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;
}
double __nexttoward(double x, long double y)
{
int32_t hx,ix,iy;
u_int32_t lx,hy,ly,esy;
EXTRACT_WORDS(hx,lx,x);
GET_LDOUBLE_WORDS(esy,hy,ly,y);
ix = hx&0x7fffffff; /* |x| */
iy = esy&0x7fff; /* |y| */
/* Intel's extended format has the normally implicit 1 explicit
present. Sigh! */
if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */
((iy>=0x7fff)&&((hy&0x7fffffff)|ly)!=0)) /* 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,(esy&0x8000)<<16,1); /* return +-minsub */
u = math_opt_barrier (x);
u = u * u;
math_force_eval (u); /* raise underflow flag */
return x;
}
if(hx>=0) { /* x > 0 */
if (x > y) { /* x -= ulp */
if(lx==0) hx -= 1;
lx -= 1;
} else { /* x < y, x += ulp */
lx += 1;
if(lx==0) hx += 1;
}
} else { /* x < 0 */
if (x < y) { /* x -= ulp */
if(lx==0) hx -= 1;
lx -= 1;
} else { /* x > y, x += ulp */
lx += 1;
if(lx==0) hx += 1;
}
}
hy = hx&0x7ff00000;
if(hy>=0x7ff00000) {
double u = x+x; /* overflow */
math_force_eval (u);
}
if(hy<0x00100000) {
double u = x*x; /* underflow */
math_force_eval (u); /* raise underflow flag */
}
INSERT_WORDS(x,hx,lx);
return x;
}
long double __nextafterl(long double x, long double y)
{
int64_t hx,hy,ix,iy;
u_int64_t lx,ly;
GET_LDOUBLE_WORDS64(hx,lx,x);
GET_LDOUBLE_WORDS64(hy,ly,y);
ix = hx&0x7fffffffffffffffLL; /* |x| */
iy = hy&0x7fffffffffffffffLL; /* |y| */
if(((ix>=0x7fff000000000000LL)&&((ix-0x7fff000000000000LL)|lx)!=0) || /* x is nan */
((iy>=0x7fff000000000000LL)&&((iy-0x7fff000000000000LL)|ly)!=0)) /* y is nan */
return x+y;
if(x==y) return y; /* x=y, return y */
if((ix|lx)==0) { /* x == 0 */
long double u;
SET_LDOUBLE_WORDS64(x,hy&0x8000000000000000ULL,1);/* return +-minsubnormal */
u = math_opt_barrier (x);
u = u * u;
math_force_eval (u); /* raise underflow flag */
return x;
}
if(hx>=0) { /* x > 0 */
if(hx>hy||((hx==hy)&&(lx>ly))) { /* x > y, x -= ulp */
if(lx==0) hx--;
lx--;
} else { /* x < y, x += ulp */
lx++;
if(lx==0) hx++;
}
} else { /* x < 0 */
if(hy>=0||hx>hy||((hx==hy)&&(lx>ly))){/* x < y, x -= ulp */
if(lx==0) hx--;
lx--;
} else { /* x > y, x += ulp */
lx++;
if(lx==0) hx++;
}
}
hy = hx&0x7fff000000000000LL;
if(hy==0x7fff000000000000LL) {
long double u = x + x; /* overflow */
math_force_eval (u);
}
if(hy==0) {
long double u = x*x; /* underflow */
math_force_eval (u); /* raise underflow flag */
}
SET_LDOUBLE_WORDS64(x,hx,lx);
return x;
}
float __nexttowardf(float x, long double y)
{
int32_t hx,ix,iy;
uint32_t hy,ly,esy;
GET_FLOAT_WORD(hx,x);
GET_LDOUBLE_WORDS(esy,hy,ly,y);
ix = hx&0x7fffffff; /* |x| */
iy = esy&0x7fff; /* |y| */
if((ix>0x7f800000) || /* x is nan */
(iy>=0x7fff&&((hy|ly)!=0))) /* 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,((esy&0x8000)<<16)|1);/* return +-minsub*/
u = math_opt_barrier (x);
u = u * u;
math_force_eval (u); /* raise underflow flag */
return x;
}
if(hx>=0) { /* x > 0 */
if(x > y) { /* x -= ulp */
hx -= 1;
} else { /* x < y, x += ulp */
hx += 1;
}
