long double
__ieee754_acoshl(long double x)
{
long double t;
int64_t hx;
uint64_t lx;
double xhi, xlo;
ldbl_unpack (x, &xhi, &xlo);
EXTRACT_WORDS64 (hx, xhi);
EXTRACT_WORDS64 (lx, xlo);
if(hx<0x3ff0000000000000LL) { /* x < 1 */
return (x-x)/(x-x);
} else if(hx >=0x41b0000000000000LL) { /* x > 2**28 */
if(hx >=0x7ff0000000000000LL) { /* x is inf of NaN */
return x+x;
} else
return __ieee754_logl(x)+ln2; /* acosh(huge)=log(2x) */
} else if (((hx-0x3ff0000000000000LL)|(lx&0x7fffffffffffffffLL))==0) {
return 0.0; /* acosh(1) = 0 */
} else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */
t=x*x;
return __ieee754_logl(2.0*x-one/(x+__ieee754_sqrtl(t-one)));
} else { /* 1<x<2 */
t = x-one;
return __log1pl(t+__ieee754_sqrtl(2.0*t+t*t));
}
}
int
FUNC (long double *x, long double payload)
{
double hi, lo;
uint64_t hx, lx;
ldbl_unpack (payload, &hi, &lo);
EXTRACT_WORDS64 (hx, hi);
EXTRACT_WORDS64 (lx, lo);
int exponent = hx >> EXPLICIT_MANT_DIG;
/* Test if argument is (a) negative or too large; (b) too small,
except for 0 when allowed; (c) not an integer. All valid
arguments have the low part zero. */
if ((lx & 0x7fffffffffffffffULL) != 0
|| exponent >= BIAS + PAYLOAD_DIG
|| (exponent < BIAS && !(SET_HIGH_BIT && hx == 0))
|| (hx & ((1ULL << (BIAS + EXPLICIT_MANT_DIG - exponent)) - 1)) != 0)
{
*x = 0.0L;
return 1;
}
if (hx != 0)
{
hx &= (1ULL << EXPLICIT_MANT_DIG) - 1;
hx |= 1ULL << EXPLICIT_MANT_DIG;
hx >>= BIAS + EXPLICIT_MANT_DIG - exponent;
}
double
__ieee754_log10 (double x)
{
double y, z;
int64_t i, hx;
int32_t k;
EXTRACT_WORDS64 (hx, x);
k = 0;
if (hx < INT64_C(0x0010000000000000))
{ /* x < 2**-1022 */
if (__builtin_expect ((hx & UINT64_C(0x7fffffffffffffff)) == 0, 0))
return -two54 / (x - x); /* log(+-0)=-inf */
if (__builtin_expect (hx < 0, 0))
return (x - x) / (x - x); /* log(-#) = NaN */
k -= 54;
x *= two54; /* subnormal number, scale up x */
EXTRACT_WORDS64 (hx, x);
}
/* scale up resulted in a NaN number */
if (__builtin_expect (hx >= UINT64_C(0x7ff0000000000000), 0))
return x + x;
k += (hx >> 52) - 1023;
i = ((uint64_t) k & UINT64_C(0x8000000000000000)) >> 63;
hx = (hx & UINT64_C(0x000fffffffffffff)) | ((0x3ff - i) << 52);
y = (double) (k + i);
INSERT_WORDS64 (x, hx);
z = y * log10_2lo + ivln10 * __ieee754_log (x);
return z + y * log10_2hi;
}
long double
__ieee754_remainderl(long double x, long double p)
{
int64_t hx,hp;
u_int64_t sx,lx,lp;
long double p_half;
double xhi, xlo, phi, plo;
ldbl_unpack (x, &xhi, &xlo);
EXTRACT_WORDS64 (hx, xhi);
EXTRACT_WORDS64 (lx, xlo);
ldbl_unpack (p, &phi, &plo);
EXTRACT_WORDS64 (hp, phi);
EXTRACT_WORDS64 (lp, plo);
sx = hx&0x8000000000000000ULL;
lp ^= hp & 0x8000000000000000ULL;
hp &= 0x7fffffffffffffffLL;
lx ^= sx;
hx &= 0x7fffffffffffffffLL;
