| blob | f655567f528f0f1544460f0628587a1a96d29b36 |
1 .file "remainder.s"
4 // Copyright (c) 2000 - 2003, Intel Corporation
5 // All rights reserved.
6 //
7 // Contributed 2000 by the Intel Numerics Group, Intel Corporation
8 //
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10 // modification, are permitted provided that the following conditions are
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12 //
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14 // notice, this list of conditions and the following disclaimer.
15 //
16 // * Redistributions in binary form must reproduce the above copyright
17 // notice, this list of conditions and the following disclaimer in the
18 // documentation and/or other materials provided with the distribution.
19 //
20 // * The name of Intel Corporation may not be used to endorse or promote
21 // products derived from this software without specific prior written
22 // permission.
24 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
25 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
26 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
27 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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34 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
35 //
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38 // http://www.intel.com/software/products/opensource/libraries/num.htm.
39 //
40 // History
41 //====================================================================
42 // 02/02/00 Initial version
43 // 03/02/00 New Algorithm
44 // 04/04/00 Unwind support added
45 // 07/21/00 Fixed quotient=2^{24*m+23}*1.q1...q23 1 bug
46 // 08/15/00 Bundle added after call to __libm_error_support to properly
47 // set [the previously overwritten] GR_Parameter_RESULT.
48 // 11/29/00 Set FR_Y to f9
49 // 05/20/02 Cleaned up namespace and sf0 syntax
50 // 02/10/03 Reordered header: .section, .global, .proc, .align
51 //
52 // API
53 //====================================================================
54 // double remainder(double,double);
55 //
56 // Overview of operation
57 //====================================================================
58 // remainder(a,b)=a-i*b,
59 // where i is an integer such that, if b!=0 and a is finite,
60 // |a/b-i|<=1/2. If |a/b-i|=1/2, i is even.
61 //
62 // Algorithm
63 //====================================================================
64 // a). eliminate special cases
65 // b). if |a/b|<0.25 (first quotient estimate), return a
66 // c). use single precision divide algorithm to get quotient q
67 // rounded to 24 bits of precision
68 // d). calculate partial remainders (using both q and q-ulp);
69 // select one and RZ(a/b) based on the sign of |a|-|b|*q
70 // e). if the exponent difference (exponent(a)-exponent(b))
71 // is less than 24 (quotient estimate<2^{24}-2), use RZ(a/b)
72 // and sticky bits to round to integer; exit loop and
73 // calculate final remainder
74 // f). if exponent(a)-exponent(b)>=24, select new value of a as
75 // the partial remainder calculated using RZ(a/b);
