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8431838dde
The dbl-64 implementation of atan2 does computations that expect to run in round-to-nearest mode, and in other modes the errors can accumulate to more than the maximum accepted 9ulp. This patch makes it use FE_TONEAREST internally, similar to other functions with such issues. Tests that previously produced large errors are added for atan2 and the closely related carg, clog and clog10 functions. Tested for x86_64 and x86 and ulps updated accordingly. [BZ #18210] [BZ #18211] * sysdeps/ieee754/dbl-64/e_atan2.c: Include <fenv.h>. (__ieee754_atan2): Set FE_TONEAREST mode for internal computations. * math/auto-libm-test-in: Add more tests of atan2, carg, clog and clog10. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
621 lines
18 KiB
C
621 lines
18 KiB
C
/*
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* IBM Accurate Mathematical Library
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* written by International Business Machines Corp.
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* Copyright (C) 2001-2015 Free Software Foundation, Inc.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with this program; if not, see <http://www.gnu.org/licenses/>.
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*/
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/************************************************************************/
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/* MODULE_NAME: atnat2.c */
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/* */
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/* FUNCTIONS: uatan2 */
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/* atan2Mp */
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/* signArctan2 */
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/* normalized */
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/* */
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/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h atnat2.h */
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/* mpatan.c mpatan2.c mpsqrt.c */
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/* uatan.tbl */
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/* */
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/* An ultimate atan2() routine. Given two IEEE double machine numbers y,*/
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/* x it computes the correctly rounded (to nearest) value of atan2(y,x).*/
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/* */
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/* Assumption: Machine arithmetic operations are performed in */
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/* round to nearest mode of IEEE 754 standard. */
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/* */
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/************************************************************************/
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#include <dla.h>
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#include "mpa.h"
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#include "MathLib.h"
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#include "uatan.tbl"
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#include "atnat2.h"
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#include <fenv.h>
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#include <float.h>
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#include <math.h>
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#include <math_private.h>
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#include <stap-probe.h>
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#ifndef SECTION
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# define SECTION
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#endif
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/************************************************************************/
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/* An ultimate atan2 routine. Given two IEEE double machine numbers y,x */
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/* it computes the correctly rounded (to nearest) value of atan2(y,x). */
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/* Assumption: Machine arithmetic operations are performed in */
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/* round to nearest mode of IEEE 754 standard. */
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/************************************************************************/
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static double atan2Mp (double, double, const int[]);
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/* Fix the sign and return after stage 1 or stage 2 */
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static double
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signArctan2 (double y, double z)
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{
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return __copysign (z, y);
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}
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static double normalized (double, double, double, double);
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void __mpatan2 (mp_no *, mp_no *, mp_no *, int);
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double
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SECTION
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__ieee754_atan2 (double y, double x)
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{
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int i, de, ux, dx, uy, dy;
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static const int pr[MM] = { 6, 8, 10, 20, 32 };
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double ax, ay, u, du, u9, ua, v, vv, dv, t1, t2, t3, t7, t8,
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z, zz, cor, s1, ss1, s2, ss2;
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#ifndef DLA_FMS
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double t4, t5, t6;
