Basic tests for complex inverse trig and hyperbolic functions.

2 files changed, 444 insertions, 1 deletions

diff --git a/tools/regression/lib/msun/Makefile b/tools/regression/lib/msun/Makefile
index 261b1cb..9559bb1 100644
--- a/tools/regression/lib/msun/Makefile
+++ b/tools/regression/lib/msun/Makefile
@@ -2,7 +2,8 @@
 
 TESTS=	test-cexp test-conj test-csqrt test-ctrig \
 	test-exponential test-fenv test-fma \
-	test-fmaxmin test-ilogb test-invtrig test-logarithm test-lrint \
+	test-fmaxmin test-ilogb test-invtrig test-invctrig \
+	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-invctrig.c b/tools/regression/lib/msun/test-invctrig.c
new file mode 100644
index 0000000..6f0fe58
--- /dev/null
+++ b/tools/regression/lib/msun/test-invctrig.c
@@ -0,0 +1,442 @@
+/*-
+ * Copyright (c) 2008-2013 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 casin[h](), cacos[h](), and catan[h]().
+ */
+
+#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	OPT_INVALID	(ALL_STD_EXCEPT & ~FE_INVALID)
+#define	OPT_INEXACT	(ALL_STD_EXCEPT & ~FE_INEXACT)
+#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)
+
+#pragma	STDC FENV_ACCESS	ON
+#pragma	STDC CX_LIMITED_RANGE	OFF
+
+/* Flags that determine whether to check the signs of the result. */
+#define	CS_REAL	1
+#define	CS_IMAG	2
+#define	CS_BOTH	(CS_REAL | CS_IMAG)
+
+#ifdef	DEBUG
+#define	debug(...)	printf(__VA_ARGS__)
+#else
+#define	debug(...)	(void)0
+#endif
+
+/*
+ * 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.
+ *
+ * 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_p(func, z, result, exceptmask, excepts, checksign)	do {	\
+	volatile long double complex _d = z;				\
+	debug("  testing %s(%Lg + %Lg I) == %Lg + %Lg I\n", #func,	\
+	    creall(_d), cimagl(_d), creall(result), cimagl(result));	\
+	assert(feclearexcept(FE_ALL_EXCEPT) == 0);			\
+	assert(cfpequal((func)(_d), (result), (checksign)));		\
+	assert(((func), fetestexcept(exceptmask) == (excepts)));	\
+} while (0)
+
+/*
+ * Test within a given tolerance.  The tolerance indicates relative error
+ * in ulps.
+ */
+#define	test_p_tol(func, z, result, tol)			do {	\
+	volatile long double complex _d = z;				\
+	debug("  testing %s(%Lg + %Lg I) ~= %Lg + %Lg I\n", #func,	\
+	    creall(_d), cimagl(_d), creall(result), cimagl(result));	\
+	assert(cfpequal_tol((func)(_d), (result), (tol)));		\
+} while (0)
+
+/* These wrappers apply the identities f(conj(z)) = conj(f(z)). */
+#define	test(func, z, result, exceptmask, excepts, checksign)	do {	\
+	test_p(func, z, result, exceptmask, excepts, checksign);	\
+	test_p(func, conjl(z), conjl(result), exceptmask, excepts, checksign); \
+} while (0)
+#define	test_tol(func, z, result, tol)				do {	\
+	test_p_tol(func, z, result, tol);				\
+	test_p_tol(func, conjl(z), conjl(result), tol);			\
+} while (0)
+
+/* Test the given function in all precisions. */
+#define	testall(func, x, result, exceptmask, excepts, checksign) do {	\
+	test(func, x, result, exceptmask, excepts, checksign);		\
+	test(func##f, x, result, exceptmask, excepts, checksign);	\
+} while (0)
+#define	testall_odd(func, x, result, exceptmask, excepts, checksign) do { \
+	testall(func, x, result, exceptmask, excepts, checksign);	\
+	testall(func, -(x), -result, exceptmask, excepts, checksign);	\
+} while (0)
+#define	testall_even(func, x, result, exceptmask, excepts, checksign) do { \
+	testall(func, x, result, exceptmask, excepts, checksign);	\
+	testall(func, -(x), result, exceptmask, excepts, checksign);	\
+} while (0)
+
+/*
+ * Test the given function in all precisions, within a given tolerance.