if (lp == 0x8000000000000000ULL)
lp = 0;
if (lx == 0x8000000000000000ULL)
lx = 0;
/* purge off exception values */
if(hp==0) return (x*p)/(x*p); /* p = 0 */
if((hx>=0x7ff0000000000000LL)|| /* x not finite */
(hp>0x7ff0000000000000LL)) /* p is NaN */
return (x*p)/(x*p);
if (hp<=0x7fdfffffffffffffLL) x = __ieee754_fmodl(x,p+p); /* now x < 2p */
if (((hx-hp)|(lx-lp))==0) return zero*x;
x = fabsl(x);
p = fabsl(p);
if (hp<0x0020000000000000LL) {
if(x+x>p) {
x-=p;
if(x+x>=p) x -= p;
}
} else {
p_half = 0.5L*p;
if(x>p_half) {
x-=p;
if(x>=p_half) x -= p;
}
}
if (sx)
x = -x;
return x;
}
long double __fabsl(long double x)
{
uint64_t hx, lx;
double xhi, xlo;
ldbl_unpack (x, &xhi, &xlo);
EXTRACT_WORDS64 (hx, xhi);
EXTRACT_WORDS64 (lx, xlo);
lx = lx ^ ( hx & 0x8000000000000000LL );
hx = hx & 0x7fffffffffffffffLL;
INSERT_WORDS64 (xhi, hx);
INSERT_WORDS64 (xlo, lx);
x = ldbl_pack (xhi, xlo);
return x;
}
int
___fpclassifyl (long double x)
{
u_int64_t hx, lx;
int retval = FP_NORMAL;
double xhi, xlo;
ldbl_unpack (x, &xhi, &xlo);
EXTRACT_WORDS64 (hx, xhi);
if ((hx & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL) {
/* +/-NaN or +/-Inf */
if (hx & 0x000fffffffffffffULL) {
/* +/-NaN */
retval = FP_NAN;
} else {
retval = FP_INFINITE;
}
} else {
/* +/-zero or +/- normal or +/- denormal */
if (hx & 0x7fffffffffffffffULL) {
/* +/- normal or +/- denormal */
if ((hx & 0x7ff0000000000000ULL) > 0x0360000000000000ULL) {
/* +/- normal */
retval = FP_NORMAL;
} else {
if ((hx & 0x7ff0000000000000ULL) == 0x0360000000000000ULL) {
EXTRACT_WORDS64 (lx, xlo);
if ((lx & 0x7fffffffffffffff) /* lower is non-zero */
&& ((lx^hx) & 0x8000000000000000ULL)) { /* and sign differs */
/* +/- denormal */
retval = FP_SUBNORMAL;
} else {
/* +/- normal */
retval = FP_NORMAL;
}
} else {
/* +/- denormal */
retval = FP_SUBNORMAL;
}
}
} else {
/* +/- zero */
retval = FP_ZERO;
}
}
return retval;
}
float __nexttowardf(float x, long double y)
{
int32_t hx,ix;
int64_t hy,iy;
double yhi;
GET_FLOAT_WORD(hx,x);
yhi = ldbl_high (y);
EXTRACT_WORDS64 (hy, yhi);
ix = hx&0x7fffffff; /* |x| */
iy = hy&0x7fffffffffffffffLL; /* |y| */
if((ix>0x7f800000) || /* x is nan */
(iy>0x7ff0000000000000LL))
/* y is nan */
return x+y;
if((long double) x==y) return y; /* x=y, return y */
if(ix==0) { /* x == 0 */
float u;
SET_FLOAT_WORD(x,(u_int32_t)((hy>>32)&0x80000000)|1);/* return +-minsub*/
u = math_opt_barrier (x);
u = u * u;
math_force_eval (u); /* raise underflow flag */
return x;
}
double __nexttoward(double x, long double y)
{
int32_t hx,ix;
int64_t hy,iy;
uint32_t lx;
double yhi;
EXTRACT_WORDS(hx,lx,x);
yhi = ldbl_high (y);
EXTRACT_WORDS64(hy,yhi);
ix = hx&0x7fffffff; /* |x| */
iy = hy&0x7fffffffffffffffLL; /* |y| */
if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */
