#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
int fegetround(void)
{
- return 0;
+ return FE_TONEAREST;
}
int fesetround(int r)
int feupdateenv(const fenv_t *envp)
{
+ #pragma STDC FENV_ACCESS ON
int ex = fetestexcept(FE_ALL_EXCEPT);
fesetenv(envp);
feraiseexcept(ex);
long double __polevll(long double, const long double *, int);
long double __p1evll(long double, const long double *, int);
-// FIXME: not needed when -fexcess-precision=standard is supported (>=gcc4.5)
-/*
- * Attempt to get strict C99 semantics for assignment with non-C99 compilers.
- */
-#if 1
+#if 0
+/* Attempt to get strict C99 semantics for assignment with non-C99 compilers. */
#define STRICT_ASSIGN(type, lval, rval) do { \
volatile type __v = (rval); \
(lval) = __v; \
} while (0)
#else
+/* Should work with -fexcess-precision=standard (>=gcc-4.5) or -ffloat-store */
#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
#include "__invtrigl.h"
#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
-/*
- * asinl() and acosl()
- */
+
+/* coefficients used in asinl() and acosl() */
const long double
pS0 = 1.66666666666666666631e-01L,
pS1 = -4.16313987993683104320e-01L,
qS4 = 3.90699412641738801874e-01L,
qS5 = -3.14365703596053263322e-02L;
-/*
- * atanl()
- */
-const long double atanhi[] = {
- 4.63647609000806116202e-01L,
- 7.85398163397448309628e-01L,
- 9.82793723247329067960e-01L,
- 1.57079632679489661926e+00L,
-};
-
-const long double atanlo[] = {
- 1.18469937025062860669e-20L,
- -1.25413940316708300586e-20L,
- 2.55232234165405176172e-20L,
- -2.50827880633416601173e-20L,
-};
-
-const long double aT[] = {
- 3.33333333333333333017e-01L,
- -1.99999999999999632011e-01L,
- 1.42857142857046531280e-01L,
- -1.11111111100562372733e-01L,
- 9.09090902935647302252e-02L,
- -7.69230552476207730353e-02L,
- 6.66661718042406260546e-02L,
- -5.88158892835030888692e-02L,
- 5.25499891539726639379e-02L,
- -4.70119845393155721494e-02L,
- 4.03539201366454414072e-02L,
- -2.91303858419364158725e-02L,
- 1.24822046299269234080e-02L,
-};
-
+const long double pi_hi = 3.1415926535897932384626433832795L;
const long double pi_lo = -5.01655761266833202345e-20L;
+const long double pio2_hi = 1.57079632679489661926L;
+const long double pio2_lo = -2.50827880633416601173e-20L;
+
#endif
#define BIAS (LDBL_MAX_EXP - 1)
#define MANH_SIZE LDBL_MANH_SIZE
-/* Approximation thresholds. */
-#define ASIN_LINEAR (BIAS - 32) /* 2**-32 */
-#define ACOS_CONST (BIAS - 65) /* 2**-65 */
-#define ATAN_CONST (BIAS + 65) /* 2**65 */
-#define ATAN_LINEAR (BIAS - 32) /* 2**-32 */
-
-/* 0.95 */
-#define THRESH ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT)
-
/* Constants shared by the long double inverse trig functions. */
#define pS0 __pS0
#define pS1 __pS1
#define qS3 __qS3
#define qS4 __qS4
#define qS5 __qS5
-#define atanhi __atanhi
-#define atanlo __atanlo
-#define aT __aT
+#define pi_hi __pi_hi
#define pi_lo __pi_lo
+#define pio2_hi __pio2_hi
+#define pio2_lo __pio2_lo
-#define pio2_hi atanhi[3]
-#define pio2_lo atanlo[3]
-#define pio4_hi atanhi[1]
-
-#ifdef STRUCT_DECLS
-typedef struct longdouble {
- uint64_t mant;
- uint16_t expsign;
-} LONGDOUBLE;
-#else
-typedef long double LONGDOUBLE;
-#endif
-
-extern const LONGDOUBLE pS0, pS1, pS2, pS3, pS4, pS5, pS6;
