long double
__modfl(long double x, long double *iptr)
{
int32_t i0,i1,j0;
u_int32_t i,se;
GET_LDOUBLE_WORDS(se,i0,i1,x);
j0 = (se&0x7fff)-0x3fff; /* exponent of x */
if(j0<32) { /* integer part in high x */
if(j0<0) { /* |x|<1 */
SET_LDOUBLE_WORDS(*iptr,se&0x8000,0,0); /* *iptr = +-0 */
return x;
} else {
i = (0x7fffffff)>>j0;
if(((i0&i)|i1)==0) { /* x is integral */
*iptr = x;
SET_LDOUBLE_WORDS(x,se&0x8000,0,0); /* return +-0 */
return x;
} else {
SET_LDOUBLE_WORDS(*iptr,se,i0&(~i),0);
return x - *iptr;
}
}
} else if (__builtin_expect(j0>63, 0)) { /* no fraction part */
long double __nextafterl(long double x, long double y)
{
int32_t ix,iy,esx,esy;
uint32_t hx,hy,lx,ly;
GET_LDOUBLE_WORDS(esx,hx,lx,x);
GET_LDOUBLE_WORDS(esy,hy,ly,y);
ix = esx&0x7fff; /* |x| */
iy = esy&0x7fff; /* |y| */
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 */
SET_LDOUBLE_WORDS(x,esy&0x8000,0,1);/* return +-minsubnormal */
y = x*x;
math_force_eval (y); /* 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 (ix != 0 && hx == 0x80000000) hx = 0;
if (hx==0) esx -= 1;
hx -= 1;
}
lx -= 1;
} else { /* x < y, x += ulp */
lx += 1;
if(lx==0) {
hx += 1;
if (hx==0) {
hx = 0x80000000;
esx += 1;
}
}
}
} else { /* x < 0 */
if(esy>=0||esx>esy||((esx==esy) && (hx>hy||((hx==hy)&&(lx>ly))))){
/* x < y, x -= ulp */
if(lx==0) {
if (ix != 0 && hx == 0x80000000) hx = 0;
if (hx==0) esx -= 1;
hx -= 1;
}
lx -= 1;
} else { /* x > y, x += ulp */
lx += 1;
if(lx==0) {
hx += 1;
if (hx==0) {
hx = 0x80000000;
esx += 1;
}
}
}
}
esy = esx&0x7fff;
if(esy==0x7fff) {
long double u = x + x; /* overflow */
math_force_eval (u);
__set_errno (ERANGE);
}
if(esy==0 && (hx & 0x80000000) == 0) { /* underflow */
y = x*x;
math_force_eval (y); /* raise underflow flag */
__set_errno (ERANGE);
}
SET_LDOUBLE_WORDS(x,esx,hx,lx);
return x;
}
long double
nextafterl(long double x, long double y)
{
int32_t hx,hy,ix,iy;
u_int32_t lx,ly,esx,esy;
GET_LDOUBLE_WORDS(esx,hx,lx,x);
GET_LDOUBLE_WORDS(esy,hy,ly,y);
ix = esx&0x7fff; /* |x| */
iy = esy&0x7fff; /* |y| */
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 */
volatile long double u;
SET_LDOUBLE_WORDS(x,esy&0x8000,0,1);/* return +-minsubnormal */
u = x;
u = u * u; /* raise underflow flag */
return x;
}
if(esx<0x8000) { /* x > 0 */
if(ix>iy||((ix==iy) && (hx>hy||((hx==hy)&&(lx>ly))))) {
/* x > y, x -= ulp */
if(lx==0) {
if ((hx&0x7fffffff)==0) esx -= 1;
hx = (hx - 1) | (hx & 0x80000000);
}
lx -= 1;
} else { /* x < y, x += ulp */
lx += 1;
if(lx==0) {
hx = (hx + 1) | (hx & 0x80000000);
if ((hx&0x7fffffff)==0) esx += 1;
}
}
} else { /* x < 0 */
if(esy>=0||(ix>iy||((ix==iy)&&(hx>hy||((hx==hy)&&(lx>ly)))))){
/* x < y, x -= ulp */
if(lx==0) {
if ((hx&0x7fffffff)==0) esx -= 1;
hx = (hx - 1) | (hx & 0x80000000);
}
lx -= 1;
} else { /* x > y, x += ulp */
lx += 1;
if(lx==0) {
hx = (hx + 1) | (hx & 0x80000000);
if ((hx&0x7fffffff)==0) esx += 1;
}
}
}
esy = esx&0x7fff;
if(esy==0x7fff) return x+x; /* overflow */
if(esy==0) {
volatile long double u = x*x; /* underflow */
if(u==x) {
SET_LDOUBLE_WORDS(x,esx,hx,lx);
return x;
}
}
SET_LDOUBLE_WORDS(x,esx,hx,lx);
return x;
}
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;
}
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;
}
long double
__roundevenl (long double x)
{
uint16_t se;
uint32_t hx, lx;
GET_LDOUBLE_WORDS (se, hx, lx, x);
int exponent = se & 0x7fff;
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 + MANT_DIG - 32)
{
/* Not necessarily an integer; integer bit is in low word.
Locate the bits with exponents 0 and -1. */
int int_pos = (BIAS + MANT_DIG - 1) - exponent;
int half_pos = int_pos - 1;
uint32_t half_bit = 1U << half_pos;
uint32_t int_bit = 1U << int_pos;
if ((lx & (int_bit | (half_bit - 1))) != 0)
{
/* No need to test whether HALF_BIT is set. */
lx += half_bit;
if (lx < half_bit)
{
hx++;
if (hx == 0)
{
hx = 0x80000000;
se++;
}
}
}
lx &= ~(int_bit - 1);
}
else if (exponent == BIAS + MANT_DIG - 33)
{
/* Not necessarily an integer; integer bit is bottom of high
word, half bit is top of low word. */
if (((hx & 1) | (lx & 0x7fffffff)) != 0)
{
lx += 0x80000000;
if (lx < 0x80000000)
{
hx++;
if (hx == 0)
{
hx = 0x80000000;
se++;
}
}
}
lx = 0;
}
else if (exponent >= BIAS)
{
/* At least 1; not necessarily an integer, integer bit and half
bit are in the high word. Locate the bits with exponents 0
and -1. */
int int_pos = (BIAS + MANT_DIG - 33) - exponent;
int half_pos = int_pos - 1;
uint32_t half_bit = 1U << half_pos;
uint32_t int_bit = 1U << int_pos;
if (((hx & (int_bit | (half_bit - 1))) | lx) != 0)
{
hx += half_bit;
if (hx < half_bit)
{
hx = 0x80000000;
se++;
}
}
hx &= ~(int_bit - 1);
lx = 0;
}
else if (exponent == BIAS - 1 && (hx > 0x80000000 || lx != 0))
{
/* Interval (0.5, 1). */
se = (se & 0x8000) | 0x3fff;
hx = 0x80000000;
lx = 0;
}
else
{
/* Rounds to 0. */
se &= 0x8000;
hx = 0;
lx = 0;
}
SET_LDOUBLE_WORDS (x, se, hx, lx);
return x;
}
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;
}