+ 0 53 +0x1921FB54442D18p-52 53   -0    53 +inf 53   -0 N N
-+ 0 53 +0x1921FB54442D18p-52 53   +0    53 +inf 53   +0 N N
-+ 0 53 +0x1921FB54442D18p-52 53   +0    53 +inf 53   +1 N N
-+ 0 53 +0x1921FB54442D18p-52 53   +0    53 +inf 53 +inf N N
-0 0 53 +0x1921FB54442D18p-52 53  nan    53 +inf 53  nan N N
-0 0 53                  +inf 53  nan    53  nan 53 -inf N N
+- 0 53 +0x1921FB54442D18p-52 53   -0    53 +inf 53 -inf N N
+- 0 53 +0x1921FB54442D18p-52 53   -0    53 +inf 53   -1 N N
+- 0 53 +0x1921FB54442D18p-52 53   -0    53 +inf 53   -0 N N
+- 0 53 +0x1921FB54442D18p-52 53   +0    53 +inf 53   +0 N N
+- 0 53 +0x1921FB54442D18p-52 53   +0    53 +inf 53   +1 N N
+- 0 53 +0x1921FB54442D18p-52 53   +0    53 +inf 53 +inf N N
+- 0 53 +0x1921FB54442D18p-52 53    0    53 +inf 53  nan N N
+0 0 53                   nan 53   -0    53  nan 53 -inf N N
 0 0 53                   nan 53  nan    53  nan 53   -1 N N
-0 0 53                   nan 53  nan    53  nan 53   -0 N N
-0 0 53                   nan 53  nan    53  nan 53   +0 N N
+0 0 53                   nan 53   -0    53  nan 53   -0 N N
+0 0 53                   nan 53   +0    53  nan 53   +0 N N
 0 0 53                   nan 53  nan    53  nan 53   +1 N N
-0 0 53                  +inf 53  nan    53  nan 53 +inf N N
+0 0 53                   nan 53   +0    53  nan 53 +inf N N
 0 0 53                   nan 53  nan    53  nan 53  nan N N
 
 # pure real argument
+- 0 53 -0x16DCC57BB565FDp-52 53   -0    53     -7 53 -0 N N
+- 0 53 -0x16DCC57BB565FDp-52 53   +0    53     -7 53 +0 N N
++ 0 53 -0x1F730BD281F69Bp-53 53   -0    53   -1.5 53 -0 N N
++ 0 53 -0x1F730BD281F69Bp-53 53   +0    53   -1.5 53 +0 N N
++ 0 53 -0x1921FB54442D18p-53 53   -0    53     -1 53 -0 N N
++ 0 53 -0x1921FB54442D18p-53 53   +0    53     -1 53 +0 N N
+- 0 53 -0x1700A7C5784634p-53 53   -0    53 -0.875 53 -0 N N
+- 0 53 -0x1700A7C5784634p-53 53   +0    53 -0.875 53 +0 N N
+- 0 53 -0x1FD5BA9AAC2F6Ep-56 53   -0    53 -0.125 53 -0 N N
+- 0 53 -0x1FD5BA9AAC2F6Ep-56 53   +0    53 -0.125 53 +0 N N
++ 0 53 +0x1FD5BA9AAC2F6Ep-56 53   +0    53 +0.125 53 +0 N N
++ 0 53 +0x1FD5BA9AAC2F6Ep-56 53   -0    53 +0.125 53 -0 N N
++ 0 53 +0x1700A7C5784634p-53 53   +0    53 +0.875 53 +0 N N
++ 0 53 +0x1700A7C5784634p-53 53   -0    53 +0.875 53 -0 N N
+- 0 53 +0x1921FB54442D18p-53 53   +0    53     +1 53 +0 N N
+- 0 53 +0x1921FB54442D18p-53 53   -0    53     +1 53 -0 N N
+- 0 53 +0x1F730BD281F69Bp-53 53   +0    53   +1.5 53 +0 N N
+- 0 53 +0x1F730BD281F69Bp-53 53   -0    53   +1.5 53 -0 N N
++ 0 53 +0x16DCC57BB565FDp-52 53   +0    53     +7 53 +0 N N
++ 0 53 +0x16DCC57BB565FDp-52 53   -0    53     +7 53 -0 N N
 
