double nextafter(double x, double y)
{
int hx,hy,ix,iy;
unsigned lx,ly;
hx = __HI(x); /* high word of x */
lx = __LO(x); /* low word of x */
hy = __HI(y); /* high word of y */
ly = __LO(y); /* low word of y */
ix = hx&0x7fffffff; /* |x| */
iy = hy&0x7fffffff; /* |y| */
if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */
((iy>=0x7ff00000)&&((iy-0x7ff00000)|ly)!=0)) /* y is nan */
return x+y;
if(x==y) return x; /* x=y, return x */
if((ix|lx)==0) { /* x == 0 */
__HI(x) = hy&0x80000000; /* return +-minsubnormal */
__LO(x) = 1;
y = x*x;
if(y==x) return y;
else return x; /* raise underflow flag */
}
if(hx>=0) { /* x > 0 */
if(hx>hy||((hx==hy)&&(lx>ly))) { /* 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(hy>=0||hx>hy||((hx==hy)&&(lx>ly))) { /* 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) return x+x; /* overflow */
if(hy<0x00100000) { /* underflow */
y = x*x;
if(y!=x) { /* raise underflow flag */
__HI(y) = hx;
__LO(y) = lx;
return y;
}
}
__HI(x) = hx;
__LO(x) = lx;
return x;
}
double
pow (double x, double y)
{
double z, ax, z_h, z_l, p_h, p_l;
double y1, t1, t2, r, s, t, u, v, w;
int i, j, k, yisint, n;
int hx, hy, ix, iy;
unsigned lx, ly;
hx = __HI (x);
lx = __LO (x);
hy = __HI (y);
ly = __LO (y);
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
/* y == zero: x**0 = 1 */
if ((iy | ly) == 0)
{
return one;
}
/* +-NaN return x + y */
if (ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0)) || iy > 0x7ff00000 || ((iy == 0x7ff00000) && (ly != 0)))
{
return x + y;
}
/* determine if y is an odd int when x < 0
* yisint = 0 ... y is not an integer
* yisint = 1 ... y is an odd int
* yisint = 2 ... y is an even int
*/
yisint = 0;
if (hx < 0)
{
if (iy >= 0x43400000) /* even integer y */
{
yisint = 2;
}
else if (iy >= 0x3ff00000)
{
k = (iy >> 20) - 0x3ff; /* exponent */
if (k > 20)
{
j = ly >> (52 - k);
if ((j << (52 - k)) == ly)
{
yisint = 2 - (j & 1);
}
}
else if (ly == 0)
double __ieee754_log(double x)
{
double hfsq,f,s,z,R,w,t1,t2,dk;
int k,hx,i,j;
unsigned lx;
hx = __HI(x); /* high word of x */
lx = __LO(x); /* low word of x */
k=0;
if (hx < 0x00100000) { /* x < 2**-1022 */
if (((hx&0x7fffffff)|lx)==0)
return -two54/zero; /* log(+-0)=-inf */
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
k -= 54; x *= two54; /* subnormal number, scale up x */
hx = __HI(x); /* high word of x */
}
if (hx >= 0x7ff00000) return x+x;
k += (hx>>20)-1023;
hx &= 0x000fffff;
i = (hx+0x95f64)&0x100000;
__HI(x) = hx|(i^0x3ff00000); /* normalize x or x/2 */
k += (i>>20);
f = x-1.0;
if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
if(f==zero) if(k==0) return zero; else {dk=(double)k;
return dk*ln2_hi+dk*ln2_lo;}
R = f*f*(0.5-0.33333333333333333*f);
if(k==0) return f-R; else {dk=(double)k;
return dk*ln2_hi-((R-dk*ln2_lo)-f);}
