| blob | fefdefdf2dbcd3b1341e59d2082656bdf562399a |
1 .file "erf.s"
4 // Copyright (c) 2001 - 2005, Intel Corporation
5 // All rights reserved.
6 //
7 //
8 // Redistribution and use in source and binary forms, with or without
9 // modification, are permitted provided that the following conditions are
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11 //
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13 // notice, this list of conditions and the following disclaimer.
14 //
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17 // documentation and/or other materials provided with the distribution.
18 //
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20 // products derived from this software without specific prior written
21 // permission.
23 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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25 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
26 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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32 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
33 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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 // 08/15/01 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 // double erf(double)
49 //
50 // Overview of operation
51 //==============================================================
52 // Background
53 //
54 //
55 // There are 9 paths:
56 // 1. x = +/-0.0
57 // Return erf(x) = +/-0.0
58 //
59 // 2. 0.0 < |x| < 0.5
60 // Return erf(x) = x *Pol9(x^2)
61 //
62 // 3. For several subranges of 0.5 <= |x| < 5.90625
63 // Return erf(x) = sign(x)*Pol19(y),
64 // where y = (|x|-b)/a, Pol19(y) = A0 + A1*y^1 + A2*y^2 + ... + A19*y^19
65 //
66 // For each subrange there is particular set of coefficients.
67 // Below is the list of subranges:
68 // 3.1 0.5 <= |x| < 1.0 b = a = 0.5
69 // 3.2 1.0 <= |x| < 2.0, b = a = 1.0
70 // 3.3 2.0 <= |x| < 3.25 b = a = 2.0
71 // 3.4 4.0 <= |x| < 5.90625 b = 4.0, a = 2.0
72 //
73 // 4. 3.25 <= |x| < 4.0
74 // Return erf(x) = sign(x)*Pol14(|x| - 3.25)
75 //
76 // 5. 5.90625 <= |x| < +INF
77 // Return erf(x) = sign(x)*(1.0d - 2^(-63))
78 //
79 // 6. |x| = INF
80 // Return erf(x) = sign(x) * 1.0
81 //
82 // 7. x = [S,Q]NaN
83 // Return erf(x) = QNaN
84 //
85 // 8. x is positive denormal
86 // Return erf(x) = A0*x - x^2,
87 // where A0 = 2.0/sqrt(Pi)
88 //
89 // 9. x is negative denormal
90 // Return erf(x) = A0*x + x^2,
91 // where A0 = 2.0/sqrt(Pi)
92 //
93 // Registers used
94 //==============================================================
95 // Floating Point registers used:
96 // f8, input, output
97 // f32 -> f63
99 // General registers used:
100 // r32 -> r48, r2, r3
102 // Predicate registers used:
103 // p0, p6 -> p15
105 // p6 to filter out case when x = denormal
106 // p7 to filter out case when x = [Q,S]NaN or +/-0,