-extern const LONGDOUBLE qS1, qS2, qS3, qS4, qS5;
-extern const LONGDOUBLE atanhi[], atanlo[], aT[];
-extern const LONGDOUBLE pi_lo;
-
-#ifndef STRUCT_DECLS
-static inline long double
-P(long double x)
-{
- return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
- (pS4 + x * (pS5 + x * pS6)))))));
-}
-
-static inline long double
-Q(long double x)
-{
- return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * qS5)))));
-}
+extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6;
+extern const long double qS1, qS2, qS3, qS4, qS5;
+extern const long double pi_hi, pi_lo, pio2_hi, pio2_lo;
-static inline long double
-T_even(long double x)
+static long double P(long double x)
{
- return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \
- (aT[8] + x * (aT[10] + x * aT[12]))))));
+ return x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 +
+ x * (pS4 + x * (pS5 + x * pS6))))));
}
-static inline long double
-T_odd(long double x)
+static long double Q(long double x)
{
- return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \
- (aT[9] + x * aT[11])))));
+ return 1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * qS5))));
}
-#endif
#endif
static const double
pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
pio2_hi = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */
+// FIXME
static const volatile double
pio2_lo = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */
static const double
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#include "__invtrigl.h"
-
-static const long double
-pi = 3.14159265358979323846264338327950280e+00L;
+#define ACOS_CONST (BIAS - 65) /* 2**-65 */
long double acosl(long double x)
{
if (expsign > 0)
return 0.0; /* acos(1) = 0 */
else
- return pi + 2.0 * pio2_lo; /* acos(-1)= pi */
+ // FIXME
+ return pi_hi + 2.0 * pio2_lo; /* acos(-1)= pi */
}
return (x - x) / (x - x); /* acos(|x|>1) is NaN */
}
s = sqrtl(z);
r = p / q;
w = r * s - pio2_lo;
- return pi - 2.0 * (s + w);
+ return pi_hi - 2.0 * (s + w);
} else { /* x > 0.5 */
z = (1.0 - x) * 0.5;
s = sqrtl(z);
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#include "__invtrigl.h"
static const long double huge = 1.000e+300;
+static const long double pio4_hi = 7.85398163397448309628e-01L;
+#define ASIN_LINEAR (BIAS - 32) /* 2**-32 */
+/* 0.95 */
+#define THRESH ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT)
long double asinl(long double x)
{
#include "libm.h"
+// FIXME
static const volatile double
tiny = 1.0e-300;
static const double
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#include "__invtrigl.h"
-static const volatile long double
-tiny = 1.0e-300;
-static const long double
-pi = 3.14159265358979323846264338327950280e+00L;
+// FIXME:
+static const volatile long double tiny = 1.0e-300;
long double atan2l(long double y, long double x)
{
if (expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==0) {
switch(m) {
case 0:
- case 1: return y; /* atan(+-0,+anything)=+-0 */
- case 2: return pi+tiny; /* atan(+0,-anything) = pi */
- case 3: return -pi-tiny; /* atan(-0,-anything) =-pi */
+ case 1: return y; /* atan(+-0,+anything)=+-0 */
+ case 2: return pi_hi+tiny; /* atan(+0,-anything) = pi */
