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| Current File : //usr/src/tools/regression/lib/msun/test-invtrig.c |
/*-
* 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 the inverse trigonometric functions. Some
* accuracy tests are included as well, but these are very basic
* sanity checks, not intended to be comprehensive.
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD: release/9.1.0/tools/regression/lib/msun/test-invtrig.c 216222 2010-12-06 00:02:49Z das $");
#include <assert.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 LEN(a) (sizeof(a) / sizeof((a)[0]))
#pragma STDC FENV_ACCESS ON
/*
* Test that a function returns the correct value and sets the
* exception flags correctly. A tolerance specifying the maximum
* relative error allowed may be specified. For the 'testall'
* functions, the tolerance is specified in ulps.
*
* These are macros instead of functions so that assert provides more
* meaningful error messages.
*/
#define test_tol(func, x, result, tol, excepts) do { \
volatile long double _in = (x), _out = (result); \
assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
assert(fpequal(func(_in), _out, (tol))); \
assert((func, fetestexcept(ALL_STD_EXCEPT) == (excepts))); \
} while (0)
#define test(func, x, result, excepts) \
test_tol(func, (x), (result), 0, (excepts))
#define testall_tol(prefix, x, result, tol, excepts) do { \
test_tol(prefix, (double)(x), (double)(result), \
(tol) * ldexp(1.0, 1 - DBL_MANT_DIG), (excepts)); \
test_tol(prefix##f, (float)(x), (float)(result), \
(tol) * ldexpf(1.0, 1 - FLT_MANT_DIG), (excepts)); \
test_tol(prefix##l, (x), (result), \
(tol) * ldexpl(1.0, 1 - LDBL_MANT_DIG), (excepts)); \
} while (0)
#define testall(prefix, x, result, excepts) \
testall_tol(prefix, (x), (result), 0, (excepts))
#define test2_tol(func, y, x, result, tol, excepts) do { \
volatile long double _iny = (y), _inx = (x), _out = (result); \
assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
assert(fpequal(func(_iny, _inx), _out, (tol))); \
assert((func, fetestexcept(ALL_STD_EXCEPT) == (excepts))); \
} while (0)
#define test2(func, y, x, result, excepts) \
test2_tol(func, (y), (x), (result), 0, (excepts))
#define testall2_tol(prefix, y, x, result, tol, excepts) do { \
test2_tol(prefix, (double)(y), (double)(x), (double)(result), \
(tol) * ldexp(1.0, 1 - DBL_MANT_DIG), (excepts)); \
test2_tol(prefix##f, (float)(y), (float)(x), (float)(result), \
(tol) * ldexpf(1.0, 1 - FLT_MANT_DIG), (excepts)); \
test2_tol(prefix##l, (y), (x), (result), \
(tol) * ldexpl(1.0, 1 - LDBL_MANT_DIG), (excepts)); \
} while (0)
#define testall2(prefix, y, x, result, excepts) \
testall2_tol(prefix, (y), (x), (result), 0, (excepts))
long double
pi = 3.14159265358979323846264338327950280e+00L,
pio3 = 1.04719755119659774615421446109316766e+00L,
c3pi = 9.42477796076937971538793014983850839e+00L,
c5pi = 1.57079632679489661923132169163975140e+01L,
c7pi = 2.19911485751285526692385036829565196e+01L,
c5pio3 = 5.23598775598298873077107230546583851e+00L,
sqrt2m1 = 4.14213562373095048801688724209698081e-01L;
/*
* Determine whether x and y are equal to within a relative error of tol,
* with two special rules:
* +0.0 != -0.0
* NaN == NaN
*/
int
fpequal(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);
ret = fabsl(x - y) <= fabsl(y * tol);
fesetenv(&env);
return (ret);
}
/*
* Test special case inputs in asin(), acos() and atan(): signed
* zeroes, infinities, and NaNs.
