| blob | 2e3eeab3c75501a457cd1de25718ddeedb25318e |
1 .file "erfcf.s"
4 // Copyright (c) 2002 - 2005, Intel Corporation
5 // All rights reserved.
6 //
7 // Contributed 2002 by the Intel Numerics Group, Intel Corporation
8 //
9 // Redistribution and use in source and binary forms, with or without
10 // modification, are permitted provided that the following conditions are
11 // met:
12 //
13 // * Redistributions of source code must retain the above copyright
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
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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
37 // problem reports or change requests be submitted to it directly at
38 // http://www.intel.com/software/products/opensource/libraries/num.htm.
39 //
40 // History
41 //==============================================================
42 // 01/17/02 Initial version
43 // 05/20/02 Cleaned up namespace and sf0 syntax
44 // 02/06/03 Reordered header: .section, .global, .proc, .align
45 // 03/31/05 Reformatted delimiters between data tables
46 //
47 // API
48 //==============================================================
49 // float erfcf(float)
50 //
51 // Overview of operation
52 //==============================================================
53 // 1. 0 <= x <= 10.06
54 //
55 // erfcf(x) = P15(x) * exp( -x^2 )
56 //
57 // Comment:
58 //
59 // Let x(0)=0, x(i) = 2^(i), i=1,...3, x(4)= 10.06
60 //
61 // Let x(i)<= x < x(i+1).
62 // We can find i as exponent of argument x (let i = 0 for 0<= x < 2 )
63 //
64 // Let P15(x) - polynomial approximation of degree 15 for function
65 // erfcf(x) * exp( x^2) and x(i) <= x <= x(i+1), i = 0,1,2,3
66 // Polynomial coeffitients we have in the table erfc_p_table.
67 //
68 // So we can find result for erfcf(x) as above.
69 // Algorithm description for exp function see below.
70 //
71 // 2. -4.4 <= x < 0
72 //
73 // erfcf(x) = 2.0 - erfcf(-x)
74 //
75 // 3. x > 10.06
76 //
77 // erfcf(x) ~=~ 0.0
78 //
79 // 4. x < -4.4
80 //
81 // erfcf(x) ~=~ 2.0
83 // Special values
84 //==============================================================
85 // erfcf(+0) = 1.0
86 // erfcf(-0) = 1.0
88 // erfcf(+qnan) = +qnan
89 // erfcf(-qnan) = -qnan
90 // erfcf(+snan) = +qnan
91 // erfcf(-snan) = -qnan
93 // erfcf(-inf) = 2.0
94 // erfcf(+inf) = +0
96 //==============================================================
97 // Take double exp(double) from libm_64.
98 //
99 // Overview of operation
100 //==============================================================
101 // Take the input x. w is "how many log2/128 in x?"
102 // w = x * 128/log2
103 // n = int(w)
104 // x = n log2/128 + r + delta
106 // n = 128M + index_1 + 2^4 index_2
107 // x = M log2 + (log2/128) index_1 + (log2/8) index_2 + r + delta
109 // exp(x) = 2^M 2^(index_1/128) 2^(index_2/8) exp(r) exp(delta)
110 // Construct 2^M
111 // Get 2^(index_1/128) from table_1;
112 // Get 2^(index_2/8) from table_2;
113 // Calculate exp(r) by series
114 // r = x - n (log2/128)_high
115 // delta = - n (log2/128)_low
116 // Calculate exp(delta) as 1 + delta
117 //
118 // Comment for erfcf:
119 //
120 // Let exp(r) = 1 + x + 0.5*x^2 + (1/6)*x^3
121 // Let delta = 0.