+ * The tolerance is specified in ulps.
+ */
+#define	testall_tol(func, x, result, tol)	       		   do { \
+	test_tol(func, x, result, (tol) * DBL_ULP());			\
+	test_tol(func##f, x, result, (tol) * FLT_ULP());		\
+} while (0)
+#define	testall_odd_tol(func, x, result, tol)	       		   do { \
+	testall_tol(func, x, result, tol);				\
+	testall_tol(func, -(x), -result, tol);				\
+} while (0)
+#define	testall_even_tol(func, x, result, tol)	       		   do { \
+	testall_tol(func, x, result, tol);				\
+	testall_tol(func, -(x), result, tol);				\
+} while (0)
+
+static const long double
+pi = 3.14159265358979323846264338327950280L,
+c3pi = 9.42477796076937971538793014983850839L;
+
+/*
+ * 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 || y == 0.0)
+		return (0);
+
+	/* Hard case: need to check the tolerance. */
+	feholdexcept(&env);
+	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 & CS_REAL)
+		&& fpequal(cimag(x), cimag(y), checksign & CS_IMAG));
+}
+
+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)
+{
+	long double complex zero = CMPLXL(0.0, 0.0);
+
+	testall_tol(cacosh, zero, CMPLXL(0.0, pi / 2), 1);
+	testall_tol(cacosh, -zero, CMPLXL(0.0, -pi / 2), 1);
+	testall_tol(cacos, zero, CMPLXL(pi / 2, -0.0), 1);
+	testall_tol(cacos, -zero, CMPLXL(pi / 2, 0.0), 1);
+
+	testall_odd(casinh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
+	testall_odd(casin, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
+
+	testall_odd(catanh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
+	testall_odd(catan, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
+}
+
+/*
+ * Tests for NaN inputs.
+ */
+void
+test_nan()
+{
+	long double complex nan_nan = CMPLXL(NAN, NAN);
+	long double complex z;
+
+	/*
+	 * IN		CACOSH	    CACOS	CASINH	    CATANH
+	 * NaN,NaN	NaN,NaN	    NaN,NaN	NaN,NaN	    NaN,NaN
+	 * finite,NaN	NaN,NaN*    NaN,NaN*	NaN,NaN*    NaN,NaN*
+	 * NaN,finite   NaN,NaN*    NaN,NaN*	NaN,NaN*    NaN,NaN*
+	 * NaN,Inf	Inf,NaN     NaN,-Inf	?Inf,NaN    ?0,pi/2	
+	 * +-Inf,NaN	Inf,NaN     NaN,?Inf	+-Inf,NaN   +-0,NaN
+	 * +-0,NaN	NaN,NaN*    pi/2,NaN	NaN,NaN*    +-0,NaN
+	 * NaN,0	NaN,NaN*    NaN,NaN*	NaN,0	    NaN,NaN*
+	 *
+	 *  * = raise invalid
+	 */
+	z = nan_nan;
+	testall(cacosh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
+	testall(cacos, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
+	testall(casinh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
+	testall(casin, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
+	testall(catanh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
+	testall(catan, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
+
+	z = CMPLXL(0.5, NAN);
+	testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
+	testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
+	testall(casinh, z, nan_nan, OPT_INVALID, 0, 0);
+	testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
+	testall(catanh, z, nan_nan, OPT_INVALID, 0, 0);
+	testall(catan, z, nan_nan, OPT_INVALID, 0, 0);
+
+	z = CMPLXL(NAN, 0.5);
+	testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
+	testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
+	testall(casinh, z, nan_nan, OPT_INVALID, 0, 0);
+	testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
