static long double complex
clog_for_large_values(long double complex z)
{
long double x, y;
long double ax, ay, t;
x = creall(z);
y = cimagl(z);
ax = fabsl(x);
ay = fabsl(y);
if (ax < ay) {
t = ax;
ax = ay;
ay = t;
}
if (ax > HALF_MAX)
return (CMPLXL(logl(hypotl(x / m_e, y / m_e)) + 1,
atan2l(y, x)));
if (ax > QUARTER_SQRT_MAX || ay < SQRT_MIN)
return (CMPLXL(logl(hypotl(x, y)), atan2l(y, x)));
return (CMPLXL(logl(ax * ax + ay * ay) / 2, atan2l(y, x)));
}
void
test_small(void)
{
static const double tests[] = {
/* csqrt(a + bI) = x + yI */
/* a b x y */
1.0, M_PI_4, M_SQRT2 * 0.5 * M_E, M_SQRT2 * 0.5 * M_E,
-1.0, M_PI_4, M_SQRT2 * 0.5 / M_E, M_SQRT2 * 0.5 / M_E,
2.0, M_PI_2, 0.0, M_E * M_E,
M_LN2, M_PI, -2.0, 0.0,
};
double a, b;
double x, y;
int i;
for (i = 0; i < N(tests); i += 4) {
printf("# Run %d..\n", i);
a = tests[i];
b = tests[i + 1];
x = tests[i + 2];
y = tests[i + 3];
test_tol(cexp, CMPLXL(a, b), CMPLXL(x, y), 3 * DBL_ULP());
/* float doesn't have enough precision to pass these tests */
if (x == 0 || y == 0)
continue;
test_tol(cexpf, CMPLXL(a, b), CMPLXL(x, y), 1 * FLT_ULP());
}
}
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);
}
}
long double complex
catanl(long double complex z)
{
long double complex w;
w = catanhl(CMPLXL(cimagl(z), creall(z)));
return (CMPLXL(cimagl(w), creall(w)));
}
// FIXME
long double complex casinl(long double complex z) {
long double complex w;
long double x, y;
x = creall(z);
y = cimagl(z);
w = CMPLXL(1.0 - (x - y) * (x + y), -2.0 * x * y);
return clogl(CMPLXL(-y, x) + csqrtl(w));
}
/*
* Test csqrt for some finite arguments where the answer is exact.
* (We do not test if it produces correctly rounded answers when the
* result is inexact, nor do we check whether it throws spurious
* exceptions.)
*/
static void
test_finite()
{
static const double tests[] = {
/* csqrt(a + bI) = x + yI */
/* a b x y */
0, 8, 2, 2,
0, -8, 2, -2,
4, 0, 2, 0,
-4, 0, 0, 2,
3, 4, 2, 1,
3, -4, 2, -1,
-3, 4, 1, 2,
-3, -4, 1, -2,
5, 12, 3, 2,
7, 24, 4, 3,
9, 40, 5, 4,
11, 60, 6, 5,
13, 84, 7, 6,
33, 56, 7, 4,
39, 80, 8, 5,
65, 72, 9, 4,
987, 9916, 74, 67,
5289, 6640, 83, 40,
460766389075.0, 16762287900.0, 678910, 12345
};
/*
* We also test some multiples of the above arguments. This
* array defines which multiples we use. Note that these have
* to be small enough to not cause overflow for float precision
* with all of the constants in the above table.
*/
static const double mults[] = {
1,
2,
3,
13,
16,
0x1.p30,
0x1.p-30,
};
double a, b;
double x, y;
int i, j;
for (i = 0; i < nitems(tests); i += 4) {
for (j = 0; j < nitems(mults); j++) {
a = tests[i] * mults[j] * mults[j];
b = tests[i + 1] * mults[j] * mults[j];
x = tests[i + 2] * mults[j];
y = tests[i + 3] * mults[j];
assert(t_csqrt(CMPLXL(a, b)) == CMPLXL(x, y));
}
}
}
/* Tests for 0 */
void
test_zero(void)
{
/* cexp(0) = 1, no exceptions raised */
testall(0.0, 1.0, ALL_STD_EXCEPT, 0, 1);
testall(-0.0, 1.0, ALL_STD_EXCEPT, 0, 1);
testall(CMPLXL(0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
testall(CMPLXL(-0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
}
/*
* Test the handling of infinities when the other argument is not NaN.
