PowerPC floating point little-endian [3 of 15]

http://sourceware.org/ml/libc-alpha/2013-08/msg00083.html

Further replacement of ieee854 macros and unions.  These files also
have some optimisations for comparison against 0.0L, infinity and nan.
Since the ABI specifies that the high double of an IBM long double
pair is the value rounded to double, a high double of 0.0 means the
low double must also be 0.0.  The ABI also says that infinity and
nan are encoded in the high double, with the low double unspecified.
This means that tests for 0.0L, +/-Infinity and +/-NaN need only check
the high double.

	* 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.

1 files changed, 55 insertions, 81 deletions

diff --git a/sysdeps/ieee754/ldbl-128ibm/e_powl.c b/sysdeps/ieee754/ldbl-128ibm/e_powl.c
index 8bd35d0c88..c942f2f249 100644
--- a/sysdeps/ieee754/ldbl-128ibm/e_powl.c
+++ b/sysdeps/ieee754/ldbl-128ibm/e_powl.c
@@ -151,37 +151,32 @@ __ieee754_powl (long double x, long double 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
@@ -192,7 +187,10 @@ __ieee754_powl (long double x, long double y)
   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 */
 	{
@@ -207,42 +205,43 @@ __ieee754_powl (long double x, long double y)
 	}
     }
 
+  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)
@@ -294,8 +293,8 @@ __ieee754_powl (long double x, long double y)
     {
       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;
@@ -312,26 +311,19 @@ __ieee754_powl (long double x, long double y)
       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) */
@@ -342,30 +334,21 @@ __ieee754_powl (long double x, long double y)
   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 */
@@ -374,21 +357,16 @@ __ieee754_powl (long double x, long double y)
     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
 	{
@@ -399,8 +377,7 @@ __ieee754_powl (long double x, long double y)
   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
 	{
@@ -419,10 +396,7 @@ __ieee754_powl (long double x, long double y)
       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;