remainder* tests: More tests.

* tests/test-remainder.h: New file, based on tests/test-fmod.h.
* tests/test-remainder.c: Include <float.h> and test-remainder.h.
(main): Invoke test_function.
* tests/test-remainderf.c: Include <float.h> and test-remainder.h.
(main): Invoke test_function.
* tests/test-remainderl.c: Include <float.h> and test-remainder.h.
(main): Invoke test_function.
* modules/remainder-tests (Files): Add tests/test-remainder.h,
tests/randomd.c.
(Makefile.am): Add randomd.c to test_remainder_SOURCES.
* modules/remainderf-tests (Files): Add tests/test-remainder.h,
tests/randomf.c.
(Makefile.am): Add randomf.c to test_remainderf_SOURCES.
* modules/remainderl-tests (Files): Add tests/test-remainder.h,
tests/randoml.c.
(Depends-on): Add 'float'.
(Makefile.am): Add randoml.c to test_remainderl_SOURCES.

8 files changed, 189 insertions, 9 deletions

diff --git a/ChangeLog b/ChangeLog
index e7139c0605..7a01288dd7 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,24 @@
+2012-03-03  Bruno Haible  <bruno@clisp.org>
+
+	remainder* tests: More tests.
+	* tests/test-remainder.h: New file, based on tests/test-fmod.h.
+	* tests/test-remainder.c: Include <float.h> and test-remainder.h.
+	(main): Invoke test_function.
+	* tests/test-remainderf.c: Include <float.h> and test-remainder.h.
+	(main): Invoke test_function.
+	* tests/test-remainderl.c: Include <float.h> and test-remainder.h.
+	(main): Invoke test_function.
+	* modules/remainder-tests (Files): Add tests/test-remainder.h,
+	tests/randomd.c.
+	(Makefile.am): Add randomd.c to test_remainder_SOURCES.
+	* modules/remainderf-tests (Files): Add tests/test-remainder.h,
+	tests/randomf.c.
+	(Makefile.am): Add randomf.c to test_remainderf_SOURCES.
+	* modules/remainderl-tests (Files): Add tests/test-remainder.h,
+	tests/randoml.c.
+	(Depends-on): Add 'float'.
+	(Makefile.am): Add randoml.c to test_remainderl_SOURCES.
+
 2012-03-04  Bruno Haible  <bruno@clisp.org>
 
 	remainder, remainderf, remainderl: Fix computation for large quotients.
diff --git a/modules/remainder-tests b/modules/remainder-tests
index 6832a49add..0ede99ab39 100644
--- a/modules/remainder-tests
+++ b/modules/remainder-tests
@@ -1,7 +1,9 @@
 Files:
 tests/test-remainder.c
+tests/test-remainder.h
 tests/signature.h
 tests/macros.h
+tests/randomd.c
 
 Depends-on:
 
@@ -10,4 +12,5 @@ configure.ac:
 Makefile.am:
 TESTS += test-remainder
 check_PROGRAMS += test-remainder
+test_remainder_SOURCES = test-remainder.c randomd.c
 test_remainder_LDADD = $(LDADD) @REMAINDER_LIBM@
diff --git a/modules/remainderf-tests b/modules/remainderf-tests
index 6f392da43e..7958022073 100644
--- a/modules/remainderf-tests
+++ b/modules/remainderf-tests
@@ -1,7 +1,9 @@
 Files:
 tests/test-remainderf.c
+tests/test-remainder.h
 tests/signature.h
 tests/macros.h
+tests/randomf.c
 
 Depends-on:
 
@@ -10,4 +12,5 @@ configure.ac:
 Makefile.am:
 TESTS += test-remainderf
 check_PROGRAMS += test-remainderf
+test_remainderf_SOURCES = test-remainderf.c randomf.c
 test_remainderf_LDADD = $(LDADD) @REMAINDERF_LIBM@
diff --git a/modules/remainderl-tests b/modules/remainderl-tests
index 4a638aa442..533930e01d 100644
--- a/modules/remainderl-tests
+++ b/modules/remainderl-tests
@@ -1,14 +1,18 @@
 Files:
 tests/test-remainderl.c
+tests/test-remainder.h
 tests/signature.h
 tests/macros.h
+tests/randoml.c
 
