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444 lines
11 KiB
C
444 lines
11 KiB
C
/* 128-bit long double support routines for Darwin.
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Copyright (C) 1993-2016 Free Software Foundation, Inc.
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This file is part of GCC.
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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 3, or (at your option) any later
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version.
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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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Under Section 7 of GPL version 3, you are granted additional
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permissions described in the GCC Runtime Library Exception, version
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3.1, as published by the Free Software Foundation.
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You should have received a copy of the GNU General Public License and
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a copy of the GCC Runtime Library Exception along with this program;
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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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<http://www.gnu.org/licenses/>. */
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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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/* 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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This code currently assumes the most significant double is in
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the lower numbered register or lower addressed memory. */
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#if defined (__MACH__) || defined (__powerpc__) || defined (_AIX)
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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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/* Define ALIASNAME as a strong alias for NAME. */
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# define strong_alias(name, aliasname) _strong_alias(name, aliasname)
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# define _strong_alias(name, aliasname) \
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extern __typeof (name) aliasname __attribute__ ((alias (#name)));
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/* All these routines actually take two long doubles as parameters,
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but GCC currently generates poor code when a union is used to turn
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a long double into a pair of doubles. */
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long double __gcc_qadd (double, double, double, double);
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long double __gcc_qsub (double, double, double, double);
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long double __gcc_qmul (double, double, double, double);
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long double __gcc_qdiv (double, double, double, double);
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#if defined __ELF__ && defined SHARED \
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&& (defined __powerpc64__ || !(defined __linux__ || defined __gnu_hurd__))
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/* Provide definitions of the old symbol names to satisfy apps and
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shared libs built against an older libgcc. To access the _xlq
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symbols an explicit version reference is needed, so these won't
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satisfy an unadorned reference like _xlqadd. If dot symbols are
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not needed, the assembler will remove the aliases from the symbol
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table. */
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__asm__ (".symver __gcc_qadd,_xlqadd@GCC_3.4\n\t"
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".symver __gcc_qsub,_xlqsub@GCC_3.4\n\t"
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".symver __gcc_qmul,_xlqmul@GCC_3.4\n\t"
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".symver __gcc_qdiv,_xlqdiv@GCC_3.4\n\t"
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".symver .__gcc_qadd,._xlqadd@GCC_3.4\n\t"
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".symver .__gcc_qsub,._xlqsub@GCC_3.4\n\t"
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".symver .__gcc_qmul,._xlqmul@GCC_3.4\n\t"
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".symver .__gcc_qdiv,._xlqdiv@GCC_3.4");
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#endif
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/* Combine two 'double' values into one 'long double' and return the result. */
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static inline long double
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pack_ldouble (double dh, double dl)
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{
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#if defined (__LONG_DOUBLE_128__) \
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&& !(defined (_SOFT_FLOAT) || defined (__NO_FPRS__))
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return __builtin_pack_longdouble (dh, dl);
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#else
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union
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{
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long double ldval;
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double dval[2];
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} x;
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x.dval[0] = dh;
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x.dval[1] = dl;
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return x.ldval;
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#endif
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}
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/* Add two 'long double' values and return the result. */
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long double
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__gcc_qadd (double a, double aa, double c, double cc)
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{
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double xh, xl, z, q, zz;
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z = a + c;
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if (nonfinite (z))
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{
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if (fabs (z) != inf())
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return 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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xh = 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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xl = a - z + c + zz;
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else
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xl = c - z + a + zz;
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}
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else
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{
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q = a - z;
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zz = q + c + (a - (q + z)) + aa + cc;
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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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xh = z + zz;
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if (nonfinite (xh))
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return xh;
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xl = z - xh + zz;
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}
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return pack_ldouble (xh, xl);
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}
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long double
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__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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#ifdef __NO_FPRS__
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static double fmsub (double, double, double);