+ case 3: return -pi_hi-tiny; /* atan(-0,-anything) =-pi */
}
}
/* when x = 0 */
switch(m) {
case 0: return pio2_hi*0.5+tiny; /* atan(+INF,+INF) */
case 1: return -pio2_hi*0.5-tiny; /* atan(-INF,+INF) */
- case 2: return 1.5*pio2_hi+tiny; /*atan(+INF,-INF)*/
- case 3: return -1.5*pio2_hi-tiny; /*atan(-INF,-INF)*/
+ case 2: return 1.5*pio2_hi+tiny; /* atan(+INF,-INF) */
+ case 3: return -1.5*pio2_hi-tiny; /* atan(-INF,-INF) */
}
} else {
switch(m) {
- case 0: return 0.0; /* atan(+...,+INF) */
- case 1: return -0.0; /* atan(-...,+INF) */
- case 2: return pi+tiny; /* atan(+...,-INF) */
- case 3: return -pi-tiny; /* atan(-...,-INF) */
+ case 0: return 0.0; /* atan(+...,+INF) */
+ case 1: return -0.0; /* atan(-...,+INF) */
+ case 2: return pi_hi+tiny; /* atan(+...,-INF) */
+ case 3: return -pi_hi-tiny; /* atan(-...,-INF) */
}
}
}
else /* safe to do y/x */
z = atanl(fabsl(y/x));
switch (m) {
- case 0: return z; /* atan(+,+) */
- case 1: return -z; /* atan(-,+) */
- case 2: return pi - (z-pi_lo); /* atan(+,-) */
+ case 0: return z; /* atan(+,+) */
+ case 1: return -z; /* atan(-,+) */
+ case 2: return pi_hi-(z-pi_lo); /* atan(+,-) */
default: /* case 3 */
- return (z-pi_lo) - pi; /* atan(-,-) */
+ return (z-pi_lo)-pi_hi; /* atan(-,-) */
}
}
#endif
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#include "__invtrigl.h"
+
+#define ATAN_CONST (BIAS + 65) /* 2**65 */
+#define ATAN_LINEAR (BIAS - 32) /* 2**-32 */
static const long double huge = 1.0e300;
+static const long double atanhi[] = {
+ 4.63647609000806116202e-01L,
+ 7.85398163397448309628e-01L,
+ 9.82793723247329067960e-01L,
+ 1.57079632679489661926e+00L,
+};
+
+static const long double atanlo[] = {
+ 1.18469937025062860669e-20L,
+ -1.25413940316708300586e-20L,
+ 2.55232234165405176172e-20L,
+ -2.50827880633416601173e-20L,
+};
+
+static const long double aT[] = {
+ 3.33333333333333333017e-01L,
+ -1.99999999999999632011e-01L,
+ 1.42857142857046531280e-01L,
+ -1.11111111100562372733e-01L,
+ 9.09090902935647302252e-02L,
+ -7.69230552476207730353e-02L,
+ 6.66661718042406260546e-02L,
+ -5.88158892835030888692e-02L,
+ 5.25499891539726639379e-02L,
+ -4.70119845393155721494e-02L,
+ 4.03539201366454414072e-02L,
+ -2.91303858419364158725e-02L,
+ 1.24822046299269234080e-02L,
+};
+
+static long double T_even(long double x)
+{
+ return aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] +
+ x * (aT[8] + x * (aT[10] + x * aT[12])))));
+}
+
+static long double T_odd(long double x)
+{
+ return aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] +
+ x * (aT[9] + x * aT[11]))));
+}
+
long double atanl(long double x)
{
union IEEEl2bits u;
long double exp10l(long double x)
{
static const long double p10[] = {
- 1e-15, 1e-14, 1e-13, 1e-12, 1e-11, 1e-10,
- 1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1,
+ 1e-15L, 1e-14L, 1e-13L, 1e-12L, 1e-11L, 1e-10L,
+ 1e-9L, 1e-8L, 1e-7L, 1e-6L, 1e-5L, 1e-4L, 1e-3L, 1e-2L, 1e-1L,
1, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1e10, 1e11, 1e12, 1e13, 1e14, 1e15
};
*
* Relative error:
* arithmetic domain # trials peak rms
- * IEEE -45,+MAXLOG 200,000 1.2e-19 2.5e-20
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * expm1l overflow x > MAXLOG MAXNUM
- *
+ * IEEE -45,+maxarg 200,000 1.2e-19 2.5e-20
