| blob | 0157cc0eff8efeb7e654ce79f7f464d3d887ac0b |
1 .file "erfcf.s"
4 // Copyright (c) 2002 - 2005, Intel Corporation
5 // All rights reserved.
6 //
7 //
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14 //
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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 // 01/17/02 Initial version
42 // 05/20/02 Cleaned up namespace and sf0 syntax
43 // 02/06/03 Reordered header: .section, .global, .proc, .align
44 // 03/31/05 Reformatted delimiters between data tables
45 //
46 // API
47 //==============================================================
48 // float erfcf(float)
49 //
50 // Overview of operation
51 //==============================================================
52 // 1. 0 <= x <= 10.06
53 //
54 // erfcf(x) = P15(x) * exp( -x^2 )
55 //
56 // Comment:
57 //
58 // Let x(0)=0, x(i) = 2^(i), i=1,...3, x(4)= 10.06
59 //
60 // Let x(i)<= x < x(i+1).
61 // We can find i as exponent of argument x (let i = 0 for 0<= x < 2 )
62 //
63 // Let P15(x) - polynomial approximation of degree 15 for function
64 // erfcf(x) * exp( x^2) and x(i) <= x <= x(i+1), i = 0,1,2,3
65 // Polynomial coefficients we have in the table erfc_p_table.
66 //
67 // So we can find result for erfcf(x) as above.
68 // Algorithm description for exp function see below.
69 //
70 // 2. -4.4 <= x < 0
71 //
72 // erfcf(x) = 2.0 - erfcf(-x)
73 //
74 // 3. x > 10.06
75 //
76 // erfcf(x) ~=~ 0.0
77 //
78 // 4. x < -4.4
79 //
80 // erfcf(x) ~=~ 2.0
82 // Special values
83 //==============================================================
84 // erfcf(+0) = 1.0
85 // erfcf(-0) = 1.0
87 // erfcf(+qnan) = +qnan
88 // erfcf(-qnan) = -qnan
89 // erfcf(+snan) = +qnan
90 // erfcf(-snan) = -qnan
92 // erfcf(-inf) = 2.0
93 // erfcf(+inf) = +0
95 //==============================================================
96 // Take double exp(double) from libm_64.
97 //
98 // Overview of operation
99 //==============================================================
100 // Take the input x. w is "how many log2/128 in x?"
101 // w = x * 128/log2
102 // n = int(w)
103 // x = n log2/128 + r + delta
105 // n = 128M + index_1 + 2^4 index_2
106 // x = M log2 + (log2/128) index_1 + (log2/8) index_2 + r + delta
108 // exp(x) = 2^M 2^(index_1/128) 2^(index_2/8) exp(r) exp(delta)
109 // Construct 2^M
110 // Get 2^(index_1/128) from table_1;
111 // Get 2^(index_2/8) from table_2;
112 // Calculate exp(r) by series
113 // r = x - n (log2/128)_high
114 // delta = - n (log2/128)_low
115 // Calculate exp(delta) as 1 + delta
116 //
117 // Comment for erfcf:
118 //
119 // Let exp(r) = 1 + x + 0.5*x^2 + (1/6)*x^3
120 // Let delta = 0.
121 //==============================================================
122 //
123 // Registers used
124 //==============================================================
125 // Floating Point registers used:
126 // f8, input
127 // f6,f7,f9 -> f11, f32 -> f92
129 // General registers used:
130 // r14 -> r22,r32 -> r50
132 // Predicate registers used:
133 // p6 -> p15
135 // Assembly macros
136 //==============================================================
137 EXP_AD_TB1 = r14
138 exp_GR_sig_inv_ln2 = r15
139 exp_TB1_size = r16
140 exp_GR_rshf_2to56 = r17
141 exp_GR_exp_2tom56 = r18
143 exp_GR_rshf = r33
144 EXP_AD_TB2 = r34
145 EXP_AD_P = r35
146 exp_GR_N = r36
147 exp_GR_index_1 = r37
148 exp_GR_index_2_16 = r38
