1 /* 128-bit long double support routines for Darwin.
2 Copyright (C) 1993, 2003, 2004 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__))
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 _xlqadd (double, double, double, double);
62 extern long double _xlqsub (double, double, double, double);
63 extern long double _xlqmul (double, double, double, double);
64 extern long double _xlqdiv (double, double, double, double);
72 static const double FPKINF = 1.0/0.0;
74 /* Add two 'long double' values and return the result. */
76 _xlqadd (double a, double b, double c, double d)
79 double t, tau, u, FPR_zero, FPR_PosInf;
84 if (unlikely (a != a) || unlikely (c != c))
85 return a + c; /* NaN result. */
87 /* Ordered operands are arranged in order of their magnitudes. */
89 /* Switch inputs if |(c,d)| > |(a,b)|. */
90 if (fabs (c) > fabs (a))
100 /* b <- second largest magnitude double. */
101 if (fabs (c) > fabs (b))
108 /* Thanks to commutivity, sum is invariant w.r.t. the next
109 conditional exchange. */
112 /* Order the smallest magnitude doubles. */
113 if (fabs (d) > fabs (c))
120 t = (tau + b) + a; /* Sum values in ascending magnitude order. */
122 /* Infinite or zero result. */
123 if (unlikely (t == FPR_zero) || unlikely (fabs (t) == FPR_PosInf))
127 tau = (((a-t) + b) + c) + d;
129 z.dval[0] = u; /* Final fixup for long double result. */
130 z.dval[1] = (t - u) + tau;
135 _xlqsub (double a, double b, double c, double d)
137 return _xlqadd (a, b, -c, -d);
141 _xlqmul (double a, double b, double c, double d)
144 double t, tau, u, v, w, FPR_zero, FPR_PosInf;
149 t = a * c; /* Highest order double term. */
151 if (unlikely (t != t) || unlikely (t == FPR_zero)
152 || unlikely (fabs (t) == FPR_PosInf))
155 /* Finite nonzero result requires summing of terms of two highest
158 /* Use fused multiply-add to get low part of a * c. */
159 asm ("fmsub %0,%1,%2,%3" : "=f"(tau) : "f"(a), "f"(c), "f"(t));
162 tau += v + w; /* Add in other second-order terms. */
165 /* Construct long double result. */
167 z.dval[1] = (t - u) + tau;
172 _xlqdiv (double a, double b, double c, double d)
175 double s, sigma, t, tau, u, v, w, FPR_zero, FPR_PosInf;
180 t = a / c; /* highest order double term */
182 if (unlikely (t != t) || unlikely (t == FPR_zero)
183 || unlikely (fabs (t) == FPR_PosInf))
186 /* Finite nonzero result requires corrections to the highest order term. */
188 s = c * t; /* (s,sigma) = c*t exactly. */
189 w = -(-b + d * t); /* Written to get fnmsub for speed, but not
190 numerically necessary. */
192 /* Use fused multiply-add to get low part of c * t. */
193 asm ("fmsub %0,%1,%2,%3" : "=f"(sigma) : "f"(c), "f"(t), "f"(s));
196 tau = ((v-sigma)+w)/c; /* Correction to t. */
199 /* Construct long double result. */
201 z.dval[1] = (t - u) + tau;