 Depends-on:
 fpucw
+float
 
 configure.ac:
 
 Makefile.am:
 TESTS += test-remainderl
 check_PROGRAMS += test-remainderl
+test_remainderl_SOURCES = test-remainderl.c randoml.c
 test_remainderl_LDADD = $(LDADD) @REMAINDERL_LIBM@
diff --git a/tests/test-remainder.c b/tests/test-remainder.c
index 5869bb7d73..c43d60639f 100644
--- a/tests/test-remainder.c
+++ b/tests/test-remainder.c
@@ -23,11 +23,17 @@
 #include "signature.h"
 SIGNATURE_CHECK (remainder, double, (double, double));
 
+#include <float.h>
+
 #include "macros.h"
 
-volatile double x;
-volatile double y;
-double z;
+#define DOUBLE double
+#define L_(literal) literal
+#define MANT_DIG DBL_MANT_DIG
+#define MAX_EXP DBL_MAX_EXP
+#define REMAINDER remainder
+#define RANDOM randomd
+#include "test-remainder.h"
 
 int
 main ()
@@ -38,5 +44,7 @@ main ()
   z = remainder (x, y);
   ASSERT (z >= -0.178870837 && z <= -0.178870835);
 
+  test_function ();
+
   return 0;
 }
diff --git a/tests/test-remainder.h b/tests/test-remainder.h
new file mode 100644
index 0000000000..a25e6b22bb
--- /dev/null
+++ b/tests/test-remainder.h
@@ -0,0 +1,124 @@
+/* Test of remainder*() function family.
+   Copyright (C) 2012 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/>.  */
+
+static DOUBLE
+my_ldexp (DOUBLE x, int d)
+{
+  for (; d > 0; d--)
+    x *= L_(2.0);
+  for (; d < 0; d++)
+    x *= L_(0.5);
+  return x;
+}
+
+static void
+test_function (void)
+{
+  int i;
+  int j;
+  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));
+
+  /* Randomized tests.  */
+  for (i = 0; i < SIZEOF (RANDOM) / 5; i++)
+    for (j = 0; j < SIZEOF (RANDOM) / 5; j++)
+      {
+        DOUBLE x = L_(16.0) * RANDOM[i]; /* 0.0 <= x <= 16.0 */
+        DOUBLE y = RANDOM[j]; /* 0.0 <= y < 1.0 */
+        if (y > L_(0.0))
+          {
+            DOUBLE z = REMAINDER (x, y);
+            ASSERT (z >= - L_(0.5) * y);
+            ASSERT (z <= L_(0.5) * y);
+            z -= x - (int) ((L_(2.0) * x + y) / (L_(2.0) * y)) * y;
+            ASSERT (/* The common case.  */
+                    (z > - L_(2.0) * L_(16.0) / TWO_MANT_DIG
+                     && z < L_(2.0) * L_(16.0) / TWO_MANT_DIG)
+                    || /* rounding error: 2x+y / 2y computed too large */
+                       (z > y - L_(2.0) * L_(16.0) / TWO_MANT_DIG
+                        && z < y + L_(2.0) * L_(16.0) / TWO_MANT_DIG)
+                    || /* rounding error: 2x+y / 2y computed too small */
+                       (z > - y - L_(2.0) * L_(16.0) / TWO_MANT_DIG
+                        && z < - y + L_(2.0) * L_(16.0) / TWO_MANT_DIG));
+          }
+      }
+
+  for (i = 0; i < SIZEOF (RANDOM) / 5; i++)
+    for (j = 0; j < SIZEOF (RANDOM) / 5; j++)
+      {
+        DOUBLE x = L_(1.0e9) * RANDOM[i]; /* 0.0 <= x <= 10^9 */
+        DOUBLE y = RANDOM[j]; /* 0.0 <= y < 1.0 */
+        if (y > L_(0.0))
+          {
+            DOUBLE z = REMAINDER (x, y);
+            DOUBLE r;
+            ASSERT (z >= - L_(0.5) * y);
+            ASSERT (z <= L_(0.5) * y);
+            {
+              /* Determine the quotient 2x+y / 2y in two steps, because it
+                 may be > 2^31.  */
+              int q1 = (int) (x / y / L_(65536.0));
+              int q2 = (int) ((L_(2.0) * (x - q1 * L_(65536.0) * y) + y)
+                              / (L_(2.0) * y));
+              DOUBLE q = (DOUBLE) q1 * L_(65536.0) + (DOUBLE) q2;
+              r = x - q * y;
+            }
+            /* The absolute error of z can be up to 1e9/2^MANT_DIG.
+               The absolute error of r can also be up to 1e9/2^MANT_DIG.
+               Therefore the error of z - r can be twice as large.  */
+            z -= r;
+            ASSERT (/* The common case.  */
+                    (z > - L_(2.0) * L_(1.0e9) / TWO_MANT_DIG
+                     && z < L_(2.0) * L_(1.0e9) / TWO_MANT_DIG)
+                    || /* rounding error: 2x+y / 2y computed too large */
+                       (z > y - L_(2.0) * L_(1.0e9) / TWO_MANT_DIG
+                        && z < y + L_(2.0) * L_(1.0e9) / TWO_MANT_DIG)
+                    || /* rounding error: 2x+y / 2y computed too small */
+                       (z > - y - L_(2.0) * L_(1.0e9) / TWO_MANT_DIG
+                        && z < - y + L_(2.0) * L_(1.0e9) / TWO_MANT_DIG));
+          }
+      }
+
+  {
+    int large_exp = (MAX_EXP - 1 < 1000 ? MAX_EXP - 1 : 1000);
+    DOUBLE large = my_ldexp (L_(1.0), large_exp); /* = 2^large_exp */
+    for (i = 0; i < SIZEOF (RANDOM) / 10; i++)
+      for (j = 0; j < SIZEOF (RANDOM) / 10; j++)
+        {
+          DOUBLE x = large * RANDOM[i]; /* 0.0 <= x <= 2^large_exp */
+          DOUBLE y = RANDOM[j]; /* 0.0 <= y < 1.0 */
+          if (y > L_(0.0))
+            {
+              DOUBLE z = REMAINDER (x, y);
+              /* Regardless how large the rounding errors are, the result
+                 must be >= -y/2, <= y/2.  */
+              ASSERT (z >= - L_(0.5) * y);
+              ASSERT (z <= L_(0.5) * y);
+            }
+        }
+  }
+}
+
+volatile DOUBLE x;
+volatile DOUBLE y;
+DOUBLE z;
diff --git a/tests/test-remainderf.c b/tests/test-remainderf.c
index fc6be7568a..0c6174fb86 100644
--- a/tests/test-remainderf.c
+++ b/tests/test-remainderf.c
@@ -23,11 +23,17 @@
 #include "signature.h"
 SIGNATURE_CHECK (remainderf, float, (float, float));
 
