invalid_fn (double x, double fn)
{
if (__rint (fn) != fn)
return (fn - fn) / (fn - fn);
else if (fn > 65000.0)
return __scalbn (x, 65000);
else
return __scalbn (x,-65000);
}
__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 __ldexp(double value, int exp)
{
if(!isfinite(value)||value==0.0) return value;
value = __scalbn(value,exp);
if(!isfinite(value)||value==0.0) __set_errno (ERANGE);
return value;
}
int
__kernel_rem_pio2 (double *x, double *y, int e0, int nx, int prec,
const int32_t *ipio2)
{
int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih;
double z, fw, f[20], fq[20], q[20];
/* initialize jk*/
jk = init_jk[prec];
jp = jk;
/* determine jx,jv,q0, note that 3>q0 */
jx = nx - 1;
jv = (e0 - 3) / 24; if (jv < 0)
jv = 0;
q0 = e0 - 24 * (jv + 1);
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
j = jv - jx; m = jx + jk;
for (i = 0; i <= m; i++, j++)
f[i] = (j < 0) ? zero : (double) ipio2[j];
/* compute q[0],q[1],...q[jk] */
for (i = 0; i <= jk; i++)
{
for (j = 0, fw = 0.0; j <= jx; j++)
fw += x[j] * f[jx + i - j];
q[i] = fw;
}
jz = jk;
recompute:
/* distill q[] into iq[] reversingly */
for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--)
{
fw = (double) ((int32_t) (twon24 * z));
iq[i] = (int32_t) (z - two24 * fw);
z = q[j - 1] + fw;
}
/* compute n */
z = __scalbn (z, q0); /* actual value of z */
z -= 8.0 * floor (z * 0.125); /* trim off integer >= 8 */
n = (int32_t) z;
z -= (double) n;
ih = 0;
if (q0 > 0) /* need iq[jz-1] to determine n */
{
i = (iq[jz - 1] >> (24 - q0)); n += i;
iq[jz - 1] -= i << (24 - q0);
ih = iq[jz - 1] >> (23 - q0);
}
double
__ieee754_scalb (double x, double fn)
{
if (__glibc_unlikely (isnan (x)))
return x * fn;
if (__glibc_unlikely (!isfinite (fn)))
{
if (isnan (fn) || fn > 0.0)
return x * fn;
if (x == 0.0)
return x;
return x / -fn;
}
if (__glibc_unlikely (fabs (fn) >= 0x1p31 || (double) (int) fn != fn))
return invalid_fn (x, fn);
return __scalbn (x, (int) fn);
}
double jumpto__scalbn(double x, int n) {
return __scalbn(x, n);
}
Err mathlib_scalbn(UInt16 refnum, double x, Int16 exponent, double *result) {
#pragma unused(refnum)
*result = __scalbn(x, exponent);
return mlErrNone;
}
double remquo ( double x, double y, int *quo)
{
int iclx,icly; /* classify results of x,y */
int32_t iquo; /* low 32 bits of integral quotient */
int32_t iscx, iscy, idiff; /* logb values and difference */
int i; /* loop variable */
double absy,x1,y1,z; /* local floating-point variables */
double rslt;
fenv_t OldEnv;
hexdouble OldEnvironment;
int newexc;
FEGETENVD ( OldEnvironment.d );
FESETENVD ( 0.0 );
__NOOP;
__NOOP;
OldEnv = OldEnvironment.i.lo;
*quo = 0; /* initialize quotient result */
iclx = ___fpclassifyd(x);
icly = ___fpclassifyd(y);
if (likely((iclx & icly) >= FP_NORMAL)) { /* x,y both nonzero finite case */
x1 = __FABS(x); /* work with absolute values */
absy = __FABS(y);
iquo = 0; /* zero local quotient */
iscx = (int32_t) __logb(x1); /* get binary exponents */
iscy = (int32_t) __logb(absy);
idiff = iscx - iscy; /* exponent difference */
if (idiff >= 0) { /* exponent of x1 >= exponent of y1 */
if (idiff != 0) { /* exponent of x1 > exponent of y1 */
y1 = __scalbn(absy,-iscy); /* scale |y| to unit binade */
x1 = __scalbn(x1,-iscx); /* ditto for |x| */
for (i = idiff; i != 0; i--) { /* begin remainder loop */