76 // repeat from c).
77 //
78 // Special cases
79 //====================================================================
80 // a=+/- Inf, or b=+/-0: return NaN, call libm_error_support
81 // a=NaN or b=NaN: return NaN
83 // Registers used
84 //====================================================================
85 // Predicate registers: p6-p14
86 // General registers: r2,r3,r28,r29,r32 (ar.pfs), r33-r39
87 // Floating point registers: f6-f15,f32
89 GR_SAVE_B0 = r33
90 GR_SAVE_PFS = r34
91 GR_SAVE_GP = r35
92 GR_SAVE_SP = r36
94 GR_Parameter_X = r37
95 GR_Parameter_Y = r38
96 GR_Parameter_RESULT = r39
97 GR_Parameter_TAG = r40
99 FR_X = f10
100 FR_Y = f9
101 FR_RESULT = f8
104 .section .text
105 GLOBAL_IEEE754_ENTRY(remainder)
107 // inputs in f8, f9
108 // result in f8
110 { .mfi
111 alloc r32=ar.pfs,1,4,4,0
112 // f13=|a|
113 fmerge.s f13=f0,f8
114 nop.i 0
115 }
116 {.mfi
117 nop.m 0
118 // f14=|b|
119 fmerge.s f14=f0,f9
120 nop.i 0;;
121 }
122 {.mlx
123 mov r28=0x2ffdd
124 // r2=2^{23}
125 movl r3=0x4b000000;;
126 }
128 // Y +-NAN, +-inf, +-0? p11
129 { .mfi
130 setf.exp f32=r28
131 fclass.m.unc p11,p0 = f9, 0xe7
132 nop.i 999
133 }
134 // qnan snan inf norm unorm 0 -+
135 // 1 1 1 0 0 0 11
136 // e 3
137 // X +-NAN, +-inf, ? p9
138 { .mfi
139 nop.m 999
140 fclass.m.unc p9,p0 = f8, 0xe3
141 nop.i 999;;
142 }
144 {.mfi
145 nop.m 0
146 mov f12=f0
147 nop.i 0
148 }
149 { .mfi
150 // set p7=1
151 cmp.eq.unc p7,p0=r0,r0
152 // Step (1)
153 // y0 = 1 / b in f10
154 frcpa.s1 f10,p6=f13,f14
155 nop.i 0;;
156 }
158 {.bbb
159 (p9) br.cond.spnt FREM_X_NAN_INF
160 (p11) br.cond.spnt FREM_Y_NAN_INF_ZERO
161 nop.b 0
162 } {.mfi
163 nop.m 0
164 // set D flag if a (f8) is denormal
165 fnma.s0 f6=f8,f1,f8
166 nop.i 0;;
167 }
170 remloop24:
171 { .mfi
172 nop.m 0
173 // Step (2)
174 // q0 = a * y0 in f12
175 (p6) fma.s1 f12=f13,f10,f0
176 nop.i 0
177 } { .mfi
178 nop.m 0
179 // Step (3)
180 // e0 = 1 - b * y0 in f7
181 (p6) fnma.s1 f7=f14,f10,f1
182 nop.i 0;;
183 } {.mlx
184 nop.m 0
185 // r2=1.25*2^{-24}
186 movl r2=0x33a00000;;
187 }
189 {.mfi
190 nop.m 0
191 // q1=q0*(1+e0)
192 (p6) fma.s1 f15=f12,f7,f12
193 nop.i 0
194 }
195 { .mfi
196 nop.m 0
197 // Step (4)
198 // e1 = e0 * e0 + E in f7
199 (p6) fma.s1 f7=f7,f7,f32
200 nop.i 0;;
201 }
202 {.mii
203 (p7) getf.exp r29=f12
204 (p7) mov r28=0xfffd
205 nop.i 0;;
206 }
207 { .mfi
208 // f12=2^{23}
209 setf.s f12=r3
210 // Step (5)
211 // q2 = q1 + e1 * q1 in f11
212 (p6) fma.s.s1 f11=f7,f15,f15
213 nop.i 0
214 } { .mfi
215 nop.m 0
216 // Step (6)
217 // q2 = q1 + e1 * q1 in f6
218 (p6) fma.s1 f6=f7,f15,f15
219 nop.i 0;;
220 }
222 {.mmi
223 // f15=1.25*2^{-24}
224 setf.s f15=r2
225 // q<1/4 ? (i.e. expon< -2)
226 (p7) cmp.gt p7,p0=r28,r29
227 nop.i 0;;
228 }
230 {.mfb
231 // r29= -32+bias
232 mov r29=0xffdf
233 // if |a/b|<1/4, set D flag before returning
234 (p7) fma.d.s0 f9=f9,f0,f8
235 nop.b 0;;
236 }
237 {.mfb
238 nop.m 0
239 // can be combined with bundle above if sign of 0 or
240 // FTZ enabled are not important
241 (p7) fmerge.s f8=f8,f9
