| blob | b8b976271ac077a4a519781907d2e8c24f2f17dd |
1 .file "nexttowardf.s"
4 // Copyright (c) 2001 - 2004, Intel Corporation
5 // All rights reserved.
6 //
7 // Contributed 2001 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
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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
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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 //
36 // Intel Corporation is the author of this code, and requests that all
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38 // http://www.intel.com/software/products/opensource/libraries/num.htm.
39 //
40 // History
41 //==============================================================
42 // 08/15/01 Initial version
43 // 08/23/01 Corrected error tag number
44 // 05/20/02 Cleaned up namespace and sf0 syntax
45 // 02/10/03 Reordered header: .section, .global, .proc, .align
46 // 12/14/04 Added error handling on underflow.
47 //
48 // API
49 //==============================================================
50 // float nexttowardf( float x, long double y );
51 // input floating point f8, f9
52 // output floating point f8
53 //
54 // Registers used
55 //==============================================================
56 GR_max_pexp = r14
57 GR_min_pexp = r15
58 GR_exp = r16
59 GR_sig = r17
60 GR_lnorm_sig = r18
61 GR_sign_mask = r19
62 GR_exp_mask = r20
63 GR_sden_sig = r21
64 GR_new_sig = r22
65 GR_new_exp = r23
66 GR_lden_sig = r24
67 GR_snorm_sig = r25
68 GR_exp1 = r26
69 GR_x_exp = r27
70 GR_min_den_rexp = r28
71 // r36-39 parameters for libm_error_support
73 GR_SAVE_B0 = r34
74 GR_SAVE_GP = r35
75 GR_SAVE_PFS = r32
77 GR_Parameter_X = r36
78 GR_Parameter_Y = r37
79 GR_Parameter_RESULT = r38
80 GR_Parameter_TAG = r39
82 FR_lnorm_sig = f10
83 FR_lnorm_exp = f11
84 FR_lnorm = f12
85 FR_sden_sig = f13
86 FR_sden_exp = f14
87 FR_sden = f15
88 FR_save_f8 = f33
89 FR_new_exp = f34
90 FR_new_sig = f35
91 FR_lden_sig = f36
92 FR_snorm_sig = f37
93 FR_exp1 = f38
94 FR_tmp = f39
96 //
97 // Overview of operation
98 //==============================================================
99 // nexttowardf determines the next representable value
100 // after x in the direction of y.
103 .section .text
104 GLOBAL_LIBM_ENTRY(nexttowardf)
106 // Extract signexp from x
107 // Form smallest denormal significand = ulp size
108 { .mlx
109 getf.exp GR_exp = f8
110 movl GR_sden_sig = 0x0000010000000000
111 }
112 // Form largest normal exponent
113 // Is x < y ? p10 if yes, p11 if no
114 // Form smallest normal exponent
115 { .mfi
116 addl GR_max_pexp = 0x1007e, r0
117 fcmp.lt.s1 p10,p11 = f8, f9
118 addl GR_min_pexp = 0x0ff81, r0 ;;
119 }
121 // Is x=y?
122 { .mfi
123 getf.sig GR_sig = f8
124 fcmp.eq.s0 p6,p0 = f8, f9
125 nop.i 0
126 }
127 // Extract significand from x
128 // Form largest normal significand
129 { .mlx
130 nop.m 0
131 movl GR_lnorm_sig = 0xffffff0000000000 ;;
132 }
134 // Move largest normal significand to fp reg for special cases
135 { .mfi
136 setf.sig FR_lnorm_sig = GR_lnorm_sig
137 nop.f 0
138 addl GR_sign_mask = 0x20000, r0 ;;
139 }
141 // Move smallest denormal significand and signexp to fp regs
142 // Is x=nan?