*/
static void
test_infinities()
{
static const double vals[] = {
0.0,
-0.0,
42.0,
-42.0,
INFINITY,
-INFINITY,
};
int i;
for (i = 0; i < nitems(vals); i++) {
if (isfinite(vals[i])) {
assert_equal(t_csqrt(CMPLXL(-INFINITY, vals[i])),
CMPLXL(0.0, copysignl(INFINITY, vals[i])));
assert_equal(t_csqrt(CMPLXL(INFINITY, vals[i])),
CMPLXL(INFINITY, copysignl(0.0, vals[i])));
}
assert_equal(t_csqrt(CMPLXL(vals[i], INFINITY)),
CMPLXL(INFINITY, INFINITY));
assert_equal(t_csqrt(CMPLXL(vals[i], -INFINITY)),
CMPLXL(INFINITY, -INFINITY));
}
}
long double complex
cacosl(long double complex z)
{
long double x, y, ax, ay, rx, ry, B, sqrt_A2mx2, new_x;
int sx, sy;
int B_is_usable;
long double complex w;
x = creall(z);
y = cimagl(z);
sx = signbit(x);
sy = signbit(y);
ax = fabsl(x);
ay = fabsl(y);
if (isnan(x) || isnan(y)) {
if (isinf(x))
return (CMPLXL(y + y, -INFINITY));
if (isinf(y))
return (CMPLXL(x + x, -y));
if (x == 0)
return (CMPLXL(pio2_hi + pio2_lo, y + y));
return (CMPLXL(nan_mix(x, y), nan_mix(x, y)));
}
if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) {
w = clog_for_large_values(z);
rx = fabsl(cimagl(w));
ry = creall(w) + m_ln2;
if (sy == 0)
ry = -ry;
return (CMPLXL(rx, ry));
}
if (x == 1 && y == 0)
return (CMPLXL(0, -y));
raise_inexact();
if (ax < SQRT_6_EPSILON / 4 && ay < SQRT_6_EPSILON / 4)
return (CMPLXL(pio2_hi - (x - pio2_lo), -y));
do_hard_work(ay, ax, &ry, &B_is_usable, &B, &sqrt_A2mx2, &new_x);
if (B_is_usable) {
if (sx == 0)
rx = acosl(B);
else
rx = acosl(-B);
} else {
if (sx == 0)
rx = atan2l(sqrt_A2mx2, new_x);
else
rx = atan2l(sqrt_A2mx2, -new_x);
}
if (sy == 0)
ry = -ry;
return (CMPLXL(rx, ry));
}
/* 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);
}
/*
* Test the handling of +/- 0.
*/
static void
test_zeros()
{
assert_equal(t_csqrt(CMPLXL(0.0, 0.0)), CMPLXL(0.0, 0.0));
assert_equal(t_csqrt(CMPLXL(-0.0, 0.0)), CMPLXL(0.0, 0.0));
assert_equal(t_csqrt(CMPLXL(0.0, -0.0)), CMPLXL(0.0, -0.0));
assert_equal(t_csqrt(CMPLXL(-0.0, -0.0)), CMPLXL(0.0, -0.0));
}
long double complex
cacoshl(long double complex z)
{
long double complex w;
long double rx, ry;
w = cacosl(z);
rx = creall(w);
ry = cimagl(w);
if (isnan(rx) && isnan(ry))
return (CMPLXL(ry, rx));
if (isnan(rx))
return (CMPLXL(fabsl(ry), rx));
if (isnan(ry))
return (CMPLXL(ry, ry));
return (CMPLXL(fabsl(ry), copysignl(rx, cimagl(z))));
}
long double complex
cprojl(long double complex z)
{
if (!isinf(creall(z)) && !isinf(cimagl(z)))
return (z);
else
return (CMPLXL(INFINITY, copysignl(0.0, cimagl(z))));
}
/*
* Test whether csqrt(a + bi) works for inputs that are large enough to
* cause overflow in hypot(a, b) + a. In this case we are using
* csqrt(115 + 252*I) == 14 + 9*I
* scaled up to near MAX_EXP.