107 // used also to process denormals
108 // p8 to filter out case when 3.25 <= |x| < 4.0,
109 // used also to process denormals
110 // p9 to filter out case when |x| = inf
111 // p10 to filter out case when |x| < 0.5
112 // p11 set when |x| < 3.25 or |x| > 4.0
113 // p12 to filter out case when |x| >= 5.90625
114 // p13 set if 4.0 <=|x| < 5.90625
115 // p14 set to 1 for positive x
116 // p15 set to 1 for negative x
118 // Assembly macros
119 //==============================================================
120 rDataPtr = r2
121 rDataPtr1 = r3
123 rBias = r33
124 rCoeffAddr3 = r34
125 rThreeAndQ = r35
126 rCoeffAddr2 = r36
127 rMask = r37
128 rArg = r38
129 rSignBit = r39
130 rAbsArg = r40
131 rSaturation = r41
132 rIndex = r42
133 rCoeffAddr1 = r43
134 rCoeffAddr4 = r44
135 rShiftedArg = r45
136 rShiftedArgMasked = r46
137 rBiasedExpOf4 = r47
138 rShiftedAbsArg = r48
140 //==============================================================
141 fA0 = f32
142 fA1 = f33
143 fA2 = f34
144 fA3 = f35
145 fA4 = f36
146 fA5 = f37
147 fA6 = f38
148 fA7 = f39
149 fA8 = f40
150 fA9 = f41
151 fA10 = f42
152 fA11 = f43
153 fA12 = f44
154 fA13 = f45
155 fA14 = f46
156 fA15 = f47
157 fA16 = f48
158 fA17 = f49
159 fA18 = f50
160 fA19 = f51
161 fArgSqr = f52
162 fArgAbsNorm = f53
163 fSignumX = f54
164 fRes = f55
165 fThreeAndQ = f56
166 fArgAbs = f57
167 fTSqr = f58
168 fTQuadr = f59
169 fTDeg3 = f60
170 fTDeg7 = f61
171 fArgAbsNormSgn = f62
172 fTQuadrSgn = f63
174 // Data tables
175 //==============================================================
176 RODATA
178 .align 64
180 LOCAL_OBJECT_START(erf_data)
181 // Coefficients ##0..15
182 // Polynomial coefficients for the erf(x), 0.5 <= |x| < 1.0
183 data8 0xB69AC40646D1F6C1, 0x00003FD2 //A19
184 data8 0x90AD48C0118FA10C, 0x00003FD7 //A18
185 data8 0x826FBAD055EA4AB8, 0x0000BFDB //A17
186 data8 0x8DAB171246CC2B89, 0x00003FDC //A16
187 data8 0xC0B1D6662F8A7564, 0x00003FDF //A15
188 data8 0xA46374AC35099BAF, 0x0000BFE1 //A14
189 data8 0xB2F230996346EF27, 0x0000BFE4 //A13
190 data8 0xCDEC50950FACE04A, 0x00003FE6 //A12
191 data8 0x826014649396E9D2, 0x00003FE9 //A11
192 data8 0xCDB787DC718B13F9, 0x0000BFEB //A10
193 data8 0x8E0B23C24EE0C8EE, 0x0000BFED //A9
194 data8 0xA49EA40A4E5A3F76, 0x00003FF0 //A8
195 data8 0xB11E30BE912617D3, 0x00003FF0 //A7
196 data8 0xCCF89D9351CE26E3, 0x0000BFF4 //A6
197 data8 0xEFF75AD1F0F22809, 0x00003FF2 //A5
198 data8 0xBB793EF404C09A22, 0x00003FF8 //A4
199 // Polynomial coefficients for the erf(x), 1.0 <= |x| < 2.0
200 data8 0xBAE93FF4174EA59B, 0x00003FE6 //A19
201 data8 0x8A0FD46092F95D44, 0x0000BFEA //A18
202 data8 0xA37B3242B7809E12, 0x00003FEC //A17
203 data8 0xA0330A5CD2E91689, 0x0000BFED //A16
204 data8 0x8E34A678F3497D17, 0x0000BFEC //A15
205 data8 0xAC185D45A2772384, 0x00003FEF //A14
206 data8 0xB0C11347CE7EEDE8, 0x00003FEF //A13
207 data8 0xD3330DC14EA0E4EB, 0x0000BFF2 //A12