} else { /* x < 0 */
if(x < y) { /* x -= ulp */
hx -= 1;
} else { /* x > y, x += ulp */
hx += 1;
}
}
hy = hx&0x7f800000;
if(hy>=0x7f800000) {
float u = x+x; /* overflow */
math_force_eval (u);
__set_errno (ERANGE);
}
if(hy<0x00800000) {
float u = x*x; /* underflow */
math_force_eval (u); /* raise underflow flag */
__set_errno (ERANGE);
}
SET_FLOAT_WORD(x,hx);
return x;
}
float __nldbl_nexttowardf(float x, double y)
{
int32_t hx,hy,ix,iy;
u_int32_t ly;
GET_FLOAT_WORD(hx,x);
EXTRACT_WORDS(hy,ly,y);
ix = hx&0x7fffffff; /* |x| */
iy = hy&0x7fffffff; /* |y| */
if((ix>0x7f800000) || /* x is nan */
((iy>=0x7ff00000)&&((iy-0x7ff00000)|ly)!=0)) /* y is nan */
return x+y;
if((double) x==y) return y; /* x=y, return y */
if(ix==0) { /* x == 0 */
float u;
SET_FLOAT_WORD(x,(u_int32_t)(hy&0x80000000)|1);/* return +-minsub*/
u = math_opt_barrier (x);
u = u * u;
math_force_eval (u); /* raise underflow flag */
return x;
}
if(hx>=0) { /* x > 0 */
if(x > y) /* x -= ulp */
hx -= 1;
else /* x < y, x += ulp */
hx += 1;
} else { /* x < 0 */
if(x < y) /* x -= ulp */
hx -= 1;
else /* x > y, x += ulp */
hx += 1;
}
hy = hx&0x7f800000;
if(hy>=0x7f800000) {
float u = x+x; /* overflow */
math_force_eval (u);
__set_errno (ERANGE);
}
if(hy<0x00800000) {
float u = x*x; /* underflow */
math_force_eval (u); /* raise underflow flag */
__set_errno (ERANGE);
}
SET_FLOAT_WORD(x,hx);
return x;
}
float __nextafterf(float x, float y)
{
int32_t hx,hy,ix,iy;
GET_FLOAT_WORD(hx,x);
GET_FLOAT_WORD(hy,y);
ix = hx&0x7fffffff; /* |x| */
iy = hy&0x7fffffff; /* |y| */
if((ix>0x7f800000) || /* x is nan */
(iy>0x7f800000)) /* y is nan */
return x+y;
if(x==y) return y; /* x=y, return y */
if(ix==0) { /* x == 0 */
float u;
SET_FLOAT_WORD(x,(hy&0x80000000)|1);/* return +-minsubnormal */
u = math_opt_barrier (x);
u = u*u;
math_force_eval (u); /* raise underflow flag */
return x;
}
if(hx>=0) { /* x > 0 */
if(hx>hy) { /* x > y, x -= ulp */
hx -= 1;
} else { /* x < y, x += ulp */
hx += 1;
}
} else { /* x < 0 */
if(hy>=0||hx>hy){ /* x < y, x -= ulp */
hx -= 1;
} else { /* x > y, x += ulp */
hx += 1;
}
}
hy = hx&0x7f800000;
if(hy>=0x7f800000) {
float u = x+x; /* overflow */
math_force_eval (u);
}
if(hy<0x00800000) {
float u = x*x; /* underflow */
math_force_eval (u); /* raise underflow flag */
}
SET_FLOAT_WORD(x,hx);
return x;
}
double
__ieee754_exp2 (double x)
{
static const double himark = (double) DBL_MAX_EXP;
static const double lomark = (double) (DBL_MIN_EXP - DBL_MANT_DIG - 1);
/* Check for usual case. */
if (__glibc_likely (isless (x, himark)))
{
/* Exceptional cases: */
if (__glibc_unlikely (!isgreaterequal (x, lomark)))
{
if (isinf (x))
/* e^-inf == 0, with no error. */
return 0;
else
/* Underflow */
return TWOM1000 * TWOM1000;
}
static const double THREEp42 = 13194139533312.0;
int tval, unsafe;
double rx, x22, result;
union ieee754_double ex2_u, scale_u;
if (fabs (x) < DBL_EPSILON / 4.0)
return 1.0 + x;
{
SET_RESTORE_ROUND_NOEX (FE_TONEAREST);
/* 1. Argument reduction.