*/
static void
test_overflow(int maxexp)
{
long double a, b;
long double complex result;
a = ldexpl(115 * 0x1p-8, maxexp);
b = ldexpl(252 * 0x1p-8, maxexp);
result = t_csqrt(CMPLXL(a, b));
assert(creall(result) == ldexpl(14 * 0x1p-4, maxexp / 2));
assert(cimagl(result) == ldexpl(9 * 0x1p-4, maxexp / 2));
}
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);
}
long double complex
catanhl(long double complex z)
{
long double x, y, ax, ay, rx, ry;
x = creall(z);
y = cimagl(z);
ax = fabsl(x);
ay = fabsl(y);
if (y == 0 && ax <= 1)
return (CMPLXL(atanhl(x), y));
if (x == 0)
return (CMPLXL(x, atanl(y)));
if (isnan(x) || isnan(y)) {
if (isinf(x))
return (CMPLXL(copysignl(0, x), y + y));
if (isinf(y))
return (CMPLXL(copysignl(0, x),
copysignl(pio2_hi + pio2_lo, y)));
return (CMPLXL(nan_mix(x, y), nan_mix(x, y)));
}
if (ax > RECIP_EPSILON || ay > RECIP_EPSILON)
return (CMPLXL(real_part_reciprocal(x, y),
copysignl(pio2_hi + pio2_lo, y)));
if (ax < SQRT_3_EPSILON / 2 && ay < SQRT_3_EPSILON / 2) {
raise_inexact();
return (z);
}
if (ax == 1 && ay < LDBL_EPSILON)
rx = (m_ln2 - logl(ay)) / 2;
else
rx = log1pl(4 * ax / sum_squares(ax - 1, ay)) / 4;
if (ax == 1)
ry = atan2l(2, -ay) / 2;
else if (ay < LDBL_EPSILON)
ry = atan2l(2 * ay, (1 - ax) * (1 + ax)) / 2;
else
ry = atan2l(2 * ay, (1 - ax) * (1 + ax) - ay * ay) / 2;
return (CMPLXL(copysignl(rx, x), copysignl(ry, y)));
}
void
test_imaginaries(void)
{
int i;
for (i = 0; i < N(finites); i++) {
printf("# Run %d..\n", i);
test(cexp, CMPLXL(0.0, finites[i]),
CMPLXL(cos(finites[i]), sin(finites[i])),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
test(cexp, CMPLXL(-0.0, finites[i]),
CMPLXL(cos(finites[i]), sin(finites[i])),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
test(cexpf, CMPLXL(0.0, finites[i]),
CMPLXL(cosf(finites[i]), sinf(finites[i])),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
test(cexpf, CMPLXL(-0.0, finites[i]),
CMPLXL(cosf(finites[i]), sinf(finites[i])),
ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
}
}
void
test_reals(void)
{
int i;
for (i = 0; i < N(finites); i++) {
/* XXX could check exceptions more meticulously */
printf("# Run %d..\n", i);
test(cexp, CMPLXL(finites[i], 0.0),
CMPLXL(exp(finites[i]), 0.0),
FE_INVALID | FE_DIVBYZERO, 0, 1);
test(cexp, CMPLXL(finites[i], -0.0),
CMPLXL(exp(finites[i]), -0.0),
FE_INVALID | FE_DIVBYZERO, 0, 1);
test(cexpf, CMPLXL(finites[i], 0.0),
CMPLXL(expf(finites[i]), 0.0),
FE_INVALID | FE_DIVBYZERO, 0, 1);
test(cexpf, CMPLXL(finites[i], -0.0),
CMPLXL(expf(finites[i]), -0.0),
FE_INVALID | FE_DIVBYZERO, 0, 1);
}
}
long double complex
casinhl(long double complex z)
{
long double x, y, ax, ay, rx, ry, B, sqrt_A2my2, new_y;
int B_is_usable;
long double complex w;
x = creall(z);
y = cimagl(z);
ax = fabsl(x);
ay = fabsl(y);
if (isnan(x) || isnan(y)) {
if (isinf(x))
return (CMPLXL(x, y + y));
if (isinf(y))
return (CMPLXL(y, x + x));
if (y == 0)
return (CMPLXL(x + x, y));
return (CMPLXL(nan_mix(x, y), nan_mix(x, y)));
}
if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) {
if (signbit(x) == 0)
w = clog_for_large_values(z) + m_ln2;
else
w = clog_for_large_values(-z) + m_ln2;
return (CMPLXL(copysignl(creall(w), x),
copysignl(cimagl(w), y)));
}
if (x == 0 && y == 0)
return (z);
raise_inexact();
if (ax < SQRT_6_EPSILON / 4 && ay < SQRT_6_EPSILON / 4)
return (z);
do_hard_work(ax, ay, &rx, &B_is_usable, &B, &sqrt_A2my2, &new_y);
if (B_is_usable)
ry = asinl(B);
else
ry = atan2l(new_y, sqrt_A2my2);
return (CMPLXL(copysignl(rx, x), copysignl(ry, y)));
}
/*
* Test the handling of NaNs.