122 //==============================================================
123 //
124 // Registers used
125 //==============================================================
126 // Floating Point registers used:
127 // f8, input
128 // f6,f7,f9 -> f11, f32 -> f92
130 // General registers used:
131 // r14 -> r22,r32 -> r50
133 // Predicate registers used:
134 // p6 -> p15
136 // Assembly macros
137 //==============================================================
138 EXP_AD_TB1 = r14
139 exp_GR_sig_inv_ln2 = r15
140 exp_TB1_size = r16
141 exp_GR_rshf_2to56 = r17
142 exp_GR_exp_2tom56 = r18
144 exp_GR_rshf = r33
145 EXP_AD_TB2 = r34
146 EXP_AD_P = r35
147 exp_GR_N = r36
148 exp_GR_index_1 = r37
149 exp_GR_index_2_16 = r38
150 exp_GR_biased_M = r39
151 EXP_AD_T1 = r40
152 EXP_AD_T2 = r41
153 exp_TB2_size = r42
155 // GR for erfcf(x)
156 //==============================================================
157 GR_IndxPlusBias = r19
158 GR_ExpMask = r20
159 GR_BIAS = r21
160 GR_ShftPi_bias = r22
162 GR_P_POINT_1 = r43
163 GR_P_POINT_2 = r44
164 GR_P_POINT_3 = r45
165 GR_P_POINT_4 = r46
167 GR_ShftPi = r47
168 GR_EpsNorm = r48
170 GR_05 = r49
171 GR_1_by_6 = r50
173 // GR for __libm_support call
174 //==============================================================
176 GR_SAVE_B0 = r43
177 GR_SAVE_PFS = r44
178 GR_SAVE_GP = r45
179 GR_SAVE_SP = r46
181 GR_Parameter_X = r47
182 GR_Parameter_Y = r48
183 GR_Parameter_RESULT = r49
184 GR_Parameter_TAG = r50
187 // FR for exp(-x^2)
188 //==============================================================
189 FR_X = f10
190 FR_Y = f1
191 FR_RESULT = f8
193 EXP_2TOM56 = f6
194 EXP_INV_LN2_2TO63 = f7
195 EXP_W_2TO56_RSH = f9
196 exp_ln2_by_128_hi = f11
198 EXP_RSHF_2TO56 = f32
199 exp_ln2_by_128_lo = f33
200 EXP_RSHF = f34
201 EXP_Nfloat = f35
202 exp_r = f36
203 exp_rsq = f37
204 EXP_2M = f38
205 exp_S1 = f39
206 exp_T1 = f40
207 exp_P = f41
208 exp_S = f42
209 EXP_NORM_f8 = f43
210 exp_S2 = f44
211 exp_T2 = f45
213 // FR for erfcf(x)
214 //==============================================================
215 FR_AbsArg = f46
216 FR_Tmp = f47
217 FR_Tmp1 = f48
218 FR_Tmpf = f49
219 FR_NormX = f50
221 FR_A15 = f51
222 FR_A14 = f52
224 FR_A13 = f53
225 FR_A12 = f54
227 FR_A11 = f55
228 FR_A10 = f56
230 FR_A9 = f57
231 FR_A8 = f58
233 FR_A7 = f59
234 FR_A6 = f60
236 FR_A5 = f61
237 FR_A4 = f62
239 FR_A3 = f63
240 FR_A2 = f64
242 FR_A1 = f65
243 FR_A0 = f66
245 FR_P15_0_1 = f67
246 FR_P15_1_1 = f68
247 FR_P15_1_2 = f69
248 FR_P15_2_1 = f70
249 FR_P15_2_2 = f71
250 FR_P15_3_1 = f72
251 FR_P15_3_2 = f73
252 FR_P15_4_1 = f74
253 FR_P15_4_2 = f75
254 FR_P15_7_1 = f76
255 FR_P15_7_2 = f77
256 FR_P15_8_1 = f78
257 FR_P15_9_1 = f79
258 FR_P15_9_2 = f80
259 FR_P15_13_1 = f81
260 FR_P15_14_1 = f82
261 FR_P15_14_2 = f83
263 FR_2 = f84
264 FR_05 = f85
265 FR_1_by_6 = f86
266 FR_Pol = f87
267 FR_Exp = f88
269 FR_POS_ARG_ASYMP = f89
270 FR_NEG_ARG_ASYMP = f90
272 FR_UnfBound = f91
273 FR_EpsNorm = f92
275 // Data tables
276 //==============================================================
277 RODATA
278 .align 16
280 // ************* DO NOT CHANGE ORDER OF THESE TABLES ********************
282 // double-extended 1/ln(2)
283 // 3fff b8aa 3b29 5c17 f0bb be87fed0691d3e88
284 // 3fff b8aa 3b29 5c17 f0bc
285 // For speed the significand will be loaded directly with a movl and setf.sig
286 // and the exponent will be bias+63 instead of bias+0. Thus subsequent
287 // computations need to scale appropriately.
288 // The constant 128/ln(2) is needed for the computation of w. This is also
289 // obtained by scaling the computations.
290 //
291 // Two shifting constants are loaded directly with movl and setf.d.
292 // 1. EXP_RSHF_2TO56 = 1.1000..00 * 2^(63-7)
293 // This constant is added to x*1/ln2 to shift the integer part of
294 // x*128/ln2 into the rightmost bits of the significand.
295 // The result of this fma is EXP_W_2TO56_RSH.
296 // 2. EXP_RSHF = 1.1000..00 * 2^(63)
297 // This constant is subtracted from EXP_W_2TO56_RSH * 2^(-56) to give
298 // the integer part of w, n, as a floating-point number.