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#endif
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number num;
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static const int ep = 59768832, /* 57*16**5 */
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em = -59768832; /* -57*16**5 */
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/* x=NaN or y=NaN */
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num.d = x;
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ux = num.i[HIGH_HALF];
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dx = num.i[LOW_HALF];
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if ((ux & 0x7ff00000) == 0x7ff00000)
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{
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if (((ux & 0x000fffff) | dx) != 0x00000000)
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return x + x;
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}
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num.d = y;
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uy = num.i[HIGH_HALF];
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dy = num.i[LOW_HALF];
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if ((uy & 0x7ff00000) == 0x7ff00000)
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{
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if (((uy & 0x000fffff) | dy) != 0x00000000)
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return y + y;
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}
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/* y=+-0 */
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if (uy == 0x00000000)
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{
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if (dy == 0x00000000)
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{
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if ((ux & 0x80000000) == 0x00000000)
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return 0;
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else
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return opi.d;
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}
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}
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else if (uy == 0x80000000)
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{
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if (dy == 0x00000000)
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{
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if ((ux & 0x80000000) == 0x00000000)
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return -0.0;
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else
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return mopi.d;
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}
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}
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/* x=+-0 */
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if (x == 0)
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{
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if ((uy & 0x80000000) == 0x00000000)
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return hpi.d;
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else
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return mhpi.d;
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}
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/* x=+-INF */
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if (ux == 0x7ff00000)
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{
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if (dx == 0x00000000)
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{
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if (uy == 0x7ff00000)
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{
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if (dy == 0x00000000)
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return qpi.d;
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}
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else if (uy == 0xfff00000)
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{
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if (dy == 0x00000000)
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return mqpi.d;
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}
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else
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{
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if ((uy & 0x80000000) == 0x00000000)
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return 0;
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else
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return -0.0;
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}
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}
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}
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else if (ux == 0xfff00000)
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{
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if (dx == 0x00000000)
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{
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if (uy == 0x7ff00000)
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{
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if (dy == 0x00000000)
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return tqpi.d;
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}
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else if (uy == 0xfff00000)
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{
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if (dy == 0x00000000)
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return mtqpi.d;
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}
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else
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{
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if ((uy & 0x80000000) == 0x00000000)
