long double __fabsl(long double x)
{
u_int32_t exp;
GET_LDOUBLE_EXP(exp,x);
SET_LDOUBLE_EXP(x,exp&0x7fff);
return x;
}
int
__signbitl (Extended x)
{
int32_t e;
GET_LDOUBLE_EXP (e, x);
return e & 0x8000;
}
int
__signbitl (long double x)
{
int32_t e;
GET_LDOUBLE_EXP (e, x);
return e & 0x8000;
}
long double __frexpl(long double x, int *eptr)
{
u_int32_t se, hx, ix, lx;
GET_LDOUBLE_WORDS(se,hx,lx,x);
ix = 0x7fff&se;
*eptr = 0;
if(ix==0x7fff||((ix|hx|lx)==0)) return x + x; /* 0,inf,nan */
if (ix==0x0000) { /* subnormal */
x *= two65;
GET_LDOUBLE_EXP(se,x);
ix = se&0x7fff;
*eptr = -65;
}
*eptr += ix-16382;
se = (se & 0x8000) | 0x3ffe;
SET_LDOUBLE_EXP(x,se);
return x;
}
long double
asinhl(long double x)
{
long double t,w;
int32_t hx,ix;
GET_LDOUBLE_EXP(hx,x);
ix = hx&0x7fff;
if(ix==0x7fff) return x+x; /* x is inf or NaN */
if(ix< 0x3fde) { /* |x|<2**-34 */
if(huge+x>one) return x; /* return x inexact except 0 */
}
if(ix>0x4020) { /* |x| > 2**34 */
w = logl(fabsl(x))+ln2;
} else if (ix>0x4000) { /* 2**34 > |x| > 2.0 */
t = fabsl(x);
w = logl(2.0*t+one/(sqrtl(x*x+one)+t));
} else { /* 2.0 > |x| > 2**-28 */
t = x*x;
w =log1pl(fabsl(x)+t/(one+sqrtl(one+t)));
}
if(hx&0x8000) return -w; else return w;
}
long double __ieee754_hypotl(long double x, long double y)
{
long double a,b,t1,t2,y1,y2,w;
u_int32_t j,k,ea,eb;
GET_LDOUBLE_EXP(ea,x);
ea &= 0x7fff;
GET_LDOUBLE_EXP(eb,y);
eb &= 0x7fff;
if(eb > ea) {a=y;b=x;j=ea; ea=eb;eb=j;} else {a=x;b=y;}
SET_LDOUBLE_EXP(a,ea); /* a <- |a| */
SET_LDOUBLE_EXP(b,eb); /* b <- |b| */
if((ea-eb)>0x46) {return a+b;} /* x/y > 2**70 */
k=0;
if(__builtin_expect(ea > 0x5f3f,0)) { /* a>2**8000 */
if(ea == 0x7fff) { /* Inf or NaN */
u_int32_t exp __attribute__ ((unused));
u_int32_t high,low;
w = a+b; /* for sNaN */
GET_LDOUBLE_WORDS(exp,high,low,a);
if(((high&0x7fffffff)|low)==0) w = a;
GET_LDOUBLE_WORDS(exp,high,low,b);
if(((eb^0x7fff)|(high&0x7fffffff)|low)==0) w = b;
return w;
}
/* scale a and b by 2**-9600 */
ea -= 0x2580; eb -= 0x2580; k += 9600;
SET_LDOUBLE_EXP(a,ea);
SET_LDOUBLE_EXP(b,eb);
}
if(__builtin_expect(eb < 0x20bf, 0)) { /* b < 2**-8000 */
if(eb == 0) { /* subnormal b or 0 */
u_int32_t exp __attribute__ ((unused));
u_int32_t high,low;
GET_LDOUBLE_WORDS(exp,high,low,b);
if((high|low)==0) return a;
SET_LDOUBLE_WORDS(t1, 0x7ffd, 0x80000000, 0); /* t1=2^16382 */
b *= t1;
a *= t1;
k -= 16382;
GET_LDOUBLE_EXP (ea, a);
GET_LDOUBLE_EXP (eb, b);
if (eb > ea)
{
t1 = a;
a = b;
b = t1;
j = ea;
ea = eb;
eb = j;
}
} else { /* scale a and b by 2^9600 */
ea += 0x2580; /* a *= 2^9600 */
eb += 0x2580; /* b *= 2^9600 */
k -= 9600;
SET_LDOUBLE_EXP(a,ea);
SET_LDOUBLE_EXP(b,eb);