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#endif
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long double
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__gcc_qmul (double a, double b, double c, double d)
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{
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double xh, xl, t, tau, u, v, w;
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t = a * c; /* Highest order double term. */
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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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/* Sum terms of two highest orders. */
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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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/* Construct long double result. */
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if (nonfinite (u))
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return u;
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xh = u;
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xl = (t - u) + tau;
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return pack_ldouble (xh, xl);
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}
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long double
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__gcc_qdiv (double a, double b, double c, double d)
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{
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double xh, xl, s, sigma, t, tau, u, v, w;
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t = a / c; /* highest order double term */
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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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/* Finite nonzero result requires corrections to the highest order
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term. These corrections require the low part of c * t to be
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exactly represented in double. */
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if (fabs (a) <= 0x1p-969)
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{
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a *= 0x1p106;
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b *= 0x1p106;
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c *= 0x1p106;
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d *= 0x1p106;
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}
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s = c * t; /* (s,sigma) = c*t exactly. */
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w = -(-b + d * t); /* Written to get fnmsub for speed, but not
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numerically necessary. */
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/* Use fused multiply-add to get low part of c * t. */
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#ifndef __NO_FPRS__
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asm ("fmsub %0,%1,%2,%3" : "=f"(sigma) : "f"(c), "f"(t), "f"(s));
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#else
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sigma = fmsub (c, t, s);
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#endif
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v = a - s;
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tau = ((v-sigma)+w)/c; /* Correction to t. */
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u = t + tau;
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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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xh = u;
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xl = (t - u) + tau;
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return pack_ldouble (xh, xl);
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}
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#if defined (_SOFT_DOUBLE) && defined (__LONG_DOUBLE_128__)
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long double __gcc_qneg (double, double);
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int __gcc_qeq (double, double, double, double);
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int __gcc_qne (double, double, double, double);
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int __gcc_qge (double, double, double, double);
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int __gcc_qle (double, double, double, double);
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long double __gcc_stoq (float);
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long double __gcc_dtoq (double);
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float __gcc_qtos (double, double);
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double __gcc_qtod (double, double);
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int __gcc_qtoi (double, double);
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unsigned int __gcc_qtou (double, double);
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long double __gcc_itoq (int);
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long double __gcc_utoq (unsigned int);
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extern int __eqdf2 (double, double);
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extern int __ledf2 (double, double);
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extern int __gedf2 (double, double);
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/* Negate 'long double' value and return the result. */
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long double
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__gcc_qneg (double a, double aa)
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{
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return pack_ldouble (-a, -aa);
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}
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/* Compare two 'long double' values for equality. */
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int
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__gcc_qeq (double a, double aa, double c, double cc)
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{
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if (__eqdf2 (a, c) == 0)
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return __eqdf2 (aa, cc);
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return 1;
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}
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strong_alias (__gcc_qeq, __gcc_qne);
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/* Compare two 'long double' values for less than or equal. */
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int
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__gcc_qle (double a, double aa, double c, double cc)
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{
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if (__eqdf2 (a, c) == 0)
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return __ledf2 (aa, cc);
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return __ledf2 (a, c);
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}
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strong_alias (__gcc_qle, __gcc_qlt);
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/* Compare two 'long double' values for greater than or equal. */
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int
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__gcc_qge (double a, double aa, double c, double cc)
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{
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if (__eqdf2 (a, c) == 0)
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return __gedf2 (aa, cc);
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return __gedf2 (a, c);
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}
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strong_alias (__gcc_qge, __gcc_qgt);
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/* Convert single to long double. */
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long double
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__gcc_stoq (float a)
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{
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return pack_ldouble ((double) a, 0.0);
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}
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/* Convert double to long double. */
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long double