*/
static void
test_special(void)
{
testall(asin, 0.0, 0.0, 0);
testall(acos, 0.0, pi / 2, FE_INEXACT);
testall(atan, 0.0, 0.0, 0);
testall(asin, -0.0, -0.0, 0);
testall(acos, -0.0, pi / 2, FE_INEXACT);
testall(atan, -0.0, -0.0, 0);
testall(asin, INFINITY, NAN, FE_INVALID);
testall(acos, INFINITY, NAN, FE_INVALID);
testall(atan, INFINITY, pi / 2, FE_INEXACT);
testall(asin, -INFINITY, NAN, FE_INVALID);
testall(acos, -INFINITY, NAN, FE_INVALID);
testall(atan, -INFINITY, -pi / 2, FE_INEXACT);
testall(asin, NAN, NAN, 0);
testall(acos, NAN, NAN, 0);
testall(atan, NAN, NAN, 0);
}
/*
* Test special case inputs in atan2(), where the exact value of y/x is
* zero or non-finite.
*/
static void
test_special_atan2(void)
{
long double z;
int e;
testall2(atan2, 0.0, -0.0, pi, FE_INEXACT);
testall2(atan2, -0.0, -0.0, -pi, FE_INEXACT);
testall2(atan2, 0.0, 0.0, 0.0, 0);
testall2(atan2, -0.0, 0.0, -0.0, 0);
testall2(atan2, INFINITY, -INFINITY, c3pi / 4, FE_INEXACT);
testall2(atan2, -INFINITY, -INFINITY, -c3pi / 4, FE_INEXACT);
testall2(atan2, INFINITY, INFINITY, pi / 4, FE_INEXACT);
testall2(atan2, -INFINITY, INFINITY, -pi / 4, FE_INEXACT);
/* Tests with one input in the range (0, Inf]. */
z = 1.23456789L;
for (e = FLT_MIN_EXP - FLT_MANT_DIG; e <= FLT_MAX_EXP; e++) {
test2(atan2f, 0.0, ldexpf(z, e), 0.0, 0);
test2(atan2f, -0.0, ldexpf(z, e), -0.0, 0);
test2(atan2f, 0.0, ldexpf(-z, e), (float)pi, FE_INEXACT);
test2(atan2f, -0.0, ldexpf(-z, e), (float)-pi, FE_INEXACT);
test2(atan2f, ldexpf(z, e), 0.0, (float)pi / 2, FE_INEXACT);
test2(atan2f, ldexpf(z, e), -0.0, (float)pi / 2, FE_INEXACT);
test2(atan2f, ldexpf(-z, e), 0.0, (float)-pi / 2, FE_INEXACT);
test2(atan2f, ldexpf(-z, e), -0.0, (float)-pi / 2, FE_INEXACT);
}
for (e = DBL_MIN_EXP - DBL_MANT_DIG; e <= DBL_MAX_EXP; e++) {
test2(atan2, 0.0, ldexp(z, e), 0.0, 0);
test2(atan2, -0.0, ldexp(z, e), -0.0, 0);
test2(atan2, 0.0, ldexp(-z, e), (double)pi, FE_INEXACT);
test2(atan2, -0.0, ldexp(-z, e), (double)-pi, FE_INEXACT);
test2(atan2, ldexp(z, e), 0.0, (double)pi / 2, FE_INEXACT);
test2(atan2, ldexp(z, e), -0.0, (double)pi / 2, FE_INEXACT);
test2(atan2, ldexp(-z, e), 0.0, (double)-pi / 2, FE_INEXACT);
test2(atan2, ldexp(-z, e), -0.0, (double)-pi / 2, FE_INEXACT);
}
for (e = LDBL_MIN_EXP - LDBL_MANT_DIG; e <= LDBL_MAX_EXP; e++) {
test2(atan2l, 0.0, ldexpl(z, e), 0.0, 0);
test2(atan2l, -0.0, ldexpl(z, e), -0.0, 0);
test2(atan2l, 0.0, ldexpl(-z, e), pi, FE_INEXACT);
test2(atan2l, -0.0, ldexpl(-z, e), -pi, FE_INEXACT);
test2(atan2l, ldexpl(z, e), 0.0, pi / 2, FE_INEXACT);
test2(atan2l, ldexpl(z, e), -0.0, pi / 2, FE_INEXACT);
test2(atan2l, ldexpl(-z, e), 0.0, -pi / 2, FE_INEXACT);
test2(atan2l, ldexpl(-z, e), -0.0, -pi / 2, FE_INEXACT);
}
/* Tests with one input in the range (0, Inf). */
for (e = FLT_MIN_EXP - FLT_MANT_DIG; e <= FLT_MAX_EXP - 1; e++) {
test2(atan2f, ldexpf(z, e), INFINITY, 0.0, 0);
