/* 128-bit long double support routines for Darwin.
- Copyright (C) 1993, 2003, 2004 Free Software Foundation, Inc.
+ Copyright (C) 1993, 2003, 2004, 2005, 2006
+ Free Software Foundation, Inc.
This file is part of GCC.
You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING. If not, write to the Free
-Software Foundation, 59 Temple Place - Suite 330, Boston, MA
-02111-1307, USA. */
+Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
+02110-1301, USA. */
/* Implementations of floating-point long double basic arithmetic
functions called by the IBM C compiler when generating code for
PowerPC platforms. In particular, the following functions are
- implemented: _xlqadd, _xlqsub, _xlqmul, and _xlqdiv. Double-double
- algorithms are based on the paper "Doubled-Precision IEEE Standard
- 754 Floating-Point Arithmetic" by W. Kahan, February 26, 1987. An
- alternative published reference is "Software for Doubled-Precision
- Floating-Point Computations", by Seppo Linnainmaa, ACM TOMS vol 7
- no 3, September 1981, pages 272-283. */
+ implemented: __gcc_qadd, __gcc_qsub, __gcc_qmul, and __gcc_qdiv.
+ Double-double algorithms are based on the paper "Doubled-Precision
+ IEEE Standard 754 Floating-Point Arithmetic" by W. Kahan, February 26,
+ 1987. An alternative published reference is "Software for
+ Doubled-Precision Floating-Point Computations", by Seppo Linnainmaa,
+ ACM TOMS vol 7 no 3, September 1981, pages 272-283. */
/* Each long double is made up of two IEEE doubles. The value of the
long double is the sum of the values of the two parts. The most
This code currently assumes big-endian. */
-#if !_SOFT_FLOAT && (defined (__MACH__) || defined (__powerpc64__))
+#if ((!defined (__NO_FPRS__) || defined (_SOFT_FLOAT)) \
+ && !defined (__LITTLE_ENDIAN__) \
+ && (defined (__MACH__) || defined (__powerpc__) || defined (_AIX)))
#define fabs(x) __builtin_fabs(x)
+#define isless(x, y) __builtin_isless (x, y)
+#define inf() __builtin_inf()
#define unlikely(x) __builtin_expect ((x), 0)
+#define nonfinite(a) unlikely (! isless (fabs (a), inf ()))
+
+/* Define ALIASNAME as a strong alias for NAME. */
+# define strong_alias(name, aliasname) _strong_alias(name, aliasname)
+# define _strong_alias(name, aliasname) \
+ extern __typeof (name) aliasname __attribute__ ((alias (#name)));
+
/* All these routines actually take two long doubles as parameters,
but GCC currently generates poor code when a union is used to turn
a long double into a pair of doubles. */
-extern long double _xlqadd (double, double, double, double);
-extern long double _xlqsub (double, double, double, double);
-extern long double _xlqmul (double, double, double, double);
-extern long double _xlqdiv (double, double, double, double);
+long double __gcc_qadd (double, double, double, double);
+long double __gcc_qsub (double, double, double, double);
+long double __gcc_qmul (double, double, double, double);
+long double __gcc_qdiv (double, double, double, double);
+
+#if defined __ELF__ && defined SHARED \
+ && (defined __powerpc64__ || !(defined __linux__ || defined __gnu_hurd__))
