From 371e27cbb492f91acc7f3cba4e52a1f46e88da52 Mon Sep 17 00:00:00 2001
From: drepper
Date: Fri, 29 Aug 1997 00:51:25 +0000
Subject: [PATCH] sqrt implementation for float.
---
sysdeps/powerpc/w_sqrtf.c | 136 ++++++++++++++++++++++++++++++++++++++++++++++
1 file changed, 136 insertions(+)
create mode 100644 sysdeps/powerpc/w_sqrtf.c
diff --git a/sysdeps/powerpc/w_sqrtf.c b/sysdeps/powerpc/w_sqrtf.c
new file mode 100644
index 0000000000..804dff3c44
--- /dev/null
+++ b/sysdeps/powerpc/w_sqrtf.c
@@ -0,0 +1,136 @@
+/* Single-precision floating point square root.
+ Copyright (C) 1997 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 Library General Public License as
+ published by the Free Software Foundation; either version 2 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
+ Library General Public License for more details.
+
+ You should have received a copy of the GNU Library General Public
+ License along with the GNU C Library; see the file COPYING.LIB. If not,
+ write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+ Boston, MA 02111-1307, USA. */
+
+#include
+#include
+#include
+#include
+
+static const float almost_half = 0.50000006; /* 0.5 + 2^-24 */
+static const uint32_t a_nan = 0x7fc00000;
+static const uint32_t a_inf = 0x7f800000;
+static const float two48 = 281474976710656.0;
+static const float twom24 = 5.9604644775390625e-8;
+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). */
+float
+__sqrtf(float x)
+{
+ const float inf = *(const float *)&a_inf;
+ /* x = f_washf(x); *//* This ensures only one exception for SNaN. */
+ if (x > 0)
+ {
+ 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. */
+ float sx; /* The value of which we're trying to find the square
+ root. */
+ float sg,g; /* Guess of the square root of x. */
+ float sd,d; /* Difference between the square of the guess and x. */
+ float sy; /* Estimate of 1/2g (overestimated by 1ulp). */
+ float sy2; /* 2*sy */
+ float e; /* Difference between y*g and 1/2 (note that e==se). */
+ float shx; /* == sx * fsg */
+ float fsg; /* sg*fsg == g. */
+ fenv_t fe; /* Saved floating-point environment (stores rounding
+ mode and whether the inexact exception is
+ enabled). */
+ uint32_t xi, sxi, fsgi;
+ const float *t_sqrt;
+
+ GET_FLOAT_WORD (xi, x);
+ fe = fegetenv_register ();
+ relax_fenv_state ();
+ sxi = xi & 0x3fffffff | 0x3f000000;
+ SET_FLOAT_WORD (sx, sxi);
+ t_sqrt = __t_sqrt + (xi >> 23-8-1 & 0x3fe);
+ sg = t_sqrt[0];
+ sy = t_sqrt[1];
+
+ /* 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 = xi + 0x40000000 >> 1 & 0x7f800000;
+ sy2 = sy + sy;
+ sg = sy*sd + sg; /* 16-bit approximation to sqrt(sx). */
+ e = -(sy*sg - almost_half);
+ SET_FLOAT_WORD (fsg, fsgi);
+ sd = -(sg*sg - sx);
+ sy = sy + e*sy2;
+ if ((xi & 0x7f800000) == 0)
+ goto denorm;
+ shx = sx * fsg;
+ sg = sg + sy*sd; /* 32-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 __sqrtf(x * two48) * twom24;
+ }
+ }
+ else if (x < 0)
+ {
+#ifdef FE_INVALID_SQRT
+ feraiseexcept (FE_INVALID_SQRT);
+ /* For some reason, some PowerPC processors don't implement
+ FE_INVALID_SQRT. I guess no-one ever thought they'd be
+ used for square roots... :-) */
+ if (!fetestexcept (FE_INVALID))
+#endif
+ feraiseexcept (FE_INVALID);
+#ifndef _IEEE_LIBM
+ if (_LIB_VERSION != _IEEE_)
+ x = __kernel_standard(x,x,126);
+ else
+#endif
+ x = *(const float*)&a_nan;
+ }
+ return f_washf(x);
+}
+
+weak_alias (__sqrtf, sqrtf)
+/* Strictly, this is wrong, but the only places where _ieee754_sqrt is
+ used will not pass in a negative result. */
+strong_alias(__sqrtf,__ieee754_sqrtf)
--
2.11.0