test2(atan2f, ldexpf(-z,e), INFINITY, -0.0, 0);
test2(atan2f, ldexpf(z, e), -INFINITY, (float)pi, FE_INEXACT);
test2(atan2f, ldexpf(-z,e), -INFINITY, (float)-pi, FE_INEXACT);
test2(atan2f, INFINITY, ldexpf(z,e), (float)pi/2, FE_INEXACT);
test2(atan2f, INFINITY, ldexpf(-z,e), (float)pi/2, FE_INEXACT);
test2(atan2f, -INFINITY, ldexpf(z,e), (float)-pi/2,FE_INEXACT);
test2(atan2f, -INFINITY, ldexpf(-z,e),(float)-pi/2,FE_INEXACT);
}
for (e = DBL_MIN_EXP - DBL_MANT_DIG; e <= DBL_MAX_EXP - 1; e++) {
test2(atan2, ldexp(z, e), INFINITY, 0.0, 0);
test2(atan2, ldexp(-z,e), INFINITY, -0.0, 0);
test2(atan2, ldexp(z, e), -INFINITY, (double)pi, FE_INEXACT);
test2(atan2, ldexp(-z,e), -INFINITY, (double)-pi, FE_INEXACT);
test2(atan2, INFINITY, ldexp(z,e), (double)pi/2, FE_INEXACT);
test2(atan2, INFINITY, ldexp(-z,e), (double)pi/2, FE_INEXACT);
test2(atan2, -INFINITY, ldexp(z,e), (double)-pi/2,FE_INEXACT);
test2(atan2, -INFINITY, ldexp(-z,e),(double)-pi/2,FE_INEXACT);
}
for (e = LDBL_MIN_EXP - LDBL_MANT_DIG; e <= LDBL_MAX_EXP - 1; e++) {
test2(atan2l, ldexpl(z, e), INFINITY, 0.0, 0);
test2(atan2l, ldexpl(-z,e), INFINITY, -0.0, 0);
test2(atan2l, ldexpl(z, e), -INFINITY, pi, FE_INEXACT);
test2(atan2l, ldexpl(-z,e), -INFINITY, -pi, FE_INEXACT);
test2(atan2l, INFINITY, ldexpl(z, e), pi / 2, FE_INEXACT);
test2(atan2l, INFINITY, ldexpl(-z, e), pi / 2, FE_INEXACT);
test2(atan2l, -INFINITY, ldexpl(z, e), -pi / 2, FE_INEXACT);
test2(atan2l, -INFINITY, ldexpl(-z, e), -pi / 2, FE_INEXACT);
}
}
/*
* Test various inputs to asin(), acos() and atan() and verify that the
* results are accurate to within 1 ulp.
*/
static void
test_accuracy(void)
{
/* We expect correctly rounded results for these basic cases. */
testall(asin, 1.0, pi / 2, FE_INEXACT);
testall(acos, 1.0, 0, 0);
testall(atan, 1.0, pi / 4, FE_INEXACT);
testall(asin, -1.0, -pi / 2, FE_INEXACT);
testall(acos, -1.0, pi, FE_INEXACT);
testall(atan, -1.0, -pi / 4, FE_INEXACT);
/*
* Here we expect answers to be within 1 ulp, although inexactness
* in the input, combined with double rounding, could cause larger
* errors.
*/
testall_tol(asin, sqrtl(2) / 2, pi / 4, 1, FE_INEXACT);
testall_tol(acos, sqrtl(2) / 2, pi / 4, 1, FE_INEXACT);
testall_tol(asin, -sqrtl(2) / 2, -pi / 4, 1, FE_INEXACT);
testall_tol(acos, -sqrtl(2) / 2, c3pi / 4, 1, FE_INEXACT);
testall_tol(asin, sqrtl(3) / 2, pio3, 1, FE_INEXACT);
testall_tol(acos, sqrtl(3) / 2, pio3 / 2, 1, FE_INEXACT);
testall_tol(atan, sqrtl(3), pio3, 1, FE_INEXACT);
testall_tol(asin, -sqrtl(3) / 2, -pio3, 1, FE_INEXACT);
testall_tol(acos, -sqrtl(3) / 2, c5pio3 / 2, 1, FE_INEXACT);
testall_tol(atan, -sqrtl(3), -pio3, 1, FE_INEXACT);
testall_tol(atan, sqrt2m1, pi / 8, 1, FE_INEXACT);
testall_tol(atan, -sqrt2m1, -pi / 8, 1, FE_INEXACT);
}
/*
* Test inputs to atan2() where x is a power of 2. These are easy cases
* because y/x is exact.
