double
hypot(double x, double y)/* wrapper hypot */
{
#ifdef _IEEE_LIBM
return __ieee754_hypot(x,y);
#else
double z;
z = __ieee754_hypot(x,y);
if(_LIB_VERSION == _IEEE_) return z;
if((!finite(z))&&finite(x)&&finite(y))
return __kernel_standard(x,y,4); /* hypot overflow */
else
return z;
#endif
}
__complex__ double
__clog10 (__complex__ double x)
{
__complex__ double result;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
{
/* Real and imaginary part are 0.0. */
__imag__ result = signbit (__real__ x) ? M_PI : 0.0;
__imag__ result = __copysign (__imag__ result, __imag__ x);
/* Yes, the following line raises an exception. */
__real__ result = -1.0 / fabs (__real__ x);
}
else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1))
{
/* Neither real nor imaginary part is NaN. */
__real__ result = __ieee754_log10 (__ieee754_hypot (__real__ x,
__imag__ x));
__imag__ result = M_LOG10E * __ieee754_atan2 (__imag__ x, __real__ x);
}
else
{
__imag__ result = __nan ("");
if (rcls == FP_INFINITE || icls == FP_INFINITE)
/* Real or imaginary part is infinite. */
__real__ result = HUGE_VAL;
else
__real__ result = __nan ("");
}
return result;
}
double hypot(double x, double y)
{
double z = __ieee754_hypot(x, y);
if (_LIB_VERSION == _IEEE_)
return z;
if ((!isfinite(z)) && isfinite(x) && isfinite(y))
return __kernel_standard(x, y, 4); /* hypot overflow */
return z;
}
void
Math_hypot(void *fp)
{
F_Math_hypot *f;
f = fp;
*f->ret = __ieee754_hypot(f->x, f->y);
}
double
__hypot (double x, double y)
{
double z = __ieee754_hypot(x,y);
if(__builtin_expect(!isfinite(z), 0)
&& isfinite(x) && isfinite(y) && _LIB_VERSION != _IEEE_)
return __kernel_standard(x, y, 4); /* hypot overflow */
return z;
}
__complex__ double
__clog (__complex__ double x)
{
__complex__ double result;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
{
/* Real and imaginary part are 0.0. */
__imag__ result = signbit (__real__ x) ? M_PI : 0.0;
__imag__ result = __copysign (__imag__ result, __imag__ x);
/* Yes, the following line raises an exception. */
__real__ result = -1.0 / fabs (__real__ x);
}
else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1))
{
/* Neither real nor imaginary part is NaN. */
double d;
int scale = 0;
if (fabs (__real__ x) > DBL_MAX / 2.0
|| fabs (__imag__ x) > DBL_MAX / 2.0)
{
scale = -1;
__real__ x = __scalbn (__real__ x, scale);
__imag__ x = __scalbn (__imag__ x, scale);
}
else if (fabs (__real__ x) < DBL_MIN
&& fabs (__imag__ x) < DBL_MIN)
{
scale = DBL_MANT_DIG;
__real__ x = __scalbn (__real__ x, scale);
__imag__ x = __scalbn (__imag__ x, scale);
}
d = __ieee754_hypot (__real__ x, __imag__ x);
__real__ result = __ieee754_log (d) - scale * M_LN2;
__imag__ result = __ieee754_atan2 (__imag__ x, __real__ x);
}
else
{
__imag__ result = __nan ("");
if (rcls == FP_INFINITE || icls == FP_INFINITE)
/* Real or imaginary part is infinite. */
__real__ result = HUGE_VAL;
else
