+2013-10-04 Alan Modra <amodra@gmail.com>
+
+ * sysdeps/ieee754/ldbl-128ibm/e_atan2l.c (__ieee754_atan2l): Rewrite
+ all uses of ieee854 long double macros and unions. Simplify tests
+ for long doubles that are fully specified by the high double.
+ * sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c (__ieee754_gammal_r):
+ Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/e_ilogbl.c (__ieee754_ilogbl): Likewise.
+ Remove dead code too.
+ * sysdeps/ieee754/ldbl-128ibm/e_jnl.c (__ieee754_jnl): Likewise.
+ (__ieee754_ynl): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/e_log10l.c (__ieee754_log10l): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/e_logl.c (__ieee754_logl): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/e_powl.c (__ieee754_powl): Likewise.
+ Remove dead code too.
+ * sysdeps/ieee754/ldbl-128ibm/k_tanl.c (__kernel_tanl): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/s_expm1l.c (__expm1l): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/s_frexpl.c (__frexpl): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/s_isinf_nsl.c (__isinf_nsl): Likewise.
+ Simplify.
+ * sysdeps/ieee754/ldbl-128ibm/s_isinfl.c (___isinfl): Likewise.
+ Simplify.
+ * sysdeps/ieee754/ldbl-128ibm/s_log1pl.c (__log1pl): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/s_modfl.c (__modfl): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c (__nextafterl): Likewise.
+ Comment on variable precision.
+ * sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c (__nexttoward): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c (__nexttowardf):
+ Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/s_remquol.c (__remquol): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/s_scalblnl.c (__scalblnl): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/s_scalbnl.c (__scalbnl): Likewise.
+ * sysdeps/ieee754/ldbl-128ibm/s_tanhl.c (__tanhl): Likewise.
+ * sysdeps/powerpc/fpu/libm-test-ulps: Adjust tan_towardzero ulps.
+
2013-10-04 Alan Modra <amodra@gmail.com>
* sysdeps/ieee754/ldbl-128ibm/math_ldbl.h (ldbl_high): Define.
{
long double z;
int64_t k,m,hx,hy,ix,iy;
- u_int64_t lx,ly;
+ uint64_t lx;
+ double xhi, xlo, yhi;
- GET_LDOUBLE_WORDS64(hx,lx,x);
+ ldbl_unpack (x, &xhi, &xlo);
+ EXTRACT_WORDS64 (hx, xhi);
+ EXTRACT_WORDS64 (lx, xlo);
ix = hx&0x7fffffffffffffffLL;
- GET_LDOUBLE_WORDS64(hy,ly,y);
+ yhi = ldbl_high (y);
+ EXTRACT_WORDS64 (hy, yhi);
iy = hy&0x7fffffffffffffffLL;
if(((ix)>0x7ff0000000000000LL)||
((iy)>0x7ff0000000000000LL)) /* x or y is NaN */
m = ((hy>>63)&1)|((hx>>62)&2); /* 2*sign(x)+sign(y) */
/* when y = 0 */
- if((iy|(ly&0x7fffffffffffffffLL))==0) {
+ if(iy==0) {
switch(m) {
case 0:
case 1: return y; /* atan(+-0,+anything)=+-0 */
}
}
/* when x = 0 */
- if((ix|(lx&0x7fffffffffffffff))==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
+ if(ix==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
/* when x is INF */
if(ix==0x7ff0000000000000LL) {
__ieee754_gammal_r (long double x, int *signgamp)
{
int64_t hx;
- u_int64_t lx;
+ double xhi;
- GET_LDOUBLE_WORDS64 (hx, lx, x);
+ xhi = ldbl_high (x);
+ EXTRACT_WORDS64 (hx, xhi);
- if (((hx | lx) & 0x7fffffffffffffffLL) == 0)
+ if ((hx & 0x7fffffffffffffffLL) == 0)
{
/* Return value for x == 0 is Inf with divide by zero exception. */
*signgamp = 0;
int __ieee754_ilogbl(long double x)
{
- int64_t hx,lx;
+ int64_t hx;
int ix;
+ double xhi;
- GET_LDOUBLE_WORDS64(hx,lx,x);
+ xhi = ldbl_high (x);
+ EXTRACT_WORDS64 (hx, xhi);
hx &= 0x7fffffffffffffffLL;
if(hx <= 0x0010000000000000LL) {
- if((hx|(lx&0x7fffffffffffffffLL))==0)
+ if(hx==0)
