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+/*-
+ * Copyright (c) 2008 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 trigonometric functions. Some accuracy tests
+ * are included as well, but these are very basic sanity checks, not
+ * intended to be comprehensive.
+ *
+ * The program for generating representable numbers near multiples of pi is
+ * available at http://www.cs.berkeley.edu/~wkahan/testpi/ .
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+#include <sys/param.h>
+
+#include <assert.h>
+#include <fenv.h>
+#include <float.h>
+#include <math.h>
+#include <stdio.h>
+
+#include "test-utils.h"
+
+#pragma STDC FENV_ACCESS ON
+
+/*
+ * 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(func, x, result, exceptmask, excepts) do { \
+ volatile long double _d = x; \
+ assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
+ assert(fpequal((func)(_d), (result))); \
+ assert(((void)(func), fetestexcept(exceptmask) == (excepts))); \
+} while (0)
+
+#define testall(prefix, x, result, exceptmask, excepts) do { \
+ test(prefix, x, (double)result, exceptmask, excepts); \
+ test(prefix##f, x, (float)result, exceptmask, excepts); \
+ test(prefix##l, x, result, exceptmask, excepts); \
+} while (0)
+
+#define testdf(prefix, x, result, exceptmask, excepts) do { \
+ test(prefix, x, (double)result, exceptmask, excepts); \
+ test(prefix##f, x, (float)result, exceptmask, excepts); \
+} while (0)
+
+/*
+ * Test special cases in sin(), cos(), and tan().
+ */
+static void
+run_special_tests(void)
+{
+
+ /* Values at 0 should be exact. */
+ testall(tan, 0.0, 0.0, ALL_STD_EXCEPT, 0);
+ testall(tan, -0.0, -0.0, ALL_STD_EXCEPT, 0);
+ testall(cos, 0.0, 1.0, ALL_STD_EXCEPT, 0);
+ testall(cos, -0.0, 1.0, ALL_STD_EXCEPT, 0);
+ testall(sin, 0.0, 0.0, ALL_STD_EXCEPT, 0);
+ testall(sin, -0.0, -0.0, ALL_STD_EXCEPT, 0);
+
+ /* func(+-Inf) == NaN */
+ testall(tan, INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID);
+ testall(sin, INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID);
+ testall(cos, INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID);
+ testall(tan, -INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID);
+ testall(sin, -INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID);
+ testall(cos, -INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID);
+
+ /* func(NaN) == NaN */
+ testall(tan, NAN, NAN, ALL_STD_EXCEPT, 0);
+ testall(sin, NAN, NAN, ALL_STD_EXCEPT, 0);
+ testall(cos, NAN, NAN, ALL_STD_EXCEPT, 0);
+}
+
+/*
+ * Tests to ensure argument reduction for large arguments is accurate.
+ */
+static void
+run_reduction_tests(void)
+{
+ /* floats very close to odd multiples of pi */
+ static const float f_pi_odd[] = {
+ 85563208.0f,
+ 43998769152.0f,
+ 9.2763667655669323e+25f,
+ 1.5458357838905804e+29f,
+ };
+ /* doubles very close to odd multiples of pi */
+ static const double d_pi_odd[] = {
+ 3.1415926535897931,
+ 91.106186954104004,
+ 642615.9188844458,
+ 3397346.5699258847,
+ 6134899525417045.0,
+ 3.0213551960457761e+43,
+ 1.2646209897993783e+295,
+ 6.2083625380677099e+307,
+ };
+ /* long doubles very close to odd multiples of pi */
+#if LDBL_MANT_DIG == 64
+ static const long double ld_pi_odd[] = {
+ 1.1891886960373841596e+101L,
+ 1.07999475322710967206e+2087L,
+ 6.522151627890431836e+2147L,
+ 8.9368974898260328229e+2484L,
+ 9.2961044110572205863e+2555L,
+ 4.90208421886578286e+3189L,
+ 1.5275546401232615884e+3317L,
+ 1.7227465626338900093e+3565L,
+ 2.4160090594000745334e+3808L,
+ 9.8477555741888350649e+4314L,
+ 1.6061597222105160737e+4326L,
+ };
+#elif LDBL_MANT_DIG == 113
+ static const long double ld_pi_odd[] = {
+ /* XXX */
+ };
+#endif
+
+ int i;
+
+ for (i = 0; i < nitems(f_pi_odd); i++) {
