gcc/libquadmath/math/acosq.c

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re PR fortran/32049 (Support on x86_64 also kind=16) / 2010-11-13 Francois-Xavier Coudert <fxcoudert@gcc.gnu.org> Tobias Burnus <burnus@net-b.de> PR fortran/32049 * Makefile.def: Add libquadmath; build it with language=fortran. * configure.ac: Add libquadmath. * Makefile.tpl: Handle multiple libs in check-[+language+]. * Makefile.in: Regenerate. * configure: Regenerate. libquadmath/ 2010-11-13 Francois-Xavier Coudert <fxcoudert@gcc.gnu.org> Tobias Burnus <burnus@net-b.de> PR fortran/32049 Initial implementation and checkin. gcc/fortran/ 2010-11-13 Francois-Xavier Coudert <fxcoudert@gcc.gnu.org> Tobias Burnus <burnus@net-b.de> PR fortran/32049 * gfortranspec.c (find_spec_file): New function. (lang_specific_driver): Try to find .spec file and use it. * trans-io.c (iocall): Define * IOCALL_X_REAL128/COMPLEX128(,write). (gfc_build_io_library_fndecls): Build decl for __float128 I/O. (transfer_expr): Call __float128 I/O functions. * trans-types.c (gfc_init_kinds): Allow kind-16 belonging to __float128. gcc/testsuite/ 2010-11-13 Francois-Xavier Coudert <fxcoudert@gcc.gnu.org> Tobias Burnus <burnus@net-b.de> PR fortran/32049 * gfortran.dg/quad_1.f90: New. * lib/gcc-defs.exp (gcc-set-multilib-library-path): Use also compiler arguments. * lib/gfortran.exp (gfortran_link_flags): Add libquadmath to library search path; call gcc-set-multilib-library-path with arguments such that libgfortran.spec is found. (gfortran_init): Add path for libgfortran.spec to GFORTRAN_UNDER_TEST. libgomp/ 2010-11-13 Francois-Xavier Coudert <fxcoudert@gcc.gnu.org> Tobias Burnus <burnus@net-b.de> PR fortran/32049 * configure.ac: * configure: Regenerate. libgfortran/ 2010-11-13 Francois-Xavier Coudert <fxcoudert@gcc.gnu.org> Tobias Burnus <burnus@net-b.de> PR fortran/32049 * Makefile.am: Add missing pow_r16_i4.c, add transfer128.c, link libquadmath, if used. * acinclude.m4 (LIBGFOR_CHECK_FLOAT128): Add. * configure.ac: Use it, touch spec file. * gfortran.map: Add pow_r16_i4 and transfer_(real,complex)128(,write) functions. * intrinsics/cshift0.c (cshift0): Handle __float128 type. * intrinsics/erfc_scaled_inc.c: Ditto. * intrinsics/pack_generic.c (pack): Ditto * intrinsics/spread_generic.c (spread): Ditto. * intrinsics/unpack_generic.c (unpack1): Ditto. * io/read.c (convert_real): Ditto. * io/transfer.c: Update comments. * io/transfer128.c: New file. * io/write_float.def (write_float): Handle __float128 type. * libgfortran.h: #include quadmath_weak.h, define __builtin_infq and nanq. * m4/mtype.m4: Handle __float128 type. * runtime/in_pack_generic.c (internal_pack): Ditto. * runtime/in_unpack_generic.c (internal_unpack): Ditto. * kinds-override.h: New file. * libgfortran.spec.in: Ditto. * generated/pow_r16_i4.c: Generated. * Makefile.in: Regenerate. * configure: Regenerate. * config.h: Regenerate. * bessel_r10.c: Regenerate. * bessel_r16.c: Regenerate. * bessel_r4.c: Regenerate. * bessel_r8.c: Regenerate. * exponent_r16.c: Regenerate. * fraction_r16.c: Regenerate. * nearest_r16.c: Regenerate. * norm2_r10.c: Regenerate. * norm2_r16.c: Regenerate. * norm2_r4.c: Regenerate. * norm2_r8.c: Regenerate. * rrspacing_r16.c: Regenerate. * set_exponent_r16.c: Regenerate. * spacing_r16.c: Regenerate. Co-Authored-By: Tobias Burnus <burnus@net-b.de> From-SVN: r166825