*/
static void
test_p2x_atan2(void)
{
testall2(atan2, 1.0, 1.0, pi / 4, FE_INEXACT);
testall2(atan2, 1.0, -1.0, c3pi / 4, FE_INEXACT);
testall2(atan2, -1.0, 1.0, -pi / 4, FE_INEXACT);
testall2(atan2, -1.0, -1.0, -c3pi / 4, FE_INEXACT);
testall2_tol(atan2, sqrt2m1 * 2, 2.0, pi / 8, 1, FE_INEXACT);
testall2_tol(atan2, sqrt2m1 * 2, -2.0, c7pi / 8, 1, FE_INEXACT);
testall2_tol(atan2, -sqrt2m1 * 2, 2.0, -pi / 8, 1, FE_INEXACT);
testall2_tol(atan2, -sqrt2m1 * 2, -2.0, -c7pi / 8, 1, FE_INEXACT);
testall2_tol(atan2, sqrtl(3) * 0.5, 0.5, pio3, 1, FE_INEXACT);
testall2_tol(atan2, sqrtl(3) * 0.5, -0.5, pio3 * 2, 1, FE_INEXACT);
testall2_tol(atan2, -sqrtl(3) * 0.5, 0.5, -pio3, 1, FE_INEXACT);
testall2_tol(atan2, -sqrtl(3) * 0.5, -0.5, -pio3 * 2, 1, FE_INEXACT);
}
/*
* Test inputs very close to 0.
*/
static void
test_tiny(void)
{
float tiny = 0x1.23456p-120f;
testall(asin, tiny, tiny, FE_INEXACT);
testall(acos, tiny, pi / 2, FE_INEXACT);
testall(atan, tiny, tiny, FE_INEXACT);
testall(asin, -tiny, -tiny, FE_INEXACT);
testall(acos, -tiny, pi / 2, FE_INEXACT);
testall(atan, -tiny, -tiny, FE_INEXACT);
/* Test inputs to atan2() that would cause y/x to underflow. */
test2(atan2f, 0x1.0p-100, 0x1.0p100, 0.0, FE_INEXACT | FE_UNDERFLOW);
test2(atan2, 0x1.0p-1000, 0x1.0p1000, 0.0, FE_INEXACT | FE_UNDERFLOW);
test2(atan2l, ldexpl(1.0, 100 - LDBL_MAX_EXP),
ldexpl(1.0, LDBL_MAX_EXP - 100), 0.0, FE_INEXACT | FE_UNDERFLOW);
test2(atan2f, -0x1.0p-100, 0x1.0p100, -0.0, FE_INEXACT | FE_UNDERFLOW);
test2(atan2, -0x1.0p-1000, 0x1.0p1000, -0.0, FE_INEXACT | FE_UNDERFLOW);
test2(atan2l, -ldexpl(1.0, 100 - LDBL_MAX_EXP),
ldexpl(1.0, LDBL_MAX_EXP - 100), -0.0, FE_INEXACT | FE_UNDERFLOW);
test2(atan2f, 0x1.0p-100, -0x1.0p100, (float)pi, FE_INEXACT);
test2(atan2, 0x1.0p-1000, -0x1.0p1000, (double)pi, FE_INEXACT);
test2(atan2l, ldexpl(1.0, 100 - LDBL_MAX_EXP),
-ldexpl(1.0, LDBL_MAX_EXP - 100), pi, FE_INEXACT);
test2(atan2f, -0x1.0p-100, -0x1.0p100, (float)-pi, FE_INEXACT);
test2(atan2, -0x1.0p-1000, -0x1.0p1000, (double)-pi, FE_INEXACT);
test2(atan2l, -ldexpl(1.0, 100 - LDBL_MAX_EXP),
-ldexpl(1.0, LDBL_MAX_EXP - 100), -pi, FE_INEXACT);
}
/*
* Test very large inputs to atan().