299 // The result of this fms is EXP_Nfloat.
302 LOCAL_OBJECT_START(exp_table_1)
304 data4 0x4120f5c3, 0x408ccccd //POS_ARG_ASYMP = 10.06, NEG_ARG_ASYMP = 4.4
305 data4 0x41131Cdf, 0x00800000 //UnfBound ~=~ 9.1, EpsNorm ~=~ 1.1754944e-38
306 //
307 data8 0xb17217f7d1cf79ab , 0x00003ff7 // ln2/128 hi
308 data8 0xc9e3b39803f2f6af , 0x00003fb7 // ln2/128 lo
309 //
310 // Table 1 is 2^(index_1/128) where
311 // index_1 goes from 0 to 15
312 //
313 data8 0x8000000000000000 , 0x00003FFF
314 data8 0x80B1ED4FD999AB6C , 0x00003FFF
315 data8 0x8164D1F3BC030773 , 0x00003FFF
316 data8 0x8218AF4373FC25EC , 0x00003FFF
317 data8 0x82CD8698AC2BA1D7 , 0x00003FFF
318 data8 0x8383594EEFB6EE37 , 0x00003FFF
319 data8 0x843A28C3ACDE4046 , 0x00003FFF
320 data8 0x84F1F656379C1A29 , 0x00003FFF
321 data8 0x85AAC367CC487B15 , 0x00003FFF
322 data8 0x8664915B923FBA04 , 0x00003FFF
323 data8 0x871F61969E8D1010 , 0x00003FFF
324 data8 0x87DB357FF698D792 , 0x00003FFF
325 data8 0x88980E8092DA8527 , 0x00003FFF
326 data8 0x8955EE03618E5FDD , 0x00003FFF
327 data8 0x8A14D575496EFD9A , 0x00003FFF
328 data8 0x8AD4C6452C728924 , 0x00003FFF
329 LOCAL_OBJECT_END(exp_table_1)
331 // Table 2 is 2^(index_1/8) where
332 // index_2 goes from 0 to 7
334 LOCAL_OBJECT_START(exp_table_2)
336 data8 0x8000000000000000 , 0x00003FFF
337 data8 0x8B95C1E3EA8BD6E7 , 0x00003FFF
338 data8 0x9837F0518DB8A96F , 0x00003FFF
339 data8 0xA5FED6A9B15138EA , 0x00003FFF
340 data8 0xB504F333F9DE6484 , 0x00003FFF
341 data8 0xC5672A115506DADD , 0x00003FFF
342 data8 0xD744FCCAD69D6AF4 , 0x00003FFF
343 data8 0xEAC0C6E7DD24392F , 0x00003FFF
344 LOCAL_OBJECT_END(exp_table_2)
346 LOCAL_OBJECT_START(erfc_p_table)
348 // Pol_0
349 data8 0xBEA3260C63CB0446 //A15 = -5.70673541831883454676e-07
350 data8 0x3EE63D6178077654 //A14 = +1.06047480138940182343e-05
351 data8 0xBF18646BC5FC70A7 //A13 = -9.30491237309283694347e-05
352 data8 0x3F40F92F909117FE //A12 = +5.17986512144075019133e-04
353 data8 0xBF611344289DE1E6 //A11 = -2.08438217390159994419e-03
354 data8 0x3F7AF9FE6AD16DC0 //A10 = +6.58606893292862351928e-03
355 data8 0xBF91D219E196CBA7 //A9 = -1.74030345858217321001e-02
356 data8 0x3FA4AFDDA355854C //A8 = +4.04042493708041968315e-02
357 data8 0xBFB5D465BB7025AE //A7 = -8.52721769916999425445e-02
358 data8 0x3FC54C15A95B717D //A6 = +1.66384418195672549029e-01
359 data8 0xBFD340A75B4B1AB5 //A5 = -3.00821150926292166899e-01
360 data8 0x3FDFFFC0BFCD247F //A4 = +4.99984919839853542841e-01
361 data8 0xBFE81270C361852B //A3 = -7.52251035312075583309e-01
362 data8 0x3FEFFFFFC67295FC //A2 = +9.99999892800303301771e-01
363 data8 0xBFF20DD74F8CD2BF //A1 = -1.12837916445020868099e+00
364 data8 0x3FEFFFFFFFFE7C1D //A0 = +9.99999999988975570714e-01
365 // Pol_1
366 data8 0xBDE8EC4BDD953B56 //A15 = -1.81338928934942767144e-10
367 data8 0x3E43607F269E2A1C //A14 = +9.02309090272196442358e-09
368 data8 0xBE8C4D9E69C10E02 //A13 = -2.10875261143659275328e-07
369 data8 0x3EC9CF2F84566725 //A12 = +3.07671055805877356583e-06
370 data8 0xBF007980B1B46A4D //A11 = -3.14228438702169818945e-05
371 data8 0x3F2F4C3AD6DEF24A //A10 = +2.38783056770846320260e-04
372 data8 0xBF56F5129F8D30FA //A9 = -1.40120333363130546426e-03
373 data8 0x3F7AA6C7ABFC38EE //A8 = +6.50671002200751820429e-03
374 data8 0xBF98E7522CB84BEF //A7 = -2.43199195666185511109e-02
375 data8 0x3FB2F68EB1C3D073 //A6 = +7.40746673580490638637e-02
376 data8 0xBFC7C16055AC6385 //A5 = -1.85588876564704611769e-01
