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Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/ldbl-128/s_cbrtl.c')
| -rw-r--r-- | REORG.TODO/sysdeps/ieee754/ldbl-128/s_cbrtl.c | 135 |
1 files changed, 135 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128/s_cbrtl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_cbrtl.c new file mode 100644 index 0000000000..eb88d29fc9 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128/s_cbrtl.c @@ -0,0 +1,135 @@ +/* cbrtl.c + * + * Cube root, long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, cbrtl(); + * + * y = cbrtl( x ); + * + * + * + * DESCRIPTION: + * + * Returns the cube root of the argument, which may be negative. + * + * Range reduction involves determining the power of 2 of + * the argument. A polynomial of degree 2 applied to the + * mantissa, and multiplication by the cube root of 1, 2, or 4 + * approximates the root to within about 0.1%. Then Newton's + * iteration is used three times to converge to an accurate + * result. + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -8,8 100000 1.3e-34 3.9e-35 + * IEEE exp(+-707) 100000 1.3e-34 4.3e-35 + * + */ + +/* +Cephes Math Library Release 2.2: January, 1991 +Copyright 1984, 1991 by Stephen L. Moshier +Adapted for glibc October, 2001. + + This 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. + + This 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 this library; if not, see + <http://www.gnu.org/licenses/>. */ + + +#include <math.h> +#include <math_private.h> + +static const _Float128 CBRT2 = L(1.259921049894873164767210607278228350570251); +static const _Float128 CBRT4 = L(1.587401051968199474751705639272308260391493); +static const _Float128 CBRT2I = L(0.7937005259840997373758528196361541301957467); +static const _Float128 CBRT4I = L(0.6299605249474365823836053036391141752851257); + + +_Float128 +__cbrtl (_Float128 x) +{ + int e, rem, sign; + _Float128 z; + + if (!isfinite (x)) + return x + x; + + if (x == 0) + return (x); + + if (x > 0) + sign = 1; + else + { + sign = -1; + x = -x; + } + + z = x; + /* extract power of 2, leaving mantissa between 0.5 and 1 */ + x = __frexpl (x, &e); + + /* Approximate cube root of number between .5 and 1, + peak relative error = 1.2e-6 */ + x = ((((L(1.3584464340920900529734e-1) * x + - L(6.3986917220457538402318e-1)) * x + + L(1.2875551670318751538055e0)) * x + - L(1.4897083391357284957891e0)) * x + + L(1.3304961236013647092521e0)) * x + L(3.7568280825958912391243e-1); + + /* exponent divided by 3 */ + if (e >= 0) + { + rem = e; + e /= 3; + rem -= 3 * e; + if (rem == 1) + x *= CBRT2; + else if (rem == 2) + x *= CBRT4; + } + else + { /* argument less than 1 */ + e = -e; + rem = e; + e /= 3; + rem -= 3 * e; + if (rem == 1) + x *= CBRT2I; + else if (rem == 2) + x *= CBRT4I; + e = -e; + } + + /* multiply by power of 2 */ + x = __ldexpl (x, e); + + /* Newton iteration */ + x -= (x - (z / (x * x))) * L(0.3333333333333333333333333333333333333333); + x -= (x - (z / (x * x))) * L(0.3333333333333333333333333333333333333333); + x -= (x - (z / (x * x))) * L(0.3333333333333333333333333333333333333333); + + if (sign < 0) + x = -x; + return (x); +} + +weak_alias (__cbrtl, cbrtl) |