static double
SECTION
power1(double x, double y) {
double z,a,aa,error, t,a1,a2,y1,y2;
z = my_log2(x,&aa,&error);
t = y*134217729.0;
y1 = t - (t-y);
y2 = y - y1;
t = z*134217729.0;
a1 = t - (t-z);
a2 = z - a1;
a = y*z;
aa = ((y1*a1-a)+y1*a2+y2*a1)+y2*a2+aa*y;
a1 = a+aa;
a2 = (a-a1)+aa;
error = error*ABS(y);
t = __exp1(a1,a2,1.9e16*error);
return (t >= 0)?t:__slowpow(x,y,z);
}
double
SECTION
__ieee754_pow(double x, double y) {
double z,a,aa,error, t,a1,a2,y1,y2;
#if 0
double gor=1.0;
#endif
mynumber u,v;
int k;
int4 qx,qy;
v.x=y;
u.x=x;
if (v.i[LOW_HALF] == 0) { /* of y */
qx = u.i[HIGH_HALF]&0x7fffffff;
/* Checking if x is not too small to compute */
if (((qx==0x7ff00000)&&(u.i[LOW_HALF]!=0))||(qx>0x7ff00000)) return NaNQ.x;
if (y == 1.0) return x;
if (y == 2.0) return x*x;
if (y == -1.0) return 1.0/x;
if (y == 0) return 1.0;
}
/* else */
if(((u.i[HIGH_HALF]>0 && u.i[HIGH_HALF]<0x7ff00000)|| /* x>0 and not x->0 */
(u.i[HIGH_HALF]==0 && u.i[LOW_HALF]!=0)) &&
/* 2^-1023< x<= 2^-1023 * 0x1.0000ffffffff */
(v.i[HIGH_HALF]&0x7fffffff) < 0x4ff00000) { /* if y<-1 or y>1 */
double retval;
SET_RESTORE_ROUND (FE_TONEAREST);
/* Avoid internal underflow for tiny y. The exact value of y does
not matter if |y| <= 2**-64. */
if (ABS (y) < 0x1p-64)
y = y < 0 ? -0x1p-64 : 0x1p-64;
z = log1(x,&aa,&error); /* x^y =e^(y log (X)) */
t = y*134217729.0;
y1 = t - (t-y);
y2 = y - y1;
t = z*134217729.0;
a1 = t - (t-z);
a2 = (z - a1)+aa;
a = y1*a1;
aa = y2*a1 + y*a2;
a1 = a+aa;
a2 = (a-a1)+aa;
error = error*ABS(y);
t = __exp1(a1,a2,1.9e16*error); /* return -10 or 0 if wasn't computed exactly */
retval = (t>0)?t:power1(x,y);
return retval;
}
if (x == 0) {
if (((v.i[HIGH_HALF] & 0x7fffffff) == 0x7ff00000 && v.i[LOW_HALF] != 0)
|| (v.i[HIGH_HALF] & 0x7fffffff) > 0x7ff00000)
return y;
if (ABS(y) > 1.0e20) return (y>0)?0:1.0/0.0;
k = checkint(y);
if (k == -1)
return y < 0 ? 1.0/x : x;
else
return y < 0 ? 1.0/0.0 : 0.0; /* return 0 */
}
qx = u.i[HIGH_HALF]&0x7fffffff; /* no sign */
qy = v.i[HIGH_HALF]&0x7fffffff; /* no sign */
if (qx >= 0x7ff00000 && (qx > 0x7ff00000 || u.i[LOW_HALF] != 0)) return NaNQ.x;
if (qy >= 0x7ff00000 && (qy > 0x7ff00000 || v.i[LOW_HALF] != 0))
return x == 1.0 ? 1.0 : NaNQ.x;
/* if x<0 */
if (u.i[HIGH_HALF] < 0) {
k = checkint(y);
if (k==0) {
if (qy == 0x7ff00000) {
if (x == -1.0) return 1.0;
else if (x > -1.0) return v.i[HIGH_HALF] < 0 ? INF.x : 0.0;
else return v.i[HIGH_HALF] < 0 ? 0.0 : INF.x;
}
else if (qx == 0x7ff00000)
return y < 0 ? 0.0 : INF.x;
return NaNQ.x; /* y not integer and x<0 */
}
else if (qx == 0x7ff00000)
{
if (k < 0)
return y < 0 ? nZERO.x : nINF.x;
else
return y < 0 ? 0.0 : INF.x;
}
return (k==1)?__ieee754_pow(-x,y):-__ieee754_pow(-x,y); /* if y even or odd */
}
/* x>0 */
if (qx == 0x7ff00000) /* x= 2^-0x3ff */
{if (y == 0) return NaNQ.x;
return (y>0)?x:0; }
if (qy > 0x45f00000 && qy < 0x7ff00000) {
if (x == 1.0) return 1.0;
if (y>0) return (x>1.0)?huge*huge:tiny*tiny;
if (y<0) return (x<1.0)?huge*huge:tiny*tiny;
}
if (x == 1.0) return 1.0;
if (y>0) return (x>1.0)?INF.x:0;
if (y<0) return (x<1.0)?INF.x:0;
return 0; /* unreachable, to make the compiler happy */
}
/* An ultimate power routine. Given two IEEE double machine numbers y, x it
computes the correctly rounded (to nearest) value of X^y. */
