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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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