return FP_ILOGB0; /* ilogbl(0) = FP_ILOGB0 */
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;
- }
+ for (ix = -1022, hx<<=11; hx>0; hx<<=1) ix -=1;
return ix;
}
else if (hx<0x7ff0000000000000LL) return (hx>>52)-0x3ff;
else if (FP_ILOGBNAN != INT_MAX) {
/* ISO C99 requires ilogbl(+-Inf) == INT_MAX. */
- if (((hx^0x7ff0000000000000LL)|lx) == 0)
+ if (hx==0x7ff0000000000000LL)
return INT_MAX;
}
return FP_ILOGBNAN;
long double
__ieee754_jnl (int n, long double x)
{
- u_int32_t se;
+ uint32_t se, lx;
int32_t i, ix, sgn;
long double a, b, temp, di;
long double z, w;
- ieee854_long_double_shape_type u;
+ double xhi;
/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
* Thus, J(-n,x) = J(n,-x)
*/
- u.value = x;
- se = u.parts32.w0;
+ xhi = ldbl_high (x);
+ EXTRACT_WORDS (se, lx, xhi);
ix = se & 0x7fffffff;
/* if J(n,NaN) is NaN */
if (ix >= 0x7ff00000)
{
- if ((u.parts32.w0 & 0xfffff) | u.parts32.w1
- | (u.parts32.w2 & 0x7fffffff) | u.parts32.w3)
+ if (((ix - 0x7ff00000) | lx) != 0)
return x + x;
}
long double
__ieee754_ynl (int n, long double x)
{
- u_int32_t se;
+ uint32_t se, lx;
int32_t i, ix;
int32_t sign;
long double a, b, temp;
- ieee854_long_double_shape_type u;
+ double xhi;
- u.value = x;
- se = u.parts32.w0;
+ xhi = ldbl_high (x);
+ EXTRACT_WORDS (se, lx, xhi);
ix = se & 0x7fffffff;
/* if Y(n,NaN) is NaN */
if (ix >= 0x7ff00000)
{
- if ((u.parts32.w0 & 0xfffff) | u.parts32.w1
- | (u.parts32.w2 & 0x7fffffff) | u.parts32.w3)
+ if (((ix - 0x7ff00000) | lx) != 0)
return x + x;
}
if (x <= 0.0L)
a = __ieee754_y0l (x);
b = __ieee754_y1l (x);
/* quit if b is -inf */
- u.value = b;
- se = u.parts32.w0 & 0xfff00000;
+ xhi = ldbl_high (b);
+ GET_HIGH_WORD (se, xhi);
+ se &= 0xfff00000;
for (i = 1; i < n && se != 0xfff00000; i++)
{
temp = b;
b = ((long double) (i + i) / x) * b - a;
- u.value = b;
- se = u.parts32.w0 & 0xfff00000;
+ xhi = ldbl_high (b);
+ GET_HIGH_WORD (se, xhi);
+ se &= 0xfff00000;
a = temp;
}
}
long double z;
long double y;
int e;
- int64_t hx, lx;
+ int64_t hx;
+ double xhi;
/* Test for domain */
- GET_LDOUBLE_WORDS64 (hx, lx, x);
- if (((hx & 0x7fffffffffffffffLL) | (lx & 0x7fffffffffffffffLL)) == 0)
+ xhi = ldbl_high (x);
+ EXTRACT_WORDS64 (hx, xhi);
+ if ((hx & 0x7fffffffffffffffLL) == 0)
return (-1.0L / (x - x));
if (hx < 0)
return (x - x) / (x - x);
long double
__ieee754_logl(long double x)
{
- long double z, y, w;
- ieee854_long_double_shape_type u, t;
+ long double z, y, w, t;
unsigned int m;
int k, e;
+ double xhi;
+ uint32_t hx, lx;
- u.value = x;
- m = u.parts32.w0;
+ xhi = ldbl_high (x);
+ EXTRACT_WORDS (hx, lx, xhi);
+ m = hx;
/* Check for IEEE special cases. */
k = m & 0x7fffffff;
/* log(0) = -infinity. */
- if ((k | u.parts32.w1 | (u.parts32.w2 & 0x7fffffff) | u.parts32.w3) == 0)
+ if ((k | lx) == 0)
{
return -0.5L / ZERO;
}
{
z = x - 1.0L;
k = 64;
- t.value = 1.0L;
+ t = 1.0L;
e = 0;
}
else
k = (m - 0xff000) >> 13;
/* t is the argument 0.5 + (k+26)/128
of the nearest item to u in the lookup table. */
- t.parts32.w0 = 0x3ff00000 + (k << 13);
- t.parts32.w1 = 0;
- t.parts32.w2 = 0;
- t.parts32.w3 = 0;
+ INSERT_WORDS (xhi, 0x3ff00000 + (k << 13), 0);
+ t = xhi;
w0 += 0x100000;
e -= 1;
k += 64;
else
{
k = (m - 0xfe000) >> 14;
- t.parts32.w0 = 0x3fe00000 + (k << 14);
- t.parts32.w1 = 0;
- t.parts32.w2 = 0;
- t.parts32.w3 = 0;
+ INSERT_WORDS (xhi, 0x3fe00000 + (k << 14), 0);
+ t = xhi;
}
- u.value = __scalbnl (u.value, ((int) ((w0 - u.parts32.w0) * 2)) >> 21);
+ x = __scalbnl (x, ((int) ((w0 - hx) * 2)) >> 21);
/* log(u) = log( t u/t ) = log(t) + log(u/t)
log(t) is tabulated in the lookup table.