}
s = f/(2.0+f);
dk = (double)k;
z = s*s;
i = hx-0x6147a;
w = z*z;
j = 0x6b851-hx;
t1= w*(Lg2+w*(Lg4+w*Lg6));
t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
i |= j;
R = t2+t1;
if(i>0) {
hfsq=0.5*f*f;
if(k==0) return f-(hfsq-s*(hfsq+R)); else
return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
} else {
if(k==0) return f-s*(f-R); else
return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
}
}
double JFP_lib_sin(double x) {
double y[2];
int n, ix;
/* High word of x. */
ix = __HI(x);
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if(ix <= 0x3fe921fb) return __kernel_sin(x,0,0);
/* sin(Inf or NaN) is NaN */
else if (ix>=0x7ff00000) return x-x;
/* argument reduction needed */
else {
n = __ieee754_rem_pio2(x,y);
switch(n&3) {
case 0: return __kernel_sin(y[0],y[1],1);
case 1: return __kernel_cos(y[0],y[1]);
case 2: return -__kernel_sin(y[0],y[1],1);
default:
return -__kernel_cos(y[0],y[1]);
}
}
}
double
acos (double x)
{
double z, p, q, r, w, s, c, df;
int hx, ix;
hx = __HI (x);
ix = hx & 0x7fffffff;
if (ix >= 0x3ff00000) /* |x| >= 1 */
{
if (((ix - 0x3ff00000) | __LO (x)) == 0) /* |x| == 1 */
{
if (hx > 0) /* acos(1) = 0 */
{
return 0.0;
}
else /* acos(-1) = pi */
{
return pi + 2.0 * pio2_lo;
}
}
return (x - x) / (x - x); /* acos(|x|>1) is NaN */
}
if (ix < 0x3fe00000) /* |x| < 0.5 */
{
if (ix <= 0x3c600000) /* if |x| < 2**-57 */
{
return pio2_hi + pio2_lo;
}
z = x * x;
p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
r = p / q;
return pio2_hi - (x - (pio2_lo - x * r));
}
else if (hx < 0) /* x < -0.5 */
{
z = (one + x) * 0.5;
p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
s = sqrt (z);
r = p / q;
w = r * s - pio2_lo;
return pi - 2.0 * (s + w);
}
else /* x > 0.5 */
{
z = (one - x) * 0.5;
s = sqrt (z);
df = s;
__LO (df) = 0;
c = (z - df * df) / (s + df);
p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
r = p / q;
w = r * s + c;
return 2.0 * (df + w);
}
} /* acos */
int
finite (double x)
{
int hx;
hx = __HI (x);
return (unsigned) ((hx & 0x7fffffff) - 0x7ff00000) >> 31;
} /* finite */
int isnan(double x)
{
int hx,lx;
hx = (__HI(x)&0x7fffffff);
lx = __LO(x);
hx |= (unsigned)(lx|(-lx))>>31;
hx = 0x7ff00000 - hx;
return ((unsigned)(hx))>>31;
}
double __ieee754_y0(double x)
{
double z, s,c,ss,cc,u,v;
int hx,ix,lx;
hx = __HI(x);
ix = 0x7fffffff&hx;
lx = __LO(x);
/* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */
if(ix>=0x7ff00000) return one/(x+x*x);
if((ix|lx)==0) return -one/zero;
if(hx<0) return zero/zero;
if(ix >= 0x40000000) { /* |x| >= 2.0 */
/* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
* where x0 = x-pi/4
* Better formula:
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
* = 1/sqrt(2) * (sin(x) + cos(x))
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.