2010-11-16 22:23:19 +01:00
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
__float128 expansions are
Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
and are incorporated herein by permission of the author. The author
reserves the right to distribute this material elsewhere under different
copying permissions. These modifications are distributed here under
the following terms:
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, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
Makefile.am (libquadmath_la_SOURCES): Add new math/* files. 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
2012-11-01 17:14:42 +01:00
/* acosq(x)
re PR fortran/32049 (Support on x86_64 also kind=16) / 2010-11-13 Francois-Xavier Coudert <fxcoudert@gcc.gnu.org> Tobias Burnus <burnus@net-b.de> PR fortran/32049 * Makefile.def: Add libquadmath; build it with language=fortran. * configure.ac: Add libquadmath. * Makefile.tpl: Handle multiple libs in check-[+language+]. * Makefile.in: Regenerate. * configure: Regenerate. libquadmath/ 2010-11-13 Francois-Xavier Coudert <fxcoudert@gcc.gnu.org> Tobias Burnus <burnus@net-b.de> PR fortran/32049 Initial implementation and checkin. gcc/fortran/ 2010-11-13 Francois-Xavier Coudert <fxcoudert@gcc.gnu.org> Tobias Burnus <burnus@net-b.de> PR fortran/32049 * gfortranspec.c (find_spec_file): New function. (lang_specific_driver): Try to find .spec file and use it. * trans-io.c (iocall): Define * IOCALL_X_REAL128/COMPLEX128(,write). (gfc_build_io_library_fndecls): Build decl for __float128 I/O. (transfer_expr): Call __float128 I/O functions. * trans-types.c (gfc_init_kinds): Allow kind-16 belonging to __float128. gcc/testsuite/ 2010-11-13 Francois-Xavier Coudert <fxcoudert@gcc.gnu.org> Tobias Burnus <burnus@net-b.de> PR fortran/32049 * gfortran.dg/quad_1.f90: New. * lib/gcc-defs.exp (gcc-set-multilib-library-path): Use also compiler arguments. * lib/gfortran.exp (gfortran_link_flags): Add libquadmath to library search path; call gcc-set-multilib-library-path with arguments such that libgfortran.spec is found. (gfortran_init): Add path for libgfortran.spec to GFORTRAN_UNDER_TEST. libgomp/ 2010-11-13 Francois-Xavier Coudert <fxcoudert@gcc.gnu.org> Tobias Burnus <burnus@net-b.de> PR fortran/32049 * configure.ac: * configure: Regenerate. libgfortran/ 2010-11-13 Francois-Xavier Coudert <fxcoudert@gcc.gnu.org> Tobias Burnus <burnus@net-b.de> PR fortran/32049 * Makefile.am: Add missing pow_r16_i4.c, add transfer128.c, link libquadmath, if used. * acinclude.m4 (LIBGFOR_CHECK_FLOAT128): Add. * configure.ac: Use it, touch spec file. * gfortran.map: Add pow_r16_i4 and transfer_(real,complex)128(,write) functions. * intrinsics/cshift0.c (cshift0): Handle __float128 type. * intrinsics/erfc_scaled_inc.c: Ditto. * intrinsics/pack_generic.c (pack): Ditto * intrinsics/spread_generic.c (spread): Ditto. * intrinsics/unpack_generic.c (unpack1): Ditto. * io/read.c (convert_real): Ditto. * io/transfer.c: Update comments. * io/transfer128.c: New file. * io/write_float.def (write_float): Handle __float128 type. * libgfortran.h: #include quadmath_weak.h, define __builtin_infq and nanq. * m4/mtype.m4: Handle __float128 type. * runtime/in_pack_generic.c (internal_pack): Ditto. * runtime/in_unpack_generic.c (internal_unpack): Ditto. * kinds-override.h: New file. * libgfortran.spec.in: Ditto. * generated/pow_r16_i4.c: Generated. * Makefile.in: Regenerate. * configure: Regenerate. * config.h: Regenerate. * bessel_r10.c: Regenerate. * bessel_r16.c: Regenerate. * bessel_r4.c: Regenerate. * bessel_r8.c: Regenerate. * exponent_r16.c: Regenerate. * fraction_r16.c: Regenerate. * nearest_r16.c: Regenerate. * norm2_r10.c: Regenerate. * norm2_r16.c: Regenerate. * norm2_r4.c: Regenerate. * norm2_r8.c: Regenerate. * rrspacing_r16.c: Regenerate. * set_exponent_r16.c: Regenerate. * spacing_r16.c: Regenerate. Co-Authored-By: Tobias Burnus <burnus@net-b.de> From-SVN: r166825
2010-11-16 22:23:19 +01:00
* Method :
* acos(x) = pi/2 - asin(x)
* acos(-x) = pi/2 + asin(x)
* For |x| <= 0.375
* acos(x) = pi/2 - asin(x)
* Between .375 and .5 the approximation is
* acos(0.4375 + x) = acos(0.4375) + x P(x) / Q(x)
* Between .5 and .625 the approximation is
* acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x)
* For x > 0.625,
* acos(x) = 2 asin(sqrt((1-x)/2))
* computed with an extended precision square root in the leading term.
* For x < -0.625
* acos(x) = pi - 2 asin(sqrt((1-|x|)/2))
*
* Special cases:
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
Makefile.am (libquadmath_la_SOURCES): Add new math/* files. 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
2012-11-01 17:14:42 +01:00
* Functions needed: sqrtq.
re PR fortran/32049 (Support on x86_64 also kind=16) / 2010-11-13 Francois-Xavier Coudert <fxcoudert@gcc.gnu.org> Tobias Burnus <burnus@net-b.de> PR fortran/32049 * Makefile.def: Add libquadmath; build it with language=fortran. * configure.ac: Add libquadmath. * Makefile.tpl: Handle multiple libs in check-[+language+]. * Makefile.in: Regenerate. * configure: Regenerate. libquadmath/ 2010-11-13 Francois-Xavier Coudert <fxcoudert@gcc.gnu.org> Tobias Burnus <burnus@net-b.de> PR fortran/32049 Initial implementation and checkin. gcc/fortran/ 2010-11-13 Francois-Xavier Coudert <fxcoudert@gcc.gnu.org> Tobias Burnus <burnus@net-b.de> PR fortran/32049 * gfortranspec.c (find_spec_file): New function. (lang_specific_driver): Try to find .spec file and use it. * trans-io.c (iocall): Define * IOCALL_X_REAL128/COMPLEX128(,write). (gfc_build_io_library_fndecls): Build decl for __float128 I/O. (transfer_expr): Call __float128 I/O functions. * trans-types.c (gfc_init_kinds): Allow kind-16 belonging to __float128. gcc/testsuite/ 