Hi,
while testing arm hardware on OpenBSD I noticed that some floating point
operations cause failures of other tests.
In fact the current libm is incorrect according to the ISO C Std Annex
G. I found this out after porting some FreeBSD lib msun tests. Many edge
cases for complex floating point operations are not covered at all.
My question on this is what I should do about this. Port the FreeBSD
msun library? Ignore the problem? Patch the current implementation?
I attached a test that is currently breaking. There are many more. To
fix these I just copied the FreeBSD file that implements the failing
function. But I am not sure if this is a good approach.
mbuhl
Index: regress/lib/libm/msun/Makefile
===================================================================
RCS file: /cvs/src/regress/lib/libm/msun/Makefile,v
retrieving revision 1.1.1.1
diff -u -p -r1.1.1.1 Makefile
--- regress/lib/libm/msun/Makefile 21 Feb 2019 16:14:03 -0000 1.1.1.1
+++ regress/lib/libm/msun/Makefile 31 May 2019 19:50:32 -0000
@@ -1,6 +1,7 @@
# $OpenBSD: Makefile,v 1.1.1.1 2019/02/21 16:14:03 bluhm Exp $
TESTS =
+TESTS += cexp_test
TESTS += conj_test
TESTS += fenv_test
TESTS += lrint_test
Index: regress/lib/libm/msun/cexp_test.c
===================================================================
RCS file: regress/lib/libm/msun/cexp_test.c
diff -N regress/lib/libm/msun/cexp_test.c
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ regress/lib/libm/msun/cexp_test.c 1 Jun 2019 05:40:51 -0000
@@ -0,0 +1,326 @@
+/*-
+ * Copyright (c) 2008-2011 David Schultz <d...@freebsd.org>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+/*
+ * Tests for corner cases in cexp*().
+ */
+
+#include <sys/cdefs.h>
+
+#include <sys/param.h>
+
+#include <assert.h>
+#include <complex.h>
+#include <fenv.h>
+#include <float.h>
+#include <math.h>
+#include <stdio.h>
+
+#include "test-utils.h"
+
+#pragma STDC FENV_ACCESS ON
+#pragma STDC CX_LIMITED_RANGE OFF
+
+/*
+ * Test that a function returns the correct value and sets the
+ * exception flags correctly. The exceptmask specifies which
+ * exceptions we should check. We need to be lenient for several
+ * reasons, but mainly because on some architectures it's impossible
+ * to raise FE_OVERFLOW without raising FE_INEXACT. In some cases,
+ * whether cexp() raises an invalid exception is unspecified.
+ *
+ * These are macros instead of functions so that assert provides more
+ * meaningful error messages.
+ *
+ * XXX The volatile here is to avoid gcc's bogus constant folding and work
+ * around the lack of support for the FENV_ACCESS pragma.
+ */
+#define test(func, z, result, exceptmask, excepts, checksign) do {
\
+ volatile long double complex _d = z; \
+ assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
+ assert(cfpequal_cs((func)(_d), (result), (checksign))); \
+ assert(((void)(func), fetestexcept(exceptmask) == (excepts))); \
+} while (0)
+
+#define test_c(t, func, z, result, exceptmask, excepts, checksign) do { \
+ volatile t complex r = result; \
+ test(func, z, r, exceptmask, excepts, checksign); \
+} while (0)
+
+#define test_f(func, z, result, exceptmask, excepts, checksign) do { \
+ test_c(float, func, z, result, exceptmask, excepts, checksign); \
+} while (0)
+
+/* Test within a given tolerance. */
+#define test_tol(func, z, result, tol) do {
\
+ volatile long double complex _d = z; \
+ assert(cfpequal_tol((func)(_d), (result), (tol), \
+ FPE_ABS_ZERO | CS_BOTH)); \
+} while (0)
+
+/* Test all the functions that compute cexp(x). */
+#define testall(x, result, exceptmask, excepts, checksign) do {
\
+ test(cexp, x, result, exceptmask, excepts, checksign); \
+ test_f(cexpf, x, result, exceptmask, excepts, checksign);
\
+} while (0)
+
+/*
+ * Test all the functions that compute cexp(x), within a given tolerance.
+ * The tolerance is specified in ulps.
+ */
+#define testall_tol(x, result, tol) do {
\
+ test_tol(cexp, x, result, tol * DBL_ULP()); \
+ test_tol(cexpf, x, result, tol * FLT_ULP()); \
+} while (0)
+
+/* Various finite non-zero numbers to test. */
+static const float finites[] =
+{ -42.0e20, -1.0, -1.0e-10, -0.0, 0.0, 1.0e-10, 1.0, 42.0e20 };
+
+
+/* Tests for 0 */
+static void
+test_zero(void)
+{
+
+ /* cexp(0) = 1, no exceptions raised */
+ testall(0.0, 1.0, ALL_STD_EXCEPT, 0, 1);
+ testall(-0.0, 1.0, ALL_STD_EXCEPT, 0, 1);
+ testall(CMPLXL(0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
+ testall(CMPLXL(-0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
+}
+
+/*
+ * Tests for NaN. The signs of the results are indeterminate unless the
+ * imaginary part is 0.
