You should have received a copy of the GNU Lesser General Public
License along with this library; if not, see
- <http://www.gnu.org/licenses/>. */
+ <https://www.gnu.org/licenses/>. */
/* __ieee754_powl(x,y) return x**y
*
#include <math.h>
#include <math_private.h>
+#include <math-underflow.h>
static const long double bp[] = {
1.0L,
one = 1.0L,
two = 2.0L,
two113 = 1.0384593717069655257060992658440192E34L,
- huge = 1.0e3000L,
- tiny = 1.0e-3000L;
+ huge = 1.0e300L,
+ tiny = 1.0e-300L;
/* 3/2 log x = 3 z + z^3 + z^3 (z^2 R(z^2))
z = (x-1)/(x+1)
__ieee754_powl (long double x, long double y)
{
long double z, ax, z_h, z_l, p_h, p_l;
- long double y1, t1, t2, r, s, t, u, v, w;
- long double s2, s_h, s_l, t_h, t_l;
+ long double y1, t1, t2, r, s, sgn, t, u, v, w;
+ long double s2, s_h, s_l, t_h, t_l, ay;
int32_t i, j, k, yisint, n;
- u_int32_t ix, iy;
- int32_t hx, hy;
- ieee854_long_double_shape_type o, p, q;
+ uint32_t ix, iy;
+ int32_t hx, hy, hax;
+ double ohi, xhi, xlo, yhi, ylo;
+ uint32_t lx, ly, lj;
- p.value = x;
- hx = p.parts32.w0;
+ ldbl_unpack (x, &xhi, &xlo);
+ EXTRACT_WORDS (hx, lx, xhi);
ix = hx & 0x7fffffff;
- q.value = y;
- hy = q.parts32.w0;
+ ldbl_unpack (y, &yhi, &ylo);
+ EXTRACT_WORDS (hy, ly, yhi);
iy = hy & 0x7fffffff;
-
/* y==zero: x**0 = 1 */
- if ((iy | q.parts32.w1 | (q.parts32.w2 & 0x7fffffff) | q.parts32.w3) == 0)
+ if ((iy | ly) == 0 && !issignaling (x))
return one;
/* 1.0**y = 1; -1.0**+-Inf = 1 */
- if (x == one)
+ if (x == one && !issignaling (y))
return one;
- if (x == -1.0L && iy == 0x7ff00000
- && (q.parts32.w1 | (q.parts32.w2 & 0x7fffffff) | q.parts32.w3) == 0)
+ if (x == -1.0L && ((iy - 0x7ff00000) | ly) == 0)
return one;
/* +-NaN return x+y */
- if ((ix > 0x7ff00000)
- || ((ix == 0x7ff00000)
- && ((p.parts32.w1 | (p.parts32.w2 & 0x7fffffff) | p.parts32.w3) != 0))
- || (iy > 0x7ff00000)
- || ((iy == 0x7ff00000)
- && ((q.parts32.w1 | (q.parts32.w2 & 0x7fffffff) | q.parts32.w3) != 0)))
+ 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;
if (hx < 0)
{
- if ((q.parts32.w2 & 0x7fffffff) >= 0x43400000) /* Low part >= 2^53 */
+ uint32_t low_ye;
+
+ GET_HIGH_WORD (low_ye, ylo);
+ if ((low_ye & 0x7fffffff) >= 0x43400000) /* Low part >= 2^53 */
yisint = 2; /* even integer y */
else if (iy >= 0x3ff00000) /* 1.0 */
{
- if (__floorl (y) == y)
+ if (floorl (y) == y)
{
z = 0.5 * y;
- if (__floorl (z) == z)
+ if (floorl (z) == z)
yisint = 2;
else
yisint = 1;
}
}
+ ax = fabsl (x);
+
/* special value of y */
- if ((q.parts32.w1 | (q.parts32.w2 & 0x7fffffff) | q.parts32.w3) == 0)
+ if (ly == 0)
{
- if (iy == 0x7ff00000 && q.parts32.w1 == 0) /* y is +-inf */
+ if (iy == 0x7ff00000) /* y is +-inf */
{
- if (((ix - 0x3ff00000) | p.parts32.w1
- | (p.parts32.w2 & 0x7fffffff) | p.parts32.w3) == 0)
- return y - y; /* inf**+-1 is NaN */
- else if (ix > 0x3ff00000 || fabsl (x) > 1.0L)