+/* Provide definitions of the old symbol names to satisfy apps and
+ shared libs built against an older libgcc. To access the _xlq
+ symbols an explicit version reference is needed, so these won't
+ satisfy an unadorned reference like _xlqadd. If dot symbols are
+ not needed, the assembler will remove the aliases from the symbol
+ table. */
+__asm__ (".symver __gcc_qadd,_xlqadd@GCC_3.4\n\t"
+ ".symver __gcc_qsub,_xlqsub@GCC_3.4\n\t"
+ ".symver __gcc_qmul,_xlqmul@GCC_3.4\n\t"
+ ".symver __gcc_qdiv,_xlqdiv@GCC_3.4\n\t"
+ ".symver .__gcc_qadd,._xlqadd@GCC_3.4\n\t"
+ ".symver .__gcc_qsub,._xlqsub@GCC_3.4\n\t"
+ ".symver .__gcc_qmul,._xlqmul@GCC_3.4\n\t"
+ ".symver .__gcc_qdiv,._xlqdiv@GCC_3.4");
+#endif
typedef union
{
double dval[2];
} longDblUnion;
-static const double FPKINF = 1.0/0.0;
-
/* Add two 'long double' values and return the result. */
long double
-_xlqadd (double a, double b, double c, double d)
+__gcc_qadd (double a, double aa, double c, double cc)
{
- longDblUnion z;
- double t, tau, u, FPR_zero, FPR_PosInf;
-
- FPR_zero = 0.0;
- FPR_PosInf = FPKINF;
+ longDblUnion x;
+ double z, q, zz, xh;
- if (unlikely (a != a) || unlikely (c != c))
- return a + c; /* NaN result. */
+ z = a + c;
- /* Ordered operands are arranged in order of their magnitudes. */
-
- /* Switch inputs if |(c,d)| > |(a,b)|. */
- if (fabs (c) > fabs (a))
+ if (nonfinite (z))
{
- t = a;
- tau = b;
- a = c;
- b = d;
- c = t;
- d = tau;
+ z = cc + aa + c + a;
+ if (nonfinite (z))
+ return z;
+ x.dval[0] = z; /* Will always be DBL_MAX. */
+ zz = aa + cc;
+ if (fabs(a) > fabs(c))
+ x.dval[1] = a - z + c + zz;
+ else
+ x.dval[1] = c - z + a + zz;
}
-
- /* b <- second largest magnitude double. */
- if (fabs (c) > fabs (b))
- {
- t = b;
- b = c;
- c = t;
- }
-
- /* Thanks to commutativity, sum is invariant w.r.t. the next
- conditional exchange. */
- tau = d + c;
-
- /* Order the smallest magnitude doubles. */
- if (fabs (d) > fabs (c))
+ else
{
- t = c;
- c = d;
- d = t;
- }
+ q = a - z;
+ zz = q + c + (a - (q + z)) + aa + cc;
- t = (tau + b) + a; /* Sum values in ascending magnitude order. */
+ /* Keep -0 result. */
+ if (zz == 0.0)
+ return z;
- /* Infinite or zero result. */
- if (unlikely (t == FPR_zero) || unlikely (fabs (t) == FPR_PosInf))
- return t;
+ xh = z + zz;
+ if (nonfinite (xh))
+ return xh;
- /* Usual case. */
- tau = (((a-t) + b) + c) + d;
- u = t + tau;
- z.dval[0] = u; /* Final fixup for long double result. */
- z.dval[1] = (t - u) + tau;
- return z.ldval;
+ x.dval[0] = xh;
+ x.dval[1] = z - xh + zz;
+ }
+ return x.ldval;
}
long double
-_xlqsub (double a, double b, double c, double d)
+__gcc_qsub (double a, double b, double c, double d)
{
- return _xlqadd (a, b, -c, -d);
+ return __gcc_qadd (a, b, -c, -d);
}
+#ifdef _SOFT_FLOAT
+static double fmsub (double, double, double);
+#endif
+
long double
-_xlqmul (double a, double b, double c, double d)
+__gcc_qmul (double a, double b, double c, double d)
{
longDblUnion z;
- double t, tau, u, v, w, FPR_zero, FPR_PosInf;
+ double t, tau, u, v, w;
- FPR_zero = 0.0;
- FPR_PosInf = FPKINF;
-
t = a * c; /* Highest order double term. */