*/
s = sin(x);
c = cos(x);
ss = s-c;
cc = s+c;
/*
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/
if(ix<0x7fe00000) { /* make sure x+x not overflow */
z = -cos(x+x);
if ((s*c)<zero) cc = z/ss;
else ss = z/cc;
}
if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x);
else {
u = pzero(x); v = qzero(x);
z = invsqrtpi*(u*ss+v*cc)/sqrt(x);
}
return z;
}
if(ix<=0x3e400000) { /* x < 2**-27 */
return(u00 + tpi*__ieee754_log(x));
}
z = x*x;
u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
v = one+z*(v01+z*(v02+z*(v03+z*v04)));
return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x)));
}
double __kernel_cos(double x, double y) {
double a,hz,z,r,qx;
int ix;
ix = __HI(x)&0x7fffffff; /* ix = |x|'s high word*/
if(ix<0x3e400000) { /* if x < 2**27 */
if(((int)x)==0) return one; /* generate inexact */
}
z = x*x;
r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
if(ix < 0x3FD33333) /* if |x| < 0.3 */
return one - (0.5*z - (z*r - x*y));
else {
if(ix > 0x3fe90000) { /* x > 0.78125 */
qx = 0.28125;
} else {
__HI(qx) = ix-0x00200000; /* x/4 */
__LO(qx) = 0;
}
hz = 0.5*z-qx;
a = one-qx;
return a - (hz - (z*r-x*y));
}
}
static double qzero(double x)
{
const double *p,*q;
double s,r,z;
int ix;
ix = 0x7fffffff&__HI(x);
if(ix>=0x40200000) {p = qR8; q= qS8;}
else if(ix>=0x40122E8B){p = qR5; q= qS5;}
else if(ix>=0x4006DB6D){p = qR3; q= qS3;}
else if(ix>=0x40000000){p = qR2; q= qS2;}
z = one/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
return (-.125 + r/s)/x;
}
static double pzero(double x)
{
const double *p,*q;
double z,r,s;
int ix;
ix = 0x7fffffff&__HI(x);
if(ix>=0x40200000) {p = pR8; q= pS8;}
else if(ix>=0x40122E8B){p = pR5; q= pS5;}
else if(ix>=0x4006DB6D){p = pR3; q= pS3;}
else if(ix>=0x40000000){p = pR2; q= pS2;}
z = one/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
return one+ r/s;
}
static double qone(double x)
{
const double *p,*q;
double s,r,z;
int ix;
ix = 0x7fffffff&__HI(x);
if(ix>=0x40200000) {p = qr8; q= qs8;}
else if(ix>=0x40122E8B){p = qr5; q= qs5;}
else if(ix>=0x4006DB6D){p = qr3; q= qs3;}
else if(ix>=0x40000000){p = qr2; q= qs2;}
z = one/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
return (.375 + r/s)/x;
}
static double pone(double x)
{
const double *p,*q;
double z,r,s;
int ix;
ix = 0x7fffffff&__HI(x);
if(ix>=0x40200000) {p = pr8; q= ps8;}
else if(ix>=0x40122E8B){p = pr5; q= ps5;}
else if(ix>=0x4006DB6D){p = pr3; q= ps3;}
else if(ix>=0x40000000){p = pr2; q= ps2;}
z = one/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
return one+ r/s;
}
double __ieee754_y1(double x)
{
double z, s,c,ss,cc,u,v;
int hx,ix,lx;
hx = __HI(x);
ix = 0x7fffffff&hx;
lx = __LO(x);
/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
if(ix>=0x7ff00000) return one/(x+x*x);
if((ix|lx)==0) return -one/zero;
if(hx<0) return zero/zero;
if(ix >= 0x40000000) { /* |x| >= 2.0 */
s = sin(x);
c = cos(x);
ss = -s-c;
cc = s-c;
if(ix<0x7fe00000) { /* make sure x+x not overflow */
z = cos(x+x);
if ((s*c)>zero) cc = z/ss;
else ss = z/cc;
}
/* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
* where x0 = x-3pi/4
* Better formula:
* cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
* = 1/sqrt(2) * (sin(x) - cos(x))
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
* = -1/sqrt(2) * (cos(x) + sin(x))
* To avoid cancellation, use
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
* to compute the worse one.