149 exp_GR_biased_M = r39
150 EXP_AD_T1 = r40
151 EXP_AD_T2 = r41
152 exp_TB2_size = r42
154 // GR for erfcf(x)
155 //==============================================================
156 GR_IndxPlusBias = r19
157 GR_ExpMask = r20
158 GR_BIAS = r21
159 GR_ShftPi_bias = r22
161 GR_P_POINT_1 = r43
162 GR_P_POINT_2 = r44
163 GR_P_POINT_3 = r45
164 GR_P_POINT_4 = r46
166 GR_ShftPi = r47
167 GR_EpsNorm = r48
169 GR_05 = r49
170 GR_1_by_6 = r50
172 // GR for __libm_support call
173 //==============================================================
175 GR_SAVE_B0 = r43
176 GR_SAVE_PFS = r44
177 GR_SAVE_GP = r45
178 GR_SAVE_SP = r46
180 GR_Parameter_X = r47
181 GR_Parameter_Y = r48
182 GR_Parameter_RESULT = r49
183 GR_Parameter_TAG = r50
186 // FR for exp(-x^2)
187 //==============================================================
188 FR_X = f10
189 FR_Y = f1
190 FR_RESULT = f8
192 EXP_2TOM56 = f6
193 EXP_INV_LN2_2TO63 = f7
194 EXP_W_2TO56_RSH = f9
195 exp_ln2_by_128_hi = f11
197 EXP_RSHF_2TO56 = f32
198 exp_ln2_by_128_lo = f33
199 EXP_RSHF = f34
200 EXP_Nfloat = f35
201 exp_r = f36
202 exp_rsq = f37
203 EXP_2M = f38
204 exp_S1 = f39
205 exp_T1 = f40
206 exp_P = f41
207 exp_S = f42
208 EXP_NORM_f8 = f43
209 exp_S2 = f44
210 exp_T2 = f45
212 // FR for erfcf(x)
213 //==============================================================
214 FR_AbsArg = f46
215 FR_Tmp = f47
216 FR_Tmp1 = f48
217 FR_Tmpf = f49
218 FR_NormX = f50
220 FR_A15 = f51
221 FR_A14 = f52
223 FR_A13 = f53
224 FR_A12 = f54
226 FR_A11 = f55
227 FR_A10 = f56
229 FR_A9 = f57
230 FR_A8 = f58
232 FR_A7 = f59
233 FR_A6 = f60
235 FR_A5 = f61
236 FR_A4 = f62
238 FR_A3 = f63
239 FR_A2 = f64
241 FR_A1 = f65
242 FR_A0 = f66
244 FR_P15_0_1 = f67
245 FR_P15_1_1 = f68
246 FR_P15_1_2 = f69
247 FR_P15_2_1 = f70
248 FR_P15_2_2 = f71
249 FR_P15_3_1 = f72
250 FR_P15_3_2 = f73
251 FR_P15_4_1 = f74
252 FR_P15_4_2 = f75
253 FR_P15_7_1 = f76
254 FR_P15_7_2 = f77
255 FR_P15_8_1 = f78
256 FR_P15_9_1 = f79
257 FR_P15_9_2 = f80
258 FR_P15_13_1 = f81
259 FR_P15_14_1 = f82
260 FR_P15_14_2 = f83
262 FR_2 = f84
263 FR_05 = f85
264 FR_1_by_6 = f86
265 FR_Pol = f87
266 FR_Exp = f88
268 FR_POS_ARG_ASYMP = f89
269 FR_NEG_ARG_ASYMP = f90
271 FR_UnfBound = f91
272 FR_EpsNorm = f92
274 // Data tables
275 //==============================================================
276 RODATA
277 .align 16
279 // ************* DO NOT CHANGE ORDER OF THESE TABLES ********************
281 // double-extended 1/ln(2)
282 // 3fff b8aa 3b29 5c17 f0bb be87fed0691d3e88
283 // 3fff b8aa 3b29 5c17 f0bc
284 // For speed the significand will be loaded directly with a movl and setf.sig
285 // and the exponent will be bias+63 instead of bias+0. Thus subsequent
286 // computations need to scale appropriately.
287 // The constant 128/ln(2) is needed for the computation of w. This is also
288 // obtained by scaling the computations.
289 //
290 // Two shifting constants are loaded directly with movl and setf.d.
291 // 1. EXP_RSHF_2TO56 = 1.1000..00 * 2^(63-7)
292 // This constant is added to x*1/ln2 to shift the integer part of
293 // x*128/ln2 into the rightmost bits of the significand.
294 // The result of this fma is EXP_W_2TO56_RSH.
295 // 2. EXP_RSHF = 1.1000..00 * 2^(63)
296 // This constant is subtracted from EXP_W_2TO56_RSH * 2^(-56) to give
297 // the integer part of w, n, as a floating-point number.
298 // The result of this fms is EXP_Nfloat.