+ if (ax > one)
/* (|x|>1)**+-inf = inf,0 */
return (hy >= 0) ? y : zero;
else
/* (|x|<1)**-,+inf = inf,0 */
return (hy < 0) ? -y : zero;
}
- if (iy == 0x3ff00000)
- { /* y is +-1 */
- if (hy < 0)
- return one / x;
- else
- return x;
- }
- if (hy == 0x40000000)
- return x * x; /* y is 2 */
- if (hy == 0x3fe00000)
- { /* y is 0.5 */
- if (hx >= 0) /* x >= +0 */
- return __ieee754_sqrtl (x);
+ if (ylo == 0.0)
+ {
+ if (iy == 0x3ff00000)
+ { /* y is +-1 */
+ if (hy < 0)
+ return one / x;
+ else
+ return x;
+ }
+ if (hy == 0x40000000)
+ return x * x; /* y is 2 */
+ if (hy == 0x3fe00000)
+ { /* y is 0.5 */
+ if (hx >= 0) /* x >= +0 */
+ return sqrtl (x);
+ }
}
}
- ax = fabsl (x);
/* special value of x */
- if ((p.parts32.w1 | (p.parts32.w2 & 0x7fffffff) | p.parts32.w3) == 0)
+ if (lx == 0)
{
- if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000)
+ if (ix == 0x7ff00000 || ix == 0 || (ix == 0x3ff00000 && xlo == 0.0))
{
z = ax; /*x is +-0,+-inf,+-1 */
if (hy < 0)
}
/* (x<0)**(non-int) is NaN */
- if (((((u_int32_t) hx >> 31) - 1) | yisint) == 0)
+ if (((((uint32_t) hx >> 31) - 1) | yisint) == 0)
return (x - x) / (x - x);
+ /* sgn (sign of result -ve**odd) = -1 else = 1 */
+ sgn = one;
+ if (((((uint32_t) hx >> 31) - 1) | (yisint - 1)) == 0)
+ sgn = -one; /* (-ve)**(odd int) */
+
/* |y| is huge.
2^-16495 = 1/2 of smallest representable value.
If (1 - 1/131072)^y underflows, y > 1.4986e9 */
if (iy > 0x47d654b0)
{
if (ix <= 0x3fefffff)
- return (hy < 0) ? huge * huge : tiny * tiny;
+ return (hy < 0) ? sgn * huge * huge : sgn * tiny * tiny;
if (ix >= 0x3ff00000)
- return (hy > 0) ? huge * huge : tiny * tiny;
+ return (hy > 0) ? sgn * huge * huge : sgn * tiny * tiny;
}
/* over/underflow if x is not close to one */
if (ix < 0x3fefffff)
- return (hy < 0) ? huge * huge : tiny * tiny;
+ return (hy < 0) ? sgn * huge * huge : sgn * tiny * tiny;
if (ix > 0x3ff00000)
- return (hy > 0) ? huge * huge : tiny * tiny;
+ return (hy > 0) ? sgn * huge * huge : sgn * tiny * tiny;
}
+ ay = y > 0 ? y : -y;
+ if (ay < 0x1p-117)
+ y = y < 0 ? -0x1p-117 : 0x1p-117;
+
n = 0;
/* take care subnormal number */
if (ix < 0x00100000)
{
ax *= two113;
n -= 113;
- o.value = ax;
- ix = o.parts32.w0;
+ ohi = ldbl_high (ax);
+ GET_HIGH_WORD (ix, ohi);
}
n += ((ix) >> 20) - 0x3ff;
j = ix & 0x000fffff;
ix -= 0x00100000;
}
- o.value = ax;
- o.value = __scalbnl (o.value, ((int) ((ix - o.parts32.w0) * 2)) >> 21);
- ax = o.value;
+ ohi = ldbl_high (ax);
+ GET_HIGH_WORD (hax, ohi);
+ ax = __scalbnl (ax, ((int) ((ix - hax) * 2)) >> 21);
/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
v = one / (ax + bp[k]);
s = u * v;
- s_h = s;
+ s_h = ldbl_high (s);
- o.value = s_h;
- o.parts32.w3 = 0;
- o.parts32.w2 &= 0xffff8000;
- s_h = o.value;
/* t_h=ax+bp[k] High */
t_h = ax + bp[k];
- o.value = t_h;
- o.parts32.w3 = 0;
- o.parts32.w2 &= 0xffff8000;
