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authorZack Weinberg <zackw@panix.com>2017-06-08 15:39:03 -0400
committerZack Weinberg <zackw@panix.com>2017-06-08 15:39:03 -0400
commit5046dbb4a7eba5eccfd258f92f4735c9ffc8d069 (patch)
tree4470480d904b65cf14ca524f96f79eca818c3eaf /REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c
parent199fc19d3aaaf57944ef036e15904febe877fc93 (diff)
downloadglibc-zack/build-layout-experiment.tar.gz
glibc-zack/build-layout-experiment.tar.xz
glibc-zack/build-layout-experiment.zip
Prepare for radical source tree reorganization. zack/build-layout-experiment
All top-level files and directories are moved into a temporary storage
directory, REORG.TODO, except for files that will certainly still
exist in their current form at top level when we're done (COPYING,
COPYING.LIB, LICENSES, NEWS, README), all old ChangeLog files (which
are moved to the new directory OldChangeLogs, instead), and the
generated file INSTALL (which is just deleted; in the new order, there
will be no generated files checked into version control).
Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c')
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diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c
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+/* @(#)e_hypotl.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+/* __ieee754_hypotl(x,y)
+ *
+ * Method :
+ *	If (assume round-to-nearest) z=x*x+y*y
+ *	has error less than sqrtl(2)/2 ulp, than
+ *	sqrtl(z) has error less than 1 ulp (exercise).
+ *
+ *	So, compute sqrtl(x*x+y*y) with some care as
+ *	follows to get the error below 1 ulp:
+ *
+ *	Assume x>y>0;
+ *	(if possible, set rounding to round-to-nearest)
+ *	1. if x > 2y  use
+ *		x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
+ *	where x1 = x with lower 53 bits cleared, x2 = x-x1; else
+ *	2. if x <= 2y use
+ *		t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
+ *	where t1 = 2x with lower 53 bits cleared, t2 = 2x-t1,
+ *	y1= y with lower 53 bits chopped, y2 = y-y1.
+ *
+ *	NOTE: scaling may be necessary if some argument is too
+ *	      large or too tiny
+ *
+ * Special cases:
+ *	hypotl(x,y) is INF if x or y is +INF or -INF; else
+ *	hypotl(x,y) is NAN if x or y is NAN.
+ *
+ * Accuracy:
+ *	hypotl(x,y) returns sqrtl(x^2+y^2) with error less
+ *	than 1 ulps (units in the last place)
+ */
+
+#include <math.h>
+#include <math_private.h>
+
+long double
+__ieee754_hypotl(long double x, long double y)
+{
+	long double a,b,a1,a2,b1,b2,w,kld;
+	int64_t j,k,ha,hb;
+	double xhi, yhi, hi, lo;
+
+	xhi = ldbl_high (x);
+	EXTRACT_WORDS64 (ha, xhi);
+	yhi = ldbl_high (y);
+	EXTRACT_WORDS64 (hb, yhi);
+	ha &= 0x7fffffffffffffffLL;
+	hb &= 0x7fffffffffffffffLL;
+	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
+	a = fabsl(a);	/* a <- |a| */
+	b = fabsl(b);	/* b <- |b| */
+	if((ha-hb)>0x0780000000000000LL) {return a+b;} /* x/y > 2**120 */
+	k=0;
+	kld = 1.0L;
+	if(ha > 0x5f30000000000000LL) {	/* a>2**500 */
+	   if(ha >= 0x7ff0000000000000LL) {	/* Inf or NaN */
+	       w = a+b;			/* for sNaN */
+	       if (issignaling (a) || issignaling (b))
+		 return w;
+	       if(ha == 0x7ff0000000000000LL)
+		 w = a;
+	       if(hb == 0x7ff0000000000000LL)
+		 w = b;
+	       return w;
+	   }
+	   /* scale a and b by 2**-600 */
+	   a *= 0x1p-600L;
+	   b *= 0x1p-600L;
+	   k = 600;
+	   kld = 0x1p+600L;
+	}
+	else if(hb < 0x23d0000000000000LL) {	/* b < 2**-450 */
+	    if(hb <= 0x000fffffffffffffLL) {	/* subnormal b or 0 */
+		if(hb==0) return a;
+		a *= 0x1p+1022L;
+		b *= 0x1p+1022L;
+		k = -1022;
+		kld = 0x1p-1022L;
+	    } else {		/* scale a and b by 2^600 */
+		a *= 0x1p+600L;
+		b *= 0x1p+600L;
+		k = -600;
+		kld = 0x1p-600L;
+	    }
+	}
+    /* medium size a and b */
+	w = a-b;
+	if (w>b) {
+	    ldbl_unpack (a, &hi, &lo);
+	    a1 = hi;
+	    a2 = lo;
+	    /* a*a + b*b
+	       = (a1+a2)*a + b*b
+	       = a1*a + a2*a + b*b
+	       = a1*(a1+a2) + a2*a + b*b
+	       = a1*a1 + a1*a2 + a2*a + b*b
+	       = a1*a1 + a2*(a+a1) + b*b  */
+	    w  = __ieee754_sqrtl(a1*a1-(b*(-b)-a2*(a+a1)));
+	} else {
+	    a  = a+a;
+	    ldbl_unpack (b, &hi, &lo);
+	    b1 = hi;
+	    b2 = lo;
+	    ldbl_unpack (a, &hi, &lo);
+	    a1 = hi;
+	    a2 = lo;
+	    /* a*a + b*b
+	       = a*a + (a-b)*(a-b) - (a-b)*(a-b) + b*b
+	       = a*a + w*w  - (a*a - 2*a*b + b*b) + b*b
+	       = w*w + 2*a*b
+	       = w*w + (a1+a2)*b
+	       = w*w + a1*b + a2*b
+	       = w*w + a1*(b1+b2) + a2*b
+	       = w*w + a1*b1 + a1*b2 + a2*b  */
+	    w  = __ieee754_sqrtl(a1*b1-(w*(-w)-(a1*b2+a2*b)));
+	}
+	if(k!=0)
+	    {
+		w *= kld;
+		math_check_force_underflow_nonneg (w);
+		return w;
+	    }
+	else
+	    return w;
+}
+strong_alias (__ieee754_hypotl, __hypotl_finite)