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[glibc.git] / sysdeps / ia64 / fpu / e_atan2.S
1 .file "atan2.s"
2
3
4 // Copyright (c) 2000 - 2003, Intel Corporation
5 // All rights reserved.
6 //
7 //
8 // Redistribution and use in source and binary forms, with or without
9 // modification, are permitted provided that the following conditions are
10 // met:
11 //
12 // * Redistributions of source code must retain the above copyright
13 // notice, this list of conditions and the following disclaimer.
14 //
15 // * Redistributions in binary form must reproduce the above copyright
16 // notice, this list of conditions and the following disclaimer in the
17 // documentation and/or other materials provided with the distribution.
18 //
19 // * The name of Intel Corporation may not be used to endorse or promote
20 // products derived from this software without specific prior written
21 // permission.
22
23 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
24 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
25 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
26 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
27 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
28 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
29 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
30 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
31 // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
32 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
33 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
34 //
35 // Intel Corporation is the author of this code, and requests that all
36 // problem reports or change requests be submitted to it directly at
37 // http://www.intel.com/software/products/opensource/libraries/num.htm.
38 //
39 // History
40 //==============================================================
41 // 02/02/00 Initial version
42 // 04/04/00 Unwind support added
43 // 08/15/00 Bundle added after call to __libm_error_support to properly
44 // set [the previously overwritten] GR_Parameter_RESULT.
45 // 08/17/00 Changed predicate register macro-usage to direct predicate
46 // names due to an assembler bug.
47 // 09/28/00 Updated to set invalid on SNaN inputs
48 // 01/19/01 Fixed flags for small results
49 // 04/13/01 Rescheduled to make all paths faster
50 // 05/20/02 Cleaned up namespace and sf0 syntax
51 // 08/20/02 Corrected inexact flag and directed rounding symmetry bugs
52 // 02/06/03 Reordered header: .section, .global, .proc, .align
53 // 04/17/03 Added missing mutex directive
54 // 12/23/03 atan2(NaN1,NaN2) now QNaN1, for consistency with atan2f, atan2l
55 //
56 // API
57 //==============================================================
58 // double atan2(double Y, double X)
59 //
60 // Overview of operation
61 //==============================================================
62 //
63 // The atan2 function returns values in the interval [-pi,+pi].
64 //
65 // There are two basic paths: swap true and swap false.
66 // atan2(Y,X) ==> atan2(V/U) where U >= V. If Y > X, we must swap.
67 //
68 // p6 swap True |Y| > |X|
69 // p7 swap False |Y| <= |X|
70 // p8 X+ (If swap=True p8=p9=0)
71 // p9 X-
72 //
73 // all the other predicates p10 thru p15 are false for the main path
74 //
75 // Simple trigonometric identities show
76 // Region 1 (-45 to +45 degrees):
77 // X>0, |Y|<=X, V=Y, U=X atan2(Y,X) = sgnY * (0 + atan(V/U))
78 //
79 // Region 2 (-90 to -45 degrees, and +45 to +90 degrees):
80 // X>0, |Y|>X, V=X, U=Y atan2(Y,X) = sgnY * (pi/2 - atan(V/U))
81 //
82 // Region 3 (-135 to -90 degrees, and +90 to +135 degrees):
83 // X<0, |Y|>X, V=X, U=Y atan2(Y,X) = sgnY * (pi/2 + atan(V/U))
84 //
85 // Region 4 (-180 to -135 degrees, and +135 to +180 degrees):
86 // X<0, |Y|<=X, V=Y, U=X atan2(Y,X) = sgnY * (pi - atan(V/U))
87 //
88 // So the result is always of the form atan2(Y,X) = P + sgnXY * atan(V/U)
89 //
90 // We compute atan(V/U) from the identity
91 // atan(z) + atan([(V/U)-z] / [1+(V/U)z])
92 // where z is a limited precision approximation (16 bits) to V/U
93 //
94 // z is calculated with the assistance of the frcpa instruction.
95 //
96 // atan(z) is calculated by a polynomial z + z^3 * p(w), w=z^2
97 // where p(w) = P0+P1*w+...+P22*w^22
98 //
99 // Let d = [(V/U)-z] / [1+(V/U)z]) = (V-U*z)/(U+V*z)
100 //
101 // Approximate atan(d) by d + P0*d^3
102 // Let F = 1/(U+V*z) * (1-a), where |a|< 2^-8.8.
103 // Compute q(a) = 1 + a + ... + a^5.
104 // Then F*q(a) approximates the reciprocal to more than 50 bits.
