first commit of the new libm!

[musl] / src / math / hypot.c

diff --git a/src/math/hypot.c b/src/math/hypot.c
new file mode 100644 (file)
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+++ b/src/math/hypot.c
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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;
+}