Implement 'round', 'roundf', 'roundl' modules.

[gnulib.git] / lib / round.c

diff --git a/lib/round.c b/lib/round.c
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+/* Round toward nearest, breaking ties away from zero.
+   Copyright (C) 2007 Free Software Foundation, Inc.
+
+   This program is free software; you can redistribute it and/or modify
+   it under the terms of the GNU General Public License as published by
+   the Free Software Foundation; either version 2, or (at your option)
+   any later version.
+
+   This program is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+   GNU General Public License for more details.
+
+   You should have received a copy of the GNU General Public License along
+   with this program; if not, write to the Free Software Foundation,
+   Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.  */
+
+/* Written by Ben Pfaff <blp@gnu.org>, 2007.
+   Based heavily on code by Bruno Haible. */
+
+#include <config.h>
+
+#include <float.h>
+#include <math.h>
+
+#ifdef USE_LONG_DOUBLE
+# define ROUND roundl
+# define FLOOR floorl
+# define CEIL ceill
+# define DOUBLE long double
+# define MANT_DIG LDBL_MANT_DIG
+# define L_(literal) literal##L
+# define HAVE_FLOOR_AND_CEIL (HAVE_DECL_FLOORL && HAVE_DECL_CEILL)
+#elif ! defined USE_FLOAT
+# define ROUND round
+# define FLOOR floor
+# define CEIL ceil
+# define DOUBLE double
+# define MANT_DIG DBL_MANT_DIG
+# define L_(literal) literal
+# define HAVE_FLOOR_AND_CEIL 1
+#else /* defined USE_FLOAT */
+# define ROUND roundf
+# define FLOOR floorf
+# define CEIL ceilf
+# define DOUBLE float
+# define MANT_DIG FLT_MANT_DIG
+# define L_(literal) literal##f
+# define HAVE_FLOOR_AND_CEIL (HAVE_DECL_FLOORF && HAVE_DECL_CEILF)
+#endif
+
+/* If we're being included from test-round2[f].c, it already defined names for
+   our round implementations.  Otherwise, pick the preferred implementation for
+   this machine. */
+#if !defined FLOOR_BASED_ROUND && !defined FLOOR_FREE_ROUND
+# if HAVE_FLOOR_AND_CEIL
+#  define FLOOR_BASED_ROUND ROUND
+# else
+#  define FLOOR_FREE_ROUND ROUND
+# endif
+#endif
+
+#ifdef FLOOR_BASED_ROUND
+/* An implementation of the C99 round function based on floor and ceil.  We use
+   this when floor and ceil are available, on the assumption that they are
+   faster than the open-coded versions below. */
+DOUBLE
+FLOOR_BASED_ROUND (DOUBLE x)
+{
+  if (x >= L_(0.0)) 
+    {
+      DOUBLE y = FLOOR (x);
+      if (x - y >= L_(0.5))
+        y += L_(1.0);
+      return y;
+    }
+  else
+    {
+      DOUBLE y = CEIL (x);
+      if (y - x >= L_(0.5))
+        y -= L_(1.0);
+      return y;
+    }
+}
+#endif /* FLOOR_BASED_ROUND */
+
+#ifdef FLOOR_FREE_ROUND
+/* An implementation of the C99 round function without floor or ceil.
+   We use this when floor or ceil is missing. */
+DOUBLE
+FLOOR_FREE_ROUND (DOUBLE x)
+{
+  /* 2^(MANT_DIG-1).  */
+  static const DOUBLE TWO_MANT_DIG =
+    /* Assume MANT_DIG <= 5 * 31.
+       Use the identity
+       n = floor(n/5) + floor((n+1)/5) + ... + floor((n+4)/5).  */
+    (DOUBLE) (1U << ((MANT_DIG - 1) / 5))
+    * (DOUBLE) (1U << ((MANT_DIG - 1 + 1) / 5))
+    * (DOUBLE) (1U << ((MANT_DIG - 1 + 2) / 5))
+    * (DOUBLE) (1U << ((MANT_DIG - 1 + 3) / 5))
+    * (DOUBLE) (1U << ((MANT_DIG - 1 + 4) / 5));
+
+  /* The use of 'volatile' guarantees that excess precision bits are dropped at
+     each addition step and before the following comparison at the caller's
+     site.  It is necessary on x86 systems where double-floats are not IEEE
+     compliant by default, to avoid that the results become platform and
+     compiler option dependent.  'volatile' is a portable alternative to gcc's
+     -ffloat-store option.  */
+  volatile DOUBLE y = x;
+  volatile DOUBLE z = y;
+
+  if (z > L_(0.0))
+    {
+      /* Avoid rounding error for x = 0.5 - 2^(-MANT_DIG-1).  */
+      if (z < L_(0.5))
+       z = L_(0.0);
+      /* Avoid rounding errors for values near 2^k, where k >= MANT_DIG-1.  */
+      else if (z < TWO_MANT_DIG)
+       {
+         /* Add 0.5 to the absolute value.  */
+         y = z += L_(0.5);
+         /* Round to the next integer (nearest or up or down, doesn't
+             matter).  */
+         z += TWO_MANT_DIG;
+         z -= TWO_MANT_DIG;
+         /* Enforce rounding down.  */
+         if (z > y)
+           z -= L_(1.0);
+       }
+    }
+  else if (z < L_(0.0))
+    {
+      /* Avoid rounding error for x = -(0.5 - 2^(-MANT_DIG-1)).  */
+      if (z > - L_(0.5))
+       z = L_(0.0);
+      /* Avoid rounding errors for values near -2^k, where k >= MANT_DIG-1.  */
+      else if (z > -TWO_MANT_DIG)
+       {
+         /* Add 0.5 to the absolute value.  */
+         y = z -= L_(0.5);
+         /* Round to the next integer (nearest or up or down, doesn't
+             matter).  */
+         z -= TWO_MANT_DIG;
+         z += TWO_MANT_DIG;
+         /* Enforce rounding up.  */
+         if (z < y)
+           z += L_(1.0);
+       }
+    }
+  return z;
+}
+#endif /* FLOOR_FREE_ROUND */
+