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Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/dbl-64/e_sqrt.c')
| -rw-r--r-- | REORG.TODO/sysdeps/ieee754/dbl-64/e_sqrt.c | 139 |
1 files changed, 139 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_sqrt.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_sqrt.c new file mode 100644 index 0000000000..017d30416c --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_sqrt.c @@ -0,0 +1,139 @@ +/* + * IBM Accurate Mathematical Library + * written by International Business Machines Corp. + * Copyright (C) 2001-2017 Free Software Foundation, Inc. + * + * This program 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. + * + * This program 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 this program; if not, see <http://www.gnu.org/licenses/>. + */ +/*********************************************************************/ +/* MODULE_NAME: uroot.c */ +/* */ +/* FUNCTION: usqrt */ +/* */ +/* FILES NEEDED: dla.h endian.h mydefs.h */ +/* uroot.tbl */ +/* */ +/* An ultimate sqrt routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of square */ +/* root of x. */ +/* Assumption: Machine arithmetic operations are performed in */ +/* round to nearest mode of IEEE 754 standard. */ +/* */ +/*********************************************************************/ + +#include "endian.h" +#include "mydefs.h" +#include <dla.h> +#include "MathLib.h" +#include "root.tbl" +#include <math_private.h> + +/*********************************************************************/ +/* An ultimate sqrt routine. Given an IEEE double machine number x */ +/* it computes the correctly rounded (to nearest) value of square */ +/* root of x. */ +/*********************************************************************/ +double +__ieee754_sqrt (double x) +{ + static const double + rt0 = 9.99999999859990725855365213134618E-01, + rt1 = 4.99999999495955425917856814202739E-01, + rt2 = 3.75017500867345182581453026130850E-01, + rt3 = 3.12523626554518656309172508769531E-01; + static const double big = 134217728.0; + double y, t, del, res, res1, hy, z, zz, p, hx, tx, ty, s; + mynumber a, c = { { 0, 0 } }; + int4 k; + + a.x = x; + k = a.i[HIGH_HALF]; + a.i[HIGH_HALF] = (k & 0x001fffff) | 0x3fe00000; + t = inroot[(k & 0x001fffff) >> 14]; + s = a.x; + /*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/ + if (k > 0x000fffff && k < 0x7ff00000) + { + int rm = __fegetround (); + fenv_t env; + libc_feholdexcept_setround (&env, FE_TONEAREST); + double ret; + y = 1.0 - t * (t * s); + t = t * (rt0 + y * (rt1 + y * (rt2 + y * rt3))); + c.i[HIGH_HALF] = 0x20000000 + ((k & 0x7fe00000) >> 1); + y = t * s; + hy = (y + big) - big; + del = 0.5 * t * ((s - hy * hy) - (y - hy) * (y + hy)); + res = y + del; + if (res == (res + 1.002 * ((y - res) + del))) + ret = res * c.x; + else + { + res1 = res + 1.5 * ((y - res) + del); + EMULV (res, res1, z, zz, p, hx, tx, hy, ty); /* (z+zz)=res*res1 */ + res = ((((z - s) + zz) < 0) ? max (res, res1) : + min (res, res1)); + ret = res * c.x; + } + math_force_eval (ret); + libc_fesetenv (&env); + double dret = x / ret; + if (dret != ret) + { + double force_inexact = 1.0 / 3.0; + math_force_eval (force_inexact); + /* The square root is inexact, ret is the round-to-nearest + value which may need adjusting for other rounding + modes. */ + switch (rm) + { +#ifdef FE_UPWARD + case FE_UPWARD: + if (dret > ret) + ret = (res + 0x1p-1022) * c.x; + break; +#endif + +#ifdef FE_DOWNWARD + case FE_DOWNWARD: +#endif +#ifdef FE_TOWARDZERO + case FE_TOWARDZERO: +#endif +#if defined FE_DOWNWARD || defined FE_TOWARDZERO + if (dret < ret) + ret = (res - 0x1p-1022) * c.x; + break; +#endif + + default: + break; + } + } + /* Otherwise (x / ret == ret), either the square root was exact or + the division was inexact. */ + return ret; + } + else + { + if ((k & 0x7ff00000) == 0x7ff00000) + return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */ + if (x == 0) + return x; /* sqrt(+0)=+0, sqrt(-0)=-0 */ + if (k < 0) + return (x - x) / (x - x); /* sqrt(-ve)=sNaN */ + return 0x1p-256 * __ieee754_sqrt (x * 0x1p512); + } +} +strong_alias (__ieee754_sqrt, __sqrt_finite) |