*/
if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x);
else {
u = pone(x); v = qone(x);
z = invsqrtpi*(u*ss+v*cc)/sqrt(x);
}
return z;
}
if(ix<=0x3c900000) { /* x < 2**-54 */
return(-tpi/x);
}
z = x*x;
u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x));
}
double __kernel_sin(double x, double y, int iy) {
double z,r,v;
int ix;
ix = __HI(x)&0x7fffffff; /* high word of x */
if(ix<0x3e400000) /* |x| < 2**-27 */
{if((int)x==0) return x;} /* generate inexact */
z = x*x;
v = z*x;
#ifdef higher_degree
r = S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*(S8+z*(S9+z*(S10+z*(S11+z*S12)))))))));
#else
r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
#endif
if(iy==0) return x+v*(S1+z*r);
else return x-((z*(half*y-v*r)-y)-v*S1);
}
double __ieee754_j0(double x)
{
double z, s,c,ss,cc,r,u,v;
int hx,ix;
hx = __HI(x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) return one/(x*x);
x = fabs(x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
s = sin(x);
c = cos(x);
ss = s-c;
cc = s+c;
if(ix<0x7fe00000) { /* make sure x+x not overflow */
z = -cos(x+x);
if ((s*c)<zero) cc = z/ss;
else ss = z/cc;
}
/*
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
*/
if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(x);
else {
u = pzero(x); v = qzero(x);
z = invsqrtpi*(u*cc-v*ss)/sqrt(x);
}
return z;
}
if(ix<0x3f200000) { /* |x| < 2**-13 */
if(Huge+x>one) { /* raise inexact if x != 0 */
if(ix<0x3e400000) return one; /* |x|<2**-27 */
else return one - 0.25*x*x;
}
}
z = x*x;
r = z*(R02+z*(R03+z*(R04+z*R05)));
s = one+z*(S01+z*(S02+z*(S03+z*S04)));
if(ix < 0x3FF00000) { /* |x| < 1.00 */
return one + z*(-0.25+(r/s));
} else {
u = 0.5*x;
return((one+u)*(one-u)+z*(r/s));
}
}
int ilogb(double x)
{
int hx,lx,ix;
hx = (__HI(x))&0x7fffffff; /* high word of x */
if(hx<0x00100000) {
lx = __LO(x);
if((hx|lx)==0)
return 0x80000001; /* ilogb(0) = 0x80000001 */
else /* subnormal x */
if(hx==0) {
for (ix = -1043; lx>0; lx<<=1) ix -=1;
} else {
for (ix = -1022,hx<<=11; hx>0; hx<<=1) ix -=1;
}
return ix;
}
else if (hx<0x7ff00000) return (hx>>20)-1023;
else return 0x7fffffff;
double asin(double x)
{
double t=0.0,w=0.0,p=0.0,q=0.0,c=0.0,r=0.0,s=0.0;
int hx=0,ix=0;
hx = __HI(x);
ix = hx&0x7fffffff;
if(ix>= 0x3ff00000) { /* |x|>= 1 */
if(((ix-0x3ff00000)|__LO(x))==0)
/* asin(1)=+-pi/2 with inexact */
return x*pio2_hi+x*pio2_lo;
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
} else if (ix<0x3fe00000) { /* |x|<0.5 */
if(ix<0x3e400000) { /* if |x| < 2**-27 */
if(huge+x>one) return x;/* return x with inexact if x!=0*/
} else
t = x*x;
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
w = p/q;
return x+x*w;
}
/* 1> |x|>= 0.5 */
w = one-fabs(x);
t = w*0.5;
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
s = sqrt(t);
if(ix>=0x3FEF3333) { /* if |x| > 0.975 */
w = p/q;
t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
} else {
w = s;
__LO(w) = 0;
c = (t-w*w)/(s+w);
r = p/q;
p = 2.0*s*r-(pio2_lo-2.0*c);
q = pio4_hi-2.0*w;
t = pio4_hi-(p-q);
}
if(hx>0) return t; else return -t;
}
double asinh(double x)
{
double t,w;
int hx,ix;
hx = __HI(x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
if(ix< 0x3e300000) { /* |x|<2**-28 */
if(Huge+x>one) return x; /* return x inexact except 0 */
}
if(ix>0x41b00000) { /* |x| > 2**28 */
w = __ieee754_log(fabs(x))+ln2;
