about summary refs log tree commit diff
path: root/sysdeps/ieee754/dbl-64/e_atan2.c
blob: 4d8c23af954433a93d7d4922eb243004414bee3b (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
/*
 * IBM Accurate Mathematical Library
 * written by International Business Machines Corp.
 * Copyright (C) 2001, 2011 Free Software Foundation
 *
 * This program 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 program 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 program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
 */
/************************************************************************/
/*  MODULE_NAME: atnat2.c                                               */
/*                                                                      */
/*  FUNCTIONS: uatan2                                                   */
/*             atan2Mp                                                  */
/*             signArctan2                                              */
/*             normalized                                               */
/*                                                                      */
/*  FILES NEEDED: dla.h endian.h mpa.h mydefs.h atnat2.h                */
/*                mpatan.c mpatan2.c mpsqrt.c                           */
/*                uatan.tbl                                             */
/*                                                                      */
/* An ultimate atan2() routine. Given two IEEE double machine numbers y,*/
/* x it computes the correctly rounded (to nearest) value of atan2(y,x).*/
/*                                                                      */
/* Assumption: Machine arithmetic operations are performed in           */
/* round to nearest mode of IEEE 754 standard.                          */
/*                                                                      */
/************************************************************************/

#include "dla.h"
#include "mpa.h"
#include "MathLib.h"
#include "uatan.tbl"
#include "atnat2.h"
#include "math_private.h"

/************************************************************************/
/* An ultimate atan2 routine. Given two IEEE double machine numbers y,x */
/* it computes the correctly rounded (to nearest) value of atan2(y,x).  */
/* Assumption: Machine arithmetic operations are performed in           */
/* round to nearest mode of IEEE 754 standard.                          */
/************************************************************************/
static double atan2Mp(double ,double ,const int[]);
static double signArctan2(double ,double);
static double normalized(double ,double,double ,double);
void __mpatan2(mp_no *,mp_no *,mp_no *,int);

double __ieee754_atan2(double y,double x) {

  int i,de,ux,dx,uy,dy;
#if 0
  int p;
#endif
  static const int pr[MM]={6,8,10,20,32};
  double ax,ay,u,du,u9,ua,v,vv,dv,t1,t2,t3,t7,t8,
	 z,zz,cor,s1,ss1,s2,ss2;
#ifndef DLA_FMA
  double t4,t5,t6;
#endif
#if 0
  double z1,z2;
#endif
  number num;
#if 0
  mp_no mperr,mpt1,mpx,mpy,mpz,mpz1,mpz2;
#endif

  static const int ep= 59768832,   /*  57*16**5   */
		   em=-59768832;   /* -57*16**5   */

  /* x=NaN or y=NaN */
  num.d = x;  ux = num.i[HIGH_HALF];  dx = num.i[LOW_HALF];
  if   ((ux&0x7ff00000)    ==0x7ff00000) {
    if (((ux&0x000fffff)|dx)!=0x00000000) return x+x; }
  num.d = y;  uy = num.i[HIGH_HALF];  dy = num.i[LOW_HALF];
  if   ((uy&0x7ff00000)    ==0x7ff00000) {
    if (((uy&0x000fffff)|dy)!=0x00000000) return y+y; }

  /* y=+-0 */
  if      (uy==0x00000000) {
    if    (dy==0x00000000) {
      if  ((ux&0x80000000)==0x00000000)  return ZERO;
      else                               return opi.d; } }
  else if (uy==0x80000000) {
    if    (dy==0x00000000) {
      if  ((ux&0x80000000)==0x00000000)  return MZERO;
      else                               return mopi.d;} }

  /* x=+-0 */
  if (x==ZERO) {
    if ((uy&0x80000000)==0x00000000)     return hpi.d;
    else                                 return mhpi.d; }

  /* x=+-INF */
  if          (ux==0x7ff00000) {
    if        (dx==0x00000000) {
      if      (uy==0x7ff00000) {
	if    (dy==0x00000000)  return qpi.d; }
      else if (uy==0xfff00000) {
	if    (dy==0x00000000)  return mqpi.d; }
      else {
	if    ((uy&0x80000000)==0x00000000)  return ZERO;
	else                                 return MZERO; }
    }
  }
  else if     (ux==0xfff00000) {
    if        (dx==0x00000000) {
      if      (uy==0x7ff00000) {
	if    (dy==0x00000000)  return tqpi.d; }
      else if (uy==0xfff00000) {
	if    (dy==0x00000000)  return mtqpi.d; }
      else                     {
	if    ((uy&0x80000000)==0x00000000)  return opi.d;
	else                                 return mopi.d; }
    }
  }

