From f964490f3c4f094fd684960c2e98885b23e31376 Mon Sep 17 00:00:00 2001 From: Roland McGrath Date: Sat, 28 Jan 2006 00:15:15 +0000 Subject: 2006-01-27 Dwayne Grant McConnell Jakub Jelinek Roland McGrath Steven Munroe Alan Modra * sysdeps/powerpc/powerpc64/fpu/s_truncf.S: Comment fix. * sysdeps/powerpc/powerpc32/fpu/s_truncf.S: Likewise. * sysdeps/powerpc/powerpc64/fpu/s_llroundf.S: Likewise. * sysdeps/powerpc/fpu/libm-test-ulps: Update. * math/libm-test.inc (check_float_internal): Allow ulp <= 0.5. (erfc_test): Don't run erfcl (27.0L) test if erfcl (27.0L) is denormal. [TEST_LDOUBLE] (ceil_test, floor_test, llrint_test, llround_test, rint_test, round_test, trunc_test): Add new tests. * sysdeps/powerpc/powerpc32/fpu/s_copysignl.S: New file. * sysdeps/powerpc/powerpc32/fpu/s_fabs.S: New file. * sysdeps/powerpc/powerpc32/fpu/s_fabsl.S: New file. * sysdeps/powerpc/powerpc32/fpu/s_fdim.c: New file. * sysdeps/powerpc/powerpc32/fpu/s_fmax.S: New file. * sysdeps/powerpc/powerpc32/fpu/s_fmin.S: New file. * sysdeps/powerpc/powerpc32/fpu/s_isnan.c: New file. * sysdeps/powerpc/powerpc64/fpu/s_ceill.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_copysignl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_fabs.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_fabsl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_fdim.c: New file. * sysdeps/powerpc/powerpc64/fpu/s_floorl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_fmax.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_fmin.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_isnan.c: New file. * sysdeps/powerpc/powerpc64/fpu/s_llrintl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_llroundl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_lrintl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_lroundl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_nearbyintl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_rintl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_roundl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_truncl.S: New file. * sysdeps/unix/sysv/linux/powerpc/Implies: New file. * sysdeps/unix/sysv/linux/powerpc/powerpc64/fpu/Implies: New file. * sysdeps/unix/sysv/linux/powerpc/powerpc32/fpu/Implies: New file. * sysdeps/unix/sysv/linux/powerpc/configure.in: New file. * sysdeps/unix/sysv/linux/powerpc/configure: New file. * sysdeps/unix/sysv/linux/powerpc/bits/wordsize.h (__LONG_DOUBLE_MATH_OPTIONAL): Define. (__NO_LONG_DOUBLE_MATH): Define. * sysdeps/unix/sysv/linux/powerpc/nldbl-abi.h: New file. * sysdeps/powerpc/fpu/s_isnan.c: Include math_ldbl_opt.h. * sysdeps/powerpc/powerpc64/fpu/s_ceil.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (ceill): Add compatibility symbols. * sysdeps/powerpc/powerpc64/fpu/s_copysign.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (copysignl): Add compatibility symbols. * sysdeps/powerpc/powerpc64/fpu/s_floor.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (floorl): Add compatibility symbols. * sysdeps/powerpc/powerpc64/fpu/s_llrint.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (llrintl, lrintl): Add compatibility symbols. * sysdeps/powerpc/powerpc64/fpu/s_llround.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (llroundl, lroundl): Add compatibility symbols. * sysdeps/powerpc/powerpc64/fpu/s_rint.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (rintl): Add compatibility symbols. * sysdeps/powerpc/powerpc64/fpu/s_round.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (roundl): Add compatibility symbols. * sysdeps/powerpc/powerpc64/fpu/s_trunc.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (truncl): Add compatibility symbols. * sysdeps/powerpc/powerpc32/fpu/s_ceil.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (ceill): Add compatibility symbols. * sysdeps/powerpc/powerpc32/fpu/s_copysign.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (copysignl): Add compatibility symbols. * sysdeps/powerpc/powerpc32/fpu/s_floor.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (floorl): Add compatibility symbols. * sysdeps/powerpc/powerpc32/fpu/s_lrint.