2010-11-13 Francois-Xavier Coudert <fxcoudert@gcc.gnu.org> Tobias Burnus <burnus@net-b.de> PR fortran/32049 * gfortran.dg/quad_1.f90: New. * lib/gcc-defs.exp (gcc-set-multilib-library-path): Use also compiler arguments. * lib/gfortran.exp (gfortran_link_flags): Add libquadmath to library search path; call gcc-set-multilib-library-path with arguments such that libgfortran.spec is found. (gfortran_init): Add path for libgfortran.spec to GFORTRAN_UNDER_TEST. libgomp/ 2010-11-13 Francois-Xavier Coudert <fxcoudert@gcc.gnu.org> Tobias Burnus <burnus@net-b.de> PR fortran/32049 * configure.ac: * configure: Regenerate. libgfortran/ 2010-11-13 Francois-Xavier Coudert <fxcoudert@gcc.gnu.org> Tobias Burnus <burnus@net-b.de> PR fortran/32049 * Makefile.am: Add missing pow_r16_i4.c, add transfer128.c, link libquadmath, if used. * acinclude.m4 (LIBGFOR_CHECK_FLOAT128): Add. * configure.ac: Use it, touch spec file. * gfortran.map: Add pow_r16_i4 and transfer_(real,complex)128(,write) functions. * intrinsics/cshift0.c (cshift0): Handle __float128 type. * intrinsics/erfc_scaled_inc.c: Ditto. * intrinsics/pack_generic.c (pack): Ditto * intrinsics/spread_generic.c (spread): Ditto. * intrinsics/unpack_generic.c (unpack1): Ditto. * io/read.c (convert_real): Ditto. * io/transfer.c: Update comments. * io/transfer128.c: New file. * io/write_float.def (write_float): Handle __float128 type. * libgfortran.h: #include quadmath_weak.h, define __builtin_infq and nanq. * m4/mtype.m4: Handle __float128 type. * runtime/in_pack_generic.c (internal_pack): Ditto. * runtime/in_unpack_generic.c (internal_unpack): Ditto. * kinds-override.h: New file. * libgfortran.spec.in: Ditto. * generated/pow_r16_i4.c: Generated. * Makefile.in: Regenerate. * configure: Regenerate. * config.h: Regenerate. * bessel_r10.c: Regenerate. * bessel_r16.c: Regenerate. * bessel_r4.c: Regenerate. * bessel_r8.c: Regenerate. * exponent_r16.c: Regenerate. * fraction_r16.c: Regenerate. * nearest_r16.c: Regenerate. * norm2_r10.c: Regenerate. * norm2_r16.c: Regenerate. * norm2_r4.c: Regenerate. * norm2_r8.c: Regenerate. * rrspacing_r16.c: Regenerate. * set_exponent_r16.c: Regenerate. * spacing_r16.c: Regenerate. Co-Authored-By: Tobias Burnus <burnus@net-b.de> From-SVN: r166825
2010-11-16 22:23:19 +01:00
*/
#include "quadmath-imp.h"
static const __float128
one = 1.0Q,
pio2_hi = 1.5707963267948966192313216916397514420986Q,
pio2_lo = 4.3359050650618905123985220130216759843812E-35Q,
/* acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x)
-0.0625 <= x <= 0.0625
peak relative error 3.3e-35 */
rS0 = 5.619049346208901520945464704848780243887E0Q,
rS1 = -4.460504162777731472539175700169871920352E1Q,
rS2 = 1.317669505315409261479577040530751477488E2Q,
rS3 = -1.626532582423661989632442410808596009227E2Q,
rS4 = 3.144806644195158614904369445440583873264E1Q,
rS5 = 9.806674443470740708765165604769099559553E1Q,
rS6 = -5.708468492052010816555762842394927806920E1Q,
rS7 = -1.396540499232262112248553357962639431922E1Q,