377 data8 0x3FD8A707AEF5A440 //A4 = +3.85194702967570635211e-01
378 data8 0xBFE547BFE39AE2EA //A3 = -6.65008492032112467310e-01
379 data8 0x3FEE7C91BDF13578 //A2 = +9.52706213932898128515e-01
380 data8 0xBFF1CB5B61F8C589 //A1 = -1.11214769621105541214e+00
381 data8 0x3FEFEA56BC81FD37 //A0 = +9.97355812243688815239e-01
382 // Pol_2
383 data8 0xBD302724A12F46E0 //A15 = -5.73866382814058809406e-14
384 data8 0x3D98889B75D3102E //A14 = +5.57829983681360947356e-12
385 data8 0xBDF16EA15074A1E9 //A13 = -2.53671153922423457844e-10
386 data8 0x3E3EC6E688CFEE5F //A12 = +7.16581828336436419561e-09
387 data8 0xBE82E5ED44C52609 //A11 = -1.40802202239825487803e-07
388 data8 0x3EC120BE5CE42353 //A10 = +2.04180535157522081699e-06
389 data8 0xBEF7B8B0311A1911 //A9 = -2.26225266204633600888e-05
390 data8 0x3F29A281F43FC238 //A8 = +1.95577968156184077632e-04
391 data8 0xBF55E19858B3B7A4 //A7 = -1.33552434527526534043e-03
392 data8 0x3F7DAC8C3D12E5FD //A6 = +7.24463253680473816303e-03
393 data8 0xBF9FF9C04613FB47 //A5 = -3.12261622211693854028e-02
394 data8 0x3FBB3D5DBF9D9366 //A4 = +1.06405123978743883370e-01
395 data8 0xBFD224DE9F62C258 //A3 = -2.83500342989133623476e-01
396 data8 0x3FE28A95CB8C6D3E //A2 = +5.79417131000276437708e-01
397 data8 0xBFEC21205D358672 //A1 = -8.79043752717008257224e-01
398 data8 0x3FEDAE44D5EDFE5B //A0 = +9.27523057776805771830e-01
399 // Pol_3
400 data8 0xBCA3BCA734AC82F1 //A15 = -1.36952437983096410260e-16
401 data8 0x3D16740DC3990612 //A14 = +1.99425676175410093285e-14
402 data8 0xBD77F4353812C46A //A13 = -1.36162367755616790260e-12
403 data8 0x3DCFD0BE13C73DB4 //A12 = +5.78718761040355136007e-11
404 data8 0xBE1D728DF71189B4 //A11 = -1.71406885583934105120e-09
405 data8 0x3E64252C8CB710B5 //A10 = +3.75233795940731111303e-08
406 data8 0xBEA514B93180F33D //A9 = -6.28261292774310809962e-07
407 data8 0x3EE1381118CC7151 //A8 = +8.21066421390821904504e-06
408 data8 0xBF1634404FB0FA72 //A7 = -8.47019436358372148764e-05
409 data8 0x3F46B2CBBCF0EB32 //A6 = +6.92700845213200923490e-04
410 data8 0xBF725C2B445E6D81 //A5 = -4.48243046949004063741e-03
411 data8 0x3F974E7CFA4D89D9 //A4 = +2.27603462002522228717e-02
412 data8 0xBFB6D7BAC2E342D1 //A3 = -8.92292714882032736443e-02
413 data8 0x3FD0D156AD9CE2A6 //A2 = +2.62777013343603696631e-01
414 data8 0xBFE1C228572AADB0 //A1 = -5.54950876471982857725e-01
415 data8 0x3FE8A739F48B9A3B //A0 = +7.70413377406675619766e-01
416 LOCAL_OBJECT_END(erfc_p_table)
419 .section .text
420 GLOBAL_LIBM_ENTRY(erfcf)
422 // Form index i for table erfc_p_table as exponent of x
423 // We use i + bias in real calculations
424 { .mlx
425 getf.exp GR_IndxPlusBias = f8 // (sign + exp + bias) of x
426 movl exp_GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc //signif.of 1/ln2
427 }
428 { .mlx
429 addl EXP_AD_TB1 = @ltoff(exp_table_1), gp
430 movl exp_GR_rshf_2to56 = 0x4768000000000000 // 1.100 2^(63+56)
431 }
432 ;;
434 // Form argument EXP_NORM_f8 for exp(-x^2)
435 { .mfi
436 ld8 EXP_AD_TB1 = [EXP_AD_TB1]
437 fcmp.ge.s1 p6,p7 = f8, f0 // p6: x >= 0 ,p7: x<0
438 mov GR_BIAS = 0x0FFFF
439 }
440 { .mfi
441 mov exp_GR_exp_2tom56 = 0xffff-56
442 fnma.s1 EXP_NORM_f8 = f8, f8, f0 // -x^2
443 mov GR_ExpMask = 0x1ffff
444 }
445 ;;
447 // Form two constants we need
448 // 1/ln2 * 2^63 to compute w = x * 1/ln2 * 128
449 // 1.1000..000 * 2^(63+63-7) to right shift int(w) into the significand
451 // p9: x = 0,+inf,-inf,nan,unnorm.