Express log(u/t) = log(1+z), where z = u/t - 1 = (u-t)/t.
cf. Cody & Waite. */
- z = (u.value - t.value) / t.value;
+ z = (x - t) / t;
}
/* Series expansion of log(1+z). */
w = z * z;
y += e * ln2b; /* Base 2 exponent offset times ln(2). */
y += z;
y += logtbl[k-26]; /* log(t) - (t-1) */
- y += (t.value - 1.0L);
+ y += (t - 1.0L);
y += e * ln2a;
return y;
}
long double y1, t1, t2, r, s, 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)
return one;
/* 1.0**y = 1; -1.0**+-Inf = 1 */
if (x == one)
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 */
{
}
}
+ 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 __ieee754_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)
{
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 = 0;
- 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 = 0;
- 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 = 0;
- 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 = 0;
- 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 = 0;
- 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; /* (-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 = 0;
- 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)
+ if (((j - 0x40d00000) | lj) != 0)
return s * huge * huge; /* overflow */
else
{
else if ((j & 0x7fffffff) >= 0x40d01b90) /* z <= -16495 */
{
/* z < -16495 */
- if (((j - 0xc0d01bc0) | o.parts32.w1
- | (o.parts32.w2 & 0x7fffffff) | o.parts32.w3) != 0)
+ if (((j - 0xc0d01bc0) | lj) != 0)
return s * tiny * tiny; /* underflow */
else
{
p_h -= t;
}
t = p_l + p_h;
- o.value = t;
- o.parts32.w3 = 0;
- o.parts32.w2 = 0;
- t = o.value;
+ t = ldbl_high (t);
u = t * lg2_h;
v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
z = u + v;
__kernel_tanl (long double x, long double y, int iy)
{
long double z, r, v, w, s;
- int32_t ix, sign;
- ieee854_long_double_shape_type u, u1;
+ int32_t ix, sign, hx, lx;
+ double xhi;
- u.value = x;
- ix = u.parts32.w0 & 0x7fffffff;
+ xhi = ldbl_high (x);
+ EXTRACT_WORDS (hx, lx, xhi);
+ ix = hx & 0x7fffffff;
if (ix < 0x3c600000) /* x < 2**-57 */
{
- if ((int) x == 0)
- { /* generate inexact */
- if ((ix | u.parts32.w1 | (u.parts32.w2 & 0x7fffffff) | u.parts32.w3
- | (iy + 1)) == 0)
+ if ((int) x == 0) /* generate inexact */
+ {
+ if ((ix | lx | (iy + 1)) == 0)
return one / fabs (x);
else
return (iy == 1) ? x : -one / x;
}
if (ix >= 0x3fe59420) /* |x| >= 0.6743316650390625 */
{
- if ((u.parts32.w0 & 0x80000000) != 0)
+ if ((hx & 0x80000000) != 0)
{
x = -x;
y = -y;
{ /* if allow error up to 2 ulp,
simply return -1.0/(x+r) here */
/* compute -1.0/(x+r) accurately */
- u1.value = w;
- u1.parts32.w2 = 0;
- u1.parts32.w3 = 0;
- v = r - (u1.value - x); /* u1+v = r+x */
+ long double u1, z1;
+