105
106 // Special values
107 //==============================================================
108 // Y x Result
109 // +number +inf +0
110 // -number +inf -0
111 // +number -inf +pi
112 // -number -inf -pi
113 //
114 // +inf +number +pi/2
115 // -inf +number -pi/2
116 // +inf -number +pi/2
117 // -inf -number -pi/2
118 //
119 // +inf +inf +pi/4
120 // -inf +inf -pi/4
121 // +inf -inf +3pi/4
122 // -inf -inf -3pi/4
123 //
124 // +1 +1 +pi/4
125 // -1 +1 -pi/4
126 // +1 -1 +3pi/4
127 // -1 -1 -3pi/4
128 //
129 // +number +0 +pi/2
130 // -number +0 -pi/2
131 // +number -0 +pi/2
132 // -number -0 -pi/2
133 //
134 // +0 +number +0
135 // -0 +number -0
136 // +0 -number +pi
137 // -0 -number -pi
138 //
139 // +0 +0 +0
140 // -0 +0 -0
141 // +0 -0 +pi
142 // -0 -0 -pi
143 //
144 // Nan anything quiet Y
145 // Not NaN NaN quiet X
146
147 // atan2(+-0/+-0) sets double error tag to 37
148
149 // Registers used
150 //==============================================================
151
152 // predicate registers used:
153 // p6 -> p15
154
155 // floating-point registers used:
156 // f8, f9 input
157 // f32 -> f119
158
159 // general registers used
160 // r32 -> r41
161
162 // Assembly macros
163 //==============================================================
164
165 EXP_AD_P1 = r33
166 EXP_AD_P2 = r34
167 rsig_near_one = r35
168
169
170 GR_SAVE_B0 = r35
171 GR_SAVE_GP = r36
172 GR_SAVE_PFS = r37
173
174 GR_Parameter_X = r38
175 GR_Parameter_Y = r39
176 GR_Parameter_RESULT = r40
177 atan2_GR_tag = r41
178
179 atan2_Y = f8
180 atan2_X = f9
181
182 atan2_u1_X = f32
183 atan2_u1_Y = f33
184 atan2_z2_X = f34
185 atan2_z2_Y = f35
186
187 atan2_two = f36
188 atan2_B1sq_Y = f37
189 atan2_z1_X = f38
190 atan2_z1_Y = f39
191 atan2_B1X = f40
192
193 atan2_B1Y = f41
194 atan2_wp_X = f42
195 atan2_B1sq_X = f43
196 atan2_z = f44
197 atan2_w = f45
198
199 atan2_P0 = f46
200 atan2_P1 = f47
201 atan2_P2 = f48
202 atan2_P3 = f49
203 atan2_P4 = f50
204
205 atan2_P5 = f51
206 atan2_P6 = f52
207 atan2_P7 = f53
208 atan2_P8 = f54
209 atan2_P9 = f55
210
211 atan2_P10 = f56
212 atan2_P11 = f57
213 atan2_P12 = f58
214 atan2_P13 = f59
215 atan2_P14 = f60
216
217 atan2_P15 = f61
218 atan2_P16 = f62
219 atan2_P17 = f63
220 atan2_P18 = f64
221 atan2_P19 = f65
222
223 atan2_P20 = f66
224 atan2_P21 = f67
225 atan2_P22 = f68
226 atan2_tmp = f68
227 atan2_pi_by_2 = f69
228 atan2_sgn_pi_by_2 = f69
229 atan2_V13 = f70
230
231 atan2_W11 = f71
232 atan2_E = f72
233 atan2_wp_Y = f73
234 atan2_V11 = f74
235 atan2_V12 = f75
236
237 atan2_V7 = f76
238 atan2_V8 = f77
239 atan2_W7 = f78
240 atan2_W8 = f79
241 atan2_W3 = f80
242
243 atan2_W4 = f81
244 atan2_V3 = f82
245 atan2_V4 = f83
246 atan2_F = f84
247 atan2_gV = f85
248
249 atan2_V10 = f86
250 atan2_zcub = f87
251 atan2_V6 = f88
252 atan2_V9 = f89
253 atan2_W10 = f90
254
255 atan2_W6 = f91
256 atan2_W2 = f92
257 atan2_V2 = f93