242 // return if |a|<4*|b| (estimated quotient < 1/4)
243 (p7) br.ret.spnt b0;;
244 }
245 {.mfi
246 // f7=2^{-32}
247 setf.exp f7=r29
248 // set f8 to current a value | sign
249 fmerge.s f8=f8,f13
250 nop.i 0;;
251 }
254 {.mfi
255 getf.exp r28=f6
256 // last step ? (q<2^{23})
257 fcmp.lt.unc.s1 p0,p12=f6,f12
258 nop.i 0;;
259 }
260 {.mfi
261 nop.m 0
262 // r=a-b*q
263 fnma.s1 f6=f14,f11,f13
264 nop.i 0
265 } {.mfi
266 // r2=23+bias
267 mov r2=0xffff+23
268 // q'=q-q*(1.25*2^{-24}) (q'=q-ulp)
269 fnma.s.s1 f15=f11,f15,f11
270 nop.i 0;;
271 }
272 {.mmi
273 nop.m 0
274 cmp.eq p11,p14=r2,r28
275 nop.i 0;;
276 }
278 .pred.rel "mutex",p11,p14
279 {.mfi
280 nop.m 0
281 // if exp_q=2^23, then r=a-b*2^{23}
282 (p11) fnma.s1 f13=f12,f14,f13
283 nop.i 0
284 }
285 {.mfi
286 nop.m 0
287 // r2=a-b*q'
288 (p14) fnma.s1 f13=f14,f15,f13
289 nop.i 0;;
290 }
291 {.mfi
292 nop.m 0
293 // r>0 iff q=RZ(a/b) and inexact
294 fcmp.gt.unc.s1 p8,p0=f6,f0
295 nop.i 0
296 } {.mfi
297 nop.m 0
298 // r<0 iff q'=RZ(a/b) and inexact
299 (p14) fcmp.lt.unc.s1 p9,p10=f6,f0
300 nop.i 0;;
301 }
303 .pred.rel "mutex",p8,p9
304 {.mfi
305 nop.m 0
306 // (p8) Q=q+(last iteration ? sticky bits:0)
307 // i.e. Q=q+q*x (x=2^{-32} or 0)
308 (p8) fma.s1 f11=f11,f7,f11
309 nop.i 0
310 } {.mfi
311 nop.m 0
312 // (p9) Q=q'+(last iteration ? sticky bits:0)
313 // i.e. Q=q'+q'*x (x=2^{-32} or 0)
314 (p9) fma.s1 f11=f15,f7,f15
315 nop.i 0;;
316 }
318 {.mfb
319 nop.m 0
320 // (p9) set r=r2 (new a, if not last iteration)
321 // (p10) new a =r
322 (p10) mov f13=f6
323 (p12) br.cond.sptk remloop24;;
324 }
326 // last iteration
327 {.mfi
328 nop.m 0
329 // set f9=|b|*sgn(a)
330 fmerge.s f9=f8,f9
331 nop.i 0
332 }
333 {.mfi
334 nop.m 0
335 // round to integer
336 fcvt.fx.s1 f11=f11
337 nop.i 0;;
338 }
339 {.mfi
340 nop.m 0
341 // save sign of a
342 fmerge.s f7=f8,f8
343 nop.i 0
344 } {.mfi
345 nop.m 0
346 // normalize
347 fcvt.xf f11=f11
348 nop.i 0;;
349 }
350 {.mfi
351 nop.m 0
352 // This can be removed if sign of 0 is not important
353 // get remainder using sf1
354 fnma.d.s1 f12=f9,f11,f8
355 nop.i 0
356 }
357 {.mfi
358 nop.m 0
359 // get remainder
360 fnma.d.s0 f8=f9,f11,f8
361 nop.i 0;;
362 }
363 {.mfi
364 nop.m 0
365 // f12=0?
366 // This can be removed if sign of 0 is not important
367 fcmp.eq.unc.s1 p8,p0=f12,f0
368 nop.i 0;;
369 }
370 {.mfb
371 nop.m 0
372 // if f8=0, set sign correctly
373 // This can be removed if sign of 0 is not important
374 (p8) fmerge.s f8=f7,f8
375 // return
376 br.ret.sptk b0;;
377 }
380 FREM_X_NAN_INF:
382 // Y zero ?
383 {.mfi
384 nop.m 0
385 fma.s1 f10=f9,f1,f0
386 nop.i 0;;
387 }
388 {.mfi
389 nop.m 0
390 fcmp.eq.unc.s1 p11,p0=f10,f0
391 nop.i 0;;
392 }
393 {.mib
394 nop.m 0
395 nop.i 0
396 // if Y zero
397 (p11) br.cond.spnt FREM_Y_ZERO;;
398 }
400 // X infinity? Return QNAN indefinite
401 { .mfi
402 nop.m 999
403 fclass.m.unc p8,p0 = f8, 0x23
404 nop.i 999
405 }
406 // X infinity? Return QNAN indefinite
407 { .mfi
408 nop.m 999
409 fclass.m.unc p11,p0 = f8, 0x23
410 nop.i 999;;
411 }
412 // Y NaN ?