} else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
t = fabs(x);
w = __ieee754_log(2.0*t+one/(sqrt(x*x+one)+t));
} else { /* 2.0 > |x| > 2**-28 */
t = x*x;
w =log1p(fabs(x)+t/(one+sqrt(one+t)));
}
if(hx>0) return w; else return -w;
}
double JFP_lib_tan(double x) {
double y[2],z=0.0;
int n, ix;
/* High word of x. */
ix = __HI(x);
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
/* tan(Inf or NaN) is NaN */
else if (ix>=0x7ff00000) return x-x; /* NaN */
/* argument reduction needed */
else {
n = __ieee754_rem_pio2(x,y);
return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
-1 -- n odd */
}
}
double __ieee754_j1(double x)
{
double z, s,c,ss,cc,r,u,v,y;
int hx,ix;
hx = __HI(x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) return one/x;
y = fabs(x);
if(ix >= 0x40000000) { /* |x| >= 2.0 */
s = sin(y);
c = cos(y);
ss = -s-c;
cc = s-c;
if(ix<0x7fe00000) { /* make sure y+y not overflow */
z = cos(y+y);
if ((s*c)>zero) cc = z/ss;
else ss = z/cc;
}
/*
* j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
* y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
*/
if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y);
else {
u = pone(y); v = qone(y);
z = invsqrtpi*(u*cc-v*ss)/sqrt(y);
}
if(hx<0) return -z;
else return z;
}
if(ix<0x3e400000) { /* |x|<2**-27 */
if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */
}
z = x*x;
r = z*(r00+z*(r01+z*(r02+z*r03)));
s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
r *= x;
return(x*0.5+r/s);
}
double __ieee754_acosh(double x)
{
double t;
int hx;
hx = __HI(x);
if(hx<0x3ff00000) { /* x < 1 */
return (x-x)/(x-x);
} else if(hx >=0x41b00000) { /* x > 2**28 */
if(hx >=0x7ff00000) { /* x is inf of NaN */
return x+x;
} else
return __ieee754_log(x)+ln2; /* acosh(Huge)=log(2x) */
} else if(((hx-0x3ff00000)|__LO(x))==0) {
return 0.0; /* acosh(1) = 0 */
} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
t=x*x;
return __ieee754_log(2.0*x-one/(x+sqrt(t-one)));
} else { /* 1<x<2 */
t = x-one;
return log1p(t+sqrt(2.0*t+t*t));
}
}
double __ieee754_hypot(double x, double y)
{
double a=x,b=y,t1,t2,y1,y2,w;
int j,k,ha,hb;
ha = __HI(x)&0x7fffffff; /* high word of x */
hb = __HI(y)&0x7fffffff; /* high word of y */
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
__HI(a) = ha; /* a <- |a| */
__HI(b) = hb; /* b <- |b| */
if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
k=0;
if(ha > 0x5f300000) { /* a>2**500 */
if(ha >= 0x7ff00000) { /* Inf or NaN */
w = a+b; /* for sNaN */
if(((ha&0xfffff)|__LO(a))==0) w = a;
if(((hb^0x7ff00000)|__LO(b))==0) w = b;
return w;
}
/* scale a and b by 2**-600 */
ha -= 0x25800000; hb -= 0x25800000; k += 600;
__HI(a) = ha;
__HI(b) = hb;
}
if(hb < 0x20b00000) { /* b < 2**-500 */
if(hb <= 0x000fffff) { /* subnormal b or 0 */
if((hb|(__LO(b)))==0) return a;
t1=0;
__HI(t1) = 0x7fd00000; /* t1=2^1022 */
b *= t1;
a *= t1;
k -= 1022;
} else { /* scale a and b by 2^600 */
ha += 0x25800000; /* a *= 2^600 */
hb += 0x25800000; /* b *= 2^600 */
k -= 600;
__HI(a) = ha;
__HI(b) = hb;
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
t1 = 0;
__HI(t1) = ha;
t2 = a-t1;
w = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
a = a+a;
y1 = 0;
__HI(y1) = hb;
y2 = b - y1;
t1 = 0;
__HI(t1) = ha+0x00100000;
t2 = a - t1;
w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
t1 = 1.0;
__HI(t1) += (k<<20);
return t1*w;
} else return w;