+	testall(catanh, z, nan_nan, OPT_INVALID, 0, 0);
+	testall(catan, z, nan_nan, OPT_INVALID, 0, 0);
+
+	z = CMPLXL(NAN, INFINITY);
+	testall(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
+	testall(cacosh, -z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
+	testall(cacos, z, CMPLXL(NAN, -INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG);
+	testall(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 0);
+	testall(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG);
+	testall_tol(catanh, z, CMPLXL(0.0, pi / 2), 1);
+	testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, CS_IMAG);
+
+	z = CMPLXL(INFINITY, NAN);
+	testall_even(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0,
+		     CS_REAL);
+	testall_even(cacos, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0);
+	testall_odd(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0,
+		    CS_REAL);
+	testall_odd(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0);
+	testall_odd(catanh, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
+	testall_odd_tol(catan, z, CMPLXL(pi / 2, 0.0), 1);
+
+	z = CMPLXL(0.0, NAN);
+        /* XXX We allow a spurious inexact exception here. */
+	testall_even(cacosh, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0);
+	testall_even_tol(cacos, z, CMPLXL(pi / 2, NAN), 1);
+	testall_odd(casinh, z, nan_nan, OPT_INVALID, 0, 0);
+	testall_odd(casin, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
+	testall_odd(catanh, z, CMPLXL(0.0, NAN), OPT_INVALID, 0, CS_REAL);
+	testall_odd(catan, z, nan_nan, OPT_INVALID, 0, 0);
+
+	z = CMPLXL(NAN, 0.0);
+	testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
+	testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
+	testall(casinh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG);
+	testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
+	testall(catanh, z, nan_nan, OPT_INVALID, 0, CS_IMAG);
+	testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 0);
+}
+
+void
+test_inf(void)
+{
+	long double complex z;
+
+	/*
+	 * IN		CACOSH	    CACOS	CASINH	    CATANH
+	 * Inf,Inf	Inf,pi/4    pi/4,-Inf	Inf,pi/4    0,pi/2
+	 * -Inf,Inf	Inf,3pi/4   3pi/4,-Inf	---	    ---
+	 * Inf,finite	Inf,0	    0,-Inf	Inf,0	    0,pi/2
+	 * -Inf,finite	Inf,pi      pi,-Inf	---	    ---
+	 * finite,Inf	Inf,pi/2    pi/2,-Inf	Inf,pi/2    0,pi/2
+	 */
+	z = CMPLXL(INFINITY, INFINITY);
+	testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 4), 1);
+	testall_tol(cacosh, -z, CMPLXL(INFINITY, -c3pi / 4), 1);
+	testall_tol(cacos, z, CMPLXL(pi / 4, -INFINITY), 1);
+	testall_tol(cacos, -z, CMPLXL(c3pi / 4, INFINITY), 1);
+	testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 4), 1);
+	testall_odd_tol(casin, z, CMPLXL(pi / 4, INFINITY), 1);
+	testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
+	testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);
+
+	z = CMPLXL(INFINITY, 0.5);
+	/* XXX We allow a spurious inexact exception here. */
+	testall(cacosh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH);
+	testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi), 1);
+	testall(cacos, z, CMPLXL(0, -INFINITY), OPT_INEXACT, 0, CS_BOTH);
+	testall_tol(cacos, -z, CMPLXL(pi, INFINITY), 1);
+	testall_odd(casinh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH);
