summaryrefslogtreecommitdiff
path: root/sysdeps/ia64/fpu/e_remainderl.S
blob: 8c1630e3ab1e25936c44ce82a09853ade0ffc943 (plain)
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
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
.file "remainderl.s"


// Copyright (c) 2000 - 2003, Intel Corporation
// All rights reserved.
//
// Contributed 2000 by the Intel Numerics Group, Intel Corporation
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// * The name of Intel Corporation may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.

// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Intel Corporation is the author of this code, and requests that all
// problem reports or change requests be submitted to it directly at
// http://www.intel.com/software/products/opensource/libraries/num.htm.
//
// History
//====================================================================
// 02/02/00 Initial version
// 03/02/00 New algorithm 
// 04/04/00 Unwind support added
// 07/21/00 Fixed quotient=2^{24*m+23}*1.q1...q23 1 bug
// 08/15/00 Bundle added after call to __libm_error_support to properly
//          set [the previously overwritten] GR_Parameter_RESULT.
// 11/29/00 Set FR_Y to f9
// 05/20/02 Cleaned up namespace and sf0 syntax
// 02/10/03 Reordered header: .section, .global, .proc, .align
//
// API
//====================================================================
// long double remainderl(long double,long double);   
//
// Overview of operation
//====================================================================
//  remainder(a,b)=a-i*b,
//  where i is an integer such that, if b!=0 and a is finite, 
//  |a/b-i|<=1/2. If |a/b-i|=1/2, i is even.
//
// Algorithm
//====================================================================
// a). eliminate special cases
// b). if |a/b|<0.25 (first quotient estimate), return a
// c). use single precision divide algorithm to get quotient q
//     rounded to 24 bits of precision 
// d). calculate partial remainders (using both q and q-ulp); 
//     select one and RZ(a/b) based on the sign of |a|-|b|*q   
// e). if the exponent difference (exponent(a)-exponent(b))
//     is less than 24 (quotient estimate<2^{24}-2), use RZ(a/b) 
//     and sticky bits to round to integer; exit loop and
//     calculate final remainder
// f). if exponent(a)-exponent(b)>=24, select new value of a as
//     the partial remainder calculated using RZ(a/b); 
//     repeat from c). 
//
// Special cases
//====================================================================
// a=+/- Inf, or b=+/-0: return NaN, call libm_error_support
// a=NaN or b=NaN: return NaN
//
// Registers used
//====================================================================
// Predicate registers: p6-p14
// General registers:   r2,r3,r28,r29,r32 (ar.pfs), r33-r39
// Floating point registers: f6-f15,f32
//

GR_SAVE_B0                    = r33
GR_SAVE_PFS                   = r34
GR_SAVE_GP                    = r35 
GR_SAVE_SP                    = r36

GR_Parameter_X                = r37
GR_Parameter_Y                = r38
GR_Parameter_RESULT           = r39
GR_Parameter_TAG              = r40

FR_X             = f10
FR_Y             = f9
FR_RESULT        = f8


.section .text
GLOBAL_IEEE754_ENTRY(remainderl)

// inputs in f8, f9
// result in f8

{ .mfi
  alloc r32=ar.pfs,1,4,4,0
  // f13=|a|
  fmerge.s f13=f0,f8
  nop.i 0
}
  {.mfi
  getf.sig r29=f9
  // f14=|b|
  fmerge.s f14=f0,f9
  nop.i 0;;
}
 {.mlx
  mov r28=0x2ffdd
  // r2=2^{23}
  movl r3=0x4b000000;;
}


{.mmi
setf.exp f32=r28
nop.m 0
// y pseudo-zero ?
cmp.eq p11,p10=r29,r0;;
}

// Y +-NAN, +-inf, +-0?     p11
{ .mfi
      nop.m 999
(p10)  fclass.m  p11,p10 = f9, 0xe7           
      nop.i 999
}
// qnan snan inf norm     unorm 0 -+
// 1    1    1   0        0     0 11
// e                      3
// X +-NAN, +-inf, ?        p9
{ .mfi
      nop.m 999
      fclass.m.unc  p9,p8 = f8, 0xe3           
      nop.i 999;; 
}