rS8 = 1.126243289311910363001762058295832610344E1Q,
rS9 = 4.956179821329901954211277873774472383512E-1Q,
rS10 = -3.313227657082367169241333738391762525780E-1Q,
sS0 = -4.645814742084009935700221277307007679325E0Q,
sS1 = 3.879074822457694323970438316317961918430E1Q,
sS2 = -1.221986588013474694623973554726201001066E2Q,
sS3 = 1.658821150347718105012079876756201905822E2Q,
sS4 = -4.804379630977558197953176474426239748977E1Q,
sS5 = -1.004296417397316948114344573811562952793E2Q,
sS6 = 7.530281592861320234941101403870010111138E1Q,
sS7 = 1.270735595411673647119592092304357226607E1Q,
sS8 = -1.815144839646376500705105967064792930282E1Q,
sS9 = -7.821597334910963922204235247786840828217E-2Q,
/* 1.000000000000000000000000000000000000000E0 */
acosr5625 = 9.7338991014954640492751132535550279812151E-1Q,
pimacosr5625 = 2.1682027434402468335351320579240000860757E0Q,
/* acos(0.4375 + x) = acos(0.4375) + x rS(x) / sS(x)
-0.0625 <= x <= 0.0625
peak relative error 2.1e-35 */
P0 = 2.177690192235413635229046633751390484892E0Q,
P1 = -2.848698225706605746657192566166142909573E1Q,
P2 = 1.040076477655245590871244795403659880304E2Q,
P3 = -1.400087608918906358323551402881238180553E2Q,
P4 = 2.221047917671449176051896400503615543757E1Q,
P5 = 9.643714856395587663736110523917499638702E1Q,
P6 = -5.158406639829833829027457284942389079196E1Q,
P7 = -1.578651828337585944715290382181219741813E1Q,
P8 = 1.093632715903802870546857764647931045906E1Q,
P9 = 5.448925479898460003048760932274085300103E-1Q,
P10 = -3.315886001095605268470690485170092986337E-1Q,
Q0 = -1.958219113487162405143608843774587557016E0Q,
Q1 = 2.614577866876185080678907676023269360520E1Q,
Q2 = -9.990858606464150981009763389881793660938E1Q,
Q3 = 1.443958741356995763628660823395334281596E2Q,
Q4 = -3.206441012484232867657763518369723873129E1Q,
Q5 = -1.048560885341833443564920145642588991492E2Q,
Q6 = 6.745883931909770880159915641984874746358E1Q,
Q7 = 1.806809656342804436118449982647641392951E1Q,
Q8 = -1.770150690652438294290020775359580915464E1Q,
Q9 = -5.659156469628629327045433069052560211164E-1Q,
/* 1.000000000000000000000000000000000000000E0 */
acosr4375 = 1.1179797320499710475919903296900511518755E0Q,
pimacosr4375 = 2.0236129215398221908706530535894517323217E0Q,
/* asin(x) = x + x^3 pS(x^2) / qS(x^2)
0 <= x <= 0.5
peak relative error 1.9e-35 */
pS0 = -8.358099012470680544198472400254596543711E2Q,
pS1 = 3.674973957689619490312782828051860366493E3Q,
pS2 = -6.730729094812979665807581609853656623219E3Q,
pS3 = 6.643843795209060298375552684423454077633E3Q,
pS4 = -3.817341990928606692235481812252049415993E3Q,
pS5 = 1.284635388402653715636722822195716476156E3Q,
pS6 = -2.410736125231549204856567737329112037867E2Q,
pS7 = 2.219191969382402856557594215833622156220E1Q,
pS8 = -7.249056260830627156600112195061001036533E-1Q,
pS9 = 1.055923570937755300061509030361395604448E-3Q,
qS0 = -5.014859407482408326519083440151745519205E3Q,
qS1 = 2.430653047950480068881028451580393430537E4Q,
qS2 = -4.997904737193653607449250593976069726962E4Q,
qS3 = 5.675712336110456923807959930107347511086E4Q,