*/
#include "libm.h"
return expm1(x);
}
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
-static const long double MAXLOGL = 1.1356523406294143949492E4L;
/* exp(x) - 1 = x + 0.5 x^2 + x^3 P(x)/Q(x)
-.5 ln 2 < x < .5 ln 2
C2 = 1.428606820309417232121458176568075500134E-6L,
/* ln 2^-65 */
minarg = -4.5054566736396445112120088E1L,
-huge = 0x1p10000L;
+/* ln 2^16384 */
+maxarg = 1.1356523406294143949492E4L;
long double expm1l(long double x)
{
long double px, qx, xx;
int k;
- /* Overflow. */
- if (x > MAXLOGL)
- return huge*huge; /* overflow */
+ if (isnan(x))
+ return x;
+ if (x > maxarg)
+ return x*0x1p16383L; /* overflow, unless x==inf */
if (x == 0.0)
return x;
- /* Minimum value.*/
if (x < minarg)
return -1.0;
double fma(double x, double y, double z)
{
+ #pragma STDC FENV_ACCESS ON
long double hi, lo1, lo2, xy;
int round, ez, exy;
*/
double fma(double x, double y, double z)
{
+ #pragma STDC FENV_ACCESS ON
double xs, ys, zs, adj;
struct dd xy, r;
int oround;
*/
float fmaf(float x, float y, float z)
{
+ #pragma STDC FENV_ACCESS ON
double xy, result;
uint32_t hr, lr;
*/
long double fmal(long double x, long double y, long double z)
{
+ #pragma STDC FENV_ACCESS ON
long double xs, ys, zs, adj;
struct dd xy, r;
int oround;
t2 = a - t1;
w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
- if (k != 0) {
- uint32_t high;
- t1 = 1.0;
- GET_HIGH_WORD(high, t1);
- SET_HIGH_WORD(t1, high+(k<<20));
- return t1*w;
- }
+ if (k)
+ w = scalbn(w, k);
return w;
}
t2 = a - t1;
w = sqrtf(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
- if (k != 0) {
- SET_FLOAT_WORD(t1, 0x3f800000+(k<<23));
- return t1*w;
- }
+ if (k)
+ w = scalbnf(w, k);
return w;
}
if (!e) {
u.bits <<= 12;
- if (u.bits == 0)
+ if (u.bits == 0) {
+ FORCE_EVAL(0/0.0f);
return FP_ILOGB0;
+ }
/* subnormal x */
for (e = -0x3ff; u.bits < (uint64_t)1<<63; e--, u.bits<<=1);
return e;
}
- if (e == 0x7ff)
+ if (e == 0x7ff) {
+ FORCE_EVAL(0/0.0f);
return u.bits<<12 ? FP_ILOGBNAN : INT_MAX;
+ }
return e - 0x3ff;
}
if (!e) {
u.bits <<= 9;
- if (u.bits == 0)
+ if (u.bits == 0) {
+ FORCE_EVAL(0/0.0f);
return FP_ILOGB0;
+ }
/* subnormal x */
for (e = -0x7f; u.bits < (uint32_t)1<<31; e--, u.bits<<=1);
return e;
}
- if (e == 0xff)
+ if (e == 0xff) {
+ FORCE_EVAL(0/0.0f);
return u.bits<<9 ? FP_ILOGBNAN : INT_MAX;
+ }
return e - 0x7f;
}
int e = u.bits.exp;
if (!e) {
- if (m == 0)
+ if (m == 0) {
+ FORCE_EVAL(0/0.0f);
return FP_ILOGB0;
+ }
/* subnormal x */
for (e = -0x3fff+1; m < (uint64_t)1<<63; e--, m<<=1);
return e;
}
- if (e == 0x7fff)
+ if (e == 0x7fff) {
+ FORCE_EVAL(0/0.0f);
/* in ld80 msb is set in inf */
return m & (uint64_t)-1>>1 ? FP_ILOGBNAN : INT_MAX;
+ }
return e - 0x3fff;
}
#endif
*/
long long llrintl(long double x)
{
+ #pragma STDC FENV_ACCESS ON
int e;
e = fetestexcept(FE_INEXACT);
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -1.0, 9.0 100000 8.2e-20 2.5e-20
- *
- * ERROR MESSAGES:
- *
- * log singularity: x-1 = 0; returns -INFINITY
- * log domain: x-1 < 0; returns NAN
*/
#include "libm.h"
/* Test for domain errors. */
if (x <= 0.0) {
if (x == 0.0)
- return -INFINITY;
- return NAN;
+ return -1/x; /* -inf with divbyzero */
+ return 0/0.0f; /* nan with invalid */
}
/* Separate mantissa from exponent.