258 atan2_alpha = f94
259 atan2_alpha_1 = f95
260
261 atan2_gVF = f96
262 atan2_V5 = f97
263 atan2_W12 = f98
264 atan2_W5 = f99
265 atan2_alpha_sq = f100
266
267 atan2_Cp = f101
268 atan2_V1 = f102
269 atan2_ysq = f103
270 atan2_W1 = f104
271 atan2_alpha_cub = f105
272
273 atan2_C = f106
274 atan2_xsq = f107
275 atan2_d = f108
276 atan2_A_hi = f109
277 atan2_dsq = f110
278
279 atan2_pd = f111
280 atan2_A_lo = f112
281 atan2_A = f113
282 atan2_Pp = f114
283 atan2_sgnY = f115
284
285 atan2_sig_near_one = f116
286 atan2_near_one = f116
287 atan2_pi = f117
288 atan2_sgn_pi = f117
289 atan2_3pi_by_4 = f118
290 atan2_pi_by_4 = f119
291
292
293 /////////////////////////////////////////////////////////////
294
295
296 RODATA
297
298 .align 16
299
300 LOCAL_OBJECT_START(atan2_tb1)
301 data8 0xA21922DC45605EA1 , 0x00003FFA // P11
302 data8 0xB199DD6D2675C40F , 0x0000BFFA // P10
303 data8 0xC2F01E5DDD100DBE , 0x00003FFA // P9
304 data8 0xD78F28FC2A592781 , 0x0000BFFA // P8
305 data8 0xF0F03ADB3FC930D3 , 0x00003FFA // P7
306 data8 0x88887EBB209E3543 , 0x0000BFFB // P6
307 data8 0x9D89D7D55C3287A5 , 0x00003FFB // P5
308 data8 0xBA2E8B9793955C77 , 0x0000BFFB // P4
309 data8 0xE38E38E320A8A098 , 0x00003FFB // P3
310 data8 0x9249249247E37913 , 0x0000BFFC // P2
311 data8 0xCCCCCCCCCCC906CD , 0x00003FFC // P1
312 data8 0xAAAAAAAAAAAAA8A9 , 0x0000BFFD // P0
313 data8 0xC90FDAA22168C235 , 0x00004000 // pi
314 LOCAL_OBJECT_END(atan2_tb1)
315
316 LOCAL_OBJECT_START(atan2_tb2)
317 data8 0xCE585A259BD8374C , 0x00003FF0 // P21
318 data8 0x9F90FB984D8E39D0 , 0x0000BFF3 // P20
319 data8 0x9D3436AABE218776 , 0x00003FF5 // P19
320 data8 0xDEC343E068A6D2A8 , 0x0000BFF6 // P18
321 data8 0xF396268151CFB11C , 0x00003FF7 // P17
322 data8 0xD818B4BB43D84BF2 , 0x0000BFF8 // P16
323 data8 0xA2270D30A90AA220 , 0x00003FF9 // P15
324 data8 0xD5F4F2182E7A8725 , 0x0000BFF9 // P14
325 data8 0x80D601879218B53A , 0x00003FFA // P13
326 data8 0x9297B23CCFFB291F , 0x0000BFFA // P12
327 data8 0xFE7E52D2A89995B3 , 0x0000BFEC // P22
328 data8 0xC90FDAA22168C235 , 0x00003FFF // pi/2
329 data8 0xC90FDAA22168C235 , 0x00003FFE // pi/4
330 data8 0x96cbe3f9990e91a8 , 0x00004000 // 3pi/4
331 LOCAL_OBJECT_END(atan2_tb2)
332
333
334
335
336 .section .text
337 GLOBAL_IEEE754_ENTRY(atan2)
338
339 { .mfi
340 alloc r32 = ar.pfs,1,5,4,0
341 frcpa.s1 atan2_u1_X,p6 = f1,atan2_X
342 nop.i 999
343 }
344 { .mfi
345 addl EXP_AD_P1 = @ltoff(atan2_tb1), gp
346 fma.s1 atan2_two = f1,f1,f1
347 nop.i 999
348 ;;
349 }
350
351 { .mfi
352 ld8 EXP_AD_P1 = [EXP_AD_P1]
353 frcpa.s1 atan2_u1_Y,p7 = f1,atan2_Y
354 nop.i 999
355 }
356 { .mfi
357 nop.m 999
358 fma.s1 atan2_xsq = atan2_X,atan2_X,f0
359 nop.i 999
360 ;;
361 }
362
363 { .mfi
364 nop.m 999
365 fclass.m p10,p0 = atan2_Y, 0xc3 // Test for y=nan
366 nop.i 999
367 }
368 { .mfi
369 nop.m 999
370 fma.s1 atan2_ysq = atan2_Y,atan2_Y,f0
371 nop.i 999