iy>0x7ff0000000000000LL) /* y is nan */
return x+y;
if((long double) x==y) return y; /* x=y, return y */
if((ix|lx)==0) { /* x == 0 */
double u;
INSERT_WORDS(x,(uint32_t)((hy>>32)&0x80000000),1);/* return +-minsub */
u = math_opt_barrier (x);
u = u * u;
math_force_eval (u); /* raise underflow flag */
return x;
}
static __always_inline int
__isinf_ns2 (double d)
{
uint64_t di;
EXTRACT_WORDS64 (di, d);
return (di & 0x7fffffffffffffffull) == 0x7ff0000000000000ull;
}
double
__ieee754_acosh (double x)
{
int64_t hx;
EXTRACT_WORDS64 (hx, x);
if (hx > INT64_C (0x4000000000000000))
{
if (__builtin_expect (hx >= INT64_C (0x41b0000000000000), 0))
{
/* x > 2**28 */
if (hx >= INT64_C (0x7ff0000000000000))
/* x is inf of NaN */
return x + x;
else
return __ieee754_log (x) + ln2;/* acosh(huge)=log(2x) */
}
/* 2**28 > x > 2 */
double t = x * x;
return __ieee754_log (2.0 * x - one / (x + __ieee754_sqrt (t - one)));
}
else if (__builtin_expect (hx > INT64_C (0x3ff0000000000000), 1))
{
/* 1<x<2 */
double t = x - one;
return __log1p (t + __ieee754_sqrt (2.0 * t + t * t));
}
else if (__builtin_expect (hx == INT64_C (0x3ff0000000000000), 1))
return 0.0; /* acosh(1) = 0 */
else /* x < 1 */
return (x - x) / (x - x);
}
int
__isinf_ns (double x)
{
int64_t ix;
EXTRACT_WORDS64(ix,x);
return (ix & UINT64_C(0x7fffffffffffffff)) == UINT64_C(0x7ff0000000000000);
}
static __always_inline int
__finite_inl (double d)
{
uint64_t di;
EXTRACT_WORDS64 (di, d);
return (di & 0x7fffffffffffffffull) < 0x7ff0000000000000ull;
}
long double __asinhl(long double x)
{
long double t,w;
int64_t hx,ix;
double xhi;
xhi = ldbl_high (x);
EXTRACT_WORDS64 (hx, xhi);
ix = hx&0x7fffffffffffffffLL;
if(ix>=0x7ff0000000000000LL) return x+x; /* x is inf or NaN */
if(ix< 0x3c70000000000000LL) { /* |x|<2**-56 */
math_check_force_underflow (x);
if(huge+x>one) return x; /* return x inexact except 0 */
}
if(ix>0x4370000000000000LL) { /* |x| > 2**56 */
w = __ieee754_logl(fabsl(x))+ln2;
} else if (ix>0x4000000000000000LL) { /* 2**56 >= |x| > 2.0 */
t = fabs(x);
w = __ieee754_logl(2.0*t+one/(sqrtl(x*x+one)+t));
} else { /* 2.0 >= |x| >= 2**-56 */
t = x*x;
w =__log1pl(fabsl(x)+t/(one+sqrtl(one+t)));
}
if(hx>0) return w; else return -w;
}
int
__finite(double x)
{
int64_t lx;
EXTRACT_WORDS64(lx,x);
return (int)((uint64_t)((lx&INT64_C(0x7ff0000000000000))-INT64_C(0x7ff0000000000000))>>63);
}
int
__isnan (double x)
{
uint64_t ix;
EXTRACT_WORDS64 (ix, x);
return ix * 2 > 0xffe0000000000000ul;
}
int
__issignalingl (long double x)
{
uint64_t xi;
/* For inspecting NaN status, we only have to look at the first of the pair
of IEEE 754 64-bit precision numbers. */
double xhi;
xhi = ldbl_high (x);
EXTRACT_WORDS64 (xi, xhi);
#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
