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Diffstat (limited to 'sysdeps/powerpc/fpu/e_sqrt.c')
| -rw-r--r-- | sysdeps/powerpc/fpu/e_sqrt.c | 186 |
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; +} |