372 }
373 ;;
374
375 { .mfi
376 add EXP_AD_P2 = 0xd0,EXP_AD_P1
377 fclass.m p12,p0 = atan2_X, 0xc3 // Test for x nan
378 nop.i 999
379 }
380 ;;
381
382
383 // p10 Y NAN, quiet and return
384 { .mfi
385 ldfe atan2_P11 = [EXP_AD_P1],16
386 fmerge.s atan2_sgnY = atan2_Y,f1
387 nop.i 999
388 }
389 { .mfb
390 ldfe atan2_P21 = [EXP_AD_P2],16
391 (p10) fma.d.s0 f8 = atan2_X,atan2_Y,f0 // If y=nan, result quietized y
392 (p10) br.ret.spnt b0 // Exit if y=nan
393 ;;
394 }
395
396
397 { .mfi
398 ldfe atan2_P10 = [EXP_AD_P1],16
399 fma.s1 atan2_z1_X = atan2_u1_X, atan2_Y, f0
400 nop.i 999
401 }
402 { .mfi
403 ldfe atan2_P20 = [EXP_AD_P2],16
404 fnma.s1 atan2_B1X = atan2_u1_X, atan2_X, atan2_two
405 nop.i 999
406 ;;
407 }
408
409 { .mfi
410 ldfe atan2_P9 = [EXP_AD_P1],16
411 fma.s1 atan2_z1_Y = atan2_u1_Y, atan2_X, f0
412 nop.i 999
413 }
414 { .mfi
415 ldfe atan2_P19 = [EXP_AD_P2],16
416 fnma.s1 atan2_B1Y = atan2_u1_Y, atan2_Y, atan2_two
417 nop.i 999
418 }
419 ;;
420
421 { .mfi
422 ldfe atan2_P8 = [EXP_AD_P1],16
423 fma.s1 atan2_z2_X = atan2_u1_X, atan2_ysq, f0
424 nop.i 999
425 }
426 { .mfi
427 ldfe atan2_P18 = [EXP_AD_P2],16
428 fma.s1 atan2_z2_Y = atan2_u1_Y, atan2_xsq, f0
429 nop.i 999
430 }
431 ;;
432
433 // p10 ==> x inf y ?
434 // p11 ==> x !inf y ?
435 { .mfi
436 ldfe atan2_P7 = [EXP_AD_P1],16
437 fclass.m p10,p11 = atan2_X, 0x23 // test for x inf
438 nop.i 999
439 }
440 { .mfb
441 ldfe atan2_P17 = [EXP_AD_P2],16
442 (p12) fma.d.s0 f8 = atan2_X,atan2_Y,f0 // If x nan, result quiet x
443 (p12) br.ret.spnt b0 // Exit for x nan
444 ;;
445 }
446
447 // p6 true if swap, means |y| > |x| or ysq > xsq
448 // p7 true if no swap, means |x| >= |y| or xsq >= ysq
449 { .mmf
450 ldfe atan2_P6 = [EXP_AD_P1],16
451 ldfe atan2_P16 = [EXP_AD_P2],16
452 fcmp.ge.s1 p7,p6 = atan2_xsq, atan2_ysq
453 ;;
454 }
455
456 { .mfi
457 ldfe atan2_P5 = [EXP_AD_P1],16
458 fma.s1 atan2_wp_X = atan2_z1_X, atan2_z1_X, f0
459 nop.i 999
460 }
461 { .mfi
462 ldfe atan2_P15 = [EXP_AD_P2],16
463 fma.s1 atan2_B1sq_X = atan2_B1X, atan2_B1X, f0
464 nop.i 999
465 ;;
466 }
467
468 { .mfi
469 ldfe atan2_P4 = [EXP_AD_P1],16
470 (p6) fma.s1 atan2_wp_Y = atan2_z1_Y, atan2_z1_Y, f0
471 nop.i 999
472 }
473 { .mfi
474 ldfe atan2_P14 = [EXP_AD_P2],16
475 (p6) fma.s1 atan2_B1sq_Y = atan2_B1Y, atan2_B1Y, f0
476 nop.i 999
477 ;;
478 }
479
480 { .mfi
481 ldfe atan2_P3 = [EXP_AD_P1],16
482 (p6) fma.s1 atan2_E = atan2_z2_Y, atan2_B1Y, atan2_Y
483 nop.i 999
484 }
485 { .mfi
486 ldfe atan2_P13 = [EXP_AD_P2],16
487 (p7) fma.s1 atan2_E = atan2_z2_X, atan2_B1X, atan2_X
488 nop.i 999
489 ;;
490 }
491
492
493 { .mfi
494 ldfe atan2_P2 = [EXP_AD_P1],16
495 (p6) fma.s1 atan2_z = atan2_z1_Y, atan2_B1Y, f0
496 nop.i 999
497 }
498 { .mfi
499 ldfe atan2_P12 = [EXP_AD_P2],16
500 (p7) fma.s1 atan2_z = atan2_z1_X, atan2_B1X, f0
501 nop.i 999
502 ;;
503 }
504
505
506 { .mfi
507 ldfe atan2_P1 = [EXP_AD_P1],16
