1 /* 2 * Borrowed from GCC 4.2.2 (which still was GPL v2+) 3 */ 4 /* 128-bit long double support routines for Darwin. 5 Copyright (C) 1993, 2003, 2004, 2005, 2006, 2007 6 Free Software Foundation, Inc. 7 8 This file is part of GCC. 9 10 GCC is free software; you can redistribute it and/or modify it under 11 the terms of the GNU General Public License as published by the Free 12 Software Foundation; either version 2, or (at your option) any later 13 version. 14 15 In addition to the permissions in the GNU General Public License, the 16 Free Software Foundation gives you unlimited permission to link the 17 compiled version of this file into combinations with other programs, 18 and to distribute those combinations without any restriction coming 19 from the use of this file. (The General Public License restrictions 20 do apply in other respects; for example, they cover modification of 21 the file, and distribution when not linked into a combine 22 executable.) 23 24 GCC is distributed in the hope that it will be useful, but WITHOUT ANY 25 WARRANTY; without even the implied warranty of MERCHANTABILITY or 26 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 27 for more details. 28 29 You should have received a copy of the GNU General Public License 30 along with GCC; see the file COPYING. If not, write to the Free 31 Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 32 02110-1301, USA. */ 33 34 /* 35 * Implementations of floating-point long double basic arithmetic 36 * functions called by the IBM C compiler when generating code for 37 * PowerPC platforms. In particular, the following functions are 38 * implemented: __gcc_qadd, __gcc_qsub, __gcc_qmul, and __gcc_qdiv. 39 * Double-double algorithms are based on the paper "Doubled-Precision 40 * IEEE Standard 754 Floating-Point Arithmetic" by W. Kahan, February 26, 41 * 1987. An alternative published reference is "Software for 42 * Doubled-Precision Floating-Point Computations", by Seppo Linnainmaa, 43 * ACM TOMS vol 7 no 3, September 1981, pages 272-283. 44 */ 45 46 /* 47 * Each long double is made up of two IEEE doubles. The value of the 48 * long double is the sum of the values of the two parts. The most 49 * significant part is required to be the value of the long double 50 * rounded to the nearest double, as specified by IEEE. For Inf 51 * values, the least significant part is required to be one of +0.0 or 52 * -0.0. No other requirements are made; so, for example, 1.0 may be 53 * represented as (1.0, +0.0) or (1.0, -0.0), and the low part of a 54 * NaN is don't-care. 55 * 56 * This code currently assumes big-endian. 57 */ 58 59 #define fabs(x) __builtin_fabs(x) 60 #define isless(x, y) __builtin_isless(x, y) 61 #define inf() __builtin_inf() 62 #define unlikely(x) __builtin_expect((x), 0) 63 #define nonfinite(a) unlikely(!isless(fabs(a), inf())) 64 65 typedef union { 66 long double ldval; 67 double dval[2]; 68 } longDblUnion; 69 70 /* Add two 'long double' values and return the result. */ 71 long double __gcc_qadd(double a, double aa, double c, double cc) 72 { 73 longDblUnion x; 74 double z, q, zz, xh; 75 76 z = a + c; 77 78 if (nonfinite(z)) { 79 z = cc + aa + c + a; 80 if (nonfinite(z)) 81 return z; 82 x.dval[0] = z; /* Will always be DBL_MAX. */ 83 zz = aa + cc; 84 if (fabs(a) > fabs(c)) 85 x.dval[1] = a - z + c + zz; 86 else 87 x.dval[1] = c - z + a + zz; 88 } else { 89 q = a - z; 90 zz = q + c + (a - (q + z)) + aa + cc; 91 92 /* Keep -0 result. */ 93 if (zz == 0.0) 94 return z; 95 96 xh = z + zz; 97 if (nonfinite(xh)) 98 return xh; 99 100 x.dval[0] = xh; 101 x.dval[1] = z - xh + zz; 102 } 103 return x.ldval; 104 } 105 106 long double __gcc_qsub(double a, double b, double c, double d) 107 { 108 return __gcc_qadd(a, b, -c, -d); 109 } 110 111 long double __gcc_qmul(double a, double b, double c, double d) 112 { 113 longDblUnion z; 114 double t, tau, u, v, w; 115 116 t = a * c; /* Highest order double term. */ 117 118 if (unlikely(t == 0) /* Preserve -0. */ 119 || nonfinite(t)) 120 return t; 121 122 /* Sum terms of two highest orders. */ 123 124 /* Use fused multiply-add to get low part of a * c. */ 125 #ifndef __NO_FPRS__ 126 asm("fmsub %0,%1,%2,%3" : "=f"(tau) : "f"(a), "f"(c), "f"(t)); 127 #else 128 tau = fmsub(a, c, t); 129 #endif 130 v = a * d; 131 w = b * c; 132 tau += v + w; /* Add in other second-order terms. */ 133 u = t + tau; 134 135 /* Construct long double result. */ 136 if (nonfinite(u)) 137 return u; 138 z.dval[0] = u; 139 z.dval[1] = (t - u) + tau; 140 return z.ldval; 141 } 142