+ */
+static void
+test_nan(void)
+{
+ unsigned i;
+
+ /* cexp(x + NaNi) = NaN + NaNi and optionally raises invalid */
+ /* cexp(NaN + yi) = NaN + NaNi and optionally raises invalid (|y|>0) */
+ for (i = 0; i < nitems(finites); i++) {
+ printf("# Run %d..\n", i);
+ testall(CMPLXL(finites[i], NAN), CMPLXL(NAN, NAN),
+ ALL_STD_EXCEPT & ~FE_INVALID, 0, 0);
+ if (finites[i] == 0.0)
+ continue;
+ /* XXX FE_INEXACT shouldn't be raised here */
+ testall(CMPLXL(NAN, finites[i]), CMPLXL(NAN, NAN),
+ ALL_STD_EXCEPT & ~(FE_INVALID | FE_INEXACT), 0, 0);
+ }
+
+ /* cexp(NaN +- 0i) = NaN +- 0i */
+ testall(CMPLXL(NAN, 0.0), CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 1);
+ testall(CMPLXL(NAN, -0.0), CMPLXL(NAN, -0.0), ALL_STD_EXCEPT, 0, 1);
+
+ /* cexp(inf + NaN i) = inf + nan i */
+ testall(CMPLXL(INFINITY, NAN), CMPLXL(INFINITY, NAN),
+ ALL_STD_EXCEPT, 0, 0);
+ /* cexp(-inf + NaN i) = 0 */
+ testall(CMPLXL(-INFINITY, NAN), CMPLXL(0.0, 0.0),
+ ALL_STD_EXCEPT, 0, 0);
+ /* cexp(NaN + NaN i) = NaN + NaN i */
+ testall(CMPLXL(NAN, NAN), CMPLXL(NAN, NAN),
+ ALL_STD_EXCEPT, 0, 0);
+}
+
+static void
+test_inf(void)
+{
+ unsigned i;
+
+ /* cexp(x + inf i) = NaN + NaNi and raises invalid */
+ for (i = 0; i < nitems(finites); i++) {
+ printf("# Run %d..\n", i);
+ testall(CMPLXL(finites[i], INFINITY), CMPLXL(NAN, NAN),
+ ALL_STD_EXCEPT, FE_INVALID, 1);
+ }
+ /* cexp(-inf + yi) = 0 * (cos(y) + sin(y)i) */
+ /* XXX shouldn't raise an inexact exception */
+ testall(CMPLXL(-INFINITY, M_PI_4), CMPLXL(0.0, 0.0),
+ ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
+ testall(CMPLXL(-INFINITY, 3 * M_PI_4), CMPLXL(-0.0, 0.0),
+ ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
+ testall(CMPLXL(-INFINITY, 5 * M_PI_4), CMPLXL(-0.0, -0.0),
+ ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
+ testall(CMPLXL(-INFINITY, 7 * M_PI_4), CMPLXL(0.0, -0.0),
+ ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
+ testall(CMPLXL(-INFINITY, 0.0), CMPLXL(0.0, 0.0),
+ ALL_STD_EXCEPT, 0, 1);
+ testall(CMPLXL(-INFINITY, -0.0), CMPLXL(0.0, -0.0),
+ ALL_STD_EXCEPT, 0, 1);
+ /* cexp(inf + yi) = inf * (cos(y) + sin(y)i) (except y=0) */
+ /* XXX shouldn't raise an inexact exception */
+ testall(CMPLXL(INFINITY, M_PI_4), CMPLXL(INFINITY, INFINITY),
+ ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
+ testall(CMPLXL(INFINITY, 3 * M_PI_4), CMPLXL(-INFINITY, INFINITY),
+ ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
+ testall(CMPLXL(INFINITY, 5 * M_PI_4), CMPLXL(-INFINITY, -INFINITY),
+ ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
+ testall(CMPLXL(INFINITY, 7 * M_PI_4), CMPLXL(INFINITY, -INFINITY),
+ ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
+ /* cexp(inf + 0i) = inf + 0i */
+ testall(CMPLXL(INFINITY, 0.0), CMPLXL(INFINITY, 0.0),
+ ALL_STD_EXCEPT, 0, 1);
+ testall(CMPLXL(INFINITY, -0.0), CMPLXL(INFINITY, -0.0),
+ ALL_STD_EXCEPT, 0, 1);
+}
+
+static void
+test_reals(void)
+{
+ unsigned i;
+
+ for (i = 0; i < nitems(finites); i++) {
+ /* XXX could check exceptions more meticulously */
+ printf("# Run %d..\n", i);
+ test(cexp, CMPLXL(finites[i], 0.0),
+ CMPLXL(exp(finites[i]), 0.0),
+ FE_INVALID | FE_DIVBYZERO, 0, 1);
+ test(cexp, CMPLXL(finites[i], -0.0),
+ CMPLXL(exp(finites[i]), -0.0),