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return opi.d;
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else
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return mopi.d;
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}
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}
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}
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/* y=+-INF */
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if (uy == 0x7ff00000)
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{
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if (dy == 0x00000000)
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return hpi.d;
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}
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else if (uy == 0xfff00000)
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{
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if (dy == 0x00000000)
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return mhpi.d;
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}
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SET_RESTORE_ROUND (FE_TONEAREST);
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/* either x/y or y/x is very close to zero */
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ax = (x < 0) ? -x : x;
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ay = (y < 0) ? -y : y;
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de = (uy & 0x7ff00000) - (ux & 0x7ff00000);
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if (de >= ep)
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{
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return ((y > 0) ? hpi.d : mhpi.d);
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}
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else if (de <= em)
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{
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if (x > 0)
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{
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double ret;
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if ((z = ay / ax) < TWOM1022)
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ret = normalized (ax, ay, y, z);
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else
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ret = signArctan2 (y, z);
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if (fabs (ret) < DBL_MIN)
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{
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double vret = ret ? ret : DBL_MIN;
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double force_underflow = vret * vret;
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math_force_eval (force_underflow);
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}
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return ret;
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}
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else
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{
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return ((y > 0) ? opi.d : mopi.d);
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}
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}
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/* if either x or y is extremely close to zero, scale abs(x), abs(y). */
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if (ax < twom500.d || ay < twom500.d)
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{
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ax *= two500.d;
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ay *= two500.d;
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}
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/* Likewise for large x and y. */
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if (ax > two500.d || ay > two500.d)
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{
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ax *= twom500.d;
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ay *= twom500.d;
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}
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/* x,y which are neither special nor extreme */
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if (ay < ax)
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{
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u = ay / ax;
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EMULV (ax, u, v, vv, t1, t2, t3, t4, t5);
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du = ((ay - v) - vv) / ax;
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}
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else
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{
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u = ax / ay;
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EMULV (ay, u, v, vv, t1, t2, t3, t4, t5);
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du = ((ax - v) - vv) / ay;
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}
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if (x > 0)
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{
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/* (i) x>0, abs(y)< abs(x): atan(ay/ax) */
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if (ay < ax)
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{
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if (u < inv16.d)
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{
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v = u * u;
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zz = du + u * v * (d3.d
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+ v * (d5.d
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+ v * (d7.d
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+ v * (d9.d
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+ v * (d11.d
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+ v * d13.d)))));
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if ((z = u + (zz - u1.d * u)) == u + (zz + u1.d * u))