}
double copysign(double x, double y)
{
__HI(x) = (__HI(x)&0x7fffffff)|(__HI(y)&0x80000000);
return x;
}
double JFP_lib_fabs(double x) {
__HI(x) &= 0x7fffffff;
return x;
}
double
_SVID_libm_err(double x, double y, int type) {
struct exception exc;
double t, w, ieee_retval;
enum version lib_version = _lib_version;
int iy;
/* force libm_ieee behavior in SUSv3 mode */
if ((__xpg6 & _C99SUSv3_math_errexcept) != 0)
lib_version = libm_ieee;
if (lib_version == c_issue_4) {
(void) fflush(stdout);
}
exc.arg1 = x;
exc.arg2 = y;
switch (type) {
case 1:
/* acos(|x|>1) */
exc.type = DOMAIN;
exc.name = "acos";
ieee_retval = setexception(3, 1.0);
exc.retval = 0.0;
if (lib_version == strict_ansi) {
errno = EDOM;
} else if (!matherr(&exc)) {
if (lib_version == c_issue_4) {
(void) write(2, "acos: DOMAIN error\n", 19);
}
errno = EDOM;
}
break;
case 2:
/* asin(|x|>1) */
exc.type = DOMAIN;
exc.name = "asin";
exc.retval = 0.0;
ieee_retval = setexception(3, 1.0);
if (lib_version == strict_ansi) {
errno = EDOM;
} else if (!matherr(&exc)) {
if (lib_version == c_issue_4) {
(void) write(2, "asin: DOMAIN error\n", 19);
}
errno = EDOM;
}
break;
case 3:
/* atan2(+-0,+-0) */
exc.arg1 = y;
exc.arg2 = x;
exc.type = DOMAIN;
exc.name = "atan2";
ieee_retval = copysign(1.0, x) == 1.0 ? y :
copysign(PI_RZ + DBL_MIN, y);
exc.retval = 0.0;
if (lib_version == strict_ansi) {
errno = EDOM;
} else if (!matherr(&exc)) {
if (lib_version == c_issue_4) {
(void) write(2, "atan2: DOMAIN error\n", 20);
}
errno = EDOM;
}
break;
case 4:
/* hypot(finite,finite) overflow */
exc.type = OVERFLOW;
exc.name = "hypot";
ieee_retval = Inf;
if (lib_version == c_issue_4)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (lib_version == strict_ansi)
errno = ERANGE;
else if (!matherr(&exc))
errno = ERANGE;
break;
case 5:
/* cosh(finite) overflow */
exc.type = OVERFLOW;
exc.name = "cosh";
ieee_retval = setexception(2, 1.0);
if (lib_version == c_issue_4)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (lib_version == strict_ansi)
errno = ERANGE;
else if (!matherr(&exc))
errno = ERANGE;
break;
case 6:
/* exp(finite) overflow */
exc.type = OVERFLOW;
exc.name = "exp";
ieee_retval = setexception(2, 1.0);
if (lib_version == c_issue_4)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (lib_version == strict_ansi)
errno = ERANGE;
else if (!matherr(&exc))
errno = ERANGE;
break;
case 7:
/* exp(finite) underflow */
exc.type = UNDERFLOW;
exc.name = "exp";
ieee_retval = setexception(1, 1.0);
exc.retval = 0.0;
if (lib_version == strict_ansi)
errno = ERANGE;
else if (!matherr(&exc))
errno = ERANGE;
break;
case 8:
/* y0(0) = -inf */
exc.type = DOMAIN; /* should be SING for IEEE */
exc.name = "y0";
ieee_retval = setexception(0, -1.0);
if (lib_version == c_issue_4)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (lib_version == strict_ansi) {
errno = EDOM;
} else if (!matherr(&exc)) {
if (lib_version == c_issue_4) {
(void) write(2, "y0: DOMAIN error\n", 17);
}
errno = EDOM;
}
break;
case 9:
/* y0(x<0) = NaN */
exc.type = DOMAIN;
exc.name = "y0";
ieee_retval = setexception(3, 1.0);
if (lib_version == c_issue_4)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (lib_version == strict_ansi) {
errno = EDOM;
} else if (!matherr(&exc)) {
if (lib_version == c_issue_4) {
(void) write(2, "y0: DOMAIN error\n", 17);
}
errno = EDOM;
}
break;
case 10:
/* y1(0) = -inf */
