From 1ec601bf9fb0fbc39b3a6cb90450500f857adae8 Mon Sep 17 00:00:00 2001 From: Francois-Xavier Coudert Date: Tue, 16 Nov 2010 21:23:19 +0000 Subject: re PR fortran/32049 (Support on x86_64 also kind=16) / 2010-11-13 Francois-Xavier Coudert Tobias Burnus 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 Tobias Burnus PR fortran/32049 Initial implementation and checkin. gcc/fortran/ 2010-11-13 Francois-Xavier Coudert Tobias Burnus 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 Tobias Burnus 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 Tobias Burnus PR fortran/32049 * configure.ac: * configure: Regenerate. libgfortran/ 2010-11-13 Francois-Xavier Coudert Tobias Burnus 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 From-SVN: r166825 --- libquadmath/math/expm1q.c | 158 ++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 158 insertions(+) create mode 100644 libquadmath/math/expm1q.c (limited to 'libquadmath/math/expm1q.c') diff --git a/libquadmath/math/expm1q.c b/libquadmath/math/expm1q.c new file mode 100644 index 0000000..510c98f --- /dev/null +++ b/libquadmath/math/expm1q.c @@ -0,0 +1,158 @@ +/* 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 "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 (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) + return (HUGE_VALQ * HUGE_VALQ); + + /* 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; +} -- cgit v1.1