about summary refs log tree commit diff
path: root/sysdeps/ia64/fpu/s_nextafterl.S
blob: cf2feba043313a1d55911a04a93f9317dfab1fe1 (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
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
.file "nextafterl.s"


// Copyright (c) 2000 - 2004, 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
// 03/03/00 Modified to conform to C9X, and improve speed of main path
// 03/14/00 Fixed case where x is a power of 2, and x > y, improved speed
// 04/04/00 Unwind support added
// 05/12/00 Fixed erroneous denormal flag setting for exponent change cases 1,3
// 08/15/00 Bundle added after call to __libm_error_support to properly
//          set [the previously overwritten] GR_Parameter_RESULT.
// 09/09/00 Updated fcmp so that qnans do not raise invalid.
// 12/15/00 Fixed case of smallest long double normal to largest denormal,
//          now adhere to C99 for two zero args, and fixed flag settings
//          for several cases
// 05/20/02 Cleaned up namespace and sf0 syntax
// 02/10/03 Reordered header: .section, .global, .proc, .align
// 12/14/04 Added error handling on underflow.
//
// API
//==============================================================
// long double nextafterl( long double x, long double y );
// input  floating point f8, f9
// output floating point f8
//
// Registers used
//==============================================================
GR_max_pexp     = r14
GR_min_pexp     = r15
GR_exp          = r16
GR_sig          = r17
GR_lnorm_sig    = r18
GR_sign_mask    = r19
GR_exp_mask     = r20
GR_sden_sig     = r21
GR_new_sig      = r22
GR_new_exp      = r23
GR_lden_sig     = r24
GR_snorm_sig    = r25
GR_exp1         = r26
GR_x_exp        = r27
// r36-39 parameters for libm_error_support

GR_SAVE_B0                = r34
GR_SAVE_GP                = r35
GR_SAVE_PFS               = r32

GR_Parameter_X            = r36
GR_Parameter_Y            = r37
GR_Parameter_RESULT       = r38
GR_Parameter_TAG          = r39

FR_lnorm_sig       = f10
FR_lnorm_exp       = f11
FR_lnorm           = f12
FR_sden_sig        = f13
FR_den_exp         = f14
FR_sden            = f15
FR_snorm_exp       = f32
FR_save_f8         = f33
FR_new_exp         = f34
FR_new_sig         = f35
FR_lden_sig        = f36
FR_snorm_sig       = f37
FR_exp1            = f38
FR_tmp             = f39

//
// Overview of operation
//==============================================================
// nextafterl determines the next representable value
// after x in the direction of y.


.section .text
GLOBAL_LIBM_ENTRY(nextafterl)

// Extract signexp from x
// Is x < y ?  p10 if yes, p11 if no
// Form smallest denormal significand = ulp size
{ .mfi
      getf.exp GR_exp      = f8
      fcmp.lt.s1 p10,p11 = f8, f9
      addl GR_sden_sig = 0x1, r0
}
// Form largest normal significand 0xffffffffffffffff
// Form smallest normal exponent
{ .mfi
      addl GR_lnorm_sig = -0x1,r0
      nop.f 999
      addl GR_min_pexp = 0x0c001, r0 ;;
}

// Extract significand from x
// Is x=y?   This fcmp also sets Invalid and Denormal if required
// Form largest normal exponent
{ .mfi
      getf.sig GR_sig      = f8
      fcmp.eq.s0 p6,p0 = f8, f9
      addl GR_max_pexp = 0x13ffe, r0
}
// Move largest normal significand to fp reg for special cases
{ .mfi
      setf.sig FR_lnorm_sig = GR_lnorm_sig
      nop.f 999
      addl GR_sign_mask = 0x20000, r0 ;;
}

// Move smallest denormal significand and exp to fp regs
// Is x=nan?
// Set p12 and p13 based on whether significand increases or decreases
// It increases (p12 set) if x<y and x>=0 or if x>y and x<0
// It decreases (p13 set) if x<y and x<0  or if x>y and x>=0
{ .mfi
      setf.sig FR_sden_sig = GR_sden_sig
      fclass.m  p8,p0 = f8, 0xc3
(p10) cmp.lt p12,p13 = GR_exp, GR_sign_mask
}
// Move smallest normal exp to fp regs
{ .mfi
      setf.exp FR_snorm_exp = GR_min_pexp
      nop.f 999
(p11) cmp.ge p12,p13 = GR_exp, GR_sign_mask ;;
}