301 LOCAL_OBJECT_START(exp_table_1)
303 data4 0x4120f5c3, 0x408ccccd //POS_ARG_ASYMP = 10.06, NEG_ARG_ASYMP = 4.4
304 data4 0x41131Cdf, 0x00800000 //UnfBound ~=~ 9.1, EpsNorm ~=~ 1.1754944e-38
305 //
306 data8 0xb17217f7d1cf79ab , 0x00003ff7 // ln2/128 hi
307 data8 0xc9e3b39803f2f6af , 0x00003fb7 // ln2/128 lo
308 //
309 // Table 1 is 2^(index_1/128) where
310 // index_1 goes from 0 to 15
311 //
312 data8 0x8000000000000000 , 0x00003FFF
313 data8 0x80B1ED4FD999AB6C , 0x00003FFF
314 data8 0x8164D1F3BC030773 , 0x00003FFF
315 data8 0x8218AF4373FC25EC , 0x00003FFF
316 data8 0x82CD8698AC2BA1D7 , 0x00003FFF
317 data8 0x8383594EEFB6EE37 , 0x00003FFF
318 data8 0x843A28C3ACDE4046 , 0x00003FFF
319 data8 0x84F1F656379C1A29 , 0x00003FFF
320 data8 0x85AAC367CC487B15 , 0x00003FFF
321 data8 0x8664915B923FBA04 , 0x00003FFF
322 data8 0x871F61969E8D1010 , 0x00003FFF
323 data8 0x87DB357FF698D792 , 0x00003FFF
324 data8 0x88980E8092DA8527 , 0x00003FFF
325 data8 0x8955EE03618E5FDD , 0x00003FFF
326 data8 0x8A14D575496EFD9A , 0x00003FFF
327 data8 0x8AD4C6452C728924 , 0x00003FFF
328 LOCAL_OBJECT_END(exp_table_1)
330 // Table 2 is 2^(index_1/8) where
331 // index_2 goes from 0 to 7
333 LOCAL_OBJECT_START(exp_table_2)
335 data8 0x8000000000000000 , 0x00003FFF
336 data8 0x8B95C1E3EA8BD6E7 , 0x00003FFF
337 data8 0x9837F0518DB8A96F , 0x00003FFF
338 data8 0xA5FED6A9B15138EA , 0x00003FFF
339 data8 0xB504F333F9DE6484 , 0x00003FFF
340 data8 0xC5672A115506DADD , 0x00003FFF
341 data8 0xD744FCCAD69D6AF4 , 0x00003FFF
342 data8 0xEAC0C6E7DD24392F , 0x00003FFF
343 LOCAL_OBJECT_END(exp_table_2)
345 LOCAL_OBJECT_START(erfc_p_table)
347 // Pol_0
348 data8 0xBEA3260C63CB0446 //A15 = -5.70673541831883454676e-07
349 data8 0x3EE63D6178077654 //A14 = +1.06047480138940182343e-05
350 data8 0xBF18646BC5FC70A7 //A13 = -9.30491237309283694347e-05
351 data8 0x3F40F92F909117FE //A12 = +5.17986512144075019133e-04
352 data8 0xBF611344289DE1E6 //A11 = -2.08438217390159994419e-03
353 data8 0x3F7AF9FE6AD16DC0 //A10 = +6.58606893292862351928e-03
354 data8 0xBF91D219E196CBA7 //A9 = -1.74030345858217321001e-02
355 data8 0x3FA4AFDDA355854C //A8 = +4.04042493708041968315e-02
356 data8 0xBFB5D465BB7025AE //A7 = -8.52721769916999425445e-02
357 data8 0x3FC54C15A95B717D //A6 = +1.66384418195672549029e-01
358 data8 0xBFD340A75B4B1AB5 //A5 = -3.00821150926292166899e-01
359 data8 0x3FDFFFC0BFCD247F //A4 = +4.99984919839853542841e-01
360 data8 0xBFE81270C361852B //A3 = -7.52251035312075583309e-01
361 data8 0x3FEFFFFFC67295FC //A2 = +9.99999892800303301771e-01
362 data8 0xBFF20DD74F8CD2BF //A1 = -1.12837916445020868099e+00
363 data8 0x3FEFFFFFFFFE7C1D //A0 = +9.99999999988975570714e-01
364 // Pol_1
365 data8 0xBDE8EC4BDD953B56 //A15 = -1.81338928934942767144e-10
366 data8 0x3E43607F269E2A1C //A14 = +9.02309090272196442358e-09
367 data8 0xBE8C4D9E69C10E02 //A13 = -2.10875261143659275328e-07
368 data8 0x3EC9CF2F84566725 //A12 = +3.07671055805877356583e-06
369 data8 0xBF007980B1B46A4D //A11 = -3.14228438702169818945e-05
370 data8 0x3F2F4C3AD6DEF24A //A10 = +2.38783056770846320260e-04
371 data8 0xBF56F5129F8D30FA //A9 = -1.40120333363130546426e-03
372 data8 0x3F7AA6C7ABFC38EE //A8 = +6.50671002200751820429e-03
373 data8 0xBF98E7522CB84BEF //A7 = -2.43199195666185511109e-02
374 data8 0x3FB2F68EB1C3D073 //A6 = +7.40746673580490638637e-02
375 data8 0xBFC7C16055AC6385 //A5 = -1.85588876564704611769e-01