413 {.mfi
414 nop.m 999
415 (p8) fclass.m.unc p0,p8=f9,0xc3
416 nop.i 0;;
417 }
418 {.mfi
419 nop.m 999
420 // also set Denormal flag if necessary
421 (p8) fma.s0 f9=f9,f1,f0
422 nop.i 0
423 }
424 { .mfi
425 nop.m 999
426 (p8) frcpa.s0 f8,p7 = f8,f8
427 nop.i 999 ;;
428 }
430 {.mfi
431 nop.m 999
432 (p11) mov f10=f8
433 nop.i 0
434 }
435 { .mfi
436 nop.m 999
437 (p8) fma.d.s0 f8=f8,f1,f0
438 nop.i 0 ;;
439 }
441 { .mfb
442 nop.m 999
443 frcpa.s0 f8,p7=f8,f9
444 (p11) br.cond.spnt EXP_ERROR_RETURN;;
445 }
446 { .mib
447 nop.m 0
448 nop.i 0
449 br.ret.spnt b0 ;;
450 }
453 FREM_Y_NAN_INF_ZERO:
455 // Y INF
456 { .mfi
457 nop.m 999
458 fclass.m.unc p7,p0 = f9, 0x23
459 nop.i 999 ;;
460 }
462 { .mfb
463 nop.m 999
464 (p7) fma.d.s0 f8=f8,f1,f0
465 (p7) br.ret.spnt b0 ;;
466 }
468 // Y NAN?
469 { .mfi
470 nop.m 999
471 fclass.m.unc p9,p0 = f9, 0xc3
472 nop.i 999 ;;
473 }
475 { .mfb
476 nop.m 999
477 (p9) fma.d.s0 f8=f9,f1,f0
478 (p9) br.ret.spnt b0 ;;
479 }
481 FREM_Y_ZERO:
482 // Y zero? Must be zero at this point
483 // because it is the only choice left.
484 // Return QNAN indefinite
486 // X NAN?
487 { .mfi
488 nop.m 999
489 fclass.m.unc p9,p10 = f8, 0xc3
490 nop.i 999 ;;
491 }
492 { .mfi
493 nop.m 999
494 (p10) fclass.nm p9,p10 = f8, 0xff
495 nop.i 999 ;;
496 }
498 {.mfi
499 nop.m 999
500 (p9) frcpa.s0 f11,p7=f8,f0
501 nop.i 0;;
502 }
504 { .mfi
505 nop.m 999
506 (p10) frcpa.s0 f11,p7 = f0,f0
507 nop.i 999;;
508 }
510 { .mfi
511 nop.m 999
512 fmerge.s f10 = f8, f8
513 nop.i 999
514 }
516 { .mfi
517 nop.m 999
518 fma.d.s0 f8=f11,f1,f0
519 nop.i 999
520 }
523 EXP_ERROR_RETURN:
525 { .mib
526 mov GR_Parameter_TAG = 124
527 nop.i 999
528 br.sptk __libm_error_region;;
529 }
531 GLOBAL_IEEE754_END(remainder)
535 LOCAL_LIBM_ENTRY(__libm_error_region)
536 .prologue
537 { .mfi
538 add GR_Parameter_Y=-32,sp // Parameter 2 value
539 nop.f 0
540 .save ar.pfs,GR_SAVE_PFS
541 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
542 }
543 { .mfi
544 .fframe 64
545 add sp=-64,sp // Create new stack
546 nop.f 0
547 mov GR_SAVE_GP=gp // Save gp
548 };;
549 { .mmi
550 stfd [GR_Parameter_Y] = FR_Y,16 // Save Parameter 2 on stack
551 add GR_Parameter_X = 16,sp // Parameter 1 address
552 .save b0, GR_SAVE_B0
553 mov GR_SAVE_B0=b0 // Save b0
554 };;
555 .body
556 { .mib
557 stfd [GR_Parameter_X] = FR_X // Store Parameter 1 on stack
558 add GR_Parameter_RESULT = 0,GR_Parameter_Y
559 nop.b 0 // Parameter 3 address
560 }
561 { .mib
562 stfd [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack
563 add GR_Parameter_Y = -16,GR_Parameter_Y
564 br.call.sptk b0=__libm_error_support# // Call error handling function
565 };;
566 { .mmi
567 nop.m 0
568 nop.m 0
569 add GR_Parameter_RESULT = 48,sp
570 };;
571 { .mmi
572 ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
573 .restore sp
574 add sp = 64,sp // Restore stack pointer
575 mov b0 = GR_SAVE_B0 // Restore return address
576 };;
577 { .mib
578 mov gp = GR_SAVE_GP // Restore gp
579 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
580 br.ret.sptk b0 // Return
581 };;
583 LOCAL_LIBM_END(__libm_error_region)
587 .type __libm_error_support#,@function
588 .global __libm_error_support#