508 fcmp.eq.s0 p14,p15=atan2_X,atan2_Y // Dummy for denorm and invalid
509 nop.i 999
510 }
511 { .mlx
512 ldfe atan2_P22 = [EXP_AD_P2],16
513 movl rsig_near_one = 0x8000000000000001 // signif near 1.0
514 ;;
515 }
516
517
518 // p12 ==> x inf y inf
519 // p13 ==> x inf y !inf
520 { .mmf
521 ldfe atan2_P0 = [EXP_AD_P1],16
522 ldfe atan2_pi_by_2 = [EXP_AD_P2],16
523 (p10) fclass.m.unc p12,p13 = atan2_Y, 0x23 // x inf, test if y inf
524 ;;
525 }
526
527 { .mfi
528 ldfe atan2_pi = [EXP_AD_P1],16
529 (p6) fma.s1 atan2_w = atan2_wp_Y, atan2_B1sq_Y,f0
530 nop.i 999
531 }
532 { .mfi
533 ldfe atan2_pi_by_4 = [EXP_AD_P2],16
534 (p7) fma.s1 atan2_w = atan2_wp_X, atan2_B1sq_X,f0
535 nop.i 999
536 ;;
537 }
538
539 { .mfi
540 ldfe atan2_3pi_by_4 = [EXP_AD_P2],16
541 (p11) fclass.m.unc p9,p0 = atan2_Y, 0x23 // x not inf, test if y inf
542 nop.i 999
543 ;;
544 }
545
546 { .mfi
547 setf.sig atan2_sig_near_one = rsig_near_one
548 (p12) fcmp.gt.unc.s1 p10,p11 = atan2_X,f0 // x inf, y inf, test if x +inf
549 nop.i 999
550 }
551 { .mfi
552 nop.m 999
553 (p6) fnma.s1 atan2_gV = atan2_Y, atan2_z, atan2_X
554 nop.i 999
555 ;;
556 }
557
558 { .mfi
559 nop.m 999
560 frcpa.s1 atan2_F,p0 = f1, atan2_E
561 nop.i 999
562 }
563 { .mfi
564 nop.m 999
565 (p7) fnma.s1 atan2_gV = atan2_X, atan2_z, atan2_Y
566 nop.i 999
567 ;;
568 }
569
570 // p13 ==> x inf y !inf
571 { .mfi
572 nop.m 999
573 (p13) fcmp.gt.unc.s1 p14,p15 = atan2_X,f0 // x inf, y !inf, test if x +inf
574 nop.i 999
575 }
576 { .mfb
577 nop.m 999
578 (p9) fma.d.s0 f8 = atan2_sgnY, atan2_pi_by_2, f0 // +-pi/2 if x !inf, y inf
579 (p9) br.ret.spnt b0 // exit if x not inf, y inf, result is +-pi/2
580 ;;
581 }
582
583 { .mfi
584 nop.m 999
585 fma.s1 atan2_V13 = atan2_w, atan2_P11, atan2_P10
586 nop.i 999
587 }
588 { .mfi
589 nop.m 999
590 fma.s1 atan2_W11 = atan2_w, atan2_P21, atan2_P20
591 nop.i 999
592 ;;
593 }
594
595 { .mfi
596 nop.m 999
597 fma.s1 atan2_V11 = atan2_w, atan2_P9, atan2_P8
598 nop.i 999
599 }
600 { .mfi
601 nop.m 999
602 fma.s1 atan2_V12 = atan2_w, atan2_w, f0
603 nop.i 999
604 ;;
605 }
606
607 { .mfi
608 nop.m 999
609 fma.s1 atan2_V8 = atan2_w, atan2_P7 , atan2_P6
610 nop.i 999
611 }
612 { .mfi
613 nop.m 999
614 fma.s1 atan2_W8 = atan2_w, atan2_P19, atan2_P18
615 nop.i 999
616 ;;
617 }
618
619 { .mfi
620 nop.m 999
621 fnma.s1 atan2_alpha = atan2_E, atan2_F, f1
622 nop.i 999
623 }
624 { .mfi
625 nop.m 999
626 fnma.s1 atan2_alpha_1 = atan2_E, atan2_F, atan2_two
627 nop.i 999
628 ;;
629 }
630
631
632 { .mfi
633 nop.m 999
634 fma.s1 atan2_V7 = atan2_w, atan2_P5 , atan2_P4
635 nop.i 999
636 }
637 { .mfi
638 nop.m 999
639 fma.s1 atan2_W7 = atan2_w, atan2_P17, atan2_P16
640 nop.i 999
641 ;;
642 }
643
644 { .mfi
645 nop.m 999
646 fma.s1 atan2_V4 = atan2_w, atan2_P3 , atan2_P2
647 nop.i 999
648 }
649 { .mfi
650 nop.m 999
651 fma.s1 atan2_W4 = atan2_w, atan2_P15, atan2_P14
652 nop.i 999