# error untested
/* We only have to care about the high-order bit of x's significand, because
having it set (sNaN) already makes the significand different from that
used to designate infinity. */
return (xi & UINT64_C (0x7ff8000000000000)) == UINT64_C (0x7ff8000000000000);
#else
/* To keep the following comparison simple, toggle the quiet/signaling bit,
so that it is set for sNaNs. This is inverse to IEEE 754-2008 (as well as
common practice for IEEE 754-1985). */
xi ^= UINT64_C (0x0008000000000000);
/* We have to compare for greater (instead of greater or equal), because x's
significand being all-zero designates infinity not NaN. */
return (xi & UINT64_C (0x7fffffffffffffff)) > UINT64_C (0x7ff8000000000000);
#endif
}
int
___signbitl (long double x)
{
int64_t e;
double xhi;
xhi = ldbl_high (x);
EXTRACT_WORDS64 (e, xhi);
return e < 0;
}
long double
getpayloadl (const long double *x)
{
double xhi = ldbl_high (*x);
uint64_t ix;
EXTRACT_WORDS64 (ix, xhi);
ix &= 0x7ffffffffffffULL;
if (FIX_INT_FP_CONVERT_ZERO && ix == 0)
return 0.0L;
return (long double) ix;
}
int
__totalordermag (double x, double y)
{
uint64_t ix, iy;
EXTRACT_WORDS64 (ix, x);
EXTRACT_WORDS64 (iy, y);
ix &= 0x7fffffffffffffffULL;
iy &= 0x7fffffffffffffffULL;
#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
/* For the preferred quiet NaN convention, this operation is a
comparison of the representations of the absolute values of the
arguments. If both arguments are NaNs, invert the
quiet/signaling bit so comparing that way works. */
if (ix > 0x7ff0000000000000ULL && iy > 0x7ff0000000000000ULL)
{
ix ^= 0x0008000000000000ULL;
iy ^= 0x0008000000000000ULL;
}
#endif
return ix <= iy;
}
int
___finitel (long double x)
{
uint64_t hx;
double xhi;
xhi = ldbl_high (x);
EXTRACT_WORDS64 (hx, xhi);
hx &= 0x7fffffffffffffffLL;
hx -= 0x7ff0000000000000LL;
return hx >> 63;
}
double
__logb (double x)
{
int64_t ix;
EXTRACT_WORDS64 (ix, x);
ix &= UINT64_C(0x7fffffffffffffff);
if (ix == 0)
return -1.0 / fabs (x);
unsigned int ex = ix >> 52;
if (ex == 0x7ff)
return x * x;
return ex == 0 ? -1022.0 : (double) (ex - 1023);
}
double
__ieee754_cosh (double x)
{
double t,w;
int32_t ix;
/* High word of |x|. */
GET_HIGH_WORD(ix,x);
ix &= 0x7fffffff;
/* |x| in [0,22] */
if (ix < 0x40360000) {
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
if(ix<0x3fd62e43) {
t = __expm1(fabs(x));
w = one+t;
if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
return one+(t*t)/(w+w);
}
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
t = __ieee754_exp(fabs(x));
return half*t+half/t;
}
/* |x| in [22, log(maxdouble)] return half*exp(|x|) */
if (ix < 0x40862e42) return half*__ieee754_exp(fabs(x));
/* |x| in [log(maxdouble), overflowthresold] */
int64_t fix;