{.mfi
  nop.m 0
  mov f12=f0
  nop.i 0
}
{ .mfi
  // set p7=1
  cmp.eq.unc p7,p0=r0,r0
  // Step (1)
  // y0 = 1 / b in f10
  frcpa.s1 f10,p6=f13,f14
  nop.i 0;;
} 
// Y +-NAN, +-inf, +-0?     p11
{ .mfi
      nop.m 999
	  // pseudo-NaN ?
(p10)  fclass.nm  p11,p0 = f9, 0xff           
      nop.i 999
}

// qnan snan inf norm     unorm 0 -+
// 1    1    1   0        0     0 11
// e                      3
// X +-NAN, +-inf, ?        p9

{ .mfi
      nop.m 999
(p8)  fclass.nm  p9,p0 = f8, 0xff          
      nop.i 999;;
}

{.bbb
  (p9) br.cond.spnt FREM_X_NAN_INF
  (p11) br.cond.spnt FREM_Y_NAN_INF_ZERO
  nop.b 0
}  {.mfi
   nop.m 0
   // set D flag if a (f8) is denormal
   fnma.s0 f6=f8,f1,f8
   nop.i 0;;
} 

remloop24: 
  { .mfi
  nop.m 0
  // Step (2)
  // q0 = a * y0 in f15
  (p6) fma.s1 f12=f13,f10,f0
  nop.i 0
} { .mfi
  nop.m 0
  // Step (3)
  // e0 = 1 - b * y0 in f7
  (p6) fnma.s1 f7=f14,f10,f1
  nop.i 0;;
}  {.mlx
  nop.m 0
  // r2=1.25*2^{-24}
  movl r2=0x33a00000;;
} 

{.mfi
  nop.m 0
  // q1=q0*(1+e0)
  (p6) fma.s1 f15=f12,f7,f12
  nop.i 0
}
{ .mfi
  nop.m 0
  // Step (4)
  // e1 = e0 * e0 + E in f7
  (p6) fma.s1 f7=f7,f7,f32
  nop.i 0;;
}
 {.mii
  (p7) getf.exp r29=f12
  (p7) mov r28=0xfffd
  nop.i 0;;
}

 { .mfi
  // f12=2^{23}
  setf.s f12=r3
  // Step (5)
  // q2 = q1 + e1 * q1 in f11
  (p6) fma.s.s1 f11=f7,f15,f15
  nop.i 0
} { .mfi
   nop.m 0
  // Step (6)
  // q2 = q1 + e1 * q1 in f6
  (p6) fma.s1 f6=f7,f15,f15
  nop.i 0;;
} 

 {.mmi
  // f15=1.25*2^{-24}
  setf.s f15=r2
  // q<1/4 ? (i.e. expon< -2) 
  (p7) cmp.gt p7,p0=r28,r29
  nop.i 0;;
}

{.mfb
  // r29= -32+bias
  mov r29=0xffdf
 // if |a/b|<1/4, set D flag before returning 
 (p7) fma.s0 f9=f9,f0,f8
  nop.b 0;;
}
 {.mfb
 nop.m 0
 // can be combined with bundle above if sign of 0 or
 // FTZ enabled are not important
 (p7) fmerge.s f8=f8,f9
 // return if |a|<4*|b| (estimated quotient < 1/4)
 (p7) br.ret.spnt b0;;
}
  {.mfi
  // f7=2^{-32}
  setf.exp f7=r29
  // set f8 to current a value | sign
  fmerge.s f8=f8,f13
  nop.i 0;;
} 
  {.mfi
  getf.exp r28=f6
  // last step ? (q<2^{23})
  fcmp.lt.unc.s1 p0,p12=f6,f12
  nop.i 0;;
}
  {.mfi
  nop.m 0
  // r=a-b*q
  fnma.s1 f6=f14,f11,f13
  nop.i 0
} {.mfi
  // r2=23+bias
  mov r2=0xffff+23
  // q'=q-q*(1.25*2^{-24})   (q'=q-ulp)
  fnma.s.s1 f15=f11,f15,f11
  nop.i 0;;
}
  {.mmi
  nop.m 0
  cmp.eq p11,p14=r2,r28
  nop.i 0;;
} 