Choose integers ex, -256 <= t < 256, and some real
-1/1024 <= x1 <= 1024 so that
x = ex + t/512 + x1.
First, calculate rx = ex + t/512. */
rx = x + THREEp42;
rx -= THREEp42;
x -= rx; /* Compute x=x1. */
/* Compute tval = (ex*512 + t)+256.
Now, t = (tval mod 512)-256 and ex=tval/512 [that's mod, NOT %;
and /-round-to-nearest not the usual c integer /]. */
tval = (int) (rx * 512.0 + 256.0);
/* 2. Adjust for accurate table entry.
Find e so that
x = ex + t/512 + e + x2
where -1e6 < e < 1e6, and
(double)(2^(t/512+e))
is accurate to one part in 2^-64. */
/* 'tval & 511' is the same as 'tval%512' except that it's always
positive.
Compute x = x2. */
x -= exp2_deltatable[tval & 511];
/* 3. Compute ex2 = 2^(t/512+e+ex). */
ex2_u.d = exp2_accuratetable[tval & 511];
tval >>= 9;
/* x2 is an integer multiple of 2^-54; avoid intermediate
underflow from the calculation of x22 * x. */
unsafe = abs (tval) >= -DBL_MIN_EXP - 56;
ex2_u.ieee.exponent += tval >> unsafe;
scale_u.d = 1.0;
scale_u.ieee.exponent += tval - (tval >> unsafe);
/* 4. Approximate 2^x2 - 1, using a fourth-degree polynomial,
with maximum error in [-2^-10-2^-30,2^-10+2^-30]
less than 10^-19. */
x22 = (((.0096181293647031180
* x + .055504110254308625)
* x + .240226506959100583)
* x + .69314718055994495) * ex2_u.d;
math_opt_barrier (x22);
}
/* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */
result = x22 * x + ex2_u.d;
if (!unsafe)
return result;
else
return result * scale_u.d;
}
else
/* Return x, if x is a NaN or Inf; or overflow, otherwise. */
return TWO1023 * x;
npy_longdouble _nextl(npy_longdouble x, int p)
{
npy_int64 hx,ihx,ilx;
npy_uint64 lx;
GET_LDOUBLE_WORDS64(hx, lx, x);
ihx = hx & 0x7fffffffffffffffLL; /* |hx| */
ilx = lx & 0x7fffffffffffffffLL; /* |lx| */
if(((ihx & 0x7ff0000000000000LL)==0x7ff0000000000000LL)&&
((ihx & 0x000fffffffffffffLL)!=0)) {
return x; /* signal the nan */
}
if(ihx == 0 && ilx == 0) { /* x == 0 */
npy_longdouble u;
SET_LDOUBLE_WORDS64(x, p, 0ULL);/* return +-minsubnormal */
u = x * x;
if (u == x) {
return u;
} else {
return x; /* raise underflow flag */
}
}
npy_longdouble u;
if(p < 0) { /* p < 0, x -= ulp */
if((hx==0xffefffffffffffffLL)&&(lx==0xfc8ffffffffffffeLL))
return x+x; /* overflow, return -inf */
if (hx >= 0x7ff0000000000000LL) {
SET_LDOUBLE_WORDS64(u,0x7fefffffffffffffLL,0x7c8ffffffffffffeLL);
return u;
}
if(ihx <= 0x0360000000000000LL) { /* x <= LDBL_MIN */
u = math_opt_barrier (x);
x -= LDBL_TRUE_MIN;
if (ihx < 0x0360000000000000LL
|| (hx > 0 && (npy_int64) lx <= 0)
|| (hx < 0 && (npy_int64) lx > 1)) {
u = u * u;
math_force_eval (u); /* raise underflow flag */
}
return x;
}
if (ihx < 0x06a0000000000000LL) { /* ulp will denormal */
SET_LDOUBLE_WORDS64(u,(hx&0x7ff0000000000000LL),0ULL);
u *= 0x1.0000000000000p-105L;
} else
SET_LDOUBLE_WORDS64(u,(hx&0x7ff0000000000000LL)-0x0690000000000000LL,0ULL);
return x - u;
} else { /* p >= 0, x += ulp */
if((hx==0x7fefffffffffffffLL)&&(lx==0x7c8ffffffffffffeLL))
return x+x; /* overflow, return +inf */
if ((npy_uint64) hx >= 0xfff0000000000000ULL) {
SET_LDOUBLE_WORDS64(u,0xffefffffffffffffLL,0xfc8ffffffffffffeLL);
return u;
}
if(ihx <= 0x0360000000000000LL) { /* x <= LDBL_MIN */
u = math_opt_barrier (x);
x += LDBL_TRUE_MIN;
