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