#define cimagf(x) __CIMAG(x, float)
#define cimagl(x) __CIMAG(x, long double)
+#define __CMPLX(x, y, t) \
+ ((union { _Complex t __z; t __xy[2]; }){.__xy = {(x),(y)}}.__z)
+
+#if __STDC_VERSION__ >= 201112L
+#define CMPLX(x, y) __CMPLX(x, y, double)
+#define CMPLXF(x, y) __CMPLX(x, y, float)
+#define CMPLXL(x, y) __CMPLX(x, y, long double)
+#endif
+
#ifdef __cplusplus
}
#endif
half_expt = expt - half_expt;
INSERT_WORDS(scale2, (0x3ff + half_expt) << 20, 0);
- return cpack(cos(y) * exp_x * scale1 * scale2, sin(y) * exp_x * scale1 * scale2);
+ return CMPLX(cos(y) * exp_x * scale1 * scale2, sin(y) * exp_x * scale1 * scale2);
}
half_expt = expt - half_expt;
SET_FLOAT_WORD(scale2, (0x7f + half_expt) << 23);
- return cpackf(cosf(y) * exp_x * scale1 * scale2,
+ return CMPLXF(cosf(y) * exp_x * scale1 * scale2,
sinf(y) * exp_x * scale1 * scale2);
}
double complex cacos(double complex z)
{
z = casin(z);
- return cpack(M_PI_2 - creal(z), -cimag(z));
+ return CMPLX(M_PI_2 - creal(z), -cimag(z));
}
float complex cacosf(float complex z)
{
z = casinf(z);
- return cpackf((float)M_PI_2 - crealf(z), -cimagf(z));
+ return CMPLXF((float)M_PI_2 - crealf(z), -cimagf(z));
}
double complex cacosh(double complex z)
{
z = cacos(z);
- return cpack(-cimag(z), creal(z));
+ return CMPLX(-cimag(z), creal(z));
}
float complex cacoshf(float complex z)
{
z = cacosf(z);
- return cpackf(-cimagf(z), crealf(z));
+ return CMPLXF(-cimagf(z), crealf(z));
}
long double complex cacoshl(long double complex z)
{
z = cacosl(z);
- return cpackl(-cimagl(z), creall(z));
+ return CMPLXL(-cimagl(z), creall(z));
}
#endif
long double complex cacosl(long double complex z)
{
z = casinl(z);
- return cpackl(PI_2 - creall(z), -cimagl(z));
+ return CMPLXL(PI_2 - creall(z), -cimagl(z));
}
#endif
x = creal(z);
y = cimag(z);
- w = cpack(1.0 - (x - y)*(x + y), -2.0*x*y);
- return clog(cpack(-y, x) + csqrt(w));
+ w = CMPLX(1.0 - (x - y)*(x + y), -2.0*x*y);
+ return clog(CMPLX(-y, x) + csqrt(w));
}
x = crealf(z);
y = cimagf(z);
- w = cpackf(1.0 - (x - y)*(x + y), -2.0*x*y);
- return clogf(cpackf(-y, x) + csqrtf(w));
+ w = CMPLXF(1.0 - (x - y)*(x + y), -2.0*x*y);
+ return clogf(CMPLXF(-y, x) + csqrtf(w));
}
double complex casinh(double complex z)
{
- z = casin(cpack(-cimag(z), creal(z)));
- return cpack(cimag(z), -creal(z));
+ z = casin(CMPLX(-cimag(z), creal(z)));
+ return CMPLX(cimag(z), -creal(z));
}
float complex casinhf(float complex z)
{
- z = casinf(cpackf(-cimagf(z), crealf(z)));
- return cpackf(cimagf(z), -crealf(z));
+ z = casinf(CMPLXF(-cimagf(z), crealf(z)));
+ return CMPLXF(cimagf(z), -crealf(z));
}
#else
long double complex casinhl(long double complex z)
{
- z = casinl(cpackl(-cimagl(z), creall(z)));
- return cpackl(cimagl(z), -creall(z));
+ z = casinl(CMPLXL(-cimagl(z), creall(z)));
+ return CMPLXL(cimagl(z), -creall(z));
}
#endif
x = creall(z);