.pred.rel "mutex",p12,p13

// Form expected new significand, adding or subtracting 1 ulp increment
// If x=y set result to y
// Form smallest normal significand and largest denormal significand
{ .mfi
(p12) add GR_new_sig = GR_sig, GR_sden_sig
(p6)  fmerge.s f8=f9,f9
      dep.z GR_snorm_sig = 1,63,1 // 0x8000000000000000
}
{ .mlx
(p13) sub GR_new_sig = GR_sig, GR_sden_sig
      movl GR_lden_sig = 0x7fffffffffffffff ;;
}

// Move expected result significand and signexp to fp regs
// Is y=nan?
// Form new exponent in case result exponent needs incrementing or decrementing
{ .mfi
      setf.exp FR_new_exp = GR_exp
      fclass.m  p9,p0 = f9, 0xc3
(p12) add GR_exp1 = 1, GR_exp
}
{ .mib
      setf.sig FR_new_sig = GR_new_sig
(p13) add GR_exp1 = -1, GR_exp
(p6)  br.ret.spnt    b0 ;;             // Exit if x=y
}

// Move largest normal signexp to fp reg for special cases
// Is x=zero?
{ .mfi
      setf.exp FR_lnorm_exp = GR_max_pexp
      fclass.m  p7,p0 = f8, 0x7
      nop.i 999
}
{ .mfb
      setf.exp FR_den_exp = GR_min_pexp
(p8)  fma.s0 f8 = f8,f1,f9
(p8)  br.ret.spnt    b0 ;;             // Exit if x=nan
}

// Move exp+-1 and smallest normal significand to fp regs for special cases
// Is x=inf?
{ .mfi
      setf.exp FR_exp1 = GR_exp1
      fclass.m  p6,p0 = f8, 0x23
      addl GR_exp_mask = 0x1ffff, r0
}
{ .mfb
      setf.sig FR_snorm_sig = GR_snorm_sig
(p9)  fma.s0 f8 = f8,f1,f9
(p9)  br.ret.spnt    b0 ;;             // Exit if y=nan
}

// Move largest denormal significand to fp regs for special cases
// Save x
{ .mfb
      setf.sig FR_lden_sig = GR_lden_sig
      mov FR_save_f8 = f8
(p7)  br.cond.spnt NEXT_ZERO ;;   // Exit if x=0
}

// Mask off the sign to get x_exp
{ .mfb
      and GR_x_exp = GR_exp_mask, GR_exp
      nop.f 999
(p6)  br.cond.spnt NEXT_INF ;;   // Exit if x=inf
}

// Check 5 special cases when significand rolls over:
//  1 sig size incr, x_sig=max_sig, x_exp < max_exp
//     Set p6, result is sig=min_sig, exp++
//  2 sig size incr, x_sig=max_sig, x_exp >= max_exp
//     Set p7, result is inf, signal overflow
//  3 sig size decr, x_sig=min_sig, x_exp > min_exp
//     Set p8, result is sig=max_sig, exp--
//  4 sig size decr, x_sig=min_sig, x_exp = min_exp
//     Set p9, result is sig=max_den_sig, exp same, signal underflow and inexact
//  5 sig size decr, x_sig=min_den_sig, x_exp = min_exp
//     Set p10, result is zero, sign of x, signal underflow and inexact
//
{ .mmi
(p12) cmp.eq.unc p6,p0 = GR_new_sig, r0
(p13) cmp.eq.unc p9,p10 = GR_new_sig, GR_lden_sig
      nop.i 999
;;
}

{ .mmi
(p6)  cmp.lt.unc p6,p7 = GR_x_exp, GR_max_pexp
(p10) cmp.eq.unc p10,p0 = GR_new_sig, r0
(p9)  cmp.le.unc p9,p8 = GR_x_exp, GR_min_pexp
;;
}

// Create small normal in case need to generate underflow flag
{ .mfi
      nop.m 999
      fmerge.se FR_tmp = FR_snorm_exp, FR_lnorm_sig
      nop.i 999
}
// Branch if cases 1, 2, 3
{ .bbb
(p6)  br.cond.spnt NEXT_EXPUP
(p7)  br.cond.spnt NEXT_OVERFLOW
(p8)  br.cond.spnt NEXT_EXPDOWN ;;
}

// Branch if cases 4, 5
{ .mbb
      nop.m 999
(p9)  br.cond.spnt NEXT_NORM_TO_DENORM
(p10) br.cond.spnt NEXT_UNDERFLOW_TO_ZERO
;;
}

// Here if no special cases
// Set p6 if result will be a denormal, so can force underflow flag
//    Case 1:  x_exp=min_exp, x_sig=unnormalized
//    Case 2:  x_exp<min_exp
{ .mfi
      cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
      fmerge.se f8 = FR_new_exp, FR_new_sig
      nop.i 999 ;;
}