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return signArctan2 (y, z);
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MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8);
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s1 = v * (f11.d + v * (f13.d
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+ v * (f15.d + v * (f17.d + v * f19.d))));
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ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (u, du, s2, ss2, s1, ss1, t1, t2);
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if ((z = s1 + (ss1 - u5.d * s1)) == s1 + (ss1 + u5.d * s1))
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return signArctan2 (y, z);
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return atan2Mp (x, y, pr);
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}
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i = (TWO52 + TWO8 * u) - TWO52;
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i -= 16;
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t3 = u - cij[i][0].d;
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EADD (t3, du, v, dv);
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t1 = cij[i][1].d;
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t2 = cij[i][2].d;
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zz = v * t2 + (dv * t2
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+ v * v * (cij[i][3].d
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+ v * (cij[i][4].d
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+ v * (cij[i][5].d
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+ v * cij[i][6].d))));
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if (i < 112)
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{
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if (i < 48)
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u9 = u91.d; /* u < 1/4 */
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else
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u9 = u92.d;
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} /* 1/4 <= u < 1/2 */
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else
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{
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if (i < 176)
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u9 = u93.d; /* 1/2 <= u < 3/4 */
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else
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u9 = u94.d;
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} /* 3/4 <= u <= 1 */
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if ((z = t1 + (zz - u9 * t1)) == t1 + (zz + u9 * t1))
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return signArctan2 (y, z);
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t1 = u - hij[i][0].d;
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EADD (t1, du, v, vv);
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s1 = v * (hij[i][11].d
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+ v * (hij[i][12].d
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+ v * (hij[i][13].d
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+ v * (hij[i][14].d
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+ v * hij[i][15].d))));
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ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
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if ((z = s2 + (ss2 - ub.d * s2)) == s2 + (ss2 + ub.d * s2))
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return signArctan2 (y, z);
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return atan2Mp (x, y, pr);
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}
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/* (ii) x>0, abs(x)<=abs(y): pi/2-atan(ax/ay) */
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if (u < inv16.d)
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{
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v = u * u;
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zz = u * v * (d3.d
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+ v * (d5.d
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+ v * (d7.d
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+ v * (d9.d
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+ v * (d11.d
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+ v * d13.d)))));
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ESUB (hpi.d, u, t2, cor);
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t3 = ((hpi1.d + cor) - du) - zz;
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if ((z = t2 + (t3 - u2.d)) == t2 + (t3 + u2.d))
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return signArctan2 (y, z);
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MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8);
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s1 = v * (f11.d
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+ v * (f13.d
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+ v * (f15.d + v * (f17.d + v * f19.d))));
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ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (u, du, s2, ss2, s1, ss1, t1, t2);
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SUB2 (hpi.d, hpi1.d, s1, ss1, s2, ss2, t1, t2);
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if ((z = s2 + (ss2 - u6.d)) == s2 + (ss2 + u6.d))
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return signArctan2 (y, z);
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return atan2Mp (x, y, pr);
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}
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i = (TWO52 + TWO8 * u) - TWO52;
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i -= 16;
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v = (u - cij[i][0].d) + du;
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zz = hpi1.d - v * (cij[i][2].d
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+ v * (cij[i][3].d
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+ v * (cij[i][4].d
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+ v * (cij[i][5].d