+ u1 = ldbl_high (w);
+ v = r - (u1 - x); /* u1+v = r+x */
z = -1.0 / w;
- u.value = z;
- u.parts32.w2 = 0;
- u.parts32.w3 = 0;
- s = 1.0 + u.value * u1.value;
- return u.value + z * (s + u.value * v);
+ z1 = ldbl_high (z);
+ s = 1.0 + z1 * u1;
+ return z1 + z * (s + z1 * v);
}
}
__expm1l (long double x)
{
long double px, qx, xx;
- int32_t ix, sign;
- ieee854_long_double_shape_type u;
+ int32_t ix, lx, sign;
int k;
+ double xhi;
/* Detect infinity and NaN. */
- u.value = x;
- ix = u.parts32.w0;
+ xhi = ldbl_high (x);
+ EXTRACT_WORDS (ix, lx, xhi);
sign = ix & 0x80000000;
ix &= 0x7fffffff;
if (ix >= 0x7ff00000)
{
/* Infinity. */
- if (((ix & 0xfffff) | u.parts32.w1 | (u.parts32.w2&0x7fffffff) | u.parts32.w3) == 0)
+ if (((ix - 0x7ff00000) | lx) == 0)
{
if (sign)
return -1.0L;
}
/* expm1(+- 0) = +- 0. */
- if ((ix == 0) && (u.parts32.w1 | (u.parts32.w2&0x7fffffff) | u.parts32.w3) == 0)
+ if ((ix | lx) == 0)
return x;
/* Overflow. */
long double __frexpl(long double x, int *eptr)
{
- u_int64_t hx, lx, ix, ixl;
+ uint64_t hx, lx, ix, ixl;
int64_t explo;
- GET_LDOUBLE_WORDS64(hx,lx,x);
+ double xhi, xlo;
+
+ ldbl_unpack (x, &xhi, &xlo);
+ EXTRACT_WORDS64 (hx, xhi);
+ EXTRACT_WORDS64 (lx, xlo);
ixl = 0x7fffffffffffffffULL&lx;
ix = 0x7fffffffffffffffULL&hx;
*eptr = 0;
- if(ix>=0x7ff0000000000000ULL||((ix|ixl)==0)) return x; /* 0,inf,nan */
+ if(ix>=0x7ff0000000000000ULL||ix==0) return x; /* 0,inf,nan */
if (ix<0x0010000000000000ULL) { /* subnormal */
x *= two107;
- GET_LDOUBLE_MSW64(hx,x);
+ xhi = ldbl_high (x);
+ EXTRACT_WORDS64 (hx, xhi);
ix = hx&0x7fffffffffffffffULL;
*eptr = -107;
}
if (ixl != 0ULL) {
explo = (ixl>>52) - (ix>>52) + 0x3fe;
if ((ixl&0x7ff0000000000000ULL) == 0LL) {
- /* the lower double is a denomal so we need to correct its
+ /* the lower double is a denormal so we need to correct its
mantissa and perhaps its exponent. */
int cnt;
lx = 0ULL;
hx = (hx&0x800fffffffffffffULL) | 0x3fe0000000000000ULL;
- SET_LDOUBLE_WORDS64(x,hx,lx);
+ INSERT_WORDS64 (xhi, hx);
+ INSERT_WORDS64 (xlo, lx);
+ x = ldbl_pack (xhi, xlo);
return x;
}
#ifdef IS_IN_libm
/*
* __isinf_nsl(x) returns != 0 if x is ±inf, else 0;
* no branching!
+ * slightly dodgy in relying on signed shift right copying sign bit
*/
#include <math.h>
int
__isinf_nsl (long double x)
{
- int64_t hx,lx;
- GET_LDOUBLE_WORDS64(hx,lx,x);
- return !((lx & 0x7fffffffffffffffLL)
- | ((hx & 0x7fffffffffffffffLL) ^ 0x7ff0000000000000LL));
+ double xhi;
+ int64_t hx, mask;
+
+ xhi = ldbl_high (x);
+ EXTRACT_WORDS64 (hx, xhi);
+
+ mask = (hx & 0x7fffffffffffffffLL) ^ 0x7ff0000000000000LL;
+ mask |= -mask;
+ mask >>= 63;
+ return ~mask;
}
/*
* isinfl(x) returns 1 if x is inf, -1 if x is -inf, else 0;
* no branching!
