Add some tests for cexp() and cexpf(). (I need to clean up all of

these tests some day, but in the mean time, they're a useful sanity
check for future changes.)

3 files changed, 391 insertions, 1 deletions

diff --git a/tools/regression/lib/msun/Makefile b/tools/regression/lib/msun/Makefile
index eb9a6ae..155fd31 100644
--- a/tools/regression/lib/msun/Makefile
+++ b/tools/regression/lib/msun/Makefile
@@ -1,6 +1,6 @@
 # $FreeBSD$
 
-TESTS=	test-conj test-csqrt test-exponential test-fenv test-fma \
+TESTS=	test-cexp test-conj test-csqrt test-exponential test-fenv test-fma \
 	test-fmaxmin test-ilogb test-invtrig test-logarithm test-lrint \
 	test-lround test-nan test-nearbyint test-next test-rem test-trig
 CFLAGS+= -O0 -lm
diff --git a/tools/regression/lib/msun/test-cexp.c b/tools/regression/lib/msun/test-cexp.c
new file mode 100644
index 0000000..2913fbd
--- /dev/null
+++ b/tools/regression/lib/msun/test-cexp.c
@@ -0,0 +1,380 @@
+/*-
+ * Copyright (c) 2008-2011 David Schultz <das@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>
+__FBSDID("$FreeBSD$");
+
+#include <assert.h>
+#include <complex.h>
+#include <fenv.h>
+#include <float.h>
+#include <math.h>
+#include <stdio.h>
+
+#define	ALL_STD_EXCEPT	(FE_DIVBYZERO | FE_INEXACT | FE_INVALID | \
+			 FE_OVERFLOW | FE_UNDERFLOW)
+#define	FLT_ULP()	ldexpl(1.0, 1 - FLT_MANT_DIG)
+#define	DBL_ULP()	ldexpl(1.0, 1 - DBL_MANT_DIG)
+#define	LDBL_ULP()	ldexpl(1.0, 1 - LDBL_MANT_DIG)
+
+#define	N(i)	(sizeof(i) / sizeof((i)[0]))
+
+#pragma STDC FENV_ACCESS	ON
+#pragma	STDC CX_LIMITED_RANGE	OFF
+
+/*
+ * XXX gcc implements complex multiplication incorrectly. In
+ * particular, it implements it as if the CX_LIMITED_RANGE pragma
+ * were ON. Consequently, we need this function to form numbers
+ * such as x + INFINITY * I, since gcc evalutes INFINITY * I as
+ * NaN + INFINITY * I.
+ */
+static inline long double complex
+cpackl(long double x, long double y)
+{
+	long double complex z;
+
+	__real__ z = x;
+	__imag__ z = y;
+	return (z);
+}
+
+/*
+ * 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((func)(_d), (result), (checksign)));		\
+	assert(((func), fetestexcept(exceptmask) == (excepts)));	\
+} 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)));		\
+} 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(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 };
+
+/*
+ * Determine whether x and y are equal, with two special rules:
+ *	+0.0 != -0.0
+ *	 NaN == NaN
+ * If checksign is 0, we compare the absolute values instead.
+ */
+static int
+fpequal(long double x, long double y, int checksign)
+{
+	if (isnan(x) || isnan(y))
+		return (1);
+	if (checksign)
+		return (x == y && !signbit(x) == !signbit(y));
+	else
+		return (fabsl(x) == fabsl(y));
+}
+
+static int
+fpequal_tol(long double x, long double y, long double tol)
+{
+	fenv_t env;
+	int ret;
+
+	if (isnan(x) && isnan(y))
+		return (1);
+	if (!signbit(x) != !signbit(y))
+		return (0);
+	if (x == y)
+		return (1);
+	if (tol == 0)
+		return (0);
+
+	/* Hard case: need to check the tolerance. */
+	feholdexcept(&env);
+	/*
+	 * For our purposes here, if y=0, we interpret tol as an absolute
+	 * tolerance. This is to account for roundoff in the input, e.g.,
+	 * cos(Pi/2) ~= 0.