376 data8 0x3FD8A707AEF5A440 //A4 = +3.85194702967570635211e-01
377 data8 0xBFE547BFE39AE2EA //A3 = -6.65008492032112467310e-01
378 data8 0x3FEE7C91BDF13578 //A2 = +9.52706213932898128515e-01
379 data8 0xBFF1CB5B61F8C589 //A1 = -1.11214769621105541214e+00
380 data8 0x3FEFEA56BC81FD37 //A0 = +9.97355812243688815239e-01
381 // Pol_2
382 data8 0xBD302724A12F46E0 //A15 = -5.73866382814058809406e-14
383 data8 0x3D98889B75D3102E //A14 = +5.57829983681360947356e-12
384 data8 0xBDF16EA15074A1E9 //A13 = -2.53671153922423457844e-10
385 data8 0x3E3EC6E688CFEE5F //A12 = +7.16581828336436419561e-09
386 data8 0xBE82E5ED44C52609 //A11 = -1.40802202239825487803e-07
387 data8 0x3EC120BE5CE42353 //A10 = +2.04180535157522081699e-06
388 data8 0xBEF7B8B0311A1911 //A9 = -2.26225266204633600888e-05
389 data8 0x3F29A281F43FC238 //A8 = +1.95577968156184077632e-04
390 data8 0xBF55E19858B3B7A4 //A7 = -1.33552434527526534043e-03
391 data8 0x3F7DAC8C3D12E5FD //A6 = +7.24463253680473816303e-03
392 data8 0xBF9FF9C04613FB47 //A5 = -3.12261622211693854028e-02
393 data8 0x3FBB3D5DBF9D9366 //A4 = +1.06405123978743883370e-01
394 data8 0xBFD224DE9F62C258 //A3 = -2.83500342989133623476e-01
395 data8 0x3FE28A95CB8C6D3E //A2 = +5.79417131000276437708e-01
396 data8 0xBFEC21205D358672 //A1 = -8.79043752717008257224e-01
397 data8 0x3FEDAE44D5EDFE5B //A0 = +9.27523057776805771830e-01
398 // Pol_3
399 data8 0xBCA3BCA734AC82F1 //A15 = -1.36952437983096410260e-16
400 data8 0x3D16740DC3990612 //A14 = +1.99425676175410093285e-14
401 data8 0xBD77F4353812C46A //A13 = -1.36162367755616790260e-12
402 data8 0x3DCFD0BE13C73DB4 //A12 = +5.78718761040355136007e-11
403 data8 0xBE1D728DF71189B4 //A11 = -1.71406885583934105120e-09
404 data8 0x3E64252C8CB710B5 //A10 = +3.75233795940731111303e-08
405 data8 0xBEA514B93180F33D //A9 = -6.28261292774310809962e-07
406 data8 0x3EE1381118CC7151 //A8 = +8.21066421390821904504e-06
407 data8 0xBF1634404FB0FA72 //A7 = -8.47019436358372148764e-05
408 data8 0x3F46B2CBBCF0EB32 //A6 = +6.92700845213200923490e-04
409 data8 0xBF725C2B445E6D81 //A5 = -4.48243046949004063741e-03
410 data8 0x3F974E7CFA4D89D9 //A4 = +2.27603462002522228717e-02
411 data8 0xBFB6D7BAC2E342D1 //A3 = -8.92292714882032736443e-02
412 data8 0x3FD0D156AD9CE2A6 //A2 = +2.62777013343603696631e-01
413 data8 0xBFE1C228572AADB0 //A1 = -5.54950876471982857725e-01
414 data8 0x3FE8A739F48B9A3B //A0 = +7.70413377406675619766e-01
415 LOCAL_OBJECT_END(erfc_p_table)
418 .section .text
419 GLOBAL_LIBM_ENTRY(erfcf)
421 // Form index i for table erfc_p_table as exponent of x
422 // We use i + bias in real calculations
423 { .mlx
424 getf.exp GR_IndxPlusBias = f8 // (sign + exp + bias) of x
425 movl exp_GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc //signif.of 1/ln2
426 }
427 { .mlx
428 addl EXP_AD_TB1 = @ltoff(exp_table_1), gp
429 movl exp_GR_rshf_2to56 = 0x4768000000000000 // 1.100 2^(63+56)
430 }
431 ;;
433 // Form argument EXP_NORM_f8 for exp(-x^2)
434 { .mfi
435 ld8 EXP_AD_TB1 = [EXP_AD_TB1]
436 fcmp.ge.s1 p6,p7 = f8, f0 // p6: x >= 0 ,p7: x<0
437 mov GR_BIAS = 0x0FFFF
438 }
439 { .mfi
440 mov exp_GR_exp_2tom56 = 0xffff-56
441 fnma.s1 EXP_NORM_f8 = f8, f8, f0 // -x^2
442 mov GR_ExpMask = 0x1ffff
443 }
444 ;;
446 // Form two constants we need
447 // 1/ln2 * 2^63 to compute w = x * 1/ln2 * 128
448 // 1.1000..000 * 2^(63+63-7) to right shift int(w) into the significand
450 // p9: x = 0,+inf,-inf,nan,unnorm.