if (ihx < 0x0360000000000000LL
|| (hx > 0 && (npy_int64) lx < 0 && lx != 0x8000000000000001LL)
|| (hx < 0 && (npy_int64) lx >= 0)) {
u = u * u;
math_force_eval (u); /* raise underflow flag */
}
if (x == 0.0L) /* handle negative LDBL_TRUE_MIN case */
x = -0.0L;
return x;
}
if (ihx < 0x06a0000000000000LL) { /* ulp will denormal */
SET_LDOUBLE_WORDS64(u,(hx&0x7ff0000000000000LL),0ULL);
u *= 0x1.0000000000000p-105L;
} else
SET_LDOUBLE_WORDS64(u,(hx&0x7ff0000000000000LL)-0x0690000000000000LL,0ULL);
return x + u;
}
}
double
__fma (double x, double y, double z)
{
union ieee754_double u, v, w;
int adjust = 0;
u.d = x;
v.d = y;
w.d = z;
if (__builtin_expect (u.ieee.exponent + v.ieee.exponent
>= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG, 0)
|| __builtin_expect (u.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0)
|| __builtin_expect (v.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0)
|| __builtin_expect (w.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0)
|| __builtin_expect (u.ieee.exponent + v.ieee.exponent
<= IEEE754_DOUBLE_BIAS + DBL_MANT_DIG, 0))
{
/* If z is Inf, but x and y are finite, the result should be
z rather than NaN. */
if (w.ieee.exponent == 0x7ff
&& u.ieee.exponent != 0x7ff
&& v.ieee.exponent != 0x7ff)
return (z + x) + y;
/* If z is zero and x are y are nonzero, compute the result
as x * y to avoid the wrong sign of a zero result if x * y
underflows to 0. */
if (z == 0 && x != 0 && y != 0)
return x * y;
/* If x or y or z is Inf/NaN, or if x * y is zero, compute as
x * y + z. */
if (u.ieee.exponent == 0x7ff
|| v.ieee.exponent == 0x7ff
|| w.ieee.exponent == 0x7ff
|| x == 0
|| y == 0)
return x * y + z;
/* If fma will certainly overflow, compute as x * y. */
if (u.ieee.exponent + v.ieee.exponent > 0x7ff + IEEE754_DOUBLE_BIAS)
return x * y;
/* If x * y is less than 1/4 of DBL_DENORM_MIN, neither the
result nor whether there is underflow depends on its exact
value, only on its sign. */
if (u.ieee.exponent + v.ieee.exponent
< IEEE754_DOUBLE_BIAS - DBL_MANT_DIG - 2)
{
int neg = u.ieee.negative ^ v.ieee.negative;
double tiny = neg ? -0x1p-1074 : 0x1p-1074;
if (w.ieee.exponent >= 3)
return tiny + z;
/* Scaling up, adding TINY and scaling down produces the
correct result, because in round-to-nearest mode adding
TINY has no effect and in other modes double rounding is
harmless. But it may not produce required underflow
exceptions. */
v.d = z * 0x1p54 + tiny;
if (TININESS_AFTER_ROUNDING
? v.ieee.exponent < 55
: (w.ieee.exponent == 0
|| (w.ieee.exponent == 1
&& w.ieee.negative != neg
&& w.ieee.mantissa1 == 0
&& w.ieee.mantissa0 == 0)))
{
volatile double force_underflow = x * y;
(void) force_underflow;
}
return v.d * 0x1p-54;
}
if (u.ieee.exponent + v.ieee.exponent
>= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG)
{
/* Compute 1p-53 times smaller result and multiply
at the end. */
if (u.ieee.exponent > v.ieee.exponent)
u.ieee.exponent -= DBL_MANT_DIG;
else
v.ieee.exponent -= DBL_MANT_DIG;
/* If x + y exponent is very large and z exponent is very small,
it doesn't matter if we don't adjust it. */
if (w.ieee.exponent > DBL_MANT_DIG)
w.ieee.exponent -= DBL_MANT_DIG;
adjust = 1;
}
else if (w.ieee.exponent >= 0x7ff - DBL_MANT_DIG)
{
/* Similarly.
