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Diffstat (limited to 'sysdeps/powerpc/e_sqrt.c')
| -rw-r--r-- | sysdeps/powerpc/e_sqrt.c | 141 |
1 files changed, 141 insertions, 0 deletions
diff --git a/sysdeps/powerpc/e_sqrt.c b/sysdeps/powerpc/e_sqrt.c new file mode 100644 index 0000000000..df80973f58 --- /dev/null +++ b/sysdeps/powerpc/e_sqrt.c @@ -0,0 +1,141 @@ +/* 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) |