y = cimagl(z);
- w = cpackl(1.0 - (x - y)*(x + y), -2.0*x*y);
- return clogl(cpackl(-y, x) + csqrtl(w));
+ w = CMPLXL(1.0 - (x - y)*(x + y), -2.0*x*y);
+ return clogl(CMPLXL(-y, x) + csqrtl(w));
}
#endif
double complex catanh(double complex z)
{
- z = catan(cpack(-cimag(z), creal(z)));
- return cpack(cimag(z), -creal(z));
+ z = catan(CMPLX(-cimag(z), creal(z)));
+ return CMPLX(cimag(z), -creal(z));
}
float complex catanhf(float complex z)
{
- z = catanf(cpackf(-cimagf(z), crealf(z)));
- return cpackf(cimagf(z), -crealf(z));
+ z = catanf(CMPLXF(-cimagf(z), crealf(z)));
+ return CMPLXF(cimagf(z), -crealf(z));
}
#else
long double complex catanhl(long double complex z)
{
- z = catanl(cpackl(-cimagl(z), creall(z)));
- return cpackl(cimagl(z), -creall(z));
+ z = catanl(CMPLXL(-cimagl(z), creall(z)));
+ return CMPLXL(cimagl(z), -creall(z));
}
#endif
double complex ccos(double complex z)
{
- return ccosh(cpack(-cimag(z), creal(z)));
+ return ccosh(CMPLX(-cimag(z), creal(z)));
}
float complex ccosf(float complex z)
{
- return ccoshf(cpackf(-cimagf(z), crealf(z)));
+ return ccoshf(CMPLXF(-cimagf(z), crealf(z)));
}
/* Handle the nearly-non-exceptional cases where x and y are finite. */
if (ix < 0x7ff00000 && iy < 0x7ff00000) {
if ((iy | ly) == 0)
- return cpack(cosh(x), x * y);
+ return CMPLX(cosh(x), x * y);
if (ix < 0x40360000) /* small x: normal case */
- return cpack(cosh(x) * cos(y), sinh(x) * sin(y));
+ return CMPLX(cosh(x) * cos(y), sinh(x) * sin(y));
/* |x| >= 22, so cosh(x) ~= exp(|x|) */
if (ix < 0x40862e42) {
/* x < 710: exp(|x|) won't overflow */
h = exp(fabs(x)) * 0.5;
- return cpack(h * cos(y), copysign(h, x) * sin(y));
+ return CMPLX(h * cos(y), copysign(h, x) * sin(y));
} else if (ix < 0x4096bbaa) {
/* x < 1455: scale to avoid overflow */
- z = __ldexp_cexp(cpack(fabs(x), y), -1);
- return cpack(creal(z), cimag(z) * copysign(1, x));
+ z = __ldexp_cexp(CMPLX(fabs(x), y), -1);
+ return CMPLX(creal(z), cimag(z) * copysign(1, x));
} else {
/* x >= 1455: the result always overflows */
h = huge * x;
- return cpack(h * h * cos(y), h * sin(y));
+ return CMPLX(h * h * cos(y), h * sin(y));
}
}
* the same as d(NaN).
*/
if ((ix | lx) == 0 && iy >= 0x7ff00000)
- return cpack(y - y, copysign(0, x * (y - y)));
+ return CMPLX(y - y, copysign(0, x * (y - y)));
/*
* cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0.
*/
if ((iy | ly) == 0 && ix >= 0x7ff00000) {
if (((hx & 0xfffff) | lx) == 0)
- return cpack(x * x, copysign(0, x) * y);
- return cpack(x * x, copysign(0, (x + x) * y));
+ return CMPLX(x * x, copysign(0, x) * y);
+ return CMPLX(x * x, copysign(0, (x + x) * y));
}
/*
* nonzero x. Choice = don't raise (except for signaling NaNs).
*/
if (ix < 0x7ff00000 && iy >= 0x7ff00000)
- return cpack(y - y, x * (y - y));
+ return CMPLX(y - y, x * (y - y));
/*
* cosh(+-Inf + I NaN) = +Inf + I d(NaN).