452 // p10: x!= 0,+inf,-inf,nan,unnorm.
453 { .mfi
454 setf.sig EXP_INV_LN2_2TO63 = exp_GR_sig_inv_ln2 // Form 1/ln2*2^63
455 fclass.m p9,p10 = f8,0xef
456 shl GR_ShftPi_bias = GR_BIAS, 7
457 }
458 { .mfi
459 setf.d EXP_RSHF_2TO56 = exp_GR_rshf_2to56 //Const 1.10*2^(63+56)
460 nop.f 0
461 and GR_IndxPlusBias = GR_IndxPlusBias, GR_ExpMask // i + bias
462 }
463 ;;
465 { .mfi
466 alloc r32 = ar.pfs, 0, 15, 4, 0
467 (p6) fma.s1 FR_AbsArg = f1, f0, f8 // |x| if x >= 0
468 cmp.lt p15,p0 = GR_IndxPlusBias, GR_BIAS//p15: i < 0 (for |x|<1)
469 }
470 { .mlx
471 setf.exp EXP_2TOM56 = exp_GR_exp_2tom56 //2^-56 for scaling Nfloat
472 movl exp_GR_rshf = 0x43e8000000000000 //1.10 2^63,right shift.
473 }
474 ;;
476 { .mfi
477 ldfps FR_POS_ARG_ASYMP, FR_NEG_ARG_ASYMP = [EXP_AD_TB1],8
478 nop.f 0
479 (p15) mov GR_IndxPlusBias = GR_BIAS //Let i = 0 if i < 0
480 }
481 { .mlx
482 mov GR_P_POINT_3 = 0x1A0
483 movl GR_05 = 0x3fe0000000000000
484 }
485 ;;
487 // Form shift GR_ShftPi from the beginning of erfc_p_table
488 // to the polynomial with number i
489 { .mfi
490 ldfps FR_UnfBound, FR_EpsNorm = [EXP_AD_TB1],8
491 nop.f 0
492 shl GR_ShftPi = GR_IndxPlusBias, 7
493 }
494 { .mfi
495 setf.d EXP_RSHF = exp_GR_rshf // Form right shift 1.100 * 2^63
496 (p7) fms.s1 FR_AbsArg = f1, f0, f8 // |x| if x < 0
497 mov exp_TB1_size = 0x100
498 }
499 ;;
501 // Form pointer GR_P_POINT_3 to the beginning of erfc_p_table
502 { .mfi
503 setf.d FR_05 = GR_05
504 nop.f 0
505 sub GR_ShftPi = GR_ShftPi,GR_ShftPi_bias
506 }
507 { .mfb
508 add GR_P_POINT_3 = GR_P_POINT_3, EXP_AD_TB1
509 nop.f 0
510 (p9) br.cond.spnt SPECIAL // For x = 0,+inf,-inf,nan,unnorm
511 }
512 ;;
514 { .mfi
515 add GR_P_POINT_1 = GR_P_POINT_3, GR_ShftPi
516 nop.f 0
517 add GR_P_POINT_2 = GR_P_POINT_3, GR_ShftPi
518 }
519 { .mfi
520 ldfe exp_ln2_by_128_hi = [EXP_AD_TB1],16
521 fma.s1 FR_NormX = f8,f1,f0
522 add GR_P_POINT_3 = GR_P_POINT_3, GR_ShftPi
523 }
524 ;;
526 // Load coefficients for polynomial P15(x)
527 { .mfi
528 ldfpd FR_A15, FR_A14 = [GR_P_POINT_1], 16
529 nop.f 0
530 add GR_P_POINT_3 = 0x30, GR_P_POINT_3
531 }
532 { .mfi
533 ldfe exp_ln2_by_128_lo = [EXP_AD_TB1], 16
534 nop.f 0
535 add GR_P_POINT_2 = 0x20, GR_P_POINT_2
