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changeset 9335:5f9727c11975

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Fix incorrect rounding of ceil, ceilf, ceill in some cases. Add new test.
author Bruno Haible <bruno@clisp.org>
date Sat, 13 Oct 2007 03:09:19 +0200
parents 094611565479
children 5c22ca8dc833
files ChangeLog lib/ceil.c modules/ceilf-tests tests/test-ceilf2.c
diffstat 4 files changed, 195 insertions(+), 11 deletions(-) [+]
line wrap: on
line diff
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,5 +1,10 @@
 2007-10-12  Bruno Haible  <bruno@clisp.org>
 
+	* lib/ceil.c (FUNC): Avoid rounding errors for values near a power
+	of 2.
+	* tests/test-ceilf2.c: New file.
+	* modules/ceilf-tests: (Files, Depends-on, Makefile.am): Add new test.
+
 	* tests/test-ceilf1.c: Renamed from tests/test-ceilf.c.
 	* modules/ceilf-tests: Update.
 
--- a/lib/ceil.c
+++ b/lib/ceil.c
@@ -63,20 +63,31 @@
   volatile DOUBLE y = x;
   volatile DOUBLE z = y;
 
-  /* Round to the next integer (nearest or up or down, doesn't matter).  */
   if (z > L_(0.0))
     {
-      z += TWO_MANT_DIG;
-      z -= TWO_MANT_DIG;
+      /* Avoid rounding errors for values near 2^k, where k >= MANT_DIG-1.  */
+      if (z < TWO_MANT_DIG)
+	{
+	  /* 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);
+	}
     }
   else if (z < L_(0.0))
     {
-      z -= TWO_MANT_DIG;
-      z += TWO_MANT_DIG;
+      /* Avoid rounding errors for values near -2^k, where k >= MANT_DIG-1.  */
+      if (z > - TWO_MANT_DIG)
+	{
+	  /* 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);
+	}
     }
-  /* Enforce rounding up.  */
-  if (z < y)
-    z += L_(1.0);
-
   return z;
 }
--- a/modules/ceilf-tests
+++ b/modules/ceilf-tests
@@ -1,14 +1,20 @@
 Files:
 tests/test-ceilf1.c
+tests/test-ceilf2.c
 
 Depends-on:
+float
+isnanf-nolibm
+stdbool
+stdint
 
 configure.ac:
 
 Makefile.am:
-TESTS += test-ceilf1
-check_PROGRAMS += test-ceilf1
+TESTS += test-ceilf1 test-ceilf2
+check_PROGRAMS += test-ceilf1 test-ceilf2
 test_ceilf1_LDADD = $(LDADD) @CEILF_LIBM@
+test_ceilf2_LDADD = $(LDADD) @CEILF_LIBM@
 
 License:
 LGPL
new file mode 100644
--- /dev/null
+++ b/tests/test-ceilf2.c
@@ -0,0 +1,162 @@
+/* Test of rounding towards positive infinity.
+   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 3 of the License, 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, see <http://www.gnu.org/licenses/>.  */
+
+/* Written by Bruno Haible <bruno@clisp.org>, 2007.  */
+
+#include <config.h>
+
+#include <math.h>
+
+#include <float.h>
+#include <stdbool.h>
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+#include "isnanf.h"
+
+#define ASSERT(expr) \
+  do									     \
+    {									     \
+      if (!(expr))							     \
+        {								     \
+          fprintf (stderr, "%s:%d: assertion failed\n", __FILE__, __LINE__); \
+          abort ();							     \
+        }								     \
+    }									     \
+  while (0)
+
+
+/* The reference implementation, taken from lib/ceil.c.  */
+
+#define DOUBLE float
+#define MANT_DIG FLT_MANT_DIG
+#define L_(literal) literal##f
+
+/* 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));
+
+DOUBLE
+ceilf_reference (DOUBLE x)
+{
+  /* 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 errors for values near 2^k, where k >= MANT_DIG-1.  */
+      if (z < TWO_MANT_DIG)
+	{
+	  /* 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);
+	}
+    }
+  else if (z < L_(0.0))
+    {
+      /* Avoid rounding errors for values near -2^k, where k >= MANT_DIG-1.  */
+      if (z > - TWO_MANT_DIG)
+	{
+	  /* 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;
+}
+
+
+/* Test for equality.  */
+static int
+equal (DOUBLE x, DOUBLE y)
+{
+  return (isnanf (x) ? isnanf (y) : x == y);
+}
+
+/* Test whether the result for a given argument is correct.  */
+static bool
+correct_result_p (DOUBLE x, DOUBLE result)
+{
+  return
+    (x > 0 && x <= 1 ? result == L_(1.0) :
+     x + 1 > x ? result >= x && result < x + 1 :
+     equal (result, x));
+}
+
+/* Test the function for a given argument.  */
+static int
+check (float x)
+{
+  /* If the reference implementation is incorrect, bail out immediately.  */
+  float reference = ceilf_reference (x);
+  ASSERT (correct_result_p (x, reference));
+  /* If the actual implementation is wrong, return an error code.  */
+  {
+    float result = ceilf (x);
+    if (correct_result_p (x, result))
+      return 0;
+    else
+      {
+	fprintf (stderr, "ceilf %g(%a) = %g(%a) or %g(%a)?\n",
+		 x, x, reference, reference, result, result);
+	return 1;
+      }
+  }
+}
+
+#define NUM_HIGHBITS 12
+#define NUM_LOWBITS 4
+
+int
+main ()
+{
+  unsigned int highbits;
+  unsigned int lowbits;
+  int error = 0;
+  for (highbits = 0; highbits < (1 << NUM_HIGHBITS); highbits++)
+    for (lowbits = 0; lowbits < (1 << NUM_LOWBITS); lowbits++)
+      {
+	/* Combine highbits and lowbits into a floating-point number,
+	   sign-extending the lowbits to 32-NUM_HIGHBITS bits.  */
+	union { float f; uint32_t i; } janus;
+	janus.i = ((uint32_t) highbits << (32 - NUM_HIGHBITS))
+		  | ((uint32_t) ((int32_t) ((uint32_t) lowbits << (32 - NUM_LOWBITS))
+				 >> (32 - NUM_LOWBITS - NUM_HIGHBITS))
+		     >> NUM_HIGHBITS);
+	error |= check (janus.f);
+      }
+  return (error ? 1 : 0);
+}