if ((z = x1 - y1) >= 0) { /* nonzero remainder step result */
x1 = z; /* update remainder (x1) */
iquo += 1; /* increment quotient */
}
iquo += iquo; /* shift quotient left one bit */
x1 += x1; /* shift (double) remainder */
} /* end of remainder loop */
x1 = __scalbn(x1,iscy); /* scale remainder to binade of |y| */
} /* remainder has exponent <= exponent of y */
if (x1 >= absy) { /* last remainder step */
x1 -= absy;
iquo +=1;
} /* end of last remainder step */
} /* remainder (x1) has smaller exponent than y */
if (likely( x1 < HugeHalved.d ))
z = x1 + x1; /* double remainder, without overflow */
else
z = Huge.d;
if ((z > absy) || ((z == absy) && ((iquo & 1) != 0))) {
x1 -= absy; /* final remainder correction */
iquo += 1;
}
if (x < 0.0)
x1 = -x1; /* remainder if x is negative */
iquo &= 0x0000007f; /* retain low 7 bits of integer quotient */
if ((___signbitd(x) ^ ___signbitd(y)) != 0) /* take care of sign of quotient */
iquo = -iquo;
*quo = iquo; /* deliver quotient result */
rslt = x1;
goto ret;
} /* end of x,y both nonzero finite case */
else if ((iclx <= FP_QNAN) || (icly <= FP_QNAN)) {
rslt = x+y; /* at least one NaN operand */
goto ret;
}
else if ((iclx == FP_INFINITE)||(icly == FP_ZERO)) { /* invalid result */
rslt = nan(REM_NAN);
OldEnvironment.i.lo |= SET_INVALID;
FESETENVD_GRP( OldEnvironment.d );
goto ret;
}
else /* trivial cases (finite REM infinite */
rslt = x; /* or zero REM nonzero) with *quo = 0 */
ret:
FEGETENVD_GRP( OldEnvironment.d );
newexc = OldEnvironment.i.lo & FE_ALL_EXCEPT;
OldEnvironment.i.lo = OldEnv;
if ((newexc & FE_INVALID) != 0)
OldEnvironment.i.lo |= SET_INVALID;
OldEnvironment.i.lo |= newexc & ( FE_INEXACT | FE_DIVBYZERO | FE_UNDERFLOW | FE_OVERFLOW );
FESETENVD_GRP( OldEnvironment.d );
return rslt;
}
__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;
}
double
__ieee754_gamma_r (double x, int *signgamp)
{
int32_t hx;
u_int32_t lx;
EXTRACT_WORDS (hx, lx, x);
if (__glibc_unlikely (((hx & 0x7fffffff) | lx) == 0))
{
/* Return value for x == 0 is Inf with divide by zero exception. */
*signgamp = 0;
return 1.0 / x;
}
if (__builtin_expect (hx < 0, 0)
&& (u_int32_t) hx < 0xfff00000 && __rint (x) == x)
{
/* Return value for integer x < 0 is NaN with invalid exception. */
*signgamp = 0;
return (x - x) / (x - x);
}
if (__glibc_unlikely ((unsigned int) hx == 0xfff00000 && lx == 0))
{
/* x == -Inf. According to ISO this is NaN. */
*signgamp = 0;
return x - x;
}
if (__glibc_unlikely ((hx & 0x7ff00000) == 0x7ff00000))
{
/* Positive infinity (return positive infinity) or NaN (return
NaN). */
*signgamp = 0;
return x + x;
}
if (x >= 172.0)
{
/* Overflow. */
*signgamp = 0;
return DBL_MAX * DBL_MAX;
}
else if (x > 0.0)
{
*signgamp = 0;
int exp2_adj;
double ret = gamma_positive (x, &exp2_adj);
return __scalbn (ret, exp2_adj);
}
else if (x >= -DBL_EPSILON / 4.0)
{
*signgamp = 0;
return 1.0 / x;
}
else
{
double tx = __trunc (x);
*signgamp = (tx == 2.0 * __trunc (tx / 2.0)) ? -1 : 1;
if (x <= -184.0)
/* Underflow. */
return DBL_MIN * DBL_MIN;
double frac = tx - x;
if (frac > 0.5)
frac = 1.0 - frac;
double sinpix = (frac <= 0.25
? __sin (M_PI * frac)
: __cos (M_PI * (0.5 - frac)));
int exp2_adj;
double ret = M_PI / (-x * sinpix * gamma_positive (-x, &exp2_adj));
return __scalbn (ret, -exp2_adj);
}
}
__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;
}