536 }
537 ;;
539 // Now EXP_AD_TB1 points to the beginning of table 1
540 { .mlx
541 ldfpd FR_A13, FR_A12 = [GR_P_POINT_1]
542 movl GR_1_by_6 = 0x3FC5555555555555
543 }
544 { .mfi
545 add GR_P_POINT_4 = 0x30, GR_P_POINT_2
546 nop.f 0
547 nop.i 0
548 }
549 ;;
551 { .mfi
552 ldfpd FR_A11, FR_A10 = [GR_P_POINT_2]
553 fma.s1 FR_2 = f1, f1, f1
554 mov exp_TB2_size = 0x80
555 }
556 { .mfi
557 ldfpd FR_A9, FR_A8 = [GR_P_POINT_3],16
558 nop.f 0
559 add GR_P_POINT_1 = 0x60 ,GR_P_POINT_1
560 }
561 ;;
563 // W = X * Inv_log2_by_128
564 // By adding 1.10...0*2^63 we shift and get round_int(W) in significand.
565 // We actually add 1.10...0*2^56 to X * Inv_log2 to do the same thing.
566 { .mfi
567 ldfpd FR_A7, FR_A6 = [GR_P_POINT_3]
568 fma.s1 EXP_W_2TO56_RSH = EXP_NORM_f8,EXP_INV_LN2_2TO63,EXP_RSHF_2TO56
569 add EXP_AD_TB2 = exp_TB1_size, EXP_AD_TB1
571 }
572 { .mfi
573 ldfpd FR_A5, FR_A4 = [GR_P_POINT_4], 16
574 nop.f 0
575 nop.i 0
576 }
577 ;;
579 { .mfi
580 ldfpd FR_A3, FR_A2 = [GR_P_POINT_4]
581 fmerge.s FR_X = f8,f8
582 nop.i 0
583 }
584 { .mfi
585 ldfpd FR_A1, FR_A0 = [GR_P_POINT_1]
586 nop.f 0
587 nop.i 0
588 }
589 ;;
591 //p14: x < - NEG_ARG_ASYMP = -4.4 -> erfcf(x) ~=~ 2.0
592 { .mfi
593 setf.d FR_1_by_6 = GR_1_by_6
594 (p7) fcmp.gt.unc.s1 p14,p0 = FR_AbsArg, FR_NEG_ARG_ASYMP //p7: x < 0
595 nop.i 0
596 }
597 ;;
599 //p15: x > POS_ARG_ASYMP = 10.06 -> erfcf(x) ~=~ 0.0
600 { .mfi
601 nop.m 0
602 (p6) fcmp.gt.unc.s1 p15,p0 = FR_AbsArg, FR_POS_ARG_ASYMP //p6: x > 0
603 nop.i 0
604 }
605 ;;
607 { .mfi
608 nop.m 0
609 fcmp.le.s1 p8,p0 = FR_NormX, FR_UnfBound // p8: x <= UnfBound
610 nop.i 0
611 }
612 { .mfb
613 nop.m 0
614 (p14) fnma.s.s0 FR_RESULT = FR_EpsNorm, FR_EpsNorm, FR_2//y = 2 if x <-4.4
615 (p14) br.ret.spnt b0
616 }
617 ;;
619 // Nfloat = round_int(W)
620 // The signficand of EXP_W_2TO56_RSH contains the rounded integer part of W,
621 // as a twos complement number in the lower bits (that is, it may be negative).
622 // That twos complement number (called N) is put into exp_GR_N.
624 // Since EXP_W_2TO56_RSH is scaled by 2^56, it must be multiplied by 2^-56
625 // before the shift constant 1.10000 * 2^63 is subtracted to yield EXP_Nfloat.