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
u_int32_t high;
GET_LDOUBLE_MSW(high,a);
SET_LDOUBLE_WORDS(t1,ea,high,0);
t2 = a-t1;
w = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
u_int32_t high;
GET_LDOUBLE_MSW(high,b);
a = a+a;
SET_LDOUBLE_WORDS(y1,eb,high,0);
y2 = b - y1;
GET_LDOUBLE_MSW(high,a);
SET_LDOUBLE_WORDS(t1,ea+1,high,0);
t2 = a - t1;
w = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
u_int32_t exp;
t1 = 1.0;
GET_LDOUBLE_EXP(exp,t1);
SET_LDOUBLE_EXP(t1,exp+k);
w *= t1;
math_check_force_underflow_nonneg (w);
return w;
} else return w;
}
npy_longdouble npy_nextafterl(npy_longdouble x, npy_longdouble y)
{
volatile npy_longdouble t;
union IEEEl2bitsrep ux;
union IEEEl2bitsrep uy;
ux.e = x;
uy.e = y;
if ((GET_LDOUBLE_EXP(ux) == 0x7fff &&
((GET_LDOUBLE_MANH(ux) & ~LDBL_NBIT) | GET_LDOUBLE_MANL(ux)) != 0) ||
(GET_LDOUBLE_EXP(uy) == 0x7fff &&
((GET_LDOUBLE_MANH(uy) & ~LDBL_NBIT) | GET_LDOUBLE_MANL(uy)) != 0)) {
return ux.e + uy.e; /* x or y is nan */
}
if (ux.e == uy.e) {
return uy.e; /* x=y, return y */
}
if (ux.e == 0.0) {
SET_LDOUBLE_MANH(ux, 0); /* return +-minsubnormal */
SET_LDOUBLE_MANL(ux, 1);
SET_LDOUBLE_SIGN(ux, GET_LDOUBLE_SIGN(uy));
t = ux.e * ux.e;
if (t == ux.e) {
return t;
} else {
return ux.e; /* raise underflow flag */
}
}
if ((ux.e > 0.0) ^ (ux.e < uy.e)) { /* x -= ulp */
if (GET_LDOUBLE_MANL(ux) == 0) {
if ((GET_LDOUBLE_MANH(ux) & ~LDBL_NBIT) == 0) {
SET_LDOUBLE_EXP(ux, GET_LDOUBLE_EXP(ux) - 1);
}
SET_LDOUBLE_MANH(ux,
(GET_LDOUBLE_MANH(ux) - 1) |
(GET_LDOUBLE_MANH(ux) & LDBL_NBIT));
}
SET_LDOUBLE_MANL(ux, GET_LDOUBLE_MANL(ux) - 1);
} else { /* x += ulp */
SET_LDOUBLE_MANL(ux, GET_LDOUBLE_MANL(ux) + 1);
if (GET_LDOUBLE_MANL(ux) == 0) {
SET_LDOUBLE_MANH(ux,
(GET_LDOUBLE_MANH(ux) + 1) |
(GET_LDOUBLE_MANH(ux) & LDBL_NBIT));
if ((GET_LDOUBLE_MANH(ux) & ~LDBL_NBIT) == 0) {
SET_LDOUBLE_EXP(ux, GET_LDOUBLE_EXP(ux) + 1);
}
}
}
if (GET_LDOUBLE_EXP(ux) == 0x7fff) {
return ux.e + ux.e; /* overflow */
}
if (GET_LDOUBLE_EXP(ux) == 0) { /* underflow */
if (LDBL_NBIT) {
SET_LDOUBLE_MANH(ux, GET_LDOUBLE_MANH(ux) & ~LDBL_NBIT);
}
t = ux.e * ux.e;
if (t != ux.e) { /* raise underflow flag */
return ux.e;
}
}
return ux.e;
}
npy_longdouble _nextl(npy_longdouble x, int p)
{
volatile npy_longdouble t;
union IEEEl2bitsrep ux;
ux.e = x;
if ((GET_LDOUBLE_EXP(ux) == 0x7fff &&
((GET_LDOUBLE_MANH(ux) & ~LDBL_NBIT) | GET_LDOUBLE_MANL(ux)) != 0)) {
return ux.e; /* x is nan */
}
if (ux.e == 0.0) {
SET_LDOUBLE_MANH(ux, 0); /* return +-minsubnormal */
SET_LDOUBLE_MANL(ux, 1);
if (p >= 0) {
SET_LDOUBLE_SIGN(ux, 0);
} else {
SET_LDOUBLE_SIGN(ux, 1);
}
t = ux.e * ux.e;
if (t == ux.e) {
return t;