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (lrintl): Add compatibility symbols. * sysdeps/powerpc/powerpc32/fpu/s_llrint.c: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (llrintl): Add compatibility symbols. * sysdeps/powerpc/powerpc32/fpu/s_lround.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (lroundl): Add compatibility symbols. * sysdeps/powerpc/powerpc32/fpu/s_rint.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (rintl): Add compatibility symbols. * sysdeps/powerpc/powerpc32/fpu/s_round.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (roundl): Add compatibility symbols. * sysdeps/powerpc/powerpc32/fpu/s_trunc.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (truncl): Add compatibility symbols. * misc/qefgcvt_r.c [LDBL_MIN_10_EXP == -291] (FLOAT_MIN_10_NORM): New. * sysdeps/powerpc/fpu/bits/mathdef.h (__NO_LONG_DOUBLE_MATH): Remove. * sysdeps/powerpc/Implies: Add ieee754/ldbl-128ibm. * sysdeps/powerpc/powerpc32/Implies: Remove powerpc/soft-fp. * sysdeps/ieee754/ldbl-128ibm/Makefile: New file. * sysdeps/ieee754/ldbl-128ibm/e_acoshl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_acosl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_asinl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_atan2l.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_atanhl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_coshl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_expl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_fmodl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_hypotl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_j0l.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_j1l.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_jnl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_lgammal_r.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_log10l.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_log2l.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_logl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_powl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_remainderl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_sinhl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_sqrtl.c: New file. * sysdeps/ieee754/ldbl-128ibm/ieee754.h: New file. * sysdeps/ieee754/ldbl-128ibm/k_cosl.c: New file. * sysdeps/ieee754/ldbl-128ibm/k_sincosl.c: New file. * sysdeps/ieee754/ldbl-128ibm/k_sinl.c: New file. * sysdeps/ieee754/ldbl-128ibm/k_tanl.c: New file. * sysdeps/ieee754/ldbl-128ibm/ldbl2mpn.c: New file. * sysdeps/ieee754/ldbl-128ibm/math_ldbl.h: New file. * sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c: New file. * sysdeps/ieee754/ldbl-128ibm/printf_fphex.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_asinhl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_atanl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_cbrtl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_cosl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_erfl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_expm1l.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_fabsl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_finitel.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_fpclassifyl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_frexpl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_ilogbl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_isinfl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_isnanl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_log1pl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_logbl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_modfl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_remquol.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_rintl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_scalblnl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_scalbnl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_signbitl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_sincosl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_sinl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_tanhl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_tanl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_truncl.c: New file. * sysdeps/ieee754/ldbl-128ibm/strtold_l.c: New file. * sysdeps/ieee754/ldbl-128ibm/t_sincosl.c: New file. * sysdeps/ieee754/ldbl-128ibm/w_expl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_copysignl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_floorl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_llrintl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_llroundl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_roundl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_ceill.