626 // Thus, EXP_Nfloat contains the floating point version of N
628 { .mfi
629 nop.m 0
630 fms.s1 EXP_Nfloat = EXP_W_2TO56_RSH, EXP_2TOM56, EXP_RSHF
631 nop.i 0
632 }
633 { .mfb
634 (p15) mov GR_Parameter_TAG = 209
635 (p15) fma.s.s0 FR_RESULT = FR_EpsNorm,FR_EpsNorm,f0 //Result.for x>10.06
636 (p15) br.cond.spnt __libm_error_region
637 }
638 ;;
640 // Now we can calculate polynomial P15(x)
641 { .mfi
642 nop.m 0
643 fma.s1 FR_P15_1_1 = FR_AbsArg, FR_AbsArg, f0 // x ^2
644 nop.i 0
645 }
646 { .mfi
647 nop.m 0
648 fma.s1 FR_P15_0_1 = FR_A15, FR_AbsArg, FR_A14
649 nop.i 0
650 }
651 ;;
653 { .mfi
654 nop.m 0
655 fma.s1 FR_P15_1_2 = FR_A13, FR_AbsArg, FR_A12
656 nop.i 0
657 }
658 ;;
660 { .mfi
661 getf.sig exp_GR_N = EXP_W_2TO56_RSH
662 fma.s1 FR_P15_2_1 = FR_A9, FR_AbsArg, FR_A8
663 nop.i 0
664 }
665 { .mfi
666 nop.m 0
667 fma.s1 FR_P15_2_2 = FR_A11, FR_AbsArg, FR_A10
668 nop.i 0
669 }
670 ;;
672 { .mfi
673 nop.m 0
674 fma.s1 FR_P15_3_1 = FR_A5, FR_AbsArg, FR_A4
675 nop.i 0
676 }
677 { .mfi
678 nop.m 0
679 fma.s1 FR_P15_3_2 = FR_A7, FR_AbsArg, FR_A6
680 nop.i 0
681 }
682 ;;
684 // exp_GR_index_1 has index_1
685 // exp_GR_index_2_16 has index_2 * 16
686 // exp_GR_biased_M has M
687 // exp_GR_index_1_16 has index_1 * 16
689 // r2 has true M
690 { .mfi
691 and exp_GR_index_1 = 0x0f, exp_GR_N
692 fma.s1 FR_P15_4_1 = FR_A1, FR_AbsArg, FR_A0
693 shr r2 = exp_GR_N, 0x7
695 }
696 { .mfi
697 and exp_GR_index_2_16 = 0x70, exp_GR_N
698 fma.s1 FR_P15_4_2 = FR_A3, FR_AbsArg, FR_A2
699 nop.i 0
700 }
701 ;;
703 // EXP_AD_T1 has address of T1
704 // EXP_AD_T2 has address if T2
706 { .mfi
707 add EXP_AD_T2 = EXP_AD_TB2, exp_GR_index_2_16
708 nop.f 0
709 shladd EXP_AD_T1 = exp_GR_index_1, 4, EXP_AD_TB1
710 }
711 { .mfi
712 addl exp_GR_biased_M = 0xffff, r2
713 fnma.s1 exp_r = EXP_Nfloat, exp_ln2_by_128_hi, EXP_NORM_f8
714 nop.i 0
715 }
716 ;;
718 // Create Scale = 2^M
719 // r = x - Nfloat * ln2_by_128_hi
721 { .mfi
722 setf.exp EXP_2M = exp_GR_biased_M
723 fma.s1 FR_P15_7_1 = FR_P15_0_1, FR_P15_1_1, FR_P15_1_2
724 nop.i 0
725 }
726 { .mfi
727 ldfe exp_T2 = [EXP_AD_T2]
728 nop.f 0
729 nop.i 0
730 }
731 ;;
733 // Load T1 and T2
735 { .mfi
736 ldfe exp_T1 = [EXP_AD_T1]
737 fma.s1 FR_P15_7_2 = FR_P15_1_1, FR_P15_1_1, f0 // x^4
738 nop.i 0
739 }
740 { .mfi
741 nop.m 0
742 fma.s1 FR_P15_8_1 = FR_P15_1_1, FR_P15_2_2, FR_P15_2_1
743 nop.i 0
744 }
745 ;;
747 { .mfi
748 nop.m 0
749 fma.s1 FR_P15_9_1 = FR_P15_1_1, FR_P15_4_2, FR_P15_4_1
750 nop.i 0
751 }
752 { .mfi
753 nop.m 0
754 fma.s1 FR_P15_9_2 = FR_P15_1_1, FR_P15_3_2, FR_P15_3_1
755 nop.i 0
756 }
757 ;;
759 { .mfi
760 nop.m 0
761 fma.s1 exp_P = FR_1_by_6, exp_r, FR_05
762 nop.i 0
763 }
764 { .mfi
765 nop.m 0
766 fma.s1 exp_rsq = exp_r, exp_r, f0