 # pure imaginary argument
++ + 53 -0x1921FB54442D18p-52 53 -0x1269621134DB92p-55    53 -0 53     -7 N N
+- + 53 +0x1921FB54442D18p-52 53 -0x1269621134DB92p-55    53 +0 53     -7 N N
++ + 53 -0x1921FB54442D18p-52 53 -0x19C041F7ED8D33p-53    53 -0 53   -1.5 N N
+- + 53 +0x1921FB54442D18p-52 53 -0x19C041F7ED8D33p-53    53 +0 53   -1.5 N N
+0 0 53                   nan 53                  -inf    53 -0 53     -1 N N
+0 0 53                   nan 53                  -inf    53 +0 53     -1 N N
+0 + 53                    -0 53 -0x15AA16394D481Fp-52    53 -0 53 -0.875 N N
+0 + 53                    +0 53 -0x15AA16394D481Fp-52    53 +0 53 -0.875 N N
+0 + 53                    -0 53 -0x1015891C9EAEF7p-55    53 -0 53 -0.125 N N
+0 + 53                    +0 53 -0x1015891C9EAEF7p-55    53 +0 53 -0.125 N N
+0 - 53                    +0 53 +0x1015891C9EAEF7p-55    53 +0 53 +0.125 N N
+0 - 53                    -0 53 +0x1015891C9EAEF7p-55    53 -0 53 +0.125 N N
+0 - 53                    +0 53 +0x15AA16394D481Fp-52    53 +0 53 +0.875 N N
+0 - 53                    -0 53 +0x15AA16394D481Fp-52    53 -0 53 +0.875 N N
+0 0 53                   nan 53                  +inf    53 +0 53     +1 N N
+0 0 53                   nan 53                  +inf    53 -0 53     +1 N N
+- - 53 +0x1921FB54442D18p-52 53 +0x19C041F7ED8D33p-53    53 +0 53   +1.5 N N
++ - 53 -0x1921FB54442D18p-52 53 +0x19C041F7ED8D33p-53    53 -0 53   +1.5 N N
+- - 53 +0x1921FB54442D18p-52 53 +0x1269621134DB92p-55    53 +0 53     +7 N N
++ - 53 -0x1921FB54442D18p-52 53 +0x1269621134DB92p-55    53 -0 53     +7 N N
 