*/
static void
test_atan_huge(void)
{
float huge = 0x1.23456p120;
testall(atan, huge, pi / 2, FE_INEXACT);
testall(atan, -huge, -pi / 2, FE_INEXACT);
/* Test inputs to atan2() that would cause y/x to overflow. */
test2(atan2f, 0x1.0p100, 0x1.0p-100, (float)pi / 2, FE_INEXACT);
test2(atan2, 0x1.0p1000, 0x1.0p-1000, (double)pi / 2, FE_INEXACT);
test2(atan2l, ldexpl(1.0, LDBL_MAX_EXP - 100),
ldexpl(1.0, 100 - LDBL_MAX_EXP), pi / 2, FE_INEXACT);
test2(atan2f, -0x1.0p100, 0x1.0p-100, (float)-pi / 2, FE_INEXACT);
test2(atan2, -0x1.0p1000, 0x1.0p-1000, (double)-pi / 2, FE_INEXACT);
test2(atan2l, -ldexpl(1.0, LDBL_MAX_EXP - 100),
ldexpl(1.0, 100 - LDBL_MAX_EXP), -pi / 2, FE_INEXACT);
test2(atan2f, 0x1.0p100, -0x1.0p-100, (float)pi / 2, FE_INEXACT);
test2(atan2, 0x1.0p1000, -0x1.0p-1000, (double)pi / 2, FE_INEXACT);
test2(atan2l, ldexpl(1.0, LDBL_MAX_EXP - 100),
-ldexpl(1.0, 100 - LDBL_MAX_EXP), pi / 2, FE_INEXACT);
test2(atan2f, -0x1.0p100, -0x1.0p-100, (float)-pi / 2, FE_INEXACT);
test2(atan2, -0x1.0p1000, -0x1.0p-1000, (double)-pi / 2, FE_INEXACT);
test2(atan2l, -ldexpl(1.0, LDBL_MAX_EXP - 100),
-ldexpl(1.0, 100 - LDBL_MAX_EXP), -pi / 2, FE_INEXACT);
}
/*
* Test that sin(asin(x)) == x, and similarly for acos() and atan().
* You need to have a working sinl(), cosl(), and tanl() for these
* tests to pass.
*/
static long double
sinasinf(float x)
{
return (sinl(asinf(x)));
}
static long double
sinasin(double x)
{
return (sinl(asin(x)));
}
static long double
sinasinl(long double x)
{
return (sinl(asinl(x)));
}
static long double
cosacosf(float x)
{
return (cosl(acosf(x)));
}
static long double
cosacos(double x)
{
return (cosl(acos(x)));
}
static long double
cosacosl(long double x)
{
return (cosl(acosl(x)));
}
static long double
tanatanf(float x)
{
return (tanl(atanf(x)));
}
static long double
tanatan(double x)
{
return (tanl(atan(x)));
}
static long double
tanatanl(long double x)
{
return (tanl(atanl(x)));
}
static void
test_inverse(void)
{
float i;
for (i = -1; i <= 1; i += 0x1.0p-12f) {
testall_tol(sinasin, i, i, 2, i == 0 ? 0 : FE_INEXACT);
/* The relative error for cosacos is very large near x=0. */
if (fabsf(i) > 0x1.0p-4f)
testall_tol(cosacos, i, i, 16, i == 1 ? 0 : FE_INEXACT);
testall_tol(tanatan, i, i, 2, i == 0 ? 0 : FE_INEXACT);
}
}
int
main(int argc, char *argv[])
{
printf("1..7\n");
test_special();
printf("ok 1 - special\n");
test_special_atan2();
printf("ok 2 - atan2 special\n");
test_accuracy();
printf("ok 3 - accuracy\n");
test_p2x_atan2();
printf("ok 4 - atan2 p2x\n");
test_tiny();
printf("ok 5 - tiny inputs\n");
test_atan_huge();
printf("ok 6 - atan huge inputs\n");
test_inverse();
printf("ok 7 - inverse\n");
return (0);
}