451 // p10: x!= 0,+inf,-inf,nan,unnorm.
452 { .mfi
453 setf.sig EXP_INV_LN2_2TO63 = exp_GR_sig_inv_ln2 // Form 1/ln2*2^63
454 fclass.m p9,p10 = f8,0xef
455 shl GR_ShftPi_bias = GR_BIAS, 7
456 }
457 { .mfi
458 setf.d EXP_RSHF_2TO56 = exp_GR_rshf_2to56 //Const 1.10*2^(63+56)
459 nop.f 0
460 and GR_IndxPlusBias = GR_IndxPlusBias, GR_ExpMask // i + bias
461 }
462 ;;
464 { .mfi
465 alloc r32 = ar.pfs, 0, 15, 4, 0
466 (p6) fma.s1 FR_AbsArg = f1, f0, f8 // |x| if x >= 0
467 cmp.lt p15,p0 = GR_IndxPlusBias, GR_BIAS//p15: i < 0 (for |x|<1)
468 }
469 { .mlx
470 setf.exp EXP_2TOM56 = exp_GR_exp_2tom56 //2^-56 for scaling Nfloat
471 movl exp_GR_rshf = 0x43e8000000000000 //1.10 2^63,right shift.
472 }
473 ;;
475 { .mfi
476 ldfps FR_POS_ARG_ASYMP, FR_NEG_ARG_ASYMP = [EXP_AD_TB1],8
477 nop.f 0
478 (p15) mov GR_IndxPlusBias = GR_BIAS //Let i = 0 if i < 0
479 }
480 { .mlx
481 mov GR_P_POINT_3 = 0x1A0
482 movl GR_05 = 0x3fe0000000000000
483 }
484 ;;
486 // Form shift GR_ShftPi from the beginning of erfc_p_table
487 // to the polynomial with number i
488 { .mfi
489 ldfps FR_UnfBound, FR_EpsNorm = [EXP_AD_TB1],8
490 nop.f 0
491 shl GR_ShftPi = GR_IndxPlusBias, 7
492 }
493 { .mfi
494 setf.d EXP_RSHF = exp_GR_rshf // Form right shift 1.100 * 2^63
495 (p7) fms.s1 FR_AbsArg = f1, f0, f8 // |x| if x < 0
496 mov exp_TB1_size = 0x100
497 }
498 ;;
500 // Form pointer GR_P_POINT_3 to the beginning of erfc_p_table
501 { .mfi
502 setf.d FR_05 = GR_05
503 nop.f 0
504 sub GR_ShftPi = GR_ShftPi,GR_ShftPi_bias
505 }
506 { .mfb
507 add GR_P_POINT_3 = GR_P_POINT_3, EXP_AD_TB1
508 nop.f 0
509 (p9) br.cond.spnt SPECIAL // For x = 0,+inf,-inf,nan,unnorm
510 }
511 ;;
513 { .mfi
514 add GR_P_POINT_1 = GR_P_POINT_3, GR_ShftPi
515 nop.f 0
516 add GR_P_POINT_2 = GR_P_POINT_3, GR_ShftPi
517 }
518 { .mfi
519 ldfe exp_ln2_by_128_hi = [EXP_AD_TB1],16
520 fma.s1 FR_NormX = f8,f1,f0
521 add GR_P_POINT_3 = GR_P_POINT_3, GR_ShftPi
522 }
523 ;;
525 // Load coefficients for polynomial P15(x)
526 { .mfi
527 ldfpd FR_A15, FR_A14 = [GR_P_POINT_1], 16
528 nop.f 0
529 add GR_P_POINT_3 = 0x30, GR_P_POINT_3
530 }
531 { .mfi
532 ldfe exp_ln2_by_128_lo = [EXP_AD_TB1], 16
533 nop.f 0
534 add GR_P_POINT_2 = 0x20, GR_P_POINT_2
535 }
536 ;;
538 // Now EXP_AD_TB1 points to the beginning of table 1
539 { .mlx
540 ldfpd FR_A13, FR_A12 = [GR_P_POINT_1]
541 movl GR_1_by_6 = 0x3FC5555555555555
542 }
543 { .mfi
544 add GR_P_POINT_4 = 0x30, GR_P_POINT_2
545 nop.f 0
546 nop.i 0
547 }
548 ;;
550 { .mfi
551 ldfpd FR_A11, FR_A10 = [GR_P_POINT_2]
552 fma.s1 FR_2 = f1, f1, f1
553 mov exp_TB2_size = 0x80
554 }
555 { .mfi
556 ldfpd FR_A9, FR_A8 = [GR_P_POINT_3],16
557 nop.f 0
558 add GR_P_POINT_1 = 0x60 ,GR_P_POINT_1
559 }
560 ;;
562 // W = X * Inv_log2_by_128
563 // By adding 1.10...0*2^63 we shift and get round_int(W) in significand.