- if (unlikely (t != t) || unlikely (t == FPR_zero)
- || unlikely (fabs (t) == FPR_PosInf))
+ if (unlikely (t == 0) /* Preserve -0. */
+ || nonfinite (t))
return t;
- /* Finite nonzero result requires summing of terms of two highest
- orders. */
+ /* Sum terms of two highest orders. */
- /* Use fused multiply-add to get low part of a * c. */
+ /* Use fused multiply-add to get low part of a * c. */
+#ifndef _SOFT_FLOAT
asm ("fmsub %0,%1,%2,%3" : "=f"(tau) : "f"(a), "f"(c), "f"(t));
+#else
+ tau = fmsub (a, c, t);
+#endif
v = a*d;
w = b*c;
tau += v + w; /* Add in other second-order terms. */
u = t + tau;
/* Construct long double result. */
+ if (nonfinite (u))
+ return u;
z.dval[0] = u;
z.dval[1] = (t - u) + tau;
return z.ldval;
}
long double
-_xlqdiv (double a, double b, double c, double d)
+__gcc_qdiv (double a, double b, double c, double d)
{
longDblUnion z;
- double s, sigma, t, tau, u, v, w, FPR_zero, FPR_PosInf;
-
- FPR_zero = 0.0;
- FPR_PosInf = FPKINF;
+ double s, sigma, t, tau, u, v, w;
t = a / c; /* highest order double term */
- if (unlikely (t != t) || unlikely (t == FPR_zero)
- || unlikely (fabs (t) == FPR_PosInf))
+ if (unlikely (t == 0) /* Preserve -0. */
+ || nonfinite (t))
return t;
/* Finite nonzero result requires corrections to the highest order term. */
numerically necessary. */
/* Use fused multiply-add to get low part of c * t. */
+#ifndef _SOFT_FLOAT
asm ("fmsub %0,%1,%2,%3" : "=f"(sigma) : "f"(c), "f"(t), "f"(s));
+#else
+ sigma = fmsub (c, t, s);
+#endif
v = a - s;
tau = ((v-sigma)+w)/c; /* Correction to t. */
u = t + tau;
/* Construct long double result. */
+ if (nonfinite (u))
+ return u;
z.dval[0] = u;
z.dval[1] = (t - u) + tau;
return z.ldval;
}
+#ifdef _SOFT_FLOAT
+
+long double __gcc_qneg (double, double);
+int __gcc_qeq (double, double, double, double);
+int __gcc_qne (double, double, double, double);
+int __gcc_qge (double, double, double, double);
+int __gcc_qle (double, double, double, double);
+int __gcc_qunord (double, double, double, double);
+long double __gcc_stoq (float);
+long double __gcc_dtoq (double);
+float __gcc_qtos (double, double);
+double __gcc_qtod (double, double);
+int __gcc_qtoi (double, double);
+unsigned int __gcc_qtou (double, double);
+long double __gcc_itoq (int);
+long double __gcc_utoq (unsigned int);
+
+extern int __eqdf2 (double, double);
+extern int __ledf2 (double, double);
+extern int __gedf2 (double, double);
+extern int __unorddf2 (double, double);
+
+/* Negate 'long double' value and return the result. */
+long double
+__gcc_qneg (double a, double aa)
+{
+ longDblUnion x;
+
+ x.dval[0] = -a;
+ x.dval[1] = -aa;
+ return x.ldval;
+}
+
+/* Compare two 'long double' values for equality. */
+int
+__gcc_qeq (double a, double aa, double c, double cc)
+{
+ if (__eqdf2 (a, c) == 0)
+ return __eqdf2 (aa, cc);
+ return 1;
+}
+
+strong_alias (__gcc_qeq, __gcc_qne);
+
+/* Compare two 'long double' values for less than or equal. */
+int
+__gcc_qle (double a, double aa, double c, double cc)
+{
+ if (__eqdf2 (a, c) == 0)
+ return __ledf2 (aa, cc);
+ return __ledf2 (a, c);
+}
+
