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);
}
}
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);
}
}
/* 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);
}
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
*/
complex long double z;
complex long double acos_z;
complex long double asin_z;
complex long double atan_z;
z = CMPLXL(0.75L, 0.25L);
acos_z = CMPLXL(pi / 4, -0.34657359027997265470861606072908828L);
asin_z = CMPLXL(pi / 4, 0.34657359027997265470861606072908828L);
atan_z = CMPLXL(0.66290883183401623252961960521423782L,
0.15899719167999917436476103600701878L);
testall_tol(cacos, z, acos_z, 2);
testall_odd_tol(casin, z, asin_z, 2);
testall_odd_tol(catan, z, atan_z, 2);
}
/*
* 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);
}
/*
* 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);
}