143 // Set p12 and p13 based on whether significand increases or decreases
144 // It increases (p12 set) if x<y and x>=0 or if x>y and x<0
145 // It decreases (p13 set) if x<y and x<0 or if x>y and x>=0
146 { .mfi
147 setf.sig FR_sden_sig = GR_sden_sig
148 fclass.m p8,p0 = f8, 0xc3
149 (p10) cmp.lt p12,p13 = GR_exp, GR_sign_mask
150 }
151 { .mfi
152 setf.exp FR_sden_exp = GR_min_pexp
153 nop.f 999
154 (p11) cmp.ge p12,p13 = GR_exp, GR_sign_mask ;;
155 }
157 .pred.rel "mutex",p12,p13
159 // Form expected new significand, adding or subtracting 1 ulp increment
160 // If x=y set result to y
161 // Form smallest normal significand and largest denormal significand
162 { .mfi
163 (p12) add GR_new_sig = GR_sig, GR_sden_sig
164 (p6) fnorm.s.s0 f8=f9 //Normalise
165 dep.z GR_snorm_sig = 1,63,1 // 0x8000000000000000
166 }
167 { .mlx
168 (p13) sub GR_new_sig = GR_sig, GR_sden_sig
169 movl GR_lden_sig = 0x7fffff0000000000 ;;
170 }
172 // Move expected result significand and signexp to fp regs
173 // Is y=nan?
174 // Form new exponent in case result exponent needs incrementing or decrementing
175 { .mfi
176 setf.exp FR_new_exp = GR_exp
177 fclass.m p9,p0 = f9, 0xc3
178 (p12) add GR_exp1 = 1, GR_exp
179 }
180 { .mib
181 setf.sig FR_new_sig = GR_new_sig
182 (p13) add GR_exp1 = -1, GR_exp
183 (p6) br.ret.spnt b0 ;; // Exit if x=y
184 }
186 // Move largest normal signexp to fp reg for special cases
187 // Is x=zero?
188 { .mfi
189 setf.exp FR_lnorm_exp = GR_max_pexp
190 fclass.m p7,p0 = f8, 0x7
191 nop.i 999
192 }
193 { .mfb
194 nop.m 999
195 (p8) fma.s0 f8 = f8,f1,f9
196 (p8) br.ret.spnt b0 ;; // Exit if x=nan
197 }
199 // Move exp+-1 and smallest normal significand to fp regs for special cases
200 // Is x=inf?
201 { .mfi
202 setf.exp FR_exp1 = GR_exp1
203 fclass.m p6,p0 = f8, 0x23
204 addl GR_exp_mask = 0x1ffff, r0
205 }
206 { .mfb
207 setf.sig FR_snorm_sig = GR_snorm_sig
208 (p9) fma.s0 f8 = f8,f1,f9
209 (p9) br.ret.spnt b0 ;; // Exit if y=nan
210 }
212 // Move largest denormal significand to fp regs for special cases
213 // Save x
214 { .mfb
215 setf.sig FR_lden_sig = GR_lden_sig
216 mov FR_save_f8 = f8
217 (p7) br.cond.spnt NEXT_ZERO ;; // Exit if x=0
218 }
220 // Mask off the sign to get x_exp
221 { .mfb
222 and GR_x_exp = GR_exp_mask, GR_exp
223 nop.f 999
224 (p6) br.cond.spnt NEXT_INF ;; // Exit if x=inf
225 }
227 // Check 6 special cases when significand rolls over:
228 // 1 sig size incr, x_sig=max_sig, x_exp < max_exp
229 // Set p6, result is sig=min_sig, exp++
230 // 2 sig size incr, x_sig=max_sig, x_exp >= max_exp
231 // Set p7, result is inf, signal overflow
232 // 3 sig size decr, x_sig=min_sig, x_exp > min_exp
233 // Set p8, result is sig=max_sig, exp--
234 // 4 sig size decr, x_sig=min_sig, x_exp = min_exp
235 // Set p9, result is sig=max_den_sig, exp same, signal underflow and inexact
236 // 5 sig size decr, x_sig=min_den_sig, x_exp = min_exp
237 // Set p10, result is zero, sign of x, signal underflow and inexact
238 // 6 sig size decr, x_sig=min_sig, x_exp < min_exp