- t_h = o.value;
+ t_h = ldbl_high (t_h);
t_l = ax - (t_h - bp[k]);
s_l = v * ((u - s_h * t_h) - s_h * t_l);
/* compute log(ax) */
r += s_l * (s_h + s);
s2 = s_h * s_h;
t_h = 3.0 + s2 + r;
- o.value = t_h;
- o.parts32.w3 = 0;
- o.parts32.w2 &= 0xffff8000;
- t_h = o.value;
+ t_h = ldbl_high (t_h);
t_l = r - ((t_h - 3.0) - s2);
/* u+v = s*(1+...) */
u = s_h * t_h;
v = s_l * t_h + t_l * s;
/* 2/(3log2)*(s+...) */
p_h = u + v;
- o.value = p_h;
- o.parts32.w3 = 0;
- o.parts32.w2 &= 0xffff8000;
- p_h = o.value;
+ p_h = ldbl_high (p_h);
p_l = v - (p_h - u);
z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */
z_l = cp_l * p_h + p_l * cp + dp_l[k];
/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
t = (long double) n;
t1 = (((z_h + z_l) + dp_h[k]) + t);
- o.value = t1;
- o.parts32.w3 = 0;
- o.parts32.w2 &= 0xffff8000;
- t1 = o.value;
+ t1 = ldbl_high (t1);
t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
- /* s (sign of result -ve**odd) = -1 else = 1 */
- s = one;
- if (((((u_int32_t) hx >> 31) - 1) | (yisint - 1)) == 0)
- s = -one; /* (-ve)**(odd int) */
-
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
- y1 = y;
- o.value = y1;
- o.parts32.w3 = 0;
- o.parts32.w2 &= 0xffff8000;
- y1 = o.value;
+ y1 = ldbl_high (y);
p_l = (y - y1) * t1 + y * t2;
p_h = y1 * t1;
z = p_l + p_h;
- o.value = z;
- j = o.parts32.w0;
+ ohi = ldbl_high (z);
+ EXTRACT_WORDS (j, lj, ohi);
if (j >= 0x40d00000) /* z >= 16384 */
{
/* if z > 16384 */
- if (((j - 0x40d00000) | o.parts32.w1
- | (o.parts32.w2 & 0x7fffffff) | o.parts32.w3) != 0)
- return s * huge * huge; /* overflow */
+ if (((j - 0x40d00000) | lj) != 0)
+ return sgn * huge * huge; /* overflow */
else
{
if (p_l + ovt > z - p_h)
- return s * huge * huge; /* overflow */
+ return sgn * huge * huge; /* overflow */
}
}
else if ((j & 0x7fffffff) >= 0x40d01b90) /* z <= -16495 */
{
/* z < -16495 */
- if (((j - 0xc0d01bc0) | o.parts32.w1
- | (o.parts32.w2 & 0x7fffffff) | o.parts32.w3) != 0)
- return s * tiny * tiny; /* underflow */
+ if (((j - 0xc0d01bc0) | lj) != 0)
+ return sgn * tiny * tiny; /* underflow */
else
{
if (p_l <= z - p_h)
- return s * tiny * tiny; /* underflow */
+ return sgn * tiny * tiny; /* underflow */
}
}
/* compute 2**(p_h+p_l) */
n = 0;
if (i > 0x3fe00000)
{ /* if |z| > 0.5, set n = [z+0.5] */
- n = __floorl (z + 0.5L);
+ n = floorl (z + 0.5L);
t = n;
p_h -= t;
}
t = p_l + p_h;
- o.value = t;
- o.parts32.w3 = 0;
- o.parts32.w2 &= 0xffff8000;
- t = o.value;
+ t = ldbl_high (t);
u = t * lg2_h;
v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
z = u + v;
t1 = z - t * u / v;
r = (z * t1) / (t1 - two) - (w + z * w);
z = one - (r - z);
- z = __scalbnl (z, n);
- return s * z;
+ z = __scalbnl (sgn * z, n);
+ math_check_force_underflow (z);
+ return z;
}
strong_alias (__ieee754_powl, __powl_finite)
projects / thirdparty / glibc.git / blobdiff