+ FE_INVALID | FE_DIVBYZERO, 0, 1);
+ test_f(cexpf, CMPLXL(finites[i], 0.0),
+ CMPLXL(expf(finites[i]), 0.0),
+ FE_INVALID | FE_DIVBYZERO, 0, 1);
+ test_f(cexpf, CMPLXL(finites[i], -0.0),
+ CMPLXL(expf(finites[i]), -0.0),
+ FE_INVALID | FE_DIVBYZERO, 0, 1);
+ }
+}
+
+static void
+test_imaginaries(void)
+{
+ unsigned i;
+
+ for (i = 0; i < nitems(finites); i++) {
+ printf("# Run %d..\n", i);
+ test(cexp, CMPLXL(0.0, finites[i]),
+ CMPLXL(cos(finites[i]), sin(finites[i])),
+ ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
+ test(cexp, CMPLXL(-0.0, finites[i]),
+ CMPLXL(cos(finites[i]), sin(finites[i])),
+ ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
+ test_f(cexpf, CMPLXL(0.0, finites[i]),
+ CMPLXL(cosf(finites[i]), sinf(finites[i])),
+ ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
+ test_f(cexpf, CMPLXL(-0.0, finites[i]),
+ CMPLXL(cosf(finites[i]), sinf(finites[i])),
+ ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
+ }
+}
+
+static void
+test_small(void)
+{
+ static const double tests[] = {
+ /* csqrt(a + bI) = x + yI */
+ /* a b x y */
+ 1.0, M_PI_4, M_SQRT2 * 0.5 * M_E, M_SQRT2 * 0.5 * M_E,
+ -1.0, M_PI_4, M_SQRT2 * 0.5 / M_E, M_SQRT2 * 0.5 / M_E,
+ 2.0, M_PI_2, 0.0, M_E * M_E,
+ M_LN2, M_PI, -2.0, 0.0,
+ };
+ double a, b;
+ double x, y;
+ unsigned i;
+
+ for (i = 0; i < nitems(tests); i += 4) {
+ printf("# Run %d..\n", i);
+ a = tests[i];
+ b = tests[i + 1];
+ x = tests[i + 2];
+ y = tests[i + 3];
+ test_tol(cexp, CMPLXL(a, b), CMPLXL(x, y), 3 * DBL_ULP());
+
+ /* float doesn't have enough precision to pass these tests */
+ if (x == 0 || y == 0)
+ continue;
+ test_tol(cexpf, CMPLXL(a, b), CMPLXL(x, y), 1 * FLT_ULP());
+ }
+}
+
+/* Test inputs with a real part r that would overflow exp(r). */
+static void
+test_large(void)
+{
+
+ test_tol(cexp, CMPLXL(709.79, 0x1p-1074),
+ CMPLXL(INFINITY, 8.94674309915433533273e-16), DBL_ULP());
+ test_tol(cexp, CMPLXL(1000, 0x1p-1074),
+ CMPLXL(INFINITY, 9.73344457300016401328e+110), DBL_ULP());
+ test_tol(cexp, CMPLXL(1400, 0x1p-1074),
+ CMPLXL(INFINITY, 5.08228858149196559681e+284), DBL_ULP());
+ test_tol(cexp, CMPLXL(900, 0x1.23456789abcdep-1020),
+ CMPLXL(INFINITY, 7.42156649354218408074e+83), DBL_ULP());
+ test_tol(cexp, CMPLXL(1300, 0x1.23456789abcdep-1020),
+ CMPLXL(INFINITY, 3.87514844965996756704e+257), DBL_ULP());
+
+ test_tol(cexpf, CMPLXL(88.73, 0x1p-149),
+ CMPLXL(INFINITY, 4.80265603e-07), 2 * FLT_ULP());
+ test_tol(cexpf, CMPLXL(90, 0x1p-149),
+ CMPLXL(INFINITY, 1.7101492622e-06f), 2 * FLT_ULP());
+ test_tol(cexpf, CMPLXL(192, 0x1p-149),
+ CMPLXL(INFINITY, 3.396809344e+38f), 2 * FLT_ULP());
+ test_tol(cexpf, CMPLXL(120, 0x1.234568p-120),
+ CMPLXL(INFINITY, 1.1163382522e+16f), 2 * FLT_ULP());
+ test_tol(cexpf, CMPLXL(170, 0x1.234568p-120),
+ CMPLXL(INFINITY, 5.7878851079e+37f), 2 * FLT_ULP());
+}
+
+int
+main(void)
+{
+
+ printf("1..7\n");
+
+ test_zero();
+ printf("ok 1 - cexp zero\n");
+
+ test_nan();
+ printf("ok 2 - cexp nan\n");
+
+ test_inf();
+ printf("ok 3 - cexp inf\n");
+
+ test_reals();
+ printf("ok 4 - cexp reals\n");
+
+ test_imaginaries();
+ printf("ok 5 - cexp imaginaries\n");
+
+ test_small();
+ printf("ok 6 - cexp small\n");
+
+ test_large();
+ printf("ok 7 - cexp large\n");
+
+ return (0);
+}