*/
if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
if (iy >= 0x7ff00000)
- return cpack(x * x, x * (y - y));
- return cpack((x * x) * cos(y), x * sin(y));
+ return CMPLX(x * x, x * (y - y));
+ return CMPLX((x * x) * cos(y), x * sin(y));
}
/*
* Optionally raises the invalid floating-point exception for finite
* nonzero y. Choice = don't raise (except for signaling NaNs).
*/
- return cpack((x * x) * (y - y), (x + x) * (y - y));
+ return CMPLX((x * x) * (y - y), (x + x) * (y - y));
}
if (ix < 0x7f800000 && iy < 0x7f800000) {
if (iy == 0)
- return cpackf(coshf(x), x * y);
+ return CMPLXF(coshf(x), x * y);
if (ix < 0x41100000) /* small x: normal case */
- return cpackf(coshf(x) * cosf(y), sinhf(x) * sinf(y));
+ return CMPLXF(coshf(x) * cosf(y), sinhf(x) * sinf(y));
/* |x| >= 9, so cosh(x) ~= exp(|x|) */
if (ix < 0x42b17218) {
/* x < 88.7: expf(|x|) won't overflow */
h = expf(fabsf(x)) * 0.5f;
- return cpackf(h * cosf(y), copysignf(h, x) * sinf(y));
+ return CMPLXF(h * cosf(y), copysignf(h, x) * sinf(y));
} else if (ix < 0x4340b1e7) {
/* x < 192.7: scale to avoid overflow */
- z = __ldexp_cexpf(cpackf(fabsf(x), y), -1);
- return cpackf(crealf(z), cimagf(z) * copysignf(1, x));
+ z = __ldexp_cexpf(CMPLXF(fabsf(x), y), -1);
+ return CMPLXF(crealf(z), cimagf(z) * copysignf(1, x));
} else {
/* x >= 192.7: the result always overflows */
h = huge * x;
- return cpackf(h * h * cosf(y), h * sinf(y));
+ return CMPLXF(h * h * cosf(y), h * sinf(y));
}
}
if (ix == 0 && iy >= 0x7f800000)
- return cpackf(y - y, copysignf(0, x * (y - y)));
+ return CMPLXF(y - y, copysignf(0, x * (y - y)));
if (iy == 0 && ix >= 0x7f800000) {
if ((hx & 0x7fffff) == 0)
- return cpackf(x * x, copysignf(0, x) * y);
- return cpackf(x * x, copysignf(0, (x + x) * y));
+ return CMPLXF(x * x, copysignf(0, x) * y);
+ return CMPLXF(x * x, copysignf(0, (x + x) * y));
}
if (ix < 0x7f800000 && iy >= 0x7f800000)
- return cpackf(y - y, x * (y - y));
+ return CMPLXF(y - y, x * (y - y));
if (ix >= 0x7f800000 && (hx & 0x7fffff) == 0) {
if (iy >= 0x7f800000)
- return cpackf(x * x, x * (y - y));
- return cpackf((x * x) * cosf(y), x * sinf(y));
+ return CMPLXF(x * x, x * (y - y));
+ return CMPLXF((x * x) * cosf(y), x * sinf(y));
}
- return cpackf((x * x) * (y - y), (x + x) * (y - y));
+ return CMPLXF((x * x) * (y - y), (x + x) * (y - y));
}
#else
long double complex ccosl(long double complex z)
{
- return ccoshl(cpackl(-cimagl(z), creall(z)));
+ return ccoshl(CMPLXL(-cimagl(z), creall(z)));
}
#endif
/* cexp(x + I 0) = exp(x) + I 0 */
if ((hy | ly) == 0)
- return cpack(exp(x), y);
+ return CMPLX(exp(x), y);
EXTRACT_WORDS(hx, lx, x);
/* cexp(0 + I y) = cos(y) + I sin(y) */
if (((hx & 0x7fffffff) | lx) == 0)
- return cpack(cos(y), sin(y));
+ return CMPLX(cos(y), sin(y));
if (hy >= 0x7ff00000) {
if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) {
/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
- return cpack(y - y, y - y);
+ return CMPLX(y - y, y - y);
} else if (hx & 0x80000000) {
/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
- return cpack(0.0, 0.0);
+ return CMPLX(0.0, 0.0);
} else {
/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
- return cpack(x, y - y);
+ return CMPLX(x, y - y);
}
}
* - x = NaN (spurious inexact exception from y)
*/
exp_x = exp(x);
- return cpack(exp_x * cos(y), exp_x * sin(y));
+ return CMPLX(exp_x * cos(y), exp_x * sin(y));
}
}
/* cexp(x + I 0) = exp(x) + I 0 */
if (hy == 0)
- return cpackf(expf(x), y);
+ return CMPLXF(expf(x), y);