+	testall_odd_tol(casin, z, CMPLXL(pi / 2, INFINITY), 1);
+	testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
+	testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);
+
+	z = CMPLXL(0.5, INFINITY);
+	testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 2), 1);
+	testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi / 2), 1);
+	testall_tol(cacos, z, CMPLXL(pi / 2, -INFINITY), 1);
+	testall_tol(cacos, -z, CMPLXL(pi / 2, INFINITY), 1);
+	testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 2), 1);
+	/* XXX We allow a spurious inexact exception here. */
+	testall_odd(casin, z, CMPLXL(0.0, INFINITY), OPT_INEXACT, 0, CS_BOTH);
+	testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
+	testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);
+}
+
+/* Tests along the real and imaginary axes. */
+void
+test_axes(void)
+{
+	static const long double nums[] = {
+		-2, -1, -0.5, 0.5, 1, 2
+	};
+	long double complex z;
+	int i;
+
+	for (i = 0; i < sizeof(nums) / sizeof(nums[0]); i++) {
+		/* Real axis */
+		z = CMPLXL(nums[i], 0.0);
+		if (fabs(nums[i]) <= 1) {
+			testall_tol(cacosh, z, CMPLXL(0.0, acos(nums[i])), 1);
+			testall_tol(cacos, z, CMPLXL(acosl(nums[i]), -0.0), 1);
+			testall_tol(casin, z, CMPLXL(asinl(nums[i]), 0.0), 1);
+			testall_tol(catanh, z, CMPLXL(atanh(nums[i]), 0.0), 1);
+		} else {
+			testall_tol(cacosh, z,
+				    CMPLXL(acosh(fabs(nums[i])),
+					   (nums[i] < 0) ? pi : 0), 1);
+			testall_tol(cacos, z,
+				    CMPLXL((nums[i] < 0) ? pi : 0,
+					   -acosh(fabs(nums[i]))), 1);
+			testall_tol(casin, z,
+				    CMPLXL(copysign(pi / 2, nums[i]),
+					   acosh(fabs(nums[i]))), 1);
+			testall_tol(catanh, z,
+				    CMPLXL(atanh(1 / nums[i]), pi / 2), 1);
+		}
+		testall_tol(casinh, z, CMPLXL(asinh(nums[i]), 0.0), 1);
+		testall_tol(catan, z, CMPLXL(atan(nums[i]), 0), 1);
+
+		/* TODO: Test the imaginary axis. */
+	}
+}
+
+void
+test_small(void)
+{
+	/*
+	 * z =  0.75 + i 0.25
+	 *     acos(z) = Pi/4 - i ln(2)/2
+	 *     asin(z) = Pi/4 + i ln(2)/2
+	 *     atan(z) = atan(4)/2 + i ln(17/9)/4
+	 */
+	static const struct {
+		complex long double z;
+		complex long double acos_z;
+		complex long double asin_z;
+		complex long double atan_z;
+	} tests[] = {
+		{ CMPLXL(0.75L, 0.25L),
+		  CMPLXL(pi / 4, -0.34657359027997265470861606072908828L),
+		  CMPLXL(pi / 4, 0.34657359027997265470861606072908828L),
+		  CMPLXL(0.66290883183401623252961960521423782L,
+			 0.15899719167999917436476103600701878L) },
+	};
+	int i;
+
+	for (i = 0; i < sizeof(tests) / sizeof(tests[0]); i++) {
+		testall_tol(cacos, tests[i].z, tests[i].acos_z, 2);
+		testall_odd_tol(casin, tests[i].z, tests[i].asin_z, 2);
+		testall_odd_tol(catan, tests[i].z, tests[i].atan_z, 2);
+        }
+}
+
+/* Test inputs that might cause overflow in a sloppy implementation. */
+void
+test_large(void)
+{
+
+	/* TODO: Write these tests */
+}
+
+int
+main(int argc, char *argv[])
+{
+
+	printf("1..6\n");
+
+	test_zero();
+	printf("ok 1 - invctrig zero\n");
+
+	test_nan();
+	printf("ok 2 - invctrig nan\n");
+
+	test_inf();
+	printf("ok 3 - invctrig inf\n");
+
+	test_axes();
+	printf("ok 4 - invctrig axes\n");
+
+	test_small();
+	printf("ok 5 - invctrig small\n");
+
+	test_large();
+	printf("ok 6 - invctrig large\n");
+
+	return (0);
+}