564 // We actually add 1.10...0*2^56 to X * Inv_log2 to do the same thing.
565 { .mfi
566 ldfpd FR_A7, FR_A6 = [GR_P_POINT_3]
567 fma.s1 EXP_W_2TO56_RSH = EXP_NORM_f8,EXP_INV_LN2_2TO63,EXP_RSHF_2TO56
568 add EXP_AD_TB2 = exp_TB1_size, EXP_AD_TB1
570 }
571 { .mfi
572 ldfpd FR_A5, FR_A4 = [GR_P_POINT_4], 16
573 nop.f 0
574 nop.i 0
575 }
576 ;;
578 { .mfi
579 ldfpd FR_A3, FR_A2 = [GR_P_POINT_4]
580 fmerge.s FR_X = f8,f8
581 nop.i 0
582 }
583 { .mfi
584 ldfpd FR_A1, FR_A0 = [GR_P_POINT_1]
585 nop.f 0
586 nop.i 0
587 }
588 ;;
590 //p14: x < - NEG_ARG_ASYMP = -4.4 -> erfcf(x) ~=~ 2.0
591 { .mfi
592 setf.d FR_1_by_6 = GR_1_by_6
593 (p7) fcmp.gt.unc.s1 p14,p0 = FR_AbsArg, FR_NEG_ARG_ASYMP //p7: x < 0
594 nop.i 0
595 }
596 ;;
598 //p15: x > POS_ARG_ASYMP = 10.06 -> erfcf(x) ~=~ 0.0
599 { .mfi
600 nop.m 0
601 (p6) fcmp.gt.unc.s1 p15,p0 = FR_AbsArg, FR_POS_ARG_ASYMP //p6: x > 0
602 nop.i 0
603 }
604 ;;
606 { .mfi
607 nop.m 0
608 fcmp.le.s1 p8,p0 = FR_NormX, FR_UnfBound // p8: x <= UnfBound
609 nop.i 0
610 }
611 { .mfb
612 nop.m 0
613 (p14) fnma.s.s0 FR_RESULT = FR_EpsNorm, FR_EpsNorm, FR_2//y = 2 if x <-4.4
614 (p14) br.ret.spnt b0
615 }
616 ;;
618 // Nfloat = round_int(W)
619 // The signficand of EXP_W_2TO56_RSH contains the rounded integer part of W,
620 // as a twos complement number in the lower bits (that is, it may be negative).
621 // That twos complement number (called N) is put into exp_GR_N.
623 // Since EXP_W_2TO56_RSH is scaled by 2^56, it must be multiplied by 2^-56
624 // before the shift constant 1.10000 * 2^63 is subtracted to yield EXP_Nfloat.
625 // Thus, EXP_Nfloat contains the floating point version of N
627 { .mfi
628 nop.m 0
629 fms.s1 EXP_Nfloat = EXP_W_2TO56_RSH, EXP_2TOM56, EXP_RSHF
630 nop.i 0
631 }
632 { .mfb
633 (p15) mov GR_Parameter_TAG = 209
634 (p15) fma.s.s0 FR_RESULT = FR_EpsNorm,FR_EpsNorm,f0 //Result.for x>10.06
635 (p15) br.cond.spnt __libm_error_region
636 }
637 ;;
639 // Now we can calculate polynomial P15(x)
640 { .mfi
641 nop.m 0
642 fma.s1 FR_P15_1_1 = FR_AbsArg, FR_AbsArg, f0 // x ^2
643 nop.i 0
644 }
645 { .mfi
646 nop.m 0
647 fma.s1 FR_P15_0_1 = FR_A15, FR_AbsArg, FR_A14
648 nop.i 0
649 }
650 ;;
652 { .mfi
653 nop.m 0
654 fma.s1 FR_P15_1_2 = FR_A13, FR_AbsArg, FR_A12
655 nop.i 0
656 }
657 ;;
659 { .mfi
660 getf.sig exp_GR_N = EXP_W_2TO56_RSH
661 fma.s1 FR_P15_2_1 = FR_A9, FR_AbsArg, FR_A8
662 nop.i 0
663 }
664 { .mfi
665 nop.m 0
666 fma.s1 FR_P15_2_2 = FR_A11, FR_AbsArg, FR_A10
667 nop.i 0
668 }
669 ;;
671 { .mfi
672 nop.m 0
673 fma.s1 FR_P15_3_1 = FR_A5, FR_AbsArg, FR_A4
674 nop.i 0
675 }
676 { .mfi
677 nop.m 0
678 fma.s1 FR_P15_3_2 = FR_A7, FR_AbsArg, FR_A6
679 nop.i 0
680 }
681 ;;
683 // exp_GR_index_1 has index_1
684 // exp_GR_index_2_16 has index_2 * 16
685 // exp_GR_biased_M has M
686 // exp_GR_index_1_16 has index_1 * 16
688 // r2 has true M
689 { .mfi
690 and exp_GR_index_1 = 0x0f, exp_GR_N
