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authorRoland McGrath <roland@gnu.org>2006-01-28 00:15:15 +0000
committerRoland McGrath <roland@gnu.org>2006-01-28 00:15:15 +0000
commitf964490f3c4f094fd684960c2e98885b23e31376 (patch)
treee10f697bd55240b9be7a9c1a5109ee07893d3136 /sysdeps/ieee754/ldbl-128ibm/s_atanl.c
parentd421a7801d1bdfd8175e53a79068833ae4de56b1 (diff)
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2006-01-27 Dwayne Grant McConnell <decimal@us.ibm.com> cvs/fedora-glibc-20060130T0922
	    Jakub Jelinek  <jakub@redhat.com>
	    Roland McGrath  <roland@redhat.com>
	    Steven Munroe  <sjmunroe@us.ibm.com>
	    Alan Modra  <amodra@bigpond.net.au>

	* 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.
Diffstat (limited to 'sysdeps/ieee754/ldbl-128ibm/s_atanl.c')
-rw-r--r--sysdeps/ieee754/ldbl-128ibm/s_atanl.c234
1 files changed, 234 insertions, 0 deletions
diff --git a/sysdeps/ieee754/ldbl-128ibm/s_atanl.c b/sysdeps/ieee754/ldbl-128ibm/s_atanl.c
new file mode 100644
index 0000000000..b6195f10be
--- /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 <moshier@na-net.ornl.gov>
+
+    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 <math_ldbl_opt.h>
+
+/* 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);