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__gcc_dtoq (double a)
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{
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return pack_ldouble (a, 0.0);
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}
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/* Convert long double to single. */
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float
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__gcc_qtos (double a, double aa __attribute__ ((__unused__)))
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{
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return (float) a;
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}
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/* Convert long double to double. */
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double
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__gcc_qtod (double a, double aa __attribute__ ((__unused__)))
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{
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return a;
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}
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/* Convert long double to int. */
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int
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__gcc_qtoi (double a, double aa)
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{
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double z = a + aa;
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return (int) z;
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}
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/* Convert long double to unsigned int. */
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unsigned int
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__gcc_qtou (double a, double aa)
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{
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double z = a + aa;
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return (unsigned int) z;
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}
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/* Convert int to long double. */
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long double
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__gcc_itoq (int a)
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{
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return __gcc_dtoq ((double) a);
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}
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/* Convert unsigned int to long double. */
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long double
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__gcc_utoq (unsigned int a)
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{
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return __gcc_dtoq ((double) a);
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}
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#endif
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#ifdef __NO_FPRS__
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int __gcc_qunord (double, double, double, double);
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extern int __eqdf2 (double, double);
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extern int __unorddf2 (double, double);
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/* Compare two 'long double' values for unordered. */
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int
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__gcc_qunord (double a, double aa, double c, double cc)
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{
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if (__eqdf2 (a, c) == 0)
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return __unorddf2 (aa, cc);
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return __unorddf2 (a, c);
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}
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#include "soft-fp/soft-fp.h"
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#include "soft-fp/double.h"
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#include "soft-fp/quad.h"
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/* Compute floating point multiply-subtract with higher (quad) precision. */
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static double
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fmsub (double a, double b, double c)
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{
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FP_DECL_EX;
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FP_DECL_D(A);
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FP_DECL_D(B);
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FP_DECL_D(C);
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FP_DECL_Q(X);
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FP_DECL_Q(Y);
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FP_DECL_Q(Z);
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FP_DECL_Q(U);
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FP_DECL_Q(V);
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FP_DECL_D(R);
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double r;
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long double u, x, y, z;
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FP_INIT_ROUNDMODE;
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FP_UNPACK_RAW_D (A, a);
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FP_UNPACK_RAW_D (B, b);
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FP_UNPACK_RAW_D (C, c);
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/* Extend double to quad. */
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#if (2 * _FP_W_TYPE_SIZE) < _FP_FRACBITS_Q
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FP_EXTEND(Q,D,4,2,X,A);
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FP_EXTEND(Q,D,4,2,Y,B);
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FP_EXTEND(Q,D,4,2,Z,C);
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#else
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FP_EXTEND(Q,D,2,1,X,A);
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FP_EXTEND(Q,D,2,1,Y,B);
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FP_EXTEND(Q,D,2,1,Z,C);
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#endif
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FP_PACK_RAW_Q(x,X);
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FP_PACK_RAW_Q(y,Y);
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FP_PACK_RAW_Q(z,Z);
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FP_HANDLE_EXCEPTIONS;
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/* Multiply. */
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FP_INIT_ROUNDMODE;
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FP_UNPACK_Q(X,x);
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FP_UNPACK_Q(Y,y);
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FP_MUL_Q(U,X,Y);
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FP_PACK_Q(u,U);
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FP_HANDLE_EXCEPTIONS;
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/* Subtract. */
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FP_INIT_ROUNDMODE;
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FP_UNPACK_SEMIRAW_Q(U,u);
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FP_UNPACK_SEMIRAW_Q(Z,z);
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FP_SUB_Q(V,U,Z);
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/* Truncate quad to double. */
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#if (2 * _FP_W_TYPE_SIZE) < _FP_FRACBITS_Q
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V_f[3] &= 0x0007ffff;
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FP_TRUNC(D,Q,2,4,R,V);
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#else
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V_f1 &= 0x0007ffffffffffffL;
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FP_TRUNC(D,Q,1,2,R,V);
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#endif
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FP_PACK_SEMIRAW_D(r,R);
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FP_HANDLE_EXCEPTIONS;
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return r;
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}
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#endif
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#endif
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