239 // Set p14, result is zero, sign of x, signal underflow and inexact
240 //
241 // Form exponent of smallest float denormal (if normalized register format)
242 { .mmi
243 adds GR_min_den_rexp = -23, GR_min_pexp
244 (p12) cmp.eq.unc p6,p0 = GR_new_sig, r0
245 (p13) cmp.eq.unc p8,p10 = GR_new_sig, GR_lden_sig ;;
246 }
248 { .mmi
249 (p6) cmp.lt.unc p6,p7 = GR_x_exp, GR_max_pexp
250 (p8) cmp.gt.unc p8,p9 = GR_x_exp, GR_min_pexp
251 (p10) cmp.eq.unc p10,p0 = GR_new_sig, r0 ;;
252 }
254 // Create small normal in case need to generate underflow flag
255 { .mfi
256 (p10) cmp.le.unc p10,p0 = GR_x_exp, GR_min_pexp
257 fmerge.se FR_tmp = FR_sden_exp, FR_lnorm_sig
258 (p9) cmp.gt.unc p9,p14 = GR_x_exp, GR_min_den_rexp
259 }
260 // Branch if cases 1, 2, 3
261 { .bbb
262 (p6) br.cond.spnt NEXT_EXPUP
263 (p7) br.cond.spnt NEXT_OVERFLOW
264 (p8) br.cond.spnt NEXT_EXPDOWN ;;
265 }
267 // Branch if cases 4, 5, 6
268 { .bbb
269 (p9) br.cond.spnt NEXT_NORM_TO_DENORM
270 (p10) br.cond.spnt NEXT_UNDERFLOW_TO_ZERO
271 (p14) br.cond.spnt NEXT_UNDERFLOW_TO_ZERO ;;
272 }
274 // Here if no special cases
275 // Set p6 if result will be a denormal, so can force underflow flag
276 // Case 1: x_exp=min_exp, x_sig=unnormalized
277 // Case 2: x_exp<min_exp
278 { .mfi
279 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
280 fmerge.se f8 = FR_new_exp, FR_new_sig
281 nop.i 999 ;;
282 }
284 { .mfi
285 nop.m 999
286 nop.f 999
287 (p7) tbit.z p6,p0 = GR_new_sig, 63 ;;
288 }
290 NEXT_COMMON_FINISH:
291 // Force underflow and inexact if denormal result
292 { .mfi
293 nop.m 999
294 (p6) fma.s.s0 FR_tmp = FR_tmp,FR_tmp,f0
295 nop.i 999
296 }
297 { .mfb
298 nop.m 999
299 fnorm.s.s0 f8 = f8 // Final normalization to result precision
300 (p6) br.cond.spnt NEXT_UNDERFLOW ;;
301 }
303 { .mfb
304 nop.m 999
305 nop.f 999
306 br.ret.sptk b0;;
307 }
309 //Special cases
310 NEXT_EXPUP:
311 { .mfb
312 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
313 fmerge.se f8 = FR_exp1, FR_snorm_sig
314 br.cond.sptk NEXT_COMMON_FINISH ;;
315 }
317 NEXT_EXPDOWN:
318 { .mfb
319 cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
320 fmerge.se f8 = FR_exp1, FR_lnorm_sig
321 br.cond.sptk NEXT_COMMON_FINISH ;;
322 }
324 NEXT_NORM_TO_DENORM:
325 { .mfi
326 nop.m 999
327 fmerge.se f8 = FR_new_exp, FR_lden_sig
328 nop.i 999
329 }
330 // Force underflow and inexact
331 { .mfb
332 nop.m 999
333 fma.s.s0 FR_tmp = FR_tmp,FR_tmp,f0
334 br.cond.sptk NEXT_UNDERFLOW ;;
335 }
337 NEXT_UNDERFLOW_TO_ZERO:
338 { .mfb
339 cmp.eq p6,p0 = r0,r0
340 fmerge.s f8 = FR_save_f8,f0
341 br.cond.sptk NEXT_COMMON_FINISH ;;
342 }
344 NEXT_INF:
345 // Here if f8 is +- infinity
346 // INF
347 // if f8 is +inf, no matter what y is return largest float
348 // if f8 is -inf, no matter what y is return -largest float
350 { .mfi
351 nop.m 999
352 fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig
353 nop.i 999 ;;
354 }
356 { .mfb
357 nop.m 999
358 fmerge.s f8 = f8,FR_lnorm
359 br.ret.sptk b0 ;;
360 }
362 NEXT_ZERO:
364 // Here if f8 is +- zero
365 // ZERO
366 // if f8 is zero and y is +, return + smallest float denormal