+	 */
+	if (y == 0.0)
+		ret = fabsl(x - y) <= fabsl(tol);
+	else
+		ret = fabsl(x - y) <= fabsl(y * tol);
+	fesetenv(&env);
+	return (ret);
+}
+
+static int
+cfpequal(long double complex x, long double complex y, int checksign)
+{
+	return (fpequal(creal(x), creal(y), checksign)
+		&& fpequal(cimag(x), cimag(y), checksign));
+}
+
+static int
+cfpequal_tol(long double complex x, long double complex y, long double tol)
+{
+	return (fpequal_tol(creal(x), creal(y), tol)
+		&& fpequal_tol(cimag(x), cimag(y), tol));
+}
+
+
+/* Tests for 0 */
+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(cpackl(0.0, -0.0), cpackl(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
+	testall(cpackl(-0.0, -0.0), cpackl(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.
+ */
+void
+test_nan()
+{
+	int 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 < N(finites); i++) {
+		testall(cpackl(finites[i], NAN), cpackl(NAN, NAN),
+			ALL_STD_EXCEPT & ~FE_INVALID, 0, 0);
+		if (finites[i] == 0.0)
+			continue;
+		/* XXX FE_INEXACT shouldn't be raised here */
+		testall(cpackl(NAN, finites[i]), cpackl(NAN, NAN),
+			ALL_STD_EXCEPT & ~(FE_INVALID | FE_INEXACT), 0, 0);
+	}
+
+	/* cexp(NaN +- 0i) = NaN +- 0i */
+	testall(cpackl(NAN, 0.0), cpackl(NAN, 0.0), ALL_STD_EXCEPT, 0, 1);
+	testall(cpackl(NAN, -0.0), cpackl(NAN, -0.0), ALL_STD_EXCEPT, 0, 1);
+
+	/* cexp(inf + NaN i) = inf + nan i */
+	testall(cpackl(INFINITY, NAN), cpackl(INFINITY, NAN),
+		ALL_STD_EXCEPT, 0, 0);
+	/* cexp(-inf + NaN i) = 0 */
+	testall(cpackl(-INFINITY, NAN), cpackl(0.0, 0.0),
+		ALL_STD_EXCEPT, 0, 0);
+	/* cexp(NaN + NaN i) = NaN + NaN i */
+	testall(cpackl(NAN, NAN), cpackl(NAN, NAN),
+		ALL_STD_EXCEPT, 0, 0);
+}
+
+void
+test_inf(void)
+{
+	int i;
+
+	/* cexp(x + inf i) = NaN + NaNi and raises invalid */
+	/* cexp(inf + yi) = 0 + 0yi */
+	/* cexp(-inf + yi) = inf + inf yi (except y=0) */
+	for (i = 0; i < N(finites); i++) {
+		testall(cpackl(finites[i], INFINITY), cpackl(NAN, NAN),
+			ALL_STD_EXCEPT, FE_INVALID, 1);
+		/* XXX shouldn't raise an inexact exception */
+		testall(cpackl(-INFINITY, finites[i]),
+			cpackl(0.0, 0.0 * finites[i]),
+			ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
+		if (finites[i] == 0)
+			continue;
+		testall(cpackl(INFINITY, finites[i]),
+			cpackl(INFINITY, INFINITY * finites[i]),
+			ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
+	}
+	testall(cpackl(INFINITY, 0.0), cpackl(INFINITY, 0.0),
+		ALL_STD_EXCEPT, 0, 1);
+	testall(cpackl(INFINITY, -0.0), cpackl(INFINITY, -0.0),
+		ALL_STD_EXCEPT, 0, 1);
+}
+
+void
+test_reals(void)
+{
+	int i;
+
+	for (i = 0; i < N(finites); i++) {
+		/* XXX could check exceptions more meticulously */
+		test(cexp, cpackl(finites[i], 0.0),
+		     cpackl(exp(finites[i]), 0.0),
+		     FE_INVALID | FE_DIVBYZERO, 0, 1);
+		test(cexp, cpackl(finites[i], -0.0),
+		     cpackl(exp(finites[i]), -0.0),
+		     FE_INVALID | FE_DIVBYZERO, 0, 1);
+		test(cexpf, cpackl(finites[i], 0.0),