691 fma.s1 FR_P15_4_1 = FR_A1, FR_AbsArg, FR_A0
692 shr r2 = exp_GR_N, 0x7
694 }
695 { .mfi
696 and exp_GR_index_2_16 = 0x70, exp_GR_N
697 fma.s1 FR_P15_4_2 = FR_A3, FR_AbsArg, FR_A2
698 nop.i 0
699 }
700 ;;
702 // EXP_AD_T1 has address of T1
703 // EXP_AD_T2 has address if T2
705 { .mfi
706 add EXP_AD_T2 = EXP_AD_TB2, exp_GR_index_2_16
707 nop.f 0
708 shladd EXP_AD_T1 = exp_GR_index_1, 4, EXP_AD_TB1
709 }
710 { .mfi
711 addl exp_GR_biased_M = 0xffff, r2
712 fnma.s1 exp_r = EXP_Nfloat, exp_ln2_by_128_hi, EXP_NORM_f8
713 nop.i 0
714 }
715 ;;
717 // Create Scale = 2^M
718 // r = x - Nfloat * ln2_by_128_hi
720 { .mfi
721 setf.exp EXP_2M = exp_GR_biased_M
722 fma.s1 FR_P15_7_1 = FR_P15_0_1, FR_P15_1_1, FR_P15_1_2
723 nop.i 0
724 }
725 { .mfi
726 ldfe exp_T2 = [EXP_AD_T2]
727 nop.f 0
728 nop.i 0
729 }
730 ;;
732 // Load T1 and T2
734 { .mfi
735 ldfe exp_T1 = [EXP_AD_T1]
736 fma.s1 FR_P15_7_2 = FR_P15_1_1, FR_P15_1_1, f0 // x^4
737 nop.i 0
738 }
739 { .mfi
740 nop.m 0
741 fma.s1 FR_P15_8_1 = FR_P15_1_1, FR_P15_2_2, FR_P15_2_1
742 nop.i 0
743 }
744 ;;
746 { .mfi
747 nop.m 0
748 fma.s1 FR_P15_9_1 = FR_P15_1_1, FR_P15_4_2, FR_P15_4_1
749 nop.i 0
750 }
751 { .mfi
752 nop.m 0
753 fma.s1 FR_P15_9_2 = FR_P15_1_1, FR_P15_3_2, FR_P15_3_1
754 nop.i 0
755 }
756 ;;
758 { .mfi
759 nop.m 0
760 fma.s1 exp_P = FR_1_by_6, exp_r, FR_05
761 nop.i 0
762 }
763 { .mfi
764 nop.m 0
765 fma.s1 exp_rsq = exp_r, exp_r, f0
766 nop.i 0
767 }
768 ;;
770 { .mfi
771 nop.m 0
772 fma.s1 FR_P15_13_1 = FR_P15_7_2, FR_P15_7_1, FR_P15_8_1
773 nop.i 0
774 }
775 ;;
777 { .mfi
778 nop.m 0
779 fma.s1 FR_P15_14_1 = FR_P15_7_2, FR_P15_9_2, FR_P15_9_1
780 nop.i 0
781 }
782 { .mfi
783 nop.m 0
784 fma.s1 FR_P15_14_2 = FR_P15_7_2, FR_P15_7_2, f0 // x^8
785 nop.i 0
786 }
787 ;;
789 { .mfi
790 nop.m 0
791 fma.s1 exp_P = exp_P, exp_rsq, exp_r
792 nop.i 0
793 }
794 { .mfi
795 nop.m 0
796 fma.s1 exp_S1 = EXP_2M, exp_T2, f0
797 nop.i 0
798 }
799 ;;
801 { .mfi
802 nop.m 0
803 fma.s1 FR_Pol = FR_P15_14_2, FR_P15_13_1, FR_P15_14_1 // P15(x)
804 nop.i 0
805 }
806 ;;
808 { .mfi
809 nop.m 0
810 fma.s1 exp_S = exp_S1, exp_T1, f0
811 nop.i 0
812 }
813 ;;
815 { .mfi
816 nop.m 0
817 fma.s1 FR_Exp = exp_S, exp_P, exp_S // exp(-x^2)
818 nop.i 0
819 }
820 ;;
822 { .mfi
823 nop.m 0
824 fma.s.s0 FR_Tmpf = f8, f1, f0 // Flag d
825 nop.i 0
826 }
827 ;;
829 //p6: result for 0 < x < = POS_ARG_ASYMP
830 //p7: result for - NEG_ARG_ASYMP <= x < 0
831 //p8: exit for - NEG_ARG_ASYMP <= x <= UnfBound, x!=0
832 .pred.rel "mutex",p6,p7
833 { .mfi
834 nop.m 0
835 (p6) fma.s.s0 f8 = FR_Exp, FR_Pol, f0
836 nop.i 0
837 }
838 { .mfb
839 mov GR_Parameter_TAG = 209
840 (p7) fnma.s.s0 f8 = FR_Exp, FR_Pol, FR_2
841 (p8) br.ret.sptk b0
842 }
843 ;;
845 //p10: branch for UnfBound < x < = POS_ARG_ASYMP
846 { .mfb
847 nop.m 0
848 nop.f 0
849 (p10) br.cond.spnt __libm_error_region
850 }
851 ;;