367 // if f8 is zero and y is -, return - smallest float denormal
369 { .mfi
370 nop.m 999
371 fmerge.se FR_sden = FR_sden_exp,FR_sden_sig
372 nop.i 999 ;;
373 }
375 // Create small normal to generate underflow flag
376 { .mfi
377 nop.m 999
378 fmerge.se FR_tmp = FR_sden_exp, FR_lnorm_sig
379 nop.i 999 ;;
380 }
382 // Add correct sign from direction arg
383 { .mfi
384 nop.m 999
385 fmerge.s f8 = f9,FR_sden
386 nop.i 999 ;;
387 }
389 // Force underflow and inexact flags
390 { .mfb
391 nop.m 999
392 fma.s.s0 FR_tmp = FR_tmp,FR_tmp,f0
393 br.cond.sptk NEXT_UNDERFLOW ;;
394 }
396 NEXT_UNDERFLOW:
397 // Here if result is a denorm, or input is finite and result is zero
398 // Call error support to report possible range error
399 { .mib
400 alloc r32=ar.pfs,2,2,4,0
401 mov GR_Parameter_TAG = 272 // Error code
402 br.cond.sptk __libm_error_region // Branch to error call
403 }
404 ;;
406 NEXT_OVERFLOW:
407 // Here if input is finite, but result will be infinite
408 // Use frcpa to generate infinity of correct sign
409 // Call error support to report possible range error
410 { .mfi
411 alloc r32=ar.pfs,2,2,4,0
412 frcpa.s1 f8,p6 = FR_save_f8, f0
413 nop.i 999 ;;
414 }
416 // Create largest double
417 { .mfi
418 nop.m 999
419 fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig
420 nop.i 999 ;;
421 }
423 // Force overflow and inexact flags to be set
424 { .mfb
425 mov GR_Parameter_TAG = 200 // Error code
426 fma.s.s0 FR_tmp = FR_lnorm,FR_lnorm,f0
427 br.cond.sptk __libm_error_region // Branch to error call
428 }
429 ;;
431 GLOBAL_LIBM_END(nexttowardf)
434 LOCAL_LIBM_ENTRY(__libm_error_region)
435 .prologue
437 // (1)
438 { .mfi
439 add GR_Parameter_Y=-32,sp // Parameter 2 value
440 nop.f 0
441 .save ar.pfs,GR_SAVE_PFS
442 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
443 }
444 { .mfi
445 .fframe 64
446 add sp=-64,sp // Create new stack
447 nop.f 0
448 mov GR_SAVE_GP=gp // Save gp
449 };;
452 // (2)
453 { .mmi
454 stfs [GR_Parameter_Y] = f9,16 // STORE Parameter 2 on stack
455 add GR_Parameter_X = 16,sp // Parameter 1 address
456 .save b0, GR_SAVE_B0
457 mov GR_SAVE_B0=b0 // Save b0
458 };;
460 .body
461 // (3)
462 { .mib
463 stfs [GR_Parameter_X] = FR_save_f8 // STORE Parameter 1 on stack
464 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
465 nop.b 0
466 }
467 { .mib
468 stfs [GR_Parameter_Y] = f8 // STORE Parameter 3 on stack
469 add GR_Parameter_Y = -16,GR_Parameter_Y
470 br.call.sptk b0=__libm_error_support# // Call error handling function
471 };;
472 { .mmi
473 nop.m 0
474 nop.m 0
475 add GR_Parameter_RESULT = 48,sp
476 };;
478 // (4)
479 { .mmi
480 ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack
481 .restore sp
482 add sp = 64,sp // Restore stack pointer
483 mov b0 = GR_SAVE_B0 // Restore return address
484 };;
485 { .mib
486 mov gp = GR_SAVE_GP // Restore gp
487 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
488 br.ret.sptk b0 // Return
489 };;
491 LOCAL_LIBM_END(__libm_error_region)
494 .type __libm_error_support#,@function
495 .global __libm_error_support#