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_nearbyintl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_lrintl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_lroundl.c: New file. * sysdeps/ieee754/ldbl-128/e_powl.c: Fix old comment. --- sysdeps/ieee754/ldbl-128ibm/s_atanl.c | 234 ++++++++++++++++++++++++++++++++++ 1 file changed, 234 insertions(+) create mode 100644 sysdeps/ieee754/ldbl-128ibm/s_atanl.c (limited to 'sysdeps/ieee754/ldbl-128ibm/s_atanl.c') diff --git a/sysdeps/ieee754/ldbl-128ibm/s_atanl.c b/sysdeps/ieee754/ldbl-128ibm/s_atanl.c new file mode 100644 index 0000000..b6195f1 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_atanl.c @@ -0,0 +1,234 @@ +/* s_atanl.c + * + * Inverse circular tangent for 128-bit long double precision + * (arctangent) + * + * + * + * SYNOPSIS: + * + * long double x, y, atanl(); + * + * y = atanl( x ); + * + * + * + * DESCRIPTION: + * + * Returns radian angle between -pi/2 and +pi/2 whose tangent is x. + * + * The function uses a rational approximation of the form + * t + t^3 P(t^2)/Q(t^2), optimized for |t| < 0.09375. + * + * The argument is reduced using the identity + * arctan x - arctan u = arctan ((x-u)/(1 + ux)) + * and an 83-entry lookup table for arctan u, with u = 0, 1/8, ..., 10.25. + * Use of the table improves the execution speed of the routine. + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -19, 19 4e5 1.7e-34 5.4e-35 + * + * + * WARNING: + * + * This program uses integer operations on bit fields of floating-point + * numbers. It does not work with data structures other than the + * structure assumed. + * + */ + +/* 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 "math_private.h" +#include + +/* arctan(k/8), k = 0, ..., 82 */ +static const long double atantbl[84] = { + 0.0000000000000000000000000000000000000000E0L, + 1.2435499454676143503135484916387102557317E-1L, /* arctan(0.125) */ + 2.4497866312686415417208248121127581091414E-1L, + 3.5877067027057222039592006392646049977698E-1L, + 4.6364760900080611621425623146121440202854E-1L, + 5.5859931534356243597150821640166127034645E-1L, + 6.4350110879328438680280922871732263804151E-1L, + 7.1882999962162450541701415152590465395142E-1L, + 7.8539816339744830961566084581987572104929E-1L, + 8.4415398611317100251784414827164750652594E-1L, + 8.9605538457134395617480071802993782702458E-1L, + 9.4200004037946366473793717053459358607166E-1L, + 9.8279372324732906798571061101466601449688E-1L, + 1.0191413442663497346383429170230636487744E0L, + 1.0516502125483736674598673120862998296302E0L, + 1.0808390005411683108871567292171998202703E0L, + 1.1071487177940905030170654601785370400700E0L, + 1.1309537439791604464709335155363278047493E0L, + 1.1525719972156675180401498626127513797495E0L, + 1.1722738811284763866005949441337046149712E0L, + 1.1902899496825317329277337748293183376012E0L, + 1.2068173702852525303955115800565576303133E0L, + 1.2220253232109896370417417439225704908830E0L, + 1.2360594894780819419094519711090786987027E0L, + 1.2490457723982544258299170772810901230778E0L, + 1.2610933822524404193139408812473357720101E0L, + 1.2722973952087173412961937498224804940684E0L, + 1.2827408797442707473628852511364955306249E0L, + 1.2924966677897852679030914214070816845853E0L, + 1.3016288340091961438047858503666855921414E0L, + 1.3101939350475556342564376891719053122733E0L, + 1.3182420510168370498593302023271362531155E0L, + 1.3258176636680324650592392104284756311844E0L, + 1.3329603993374458675538498697331558093700E0L, + 1.3397056595989995393283037525895557411039E0L, + 1.3460851583802539310489409282517796256512E0L, + 1.3521273809209546571891479413898128509842E0L, + 