} else {
return ux.e; /* raise underflow flag */
}
}
if (p < 0) { /* x -= ulp */
if (GET_LDOUBLE_MANL(ux) == 0) {
if ((GET_LDOUBLE_MANH(ux) & ~LDBL_NBIT) == 0) {
SET_LDOUBLE_EXP(ux, GET_LDOUBLE_EXP(ux) - 1);
}
SET_LDOUBLE_MANH(ux,
(GET_LDOUBLE_MANH(ux) - 1) |
(GET_LDOUBLE_MANH(ux) & LDBL_NBIT));
}
SET_LDOUBLE_MANL(ux, GET_LDOUBLE_MANL(ux) - 1);
} else { /* x += ulp */
SET_LDOUBLE_MANL(ux, GET_LDOUBLE_MANL(ux) + 1);
if (GET_LDOUBLE_MANL(ux) == 0) {
SET_LDOUBLE_MANH(ux,
(GET_LDOUBLE_MANH(ux) + 1) |
(GET_LDOUBLE_MANH(ux) & LDBL_NBIT));
if ((GET_LDOUBLE_MANH(ux) & ~LDBL_NBIT) == 0) {
SET_LDOUBLE_EXP(ux, GET_LDOUBLE_EXP(ux) + 1);
}
}
}
if (GET_LDOUBLE_EXP(ux) == 0x7fff) {
return ux.e + ux.e; /* overflow */
}
if (GET_LDOUBLE_EXP(ux) == 0) { /* underflow */
if (LDBL_NBIT) {
SET_LDOUBLE_MANH(ux, GET_LDOUBLE_MANH(ux) & ~LDBL_NBIT);
}
t = ux.e * ux.e;
if (t != ux.e) { /* raise underflow flag */
return ux.e;
}
}
return ux.e;
}
long double
hypotl(long double x, long double y)
{
long double a,b,t1,t2,yy1,y2,w;
u_int32_t j,k,ea,eb;
GET_LDOUBLE_EXP(ea,x);
ea &= 0x7fff;
GET_LDOUBLE_EXP(eb,y);
eb &= 0x7fff;
if(eb > ea) {a=y;b=x;j=ea; ea=eb;eb=j;} else {a=x;b=y;}
SET_LDOUBLE_EXP(a,ea); /* a <- |a| */
SET_LDOUBLE_EXP(b,eb); /* b <- |b| */
if((ea-eb)>0x46) {return a+b;} /* x/y > 2**70 */
k=0;
if(ea > 0x5f3f) { /* a>2**8000 */
if(ea == 0x7fff) { /* Inf or NaN */
u_int32_t es,high,low;
w = a+b; /* for sNaN */
GET_LDOUBLE_WORDS(es,high,low,a);
if(((high&0x7fffffff)|low)==0) w = a;
GET_LDOUBLE_WORDS(es,high,low,b);
if(((eb^0x7fff)|(high&0x7fffffff)|low)==0) w = b;
return w;
}
/* scale a and b by 2**-9600 */
ea -= 0x2580; eb -= 0x2580; k += 9600;
SET_LDOUBLE_EXP(a,ea);
SET_LDOUBLE_EXP(b,eb);
}
if(eb < 0x20bf) { /* b < 2**-8000 */
if(eb == 0) { /* subnormal b or 0 */
u_int32_t es,high,low;
GET_LDOUBLE_WORDS(es,high,low,b);
if((high|low)==0) return a;
SET_LDOUBLE_WORDS(t1, 0x7ffd, 0, 0); /* t1=2^16382 */
b *= t1;
a *= t1;
k -= 16382;
} else { /* scale a and b by 2^9600 */
ea += 0x2580; /* a *= 2^9600 */
eb += 0x2580; /* b *= 2^9600 */
k -= 9600;
SET_LDOUBLE_EXP(a,ea);
SET_LDOUBLE_EXP(b,eb);
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
u_int32_t high;
GET_LDOUBLE_MSW(high,a);
SET_LDOUBLE_WORDS(t1,ea,high,0);
t2 = a-t1;
w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
u_int32_t high;
GET_LDOUBLE_MSW(high,b);
a = a+a;
SET_LDOUBLE_WORDS(yy1,eb,high,0);
y2 = b - yy1;
GET_LDOUBLE_MSW(high,a);
SET_LDOUBLE_WORDS(t1,ea+1,high,0);
t2 = a - t1;
w = sqrtl(t1*yy1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
u_int32_t es;
t1 = 1.0;
GET_LDOUBLE_EXP(es,t1);
SET_LDOUBLE_EXP(t1,es+k);
return t1*w;
} else return w;
}