1 files changed, 76 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/x2y2m1l.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/x2y2m1l.c
new file mode 100644
index 0000000000..d3f88331b5
--- /dev/null
+++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/x2y2m1l.c
@@ -0,0 +1,76 @@
+/* Compute x^2 + y^2 - 1, without large cancellation error.
+   Copyright (C) 2012-2017 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include <math.h>
+#include <math_private.h>
+#include <mul_splitl.h>
+#include <stdlib.h>
+
+
+/* Calculate X + Y exactly and store the result in *HI + *LO.  It is
+   given that |X| >= |Y| and the values are small enough that no
+   overflow occurs.  */
+
+static inline void
+add_split (_Float128 *hi, _Float128 *lo, _Float128 x, _Float128 y)
+{
+  /* Apply Dekker's algorithm.  */
+  *hi = x + y;
+  *lo = (x - *hi) + y;
+}
+
+/* Compare absolute values of floating-point values pointed to by P
+   and Q for qsort.  */
+
+static int
+compare (const void *p, const void *q)
+{
+  _Float128 pld = fabsl (*(const _Float128 *) p);
+  _Float128 qld = fabsl (*(const _Float128 *) q);
+  if (pld < qld)
+    return -1;
+  else if (pld == qld)
+    return 0;
+  else
+    return 1;
+}
+
+/* Return X^2 + Y^2 - 1, computed without large cancellation error.
+   It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >=
+   0.5.  */
+
+_Float128
+__x2y2m1l (_Float128 x, _Float128 y)
+{
+  _Float128 vals[5];
+  SET_RESTORE_ROUNDL (FE_TONEAREST);
+  mul_splitl (&vals[1], &vals[0], x, x);
+  mul_splitl (&vals[3], &vals[2], y, y);
+  vals[4] = -1;
+  qsort (vals, 5, sizeof (_Float128), compare);
+  /* Add up the values so that each element of VALS has absolute value
+     at most equal to the last set bit of the next nonzero
+     element.  */
+  for (size_t i = 0; i <= 3; i++)
+    {
+      add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]);
+      qsort (vals + i + 1, 4 - i, sizeof (_Float128), compare);
+    }
+  /* Now any error from this addition will be small.  */
+  return vals[4] + vals[3] + vals[2] + vals[1] + vals[0];
+}