+ * slightly dodgy in relying on signed shift right copying sign bit
*/
#include <math.h>
int
___isinfl (long double x)
{
- int64_t hx,lx;
- GET_LDOUBLE_WORDS64(hx,lx,x);
- lx = (lx & 0x7fffffffffffffffLL);
- lx |= (hx & 0x7fffffffffffffffLL) ^ 0x7ff0000000000000LL;
- lx |= -lx;
- return ~(lx >> 63) & (hx >> 62);
+ double xhi;
+ int64_t hx, mask;
+
+ xhi = ldbl_high (x);
+ EXTRACT_WORDS64 (hx, xhi);
+
+ mask = (hx & 0x7fffffffffffffffLL) ^ 0x7ff0000000000000LL;
+ mask |= -mask;
+ mask >>= 63;
+ return ~mask & (hx >> 62);
}
hidden_ver (___isinfl, __isinfl)
#ifndef IS_IN_libm
__log1pl (long double xm1)
{
long double x, y, z, r, s;
- ieee854_long_double_shape_type u;
- int32_t hx;
+ double xhi;
+ int32_t hx, lx;
int e;
/* Test for NaN or infinity input. */
- u.value = xm1;
- hx = u.parts32.w0;
+ xhi = ldbl_high (xm1);
+ EXTRACT_WORDS (hx, lx, xhi);
if (hx >= 0x7ff00000)
return xm1;
/* log1p(+- 0) = +- 0. */
- if (((hx & 0x7fffffff) == 0)
- && (u.parts32.w1 | (u.parts32.w2 & 0x7fffffff) | u.parts32.w3) == 0)
+ if (((hx & 0x7fffffff) | lx) == 0)
return xm1;
x = xm1 + 1.0L;
{
int64_t i0,i1,j0;
u_int64_t i;
- GET_LDOUBLE_WORDS64(i0,i1,x);
+ double xhi, xlo;
+
+ ldbl_unpack (x, &xhi, &xlo);
+ EXTRACT_WORDS64 (i0, xhi);
+ EXTRACT_WORDS64 (i1, xlo);
i1 &= 0x000fffffffffffffLL;
j0 = ((i0>>52)&0x7ff)-0x3ff; /* exponent of x */
if(j0<52) { /* integer part in high x */
if(j0<0) { /* |x|<1 */
/* *iptr = +-0 */
- SET_LDOUBLE_WORDS64(*iptr,i0&0x8000000000000000ULL,0);
+ INSERT_WORDS64 (xhi, i0&0x8000000000000000ULL);
+ *iptr = xhi;
return x;
} else {
i = (0x000fffffffffffffLL)>>j0;
if(((i0&i)|(i1&0x7fffffffffffffffLL))==0) { /* x is integral */
*iptr = x;
/* return +-0 */
- SET_LDOUBLE_WORDS64(x,i0&0x8000000000000000ULL,0);
+ INSERT_WORDS64 (xhi, i0&0x8000000000000000ULL);
+ x = xhi;
return x;
} else {
- SET_LDOUBLE_WORDS64(*iptr,i0&(~i),0);
+ INSERT_WORDS64 (xhi, i0&(~i));
+ *iptr = xhi;
return x - *iptr;
}
}
} else if (j0>103) { /* no fraction part */
*iptr = x*one;
/* We must handle NaNs separately. */
- if (j0 == 0x400 && ((i0 & 0x000fffffffffffffLL) | i1))
+ if ((i0 & 0x7fffffffffffffffLL) > 0x7ff0000000000000LL)
return x*one;
/* return +-0 */
- SET_LDOUBLE_WORDS64(x,i0&0x8000000000000000ULL,0);
+ INSERT_WORDS64 (xhi, i0&0x8000000000000000ULL);
+ x = xhi;
return x;
} else { /* fraction part in low x */
i = -1ULL>>(j0-52);
if((i1&i)==0) { /* x is integral */
*iptr = x;
/* return +-0 */
- SET_LDOUBLE_WORDS64(x,i0&0x8000000000000000ULL,0);
+ INSERT_WORDS64 (xhi, i0&0x8000000000000000ULL);
+ x = xhi;
return x;
} else {
- SET_LDOUBLE_WORDS64(*iptr,i0,i1&(~i));
+ INSERT_WORDS64 (xhi, i0);
+ INSERT_WORDS64 (xlo, i1&(~i));
+ *iptr = ldbl_pack (xhi, xlo);
return x - *iptr;
}
}
long double __nextafterl(long double x, long double y)
{
- int64_t hx,hy,ihx,ihy,ilx;
- u_int64_t lx;