653 ;;
654 }
655
656 { .mfi
657 nop.m 999
658 fma.s1 atan2_V3 = atan2_w, atan2_P1 , atan2_P0
659 nop.i 999
660 }
661 { .mfi
662 nop.m 999
663 fma.s1 atan2_W3 = atan2_w, atan2_P13, atan2_P12
664 nop.i 999
665 ;;
666 }
667
668 { .mfi
669 nop.m 999
670 fma.s1 atan2_V10 = atan2_V12, atan2_V13, atan2_V11
671 nop.i 999
672 }
673 { .mfi
674 nop.m 999
675 fma.s1 atan2_gVF = atan2_gV, atan2_F, f0
676 nop.i 999
677 ;;
678 }
679
680 { .mfi
681 nop.m 999
682 fma.s1 atan2_alpha_sq = atan2_alpha, atan2_alpha, f0
683 nop.i 999
684 }
685 { .mfi
686 nop.m 999
687 fma.s1 atan2_Cp = atan2_alpha, atan2_alpha_1, f1
688 nop.i 999
689 ;;
690 }
691
692 { .mfi
693 nop.m 999
694 fma.s1 atan2_V9 = atan2_V12, atan2_V12, f0
695 nop.i 999
696 }
697 { .mfi
698 nop.m 999
699 fma.s1 atan2_W10 = atan2_V12, atan2_P22 , atan2_W11
700 nop.i 999
701 ;;
702 }
703
704 { .mfi
705 nop.m 999
706 fma.s1 atan2_V6 = atan2_V12, atan2_V8 , atan2_V7
707 nop.i 999
708 }
709 { .mfi
710 nop.m 999
711 fma.s1 atan2_W6 = atan2_V12, atan2_W8 , atan2_W7
712 nop.i 999
713 ;;
714 }
715
716 { .mfi
717 nop.m 999
718 fma.s1 atan2_V2 = atan2_V12, atan2_V4 , atan2_V3
719 nop.i 999
720 }
721 { .mfi
722 nop.m 999
723 fma.s1 atan2_W2 = atan2_V12, atan2_W4 , atan2_W3
724 nop.i 999
725 ;;
726 }
727
728 // p8 ==> y 0 x?
729 // p9 ==> y !0 x?
730 { .mfi
731 nop.m 999
732 fclass.m p8,p9 = atan2_Y, 0x07 // Test for y=0
733 nop.i 999
734 }
735 { .mfi
736 nop.m 999
737 fma.s1 atan2_zcub = atan2_z, atan2_w, f0
738 nop.i 999
739 ;;
740 }
741
742 { .mfi
743 nop.m 999
744 fma.s1 atan2_alpha_cub = atan2_alpha, atan2_alpha_sq, f0
745 nop.i 999
746 }
747 { .mfi
748 nop.m 999
749 fma.s1 atan2_C = atan2_gVF, atan2_Cp, f0
750 nop.i 999
751 ;;
752 }
753
754 // p12 ==> y0 x0
755 // p13 ==> y0 x!0
756 { .mfi
757 nop.m 999
758 (p8) fclass.m.unc p12,p13 = atan2_X, 0x07 // y=0, test if x is 0
759 nop.i 999
760 }
761 { .mfi
762 nop.m 999
763 fma.s1 atan2_W12 = atan2_V9, atan2_V9, f0
764 nop.i 999
765 ;;
766 }
767
768 { .mfi
769 nop.m 999
770 fma.s1 atan2_V5 = atan2_V9, atan2_V10, atan2_V6
771 nop.i 999
772 }
773 { .mfi
774 nop.m 999
775 fma.s1 atan2_W5 = atan2_V9, atan2_W10, atan2_W6
776 nop.i 999
777 ;;
778 }
779
780
781 // p9 ==> y!0 x0
782 { .mfi
783 nop.m 999
784 (p9) fclass.m.unc p9,p0 = atan2_X, 0x07 // y not 0, test if x is 0
785 nop.i 999
786 }
787 // p10 ==> X +INF, Y +-INF
788 { .mfb
789 nop.m 999
790 (p10) fma.d.s0 f8 = atan2_sgnY, atan2_pi_by_4, f0 // x=+inf, y=inf
791 (p10) br.ret.spnt b0 // Exit for x=+inf, y=inf, result is +-pi/4
792 ;;
793 }
794
795 .pred.rel "mutex",p11,p14
796 { .mfi
797 nop.m 999
798 (p14) fmerge.s f8 = atan2_sgnY, f0 // x=+inf, y !inf, result +-0
799 nop.i 999
800 }
801 // p11 ==> X -INF, Y +-INF
802 { .mfb
803 nop.m 999
804 (p11) fma.d.s0 f8 = atan2_sgnY, atan2_3pi_by_4, f0 // x=-inf, y=inf
805 (p11) br.ret.spnt b0 // Exit for x=-inf, y=inf, result is +-3pi/4
806 ;;
807 }
808
