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 along the real and imaginary axes. */
void
test_axes(void)
{
static const long double nums[] = {
M_PI / 4, M_PI / 2, 3 * M_PI / 4,
5 * M_PI / 4, 3 * M_PI / 2, 7 * M_PI / 4,
};
long double complex z;
int i;
for (i = 0; i < sizeof(nums) / sizeof(nums[0]); i++) {
/* Real axis */
z = cpackl(nums[i], 0.0);
testall_odd_tol(csinh, z, cpackl(sinh(nums[i]), 0), 0);
testall_even_tol(ccosh, z, cpackl(cosh(nums[i]), 0), 0);
testall_odd_tol(ctanh, z, cpackl(tanh(nums[i]), 0), 1);
testall_odd_tol(csin, z, cpackl(sin(nums[i]),
copysign(0, cos(nums[i]))), 0);
testall_even_tol(ccos, z, cpackl(cos(nums[i]),
-copysign(0, sin(nums[i]))), 0);
testall_odd_tol(ctan, z, cpackl(tan(nums[i]), 0), 1);
/* Imaginary axis */
z = cpackl(0.0, nums[i]);
testall_odd_tol(csinh, z, cpackl(copysign(0, cos(nums[i])),
sin(nums[i])), 0);
testall_even_tol(ccosh, z, cpackl(cos(nums[i]),
copysign(0, sin(nums[i]))), 0);
testall_odd_tol(ctanh, z, cpackl(0, tan(nums[i])), 1);
testall_odd_tol(csin, z, cpackl(0, sinh(nums[i])), 0);
testall_even_tol(ccos, z, cpackl(cosh(nums[i]), -0.0), 0);
testall_odd_tol(ctan, z, cpackl(0, tanh(nums[i])), 1);
}
}
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);
}
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 inputs that might cause overflow in a sloppy implementation. */
void
test_large(void)
{
long double complex z;
/* tanh() uses a threshold around x=22, so check both sides. */
z = cpackl(21, 0.78539816339744830961566084581987572L);
testall_odd_tol(ctanh, z,
cpackl(1.0, 1.14990445285871196133287617611468468e-18L), 1);
z++;
testall_odd_tol(ctanh, z,
cpackl(1.0, 1.55622644822675930314266334585597964e-19L), 1);
z = cpackl(355, 0.78539816339744830961566084581987572L);
testall_odd_tol(ctanh, z,
cpackl(1.0, 8.95257245135025991216632140458264468e-309L), 1);
z = cpackl(30, 0x1p1023L);
testall_odd_tol(ctanh, z,
cpackl(1.0, -1.62994325413993477997492170229268382e-26L), 1);
z = cpackl(1, 0x1p1023L);
testall_odd_tol(ctanh, z,
cpackl(0.878606311888306869546254022621986509L,
-0.225462792499754505792678258169527424L), 1);
z = cpackl(710.6, 0.78539816339744830961566084581987572L);
testall_odd_tol(csinh, z,
cpackl(1.43917579766621073533185387499658944e308L,
1.43917579766621073533185387499658944e308L), 1);
testall_even_tol(ccosh, z,
cpackl(1.43917579766621073533185387499658944e308L,
1.43917579766621073533185387499658944e308L), 1);
z = cpackl(1500, 0.78539816339744830961566084581987572L);
testall_odd(csinh, z, cpackl(INFINITY, INFINITY), OPT_INEXACT,
FE_OVERFLOW, CS_BOTH);
testall_even(ccosh, z, cpackl(INFINITY, INFINITY), OPT_INEXACT,
FE_OVERFLOW, CS_BOTH);
}
void
test_small(void)
{
/*
* z = 0.5 + i Pi/4
* sinh(z) = (sinh(0.5) + i cosh(0.5)) * sqrt(2)/2
* cosh(z) = (cosh(0.5) + i sinh(0.5)) * sqrt(2)/2
* tanh(z) = (2cosh(0.5)sinh(0.5) + i) / (2 cosh(0.5)**2 - 1)
* z = -0.5 + i Pi/2
* sinh(z) = cosh(0.5)
* cosh(z) = -i sinh(0.5)
* tanh(z) = -coth(0.5)
* z = 1.0 + i 3Pi/4
* sinh(z) = (-sinh(1) + i cosh(1)) * sqrt(2)/2
* cosh(z) = (-cosh(1) + i sinh(1)) * sqrt(2)/2
* tanh(z) = (2cosh(1)sinh(1) - i) / (2cosh(1)**2 - 1)
*/
static const struct {
long double a, b;
long double sinh_a, sinh_b;
long double cosh_a, cosh_b;
long double tanh_a, tanh_b;
} tests[] = {
{ 0.5L,
0.78539816339744830961566084581987572L,
0.36847002415910435172083660522240710L,
0.79735196663945774996093142586179334L,
0.79735196663945774996093142586179334L,
0.36847002415910435172083660522240710L,
0.76159415595576488811945828260479359L,
0.64805427366388539957497735322615032L },
{ -0.5L,
1.57079632679489661923132169163975144L,
0.0L,
1.12762596520638078522622516140267201L,
0.0L,
-0.52109530549374736162242562641149156L,
-2.16395341373865284877000401021802312L,
0.0L },
{ 1.0L,
2.35619449019234492884698253745962716L,
-0.83099273328405698212637979852748608L,
1.09112278079550143030545602018565236L,
-1.09112278079550143030545602018565236L,
0.83099273328405698212637979852748609L,
0.96402758007581688394641372410092315L,
-0.26580222883407969212086273981988897L }
};
long double complex z;
int i;
for (i = 0; i < sizeof(tests) / sizeof(tests[0]); i++) {
z = cpackl(tests[i].a, tests[i].b);
testall_odd_tol(csinh, z,
cpackl(tests[i].sinh_a, tests[i].sinh_b), 1.1);
testall_even_tol(ccosh, z,
cpackl(tests[i].cosh_a, tests[i].cosh_b), 1.1);
testall_odd_tol(ctanh, z,
cpackl(tests[i].tanh_a, tests[i].tanh_b), 1.1);
}
}
/*
* 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);
}