+ assert(fabs(sinf(f_pi_odd[i])) < FLT_EPSILON);
+ assert(cosf(f_pi_odd[i]) == -1.0);
+ assert(fabs(tan(f_pi_odd[i])) < FLT_EPSILON);
+
+ assert(fabs(sinf(-f_pi_odd[i])) < FLT_EPSILON);
+ assert(cosf(-f_pi_odd[i]) == -1.0);
+ assert(fabs(tanf(-f_pi_odd[i])) < FLT_EPSILON);
+
+ assert(fabs(sinf(f_pi_odd[i] * 2)) < FLT_EPSILON);
+ assert(cosf(f_pi_odd[i] * 2) == 1.0);
+ assert(fabs(tanf(f_pi_odd[i] * 2)) < FLT_EPSILON);
+
+ assert(fabs(sinf(-f_pi_odd[i] * 2)) < FLT_EPSILON);
+ assert(cosf(-f_pi_odd[i] * 2) == 1.0);
+ assert(fabs(tanf(-f_pi_odd[i] * 2)) < FLT_EPSILON);
+ }
+
+ for (i = 0; i < nitems(d_pi_odd); i++) {
+ assert(fabs(sin(d_pi_odd[i])) < 2 * DBL_EPSILON);
+ assert(cos(d_pi_odd[i]) == -1.0);
+ assert(fabs(tan(d_pi_odd[i])) < 2 * DBL_EPSILON);
+
+ assert(fabs(sin(-d_pi_odd[i])) < 2 * DBL_EPSILON);
+ assert(cos(-d_pi_odd[i]) == -1.0);
+ assert(fabs(tan(-d_pi_odd[i])) < 2 * DBL_EPSILON);
+
+ assert(fabs(sin(d_pi_odd[i] * 2)) < 2 * DBL_EPSILON);
+ assert(cos(d_pi_odd[i] * 2) == 1.0);
+ assert(fabs(tan(d_pi_odd[i] * 2)) < 2 * DBL_EPSILON);
+
+ assert(fabs(sin(-d_pi_odd[i] * 2)) < 2 * DBL_EPSILON);
+ assert(cos(-d_pi_odd[i] * 2) == 1.0);
+ assert(fabs(tan(-d_pi_odd[i] * 2)) < 2 * DBL_EPSILON);
+ }
+
+#if LDBL_MANT_DIG > 53
+ for (i = 0; i < nitems(ld_pi_odd); i++) {
+ assert(fabsl(sinl(ld_pi_odd[i])) < LDBL_EPSILON);
+ assert(cosl(ld_pi_odd[i]) == -1.0);
+ assert(fabsl(tanl(ld_pi_odd[i])) < LDBL_EPSILON);
+
+ assert(fabsl(sinl(-ld_pi_odd[i])) < LDBL_EPSILON);
+ assert(cosl(-ld_pi_odd[i]) == -1.0);
+ assert(fabsl(tanl(-ld_pi_odd[i])) < LDBL_EPSILON);
+
+ assert(fabsl(sinl(ld_pi_odd[i] * 2)) < LDBL_EPSILON);
+ assert(cosl(ld_pi_odd[i] * 2) == 1.0);
+ assert(fabsl(tanl(ld_pi_odd[i] * 2)) < LDBL_EPSILON);
+
+ assert(fabsl(sinl(-ld_pi_odd[i] * 2)) < LDBL_EPSILON);
+ assert(cosl(-ld_pi_odd[i] * 2) == 1.0);
+ assert(fabsl(tanl(-ld_pi_odd[i] * 2)) < LDBL_EPSILON);
+ }
+#endif
+}
+
+/*
+ * Tests the accuracy of these functions over the primary range.
+ */
+static void
+run_accuracy_tests(void)
+{
+
+ /* For small args, sin(x) = tan(x) = x, and cos(x) = 1. */
+ testall(sin, 0xd.50ee515fe4aea16p-114L, 0xd.50ee515fe4aea16p-114L,
+ ALL_STD_EXCEPT, FE_INEXACT);
+ testall(tan, 0xd.50ee515fe4aea16p-114L, 0xd.50ee515fe4aea16p-114L,
+ ALL_STD_EXCEPT, FE_INEXACT);
+ testall(cos, 0xd.50ee515fe4aea16p-114L, 1.0,
+ ALL_STD_EXCEPT, FE_INEXACT);
+
+ /*
+ * These tests should pass for f32, d64, and ld80 as long as
+ * the error is <= 0.75 ulp (round to nearest)
+ */
+#if LDBL_MANT_DIG <= 64
+#define testacc testall
+#else
+#define testacc testdf
+#endif
+ testacc(sin, 0.17255452780841205174L, 0.17169949801444412683L,
+ ALL_STD_EXCEPT, FE_INEXACT);
+ testacc(sin, -0.75431944555904520893L, -0.68479288156557286353L,
+ ALL_STD_EXCEPT, FE_INEXACT);
+ testacc(cos, 0.70556358769838947292L, 0.76124620693117771850L,
+ ALL_STD_EXCEPT, FE_INEXACT);
+ testacc(cos, -0.34061437849088045332L, 0.94254960031831729956L,
+ ALL_STD_EXCEPT, FE_INEXACT);
+ testacc(tan, -0.15862817413325692897L, -0.15997221861309522115L,
+ ALL_STD_EXCEPT, FE_INEXACT);
+ testacc(tan, 0.38374784931303813530L, 0.40376500259976759951L,
+ ALL_STD_EXCEPT, FE_INEXACT);
+
+ /*
+ * XXX missing:
+ * - tests for ld128
+ * - tests for other rounding modes (probably won't pass for now)
+ * - tests for large numbers that get reduced to hi+lo with lo!=0
+ */
+}
+
+int
+main(int argc, char *argv[])
+{
+
+ printf("1..3\n");
+
+ run_special_tests();
+ printf("ok 1 - trig\n");
+
+#ifndef __i386__
+ run_reduction_tests();
+#endif
+ printf("ok 2 - trig\n");
+
+#ifndef __i386__
+ run_accuracy_tests();
+#endif
+ printf("ok 3 - trig\n");
+
+ return (0);
+}
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