+#include <float.h>
+
 #include "macros.h"
 
-volatile float x;
-volatile float y;
-float z;
+#define DOUBLE float
+#define L_(literal) literal##f
+#define MANT_DIG FLT_MANT_DIG
+#define MAX_EXP FLT_MAX_EXP
+#define REMAINDER remainderf
+#define RANDOM randomf
+#include "test-remainder.h"
 
 int
 main ()
@@ -37,5 +43,8 @@ main ()
   y = 3.141592654f;
   z = remainderf (x, y);
   ASSERT (z >= -0.1788714f && z <= -0.1788708f);
+
+  test_function ();
+
   return 0;
 }
diff --git a/tests/test-remainderl.c b/tests/test-remainderl.c
index 3307d8064e..09dc7c7263 100644
--- a/tests/test-remainderl.c
+++ b/tests/test-remainderl.c
@@ -23,12 +23,18 @@
 #include "signature.h"
 SIGNATURE_CHECK (remainderl, long double, (long double, long double));
 
+#include <float.h>
+
 #include "fpucw.h"
 #include "macros.h"
 
-volatile long double x;
-volatile long double y;
-long double z;
+#define DOUBLE long double
+#define L_(literal) literal##L
+#define MANT_DIG LDBL_MANT_DIG
+#define MAX_EXP LDBL_MAX_EXP
+#define REMAINDER remainderl
+#define RANDOM randoml
+#include "test-remainder.h"
 
 int
 main ()
@@ -43,5 +49,7 @@ main ()
   z = remainderl (x, y);
   ASSERT (z >= -0.178870837L && z <= -0.178870835L);
 
+  test_function ();
+
   return 0;
 }