__real__ result = __nan ("");
}
return result;
}
//------------------------------------------------------------------------------
double Cmath::hypot( double x, double y ) // wrapper hypot
{
double z;
struct fexception exc;
z = __ieee754_hypot( x, y );
if( m_fdlib_version == _IEEE_ )
{
return z;
}
if( (!finite( z ) ) && finite( x ) && finite( y ) )
{
// hypot(finite,finite) overflow
# ifndef HUGE_VAL
# define HUGE_VAL inf
double inf = 0.0;
set_high_word( inf, 0x7ff00000 ); // set inf to infinite
# endif
exc.type = EX_OVERFLOW;
exc.name = "hypot";
exc.err = 0;
exc.arg1 = x;
exc.arg2 = y;
if( m_fdlib_version == _SVID_ )
{
exc.retval = Huge();
}
else
{
exc.retval = HUGE_VAL;
}
if( m_fdlib_version == _POSIX_ )
{
errno = ERANGE;
}
else if( !matherr( &exc ) )
{
errno = ERANGE;
}
if( exc.err != 0 )
{
errno = exc.err;
}
return exc.retval;
}
else
{
return z;
}
}
EXPORT(sqInt) primitiveHypot(void) {
double rcvr;
double result;
double arg;
arg = interpreterProxy->stackFloatValue(0);
rcvr = interpreterProxy->stackFloatValue(1);
if (interpreterProxy->failed()) {
return null;
}
result = __ieee754_hypot(rcvr, arg);
if (isnan(result)) {
return interpreterProxy->primitiveFail();
}
interpreterProxy->pop((interpreterProxy->methodArgumentCount()) + 1);
interpreterProxy->pushFloat(result);
}
primitiveHypot(void)
{
// FloatMathPlugin>>#primitiveHypot
double arg;
double rcvr;
double result;
arg = stackFloatValue(0);
rcvr = stackFloatValue(1);
if (failed()) {
return null;
}
result = __ieee754_hypot(rcvr, arg);
if (isnan(result)) {
return primitiveFail();
}
pop((methodArgumentCount()) + 1);
pushFloat(result);
}
double hypot(double x, double y)/* wrapper hypot */
{
return __ieee754_hypot(x,y);
}
Err mathlib_hypot(UInt16 refnum, double x, double y, double *result) {
#pragma unused(refnum)
*result = __ieee754_hypot(x, y);
return mlErrNone;
}
__complex__ double
__kernel_casinh (__complex__ double x, int adj)
{
__complex__ double res;
double rx, ix;
__complex__ double y;
/* Avoid cancellation by reducing to the first quadrant. */
rx = fabs (__real__ x);
ix = fabs (__imag__ x);
if (rx >= 1.0 / DBL_EPSILON || ix >= 1.0 / DBL_EPSILON)
{
/* For large x in the first quadrant, x + csqrt (1 + x * x)
is sufficiently close to 2 * x to make no significant
difference to the result; avoid possible overflow from
the squaring and addition. */
__real__ y = rx;
__imag__ y = ix;
if (adj)
{
double t = __real__ y;
__real__ y = __copysign (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = __clog (y);
__real__ res += M_LN2;
}
else if (rx >= 0.5 && ix < DBL_EPSILON / 8.0)
{
double s = __ieee754_hypot (1.0, rx);
__real__ res = __ieee754_log (rx + s);
if (adj)
__imag__ res = __ieee754_atan2 (s, __imag__ x);
else
__imag__ res = __ieee754_atan2 (ix, s);
}
else if (rx < DBL_EPSILON / 8.0 && ix >= 1.5)
{
double s = __ieee754_sqrt ((ix + 1.0) * (ix - 1.0));
__real__ res = __ieee754_log (ix + s);
if (adj)
__imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x));
else
__imag__ res = __ieee754_atan2 (s, rx);
}
else if (ix > 1.0 && ix < 1.5 && rx < 0.5)
{
if (rx < DBL_EPSILON * DBL_EPSILON)
{
double ix2m1 = (ix + 1.0) * (ix - 1.0);
double s = __ieee754_sqrt (ix2m1);
__real__ res = __log1p (2.0 * (ix2m1 + ix * s)) / 2.0;
if (adj)
__imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x));
else
__imag__ res = __ieee754_atan2 (s, rx);
}
else
{
double ix2m1 = (ix + 1.0) * (ix - 1.0);
double rx2 = rx * rx;
double f = rx2 * (2.0 + rx2 + 2.0 * ix * ix);
double d = __ieee754_sqrt (ix2m1 * ix2m1 + f);
double dp = d + ix2m1;
double dm = f / dp;
double r1 = __ieee754_sqrt ((dm + rx2) / 2.0);
double r2 = rx * ix / r1;
__real__ res = __log1p (rx2 + dp + 2.0 * (rx * r1 + ix * r2)) / 2.0;
if (adj)
__imag__ res = __ieee754_atan2 (rx + r1, __copysign (ix + r2,
__imag__ x));
else
__imag__ res = __ieee754_atan2 (ix + r2, rx + r1);
}
}
else if (ix == 1.0 && rx < 0.5)
{
if (rx < DBL_EPSILON / 8.0)
{
__real__ res = __log1p (2.0 * (rx + __ieee754_sqrt (rx))) / 2.0;
if (adj)
__imag__ res = __ieee754_atan2 (__ieee754_sqrt (rx),
__copysign (1.0, __imag__ x));
else
__imag__ res = __ieee754_atan2 (1.0, __ieee754_sqrt (rx));
}
else
{
double d = rx * __ieee754_sqrt (4.0 + rx * rx);
double s1 = __ieee754_sqrt ((d + rx * rx) / 2.0);
double s2 = __ieee754_sqrt ((d - rx * rx) / 2.0);
__real__ res = __log1p (rx * rx + d + 2.0 * (rx * s1 + s2)) / 2.0;
if (adj)
__imag__ res = __ieee754_atan2 (rx + s1, __copysign (1.0 + s2,
__imag__ x));
else
__imag__ res = __ieee754_atan2 (1.0 + s2, rx + s1);
}
}
else if (ix < 1.0 && rx < 0.5)
{
if (ix >= DBL_EPSILON)
{
if (rx < DBL_EPSILON * DBL_EPSILON)
{
double onemix2 = (1.0 + ix) * (1.0 - ix);
double s = __ieee754_sqrt (onemix2);
__real__ res = __log1p (2.0 * rx / s) / 2.0;
if (adj)
__imag__ res = __ieee754_atan2 (s, __imag__ x);
else
__imag__ res = __ieee754_atan2 (ix, s);
}
else
{
double onemix2 = (1.0 + ix) * (1.0 - ix);
double rx2 = rx * rx;
double f = rx2 * (2.0 + rx2 + 2.0 * ix * ix);
double d = __ieee754_sqrt (onemix2 * onemix2 + f);
double dp = d + onemix2;
double dm = f / dp;
double r1 = __ieee754_sqrt ((dp + rx2) / 2.0);
double r2 = rx * ix / r1;
__real__ res
= __log1p (rx2 + dm + 2.0 * (rx * r1 + ix * r2)) / 2.0;
if (adj)
__imag__ res = __ieee754_atan2 (rx + r1,
__copysign (ix + r2,
__imag__ x));
else
__imag__ res = __ieee754_atan2 (ix + r2, rx + r1);
}
}
else
{
double s = __ieee754_hypot (1.0, rx);
__real__ res = __log1p (2.0 * rx * (rx + s)) / 2.0;
if (adj)
__imag__ res = __ieee754_atan2 (s, __imag__ x);
else
__imag__ res = __ieee754_atan2 (ix, s);
}
math_check_force_underflow_nonneg (__real__ res);
}
else
{
__real__ y = (rx - ix) * (rx + ix) + 1.0;
__imag__ y = 2.0 * rx * ix;
y = __csqrt (y);
__real__ y += rx;
__imag__ y += ix;
if (adj)
{
double t = __real__ y;
__real__ y = __copysign (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = __clog (y);
}