* In the tests over the interval exp(+-10000), the logarithms
* of the random arguments were uniformly distributed over
* [-10000, +10000].
- *
- * ERROR MESSAGES:
- *
- * log singularity: x = 0; returns -INFINITY
- * log domain: x < 0; returns NAN
*/
#include "libm.h"
long double log2l(long double x)
{
- volatile long double z;
- long double y;
+ long double y, z;
int e;
if (isnan(x))
return x;
if (x <= 0.0) {
if (x == 0.0)
- return -INFINITY;
- return NAN;
+ return -1/(x+0); /* -inf with divbyzero */
+ return 0/0.0f; /* nan with invalid */
}
/* separate mantissa from exponent */
-#include <limits.h>
#include "libm.h"
/*
special cases:
- logb(+-0) = -inf
+ logb(+-0) = -inf, and raise divbyzero
logb(+-inf) = +inf
logb(nan) = nan
-these are calculated at runtime to raise fp exceptions
*/
-double logb(double x) {
- int i = ilogb(x);
-
- if (i == FP_ILOGB0)
- return -1.0/fabs(x);
- if (i == FP_ILOGBNAN || i == INT_MAX)
+double logb(double x)
+{
+ if (!isfinite(x))
return x * x;
- return i;
+ if (x == 0)
+ return -1/(x+0);
+ return ilogb(x);
}
-#include <limits.h>
#include "libm.h"
-float logbf(float x) {
- int i = ilogbf(x);
-
- if (i == FP_ILOGB0)
- return -1.0f/fabsf(x);
- if (i == FP_ILOGBNAN || i == INT_MAX)
+float logbf(float x)
+{
+ if (!isfinite(x))
return x * x;
- return i;
+ if (x == 0)
+ return -1/(x+0);
+ return ilogbf(x);
}
-#include <limits.h>
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double logbl(long double x)
#else
long double logbl(long double x)
{
- int i = ilogbl(x);
-
- if (i == FP_ILOGB0)
- return -1.0/fabsl(x);
- if (i == FP_ILOGBNAN || i == INT_MAX)
+ if (!isfinite(x))
return x * x;
- return i;
+ if (x == 0)
+ return -1/(x+0);
+ return ilogbl(x);
}
#endif
* In the tests over the interval exp(+-10000), the logarithms
* of the random arguments were uniformly distributed over
* [-10000, +10000].