qS4 = -3.881523118339661268482937768522572588022E4Q,
qS5 = 1.634202194895541569749717032234510811216E4Q,
qS6 = -4.151452662440709301601820849901296953752E3Q,
qS7 = 5.956050864057192019085175976175695342168E2Q,
qS8 = -4.175375777334867025769346564600396877176E1Q;
/* 1.000000000000000000000000000000000000000E0 */
__float128
acosq (__float128 x)
{
__float128 z, r, w, p, q, s, t, f2;
int32_t ix, sign;
ieee854_float128 u;
u.value = x;
sign = u.words32.w0;
ix = sign & 0x7fffffff;
u.words32.w0 = ix; /* |x| */
if (ix >= 0x3fff0000) /* |x| >= 1 */
{
if (ix == 0x3fff0000
&& (u.words32.w1 | u.words32.w2 | u.words32.w3) == 0)
{ /* |x| == 1 */
if ((sign & 0x80000000) == 0)
return 0.0; /* acos(1) = 0 */
else
return (2.0 * pio2_hi) + (2.0 * pio2_lo); /* acos(-1)= pi */
}
return (x - x) / (x - x); /* acos(|x| > 1) is NaN */
}
else if (ix < 0x3ffe0000) /* |x| < 0.5 */
{
if (ix < 0x3fc60000) /* |x| < 2**-57 */
return pio2_hi + pio2_lo;
if (ix < 0x3ffde000) /* |x| < .4375 */
{
/* Arcsine of x. */
z = x * x;
p = (((((((((pS9 * z
+ pS8) * z
+ pS7) * z
+ pS6) * z
+ pS5) * z
+ pS4) * z
+ pS3) * z
+ pS2) * z
+ pS1) * z
+ pS0) * z;
q = (((((((( z
+ qS8) * z
+ qS7) * z
+ qS6) * z
+ qS5) * z
+ qS4) * z
+ qS3) * z
+ qS2) * z
+ qS1) * z
+ qS0;
r = x + x * p / q;
z = pio2_hi - (r - pio2_lo);
return z;
}
/* .4375 <= |x| < .5 */
t = u.value - 0.4375Q;
p = ((((((((((P10 * t
+ P9) * t
+ P8) * t
+ P7) * t
+ P6) * t
+ P5) * t
+ P4) * t
+ P3) * t
+ P2) * t
+ P1) * t
+ P0) * t;
q = (((((((((t
+ Q9) * t
+ Q8) * t
+ Q7) * t
+ Q6) * t
+ Q5) * t
+ Q4) * t
+ Q3) * t
+ Q2) * t
+ Q1) * t
+ Q0;
r = p / q;
if (sign & 0x80000000)
r = pimacosr4375 - r;
else
r = acosr4375 + r;
return r;
}
else if (ix < 0x3ffe4000) /* |x| < 0.625 */
{
t = u.value - 0.5625Q;
p = ((((((((((rS10 * t
+ rS9) * t
+ rS8) * t
+ rS7) * t
+ rS6) * t
+ rS5) * t
+ rS4) * t
+ rS3) * t
+ rS2) * t
+ rS1) * t
+ rS0) * t;
q = (((((((((t
+ sS9) * t
+ sS8) * t
+ sS7) * t
+ sS6) * t
+ sS5) * t
+ sS4) * t
+ sS3) * t
+ sS2) * t
+ sS1) * t
+ sS0;
if (sign & 0x80000000)
r = pimacosr5625 - p / q;
else
r = acosr5625 + p / q;
return r;
}
else
{ /* |x| >= .625 */
z = (one - u.value) * 0.5;
s = sqrtq (z);
/* Compute an extended precision square root from
the Newton iteration s -> 0.5 * (s + z / s).
The change w from s to the improved value is
w = 0.5 * (s + z / s) - s = (s^2 + z)/2s - s = (z - s^2)/2s.
Express s = f1 + f2 where f1 * f1 is exactly representable.
w = (z - s^2)/2s = (z - f1^2 - 2 f1 f2 - f2^2)/2s .
s + w has extended precision. */
u.value = s;
u.words32.w2 = 0;
u.words32.w3 = 0;
f2 = s - u.value;
w = z - u.value * u.value;
w = w - 2.0 * u.value * f2;
w = w - f2 * f2;
w = w / (2.0 * s);
/* Arcsine of s. */
p = (((((((((pS9 * z
+ pS8) * z
+ pS7) * z
+ pS6) * z
+ pS5) * z
+ pS4) * z
+ pS3) * z
+ pS2) * z
+ pS1) * z
+ pS0) * z;
q = (((((((( z
+ qS8) * z
+ qS7) * z
+ qS6) * z
+ qS5) * z
+ qS4) * z
+ qS3) * z
+ qS2) * z
+ qS1) * z
+ qS0;
r = s + (w + s * p / q);
if (sign & 0x80000000)
w = pio2_hi + (pio2_lo - r);
else
w = r;
return 2.0 * w;
}
}