 # IEEE-754 double precision
 
diff --git a/tests/atanh.dat b/tests/atanh.dat
index ad075c2..1b4227d 100644
--- a/tests/atanh.dat
+++ b/tests/atanh.dat
@@ -57,13 +57,13 @@
 0 - 53   -0 53 +0x1921FB54442D18p-52    53 -inf 53   +1 N N
 0 - 53   -0 53 +0x1921FB54442D18p-52    53 -inf 53 +inf N N
 0 0 53   -0 53                   nan    53 -inf 53  nan N N
-0 + 53   +0 53 -0x1921FB54442D18p-52    53   -6 53 -inf N N
-0 - 53   +0 53  0x1921FB54442D18p-52    53   -6 53 +inf N N
+0 + 53   -0 53 -0x1921FB54442D18p-52    53   -6 53 -inf N N
+0 - 53   -0 53 +0x1921FB54442D18p-52    53   -6 53 +inf N N
 0 0 53  nan 53                   nan    53   -6 53  nan N N
 0 + 53   -0 53 -0x1921FB54442D18p-52    53   -0 53 -inf N N
 0 0 53   -0 53                    -0    53   -0 53   -0 N N
 0 0 53   -0 53                    +0    53   -0 53   +0 N N
-0 - 53   -0 53  0x1921FB54442D18p-52    53   -0 53 +inf N N
+0 - 53   -0 53 +0x1921FB54442D18p-52    53   -0 53 +inf N N
 0 0 53   -0 53                   nan    53   -0 53  nan N N
 0 + 53   +0 53 -0x1921FB54442D18p-52    53   +0 53 -inf N N
 0 0 53   +0 53                    -0    53   +0 53   -0 N N
@@ -71,26 +71,42 @@
 0 - 53   +0 53 +0x1921FB54442D18p-52    53   +0 53 +inf N N
 0 0 53   +0 53                   nan    53   +0 53  nan N N
 0 + 53   +0 53 -0x1921FB54442D18p-52    53   +6 53 -inf N N
-0 - 53   +0 53  0x1921FB54442D18p-52    53   +6 53 +inf N N
+0 - 53   +0 53 +0x1921FB54442D18p-52    53   +6 53 +inf N N
 0 0 53  nan 53                   nan    53   +6 53  nan N N
 0 + 53   +0 53 -0x1921FB54442D18p-52    53 +inf 53 -inf N N
 0 + 53   +0 53 -0x1921FB54442D18p-52    53 +inf 53   -1 N N
 0 + 53   +0 53 -0x1921FB54442D18p-52    53 +inf 53   -0 N N
-0 - 53   +0 53  0x1921FB54442D18p-52    53 +inf 53   +0 N N
-0 - 53   +0 53  0x1921FB54442D18p-52    53 +inf 53   +1 N N
-0 - 53   +0 53  0x1921FB54442D18p-52    53 +inf 53 +inf N N
+0 - 53   +0 53 +0x1921FB54442D18p-52    53 +inf 53   +0 N N
+0 - 53   +0 53 +0x1921FB54442D18p-52    53 +inf 53   +1 N N
+0 - 53   +0 53 +0x1921FB54442D18p-52    53 +inf 53 +inf N N
 0 0 53   +0 53                   nan    53 +inf 53  nan N N
-0 + 53   +0 53 -0x1921FB54442D18p-52    53  nan 53 -inf N N
+0 + 53    0 53 -0x1921FB54442D18p-52    53  nan 53 -inf N N
 0 0 53  nan 53                   nan    53  nan 53   -1 N N
 0 0 53  nan 53                   nan    53  nan 53   -0 N N
 0 0 53  nan 53                   nan    53  nan 53   +0 N N
 0 0 53  nan 53                   nan    53  nan 53   +1 N N
-0 - 53   +0 53  0x1921FB54442D18p-52    53  nan 53 +inf N N
+0 - 53    0 53 +0x1921FB54442D18p-52    53  nan 53 +inf N N
 0 0 53  nan 53                   nan    53  nan 53  nan N N
 
 # pure real argument
+- + 53 -0x1E27076E2AF2E6p-57 53 -0x1921FB54442D18p-52    53  -17 53   -0 N N
+- - 53 -0x1E27076E2AF2E6p-57 53 +0x1921FB54442D18p-52    53  -17 53   +0 N N
++ + 53 +0x1E27076E2AF2E6p-57 53 -0x1921FB54442D18p-52    53  +17 53   -0 N N
++ - 53 +0x1E27076E2AF2E6p-57 53 +0x1921FB54442D18p-52    53  +17 53   +0 N N
++ 0 53 -0x1F2272AE325A57p-53 53                    -0    53 -.75 53   -0 N N
++ 0 53 -0x1F2272AE325A57p-53 53                    +0    53 -.75 53   +0 N N
+- 0 53 +0x1F2272AE325A57p-53 53                    -0    53 +.75 53   -0 N N
+- 0 53 +0x1F2272AE325A57p-53 53                    +0    53 +.75 53   +0 N N
 
 # pure imaginary argument
+0 - 53   -0 53 -0x167D8863BC99BDp-52    53   -0 53   -6 N N
+0 - 53   +0 53 -0x167D8863BC99BDp-52    53   +0 53   -6 N N
+0 + 53   -0 53 +0x167D8863BC99BDp-52    53   -0 53   +6 N N
+0 + 53   +0 53 +0x167D8863BC99BDp-52    53   +0 53   +6 N N
+0 + 53   -0 53 -0x1F5B75F92C80DDp-55    53   -0 53 -.25 N N
+0 + 53   +0 53 -0x1F5B75F92C80DDp-55    53   +0 53 -.25 N N
+0 - 53   -0 53 +0x1F5B75F92C80DDp-55    53   -0 53 +.25 N N
+0 - 53   +0 53 +0x1F5B75F92C80DDp-55    53   +0 53 +.25 N N
 
 # IEEE-754 double precision