*/
static void
test_nans()
{
assert(creall(t_csqrt(CMPLXL(INFINITY, NAN))) == INFINITY);
assert(isnan(cimagl(t_csqrt(CMPLXL(INFINITY, NAN)))));
assert(isnan(creall(t_csqrt(CMPLXL(-INFINITY, NAN)))));
assert(isinf(cimagl(t_csqrt(CMPLXL(-INFINITY, NAN)))));
assert_equal(t_csqrt(CMPLXL(NAN, INFINITY)),
CMPLXL(INFINITY, INFINITY));
assert_equal(t_csqrt(CMPLXL(NAN, -INFINITY)),
CMPLXL(INFINITY, -INFINITY));
assert_equal(t_csqrt(CMPLXL(0.0, NAN)), CMPLXL(NAN, NAN));
assert_equal(t_csqrt(CMPLXL(-0.0, NAN)), CMPLXL(NAN, NAN));
assert_equal(t_csqrt(CMPLXL(42.0, NAN)), CMPLXL(NAN, NAN));
assert_equal(t_csqrt(CMPLXL(-42.0, NAN)), CMPLXL(NAN, NAN));
assert_equal(t_csqrt(CMPLXL(NAN, 0.0)), CMPLXL(NAN, NAN));
assert_equal(t_csqrt(CMPLXL(NAN, -0.0)), CMPLXL(NAN, NAN));
assert_equal(t_csqrt(CMPLXL(NAN, 42.0)), CMPLXL(NAN, NAN));
assert_equal(t_csqrt(CMPLXL(NAN, -42.0)), CMPLXL(NAN, NAN));
assert_equal(t_csqrt(CMPLXL(NAN, NAN)), CMPLXL(NAN, NAN));
}
long double complex
clogl(long double complex z)
{
long double ax, ax2h, ax2l, axh, axl, ay, ay2h, ay2l, ayh, ayl;
long double sh, sl, t;
long double x, y, v;
uint16_t hax, hay;
int kx, ky;
ENTERIT(long double complex);
x = creall(z);
y = cimagl(z);
v = atan2l(y, x);
ax = fabsl(x);
ay = fabsl(y);
if (ax < ay) {
t = ax;
ax = ay;
ay = t;
}
GET_LDBL_EXPSIGN(hax, ax);
kx = hax - 16383;
GET_LDBL_EXPSIGN(hay, ay);
ky = hay - 16383;
/* Handle NaNs and Infs using the general formula. */
if (kx == MAX_EXP || ky == MAX_EXP)
RETURNI(CMPLXL(logl(hypotl(x, y)), v));
/* Avoid spurious underflow, and reduce inaccuracies when ax is 1. */
if (ax == 1) {
if (ky < (MIN_EXP - 1) / 2)
RETURNI(CMPLXL((ay / 2) * ay, v));
RETURNI(CMPLXL(log1pl(ay * ay) / 2, v));
}
/* Avoid underflow when ax is not small. Also handle zero args. */
if (kx - ky > MANT_DIG || ay == 0)
RETURNI(CMPLXL(logl(ax), v));
/* Avoid overflow. */
if (kx >= MAX_EXP - 1)
RETURNI(CMPLXL(logl(hypotl(x * 0x1p-16382L, y * 0x1p-16382L)) +
(MAX_EXP - 2) * ln2l_lo + (MAX_EXP - 2) * ln2_hi, v));
if (kx >= (MAX_EXP - 1) / 2)
RETURNI(CMPLXL(logl(hypotl(x, y)), v));
/* Reduce inaccuracies and avoid underflow when ax is denormal. */
if (kx <= MIN_EXP - 2)
RETURNI(CMPLXL(logl(hypotl(x * 0x1p16383L, y * 0x1p16383L)) +
(MIN_EXP - 2) * ln2l_lo + (MIN_EXP - 2) * ln2_hi, v));
/* Avoid remaining underflows (when ax is small but not denormal). */
if (ky < (MIN_EXP - 1) / 2 + MANT_DIG)
RETURNI(CMPLXL(logl(hypotl(x, y)), v));
/* Calculate ax*ax and ay*ay exactly using Dekker's algorithm. */
t = (long double)(ax * (MULT_REDUX + 1));
axh = (long double)(ax - t) + t;