767 nop.i 0
768 }
769 ;;
771 { .mfi
772 nop.m 0
773 fma.s1 FR_P15_13_1 = FR_P15_7_2, FR_P15_7_1, FR_P15_8_1
774 nop.i 0
775 }
776 ;;
778 { .mfi
779 nop.m 0
780 fma.s1 FR_P15_14_1 = FR_P15_7_2, FR_P15_9_2, FR_P15_9_1
781 nop.i 0
782 }
783 { .mfi
784 nop.m 0
785 fma.s1 FR_P15_14_2 = FR_P15_7_2, FR_P15_7_2, f0 // x^8
786 nop.i 0
787 }
788 ;;
790 { .mfi
791 nop.m 0
792 fma.s1 exp_P = exp_P, exp_rsq, exp_r
793 nop.i 0
794 }
795 { .mfi
796 nop.m 0
797 fma.s1 exp_S1 = EXP_2M, exp_T2, f0
798 nop.i 0
799 }
800 ;;
802 { .mfi
803 nop.m 0
804 fma.s1 FR_Pol = FR_P15_14_2, FR_P15_13_1, FR_P15_14_1 // P15(x)
805 nop.i 0
806 }
807 ;;
809 { .mfi
810 nop.m 0
811 fma.s1 exp_S = exp_S1, exp_T1, f0
812 nop.i 0
813 }
814 ;;
816 { .mfi
817 nop.m 0
818 fma.s1 FR_Exp = exp_S, exp_P, exp_S // exp(-x^2)
819 nop.i 0
820 }
821 ;;
823 { .mfi
824 nop.m 0
825 fma.s.s0 FR_Tmpf = f8, f1, f0 // Flag d
826 nop.i 0
827 }
828 ;;
830 //p6: result for 0 < x < = POS_ARG_ASYMP
831 //p7: result for - NEG_ARG_ASYMP <= x < 0
832 //p8: exit for - NEG_ARG_ASYMP <= x <= UnfBound, x!=0
833 .pred.rel "mutex",p6,p7
834 { .mfi
835 nop.m 0
836 (p6) fma.s.s0 f8 = FR_Exp, FR_Pol, f0
837 nop.i 0
838 }
839 { .mfb
840 mov GR_Parameter_TAG = 209
841 (p7) fnma.s.s0 f8 = FR_Exp, FR_Pol, FR_2
842 (p8) br.ret.sptk b0
843 }
844 ;;
846 //p10: branch for UnfBound < x < = POS_ARG_ASYMP
847 { .mfb
848 nop.m 0
849 nop.f 0
850 (p10) br.cond.spnt __libm_error_region
851 }
852 ;;
854 //Only via (p9) br.cond.spnt SPECIAL for x = 0,+inf,-inf,nan,unnorm
855 SPECIAL:
857 { .mfi
858 nop.m 0
859 fclass.m.unc p10,p0 = f8,0x07 // p10: x = 0
860 nop.i 0
861 }
862 ;;
864 { .mfi
865 nop.m 0
866 fclass.m.unc p11,p0 = f8,0x21 // p11: x = +inf
867 nop.i 0
868 }
869 ;;
871 { .mfi
872 nop.m 0
873 fclass.m.unc p12,p0 = f8,0x22 // p12 x = -inf
874 nop.i 0
875 }
876 { .mfb
877 nop.m 0
878 (p10) fma.s.s0 f8 = f1, f1, f0
879 (p10) br.ret.sptk b0 // Quick exit for x = 0
880 }
881 ;;
883 { .mfi
884 nop.m 0
885 fclass.m.unc p13,p0 = f8,0xc3 // p13: x = nan
886 nop.i 0
887 }
888 { .mfb
889 nop.m 0
890 (p11) fma.s.s0 f8 = f0, f1, f0
891 (p11) br.ret.spnt b0 // Quick exit for x = +inf
892 }
893 ;;
894 { .mfi
895 nop.m 0
896 fclass.m.unc p14,p0 = f8,0x0b // P14: x = unnormalized
897 nop.i 0
898 }
899 { .mfb
900 nop.m 0
901 (p12) fma.s.s0 f8 = f1, f1, f1
902 (p12) br.ret.spnt b0 // Quick exit for x = -inf
903 }
904 ;;
906 { .mfb
907 nop.m 0
908 (p13) fma.s.s0 f8 = f8, f1, f0
909 (p13) br.ret.sptk b0 // Quick exit for x = nan
910 }
911 ;;
913 { .mfb
914 nop.m 0
915 (p14) fnma.s.s0 f8 = f8, f1, f1
916 (p14) br.ret.sptk b0 // Quick exit for x = unnormalized
917 }
918 ;;
920 GLOBAL_LIBM_END(erfcf)
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#