GET_FLOAT_WORD(hx, x);
/* cexp(0 + I y) = cos(y) + I sin(y) */
if ((hx & 0x7fffffff) == 0)
- return cpackf(cosf(y), sinf(y));
+ return CMPLXF(cosf(y), sinf(y));
if (hy >= 0x7f800000) {
if ((hx & 0x7fffffff) != 0x7f800000) {
/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
- return cpackf(y - y, y - y);
+ return CMPLXF(y - y, y - y);
} else if (hx & 0x80000000) {
/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
- return cpackf(0.0, 0.0);
+ return CMPLXF(0.0, 0.0);
} else {
/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
- return cpackf(x, y - y);
+ return CMPLXF(x, y - y);
}
}
* - x = NaN (spurious inexact exception from y)
*/
exp_x = expf(x);
- return cpackf(exp_x * cosf(y), exp_x * sinf(y));
+ return CMPLXF(exp_x * cosf(y), exp_x * sinf(y));
}
}
r = cabs(z);
phi = carg(z);
- return cpack(log(r), phi);
+ return CMPLX(log(r), phi);
}
r = cabsf(z);
phi = cargf(z);
- return cpackf(logf(r), phi);
+ return CMPLXF(logf(r), phi);
}
r = cabsl(z);
phi = cargl(z);
- return cpackl(logl(r), phi);
+ return CMPLXL(logl(r), phi);
}
#endif
double complex conj(double complex z)
{
- return cpack(creal(z), -cimag(z));
+ return CMPLX(creal(z), -cimag(z));
}
float complex conjf(float complex z)
{
- return cpackf(crealf(z), -cimagf(z));
+ return CMPLXF(crealf(z), -cimagf(z));
}
long double complex conjl(long double complex z)
{
- return cpackl(creall(z), -cimagl(z));
+ return CMPLXL(creall(z), -cimagl(z));
}
double complex cproj(double complex z)
{
if (isinf(creal(z)) || isinf(cimag(z)))
- return cpack(INFINITY, copysign(0.0, creal(z)));
+ return CMPLX(INFINITY, copysign(0.0, creal(z)));
return z;
}
float complex cprojf(float complex z)
{
if (isinf(crealf(z)) || isinf(cimagf(z)))
- return cpackf(INFINITY, copysignf(0.0, crealf(z)));
+ return CMPLXF(INFINITY, copysignf(0.0, crealf(z)));
return z;
}
long double complex cprojl(long double complex z)
{
if (isinf(creall(z)) || isinf(cimagl(z)))
- return cpackl(INFINITY, copysignl(0.0, creall(z)));
+ return CMPLXL(INFINITY, copysignl(0.0, creall(z)));
return z;
}
#endif
double complex csin(double complex z)
{
- z = csinh(cpack(-cimag(z), creal(z)));
- return cpack(cimag(z), -creal(z));
+ z = csinh(CMPLX(-cimag(z), creal(z)));
+ return CMPLX(cimag(z), -creal(z));
}
float complex csinf(float complex z)
{
- z = csinhf(cpackf(-cimagf(z), crealf(z)));
- return cpackf(cimagf(z), -crealf(z));
+ z = csinhf(CMPLXF(-cimagf(z), crealf(z)));
+ return CMPLXF(cimagf(z), -crealf(z));
}
/* Handle the nearly-non-exceptional cases where x and y are finite. */
if (ix < 0x7ff00000 && iy < 0x7ff00000) {
if ((iy | ly) == 0)
- return cpack(sinh(x), y);
+ return CMPLX(sinh(x), y);
if (ix < 0x40360000) /* small x: normal case */
- return cpack(sinh(x) * cos(y), cosh(x) * sin(y));
+ return CMPLX(sinh(x) * cos(y), cosh(x) * sin(y));
/* |x| >= 22, so cosh(x) ~= exp(|x|) */
if (ix < 0x40862e42) {
/* x < 710: exp(|x|) won't overflow */
h = exp(fabs(x)) * 0.5;
- return cpack(copysign(h, x) * cos(y), h * sin(y));
+ return CMPLX(copysign(h, x) * cos(y), h * sin(y));
} else if (ix < 0x4096bbaa) {
/* x < 1455: scale to avoid overflow */
- z = __ldexp_cexp(cpack(fabs(x), y), -1);
- return cpack(creal(z) * copysign(1, x), cimag(z));
+ z = __ldexp_cexp(CMPLX(fabs(x), y), -1);
+ return CMPLX(creal(z) * copysign(1, x), cimag(z));
} else {
/* x >= 1455: the result always overflows */
h = huge * x;
- return cpack(h * cos(y), h * h * sin(y));
+ return CMPLX(h * cos(y), h * h * sin(y));
}
}
* the same as d(NaN).