.pred.rel "mutex",p11,p14
  {.mfi
  nop.m 0
  // if exp_q=2^23, then r=a-b*2^{23}
  (p11) fnma.s1 f13=f12,f14,f13
  nop.i 0
} 
{.mfi
  nop.m 0
  // r2=a-b*q'
  (p14) fnma.s1 f13=f14,f15,f13
  nop.i 0;;
}
  {.mfi
  nop.m 0
  // r>0 iff q=RZ(a/b) and inexact
  fcmp.gt.unc.s1 p8,p0=f6,f0
  nop.i 0
} {.mfi
  nop.m 0
  // r<0 iff q'=RZ(a/b) and inexact
  (p14) fcmp.lt.unc.s1 p9,p10=f6,f0
  nop.i 0;;
}

.pred.rel "mutex",p8,p9
  {.mfi
   nop.m 0 
  // (p8) Q=q+(last iteration ? sticky bits:0)
  // i.e. Q=q+q*x  (x=2^{-32} or 0)
  (p8) fma.s1 f11=f11,f7,f11
  nop.i 0
} {.mfi
  nop.m 0
  // (p9) Q=q'+(last iteration ? sticky bits:0)
  // i.e. Q=q'+q'*x  (x=2^{-32} or 0)
  (p9) fma.s1 f11=f15,f7,f15
  nop.i 0;;
}

  {.mfb
  nop.m 0
  //  (p9) set r=r2 (new a, if not last iteration)
  // (p10) new a =r
  (p10) mov f13=f6
  (p12) br.cond.sptk remloop24;;
} 

// last iteration
  {.mfi
  nop.m 0
  // set f9=|b|*sgn(a)
  fmerge.s f9=f8,f9
  nop.i 0
}
  {.mfi
  nop.m 0
  // round to integer
  fcvt.fx.s1 f11=f11
  nop.i 0;;
}
  {.mfi
  nop.m 0
  // save sign of a
  fmerge.s f7=f8,f8
  nop.i 0
} {.mfi 
  nop.m 0
  // normalize
  fcvt.xf f11=f11
  nop.i 0;;
} 
  {.mfi
  nop.m 0
  // This can be removed if sign of 0 is not important 
  // get remainder using sf1
  fnma.s1 f12=f9,f11,f8
  nop.i 0
}
  {.mfi
  nop.m 0
  // get remainder
  fnma.s0 f8=f9,f11,f8
  nop.i 0;;
}
  {.mfi
  nop.m 0
  // f12=0?
  // This can be removed if sign of 0 is not important 
  fcmp.eq.unc.s1 p8,p0=f12,f0
  nop.i 0;;
}
  {.mfb
  nop.m 0
  // if f8=0, set sign correctly
  // This can be removed if sign of 0 is not important 
  (p8) fmerge.s f8=f7,f8
  // return
  br.ret.sptk b0;;
}



FREM_X_NAN_INF: 

// Y zero ?
{.mfi 
  nop.m 0
  fma.s1 f10=f9,f1,f0
  nop.i 0;;
}
{.mfi
 nop.m 0
 fcmp.eq.unc.s1 p11,p0=f10,f0
 nop.i 0;;
}
{.mib
  nop.m 0
  nop.i 0
  // if Y zero
  (p11) br.cond.spnt FREM_Y_ZERO;;                        
}

// X infinity? Return QNAN indefinite
{ .mfi
      nop.m 999
      fclass.m.unc  p8,p0 = f8, 0x23 
      nop.i 999
}
// X infinity? Return QNAN indefinite
{ .mfi
      nop.m 999
      fclass.m.unc  p11,p0 = f8, 0x23 
      nop.i 999;; 
}
// Y NaN ?
{.mfi
	 nop.m 999
(p8) fclass.m.unc p0,p8=f9,0xc3
	 nop.i 0;;
}
{.mfi
	nop.m 999
	// also set Denormal flag if necessary
(p8) fnma.s0 f9=f9,f1,f9
    nop.i 0
} 
{ .mfi
      nop.m 999
(p8)  frcpa.s0 f8,p7 = f8,f8           
      nop.i 999 ;;
}

{.mfi
      nop.m 999
(p11) mov f10=f8
	  nop.i 0
}
{ .mfi
     nop.m 999
(p8) fma.s0 f8=f8,f1,f0                     
	 nop.i 0 ;;                        
}