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+ v * cij[i][6].d))));
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t1 = hpi.d - cij[i][1].d;
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if (i < 112)
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ua = ua1.d; /* w < 1/2 */
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else
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ua = ua2.d; /* w >= 1/2 */
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if ((z = t1 + (zz - ua)) == t1 + (zz + ua))
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return signArctan2 (y, z);
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t1 = u - hij[i][0].d;
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EADD (t1, du, v, vv);
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s1 = v * (hij[i][11].d
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+ v * (hij[i][12].d
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+ v * (hij[i][13].d
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+ v * (hij[i][14].d
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+ v * hij[i][15].d))));
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ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
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MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
|
|
SUB2 (hpi.d, hpi1.d, s2, ss2, s1, ss1, t1, t2);
|
|
|
|
if ((z = s1 + (ss1 - uc.d)) == s1 + (ss1 + uc.d))
|
|
return signArctan2 (y, z);
|
|
return atan2Mp (x, y, pr);
|
|
}
|
|
|
|
/* (iii) x<0, abs(x)< abs(y): pi/2+atan(ax/ay) */
|
|
if (ax < ay)
|
|
{
|
|
if (u < inv16.d)
|
|
{
|
|
v = u * u;
|
|
zz = u * v * (d3.d
|
|
+ v * (d5.d
|
|
+ v * (d7.d
|
|
+ v * (d9.d
|
|
+ v * (d11.d + v * d13.d)))));
|
|
EADD (hpi.d, u, t2, cor);
|
|
t3 = ((hpi1.d + cor) + du) + zz;
|
|
if ((z = t2 + (t3 - u3.d)) == t2 + (t3 + u3.d))
|
|
return signArctan2 (y, z);
|
|
|
|
MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
s1 = v * (f11.d
|
|
+ v * (f13.d + v * (f15.d + v * (f17.d + v * f19.d))));
|
|
ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (u, du, s2, ss2, s1, ss1, t1, t2);
|
|
ADD2 (hpi.d, hpi1.d, s1, ss1, s2, ss2, t1, t2);
|
|
|
|
if ((z = s2 + (ss2 - u7.d)) == s2 + (ss2 + u7.d))
|
|
return signArctan2 (y, z);
|
|
return atan2Mp (x, y, pr);
|
|
}
|
|
|
|
i = (TWO52 + TWO8 * u) - TWO52;
|
|
i -= 16;
|
|
v = (u - cij[i][0].d) + du;
|
|
zz = hpi1.d + v * (cij[i][2].d
|
|
+ v * (cij[i][3].d
|
|
+ v * (cij[i][4].d
|
|
+ v * (cij[i][5].d
|
|
+ v * cij[i][6].d))));
|
|
t1 = hpi.d + cij[i][1].d;
|
|
if (i < 112)
|
|
ua = ua1.d; /* w < 1/2 */
|
|
else
|
|
ua = ua2.d; /* w >= 1/2 */
|
|
if ((z = t1 + (zz - ua)) == t1 + (zz + ua))
|
|
return signArctan2 (y, z);
|
|
|
|
t1 = u - hij[i][0].d;
|
|
EADD (t1, du, v, vv);
|
|
s1 = v * (hij[i][11].d
|
|
+ v * (hij[i][12].d
|
|
+ v * (hij[i][13].d
|
|
+ v * (hij[i][14].d
|
|
+ v * hij[i][15].d))));
|
|
ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
|
|
ADD2 (hpi.d, hpi1.d, s2, ss2, s1, ss1, t1, t2);
|
|
|
|
if ((z = s1 + (ss1 - uc.d)) == s1 + (ss1 + uc.d))
|
|
return signArctan2 (y, z);
|
|
return atan2Mp (x, y, pr);
|
|
}
|
|
|
|
/* (iv) x<0, abs(y)<=abs(x): pi-atan(ax/ay) */
|
|
if (u < inv16.d)
|
|
{
|
|
v = u * u;
|
|
zz = u * v * (d3.d
|
|
+ v * (d5.d
|
|
+ v * (d7.d
|
|
+ v * (d9.d + v * (d11.d + v * d13.d)))));
|
|
ESUB (opi.d, u, t2, cor);
|
|
t3 = ((opi1.d + cor) - du) - zz;
|
|
if ((z = t2 + (t3 - u4.d)) == t2 + (t3 + u4.d))
|
|
return signArctan2 (y, z);
|
|
|
|
MUL2 (u, du, u, du, v, vv, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
s1 = v * (f11.d + v * (f13.d + v * (f15.d + v * (f17.d + v * f19.d))));
|
|
ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
MUL2 (u, du, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (u, du, s2, ss2, s1, ss1, t1, t2);
|
|
SUB2 (opi.d, opi1.d, s1, ss1, s2, ss2, t1, t2);
|
|
|
|
if ((z = s2 + (ss2 - u8.d)) == s2 + (ss2 + u8.d))
|
|
return signArctan2 (y, z);
|
|
return atan2Mp (x, y, pr);
|
|
}
|
|
|
|
i = (TWO52 + TWO8 * u) - TWO52;
|
|
i -= 16;
|
|
v = (u - cij[i][0].d) + du;
|
|
zz = opi1.d - v * (cij[i][2].d
|
|
+ v * (cij[i][3].d
|
|
+ v * (cij[i][4].d
|
|
+ v * (cij[i][5].d + v * cij[i][6].d))));
|
|
t1 = opi.d - cij[i][1].d;
|
|
if (i < 112)
|
|
ua = ua1.d; /* w < 1/2 */
|
|
else
|
|
ua = ua2.d; /* w >= 1/2 */
|
|
if ((z = t1 + (zz - ua)) == t1 + (zz + ua))
|
|
return signArctan2 (y, z);
|
|
|
|
t1 = u - hij[i][0].d;
|
|
|
|
EADD (t1, du, v, vv);
|
|
|
|
s1 = v * (hij[i][11].d
|
|
+ v * (hij[i][12].d
|
|
+ v * (hij[i][13].d
|
|
+ v * (hij[i][14].d + v * hij[i][15].d))));
|
|
|
|
ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
|
|
SUB2 (opi.d, opi1.d, s2, ss2, s1, ss1, t1, t2);
|
|
|
|
if ((z = s1 + (ss1 - uc.d)) == s1 + (ss1 + uc.d))
|
|
return signArctan2 (y, z);
|
|
return atan2Mp (x, y, pr);
|
|
}
|
|
|
|
#ifndef __ieee754_atan2
|
|
strong_alias (__ieee754_atan2, __atan2_finite)
|
|
#endif
|
|
|
|
/* Treat the Denormalized case */
|
|
static double
|
|
SECTION
|
|
normalized (double ax, double ay, double y, double z)
|
|
{
|
|
int p;
|
|
mp_no mpx, mpy, mpz, mperr, mpz2, mpt1;
|
|
p = 6;
|
|
__dbl_mp (ax, &mpx, p);
|
|
__dbl_mp (ay, &mpy, p);
|
|
__dvd (&mpy, &mpx, &mpz, p);
|
|
__dbl_mp (ue.d, &mpt1, p);
|
|
__mul (&mpz, &mpt1, &mperr, p);
|
|
__sub (&mpz, &mperr, &mpz2, p);
|
|
__mp_dbl (&mpz2, &z, p);
|
|
return signArctan2 (y, z);
|
|
}
|
|
|
|
/* Stage 3: Perform a multi-Precision computation */
|
|
static double
|
|
SECTION
|
|
atan2Mp (double x, double y, const int pr[])
|
|
{
|
|
double z1, z2;
|
|
int i, p;
|
|
mp_no mpx, mpy, mpz, mpz1, mpz2, mperr, mpt1;
|
|
for (i = 0; i < MM; i++)
|
|
{
|
|
p = pr[i];
|
|
__dbl_mp (x, &mpx, p);
|
|
__dbl_mp (y, &mpy, p);
|
|
__mpatan2 (&mpy, &mpx, &mpz, p);
|
|
__dbl_mp (ud[i].d, &mpt1, p);
|
|
__mul (&mpz, &mpt1, &mperr, p);
|
|
__add (&mpz, &mperr, &mpz1, p);
|
|
__sub (&mpz, &mperr, &mpz2, p);
|
|
__mp_dbl (&mpz1, &z1, p);
|
|
__mp_dbl (&mpz2, &z2, p);
|
|
if (z1 == z2)
|
|
{
|
|
LIBC_PROBE (slowatan2, 4, &p, &x, &y, &z1);
|
|
return z1;
|
|
}
|
|
}
|
|
LIBC_PROBE (slowatan2_inexact, 4, &p, &x, &y, &z1);
|
|
return z1; /*if impossible to do exact computing */
|
|
}
|