/* Give results the correct sign for the original argument. */
__real__ res = __copysign (__real__ res, __real__ x);
__imag__ res = __copysign (__imag__ res, (adj ? 1.0 : __imag__ x));
return res;
}
__complex__ double
__catanh (__complex__ double x)
{
__complex__ double res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
{
if (icls == FP_INFINITE)
{
__real__ res = __copysign (0.0, __real__ x);
__imag__ res = __copysign (M_PI_2, __imag__ x);
}
else if (rcls == FP_INFINITE || rcls == FP_ZERO)
{
__real__ res = __copysign (0.0, __real__ x);
if (icls >= FP_ZERO)
__imag__ res = __copysign (M_PI_2, __imag__ x);
else
__imag__ res = __nan ("");
}
else
{
__real__ res = __nan ("");
__imag__ res = __nan ("");
}
}
else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
{
res = x;
}
else
{
if (fabs (__real__ x) >= 16.0 / DBL_EPSILON
|| fabs (__imag__ x) >= 16.0 / DBL_EPSILON)
{
__imag__ res = __copysign (M_PI_2, __imag__ x);
if (fabs (__imag__ x) <= 1.0)
__real__ res = 1.0 / __real__ x;
else if (fabs (__real__ x) <= 1.0)
__real__ res = __real__ x / __imag__ x / __imag__ x;
else
{
double h = __ieee754_hypot (__real__ x / 2.0, __imag__ x / 2.0);
__real__ res = __real__ x / h / h / 4.0;
}
}
else
{
if (fabs (__real__ x) == 1.0
&& fabs (__imag__ x) < DBL_EPSILON * DBL_EPSILON)
__real__ res = (__copysign (0.5, __real__ x)
* (M_LN2 - __ieee754_log (fabs (__imag__ x))));
else
{
double i2 = 0.0;
if (fabs (__imag__ x) >= DBL_EPSILON * DBL_EPSILON)
i2 = __imag__ x * __imag__ x;
double num = 1.0 + __real__ x;
num = i2 + num * num;
double den = 1.0 - __real__ x;
den = i2 + den * den;
double f = num / den;
if (f < 0.5)
__real__ res = 0.25 * __ieee754_log (f);
else
{
num = 4.0 * __real__ x;
__real__ res = 0.25 * __log1p (num / den);
}
}
double absx, absy, den;
absx = fabs (__real__ x);
absy = fabs (__imag__ x);
if (absx < absy)
{
double t = absx;
absx = absy;
absy = t;
}
if (absy < DBL_EPSILON / 2.0)
{
den = (1.0 - absx) * (1.0 + absx);
if (den == -0.0)
den = 0.0;
}
else if (absx >= 1.0)
den = (1.0 - absx) * (1.0 + absx) - absy * absy;
else if (absx >= 0.75 || absy >= 0.5)
den = -__x2y2m1 (absx, absy);
else
den = (1.0 - absx) * (1.0 + absx) - absy * absy;
__imag__ res = 0.5 * __ieee754_atan2 (2.0 * __imag__ x, den);
}
math_check_force_underflow_complex (res);
}
return res;
}
__complex__ double
__csqrt (__complex__ double x)
{
__complex__ double res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__builtin_expect (rcls <= FP_INFINITE || icls <= FP_INFINITE, 0))
{
if (icls == FP_INFINITE)
{
__real__ res = HUGE_VAL;
__imag__ res = __imag__ x;
}
else if (rcls == FP_INFINITE)
{
if (__real__ x < 0.0)
{
__real__ res = icls == FP_NAN ? __nan ("") : 0;
__imag__ res = __copysign (HUGE_VAL, __imag__ x);
}
else
{
__real__ res = __real__ x;
__imag__ res = (icls == FP_NAN
? __nan ("") : __copysign (0.0, __imag__ x));
}
}
else
{