809 { .mfi
810 nop.m 999
811 (p13) fcmp.gt.unc.s1 p10,p11 = atan2_X,f0 // x not 0, y=0, test if x>0
812 nop.i 999
813 }
814 { .mfb
815 nop.m 999
816 fma.s1 atan2_d = atan2_alpha_cub, atan2_C, atan2_C
817 (p14) br.ret.spnt b0 // Exit if x=+inf, y !inf, result +-0
818 ;;
819 }
820
821 { .mfi
822 nop.m 999
823 fma.s1 atan2_W12 = atan2_V9, atan2_W12, f0
824 nop.i 999
825 }
826 { .mfb
827 nop.m 999
828 (p9) fma.d.s0 f8 = atan2_sgnY, atan2_pi_by_2, f0 // x=0, y not 0
829 (p9) br.ret.spnt b0 // Exit if x=0 and y not 0, result is +-pi/2
830 ;;
831 }
832
833 { .mfi
834 nop.m 999
835 fma.s1 atan2_V1 = atan2_V9, atan2_V5, atan2_V2
836 nop.i 999
837 }
838 { .mfb
839 nop.m 999
840 fma.s1 atan2_W1 = atan2_V9, atan2_W5, atan2_W2
841 (p12) br.spnt ATAN2_ERROR // Branch if x=0 and y=0
842 ;;
843 }
844
845 { .mfi
846 nop.m 999
847 (p10) fmerge.s f8 = atan2_sgnY, f0 // +-0 if x>0, y=0
848 nop.i 999
849 }
850 { .mfb
851 nop.m 999
852 (p11) fma.d.s0 f8 = atan2_sgnY, atan2_pi, f0 // +-pi if x<0, y=0
853 (p13) br.ret.spnt b0 // Exit if x!0 and y=0
854 ;;
855 }
856
857
858 { .mfi
859 nop.m 999
860 fma.s1 atan2_pd = atan2_P0, atan2_d, f0
861 nop.i 999
862 }
863 { .mfi
864 nop.m 999
865 fma.s1 atan2_dsq = atan2_d, atan2_d, f0
866 nop.i 999
867 ;;
868 }
869
870
871 { .mfi
872 nop.m 999
873 fmerge.se atan2_near_one = f1, atan2_sig_near_one // Const ~1.0
874 nop.i 999
875 }
876 { .mfi
877 nop.m 999
878 fma.s1 atan2_Pp = atan2_W12, atan2_W1, atan2_V1
879 nop.i 999
880 ;;
881 }
882
883 // p8 true if no swap and X positive
884 // p9 true if no swap and X negative
885 // both are false is swap is true
886 { .mfi
887 nop.m 999
888 (p7) fcmp.ge.unc.s1 p8,p9 = atan2_X,f0
889 nop.i 999
890 }
891 { .mfb
892 nop.m 999
893 (p15) fma.d.s0 f8 = atan2_sgnY, atan2_pi, f0
894 (p15) br.ret.spnt b0 // Exit if x=-inf, y !inf, result +-pi
895 ;;
896 }
897
898 { .mfi
899 nop.m 999
900 fma.s1 atan2_sgn_pi_by_2 = atan2_pi_by_2, atan2_sgnY, f0
901 nop.i 999
902 }
903 { .mfi
904 nop.m 999
905 fma.s1 atan2_A_lo = atan2_pd, atan2_dsq, atan2_d
906 nop.i 999
907 ;;
908 }
909
910
911 { .mfi
912 nop.m 999
913 fma.s1 atan2_sgn_pi = atan2_pi, atan2_sgnY, f0
914 nop.i 999
915 }
916 { .mfi
917 nop.m 999
918 fma.s1 atan2_A_hi = atan2_zcub, atan2_Pp, atan2_z
919 nop.i 999
920 ;;
921 }
922
923
924 // For |Y| <= |X| and X > 0, force inexact in case A_lo is zero
925 { .mfi
926 nop.m 999
927 (p8) fmpy.s0 atan2_tmp = atan2_P22, atan2_P22
928 nop.i 999
929 ;;
930 }
931
932 { .mfi
933 nop.m 999
934 fma.s1 atan2_A = atan2_A_hi, f1, atan2_A_lo
935 nop.i 999
936 }
937 // For |Y| <= |X| and X > 0, result is A_hi + A_lo
938 { .mfi
939 nop.m 999
940 (p8) fma.d.s0 f8 = atan2_A_hi, f1, atan2_A_lo
941 nop.i 999
942 ;;
943 }
944
945 .pred.rel "mutex",p6,p9
946 // We perturb A by multiplying by 1.0+1ulp as we produce the result
947 // in order to get symmetrically rounded results in directed rounding modes.