- u_int64_t ly __attribute__ ((unused));
+ int64_t hx,hy,ihx,ihy;
+ uint64_t lx;
+ double xhi, xlo, yhi;
- GET_LDOUBLE_WORDS64(hx,lx,x);
- GET_LDOUBLE_WORDS64(hy,ly,y);
+ ldbl_unpack (x, &xhi, &xlo);
+ EXTRACT_WORDS64 (hx, xhi);
+ EXTRACT_WORDS64 (lx, xlo);
+ yhi = ldbl_high (y);
+ EXTRACT_WORDS64 (hy, yhi);
ihx = hx&0x7fffffffffffffffLL; /* |hx| */
- ilx = lx&0x7fffffffffffffffLL; /* |lx| */
ihy = hy&0x7fffffffffffffffLL; /* |hy| */
- if((((ihx&0x7ff0000000000000LL)==0x7ff0000000000000LL)&&
- ((ihx&0x000fffffffffffffLL)!=0)) || /* x is nan */
- (((ihy&0x7ff0000000000000LL)==0x7ff0000000000000LL)&&
- ((ihy&0x000fffffffffffffLL)!=0))) /* y is nan */
+ if((ihx>0x7ff0000000000000LL) || /* x is nan */
+ (ihy>0x7ff0000000000000LL)) /* y is nan */
return x+y; /* signal the nan */
if(x==y)
return y; /* x=y, return y */
- if(ihx == 0 && ilx == 0) { /* x == 0 */
- long double u;
+ if(ihx == 0) { /* x == 0 */
+ long double u; /* return +-minsubnormal */
hy = (hy & 0x8000000000000000ULL) | 1;
- SET_LDOUBLE_WORDS64(x,hy,0ULL);/* return +-minsubnormal */
+ INSERT_WORDS64 (yhi, hy);
+ x = yhi;
u = math_opt_barrier (x);
u = u * u;
math_force_eval (u); /* raise underflow flag */
long double u;
if(x > y) { /* x > y, x -= ulp */
+ /* This isn't the largest magnitude correctly rounded
+ long double as you can see from the lowest mantissa
+ bit being zero. It is however the largest magnitude
+ long double with a 106 bit mantissa, and nextafterl
+ is insane with variable precision. So to make
+ nextafterl sane we assume 106 bit precision. */
if((hx==0xffefffffffffffffLL)&&(lx==0xfc8ffffffffffffeLL))
return x+x; /* overflow, return -inf */
if (hx >= 0x7ff0000000000000LL) {
- SET_LDOUBLE_WORDS64(u,0x7fefffffffffffffLL,0x7c8ffffffffffffeLL);
+ u = 0x1.fffffffffffff7ffffffffffff8p+1023L;
return u;
}
if(ihx <= 0x0360000000000000LL) { /* x <= LDBL_MIN */
return x;
}
if (ihx < 0x06a0000000000000LL) { /* ulp will denormal */
- SET_LDOUBLE_WORDS64(u,(hx&0x7ff0000000000000LL),0ULL);
+ INSERT_WORDS64 (yhi, hx & (0x7ffLL<<52));
+ u = yhi;
u *= 0x1.0000000000000p-105L;
- } else
- SET_LDOUBLE_WORDS64(u,(hx&0x7ff0000000000000LL)-0x0690000000000000LL,0ULL);
+ } else {
+ INSERT_WORDS64 (yhi, (hx & (0x7ffLL<<52))-(0x069LL<<52));
+ u = yhi;
+ }
return x - u;
} else { /* x < y, x += ulp */
if((hx==0x7fefffffffffffffLL)&&(lx==0x7c8ffffffffffffeLL))
return x+x; /* overflow, return +inf */
- if ((u_int64_t) hx >= 0xfff0000000000000ULL) {
- SET_LDOUBLE_WORDS64(u,0xffefffffffffffffLL,0xfc8ffffffffffffeLL);
+ if ((uint64_t) hx >= 0xfff0000000000000ULL) {
+ u = -0x1.fffffffffffff7ffffffffffff8p+1023L;
return u;
}
if(ihx <= 0x0360000000000000LL) { /* x <= LDBL_MIN */
return x;
}
if (ihx < 0x06a0000000000000LL) { /* ulp will denormal */
- SET_LDOUBLE_WORDS64(u,(hx&0x7ff0000000000000LL),0ULL);
+ INSERT_WORDS64 (yhi, hx & (0x7ffLL<<52));