__real__ res = __nan ("");
__imag__ res = __nan ("");
}
}
else
{
if (__builtin_expect (icls == FP_ZERO, 0))
{
if (__real__ x < 0.0)
{
__real__ res = 0.0;
__imag__ res = __copysign (__ieee754_sqrt (-__real__ x),
__imag__ x);
}
else
{
__real__ res = fabs (__ieee754_sqrt (__real__ x));
__imag__ res = __copysign (0.0, __imag__ x);
}
}
else if (__builtin_expect (rcls == FP_ZERO, 0))
{
double r;
if (fabs (__imag__ x) >= 2.0 * DBL_MIN)
r = __ieee754_sqrt (0.5 * fabs (__imag__ x));
else
r = 0.5 * __ieee754_sqrt (2.0 * fabs (__imag__ x));
__real__ res = r;
__imag__ res = __copysign (r, __imag__ x);
}
else
{
double d, r, s;
int scale = 0;
if (fabs (__real__ x) > DBL_MAX / 4.0)
{
scale = 1;
__real__ x = __scalbn (__real__ x, -2 * scale);
__imag__ x = __scalbn (__imag__ x, -2 * scale);
}
else if (fabs (__imag__ x) > DBL_MAX / 4.0)
{
scale = 1;
if (fabs (__real__ x) >= 4.0 * DBL_MIN)
__real__ x = __scalbn (__real__ x, -2 * scale);
else
__real__ x = 0.0;
__imag__ x = __scalbn (__imag__ x, -2 * scale);
}
else if (fabs (__real__ x) < DBL_MIN
&& fabs (__imag__ x) < DBL_MIN)
{
scale = -(DBL_MANT_DIG / 2);
__real__ x = __scalbn (__real__ x, -2 * scale);
__imag__ x = __scalbn (__imag__ x, -2 * scale);
}
d = __ieee754_hypot (__real__ x, __imag__ x);
/* Use the identity 2 Re res Im res = Im x
to avoid cancellation error in d +/- Re x. */
if (__real__ x > 0)
{
r = __ieee754_sqrt (0.5 * (d + __real__ x));
s = 0.5 * (__imag__ x / r);
}
else
{
s = __ieee754_sqrt (0.5 * (d - __real__ x));
r = fabs (0.5 * (__imag__ x / s));
}
if (scale)
{
r = __scalbn (r, scale);
s = __scalbn (s, scale);
}
__real__ res = r;
__imag__ res = __copysign (s, __imag__ x);
}
}
return res;
}
__complex__ double
__clog (__complex__ double x)
{
__complex__ double result;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
{
/* Real and imaginary part are 0.0. */
__imag__ result = signbit (__real__ x) ? M_PI : 0.0;
__imag__ result = __copysign (__imag__ result, __imag__ x);
/* Yes, the following line raises an exception. */
__real__ result = -1.0 / fabs (__real__ x);
}
else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN))
{
/* Neither real nor imaginary part is NaN. */
double absx = fabs (__real__ x), absy = fabs (__imag__ x);
int scale = 0;
if (absx < absy)
{
double t = absx;
absx = absy;
absy = t;
}
if (absx > DBL_MAX / 2.0)
{
scale = -1;
absx = __scalbn (absx, scale);
absy = (absy >= DBL_MIN * 2.0 ? __scalbn (absy, scale) : 0.0);
}
else if (absx < DBL_MIN && absy < DBL_MIN)
{
scale = DBL_MANT_DIG;
absx = __scalbn (absx, scale);
absy = __scalbn (absy, scale);
}
if (absx == 1.0 && scale == 0)
{
__real__ result = __log1p (absy * absy) / 2.0;
math_check_force_underflow_nonneg (__real__ result);
}
else if (absx > 1.0 && absx < 2.0 && absy < 1.0 && scale == 0)
{
double d2m1 = (absx - 1.0) * (absx + 1.0);
if (absy >= DBL_EPSILON)
d2m1 += absy * absy;
__real__ result = __log1p (d2m1) / 2.0;
}
else if (absx < 1.0
&& absx >= 0.5
