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authorUlrich Drepper <drepper@redhat.com>2004-05-26 04:47:00 +0000
committerUlrich Drepper <drepper@redhat.com>2004-05-26 04:47:00 +0000
commitffdd5e50e18b0cb212acad135e421d932cf3d3a2 (patch)
tree0a2b8dfc93270b99dbbb314cc68152ea2c5b230a /sysdeps/powerpc/fpu/e_sqrt.c
parenta752d0cc542a891a086d486654a43212f1821360 (diff)
Update.
2004-05-25 Steven Munroe <sjmunroe@us.ibm.com> * sysdeps/powerpc/fpu/Makefile: Make ld.so a dependency of libm.so. * sysdeps/powerpc/fpu/bits/mathinline.h [__LIBC_INERNAL_MATH_INLINES] (__ieee754_sqrt): Define as __MATH_INLINE using fsqrt instruction. (__ieee754_sqrtf): Define as __MATH_INLINE using fsqrts instruction. * sysdeps/powerpc/fpu/e_sqrt.c (__slow_ieee754_sqrt): Moved implementation from w_sqrt.c. * sysdeps/powerpc/fpu/e_sqrtf.c (__slow_ieee754_sqrtf): Moved implementation from w_sqrtf.c. * sysdeps/powerpc/fpu/w_sqrt.c (__sqrt): Wrapper implementation using inline __ieee754_sqrt(). * sysdeps/powerpc/fpu/w_sqrtf.c (__sqrtf): Wrapper implementation using inline __ieee754_sqrtf(). * sysdeps/powerpc/powerpc32/sysdep.h [__ASSEMBLER__]: Include <sysdeps/powerpc/sysdep.h> independent of __ASSEMBLER__. * sysdeps/powerpc/sysdep.h [__ASSEMBLER__] (PPC_FEATURE_*): Define PPC_FEATURE_* independent of __ASSEMBLER__. 2004-05-25 Jakub Jelinek <jakub@redhat.com> * sysdeps/pthread/aio_notify.c: Use <> instead of "" for aio_misc.h include. (aio_start_notify_thread): Define if not defined. (notify_func_wrapper): Use it. * sysdeps/pthread/aio_misc.c: Use <> instead of "" for aio_misc.h include. (aio_create_helper_thread): Define if not defined. (__aio_create_helper_thread): New function. (__aio_enqueue_request): Use aio_create_helper_thread. * nis/ypclnt.c (ypall_data, ypall_foreach): Remove. (struct ypresp_all_data): New type. (__xdr_ypresp_all): Change second argument to struct ypresp_all_data *. Replace ypall_foreach and ypall_data with objp->foreach and objp->data. (yp_all): Remove status variable, add data. Replace all uses of status with data.status. Initialize data.foreach and data.data instead of ypall_foreach and ypall_data. 2004-05-24 Jakub Jelinek <jakub@redhat.com> * elf/dl-lookup.c (add_dependency): Set DF_1_NODELETE bit in l_flags_1, not in l_flags.
Diffstat (limited to 'sysdeps/powerpc/fpu/e_sqrt.c')
-rw-r--r--sysdeps/powerpc/fpu/e_sqrt.c186
1 files changed, 185 insertions, 1 deletions
diff --git a/sysdeps/powerpc/fpu/e_sqrt.c b/sysdeps/powerpc/fpu/e_sqrt.c
index 9416ea60c8..eb9984d0a1 100644
--- a/sysdeps/powerpc/fpu/e_sqrt.c
+++ b/sysdeps/powerpc/fpu/e_sqrt.c
@@ -1 +1,185 @@
-/* __ieee754_sqrt is in w_sqrt.c */
+/* Double-precision floating point square root.
+ Copyright (C) 1997, 2002, 2003, 2004 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, write to the Free
+ Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
+ 02111-1307 USA. */
+
+#include <math.h>
+#include <math_private.h>
+#include <fenv_libc.h>
+#include <inttypes.h>
+
+#include <sysdep.h>
+#include <ldsodefs.h>
+#include <dl-procinfo.h>
+
+static const double almost_half = 0.5000000000000001; /* 0.5 + 2^-53 */
+static const ieee_float_shape_type a_nan = {.word = 0x7fc00000 };
+static const ieee_float_shape_type a_inf = {.word = 0x7f800000 };
+static const float two108 = 3.245185536584267269e+32;
+static const float twom54 = 5.551115123125782702e-17;
+extern const float __t_sqrt[1024];
+
+/* The method is based on a description in
+ Computation of elementary functions on the IBM RISC System/6000 processor,
+ P. W. Markstein, IBM J. Res. Develop, 34(1) 1990.
+ Basically, it consists of two interleaved Newton-Rhapson approximations,
+ one to find the actual square root, and one to find its reciprocal
+ without the expense of a division operation. The tricky bit here
+ is the use of the POWER/PowerPC multiply-add operation to get the
+ required accuracy with high speed.