- *
- * ERROR MESSAGES:
- *
- * log singularity: x = 0; returns -INFINITY
- * log domain: x < 0; returns NAN
*/
#include "libm.h"
return x;
if (x <= 0.0) {
if (x == 0.0)
- return -INFINITY;
- return NAN;
+ return -1/(x+0); /* -inf with divbyzero */
+ return 0/0.0f; /* nan with invalid */
}
/* separate mantissa from exponent */
#if LONG_MAX < 1U<<53 && defined(FE_INEXACT)
long lrint(double x)
{
+ #pragma STDC FENV_ACCESS ON
int e;
e = fetestexcept(FE_INEXACT);
*/
long lrintl(long double x)
{
+ #pragma STDC FENV_ACCESS ON
int e;
e = fetestexcept(FE_INEXACT);
-#include <math.h>
-#include <stdint.h>
+#include "libm.h"
double modf(double x, double *iptr)
{
}
u.n &= ~mask;
*iptr = u.x;
- return x - *iptr;
+ STRICT_ASSIGN(double, x, x - *iptr);
+ return x;
}
-#include <math.h>
-#include <stdint.h>
+#include "libm.h"
float modff(float x, float *iptr)
{
}
u.n &= ~mask;
*iptr = u.x;
- return x - *iptr;
+ STRICT_ASSIGN(float, x, x - *iptr);
+ return x;
}
double nearbyint(double x)
{
#ifdef FE_INEXACT
+ #pragma STDC FENV_ACCESS ON
int e;
e = fetestexcept(FE_INEXACT);
float nearbyintf(float x)
{
#ifdef FE_INEXACT
+ #pragma STDC FENV_ACCESS ON
int e;
e = fetestexcept(FE_INEXACT);
long double nearbyintl(long double x)
{
#ifdef FE_INEXACT
+ #pragma STDC FENV_ACCESS ON
int e;
e = fetestexcept(FE_INEXACT);
e = ux.bits >> 52 & 0x7ff;
/* raise overflow if ux.value is infinite and x is finite */
if (e == 0x7ff)
- return x + x;
+ FORCE_EVAL(x+x);
/* raise underflow if ux.value is subnormal or zero */
if (e == 0)
FORCE_EVAL(x*x + ux.value*ux.value);
e = ux.bits & 0x7f800000;
/* raise overflow if ux.value is infinite and x is finite */
if (e == 0x7f800000)
- return x + x;
+ FORCE_EVAL(x+x);
/* raise underflow if ux.value is subnormal or zero */
if (e == 0)
FORCE_EVAL(x*x + ux.value*ux.value);
e = ux.bits>>52 & 0x7ff;
/* raise overflow if ux.value is infinite and x is finite */
if (e == 0x7ff)
- return x + x;
+ FORCE_EVAL(x+x);
/* raise underflow if ux.value is subnormal or zero */
if (e == 0)
FORCE_EVAL(x*x + ux.value*ux.value);
e = ux.bits & 0x7f800000;
/* raise overflow if ux.value is infinite and x is finite */
if (e == 0x7f800000)
- return x + x;
+ FORCE_EVAL(x+x);
/* raise underflow if ux.value is subnormal or zero */
if (e == 0)
FORCE_EVAL(x*x + ux.value*ux.value);
if (n > 1023) {
x *= 0x1p1023;
n -= 1023;
- if (n > 1023)
- return x * 0x1p1023;
+ if (n > 1023) {
+ STRICT_ASSIGN(double, x, x * 0x1p1023);
+ return x;
+ }
}
} else if (n < -1022) {
x *= 0x1p-1022;
if (n < -1022) {
x *= 0x1p-1022;
n += 1022;
- if (n < -1022)
- return x * 0x1p-1022;
+ if (n < -1022) {
+ STRICT_ASSIGN(double, x, x * 0x1p-1022);
+ return x;
+ }
}
}
INSERT_WORDS(scale, (uint32_t)(0x3ff+n)<<20, 0);
- return x * scale;
+ STRICT_ASSIGN(double, x, x * scale);
+ return x;
}
if (n > 127) {
x *= 0x1p127f;
n -= 127;
- if (n > 127)
- return x * 0x1p127f;
+ if (n > 127) {
+ STRICT_ASSIGN(float, x, x * 0x1p127f);
+ return x;
+ }
}
} else if (n < -126) {
x *= 0x1p-126f;
if (n < -126) {
x *= 0x1p-126f;
n += 126;
- if (n < -126)
- return x * 0x1p-126f;
+ if (n < -126) {
+ STRICT_ASSIGN(float, x, x * 0x1p-126f);
+ return x;
+ }
}
}
SET_FLOAT_WORD(scale, (uint32_t)(0x7f+n)<<23);
- return x * scale;
+ STRICT_ASSIGN(float, x, x * scale);
+ return x;
}
projects / musl / commitdiff