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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-96/e_hypotl.c
parent199fc19d3aaaf57944ef036e15904febe877fc93 (diff)
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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).
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+/* e_hypotl.c -- long double version of e_hypot.c.
+ * Conversion to long double by Ulrich Drepper,
+ * Cygnus Support, drepper@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * 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 sqrt(2)/2 ulp, than
+ * sqrt(z) has error less than 1 ulp (exercise).
+ *
+ * So, compute sqrt(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 32 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 32 bits cleared, t2 = 2x-t1,
+ * y1= y with lower 32 bits chopped, y2 = y-y1.
+ *
+ * NOTE: scaling may be necessary if some argument is too
+ * large or too tiny
+ *
+ * Special cases:
+ * hypot(x,y) is INF if x or y is +INF or -INF; else
+ * hypot(x,y) is NAN if x or y is NAN.
+ *
+ * Accuracy:
+ * hypot(x,y) returns sqrt(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,t1,t2,y1,y2,w;
+ u_int32_t j,k,ea,eb;
+
+ GET_LDOUBLE_EXP(ea,x);
+ ea &= 0x7fff;
+ GET_LDOUBLE_EXP(eb,y);
+ eb &= 0x7fff;
+ if(eb > ea) {a=y;b=x;j=ea; ea=eb;eb=j;} else {a=x;b=y;}
+ SET_LDOUBLE_EXP(a,ea); /* a <- |a| */
+ SET_LDOUBLE_EXP(b,eb); /* b <- |b| */
+ if((ea-eb)>0x46) {return a+b;} /* x/y > 2**70 */
+ k=0;
+ if(__builtin_expect(ea > 0x5f3f,0)) { /* a>2**8000 */
+ if(ea == 0x7fff) { /* Inf or NaN */
+ u_int32_t exp __attribute__ ((unused));
+ u_int32_t high,low;
+ w = a+b; /* for sNaN */
+ if (issignaling (a) || issignaling (b))
+ return w;
+ GET_LDOUBLE_WORDS(exp,high,low,a);
+ if(((high&0x7fffffff)|low)==0) w = a;
+ GET_LDOUBLE_WORDS(exp,high,low,b);
+ if(((eb^0x7fff)|(high&0x7fffffff)|low)==0) w = b;
+ return w;
+ }
+ /* scale a and b by 2**-9600 */
+ ea -= 0x2580; eb -= 0x2580; k += 9600;
+ SET_LDOUBLE_EXP(a,ea);
+ SET_LDOUBLE_EXP(b,eb);
+ }
+ if(__builtin_expect(eb < 0x20bf, 0)) { /* b < 2**-8000 */
+ if(eb == 0) { /* subnormal b or 0 */
+ u_int32_t exp __attribute__ ((unused));
+ u_int32_t high,low;
+ GET_LDOUBLE_WORDS(exp,high,low,b);
+ if((high|low)==0) return a;
+ SET_LDOUBLE_WORDS(t1, 0x7ffd, 0x80000000, 0); /* t1=2^16382 */
+ b *= t1;
+ a *= t1;
+ k -= 16382;
+ GET_LDOUBLE_EXP (ea, a);
+ GET_LDOUBLE_EXP (eb, b);
+ if (eb > ea)
+ {
+ t1 = a;
+ a = b;
+ b = t1;
+ j = ea;
+ ea = eb;
+ eb = j;
+ }
+ } else { /* scale a and b by 2^9600 */
+ ea += 0x2580; /* a *= 2^9600 */
+ eb += 0x2580; /* b *= 2^9600 */
+ k -= 9600;
+ SET_LDOUBLE_EXP(a,ea);
+ SET_LDOUBLE_EXP(b,eb);
+ }
+ }
+ /* medium size a and b */
+ w = a-b;
+ if (w>b) {
+ u_int32_t high;
+ GET_LDOUBLE_MSW(high,a);
+ SET_LDOUBLE_WORDS(t1,ea,high,0);
+ t2 = a-t1;
+ w = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
+ } else {
+ u_int32_t high;
+ GET_LDOUBLE_MSW(high,b);
+ a = a+a;
+ SET_LDOUBLE_WORDS(y1,eb,high,0);
+ y2 = b - y1;
+ GET_LDOUBLE_MSW(high,a);
+ SET_LDOUBLE_WORDS(t1,ea+1,high,0);
+ t2 = a - t1;
+ w = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
+ }
+ if(k!=0) {
+ u_int32_t exp;
+ t1 = 1.0;
+ GET_LDOUBLE_EXP(exp,t1);
+ SET_LDOUBLE_EXP(t1,exp+k);
+ w *= t1;
+ math_check_force_underflow_nonneg (w);
+ return w;
+ } else return w;
+}
+strong_alias (__ieee754_hypotl, __hypotl_finite)