1 /* 128-bit long double support routines for Darwin.
2 Copyright (C) 1993, 2003, 2004, 2005 Free Software Foundation, Inc.
4 This file is part of GCC.
6 GCC is free software; you can redistribute it and/or modify it under
7 the terms of the GNU General Public License as published by the Free
8 Software Foundation; either version 2, or (at your option) any later
11 In addition to the permissions in the GNU General Public License, the
12 Free Software Foundation gives you unlimited permission to link the
13 compiled version of this file into combinations with other programs,
14 and to distribute those combinations without any restriction coming
15 from the use of this file. (The General Public License restrictions
16 do apply in other respects; for example, they cover modification of
17 the file, and distribution when not linked into a combine
20 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
21 WARRANTY; without even the implied warranty of MERCHANTABILITY or
22 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
25 You should have received a copy of the GNU General Public License
26 along with GCC; see the file COPYING. If not, write to the Free
27 Software Foundation, 59 Temple Place - Suite 330, Boston, MA
30 /* Implementations of floating-point long double basic arithmetic
31 functions called by the IBM C compiler when generating code for
32 PowerPC platforms. In particular, the following functions are
33 implemented: _xlqadd, _xlqsub, _xlqmul, and _xlqdiv. Double-double
34 algorithms are based on the paper "Doubled-Precision IEEE Standard
35 754 Floating-Point Arithmetic" by W. Kahan, February 26, 1987. An
36 alternative published reference is "Software for Doubled-Precision
37 Floating-Point Computations", by Seppo Linnainmaa, ACM TOMS vol 7
38 no 3, September 1961, pages 272-283. */
40 /* Each long double is made up of two IEEE doubles. The value of the
41 long double is the sum of the values of the two parts. The most
42 significant part is required to be the value of the long double
43 rounded to the nearest double, as specified by IEEE. For Inf
44 values, the least significant part is required to be one of +0.0 or
45 -0.0. No other requirements are made; so, for example, 1.0 may be
46 represented as (1.0, +0.0) or (1.0, -0.0), and the low part of a
49 This code currently assumes big-endian. */
51 #if !_SOFT_FLOAT && (defined (__MACH__) || defined (__powerpc64__) || defined (_AIX))
53 #define fabs(x) __builtin_fabs(x)
55 #define unlikely(x) __builtin_expect ((x), 0)
57 /* All these routines actually take two long doubles as parameters,
58 but GCC currently generates poor code when a union is used to turn
59 a long double into a pair of doubles. */
61 extern long double __gcc_qadd (double, double, double, double);
62 extern long double __gcc_qsub (double, double, double, double);
63 extern long double __gcc_qmul (double, double, double, double);
64 extern long double __gcc_qdiv (double, double, double, double);
66 #if defined __ELF__ && defined IN_LIBGCC2_S
67 /* Provide definitions of the old symbol names to statisfy apps and
68 shared libs built against an older libgcc. To access the _xlq
69 symbols an explicit version reference is needed, so these won't
70 satisfy an unadorned reference like _xlqadd. If dot symbols are
71 not needed, the assembler will remove the aliases from the symbol
73 __asm__ (".symver __gcc_qadd,_xlqadd@GCC_3.4\n\t"
74 ".symver __gcc_qsub,_xlqsub@GCC_3.4\n\t"
75 ".symver __gcc_qmul,_xlqmul@GCC_3.4\n\t"
76 ".symver __gcc_qdiv,_xlqdiv@GCC_3.4\n\t"
77 ".symver .__gcc_qadd,._xlqadd@GCC_3.4\n\t"
78 ".symver .__gcc_qsub,._xlqsub@GCC_3.4\n\t"
79 ".symver .__gcc_qmul,._xlqmul@GCC_3.4\n\t"
80 ".symver .__gcc_qdiv,._xlqdiv@GCC_3.4");
89 static const double FPKINF = 1.0/0.0;
91 /* Add two 'long double' values and return the result. */
93 __gcc_qadd (double a, double b, double c, double d)
96 double t, tau, u, FPR_zero, FPR_PosInf;
101 if (unlikely (a != a) || unlikely (c != c))
102 return a + c; /* NaN result. */
104 /* Ordered operands are arranged in order of their magnitudes. */
106 /* Switch inputs if |(c,d)| > |(a,b)|. */
107 if (fabs (c) > fabs (a))
117 /* b <- second largest magnitude double. */
118 if (fabs (c) > fabs (b))
125 /* Thanks to commutivity, sum is invariant w.r.t. the next
126 conditional exchange. */
129 /* Order the smallest magnitude doubles. */
130 if (fabs (d) > fabs (c))
137 t = (tau + b) + a; /* Sum values in ascending magnitude order. */
139 /* Infinite or zero result. */
140 if (unlikely (t == FPR_zero) || unlikely (fabs (t) == FPR_PosInf))
144 tau = (((a-t) + b) + c) + d;
146 z.dval[0] = u; /* Final fixup for long double result. */
147 z.dval[1] = (t - u) + tau;
152 __gcc_qsub (double a, double b, double c, double d)
154 return __gcc_qadd (a, b, -c, -d);
158 __gcc_qmul (double a, double b, double c, double d)
161 double t, tau, u, v, w, FPR_zero, FPR_PosInf;
166 t = a * c; /* Highest order double term. */
168 if (unlikely (t != t) || unlikely (t == FPR_zero)
169 || unlikely (fabs (t) == FPR_PosInf))
172 /* Finite nonzero result requires summing of terms of two highest
175 /* Use fused multiply-add to get low part of a * c. */
176 asm ("fmsub %0,%1,%2,%3" : "=f"(tau) : "f"(a), "f"(c), "f"(t));
179 tau += v + w; /* Add in other second-order terms. */
182 /* Construct long double result. */
184 z.dval[1] = (t - u) + tau;
189 __gcc_qdiv (double a, double b, double c, double d)
192 double s, sigma, t, tau, u, v, w, FPR_zero, FPR_PosInf;
197 t = a / c; /* highest order double term */
199 if (unlikely (t != t) || unlikely (t == FPR_zero)
200 || unlikely (fabs (t) == FPR_PosInf))
203 /* Finite nonzero result requires corrections to the highest order term. */
205 s = c * t; /* (s,sigma) = c*t exactly. */
206 w = -(-b + d * t); /* Written to get fnmsub for speed, but not
207 numerically necessary. */
209 /* Use fused multiply-add to get low part of c * t. */
210 asm ("fmsub %0,%1,%2,%3" : "=f"(sigma) : "f"(c), "f"(t), "f"(s));
213 tau = ((v-sigma)+w)/c; /* Correction to t. */
216 /* Construct long double result. */
218 z.dval[1] = (t - u) + tau;