948 // If we don't do this, there are a few cases where the trailing 11 bits of
949 // the significand of the result, before converting to double, are zero. These
950 // cases do not round symmetrically in round to +infinity or round to -infinity.
951 // The perturbation also insures that the inexact flag is set.
952 // For |Y| > |X|, result is +- pi/2 - (A_hi + A_lo)
953 { .mfi
954 nop.m 999
955 (p6) fnma.d.s0 f8 = atan2_A, atan2_near_one, atan2_sgn_pi_by_2
956 nop.i 999
957 }
958 // For |Y| <= |X|, and X < 0, result is +- pi + (A_hi + A_lo)
959 { .mfb
960 nop.m 999
961 (p9) fma.d.s0 f8 = atan2_A, atan2_near_one, atan2_sgn_pi
962 br.ret.sptk b0
963 ;;
964 }
965
966 ATAN2_ERROR:
967 // Here if x=0 and y=0
968 { .mfi
969 nop.m 999
970 fclass.m p10,p11 = atan2_X,0x05 // Test if x=+0
971 nop.i 999
972 }
973 ;;
974
975 { .mfi
976 mov atan2_GR_tag = 37
977 (p10) fmerge.s f10 = atan2_sgnY, f0 // x=+0, y=0
978 nop.i 999
979 }
980 { .mfi
981 nop.m 999
982 (p11) fma.d.s0 f10 = atan2_sgnY, atan2_pi, f0 // x=-0, y=0
983 nop.i 999
984 ;;
985 }
986 GLOBAL_IEEE754_END(atan2)
987 libm_alias_double_other (__atan2, atan2)
988
989
990 LOCAL_LIBM_ENTRY(__libm_error_region)
991 .prologue
992 // (1)
993 { .mfi
994 add GR_Parameter_Y=-32,sp // Parameter 2 value
995 nop.f 999
996 .save ar.pfs,GR_SAVE_PFS
997 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
998 }
999 { .mfi
1000 .fframe 64
1001 add sp=-64,sp // Create new stack
1002 nop.f 0
1003 mov GR_SAVE_GP=gp // Save gp
1004 };;
1005
1006
1007 // (2)
1008 { .mmi
1009 stfd [GR_Parameter_Y] = f8,16 // STORE Parameter 2 on stack
1010 add GR_Parameter_X = 16,sp // Parameter 1 address
1011 .save b0, GR_SAVE_B0
1012 mov GR_SAVE_B0=b0 // Save b0
1013 };;
1014
1015 .body
1016 // (3)
1017 { .mib
1018 stfd [GR_Parameter_X] = f9 // STORE Parameter 1 on stack
1019 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
1020 nop.b 0
1021 }
1022 { .mib
1023 stfd [GR_Parameter_Y] = f10 // STORE Parameter 3 on stack
1024 add GR_Parameter_Y = -16,GR_Parameter_Y
1025 br.call.sptk b0=__libm_error_support# // Call error handling function
1026 };;
1027 { .mmi
1028 add GR_Parameter_RESULT = 48,sp
1029 nop.m 0
1030 nop.i 0
1031 };;
1032
1033 // (4)
1034 { .mmi
1035 ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
1036 .restore sp
1037 add sp = 64,sp // Restore stack pointer
1038 mov b0 = GR_SAVE_B0 // Restore return address
1039 };;
1040 { .mib
1041 mov gp = GR_SAVE_GP // Restore gp
1042 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
1043 br.ret.sptk b0 // Return
1044 };;
1045
1046 LOCAL_LIBM_END(__libm_error_region)
1047
1048 .type __libm_error_support#,@function
1049 .global __libm_error_support#