+		     cpackl(expf(finites[i]), 0.0),
+		     FE_INVALID | FE_DIVBYZERO, 0, 1);
+		test(cexpf, cpackl(finites[i], -0.0),
+		     cpackl(expf(finites[i]), -0.0),
+		     FE_INVALID | FE_DIVBYZERO, 0, 1);
+	}
+}
+
+void
+test_imaginaries(void)
+{
+	int i;
+
+	for (i = 0; i < N(finites); i++) {
+		test(cexp, cpackl(0.0, finites[i]),
+		     cpackl(cos(finites[i]), sin(finites[i])),
+		     ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
+		test(cexp, cpackl(-0.0, finites[i]),
+		     cpackl(cos(finites[i]), sin(finites[i])),
+		     ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
+		test(cexpf, cpackl(0.0, finites[i]),
+		     cpackl(cosf(finites[i]), sinf(finites[i])),
+		     ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
+		test(cexpf, cpackl(-0.0, finites[i]),
+		     cpackl(cosf(finites[i]), sinf(finites[i])),
+		     ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
+	}
+}
+
+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;
+	int i;
+
+	for (i = 0; i < N(tests); i += 4) {
+		a = tests[i];
+		b = tests[i + 1];
+		x = tests[i + 2];
+		y = tests[i + 3];
+		test_tol(cexp, cpackl(a, b), cpackl(x, y), 3 * DBL_ULP());
+
+		/* float doesn't have enough precision to pass these tests */
+		if (x == 0 || y == 0)
+			continue;
+		test_tol(cexpf, cpackl(a, b), cpackl(x, y), 1 * FLT_ULP());
+        }
+}
+
+/* Test inputs with a real part r that would overflow exp(r). */
+void
+test_large(void)
+{
+
+	test_tol(cexp, cpackl(709.79, 0x1p-1074),
+		 cpackl(INFINITY, 8.94674309915433533273e-16), DBL_ULP());
+	test_tol(cexp, cpackl(1000, 0x1p-1074),
+		 cpackl(INFINITY, 9.73344457300016401328e+110), DBL_ULP());
+	test_tol(cexp, cpackl(1400, 0x1p-1074),
+		 cpackl(INFINITY, 5.08228858149196559681e+284), DBL_ULP());
+	test_tol(cexp, cpackl(900, 0x1.23456789abcdep-1020),
+		 cpackl(INFINITY, 7.42156649354218408074e+83), DBL_ULP());
+	test_tol(cexp, cpackl(1300, 0x1.23456789abcdep-1020),
+		 cpackl(INFINITY, 3.87514844965996756704e+257), DBL_ULP());
+
+	test_tol(cexpf, cpackl(88.73, 0x1p-149),
+		 cpackl(INFINITY, 4.80265603e-07), 2 * FLT_ULP());
+	test_tol(cexpf, cpackl(90, 0x1p-149),
+		 cpackl(INFINITY, 1.7101492622e-06f), 2 * FLT_ULP());
+	test_tol(cexpf, cpackl(192, 0x1p-149),
+		 cpackl(INFINITY, 3.396809344e+38f), 2 * FLT_ULP());
+	test_tol(cexpf, cpackl(120, 0x1.234568p-120),
+		 cpackl(INFINITY, 1.1163382522e+16f), 2 * FLT_ULP());
+	test_tol(cexpf, cpackl(170, 0x1.234568p-120),
+		 cpackl(INFINITY, 5.7878851079e+37f), 2 * FLT_ULP());
+}
+
+int
+main(int argc, char *argv[])
+{
+
+	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);
+}
diff --git a/tools/regression/lib/msun/test-cexp.t b/tools/regression/lib/msun/test-cexp.t
new file mode 100644
index 0000000..8bdfd03
--- /dev/null
+++ b/tools/regression/lib/msun/test-cexp.t
@@ -0,0 +1,10 @@
+#!/bin/sh
+# $FreeBSD$
+
+cd `dirname $0`
+
+executable=`basename $0 .t`
+
+make $executable 2>&1 > /dev/null
+
+exec ./$executable