EXTRACT_WORDS64(fix, x);
fix &= UINT64_C(0x7fffffffffffffff);
if (fix <= UINT64_C(0x408633ce8fb9f87d)) {
w = __ieee754_exp(half*fabs(x));
t = half*w;
return t*w;
}
/* x is INF or NaN */
if(ix>=0x7ff00000) return x*x;
/* |x| > overflowthresold, cosh(x) overflow */
return huge*huge;
}
double
__logb (double x)
{
int64_t ix, ex;
EXTRACT_WORDS64 (ix, x);
ix &= UINT64_C(0x7fffffffffffffff);
if (ix == 0)
return -1.0 / fabs (x);
ex = ix >> 52;
if (ex == 0x7ff)
return x * x;
if (__builtin_expect (ex == 0, 0))
{
int m = __builtin_clzll (ix);
ex -= m - 12;
}
return (double) (ex - 1023);
}
long double
__ieee754_sinhl(long double x)
{
long double t,w,h;
int64_t ix,jx;
double xhi;
/* High word of |x|. */
xhi = ldbl_high (x);
EXTRACT_WORDS64 (jx, xhi);
ix = jx&0x7fffffffffffffffLL;
/* x is INF or NaN */
if(ix>=0x7ff0000000000000LL) return x+x;
h = 0.5;
if (jx<0) h = -h;
/* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */
if (ix < 0x4044000000000000LL) { /* |x|<40 */
if (ix<0x3c90000000000000LL) { /* |x|<2**-54 */
math_check_force_underflow (x);
if(shuge+x>one) return x;/* sinhl(tiny) = tiny with inexact */
}
t = __expm1l(fabsl(x));
if(ix<0x3ff0000000000000LL) return h*(2.0*t-t*t/(t+one));
w = t/(t+one);
return h*(t+w);
}
/* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
if (ix < 0x40862e42fefa39efLL) return h*__ieee754_expl(fabsl(x));
/* |x| in [log(maxdouble), overflowthresold] */
if (ix <= 0x408633ce8fb9f87eLL) {
w = __ieee754_expl(0.5*fabsl(x));
t = h*w;
return t*w;
}
/* |x| > overflowthresold, sinh(x) overflow */
return x*shuge;
}
int
__issignaling (double x)
{
u_int64_t xi;
EXTRACT_WORDS64 (xi, x);
#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
/* We only have to care about the high-order bit of x's significand, because
having it set (sNaN) already makes the significand different from that
used to designate infinity. */
return (xi & UINT64_C (0x7ff8000000000000)) == UINT64_C (0x7ff8000000000000);
#else
/* To keep the following comparison simple, toggle the quiet/signaling bit,
so that it is set for sNaNs. This is inverse to IEEE 754-2008 (as well as
common practice for IEEE 754-1985). */
xi ^= UINT64_C (0x0008000000000000);
/* We have to compare for greater (instead of greater or equal), because x's
significand being all-zero designates infinity not NaN. */
return (xi & UINT64_C (0x7fffffffffffffff)) > UINT64_C (0x7ff8000000000000);
#endif
}
double
__roundeven (double x)
{
uint64_t ix, ux;
EXTRACT_WORDS64 (ix, x);
ux = ix & 0x7fffffffffffffffULL;
int exponent = ux >> (MANT_DIG - 1);
if (exponent >= BIAS + MANT_DIG - 1)
{
/* Integer, infinity or NaN. */
if (exponent == MAX_EXP)
/* Infinity or NaN; quiet signaling NaNs. */
return x + x;
else
return x;
}
else if (exponent >= BIAS)
{