exc.type = DOMAIN; /* should be SING for IEEE */
exc.name = "y1";
ieee_retval = setexception(0, -1.0);
if (lib_version == c_issue_4)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (lib_version == strict_ansi) {
errno = EDOM;
} else if (!matherr(&exc)) {
if (lib_version == c_issue_4) {
(void) write(2, "y1: DOMAIN error\n", 17);
}
errno = EDOM;
}
break;
case 11:
/* y1(x<0) = NaN */
exc.type = DOMAIN;
exc.name = "y1";
ieee_retval = setexception(3, 1.0);
if (lib_version == c_issue_4)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (lib_version == strict_ansi) {
errno = EDOM;
} else if (!matherr(&exc)) {
if (lib_version == c_issue_4) {
(void) write(2, "y1: DOMAIN error\n", 17);
}
errno = EDOM;
}
break;
case 12:
/* yn(n,0) = -inf */
exc.type = DOMAIN; /* should be SING for IEEE */
exc.name = "yn";
ieee_retval = setexception(0, -1.0);
if (lib_version == c_issue_4)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (lib_version == strict_ansi) {
errno = EDOM;
} else if (!matherr(&exc)) {
if (lib_version == c_issue_4) {
(void) write(2, "yn: DOMAIN error\n", 17);
}
errno = EDOM;
}
break;
case 13:
/* yn(x<0) = NaN */
exc.type = DOMAIN;
exc.name = "yn";
ieee_retval = setexception(3, 1.0);
if (lib_version == c_issue_4)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (lib_version == strict_ansi) {
errno = EDOM;
} else if (!matherr(&exc)) {
if (lib_version == c_issue_4) {
(void) write(2, "yn: DOMAIN error\n", 17);
}
errno = EDOM;
}
break;
case 14:
/* lgamma(finite) overflow */
exc.type = OVERFLOW;
exc.name = "lgamma";
ieee_retval = setexception(2, 1.0);
if (lib_version == c_issue_4)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (lib_version == strict_ansi)
errno = ERANGE;
else if (!matherr(&exc))
errno = ERANGE;
break;
case 15:
/* lgamma(-integer) or lgamma(0) */
exc.type = SING;
exc.name = "lgamma";
ieee_retval = setexception(0, 1.0);
if (lib_version == c_issue_4)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
if (lib_version == strict_ansi) {
errno = EDOM;
} else if (!matherr(&exc)) {
if (lib_version == c_issue_4) {
(void) write(2, "lgamma: SING error\n", 19);
}
errno = EDOM;
}
break;
case 16:
/* log(0) */
exc.type = SING;
exc.name = "log";
ieee_retval = setexception(0, -1.0);
if (lib_version == c_issue_4)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (lib_version == strict_ansi) {
errno = ERANGE;
} else if (!matherr(&exc)) {
if (lib_version == c_issue_4) {
(void) write(2, "log: SING error\n", 16);
errno = EDOM;
} else {
errno = ERANGE;
}
}
break;
case 17:
/* log(x<0) */
exc.type = DOMAIN;
exc.name = "log";
ieee_retval = setexception(3, 1.0);
if (lib_version == c_issue_4)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (lib_version == strict_ansi) {
errno = EDOM;
} else if (!matherr(&exc)) {
if (lib_version == c_issue_4) {
(void) write(2, "log: DOMAIN error\n", 18);
}
errno = EDOM;
}
break;
case 18:
/* log10(0) */
exc.type = SING;
exc.name = "log10";
ieee_retval = setexception(0, -1.0);
if (lib_version == c_issue_4)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (lib_version == strict_ansi) {
errno = ERANGE;
} else if (!matherr(&exc)) {
if (lib_version == c_issue_4) {
(void) write(2, "log10: SING error\n", 18);
errno = EDOM;
} else {
errno = ERANGE;
}
}
break;
case 19:
/* log10(x<0) */
exc.type = DOMAIN;
exc.name = "log10";
ieee_retval = setexception(3, 1.0);