853 //Only via (p9) br.cond.spnt SPECIAL for x = 0,+inf,-inf,nan,unnorm
854 SPECIAL:
856 { .mfi
857 nop.m 0
858 fclass.m.unc p10,p0 = f8,0x07 // p10: x = 0
859 nop.i 0
860 }
861 ;;
863 { .mfi
864 nop.m 0
865 fclass.m.unc p11,p0 = f8,0x21 // p11: x = +inf
866 nop.i 0
867 }
868 ;;
870 { .mfi
871 nop.m 0
872 fclass.m.unc p12,p0 = f8,0x22 // p12 x = -inf
873 nop.i 0
874 }
875 { .mfb
876 nop.m 0
877 (p10) fma.s.s0 f8 = f1, f1, f0
878 (p10) br.ret.sptk b0 // Quick exit for x = 0
879 }
880 ;;
882 { .mfi
883 nop.m 0
884 fclass.m.unc p13,p0 = f8,0xc3 // p13: x = nan
885 nop.i 0
886 }
887 { .mfb
888 nop.m 0
889 (p11) fma.s.s0 f8 = f0, f1, f0
890 (p11) br.ret.spnt b0 // Quick exit for x = +inf
891 }
892 ;;
893 { .mfi
894 nop.m 0
895 fclass.m.unc p14,p0 = f8,0x0b // P14: x = unnormalized
896 nop.i 0
897 }
898 { .mfb
899 nop.m 0
900 (p12) fma.s.s0 f8 = f1, f1, f1
901 (p12) br.ret.spnt b0 // Quick exit for x = -inf
902 }
903 ;;
905 { .mfb
906 nop.m 0
907 (p13) fma.s.s0 f8 = f8, f1, f0
908 (p13) br.ret.sptk b0 // Quick exit for x = nan
909 }
910 ;;
912 { .mfb
913 nop.m 0
914 (p14) fnma.s.s0 f8 = f8, f1, f1
915 (p14) br.ret.sptk b0 // Quick exit for x = unnormalized
916 }
917 ;;
919 GLOBAL_LIBM_END(erfcf)
920 libm_alias_float_other (erfc, erfc)
923 // Call via (p10) br.cond.spnt __libm_error_region
924 // for UnfBound < x < = POS_ARG_ASYMP
925 // and
926 //
927 // call via (p15) br.cond.spnt __libm_error_region
928 // for x > POS_ARG_ASYMP
930 LOCAL_LIBM_ENTRY(__libm_error_region)
931 .prologue
932 { .mfi
933 add GR_Parameter_Y=-32,sp // Parameter 2 value
934 nop.f 0
935 .save ar.pfs,GR_SAVE_PFS
936 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
937 }
938 { .mfi
939 .fframe 64
940 add sp=-64,sp // Create new stack
941 nop.f 0
942 mov GR_SAVE_GP=gp // Save gp
943 };;
944 { .mmi
945 stfs [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack
946 add GR_Parameter_X = 16,sp // Parameter 1 address
947 .save b0, GR_SAVE_B0
948 mov GR_SAVE_B0=b0 // Save b0
949 };;
950 .body
951 { .mib
952 stfs [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack
953 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
954 nop.b 0
955 }
956 { .mib
957 stfs [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack
958 add GR_Parameter_Y = -16,GR_Parameter_Y
959 br.call.sptk b0=__libm_error_support# // Call error handling function
960 };;
961 { .mmi
962 nop.m 0
963 nop.m 0
964 add GR_Parameter_RESULT = 48,sp
965 };;
966 { .mmi
967 ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack
968 .restore sp
969 add sp = 64,sp // Restore stack pointer
970 mov b0 = GR_SAVE_B0 // Restore return address
971 };;
972 { .mib
973 mov gp = GR_SAVE_GP // Restore gp
974 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
975 br.ret.sptk b0 // Return
976 };;
978 LOCAL_LIBM_END(__libm_error_region)
979 .type __libm_error_support#,@function
980 .global __libm_error_support#