If z exponent is very large and x and y exponents are
very small, adjust them up to avoid spurious underflows,
rather than down. */
if (u.ieee.exponent + v.ieee.exponent
<= IEEE754_DOUBLE_BIAS + DBL_MANT_DIG)
{
if (u.ieee.exponent > v.ieee.exponent)
u.ieee.exponent += 2 * DBL_MANT_DIG + 2;
else
v.ieee.exponent += 2 * DBL_MANT_DIG + 2;
}
else if (u.ieee.exponent > v.ieee.exponent)
{
if (u.ieee.exponent > DBL_MANT_DIG)
u.ieee.exponent -= DBL_MANT_DIG;
}
else if (v.ieee.exponent > DBL_MANT_DIG)
v.ieee.exponent -= DBL_MANT_DIG;
w.ieee.exponent -= DBL_MANT_DIG;
adjust = 1;
}
else if (u.ieee.exponent >= 0x7ff - DBL_MANT_DIG)
{
u.ieee.exponent -= DBL_MANT_DIG;
if (v.ieee.exponent)
v.ieee.exponent += DBL_MANT_DIG;
else
v.d *= 0x1p53;
}
else if (v.ieee.exponent >= 0x7ff - DBL_MANT_DIG)
{
v.ieee.exponent -= DBL_MANT_DIG;
if (u.ieee.exponent)
u.ieee.exponent += DBL_MANT_DIG;
else
u.d *= 0x1p53;
}
else /* if (u.ieee.exponent + v.ieee.exponent
<= IEEE754_DOUBLE_BIAS + DBL_MANT_DIG) */
{
if (u.ieee.exponent > v.ieee.exponent)
u.ieee.exponent += 2 * DBL_MANT_DIG + 2;
else
v.ieee.exponent += 2 * DBL_MANT_DIG + 2;
if (w.ieee.exponent <= 4 * DBL_MANT_DIG + 6)
{
if (w.ieee.exponent)
w.ieee.exponent += 2 * DBL_MANT_DIG + 2;
else
w.d *= 0x1p108;
adjust = -1;
}
/* Otherwise x * y should just affect inexact
and nothing else. */
}
x = u.d;
y = v.d;
z = w.d;
}
/* Ensure correct sign of exact 0 + 0. */
if (__glibc_unlikely ((x == 0 || y == 0) && z == 0))
return x * y + z;
fenv_t env;
libc_feholdexcept_setround (&env, FE_TONEAREST);
/* Multiplication m1 + m2 = x * y using Dekker's algorithm. */
#define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
double x1 = x * C;
double y1 = y * C;
double m1 = x * y;
x1 = (x - x1) + x1;
y1 = (y - y1) + y1;
double x2 = x - x1;
double y2 = y - y1;
double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
/* Addition a1 + a2 = z + m1 using Knuth's algorithm. */
double a1 = z + m1;
double t1 = a1 - z;
double t2 = a1 - t1;
t1 = m1 - t1;
t2 = z - t2;
double a2 = t1 + t2;
/* Ensure the arithmetic is not scheduled after feclearexcept call. */
math_force_eval (m2);
math_force_eval (a2);
feclearexcept (FE_INEXACT);
/* If the result is an exact zero, ensure it has the correct sign. */
if (a1 == 0 && m2 == 0)
{
libc_feupdateenv (&env);
/* Ensure that round-to-nearest value of z + m1 is not reused. */
z = math_opt_barrier (z);
return z + m1;
}
libc_fesetround (FE_TOWARDZERO);
/* Perform m2 + a2 addition with round to odd. */
u.d = a2 + m2;
if (__glibc_unlikely (adjust < 0))
{
if ((u.ieee.mantissa1 & 1) == 0)
u.ieee.mantissa1 |= libc_fetestexcept (FE_INEXACT) != 0;
v.d = a1 + u.d;
/* Ensure the addition is not scheduled after fetestexcept call. */
math_force_eval (v.d);
}
/* Reset rounding mode and test for inexact simultaneously. */
int j = libc_feupdateenv_test (&env, FE_INEXACT) != 0;
if (__glibc_likely (adjust == 0))
{
if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff)
u.ieee.mantissa1 |= j;
/* Result is a1 + u.d. */
return a1 + u.d;
}
else if (__glibc_likely (adjust > 0))
{
if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff)
u.ieee.mantissa1 |= j;
/* Result is a1 + u.d, scaled up. */
return (a1 + u.d) * 0x1p53;
}
else
{
/* If a1 + u.d is exact, the only rounding happens during
scaling down. */
if (j == 0)
return v.d * 0x1p-108;
/* If result rounded to zero is not subnormal, no double
rounding will occur. */
if (v.ieee.exponent > 108)
return (a1 + u.d) * 0x1p-108;
/* If v.d * 0x1p-108 with round to zero is a subnormal above
or equal to DBL_MIN / 2, then v.d * 0x1p-108 shifts mantissa
down just by 1 bit, which means v.ieee.mantissa1 |= j would
change the round bit, not sticky or guard bit.