+
+ The argument reduction works by a combination of table lookup to
+ obtain the initial guesses, and some careful modification of the
+ generated guesses (which mostly runs on the integer unit, while the
+ Newton-Rhapson is running on the FPU). */
+
+#ifdef __STDC__
+double
+__slow_ieee754_sqrt (double x)
+#else
+double
+__slow_ieee754_sqrt (x)
+ double x;
+#endif
+{
+ const float inf = a_inf.value;
+
+ if (x > 0)
+ {
+ /* schedule the EXTRACT_WORDS to get separation between the store
+ and the load. */
+ ieee_double_shape_type ew_u;
+ ieee_double_shape_type iw_u;
+ ew_u.value = (x);
+ if (x != inf)
+ {
+ /* Variables named starting with 's' exist in the
+ argument-reduced space, so that 2 > sx >= 0.5,
+ 1.41... > sg >= 0.70.., 0.70.. >= sy > 0.35... .
+ Variables named ending with 'i' are integer versions of
+ floating-point values. */
+ double sx; /* The value of which we're trying to find the
+ square root. */
+ double sg, g; /* Guess of the square root of x. */
+ double sd, d; /* Difference between the square of the guess and x. */
+ double sy; /* Estimate of 1/2g (overestimated by 1ulp). */
+ double sy2; /* 2*sy */
+ double e; /* Difference between y*g and 1/2 (se = e * fsy). */
+ double shx; /* == sx * fsg */
+ double fsg; /* sg*fsg == g. */
+ fenv_t fe; /* Saved floating-point environment (stores rounding
+ mode and whether the inexact exception is
+ enabled). */
+ uint32_t xi0, xi1, sxi, fsgi;
+ const float *t_sqrt;
+
+ fe = fegetenv_register ();
+ /* complete the EXTRACT_WORDS (xi0,xi1,x) operation. */
+ xi0 = ew_u.parts.msw;
+ xi1 = ew_u.parts.lsw;
+ relax_fenv_state ();
+ sxi = (xi0 & 0x3fffffff) | 0x3fe00000;
+ /* schedule the INSERT_WORDS (sx, sxi, xi1) to get separation
+ between the store and the load. */
+ iw_u.parts.msw = sxi;
+ iw_u.parts.lsw = xi1;
+ t_sqrt = __t_sqrt + (xi0 >> (52 - 32 - 8 - 1) & 0x3fe);
+ sg = t_sqrt[0];
+ sy = t_sqrt[1];
+ /* complete the INSERT_WORDS (sx, sxi, xi1) operation. */
+ sx = iw_u.value;
+
+ /* Here we have three Newton-Rhapson iterations each of a
+ division and a square root and the remainder of the
+ argument reduction, all interleaved. */
+ sd = -(sg * sg - sx);
+ fsgi = (xi0 + 0x40000000) >> 1 & 0x7ff00000;
+ sy2 = sy + sy;
+ sg = sy * sd + sg; /* 16-bit approximation to sqrt(sx). */
+
+ /* schedule the INSERT_WORDS (fsg, fsgi, 0) to get separation
+ between the store and the load. */
+ INSERT_WORDS (fsg, fsgi, 0);
+ iw_u.parts.msw = fsgi;
+ iw_u.parts.lsw = (0);
+ e = -(sy * sg - almost_half);
+ sd = -(sg * sg - sx);
+ if ((xi0 & 0x7ff00000) == 0)
+ goto denorm;
+ sy = sy + e * sy2;
+ sg = sg + sy * sd; /* 32-bit approximation to sqrt(sx). */
+ sy2 = sy + sy;
+ /* complete the INSERT_WORDS (fsg, fsgi, 0) operation. */
+ fsg = iw_u.value;
+ e = -(sy * sg - almost_half);
+ sd = -(sg * sg - sx);
+ sy = sy + e * sy2;
+ shx = sx * fsg;
+ sg = sg + sy * sd; /* 64-bit approximation to sqrt(sx),
+ but perhaps rounded incorrectly. */
+ sy2 = sy + sy;
+ g = sg * fsg;
+ e = -(sy * sg - almost_half);
+ d = -(g * sg - shx);
+ sy = sy + e * sy2;
+ fesetenv_register (fe);
+ return g + sy * d;
+ denorm:
+ /* For denormalised numbers, we normalise, calculate the
+ square root, and return an adjusted result. */
+ fesetenv_register (fe);
+ return __slow_ieee754_sqrt (x * two108) * twom54;
+ }
+ }
+ else if (x < 0)
+ {
+ /* For some reason, some PowerPC32 processors don't implement
+ FE_INVALID_SQRT. */
+#ifdef FE_INVALID_SQRT
+ feraiseexcept (FE_INVALID_SQRT);
+ if (!fetestexcept (FE_INVALID))
+#endif
+ feraiseexcept (FE_INVALID);
+ x = a_nan.value;
+ }
+ return f_wash (x);
+}
+
+#ifdef __STDC__
+double
+__ieee754_sqrt (double x)
+#else
+double
+__ieee754_sqrt (x)
+ double x;
+#endif
+{
+ double z;
+
+ /* If the CPU is 64-bit we can use the optional FP instructions we. */
+ if ((GLRO (dl_hwcap) & PPC_FEATURE_64) != 0)
+ {
+ /* Volatile is required to prevent the compiler from moving the
+ fsqrt instruction above the branch. */
+ __asm __volatile (" fsqrt %0,%1\n"
+ :"=f" (z):"f" (x));
+ }
+ else
+ z = __slow_ieee754_sqrt (x);
+
+ return z;
+}