/* At least 1; not necessarily an integer. Locate the bits with
exponents 0 and -1 (when the unbiased exponent is 0, the bit
with exponent 0 is implicit, but as the bias is odd it is OK
to take it from the low bit of the exponent). */
int int_pos = (BIAS + MANT_DIG - 1) - exponent;
int half_pos = int_pos - 1;
uint64_t half_bit = 1ULL << half_pos;
uint64_t int_bit = 1ULL << int_pos;
if ((ix & (int_bit | (half_bit - 1))) != 0)
/* Carry into the exponent works correctly. No need to test
whether HALF_BIT is set. */
ix += half_bit;
ix &= ~(int_bit - 1);
}
else if (exponent == BIAS - 1 && ux > 0x3fe0000000000000ULL)
/* Interval (0.5, 1). */
ix = (ix & 0x8000000000000000ULL) | 0x3ff0000000000000ULL;
else
/* Rounds to 0. */
ix &= 0x8000000000000000ULL;
INSERT_WORDS64 (x, ix);
return x;
}
long double __tanhl(long double x)
{
long double t,z;
int64_t jx,ix;
double xhi;
/* High word of |x|. */
xhi = ldbl_high (x);
EXTRACT_WORDS64 (jx, xhi);
ix = jx&0x7fffffffffffffffLL;
/* x is INF or NaN */
if(ix>=0x7ff0000000000000LL) {
if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
else return one/x-one; /* tanh(NaN) = NaN */
}
/* |x| < 40 */
if (ix < 0x4044000000000000LL) { /* |x|<40 */
if (ix == 0)
return x; /* x == +-0 */
if (ix<0x3c60000000000000LL) /* |x|<2**-57 */
{
math_check_force_underflow (x);
return x; /* tanh(small) = small */
}
if (ix>=0x3ff0000000000000LL) { /* |x|>=1 */
t = __expm1l(two*fabsl(x));
z = one - two/(t+two);
} else {
t = __expm1l(-two*fabsl(x));
z= -t/(t+two);
}
/* |x| > 40, return +-1 */
} else {
z = one - tiny; /* raised inexact flag */
}
return (jx>=0)? z: -z;
}
long double
__ieee754_log10l (long double x)
{
long double z;
long double y;
int e;
int64_t hx;
double xhi;
/* Test for domain */
xhi = ldbl_high (x);
EXTRACT_WORDS64 (hx, xhi);
if ((hx & 0x7fffffffffffffffLL) == 0)
return (-1.0L / (x - x));
if (hx < 0)
return (x - x) / (x - x);
if (hx >= 0x7ff0000000000000LL)
return (x + x);
if (x == 1.0L)
return 0.0L;
/* separate mantissa from exponent */
/* Note, frexp is used so that denormal numbers
* will be handled properly.
*/
x = __frexpl (x, &e);
/* logarithm using log(x) = z + z**3 P(z)/Q(z),
* where z = 2(x-1)/x+1)
*/
if ((e > 2) || (e < -2))
{
if (x < SQRTH)
{ /* 2( 2x-1 )/( 2x+1 ) */
e -= 1;
z = x - 0.5L;
y = 0.5L * z + 0.5L;
}
else
{ /* 2 (x-1)/(x+1) */
z = x - 0.5L;
z -= 0.5L;
y = 0.5L * x + 0.5L;
}
x = z / y;
z = x * x;
y = x * (z * neval (z, R, 5) / deval (z, S, 5));
goto done;
}
/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
if (x < SQRTH)
{
e -= 1;
x = 2.0 * x - 1.0L; /* 2x - 1 */
}
else
{
x = x - 1.0L;
}
z = x * x;
y = x * (z * neval (x, P, 12) / deval (x, Q, 11));
y = y - 0.5 * z;
done:
/* Multiply log of fraction by log10(e)
* and base 2 exponent by log10(2).