if (lib_version == c_issue_4)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
if (lib_version == strict_ansi) {
errno = EDOM;
} else if (!matherr(&exc)) {
if (lib_version == c_issue_4) {
(void) write(2, "log10: DOMAIN error\n", 20);
}
errno = EDOM;
}
break;
case 20:
/* pow(0.0,0.0) */
/* error only if lib_version == c_issue_4 */
exc.type = DOMAIN;
exc.name = "pow";
exc.retval = 0.0;
ieee_retval = 1.0;
if (lib_version != c_issue_4) {
exc.retval = 1.0;
} else if (!matherr(&exc)) {
(void) write(2, "pow(0,0): DOMAIN error\n", 23);
errno = EDOM;
}
break;
case 21:
/* pow(x,y) overflow */
exc.type = OVERFLOW;
exc.name = "pow";
exc.retval = (lib_version == c_issue_4)? HUGE : HUGE_VAL;
if (signbit(x)) {
t = rint(y);
if (t == y) {
w = rint(0.5 * y);
if (t != w + w) { /* y is odd */
exc.retval = -exc.retval;
}
}
}
ieee_retval = setexception(2, exc.retval);
if (lib_version == strict_ansi)
errno = ERANGE;
else if (!matherr(&exc))
errno = ERANGE;
break;
case 22:
/* pow(x,y) underflow */
exc.type = UNDERFLOW;
exc.name = "pow";
exc.retval = 0.0;
if (signbit(x)) {
t = rint(y);
if (t == y) {
w = rint(0.5 * y);
if (t != w + w) /* y is odd */
exc.retval = -exc.retval;
}
}
ieee_retval = setexception(1, exc.retval);
if (lib_version == strict_ansi)
errno = ERANGE;
else if (!matherr(&exc))
errno = ERANGE;
break;
case 23:
/* (+-0)**neg */
exc.type = DOMAIN;
exc.name = "pow";
ieee_retval = setexception(0, 1.0);
{
int ahy, k, j, yisint, ly, hx;
/* INDENT OFF */
/*
* determine if y is an odd int when x = -0
* yisint = 0 ... y is not an integer
* yisint = 1 ... y is an odd int
* yisint = 2 ... y is an even int
*/
/* INDENT ON */
hx = __HI(x);
ahy = __HI(y)&0x7fffffff;
ly = __LO(y);
yisint = 0;
if (ahy >= 0x43400000) {
yisint = 2; /* even integer y */
} else if (ahy >= 0x3ff00000) {
k = (ahy >> 20) - 0x3ff; /* exponent */
if (k > 20) {
j = ly >> (52 - k);
if ((j << (52 - k)) == ly)
yisint = 2 - (j & 1);
} else if (ly == 0) {
j = ahy >> (20 - k);
if ((j << (20 - k)) == ahy)
yisint = 2 - (j & 1);
}
double
atan (double x)
{
double w, s1, s2, z;
int ix, hx, id;
hx = __HI (x);
ix = hx & 0x7fffffff;
if (ix >= 0x44100000) /* if |x| >= 2^66 */
{
if (ix > 0x7ff00000 || (ix == 0x7ff00000 && (__LO (x) != 0)))
{
return x + x; /* NaN */
}
if (hx > 0)
{
return atanhi[3] + atanlo[3];
}
else
{
return -atanhi[3] - atanlo[3];
}
}
if (ix < 0x3fdc0000) /* |x| < 0.4375 */
{
if (ix < 0x3e200000) /* |x| < 2^-29 */
{
if (huge + x > one) /* raise inexact */
{
return x;
}
}
id = -1;
}
else
{
x = fabs (x);
if (ix < 0x3ff30000) /* |x| < 1.1875 */
{
if (ix < 0x3fe60000) /* 7/16 <= |x| < 11/16 */
{
id = 0;
x = (2.0 * x - one) / (2.0 + x);
}
else /* 11/16 <= |x| < 19/16 */
{
id = 1;
x = (x - one) / (x + one);
}
}
else
{
if (ix < 0x40038000) /* |x| < 2.4375 */
{
id = 2;
x = (x - 1.5) / (one + 1.5 * x);
}
else /* 2.4375 <= |x| < 2^66 */
{
id = 3;
x = -1.0 / x;
}
}
}
/* end of argument reduction */
z = x * x;
w = z * z;
/* break sum from i=0 to 10 aT[i] z**(i+1) into odd and even poly */
s1 = z * (aT0 + w * (aT2 + w * (aT4 + w * (aT6 + w * (aT8 + w * aT10)))));
s2 = w * (aT1 + w * (aT3 + w * (aT5 + w * (aT7 + w * aT9))));
if (id < 0)
{
return x - x * (s1 + s2);
}
else
{
z = atanhi[id] - ((x * (s1 + s2) - atanlo[id]) - x);
return (hx < 0) ? -z : z;
}
} /* atan */
double fabs(double x)
{
__HI(x) &= 0x7fffffff;
return x;
}