+ u = yhi;
u *= 0x1.0000000000000p-105L;
- } else
- SET_LDOUBLE_WORDS64(u,(hx&0x7ff0000000000000LL)-0x0690000000000000LL,0ULL);
+ } else {
+ INSERT_WORDS64 (yhi, (hx & (0x7ffLL<<52))-(0x069LL<<52));
+ u = yhi;
+ }
return x + u;
}
}
{
int32_t hx,ix;
int64_t hy,iy;
- u_int32_t lx;
- u_int64_t ly,uly;
+ uint32_t lx;
+ double yhi;
EXTRACT_WORDS(hx,lx,x);
- GET_LDOUBLE_WORDS64(hy,ly,y);
+ yhi = ldbl_high (y);
+ EXTRACT_WORDS64(hy,yhi);
ix = hx&0x7fffffff; /* |x| */
iy = hy&0x7fffffffffffffffLL; /* |y| */
- uly = ly&0x7fffffffffffffffLL; /* |y| */
if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */
- ((iy>=0x7ff0000000000000LL)&&((iy-0x7ff0000000000000LL)|uly)!=0))
- /* y is nan */
+ iy>0x7ff0000000000000LL) /* y is nan */
return x+y;
if((long double) x==y) return y; /* x=y, return y */
if((ix|lx)==0) { /* x == 0 */
double u;
- INSERT_WORDS(x,(u_int32_t)((hy>>32)&0x80000000),1);/* return +-minsub */
+ INSERT_WORDS(x,(uint32_t)((hy>>32)&0x80000000),1);/* return +-minsub */
u = math_opt_barrier (x);
u = u * u;
math_force_eval (u); /* raise underflow flag */
{
int32_t hx,ix;
int64_t hy,iy;
- u_int64_t ly, uly;
+ double yhi;
GET_FLOAT_WORD(hx,x);
- GET_LDOUBLE_WORDS64(hy,ly,y);
+ yhi = ldbl_high (y);
+ EXTRACT_WORDS64 (hy, yhi);
ix = hx&0x7fffffff; /* |x| */
iy = hy&0x7fffffffffffffffLL; /* |y| */
- uly = ly&0x7fffffffffffffffLL; /* |y| */
if((ix>0x7f800000) || /* x is nan */
- ((iy>=0x7ff0000000000000LL)&&((iy-0x7ff0000000000000LL)|uly)!=0))
+ (iy>0x7ff0000000000000LL))
/* y is nan */
return x+y;
if((long double) x==y) return y; /* x=y, return y */
int64_t hx,hy;
u_int64_t sx,lx,ly,qs;
int cquo;
-
- GET_LDOUBLE_WORDS64 (hx, lx, x);
- GET_LDOUBLE_WORDS64 (hy, ly, y);
+ double xhi, xlo, yhi, ylo;
+
+ ldbl_unpack (x, &xhi, &xlo);
+ EXTRACT_WORDS64 (hx, xhi);
+ EXTRACT_WORDS64 (lx, xlo);
+ ldbl_unpack (y, &yhi, &ylo);
+ EXTRACT_WORDS64 (hy, yhi);
+ EXTRACT_WORDS64 (ly, ylo);
sx = hx & 0x8000000000000000ULL;
qs = sx ^ (hy & 0x8000000000000000ULL);
hy &= 0x7fffffffffffffffLL;
hx &= 0x7fffffffffffffffLL;
/* Purge off exception values. */
- if ((hy | (ly & 0x7fffffffffffffff)) == 0)
+ if (hy == 0)
return (x * y) / (x * y); /* y = 0 */
if ((hx >= 0x7ff0000000000000LL) /* x not finite */
- || ((hy >= 0x7ff0000000000000LL) /* y is NaN */
- && (((hy - 0x7ff0000000000000LL) | ly) != 0)))
+ || (hy > 0x7ff0000000000000LL)) /* y is NaN */
return (x * y) / (x * y);
if (hy <= 0x7fbfffffffffffffLL)
{
int64_t k,l,hx,lx;
union { int64_t i; double d; } u;
- GET_LDOUBLE_WORDS64(hx,lx,x);
+ double xhi, xlo;
+
+ ldbl_unpack (x, &xhi, &xlo);
+ EXTRACT_WORDS64 (hx, xhi);
+ EXTRACT_WORDS64 (lx, xlo);
k = (hx>>52)&0x7ff; /* extract exponent */
l = (lx>>52)&0x7ff;
if (k==0) { /* 0 or subnormal x */
- if (((hx|lx)&0x7fffffffffffffffULL)==0) return x; /* +-0 */
+ if ((hx&0x7fffffffffffffffULL)==0) return x; /* +-0 */
