/* Double-precision floating point square root.
- Copyright (C) 1997, 2002, 2003, 2004 Free Software Foundation, Inc.
+ Copyright (C) 1997-2019 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
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. */
+ License along with the GNU C Library; if not, see
+ <https://www.gnu.org/licenses/>. */
#include <math.h>
#include <math_private.h>
+#include <fenv.h>
#include <fenv_libc.h>
#include <inttypes.h>
-
+#include <stdint.h>
#include <sysdep.h>
#include <ldsodefs.h>
+#ifndef _ARCH_PPCSQ
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 };
/* 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,
+ Basically, it consists of two interleaved Newton-Raphson 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
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). */
+ Newton-Raphson 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. */
+ and the load. */
ieee_double_shape_type ew_u;
ieee_double_shape_type iw_u;
ew_u.value = (x);
/* complete the INSERT_WORDS (sx, sxi, xi1) operation. */
sx = iw_u.value;
- /* Here we have three Newton-Rhapson iterations each of a
+ /* Here we have three Newton-Raphson iterations each of a
division and a square root and the remainder of the
argument reduction, all interleaved. */
- sd = -(sg * sg - sx);
+ sd = -__builtin_fma (sg, sg, -sx);
fsgi = (xi0 + 0x40000000) >> 1 & 0x7ff00000;
sy2 = sy + sy;
- sg = sy * sd + sg; /* 16-bit approximation to sqrt(sx). */
+ sg = __builtin_fma (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);
+ e = -__builtin_fma (sy, sg, -almost_half);
+ sd = -__builtin_fma (sg, sg, -sx);
if ((xi0 & 0x7ff00000) == 0)
goto denorm;
- sy = sy + e * sy2;
- sg = sg + sy * sd; /* 32-bit approximation to sqrt(sx). */
+ sy = __builtin_fma (e, sy2, sy);
+ sg = __builtin_fma (sy, sd, sg); /* 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;
+ e = -__builtin_fma (sy, sg, -almost_half);
+ sd = -__builtin_fma (sg, sg, -sx);
+ sy = __builtin_fma (e, sy2, sy);
shx = sx * fsg;
- sg = sg + sy * sd; /* 64-bit approximation to sqrt(sx),
- but perhaps rounded incorrectly. */
+ sg = __builtin_fma (sy, sd, sg); /* 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;
+ e = -__builtin_fma (sy, sg, -almost_half);
+ d = -__builtin_fma (g, sg, -shx);
+ sy = __builtin_fma (e, sy2, sy);
fesetenv_register (fe);
- return g + sy * d;
+ return __builtin_fma (sy, d, g);
denorm:
/* For denormalised numbers, we normalise, calculate the
square root, and return an adjusted result. */
else if (x < 0)
{
/* For some reason, some PowerPC32 processors don't implement
- FE_INVALID_SQRT. */
+ FE_INVALID_SQRT. */
#ifdef FE_INVALID_SQRT
- feraiseexcept (FE_INVALID_SQRT);
- if (!fetestexcept (FE_INVALID))
+ __feraiseexcept (FE_INVALID_SQRT);
+
+ fenv_union_t u = { .fenv = fegetenv_register () };
+ if ((u.l & FE_INVALID) == 0)
#endif
- feraiseexcept (FE_INVALID);
+ __feraiseexcept (FE_INVALID);
x = a_nan.value;
}
return f_wash (x);
}
+#endif /* _ARCH_PPCSQ */
-#ifdef __STDC__
+#undef __ieee754_sqrt
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);
+#ifdef _ARCH_PPCSQ
+ asm ("fsqrt %0,%1\n" :"=f" (z):"f" (x));
+#else
+ z = __slow_ieee754_sqrt (x);
+#endif
return z;
}
+strong_alias (__ieee754_sqrt, __sqrt_finite)