--- /dev/null
+/*
+ * Borrowed from GCC 4.2.2 (which still was GPL v2+)
+ */
+/* 128-bit long double support routines for Darwin.
+ Copyright (C) 1993, 2003, 2004, 2005, 2006, 2007
+ Free Software Foundation, Inc.
+
+This file is part of GCC.
+
+GCC is free software; you can redistribute it and/or modify it under
+the terms of the GNU General Public License as published by the Free
+Software Foundation; either version 2, or (at your option) any later
+version.
+
+In addition to the permissions in the GNU General Public License, the
+Free Software Foundation gives you unlimited permission to link the
+compiled version of this file into combinations with other programs,
+and to distribute those combinations without any restriction coming
+from the use of this file. (The General Public License restrictions
+do apply in other respects; for example, they cover modification of
+the file, and distribution when not linked into a combine
+executable.)
+
+GCC 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 General Public License
+for more details.
+
+You should have received a copy of the GNU General Public License
+along with GCC; see the file COPYING. If not, write to the Free
+Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
+02110-1301, USA. */
+
+/*
+ * Implementations of floating-point long double basic arithmetic
+ * functions called by the IBM C compiler when generating code for
+ * PowerPC platforms. In particular, the following functions are
+ * implemented: __gcc_qadd, __gcc_qsub, __gcc_qmul, and __gcc_qdiv.
+ * Double-double algorithms are based on the paper "Doubled-Precision
+ * IEEE Standard 754 Floating-Point Arithmetic" by W. Kahan, February 26,
+ * 1987. An alternative published reference is "Software for
+ * Doubled-Precision Floating-Point Computations", by Seppo Linnainmaa,
+ * ACM TOMS vol 7 no 3, September 1981, pages 272-283.
+ */
+
+/*
+ * Each long double is made up of two IEEE doubles. The value of the
+ * long double is the sum of the values of the two parts. The most
+ * significant part is required to be the value of the long double
+ * rounded to the nearest double, as specified by IEEE. For Inf
+ * values, the least significant part is required to be one of +0.0 or
+ * -0.0. No other requirements are made; so, for example, 1.0 may be
+ * represented as (1.0, +0.0) or (1.0, -0.0), and the low part of a
+ * NaN is don't-care.
+ *
+ * This code currently assumes big-endian.
+ */
+
+#define fabs(x) __builtin_fabs(x)
+#define isless(x, y) __builtin_isless(x, y)
+#define inf() __builtin_inf()
+#define unlikely(x) __builtin_expect((x), 0)
+#define nonfinite(a) unlikely(!isless(fabs(a), inf()))
+
+typedef union {
+ long double ldval;
+ double dval[2];
+} longDblUnion;
+
+/* Add two 'long double' values and return the result. */
+long double __gcc_qadd(double a, double aa, double c, double cc)
+{
+ longDblUnion x;
+ double z, q, zz, xh;
+
+ z = a + c;
+
+ if (nonfinite(z)) {
+ z = cc + aa + c + a;
+ if (nonfinite(z))
+ return z;
+ x.dval[0] = z; /* Will always be DBL_MAX. */
+ zz = aa + cc;
+ if (fabs(a) > fabs(c))
+ x.dval[1] = a - z + c + zz;
+ else
+ x.dval[1] = c - z + a + zz;
+ } else {
+ q = a - z;
+ zz = q + c + (a - (q + z)) + aa + cc;
+
+ /* Keep -0 result. */
+ if (zz == 0.0)
+ return z;
+
+ xh = z + zz;
+ if (nonfinite(xh))
+ return xh;
+
+ x.dval[0] = xh;
+ x.dval[1] = z - xh + zz;
+ }
+ return x.ldval;
+}
+
+long double __gcc_qsub(double a, double b, double c, double d)
+{
+ return __gcc_qadd(a, b, -c, -d);
+}
+
+long double __gcc_qmul(double a, double b, double c, double d)
+{
+ longDblUnion z;
+ double t, tau, u, v, w;
+
+ t = a * c; /* Highest order double term. */
+
+ if (unlikely(t == 0) /* Preserve -0. */
+ || nonfinite(t))
+ return t;
+
+ /* Sum terms of two highest orders. */
+
+ /* Use fused multiply-add to get low part of a * c. */
+#ifndef __NO_FPRS__
+ asm("fmsub %0,%1,%2,%3" : "=f"(tau) : "f"(a), "f"(c), "f"(t));
+#else
+ tau = fmsub(a, c, t);
+#endif
+ v = a * d;
+ w = b * c;
+ tau += v + w; /* Add in other second-order terms. */
+ u = t + tau;
+
+ /* Construct long double result. */
+ if (nonfinite(u))
+ return u;
+ z.dval[0] = u;
+ z.dval[1] = (t - u) + tau;
+ return z.ldval;
+}