f029f4be17
2012-11-01 Tobias Burnus <burnus@net-b.de>
* Makefile.am (libquadmath_la_SOURCES): Add new math/* files.
* Makefile.in: Regenerated.
* math/acoshq.c: Update comment.
* math/acosq.c: Ditto.
* math/asinhq.c: Ditto.
* math/asinq.c: Ditto.
* math/atan2q.c: Ditto.
* math/atanhq.c: Ditto.
* math/ceilq.c: Ditto.
* math/copysignq.c: Ditto.
* math/cosq.c: Ditto.
* math/coshq.c: Ditto.
* math/erfq.c: Ditto.
* math/fabsq.c: Ditto.
* math/finiteq.c: Ditto.
* math/floorq.c: Ditto.
* math/fmodq.c: Ditto.
* math/frexpq.c: Ditto.
* math/isnanq.c: Ditto.
* math/j0q.c: Ditto.
* math/j1q.c: Ditto.
* math/ldexpq.c: Ditto.
* math/llroundq.c: Ditto.
* math/log10q.c: Ditto.
* math/log1pq.c: Ditto.
* math/log2q.c: Ditto.
* math/logq.c: Ditto.
* math/lroundq.c: Ditto.
* math/modfq.c: Ditto.
* math/nextafterq.c: Ditto.
* math/powq.c: Ditto.
* math/rem_pio2q.c: Ditto.
* math/remainderq.c: Ditto.
* math/rintq.c: Ditto.
* math/roundq.c: Ditto.
* math/scalblnq.c: Ditto.
* math/scalbnq.c: Ditto.
* math/sincosq_kernel.c: Ditto.
* math/sinq.c: Ditto.
* math/tanq.c: Ditto.
* math/expq.c: Ditto.
(__expq_table, expq): Renamed local array from __expl_table.
* math/cosq_kernel.c (__quadmath_kernel_cosq): Fix sign
* handling.
* math/cacoshq.c: Changes from GLIBC; fix returned sign.
* math/casinhq.c: Changes from GLIBC to fix special-case.
* math/cbrtq.c: Use modified GLIBC version.
* math/complex.c (ccoshd, cexpq, clog10q, clogq, csinhq, csinq,
ctanhq, ctanq): Moved to separates files.
(mult_c128, div_c128): Removed no longer needed functions.
(cexpiq): Call sincosq instead of sinq and cosq.
(cosq): Call cosh(-re,im) instead of cosq/sinq/sinh/cosh.
* math/ccoshq.c (ccoshq): New file, moved from complex.c and
modified based on GLIBC.
* math/cexpq.c (cexp): Ditto.
* math/clog10q.c (clog10q): Ditto.
* math/clogq.c (clogq): Ditto.
* math/csinhq.c: Ditto.
* math/csinq.c: Ditto.
* math/csqrtq.c: Ditto.
* math/ctanhq.c: Ditto.
* math/ctanq.c: Ditto.
* math/fmaq.c (fmaq): Port TININESS_AFTER_ROUNDING handling
from GLIBC.
* math/ilogbq.c (ilogbq): Add errno = EDOM handling.
* math/isinf_nsq.c (__quadmath_isinf_nsq): New file, ported
from GLIBC.
* math/lgammaq.c (lgammaq): Add signgam handling.
* math/sinhq.c (sinhq): Fix sign handling.
* math/sinq_kernel.c (__quadmath_kernel_sinq): Ditto.
* math/tgammaq.c (tgammaq): Ditto.
* math/x2y2m1q.c: New file.
* quadmath-imp.h (TININESS_AFTER_ROUNDING): New define.
(__quadmath_x2y2m1q, __quadmath_isinf_nsq): New prototypes.
From-SVN: r193063
133 lines
3.2 KiB
C
133 lines
3.2 KiB
C
/* cbrtq.c
|
|
*
|
|
* Cube root, __float128 precision
|
|
*
|
|
*
|
|
*
|
|
* SYNOPSIS:
|
|
*
|
|
* __float128 x, y, cbrtq();
|
|
*
|
|
* y = cbrtq( 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 "quadmath-imp.h"
|
|
|
|
static const long double CBRT2 = 1.259921049894873164767210607278228350570251Q;
|
|
static const long double CBRT4 = 1.587401051968199474751705639272308260391493Q;
|
|
static const long double CBRT2I = 0.7937005259840997373758528196361541301957467Q;
|
|
static const long double CBRT4I = 0.6299605249474365823836053036391141752851257Q;
|
|
|
|
|
|
__float128
|
|
cbrtq ( __float128 x)
|
|
{
|
|
int e, rem, sign;
|
|
__float128 z;
|
|
|
|
if (!finiteq (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 = frexpq (x, &e);
|
|
|
|
/* Approximate cube root of number between .5 and 1,
|
|
peak relative error = 1.2e-6 */
|
|
x = ((((1.3584464340920900529734e-1L * x
|
|
- 6.3986917220457538402318e-1L) * x
|
|
+ 1.2875551670318751538055e0L) * x
|
|
- 1.4897083391357284957891e0L) * x
|
|
+ 1.3304961236013647092521e0L) * x + 3.7568280825958912391243e-1L;
|
|
|
|
/* 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 = ldexpq (x, e);
|
|
|
|
/* Newton iteration */
|
|
x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333L;
|
|
x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333L;
|
|
x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333L;
|
|
|
|
if (sign < 0)
|
|
x = -x;
|
|
return (x);
|
|
}
|