  /* y=+-INF */
  if      (uy==0x7ff00000) {
    if    (dy==0x00000000)  return hpi.d; }
  else if (uy==0xfff00000) {
    if    (dy==0x00000000)  return mhpi.d; }

  /* either x/y or y/x is very close to zero */
  ax = (x<ZERO) ? -x : x;    ay = (y<ZERO) ? -y : y;
  de = (uy & 0x7ff00000) - (ux & 0x7ff00000);
  if      (de>=ep)  { return ((y>ZERO) ? hpi.d : mhpi.d); }
  else if (de<=em)  {
    if    (x>ZERO)  {
      if  ((z=ay/ax)<TWOM1022)  return normalized(ax,ay,y,z);
      else                      return signArctan2(y,z); }
    else            { return ((y>ZERO) ? opi.d : mopi.d); } }

  /* if either x or y is extremely close to zero, scale abs(x), abs(y). */
  if (ax<twom500.d || ay<twom500.d) { ax*=two500.d;  ay*=two500.d; }

  /* x,y which are neither special nor extreme */
  if (ay<ax) {
    u=ay/ax;
    EMULV(ax,u,v,vv,t1,t2,t3,t4,t5)
    du=((ay-v)-vv)/ax; }
  else {
    u=ax/ay;
    EMULV(ay,u,v,vv,t1,t2,t3,t4,t5)
    du=((ax-v)-vv)/ay; }

  if (x>ZERO) {

    /* (i)   x>0, abs(y)< abs(x):  atan(ay/ax) */
    if (ay<ax) {
      if (u<inv16.d) {
	v=u*u;  zz=du+u*v*(d3.d+v*(d5.d+v*(d7.d+v*(d9.d+v*(d11.d+v*d13.d)))));
	if ((z=u+(zz-u1.d*u)) == u+(zz+u1.d*u))  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,ZERO,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)
	if ((z=s1+(ss1-u5.d*s1)) == s1+(ss1+u5.d*s1))  return signArctan2(y,z);
	return atan2Mp(x,y,pr);
      }
      else {
	i=(TWO52+TWO8*u)-TWO52;  i-=16;
	t3=u-cij[i][0].d;
	EADD(t3,du,v,dv)
	t1=cij[i][1].d;  t2=cij[i][2].d;
	zz=v*t2+(dv*t2+v*v*(cij[i][3].d+v*(cij[i][4].d+
			 v*(cij[i][5].d+v* cij[i][6].d))));
	if (i<112) {
	  if (i<48)  u9=u91.d;    /* u < 1/4        */
	  else       u9=u92.d; }  /* 1/4 <= u < 1/2 */
	else {
	  if (i<176) u9=u93.d;    /* 1/2 <= u < 3/4 */
	  else       u9=u94.d; }  /* 3/4 <= u <= 1  */
	if ((z=t1+(zz-u9*t1)) == t1+(zz+u9*t1))  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,ZERO,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)
	if ((z=s2+(ss2-ub.d*s2)) == s2+(ss2+ub.d*s2))  return signArctan2(y,z);
	return atan2Mp(x,y,pr);
      }
    }

    /* (ii)  x>0, abs(x)<=abs(y):  pi/2-atan(ax/ay) */
    else {
      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(hpi.d,u,t2,cor)
	t3=((hpi1.d+cor)-du)-zz;
	if ((z=t2+(t3-u2.d)) == t2+(t3+u2.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,ZERO,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(hpi.d,hpi1.d,s1,ss1,s2,ss2,t1,t2)
	if ((z=s2+(ss2-u6.d)) == s2+(ss2+u6.d))  return signArctan2(y,z);
	return atan2Mp(x,y,pr);
      }
      else {
	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,ZERO,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(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);
      }
    }
  }
  else {

    /* (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,ZERO,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);
      }
      else {
	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,ZERO,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) */
    else {
      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,ZERO,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);
      }
      else {
	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,ZERO,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);
      }
    }
  }
}
strong_alias (__ieee754_atan2, __atan2_finite)

  /* Treat the Denormalized case */
static double  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);
}
  /* Fix the sign and return after stage 1 or stage 2 */
static double signArctan2(double y,double z)
{
  return ((y<ZERO) ? -z : z);
}
  /* Stage 3: Perform a multi-Precision computation */
static double  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)   return z1;
  }
  return z1; /*if unpossible to do exact computing */
}