From 6d3144f9382a4aede51913d7465d300a320412e3 Mon Sep 17 00:00:00 2001
From: Raymond Toy <toy.raymond@gmail.com>
Date: Fri, 1 Aug 2014 19:54:27 -0700
Subject: [PATCH] Update to use unions.

 * e_pow.c:
   * Use unions to get to the parts of a double
 * fdlibm.h:
   * Declare sqrt function.
---
 src/lisp/e_pow.c  | 71 +++++++++++++++++++++++++++++++++++------------
 src/lisp/fdlibm.h |  1 +
 2 files changed, 54 insertions(+), 18 deletions(-)

diff --git a/src/lisp/e_pow.c b/src/lisp/e_pow.c
index 5683bf5fd..9dafc2649 100644
--- a/src/lisp/e_pow.c
+++ b/src/lisp/e_pow.c
@@ -109,10 +109,15 @@ ivln2_l  =  1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
 	int i0,i1,i,j,k,yisint,n;
 	int hx,hy,ix,iy;
 	unsigned lx,ly;
+	union { int i[2]; double d; } ux;
+	union { int i[2]; double d; } uy;
+	union { int i[2]; double d; } utmp;
 
 	i0 = ((*(int*)&one)>>29)^1; i1=1-i0;
-	hx = __HI(x); lx = __LO(x);
-	hy = __HI(y); ly = __LO(y);
+	ux.d = x;
+	hx = ux.i[HIWORD]; lx = ux.i[LOWORD];
+	uy.d = y;
+	hy = uy.i[HIWORD]; ly = uy.i[LOWORD];
 	ix = hx&0x7fffffff;  iy = hy&0x7fffffff;
 
     /* y==zero: x**0 = 1 */
@@ -203,14 +208,20 @@ ivln2_l  =  1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
 	    u = ivln2_h*t;	/* ivln2_h has 21 sig. bits */
 	    v = t*ivln2_l-w*ivln2;
 	    t1 = u+v;
-	    __LO(t1) = 0;
+	    utmp.d = t1;
+	    utmp.i[LOWORD] = 0;
+	    t1 = utmp.d;
 	    t2 = v-(t1-u);
 	} else {
 	    double ss,s2,s_h,s_l,t_h,t_l;
 	    n = 0;
 	/* take care subnormal number */
-	    if(ix<0x00100000)
-		{ax *= two53; n -= 53; ix = __HI(ax); }
+	    if(ix<0x00100000) {
+		ax *= two53;
+		n -= 53;
+		utmp.d = ax;
+		ix = utmp.i[HIWORD];
+	    }
 	    n  += ((ix)>>20)-0x3ff;
 	    j  = ix&0x000fffff;
 	/* determine interval */
@@ -218,17 +229,23 @@ ivln2_l  =  1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
 	    if(j<=0x3988E) k=0;		/* |x|<sqrt(3/2) */
 	    else if(j<0xBB67A) k=1;	/* |x|<sqrt(3)   */
 	    else {k=0;n+=1;ix -= 0x00100000;}
-	    __HI(ax) = ix;
+	    utmp.d = ax;
+	    utmp.i[HIWORD] = ix;
+	    ax = utmp.d;
 
