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+/* origin: FreeBSD /usr/src/lib/msun/src/e_hypot.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* hypot(x,y)
+ *
+ * Method :
+ * If (assume round-to-nearest) z=x*x+y*y
+ * has error less than sqrt(2)/2 ulp, then
+ * 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 "libm.h"
+
+double hypot(double x, double y)
+{
+ double a,b,t1,t2,y1,y2,w;
+ int32_t j,k,ha,hb;
+
+ GET_HIGH_WORD(ha, x);
+ ha &= 0x7fffffff;
+ GET_HIGH_WORD(hb, y);
+ hb &= 0x7fffffff;
+ if (hb > ha) {
+ a = y;
+ b = x;
+ j=ha; ha=hb; hb=j;
+ } else {
+ a = x;
+ b = y;
+ }
+ a = fabs(a);
+ b = fabs(b);
+ if (ha - hb > 0x3c00000) /* x/y > 2**60 */
+ return a+b;
+ k = 0;
+ if (ha > 0x5f300000) { /* a > 2**500 */
+ if(ha >= 0x7ff00000) { /* Inf or NaN */
+ uint32_t low;
+ /* Use original arg order iff result is NaN; quieten sNaNs. */
+ w = fabs(x+0.0) - fabs(y+0.0);
+ GET_LOW_WORD(low, a);
+ if (((ha&0xfffff)|low) == 0) w = a;
+ GET_LOW_WORD(low, b);
+ if (((hb^0x7ff00000)|low) == 0) w = b;
+ return w;
+ }
+ /* scale a and b by 2**-600 */
+ ha -= 0x25800000; hb -= 0x25800000; k += 600;
+ SET_HIGH_WORD(a, ha);
+ SET_HIGH_WORD(b, hb);
+ }
+ if (hb < 0x20b00000) { /* b < 2**-500 */
+ if (hb <= 0x000fffff) { /* subnormal b or 0 */
+ uint32_t low;
+ GET_LOW_WORD(low, b);
+ if ((hb|low) == 0)
+ return a;
+ t1 = 0;
+ SET_HIGH_WORD(t1, 0x7fd00000); /* t1 = 2^1022 */
+ b *= t1;
+ a *= t1;
+ k -= 1022;
+ } else { /* scale a and b by 2^600 */
+ ha += 0x25800000; /* a *= 2^600 */
+ hb += 0x25800000; /* b *= 2^600 */
+ k -= 600;
+ SET_HIGH_WORD(a, ha);
+ SET_HIGH_WORD(b, hb);
+ }
+ }
+ /* medium size a and b */
+ w = a - b;
+ if (w > b) {
+ t1 = 0;
+ SET_HIGH_WORD(t1, ha);
+ t2 = a-t1;
+ w = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
+ } else {
+ a = a + a;
+ y1 = 0;
+ SET_HIGH_WORD(y1, hb);
+ y2 = b - y1;
+ t1 = 0;
+ SET_HIGH_WORD(t1, ha+0x00100000);
+ t2 = a - t1;
+ w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
+ }
+ if (k != 0) {
+ uint32_t high;
+ t1 = 1.0;
+ GET_HIGH_WORD(high, t1);
+ SET_HIGH_WORD(t1, high+(k<<20));
+ return t1*w;
+ }
+ return w;
+}