1.3578579772154994751124898859640585287459E0L, + 1.3633001003596939542892985278250991189943E0L, + 1.3684746984165928776366381936948529556191E0L, + 1.3734007669450158608612719264449611486510E0L, + 1.3780955681325110444536609641291551522494E0L, + 1.3825748214901258580599674177685685125566E0L, + 1.3868528702577214543289381097042486034883E0L, + 1.3909428270024183486427686943836432060856E0L, + 1.3948567013423687823948122092044222644895E0L, + 1.3986055122719575950126700816114282335732E0L, + 1.4021993871854670105330304794336492676944E0L, + 1.4056476493802697809521934019958079881002E0L, + 1.4089588955564736949699075250792569287156E0L, + 1.4121410646084952153676136718584891599630E0L, + 1.4152014988178669079462550975833894394929E0L, + 1.4181469983996314594038603039700989523716E0L, + 1.4209838702219992566633046424614466661176E0L, + 1.4237179714064941189018190466107297503086E0L, + 1.4263547484202526397918060597281265695725E0L, + 1.4288992721907326964184700745371983590908E0L, + 1.4313562697035588982240194668401779312122E0L, + 1.4337301524847089866404719096698873648610E0L, + 1.4360250423171655234964275337155008780675E0L, + 1.4382447944982225979614042479354815855386E0L, + 1.4403930189057632173997301031392126865694E0L, + 1.4424730991091018200252920599377292525125E0L, + 1.4444882097316563655148453598508037025938E0L, + 1.4464413322481351841999668424758804165254E0L, + 1.4483352693775551917970437843145232637695E0L, + 1.4501726582147939000905940595923466567576E0L, + 1.4519559822271314199339700039142990228105E0L, + 1.4536875822280323362423034480994649820285E0L, + 1.4553696664279718992423082296859928222270E0L, + 1.4570043196511885530074841089245667532358E0L, + 1.4585935117976422128825857356750737658039E0L, + 1.4601391056210009726721818194296893361233E0L, + 1.4616428638860188872060496086383008594310E0L, + 1.4631064559620759326975975316301202111560E0L, + 1.4645314639038178118428450961503371619177E0L, + 1.4659193880646627234129855241049975398470E0L, + 1.4672716522843522691530527207287398276197E0L, + 1.4685896086876430842559640450619880951144E0L, + 1.4698745421276027686510391411132998919794E0L, + 1.4711276743037345918528755717617308518553E0L, + 1.4723501675822635384916444186631899205983E0L, + 1.4735431285433308455179928682541563973416E0L, /* arctan(10.25) */ + 1.5707963267948966192313216916397514420986E0L /* pi/2 */ +}; + + +/* arctan t = t + t^3 p(t^2) / q(t^2) + |t| <= 0.09375 + peak relative error 5.3e-37 */ + +static const long double + p0 = -4.283708356338736809269381409828726405572E1L, + p1 = -8.636132499244548540964557273544599863825E1L, + p2 = -5.713554848244551350855604111031839613216E1L, + p3 = -1.371405711877433266573835355036413750118E1L, + p4 = -8.638214309119210906997318946650189640184E-1L, + q0 = 1.285112506901621042780814422948906537959E2L, + q1 = 3.361907253914337187957855834229672347089E2L, + q2 = 3.180448303864130128268191635189365331680E2L, + q3 = 1.307244136980865800160844625025280344686E2L, + q4 = 2.173623741810414221251136181221172551416E1L; + /* q5 = 1.000000000000000000000000000000000000000E0 */ + + +long double +__atanl (long double x) +{ + int k, sign; + long double t, u, p, q; + ieee854_long_double_shape_type s; + + s.value = x; + k = s.parts32.w0; + if (k & 0x80000000) + sign = 1; + else + sign = 0; + + /* Check for IEEE special cases. */ + k &= 0x7fffffff; + if (k >= 0x7ff00000) + { + /* NaN. */ + if ((k & 0xfffff) | s.parts32.w1 ) + return (x + x); + + /* Infinity. */ + if (sign) + return -atantbl[83]; + else + return atantbl[83]; + } + + if (sign) + x = -x; + + if (k >= 0x40248000) /* 10.25 */ + { + k = 83; + t = -1.0/x; + } + else + { + /* Index of nearest table element. + Roundoff to integer is asymmetrical to avoid cancellation when t < 0 + (cf. fdlibm). */ + k = 8.0 * x + 0.25; + u = 0.125 * k; + /* Small arctan argument. */ + t = (x - u) / (1.0 + x * u); + } + + /* Arctan of small argument t. */ + u = t * t; + p = ((((p4 * u) + p3) * u + p2) * u + p1) * u + p0; + q = ((((u + q4) * u + q3) * u + q2) * u + q1) * u + q0; + u = t * u * p / q + t; + + /* arctan x = arctan u + arctan t */ + u = atantbl[k] + u; + if (sign) + return (-u); + else + return u; +} + +long_double_symbol (libm, __atanl, atanl); -- cgit v1.1