Differential D28798 Diff 85215 lib/msun/tests/invtrig_test.c

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lib/msun/tests/invtrig_test.c

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* 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("$FreeBSD$");

#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. 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); \

ATF_REQUIRE_EQ(0, feclearexcept(FE_ALL_EXCEPT)); \

assert(fpequal_tol(func(_in), _out, (tol), CS_BOTH)); \

ATF_CHECK(fpequal_tol(func(_in), _out, (tol), CS_BOTH)); \

assert(((void)func, fetestexcept(ALL_STD_EXCEPT) == (excepts))); \

CHECK_FP_EXCEPTIONS_MSG(excepts, ALL_STD_EXCEPT, "for %s(%s)", \

#func, #x); \

} 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), \

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} while (0)

#endif

#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); \

ATF_REQUIRE_EQ(0, feclearexcept(FE_ALL_EXCEPT)); \

assert(fpequal_tol(func(_iny, _inx), _out, (tol), CS_BOTH)); \

ATF_CHECK(fpequal_tol(func(_iny, _inx), _out, (tol), CS_BOTH)); \

assert(((void)func, fetestexcept(ALL_STD_EXCEPT) == (excepts))); \

CHECK_FP_EXCEPTIONS_MSG(excepts, ALL_STD_EXCEPT, "for %s(%s)", \

#func, #x); \

} 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), \

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c5pio3 = 5.23598775598298873077107230546583851e+00L,

sqrt2m1 = 4.14213562373095048801688724209698081e-01L;

* Test special case inputs in asin(), acos() and atan(): signed

* zeroes, infinities, and NaNs.

static void

ATF_TC_WITHOUT_HEAD(special);

test_special(void)

ATF_TC_BODY(special, tc)

{

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);

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ATF_TC_BODY(special, tc)

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

ATF_TC_WITHOUT_HEAD(special_atan2);

test_special_atan2(void)

ATF_TC_BODY(special_atan2, tc)

{

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);

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for (e = LDBL_MIN_EXP - LDBL_MANT_DIG; e <= LDBL_MAX_EXP - 1; e++) {

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

ATF_TC_WITHOUT_HEAD(accuracy);

test_accuracy(void)

ATF_TC_BODY(accuracy, tc)

{

/* 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);

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ATF_TC_BODY(accuracy, tc)

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

ATF_TC_WITHOUT_HEAD(p2x_atan2);

test_p2x_atan2(void)

ATF_TC_BODY(p2x_atan2, tc)

{

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

ATF_TC_WITHOUT_HEAD(tiny);

test_tiny(void)

ATF_TC_BODY(tiny, tc)

{

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);

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ATF_TC_BODY(tiny, tc)

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

ATF_TC_WITHOUT_HEAD(atan_huge);

test_atan_huge(void)

ATF_TC_BODY(atan_huge, tc)

{

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);

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static long double

tanatanl(long double x)

{

return (tanl(atanl(x)));

}

static void

ATF_TC_WITHOUT_HEAD(inverse);

test_inverse(void)

ATF_TC_BODY(inverse, tc)

{

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

ATF_TP_ADD_TCS(tp)

main(void)

{

ATF_TP_ADD_TC(tp, special);

ATF_TP_ADD_TC(tp, special_atan2);

ATF_TP_ADD_TC(tp, accuracy);

ATF_TP_ADD_TC(tp, p2x_atan2);

ATF_TP_ADD_TC(tp, tiny);

ATF_TP_ADD_TC(tp, atan_huge);

ATF_TP_ADD_TC(tp, inverse);

ngieUnsubmitted

Done

ATF_TP_ADD_TC(tp, atan_huge);

ATF_TP_ADD_TC(tp, inverse);

return (atf_no_error());

}

newline

ngie: newline

#if defined(__i386__)

return (atf_no_error());

printf("1..0 # SKIP fails all assertions on i386\n");

return (0);

#endif

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);

}