{ .mfb
      nop.m 999
      frcpa.s0 f8,p7=f8,f9                     
	  (p11) br.cond.spnt EXP_ERROR_RETURN;;                        
}
{ .mib
	nop.m 0
	nop.i 0
	br.ret.spnt    b0 ;;                        
}


FREM_Y_NAN_INF_ZERO: 
// Y INF
{ .mfi
      nop.m 999
      fclass.m.unc  p7,p0 = f9, 0x23           
      nop.i 999 ;;
}

{ .mfb
      nop.m 999
(p7)  fma.s0 f8=f8,f1,f0                     
(p7)  br.ret.spnt    b0 ;;                        
}

// Y NAN?
{ .mfi
      nop.m 999
      fclass.m.unc  p9,p10 = f9, 0xc3           
      nop.i 999 ;;
}
{ .mfi
      nop.m 999
(p10)  fclass.nm  p9,p0 = f9, 0xff           
      nop.i 999 ;;
}

{ .mfb
      nop.m 999
(p9)  fma.s0 f8=f9,f1,f0                     
(p9)  br.ret.spnt    b0 ;;                        
}

FREM_Y_ZERO:
// Y zero? Must be zero at this point
// because it is the only choice left.
// Return QNAN indefinite

// X NAN?
{ .mfi
      nop.m 999
      fclass.m.unc  p9,p10 = f8, 0xc3           
      nop.i 999 ;;
}
{ .mfi
      nop.m 999
(p10)  fclass.nm  p9,p10 = f8, 0xff           
      nop.i 999 ;;
}

{.mfi
 nop.m 999
 (p9) frcpa.s0 f11,p7=f8,f0
 nop.i 0;;
}
{ .mfi
      nop.m 999
(p10)  frcpa.s0   f11,p7 = f0,f0           
	  nop.i 999;;
}

{ .mfi
      nop.m 999
      fmerge.s      f10 = f8, f8             
      nop.i 999
}

{ .mfi
      nop.m 999
      fma.s0 f8=f11,f1,f0                     
      nop.i 999;;
}

EXP_ERROR_RETURN: 

{ .mib
      mov   GR_Parameter_TAG = 123                                 
	  nop.i 999
      br.sptk __libm_error_region;; 
}

GLOBAL_IEEE754_END(remainderl)

LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
{ .mfi
        add   GR_Parameter_Y=-32,sp             // Parameter 2 value
        nop.f 0
.save   ar.pfs,GR_SAVE_PFS
        mov  GR_SAVE_PFS=ar.pfs                 // Save ar.pfs 
}
{ .mfi
.fframe 64 
        add sp=-64,sp                           // Create new stack
        nop.f 0
        mov GR_SAVE_GP=gp                       // Save gp
};;
{ .mmi
        stfe [GR_Parameter_Y] = FR_Y,16         // Save Parameter 2 on stack
        add GR_Parameter_X = 16,sp              // Parameter 1 address
.save   b0, GR_SAVE_B0                      
        mov GR_SAVE_B0=b0                       // Save b0 
};;
.body
{ .mib
        stfe [GR_Parameter_X] = FR_X            // Store Parameter 1 on stack 
        add   GR_Parameter_RESULT = 0,GR_Parameter_Y  
	nop.b 0                                 // Parameter 3 address
}
{ .mib
        stfe [GR_Parameter_Y] = FR_RESULT      // Store Parameter 3 on stack
        add   GR_Parameter_Y = -16,GR_Parameter_Y  
        br.call.sptk b0=__libm_error_support#  // Call error handling function
};;
{ .mmi
        nop.m 0
        nop.m 0
        add   GR_Parameter_RESULT = 48,sp
};;
{ .mmi
        ldfe  f8 = [GR_Parameter_RESULT]       // Get return result off stack
.restore sp
        add   sp = 64,sp                       // Restore stack pointer
        mov   b0 = GR_SAVE_B0                  // Restore return address
};;
{ .mib
        mov   gp = GR_SAVE_GP                  // Restore gp 
        mov   ar.pfs = GR_SAVE_PFS             // Restore ar.pfs
        br.ret.sptk     b0                     // Return
};; 

LOCAL_LIBM_END(__libm_error_region)


.type   __libm_error_support#,@function
.global __libm_error_support#