diff options
Diffstat (limited to 'sysdeps/powerpc/e_sqrt.c')
| -rw-r--r-- | sysdeps/powerpc/e_sqrt.c | 142 |
1 files changed, 1 insertions, 141 deletions
diff --git a/sysdeps/powerpc/e_sqrt.c b/sysdeps/powerpc/e_sqrt.c index df80973f58..9416ea60c8 100644 --- a/sysdeps/powerpc/e_sqrt.c +++ b/sysdeps/powerpc/e_sqrt.c @@ -1,141 +1 @@ -/* 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 <math.h> -#include <math_private.h> -#include <fenv_libc.h> -#include <inttypes.h> - -static const double almost_half = 0.5000000000000001; /* 0.5 + 2^-53 */ -static const uint32_t a_nan = 0x7fc00000; -static const uint32_t a_inf = 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). */ -double -__sqrt(double x) -{ - const float inf = *(const float *)&a_inf; - /* x = f_wash(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. */ - 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(); - EXTRACT_WORDS (xi0,xi1,x); - relax_fenv_state(); - sxi = xi0 & 0x3fffffff | 0x3fe00000; - INSERT_WORDS (sx, sxi, xi1); - t_sqrt = __t_sqrt + (xi0 >> 52-32-8-1 & 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 = xi0 + 0x40000000 >> 1 & 0x7ff00000; - sy2 = sy + sy; - sg = sy*sd + sg; /* 16-bit approximation to sqrt(sx). */ - INSERT_WORDS (fsg, fsgi, 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; - 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 __sqrt(x * two108) * twom54; - } - } - 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,26); - else -#endif - x = *(const float*)&a_nan; - } - return f_wash(x); -} - -weak_alias (__sqrt, sqrt) -/* Strictly, this is wrong, but the only places where _ieee754_sqrt is - used will not pass in a negative result. */ -strong_alias(__sqrt,__ieee754_sqrt) +/* __ieee754_sqrt is in w_sqrt.c */ |