*/
z = y * L10EB;
z += x * L10EB;
z += e * L102B;
z += y * L10EA;
z += x * L10EA;
z += e * L102A;
return (z);
}
long double
__remquol (long double x, long double y, int *quo)
{
int64_t hx,hy;
u_int64_t sx,lx,ly,qs;
int cquo;
double xhi, xlo, yhi, ylo;
ldbl_unpack (x, &xhi, &xlo);
EXTRACT_WORDS64 (hx, xhi);
EXTRACT_WORDS64 (lx, xlo);
ldbl_unpack (y, &yhi, &ylo);
EXTRACT_WORDS64 (hy, yhi);
EXTRACT_WORDS64 (ly, ylo);
sx = hx & 0x8000000000000000ULL;
qs = sx ^ (hy & 0x8000000000000000ULL);
hy &= 0x7fffffffffffffffLL;
hx &= 0x7fffffffffffffffLL;
/* Purge off exception values. */
if (hy == 0)
return (x * y) / (x * y); /* y = 0 */
if ((hx >= 0x7ff0000000000000LL) /* x not finite */
|| (hy > 0x7ff0000000000000LL)) /* y is NaN */
return (x * y) / (x * y);
if (hy <= 0x7fbfffffffffffffLL)
x = __ieee754_fmodl (x, 8 * y); /* now x < 8y */
if (((hx - hy) | (lx - ly)) == 0)
{
*quo = qs ? -1 : 1;
return zero * x;
}
x = fabsl (x);
y = fabsl (y);
cquo = 0;
if (hy <= 0x7fcfffffffffffffLL && x >= 4 * y)
{
x -= 4 * y;
cquo += 4;
}
if (hy <= 0x7fdfffffffffffffLL && x >= 2 * y)
{
x -= 2 * y;
cquo += 2;
}
if (hy < 0x0020000000000000LL)
{
if (x + x > y)
{
x -= y;
++cquo;
if (x + x >= y)
{
x -= y;
++cquo;
}
}
}
else
{
long double y_half = 0.5L * y;
if (x > y_half)
{
x -= y;
++cquo;
if (x >= y_half)
{
x -= y;
++cquo;
}
}
}
*quo = qs ? -cquo : cquo;
/* Ensure correct sign of zero result in round-downward mode. */
if (x == 0.0L)
x = 0.0L;
if (sx)
x = -x;
return x;
}
double
__remquo (double x, double y, int *quo)
{
int64_t hx, hy;
uint64_t sx, qs;
int cquo;
EXTRACT_WORDS64 (hx, x);
EXTRACT_WORDS64 (hy, y);
sx = hx & UINT64_C(0x8000000000000000);
qs = sx ^ (hy & UINT64_C(0x8000000000000000));
hy &= UINT64_C(0x7fffffffffffffff);
hx &= UINT64_C(0x7fffffffffffffff);
/* Purge off exception values. */
if (__glibc_unlikely (hy == 0))
return (x * y) / (x * y); /* y = 0 */
if (__builtin_expect (hx >= UINT64_C(0x7ff0000000000000) /* x not finite */
|| hy > UINT64_C(0x7ff0000000000000), 0))/* y is NaN */
return (x * y) / (x * y);
if (hy <= UINT64_C(0x7fbfffffffffffff))
x = __ieee754_fmod (x, 8 * y); /* now x < 8y */
if (__glibc_unlikely (hx == hy))
{
*quo = qs ? -1 : 1;
return zero * x;
}
x = fabs (x);
INSERT_WORDS64 (y, hy);
cquo = 0;
if (hy <= UINT64_C(0x7fcfffffffffffff) && x >= 4 * y)
{
x -= 4 * y;
cquo += 4;
}
if (hy <= UINT64_C(0x7fdfffffffffffff) && x >= 2 * y)
{
x -= 2 * y;
cquo += 2;
}
if (hy < UINT64_C(0x0020000000000000))
{
if (x + x > y)
{
x -= y;
++cquo;
if (x + x >= y)
{
x -= y;
++cquo;
}
}
}
else
{
double y_half = 0.5 * y;
if (x > y_half)
{
x -= y;
++cquo;
if (x >= y_half)
{
x -= y;
++cquo;
}
}
}
*quo = qs ? -cquo : cquo;
/* Ensure correct sign of zero result in round-downward mode. */
if (x == 0.0)
x = 0.0;
if (sx)
x = -x;
return x;
}