axl = ax - axh;
ax2h = ax * ax;
ax2l = axh * axh - ax2h + 2 * axh * axl + axl * axl;
t = (long double)(ay * (MULT_REDUX + 1));
ayh = (long double)(ay - t) + t;
ayl = ay - ayh;
ay2h = ay * ay;
ay2l = ayh * ayh - ay2h + 2 * ayh * ayl + ayl * ayl;
/*
* When log(|z|) is far from 1, accuracy in calculating the sum
* of the squares is not very important since log() reduces
* inaccuracies. We depended on this to use the general
* formula when log(|z|) is very far from 1. When log(|z|) is
* moderately far from 1, we go through the extra-precision
* calculations to reduce branches and gain a little accuracy.
*
* When |z| is near 1, we subtract 1 and use log1p() and don't
* leave it to log() to subtract 1, since we gain at least 1 bit
* of accuracy in this way.
*
* When |z| is very near 1, subtracting 1 can cancel almost
* 3*MANT_DIG bits. We arrange that subtracting 1 is exact in
* doubled precision, and then do the rest of the calculation
* in sloppy doubled precision. Although large cancellations
* often lose lots of accuracy, here the final result is exact
* in doubled precision if the large calculation occurs (because
* then it is exact in tripled precision and the cancellation
* removes enough bits to fit in doubled precision). Thus the
* result is accurate in sloppy doubled precision, and the only
* significant loss of accuracy is when it is summed and passed
* to log1p().
*/
sh = ax2h;
sl = ay2h;
_2sumF(sh, sl);
if (sh < 0.5 || sh >= 3)
RETURNI(CMPLXL(logl(ay2l + ax2l + sl + sh) / 2, v));
sh -= 1;
_2sum(sh, sl);
_2sum(ax2l, ay2l);
/* Briggs-Kahan algorithm (except we discard the final low term): */
_2sum(sh, ax2l);
_2sum(sl, ay2l);
t = ax2l + sl;
_2sumF(sh, t);
RETURNI(CMPLXL(log1pl(ay2l + t + sh) / 2, v));
}
long double complex catanhl(long double complex z) {
z = catanl(CMPLXL(-cimagl(z), creall(z)));
return CMPLXL(cimagl(z), -creall(z));
}
long double complex cprojl(long double complex z) {
if (isinf(creall(z)) || isinf(cimagl(z)))
return CMPLXL(INFINITY, copysignl(0.0, creall(z)));
return z;
}
long double complex conjl(long double complex z)
{
return CMPLXL(creall(z), -cimagl(z));
}
long double complex ccosl(long double complex z)
{
return ccoshl(CMPLXL(-cimagl(z), creall(z)));
}
/*
* 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);
}
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. */
}
}
long double complex cacoshl(long double complex z) {
z = cacosl(z);
return CMPLXL(-cimagl(z), creall(z));
}
long double complex cacosl(long double complex z)
{
z = casinl(z);
return CMPLXL(PI_2 - creall(z), -cimagl(z));
}