{ .mfi
      nop.m 999
      nop.f 999
(p6)  tbit.z p6,p0 = GR_new_sig, 63 ;;
}

NEXT_COMMON_FINISH:
// Force underflow and inexact if denormal result
{ .mfi
      nop.m 999
(p6)  fma.s0 FR_tmp = FR_tmp,FR_tmp,f0
      nop.i 999
}
{ .mfb
      nop.m 999
      fnorm.s0 f8 = f8 // Final normalization to result precision
(p6)  br.cond.spnt NEXT_UNDERFLOW ;;
}

{ .mfb
      nop.m 999
      nop.f 999
      br.ret.sptk b0;;
}

//Special cases
NEXT_EXPUP:
{ .mfb
      cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
      fmerge.se f8 = FR_exp1, FR_snorm_sig
      br.cond.sptk NEXT_COMMON_FINISH ;;
}

NEXT_EXPDOWN:
{ .mfb
      cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
      fmerge.se f8 = FR_exp1, FR_lnorm_sig
      br.cond.sptk NEXT_COMMON_FINISH ;;
}

NEXT_NORM_TO_DENORM:
{ .mfi
      nop.m 999
      fmerge.se f8 = FR_exp1, FR_lden_sig
      nop.i 999
}
// Force underflow and inexact
{ .mfb
      nop.m 999
      fma.s0 FR_tmp = FR_tmp,FR_tmp,f0
      br.cond.sptk NEXT_UNDERFLOW ;;
}

NEXT_UNDERFLOW_TO_ZERO:
{ .mfb
      cmp.eq p6,p0 = r0,r0
      fmerge.s f8 = FR_save_f8,f0
      br.cond.sptk NEXT_COMMON_FINISH ;;
}

NEXT_INF:
// Here if f8 is +- infinity
// INF
// if f8 is +inf, no matter what y is return  largest long double
// if f8 is -inf, no matter what y is return -largest long double

// Create largest long double
{ .mfi
      nop.m 999
      fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig
      nop.i 999 ;;
}

{ .mfb
      nop.m 999
      fmerge.s f8 = f8,FR_lnorm
      br.ret.sptk    b0 ;;
}

NEXT_ZERO:

// Here if f8 is +- zero
// ZERO
// if f8 is zero and y is +, return + smallest long double denormal
// if f8 is zero and y is -, return - smallest long double denormal

{ .mfi
      nop.m 999
      fmerge.se FR_sden = f0,FR_sden_sig
      nop.i 999 ;;
}

// Create small normal to generate underflow flag
{ .mfi
      nop.m 999
      fmerge.se FR_tmp = FR_snorm_exp, FR_lnorm_sig
      nop.i 999 ;;
}

// Add correct sign from direction arg
{ .mfi
      nop.m 999
      fmerge.s f8 = f9,FR_sden
      nop.i 999 ;;
}

// Force underflow and inexact flags
{ .mfb
      nop.m 999
      fma.s0 FR_tmp = FR_tmp,FR_tmp,f0
      br.cond.sptk NEXT_UNDERFLOW ;;
}

NEXT_UNDERFLOW:
// Here if result is a denorm, or input is finite and result is zero
// Call error support to report possible range error
{ .mib
      alloc          r32=ar.pfs,2,2,4,0
      mov           GR_Parameter_TAG = 267      // Error code
      br.cond.sptk  __libm_error_region    // Branch to error call
}
;;

NEXT_OVERFLOW:
// Here if input is finite, but result will be infinite
// Use frcpa to generate infinity of correct sign
// Call error support to report possible range error
{ .mfi
      alloc          r32=ar.pfs,2,2,4,0
      frcpa.s1 f8,p6 = FR_save_f8, f0
      nop.i 999 ;;
}

// Create largest double
{ .mfi
      nop.m 999
      fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig
      nop.i 999 ;;
}

// Force overflow and inexact flags to be set
{ .mfb
      mov           GR_Parameter_TAG = 153      // Error code
      fma.s0 FR_tmp = FR_lnorm,FR_lnorm,f0
      br.cond.sptk  __libm_error_region    // Branch to error call
}
;;

GLOBAL_LIBM_END(nextafterl)
libm_alias_ldouble_other (nextafter, nextafter)


LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue

// (1)
{ .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
};;


// (2)
{ .mmi
        stfe [GR_Parameter_Y] = f9,16         // STORE 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
// (3)
{ .mib
        stfe [GR_Parameter_X] = FR_save_f8              // STORE Parameter 1 on stack
        add   GR_Parameter_RESULT = 0,GR_Parameter_Y           // Parameter 3 address
        nop.b 0
}
{ .mib
        stfe [GR_Parameter_Y] = f8              // 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
};;

// (4)
{ .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#