v.d * 0x1p-108 never normalizes by shifting up,
so round bit plus sticky bit should be already enough
for proper rounding. */
if (v.ieee.exponent == 108)
{
/* If the exponent would be in the normal range when
rounding to normal precision with unbounded exponent
range, the exact result is known and spurious underflows
must be avoided on systems detecting tininess after
rounding. */
if (TININESS_AFTER_ROUNDING)
{
w.d = a1 + u.d;
if (w.ieee.exponent == 109)
return w.d * 0x1p-108;
}
/* v.ieee.mantissa1 & 2 is LSB bit of the result before rounding,
v.ieee.mantissa1 & 1 is the round bit and j is our sticky
bit. */
w.d = 0.0;
w.ieee.mantissa1 = ((v.ieee.mantissa1 & 3) << 1) | j;
w.ieee.negative = v.ieee.negative;
v.ieee.mantissa1 &= ~3U;
v.d *= 0x1p-108;
w.d *= 0x1p-2;
return v.d + w.d;
}
v.ieee.mantissa1 |= j;
return v.d * 0x1p-108;
}
}
long double __nextafterl(long double x, long double y)
{
int64_t hx,hy,ihx,ihy,ilx;
u_int64_t lx,ly;
GET_LDOUBLE_WORDS64(hx,lx,x);
GET_LDOUBLE_WORDS64(hy,ly,y);
ihx = hx&0x7fffffffffffffffLL; /* |hx| */
ilx = lx&0x7fffffffffffffffLL; /* |lx| */
ihy = hy&0x7fffffffffffffffLL; /* |hy| */
if((((ihx&0x7ff0000000000000LL)==0x7ff0000000000000LL)&&
((ihx&0x000fffffffffffffLL)!=0)) || /* x is nan */
(((ihy&0x7ff0000000000000LL)==0x7ff0000000000000LL)&&
((ihy&0x000fffffffffffffLL)!=0))) /* y is nan */
return x+y; /* signal the nan */
if(x==y)
return y; /* x=y, return y */
if(ihx == 0 && ilx == 0) { /* x == 0 */
long double u;
hy = (hy & 0x8000000000000000ULL) | 1;
SET_LDOUBLE_WORDS64(x,hy,0ULL);/* return +-minsubnormal */
u = math_opt_barrier (x);
u = u * u;
math_force_eval (u); /* raise underflow flag */
return x;
}
long double u;
if(x > y) { /* x > y, x -= ulp */
if((hx==0xffefffffffffffffLL)&&(lx==0xfc8ffffffffffffeLL))
return x+x; /* overflow, return -inf */
if (hx >= 0x7ff0000000000000LL) {
SET_LDOUBLE_WORDS64(u,0x7fefffffffffffffLL,0x7c8ffffffffffffeLL);
return u;
}
if(ihx <= 0x0360000000000000LL) { /* x <= LDBL_MIN */
u = math_opt_barrier (x);
x -= __LDBL_DENORM_MIN__;
if (ihx < 0x0360000000000000LL
|| (hx > 0 && (int64_t) lx <= 0)
|| (hx < 0 && (int64_t) lx > 1)) {
u = u * u;
math_force_eval (u); /* raise underflow flag */
}
return x;
}
if (ihx < 0x06a0000000000000LL) { /* ulp will denormal */
SET_LDOUBLE_WORDS64(u,(hx&0x7ff0000000000000LL),0ULL);
u *= 0x1.0000000000000p-105L;
} else
SET_LDOUBLE_WORDS64(u,(hx&0x7ff0000000000000LL)-0x0690000000000000LL,0ULL);
return x - u;
} else { /* x < y, x += ulp */
if((hx==0x7fefffffffffffffLL)&&(lx==0x7c8ffffffffffffeLL))
return x+x; /* overflow, return +inf */