&& absy < DBL_EPSILON / 2.0
&& scale == 0)
{
double d2m1 = (absx - 1.0) * (absx + 1.0);
__real__ result = __log1p (d2m1) / 2.0;
}
else if (absx < 1.0
&& absx >= 0.5
&& scale == 0
&& absx * absx + absy * absy >= 0.5)
{
double d2m1 = __x2y2m1 (absx, absy);
__real__ result = __log1p (d2m1) / 2.0;
}
else
{
double d = __ieee754_hypot (absx, absy);
__real__ result = __ieee754_log (d) - scale * M_LN2;
}
__imag__ result = __ieee754_atan2 (__imag__ x, __real__ x);
}
else
{
__imag__ result = __nan ("");
if (rcls == FP_INFINITE || icls == FP_INFINITE)
/* Real or imaginary part is infinite. */
__real__ result = HUGE_VAL;
else
__real__ result = __nan ("");
}
return result;
}
__complex__ double
__clog10 (__complex__ double x)
{
__complex__ double result;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
{
/* Real and imaginary part are 0.0. */
__imag__ result = signbit (__real__ x) ? M_PI : 0.0;
__imag__ result = __copysign (__imag__ result, __imag__ x);
/* Yes, the following line raises an exception. */
__real__ result = -1.0 / fabs (__real__ x);
}
else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1))
{
/* Neither real nor imaginary part is NaN. */
double absx = fabs (__real__ x), absy = fabs (__imag__ x);
int scale = 0;
if (absx < absy)
{
double t = absx;
absx = absy;
absy = t;
}
if (absx > DBL_MAX / 2.0)
{
scale = -1;
absx = __scalbn (absx, scale);
absy = (absy >= DBL_MIN * 2.0 ? __scalbn (absy, scale) : 0.0);
}
else if (absx < DBL_MIN && absy < DBL_MIN)
{
scale = DBL_MANT_DIG;
absx = __scalbn (absx, scale);
absy = __scalbn (absy, scale);
}
if (absx == 1.0 && scale == 0)
{
double absy2 = absy * absy;
if (absy2 <= DBL_MIN * 2.0 * M_LN10)
{
#if __FLT_EVAL_METHOD__ == 0
__real__ result = (absy2 / 2.0 - absy2 * absy2 / 4.0) * M_LOG10E;
#else
volatile double force_underflow = absy2 * absy2 / 4.0;
__real__ result = (absy2 / 2.0 - force_underflow) * M_LOG10E;
#endif
}
else
__real__ result = __log1p (absy2) * (M_LOG10E / 2.0);
}
else if (absx > 1.0 && absx < 2.0 && absy < 1.0 && scale == 0)
{
double d2m1 = (absx - 1.0) * (absx + 1.0);
if (absy >= DBL_EPSILON)
d2m1 += absy * absy;
__real__ result = __log1p (d2m1) * (M_LOG10E / 2.0);
}
else if (absx < 1.0
&& absx >= 0.75
&& absy < DBL_EPSILON / 2.0
&& scale == 0)
{
double d2m1 = (absx - 1.0) * (absx + 1.0);
__real__ result = __log1p (d2m1) * (M_LOG10E / 2.0);
}
else if (absx < 1.0 && (absx >= 0.75 || absy >= 0.5) && scale == 0)
{
double d2m1 = __x2y2m1 (absx, absy);
__real__ result = __log1p (d2m1) * (M_LOG10E / 2.0);
}
else
{
double d = __ieee754_hypot (absx, absy);
__real__ result = __ieee754_log10 (d) - scale * M_LOG10_2;
}
__imag__ result = M_LOG10E * __ieee754_atan2 (__imag__ x, __real__ x);
}
else
{
__imag__ result = __nan ("");
if (rcls == FP_INFINITE || icls == FP_INFINITE)
/* Real or imaginary part is infinite. */
__real__ result = HUGE_VAL;
else
__real__ result = __nan ("");
}
return result;
}