u.i = hx;
u.d *= two54;
hx = u.i;
if (k > 0) { /* normal result */
hx = (hx&0x800fffffffffffffULL)|(k<<52);
if ((lx & 0x7fffffffffffffffULL) == 0) { /* low part +-0 */
- SET_LDOUBLE_WORDS64(x,hx,lx);
+ INSERT_WORDS64 (xhi, hx);
+ INSERT_WORDS64 (xlo, lx);
+ x = ldbl_pack (xhi, xlo);
return x;
}
if (l == 0) { /* low part subnormal */
u.d *= twom54;
lx = u.i;
}
- SET_LDOUBLE_WORDS64(x,hx,lx);
+ INSERT_WORDS64 (xhi, hx);
+ INSERT_WORDS64 (xlo, lx);
+ x = ldbl_pack (xhi, xlo);
return x;
}
if (k <= -54)
return tiny*__copysignl(tiny,x); /*underflow*/
k += 54; /* subnormal result */
lx &= 0x8000000000000000ULL;
- SET_LDOUBLE_WORDS64(x,(hx&0x800fffffffffffffULL)|(k<<52),lx);
+ hx &= 0x800fffffffffffffULL;
+ INSERT_WORDS64 (xhi, hx|(k<<52));
+ INSERT_WORDS64 (xlo, lx);
+ x = ldbl_pack (xhi, xlo);
return x*twolm54;
}
long_double_symbol (libm, __scalblnl, scalblnl);
{
int64_t k,l,hx,lx;
union { int64_t i; double d; } u;
- GET_LDOUBLE_WORDS64(hx,lx,x);
+ double xhi, xlo;
+
+ ldbl_unpack (x, &xhi, &xlo);
+ EXTRACT_WORDS64 (hx, xhi);
+ EXTRACT_WORDS64 (lx, xlo);
k = (hx>>52)&0x7ff; /* extract exponent */
l = (lx>>52)&0x7ff;
if (k==0) { /* 0 or subnormal x */
- if (((hx|lx)&0x7fffffffffffffffULL)==0) return x; /* +-0 */
+ if ((hx&0x7fffffffffffffffULL)==0) return x; /* +-0 */
u.i = hx;
u.d *= two54;
hx = u.i;
if (k > 0) { /* normal result */
hx = (hx&0x800fffffffffffffULL)|(k<<52);
if ((lx & 0x7fffffffffffffffULL) == 0) { /* low part +-0 */
- SET_LDOUBLE_WORDS64(x,hx,lx);
+ INSERT_WORDS64 (xhi, hx);
+ INSERT_WORDS64 (xlo, lx);
+ x = ldbl_pack (xhi, xlo);
return x;
}
if (l == 0) { /* low part subnormal */
u.d *= twom54;
lx = u.i;
}
- SET_LDOUBLE_WORDS64(x,hx,lx);
+ INSERT_WORDS64 (xhi, hx);
+ INSERT_WORDS64 (xlo, lx);
+ x = ldbl_pack (xhi, xlo);
return x;
}
if (k <= -54)
return tiny*__copysignl(tiny,x); /*underflow*/
k += 54; /* subnormal result */
lx &= 0x8000000000000000ULL;
- SET_LDOUBLE_WORDS64(x,(hx&0x800fffffffffffffULL)|(k<<52),lx);
+ hx &= 0x800fffffffffffffULL;
+ INSERT_WORDS64 (xhi, hx|(k<<52));
+ INSERT_WORDS64 (xlo, lx);
+ x = ldbl_pack (xhi, xlo);
return x*twolm54;
}
#ifdef IS_IN_libm
long double __tanhl(long double x)
{
long double t,z;
- int64_t jx,ix,lx;
+ int64_t jx,ix;
+ double xhi;
/* High word of |x|. */
- GET_LDOUBLE_WORDS64(jx,lx,x);
+ xhi = ldbl_high (x);
+ EXTRACT_WORDS64 (jx, xhi);
ix = jx&0x7fffffffffffffffLL;
/* x is INF or NaN */
/* |x| < 22 */
if (ix < 0x4036000000000000LL) { /* |x|<22 */
- if ((ix | (lx&0x7fffffffffffffffLL)) == 0)
+ if (ix == 0)
return x; /* x == +-0 */
if (ix<0x3c60000000000000LL) /* |x|<2**-57 */
return x*(one+x); /* tanh(small) = small */
ifloat: 1
ildouble: 2
ldouble: 2
+Test "tan_towardzero (2)":
+ildouble: 1
+ldouble: 1
Test "tan_towardzero (3)":
float: 1
ifloat: 1
projects / thirdparty / glibc.git / commitdiff