if ((u_int64_t) hx >= 0xfff0000000000000ULL) {
SET_LDOUBLE_WORDS64(u,0xffefffffffffffffLL,0xfc8ffffffffffffeLL);
return u;
}
if(ihx <= 0x0360000000000000LL) { /* x <= LDBL_MIN */
u = math_opt_barrier (x);
x += __LDBL_DENORM_MIN__;
if (ihx < 0x0360000000000000LL
|| (hx > 0 && (int64_t) lx < 0 && lx != 0x8000000000000001LL)
|| (hx < 0 && (int64_t) lx >= 0)) {
u = u * u;
math_force_eval (u); /* raise underflow flag */
}
if (x == 0.0L) /* handle negative __LDBL_DENORM_MIN__ case */
x = -0.0L;
return x;
}
if (ihx < 0x06a0000000000000LL) { /* ulp will denormal */
SET_LDOUBLE_WORDS64(u,(hx&0x7ff0000000000000LL),0ULL);
u *= 0x1.0000000000000p-105L;
} else
SET_LDOUBLE_WORDS64(u,(hx&0x7ff0000000000000LL)-0x0690000000000000LL,0ULL);
return x + u;
}
}
long double __nextafterl(long double x, long double y)
{
u_int32_t hx,hy,ix,iy;
u_int32_t lx,ly;
int32_t esx,esy;
GET_LDOUBLE_WORDS(esx,hx,lx,x);
GET_LDOUBLE_WORDS(esy,hy,ly,y);
ix = esx&0x7fff; /* |x| */
iy = esy&0x7fff; /* |y| */
/* Intel's extended format has the normally implicit 1 explicit
present. Sigh! */
if(((ix==0x7fff)&&(((hx&0x7fffffff)|lx)!=0)) || /* x is nan */
((iy==0x7fff)&&(((hy&0x7fffffff)|ly)!=0))) /* y is nan */
return x+y;
if(x==y) return y; /* x=y, return y */
if((ix|hx|lx)==0) { /* x == 0 */
long double u;
SET_LDOUBLE_WORDS(x,esy&0x8000,0,1);/* return +-minsubnormal */
u = math_opt_barrier (x);
u = u * u;
math_force_eval (u); /* raise underflow flag */
return x;
}
if(esx>=0) { /* x > 0 */
if(esx>esy||((esx==esy) && (hx>hy||((hx==hy)&&(lx>ly))))) {
/* x > y, x -= ulp */
if(lx==0) {
if (hx <= 0x80000000) {
if (esx == 0) {
--hx;
} else {
esx -= 1;
hx = hx - 1;
if (esx > 0)
hx |= 0x80000000;
}
} else
hx -= 1;
}
lx -= 1;
} else { /* x < y, x += ulp */
lx += 1;
if(lx==0) {
hx += 1;
if (hx==0 || (esx == 0 && hx == 0x80000000)) {
esx += 1;
hx |= 0x80000000;
}
}
}
} else { /* x < 0 */
if(esy>=0||(esx>esy||((esx==esy)&&(hx>hy||((hx==hy)&&(lx>ly)))))){
/* x < y, x -= ulp */
if(lx==0) {
if (hx <= 0x80000000 && esx != 0xffff8000) {
esx -= 1;
hx = hx - 1;
if ((esx&0x7fff) > 0)
hx |= 0x80000000;
} else
hx -= 1;
}
lx -= 1;
} else { /* x > y, x += ulp */
lx += 1;
if(lx==0) {
hx += 1;
if (hx==0 || (esx == 0xffff8000 && hx == 0x80000000)) {
esx += 1;
hx |= 0x80000000;
}
}
}
}
esy = esx&0x7fff;
if(esy==0x7fff) {
long double u = x + x; /* overflow */
math_force_eval (u);
__set_errno (ERANGE);
}
if(esy==0) {
long double u = x*x; /* underflow */
math_force_eval (u); /* raise underflow flag */
__set_errno (ERANGE);
}
SET_LDOUBLE_WORDS(x,esx,hx,lx);
return x;
}