*/
if ((ix | lx) == 0 && iy >= 0x7ff00000)
- return cpack(copysign(0, x * (y - y)), y - y);
+ return CMPLX(copysign(0, x * (y - y)), y - y);
/*
* sinh(+-Inf +- I 0) = +-Inf + I +-0.
*/
if ((iy | ly) == 0 && ix >= 0x7ff00000) {
if (((hx & 0xfffff) | lx) == 0)
- return cpack(x, y);
- return cpack(x, copysign(0, y));
+ return CMPLX(x, y);
+ return CMPLX(x, copysign(0, y));
}
/*
* nonzero x. Choice = don't raise (except for signaling NaNs).
*/
if (ix < 0x7ff00000 && iy >= 0x7ff00000)
- return cpack(y - y, x * (y - y));
+ return CMPLX(y - y, x * (y - y));
/*
* sinh(+-Inf + I NaN) = +-Inf + I d(NaN).
*/
if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
if (iy >= 0x7ff00000)
- return cpack(x * x, x * (y - y));
- return cpack(x * cos(y), INFINITY * sin(y));
+ return CMPLX(x * x, x * (y - y));
+ return CMPLX(x * cos(y), INFINITY * sin(y));
}
/*
* Optionally raises the invalid floating-point exception for finite
* nonzero y. Choice = don't raise (except for signaling NaNs).
*/
- return cpack((x * x) * (y - y), (x + x) * (y - y));
+ return CMPLX((x * x) * (y - y), (x + x) * (y - y));
}
if (ix < 0x7f800000 && iy < 0x7f800000) {
if (iy == 0)
- return cpackf(sinhf(x), y);
+ return CMPLXF(sinhf(x), y);
if (ix < 0x41100000) /* small x: normal case */
- return cpackf(sinhf(x) * cosf(y), coshf(x) * sinf(y));
+ return CMPLXF(sinhf(x) * cosf(y), coshf(x) * sinf(y));
/* |x| >= 9, so cosh(x) ~= exp(|x|) */
if (ix < 0x42b17218) {
/* x < 88.7: expf(|x|) won't overflow */
h = expf(fabsf(x)) * 0.5f;
- return cpackf(copysignf(h, x) * cosf(y), h * sinf(y));
+ return CMPLXF(copysignf(h, x) * cosf(y), h * sinf(y));
} else if (ix < 0x4340b1e7) {
/* x < 192.7: scale to avoid overflow */
- z = __ldexp_cexpf(cpackf(fabsf(x), y), -1);
- return cpackf(crealf(z) * copysignf(1, x), cimagf(z));
+ z = __ldexp_cexpf(CMPLXF(fabsf(x), y), -1);
+ return CMPLXF(crealf(z) * copysignf(1, x), cimagf(z));
} else {
/* x >= 192.7: the result always overflows */
h = huge * x;
- return cpackf(h * cosf(y), h * h * sinf(y));
+ return CMPLXF(h * cosf(y), h * h * sinf(y));
}
}
if (ix == 0 && iy >= 0x7f800000)
- return cpackf(copysignf(0, x * (y - y)), y - y);
+ return CMPLXF(copysignf(0, x * (y - y)), y - y);
if (iy == 0 && ix >= 0x7f800000) {
if ((hx & 0x7fffff) == 0)
- return cpackf(x, y);
- return cpackf(x, copysignf(0, y));
+ return CMPLXF(x, y);
+ return CMPLXF(x, copysignf(0, y));
}
if (ix < 0x7f800000 && iy >= 0x7f800000)
- return cpackf(y - y, x * (y - y));
+ return CMPLXF(y - y, x * (y - y));
if (ix >= 0x7f800000 && (hx & 0x7fffff) == 0) {
if (iy >= 0x7f800000)
- return cpackf(x * x, x * (y - y));
- return cpackf(x * cosf(y), INFINITY * sinf(y));
+ return CMPLXF(x * x, x * (y - y));
