gcc/libquadmath/math/expm1q.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
/* expm1l.c
*
* Exponential function, minus 1
* 128-bit __float128 precision
*
*
*
* SYNOPSIS:
*
* __float128 x, y, expm1l();
*
* y = expm1l( x );
*
*
*
* DESCRIPTION:
*
* Returns e (2.71828...) raised to the x power, minus one.
*
* Range reduction is accomplished by separating the argument
* into an integer k and fraction f such that
*
* x k f
* e = 2 e.
*
* An expansion x + .5 x^2 + x^3 R(x) approximates exp(f) - 1
* in the basic range [-0.5 ln 2, 0.5 ln 2].
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -79,+MAXLOG 100,000 1.7e-34 4.5e-35
*
*/
/* Copyright 2001 by Stephen L. Moshier
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 */
#include <errno.h>
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"
/* exp(x) - 1 = x + 0.5 x^2 + x^3 P(x)/Q(x)
-.5 ln 2 < x < .5 ln 2
Theoretical peak relative error = 8.1e-36 */
static const __float128
P0 = 2.943520915569954073888921213330863757240E8Q,
P1 = -5.722847283900608941516165725053359168840E7Q,
P2 = 8.944630806357575461578107295909719817253E6Q,
P3 = -7.212432713558031519943281748462837065308E5Q,
P4 = 4.578962475841642634225390068461943438441E4Q,
P5 = -1.716772506388927649032068540558788106762E3Q,
P6 = 4.401308817383362136048032038528753151144E1Q,
P7 = -4.888737542888633647784737721812546636240E-1Q,
Q0 = 1.766112549341972444333352727998584753865E9Q,
Q1 = -7.848989743695296475743081255027098295771E8Q,
Q2 = 1.615869009634292424463780387327037251069E8Q,
Q3 = -2.019684072836541751428967854947019415698E7Q,
Q4 = 1.682912729190313538934190635536631941751E6Q,
Q5 = -9.615511549171441430850103489315371768998E4Q,
Q6 = 3.697714952261803935521187272204485251835E3Q,
Q7 = -8.802340681794263968892934703309274564037E1Q,
/* Q8 = 1.000000000000000000000000000000000000000E0 */
/* C1 + C2 = ln 2 */
C1 = 6.93145751953125E-1Q,
C2 = 1.428606820309417232121458176568075500134E-6Q,
/* ln (2^16384 * (1 - 2^-113)) */
maxlog = 1.1356523406294143949491931077970764891253E4Q,
/* ln 2^-114 */
minarg = -7.9018778583833765273564461846232128760607E1Q;
__float128
expm1q (__float128 x)
{
__float128 px, qx, xx;
int32_t ix, sign;
ieee854_float128 u;
int k;
/* Detect infinity and NaN. */
u.value = x;
ix = u.words32.w0;
sign = ix & 0x80000000;
ix &= 0x7fffffff;
if (!sign && ix >= 0x40060000)
{
/* If num is positive and exp >= 6 use plain exp. */
return expq (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
if (ix >= 0x7fff0000)
{
/* Infinity. */
if (((ix & 0xffff) | u.words32.w1 | u.words32.w2 | u.words32.w3) == 0)
{
if (sign)
return -1.0Q;
else
return x;
}
/* NaN. No invalid exception. */
return x;
}
/* expm1(+- 0) = +- 0. */
if ((ix == 0) && (u.words32.w1 | u.words32.w2 | u.words32.w3) == 0)
return x;
/* Overflow. */
if (x > maxlog)
{
errno = ERANGE;
return (HUGE_VALQ * HUGE_VALQ);
}
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
/* Minimum value. */
if (x < minarg)
return (4.0/HUGE_VALQ - 1.0Q);
/* Express x = ln 2 (k + remainder), remainder not exceeding 1/2. */
xx = C1 + C2; /* ln 2. */
px = floorq (0.5 + x / xx);
k = px;
/* remainder times ln 2 */
x -= px * C1;
x -= px * C2;
/* Approximate exp(remainder ln 2). */
px = (((((((P7 * x
+ P6) * x
+ P5) * x + P4) * x + P3) * x + P2) * x + P1) * x + P0) * x;
qx = (((((((x
+ Q7) * x
+ Q6) * x + Q5) * x + Q4) * x + Q3) * x + Q2) * x + Q1) * x + Q0;
xx = x * x;
qx = x + (0.5 * xx + xx * px / qx);
/* exp(x) = exp(k ln 2) exp(remainder ln 2) = 2^k exp(remainder ln 2).
We have qx = exp(remainder ln 2) - 1, so
exp(x) - 1 = 2^k (qx + 1) - 1
= 2^k qx + 2^k - 1. */
px = ldexpq (1.0Q, k);
x = px * qx + (px - 1.0);
return x;
}