+strong_alias (__gcc_qle, __gcc_qlt);
+
+/* Compare two 'long double' values for greater than or equal. */
+int
+__gcc_qge (double a, double aa, double c, double cc)
+{
+ if (__eqdf2 (a, c) == 0)
+ return __gedf2 (aa, cc);
+ return __gedf2 (a, c);
+}
+
+strong_alias (__gcc_qge, __gcc_qgt);
+
+/* Compare two 'long double' values for unordered. */
+int
+__gcc_qunord (double a, double aa, double c, double cc)
+{
+ if (__eqdf2 (a, c) == 0)
+ return __unorddf2 (aa, cc);
+ return __unorddf2 (a, c);
+}
+
+/* Convert single to long double. */
+long double
+__gcc_stoq (float a)
+{
+ longDblUnion x;
+
+ x.dval[0] = (double) a;
+ x.dval[1] = 0.0;
+
+ return x.ldval;
+}
+
+/* Convert double to long double. */
+long double
+__gcc_dtoq (double a)
+{
+ longDblUnion x;
+
+ x.dval[0] = a;
+ x.dval[1] = 0.0;
+
+ return x.ldval;
+}
+
+/* Convert long double to single. */
+float
+__gcc_qtos (double a, double aa __attribute__ ((__unused__)))
+{
+ return (float) a;
+}
+
+/* Convert long double to double. */
+double
+__gcc_qtod (double a, double aa __attribute__ ((__unused__)))
+{
+ return a;
+}
+
+/* Convert long double to int. */
+int
+__gcc_qtoi (double a, double aa)
+{
+ double z = a + aa;
+ return (int) z;
+}
+
+/* Convert long double to unsigned int. */
+unsigned int
+__gcc_qtou (double a, double aa)
+{
+ double z = a + aa;
+ return (unsigned int) z;
+}
+
+/* Convert int to long double. */
+long double
+__gcc_itoq (int a)
+{
+ return __gcc_dtoq ((double) a);
+}
+
+/* Convert unsigned int to long double. */
+long double
+__gcc_utoq (unsigned int a)
+{
+ return __gcc_dtoq ((double) a);
+}
+
+#include "config/soft-fp/soft-fp.h"
+#include "config/soft-fp/double.h"
+#include "config/soft-fp/quad.h"
+
+/* Compute floating point multiply-subtract with higher (quad) precision. */
+static double
+fmsub (double a, double b, double c)
+{
+ FP_DECL_EX;
+ FP_DECL_D(A);
+ FP_DECL_D(B);
+ FP_DECL_D(C);
+ FP_DECL_Q(X);
+ FP_DECL_Q(Y);
+ FP_DECL_Q(Z);
+ FP_DECL_Q(U);
+ FP_DECL_Q(V);
+ FP_DECL_D(R);
+ double r;
+ long double u, v, x, y, z;
+
+ FP_INIT_ROUNDMODE;
+ FP_UNPACK_RAW_D (A, a);
+ FP_UNPACK_RAW_D (B, b);
+ FP_UNPACK_RAW_D (C, c);
+
+ /* Extend double to quad. */
+#if (2 * _FP_W_TYPE_SIZE) < _FP_FRACBITS_Q
+ FP_EXTEND(Q,D,4,2,X,A);
+ FP_EXTEND(Q,D,4,2,Y,B);
+ FP_EXTEND(Q,D,4,2,Z,C);
+#else
+ FP_EXTEND(Q,D,2,1,X,A);
+ FP_EXTEND(Q,D,2,1,Y,B);
+ FP_EXTEND(Q,D,2,1,Z,C);
+#endif
+ FP_PACK_RAW_Q(x,X);
+ FP_PACK_RAW_Q(y,Y);
+ FP_PACK_RAW_Q(z,Z);
+ FP_HANDLE_EXCEPTIONS;
+
+ /* Multiply. */
+ FP_INIT_ROUNDMODE;
+ FP_UNPACK_Q(X,x);
+ FP_UNPACK_Q(Y,y);
+ FP_MUL_Q(U,X,Y);
+ FP_PACK_Q(u,U);
+ FP_HANDLE_EXCEPTIONS;
+
+ /* Subtract. */
+ FP_INIT_ROUNDMODE;
+ FP_UNPACK_SEMIRAW_Q(U,u);
+ FP_UNPACK_SEMIRAW_Q(Z,z);
+ FP_SUB_Q(V,U,Z);
+ FP_PACK_SEMIRAW_Q(v,V);
+ FP_HANDLE_EXCEPTIONS;
+
+ /* Truncate quad to double. */
+ FP_INIT_ROUNDMODE;
+ FP_UNPACK_SEMIRAW_Q(V,v);
+#if (2 * _FP_W_TYPE_SIZE) < _FP_FRACBITS_Q
+ FP_TRUNC(D,Q,2,4,R,V);
+#else
+ FP_TRUNC(D,Q,1,2,R,V);
+#endif
+ FP_PACK_SEMIRAW_D(r,R);
+ FP_HANDLE_EXCEPTIONS;
+
+ return r;
+}
+
+#endif
+
#endif
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