+ return CMPLXF(x * cosf(y), INFINITY * sinf(y));
}
- return cpackf((x * x) * (y - y), (x + x) * (y - y));
+ return CMPLXF((x * x) * (y - y), (x + x) * (y - y));
}
#else
long double complex csinl(long double complex z)
{
- z = csinhl(cpackl(-cimagl(z), creall(z)));
- return cpackl(cimagl(z), -creall(z));
+ z = csinhl(CMPLXL(-cimagl(z), creall(z)));
+ return CMPLXL(cimagl(z), -creall(z));
}
#endif
/* Handle special cases. */
if (z == 0)
- return cpack(0, b);
+ return CMPLX(0, b);
if (isinf(b))
- return cpack(INFINITY, b);
+ return CMPLX(INFINITY, b);
if (isnan(a)) {
t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
- return cpack(a, t); /* return NaN + NaN i */
+ return CMPLX(a, t); /* return NaN + NaN i */
}
if (isinf(a)) {
/*
* csqrt(-inf + y i) = 0 + inf i
*/
if (signbit(a))
- return cpack(fabs(b - b), copysign(a, b));
+ return CMPLX(fabs(b - b), copysign(a, b));
else
- return cpack(a, copysign(b - b, b));
+ return CMPLX(a, copysign(b - b, b));
}
/*
* The remaining special case (b is NaN) is handled just fine by
/* Algorithm 312, CACM vol 10, Oct 1967. */
if (a >= 0) {
t = sqrt((a + hypot(a, b)) * 0.5);
- result = cpack(t, b / (2 * t));
+ result = CMPLX(t, b / (2 * t));
} else {
t = sqrt((-a + hypot(a, b)) * 0.5);
- result = cpack(fabs(b) / (2 * t), copysign(t, b));
+ result = CMPLX(fabs(b) / (2 * t), copysign(t, b));
}
/* Rescale. */
/* Handle special cases. */
if (z == 0)
- return cpackf(0, b);
+ return CMPLXF(0, b);
if (isinf(b))
- return cpackf(INFINITY, b);
+ return CMPLXF(INFINITY, b);
if (isnan(a)) {
t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
- return cpackf(a, t); /* return NaN + NaN i */
+ return CMPLXF(a, t); /* return NaN + NaN i */
}
if (isinf(a)) {
/*
* csqrtf(-inf + y i) = 0 + inf i
*/
if (signbit(a))
- return cpackf(fabsf(b - b), copysignf(a, b));
+ return CMPLXF(fabsf(b - b), copysignf(a, b));
else
- return cpackf(a, copysignf(b - b, b));
+ return CMPLXF(a, copysignf(b - b, b));
}
/*
* The remaining special case (b is NaN) is handled just fine by
*/
if (a >= 0) {
t = sqrt((a + hypot(a, b)) * 0.5);
- return cpackf(t, b / (2.0 * t));
+ return CMPLXF(t, b / (2.0 * t));
} else {
t = sqrt((-a + hypot(a, b)) * 0.5);
- return cpackf(fabsf(b) / (2.0 * t), copysignf(t, b));
+ return CMPLXF(fabsf(b) / (2.0 * t), copysignf(t, b));
}
}
double complex ctan(double complex z)
{
- z = ctanh(cpack(-cimag(z), creal(z)));
- return cpack(cimag(z), -creal(z));
+ z = ctanh(CMPLX(-cimag(z), creal(z)));
+ return CMPLX(cimag(z), -creal(z));
}
float complex ctanf(float complex z)
{
- z = ctanhf(cpackf(-cimagf(z), crealf(z)));
- return cpackf(cimagf(z), -crealf(z));
+ z = ctanhf(CMPLXF(-cimagf(z), crealf(z)));