 	/* compute ss = 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]);
 	    ss = u*v;
 	    s_h = ss;
-	    __LO(s_h) = 0;
+	    utmp.d = s_h;
+	    utmp.i[LOWORD] = 0;
+	    s_h = utmp.d;
 	/* t_h=ax+bp[k] High */
 	    t_h = zero;
-	    __HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18); 
+	    utmp.d = t_h;
+	    utmp.i[HIWORD]=((ix>>1)|0x20000000)+0x00080000+(k<<18);
+	    t_h = utmp.d;
 	    t_l = ax - (t_h-bp[k]);
 	    s_l = v*((u-s_h*t_h)-s_h*t_l);
 	/* compute log(ax) */
@@ -237,32 +254,41 @@ ivln2_l  =  1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
 	    r += s_l*(s_h+ss);
 	    s2  = s_h*s_h;
 	    t_h = 3.0+s2+r;
-	    __LO(t_h) = 0;
+	    utmp.d = t_h;
+	    utmp.i[LOWORD] = 0;
+	    t_h = utmp.d;
 	    t_l = r-((t_h-3.0)-s2);
 	/* u+v = ss*(1+...) */
 	    u = s_h*t_h;
 	    v = s_l*t_h+t_l*ss;
 	/* 2/(3log2)*(ss+...) */
 	    p_h = u+v;
-	    __LO(p_h) = 0;
+	    utmp.d = p_h;
+	    utmp.i[LOWORD] = 0;
+	    p_h = utmp.d;
 	    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) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
 	    t = (double)n;
 	    t1 = (((z_h+z_l)+dp_h[k])+t);
-	    __LO(t1) = 0;
+	    utmp.d = t1;
+	    utmp.i[LOWORD] = 0;
+	    t1 = utmp.d;
 	    t2 = z_l-(((t1-t)-dp_h[k])-z_h);
 	}
 
     /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
 	y1  = y;
-	__LO(y1) = 0;
+	utmp.d = y1;
+	utmp.i[LOWORD] = 0;
+	y1 = utmp.d;
 	p_l = (y-y1)*t1+y*t2;
 	p_h = y1*t1;
 	z = p_l+p_h;
-	j = __HI(z);
-	i = __LO(z);
+	utmp.d = z;
+	j = utmp.i[HIWORD];
+	i = utmp.i[LOWORD];
 	if (j>=0x40900000) {				/* z >= 1024 */
 	    if(((j-0x40900000)|i)!=0)			/* if z > 1024 */
 		return s*huge*huge;			/* overflow */
@@ -286,13 +312,17 @@ ivln2_l  =  1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
 	    n = j+(0x00100000>>(k+1));
 	    k = ((n&0x7fffffff)>>20)-0x3ff;	/* new k for n */
 	    t = zero;
-	    __HI(t) = (n&~(0x000fffff>>k));
+	    utmp.d = t;
+	    utmp.i[HIWORD] = (n&~(0x000fffff>>k));
+	    t = utmp.d;
 	    n = ((n&0x000fffff)|0x00100000)>>(20-k);
 	    if(j<0) n = -n;
 	    p_h -= t;
 	} 
 	t = p_l+p_h;
-	__LO(t) = 0;
+	utmp.d = t;
+	utmp.i[LOWORD] = 0;
+	t = utmp.d;
 	u = t*lg2_h;
 	v = (p_l-(t-p_h))*lg2+t*lg2_l;
 	z = u+v;
@@ -301,9 +331,14 @@ ivln2_l  =  1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
 	t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
 	r  = (z*t1)/(t1-two)-(w+z*w);
 	z  = one-(r-z);
-	j  = __HI(z);
+	utmp.d = z;
+	j  = utmp.i[HIWORD];
 	j += (n<<20);
 	if((j>>20)<=0) z = scalbn(z,n);	/* subnormal output */
-	else __HI(z) += (n<<20);
+	else {
+	    utmp.d = z;
+	    utmp.i[HIWORD] += (n<<20);
+	    z = utmp.d;
+	}
 	return s*z;
 }
diff --git a/src/lisp/fdlibm.h b/src/lisp/fdlibm.h
index 467daa537..180137baf 100644
--- a/src/lisp/fdlibm.h
+++ b/src/lisp/fdlibm.h
@@ -32,6 +32,7 @@ enum { HIWORD = 0, LOWORD = 1 };
  */
 extern double fabs(double);
 extern double floor(double);
+extern double sqrt(double);
 
 /* ieee style elementary functions */
 extern int    __ieee754_rem_pio2(double,double*);
-- 
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