double
SECTION
__ieee754_pow (double x, double y)
{
double z, a, aa, error, t, a1, a2, y1, y2;
mynumber u, v;
int k;
int4 qx, qy;
v.x = y;
u.x = x;
if (v.i[LOW_HALF] == 0)
{ /* of y */
qx = u.i[HIGH_HALF] & 0x7fffffff;
/* Is x a NaN? */
if ((((qx == 0x7ff00000) && (u.i[LOW_HALF] != 0)) || (qx > 0x7ff00000))
&& (y != 0 || issignaling (x)))
return x + x;
if (y == 1.0)
return x;
if (y == 2.0)
return x * x;
if (y == -1.0)
return 1.0 / x;
if (y == 0)
return 1.0;
}
/* else */
if (((u.i[HIGH_HALF] > 0 && u.i[HIGH_HALF] < 0x7ff00000) || /* x>0 and not x->0 */
(u.i[HIGH_HALF] == 0 && u.i[LOW_HALF] != 0)) &&
/* 2^-1023< x<= 2^-1023 * 0x1.0000ffffffff */
(v.i[HIGH_HALF] & 0x7fffffff) < 0x4ff00000)
{ /* if y<-1 or y>1 */
double retval;
{
SET_RESTORE_ROUND (FE_TONEAREST);
/* Avoid internal underflow for tiny y. The exact value of y does
not matter if |y| <= 2**-64. */
if (fabs (y) < 0x1p-64)
y = y < 0 ? -0x1p-64 : 0x1p-64;
z = log1 (x, &aa, &error); /* x^y =e^(y log (X)) */
t = y * CN;
y1 = t - (t - y);
y2 = y - y1;
t = z * CN;
a1 = t - (t - z);
a2 = (z - a1) + aa;
a = y1 * a1;
aa = y2 * a1 + y * a2;
a1 = a + aa;
a2 = (a - a1) + aa;
error = error * fabs (y);
t = __exp1 (a1, a2, 1.9e16 * error); /* return -10 or 0 if wasn't computed exactly */
retval = (t > 0) ? t : power1 (x, y);
}
if (isinf (retval))
retval = huge * huge;
else if (retval == 0)
retval = tiny * tiny;
else
math_check_force_underflow_nonneg (retval);
return retval;
}
if (x == 0)
{
if (((v.i[HIGH_HALF] & 0x7fffffff) == 0x7ff00000 && v.i[LOW_HALF] != 0)
|| (v.i[HIGH_HALF] & 0x7fffffff) > 0x7ff00000) /* NaN */
return y + y;
if (fabs (y) > 1.0e20)
return (y > 0) ? 0 : 1.0 / 0.0;
k = checkint (y);
if (k == -1)
return y < 0 ? 1.0 / x : x;
else
return y < 0 ? 1.0 / 0.0 : 0.0; /* return 0 */
}
qx = u.i[HIGH_HALF] & 0x7fffffff; /* no sign */
qy = v.i[HIGH_HALF] & 0x7fffffff; /* no sign */
if (qx >= 0x7ff00000 && (qx > 0x7ff00000 || u.i[LOW_HALF] != 0)) /* NaN */
return x + y;
if (qy >= 0x7ff00000 && (qy > 0x7ff00000 || v.i[LOW_HALF] != 0)) /* NaN */
return x == 1.0 && !issignaling (y) ? 1.0 : y + y;
/* if x<0 */
if (u.i[HIGH_HALF] < 0)
{
k = checkint (y);
if (k == 0)
{
if (qy == 0x7ff00000)
{
if (x == -1.0)
return 1.0;
else if (x > -1.0)
return v.i[HIGH_HALF] < 0 ? INF.x : 0.0;
else
return v.i[HIGH_HALF] < 0 ? 0.0 : INF.x;
}
else if (qx == 0x7ff00000)
return y < 0 ? 0.0 : INF.x;
return (x - x) / (x - x); /* y not integer and x<0 */
}
else if (qx == 0x7ff00000)
{
if (k < 0)
return y < 0 ? nZERO.x : nINF.x;
else
return y < 0 ? 0.0 : INF.x;
}
/* if y even or odd */
if (k == 1)
return __ieee754_pow (-x, y);
else
{
double retval;
{
SET_RESTORE_ROUND (FE_TONEAREST);
retval = -__ieee754_pow (-x, y);
}
if (isinf (retval))
retval = -huge * huge;
else if (retval == 0)
retval = -tiny * tiny;
return retval;
}
}
/* x>0 */
if (qx == 0x7ff00000) /* x= 2^-0x3ff */
return y > 0 ? x : 0;
if (qy > 0x45f00000 && qy < 0x7ff00000)
{
if (x == 1.0)
return 1.0;
if (y > 0)
return (x > 1.0) ? huge * huge : tiny * tiny;
if (y < 0)
return (x < 1.0) ? huge * huge : tiny * tiny;
}
if (x == 1.0)
return 1.0;
if (y > 0)
return (x > 1.0) ? INF.x : 0;
if (y < 0)
return (x < 1.0) ? INF.x : 0;
return 0; /* unreachable, to make the compiler happy */
}