+ return CMPLXF(cimagf(z), -crealf(z));
}
*/
if (ix >= 0x7ff00000) {
if ((ix & 0xfffff) | lx) /* x is NaN */
- return cpack(x, (y == 0 ? y : x * y));
+ return CMPLX(x, (y == 0 ? y : x * y));
SET_HIGH_WORD(x, hx - 0x40000000); /* x = copysign(1, x) */
- return cpack(x, copysign(0, isinf(y) ? y : sin(y) * cos(y)));
+ return CMPLX(x, copysign(0, isinf(y) ? y : sin(y) * cos(y)));
}
/*
* ctanh(x +- i Inf) = NaN + i NaN
*/
if (!isfinite(y))
- return cpack(y - y, y - y);
+ return CMPLX(y - y, y - y);
/*
* ctanh(+-huge + i +-y) ~= +-1 +- i 2sin(2y)/exp(2x), using the
*/
if (ix >= 0x40360000) { /* x >= 22 */
double exp_mx = exp(-fabs(x));
- return cpack(copysign(1, x), 4 * sin(y) * cos(y) * exp_mx * exp_mx);
+ return CMPLX(copysign(1, x), 4 * sin(y) * cos(y) * exp_mx * exp_mx);
}
/* Kahan's algorithm */
s = sinh(x);
rho = sqrt(1 + s * s); /* = cosh(x) */
denom = 1 + beta * s * s;
- return cpack((beta * rho * s) / denom, t / denom);
+ return CMPLX((beta * rho * s) / denom, t / denom);
}
if (ix >= 0x7f800000) {
if (ix & 0x7fffff)
- return cpackf(x, (y == 0 ? y : x * y));
+ return CMPLXF(x, (y == 0 ? y : x * y));
SET_FLOAT_WORD(x, hx - 0x40000000);
- return cpackf(x, copysignf(0, isinf(y) ? y : sinf(y) * cosf(y)));
+ return CMPLXF(x, copysignf(0, isinf(y) ? y : sinf(y) * cosf(y)));
}
if (!isfinite(y))
- return cpackf(y - y, y - y);
+ return CMPLXF(y - y, y - y);
if (ix >= 0x41300000) { /* x >= 11 */
float exp_mx = expf(-fabsf(x));
- return cpackf(copysignf(1, x), 4 * sinf(y) * cosf(y) * exp_mx * exp_mx);
+ return CMPLXF(copysignf(1, x), 4 * sinf(y) * cosf(y) * exp_mx * exp_mx);
}
t = tanf(y);
s = sinhf(x);
rho = sqrtf(1 + s * s);
denom = 1 + beta * s * s;
- return cpackf((beta * rho * s) / denom, t / denom);
+ return CMPLXF((beta * rho * s) / denom, t / denom);
}
#else
long double complex ctanl(long double complex z)
{
- z = ctanhl(cpackl(-cimagl(z), creall(z)));
- return cpackl(cimagl(z), -creall(z));
+ z = ctanhl(CMPLXL(-cimagl(z), creall(z)));
+ return CMPLXL(cimagl(z), -creall(z));
}
#endif
#define STRICT_ASSIGN(type, lval, rval) ((lval) = (type)(rval))
#endif
-
/* complex */
-union dcomplex {
- double complex z;
- double a[2];
-};
-union fcomplex {
- float complex z;
- float a[2];
-};
-union lcomplex {
- long double complex z;
- long double a[2];
-};
-
-/* x + y*I is not supported properly by gcc */
-#define cpack(x,y) ((union dcomplex){.a={(x),(y)}}.z)
-#define cpackf(x,y) ((union fcomplex){.a={(x),(y)}}.z)
-#define cpackl(x,y) ((union lcomplex){.a={(x),(y)}}.z)
+#ifndef CMPLX
+#define CMPLX(x, y) __CMPLX(x, y, double)
+#define CMPLXF(x, y) __CMPLX(x, y, float)
+#define CMPLXL(x, y) __CMPLX(x, y, long double)
+#endif
#endif
projects / musl / commitdiff