208 data8 0xB4A6DFDE578A428F, 0x00003FF1 //A11
209 data8 0xA0B4034310D2D9CB, 0x00003FF5 //A10
210 data8 0xF71662D3132B7759, 0x0000BFF5 //A9
211 data8 0x9C88BF157695E9EC, 0x0000BFF7 //A8
212 data8 0xF84B80EFCA43895D, 0x00003FF8 //A7
213 data8 0x9722D22DA628A17B, 0x00003FF7 //A6
214 data8 0x8DB0A586F8F3381F, 0x0000BFFB //A5
215 data8 0x8DB0A5879F87E5BE, 0x00003FFB //A4
216 // Polynomial coefficients for the erf(x), 2.0 <= |x| < 3.25
217 data8 0x9C4AF1F3A4B21AFC, 0x00003FF6 //A19
218 data8 0x8D40D5D5DB741AB8, 0x0000BFF9 //A18
219 data8 0xDEBE7099E0A75BA4, 0x00003FFA //A17
220 data8 0xB99A33294D32429D, 0x0000BFFB //A16
221 data8 0x8109D9C7197BC7C9, 0x00003FFB //A15
222 data8 0xC30DE8E2EFC2D760, 0x00003FFA //A14
223 data8 0x80DDA28C5B35DC73, 0x0000BFFC //A13
224 data8 0x9BE4DE5095BACE0D, 0x00003FF9 //A12
225 data8 0xDA4092509EE7D111, 0x00003FFC //A11
226 data8 0x89D98C561B0C9040, 0x0000BFFD //A10
227 data8 0xD20B26EB2F0881D4, 0x0000BFF9 //A9
228 data8 0xD089C56948731561, 0x00003FFD //A8
229 data8 0xDD704DEFFB21B7E7, 0x0000BFFD //A7
230 data8 0xF0C9A6BBDE469115, 0x00003FF9 //A6
231 data8 0xD673A02CB5766633, 0x00003FFD //A5
232 data8 0x8D162CBAD8A12649, 0x0000BFFE //A4
233 // Polynomial coefficients for the erf(x), 4.0 <= |x| < 6.0
234 data8 0xD4428B75C6FE8FD1, 0x0000BFFC //A19
235 data8 0xF76BE1935675D5C8, 0x00003FFE //A18
236 data8 0xFD6BB3B14AA7A8E6, 0x0000BFFF //A17
237 data8 0x8BE8F573D348DDA4, 0x00004000 //A16
238 data8 0x81E91923A1030502, 0x0000BFFF //A15
239 data8 0xCE7FE87B26CFD286, 0x0000BFFE //A14
240 data8 0x84EF6B4E17404384, 0x00004000 //A13
241 data8 0x91FEF33015404991, 0x0000C000 //A12
242 data8 0xDEDF6A9370747E56, 0x00003FFF //A11
243 data8 0x8397E6FF56CDFD9D, 0x0000BFFF //A10
244 data8 0xFAD1CE912473937B, 0x00003FFD //A9
245 data8 0xC48C1EA8AAA624EA, 0x0000BFFC //A8
246 data8 0xFECAF0097ACF981B, 0x00003FFA //A7
247 data8 0x8829A394065E4B95, 0x0000BFF9 //A6
248 data8 0xED3003E477A53EE7, 0x00003FF6 //A5
249 data8 0xA4C07E9BB3FCB0F3, 0x0000BFF4 //A4
250 //
251 // Coefficients ##16..19
252 // Polynomial coefficients for the erf(x), 0.5 <= |x| < 1.0
253 data8 0x95FA98C337005D13, 0x0000BFF9 //A3
254 data8 0xE0F7E524D2808A97, 0x0000BFFB //A2
255 data8 0xE0F7E524D2808A98, 0x00003FFD //A1
256 data8 0x853F7AE0C76E915F, 0x00003FFE //A0
257 // Polynomial coefficients for the erf(x), 1.0 <= |x| < 2.0
258 data8 0x8DB0A587A96ABCF0, 0x00003FFC //A3
259 data8 0xD488F84B7DE18DA8, 0x0000BFFD //A2
260 data8 0xD488F84B7DE12E9C, 0x00003FFD //A1
261 data8 0xD7BB3D3A08445636, 0x00003FFE //A0
262 // Polynomial coefficients for the erf(x), 2.0 <= |x| < 3.25
263 data8 0xC58571D23D5C4B3A, 0x00003FFD //A3
264 data8 0xA94DCF467CD6AFF3, 0x0000BFFC //A2
265 data8 0xA94DCF467CD10A16, 0x00003FFA //A1
266 data8 0xFECD70A13CAF1997, 0x00003FFE //A0
267 // Polynomial coefficients for the erf(x), 4.0 <= |x| < 6.0
268 data8 0xB01D2B4F0D5AB8B0, 0x00003FF1 //A3
269 data8 0x8858A465CE594BD1, 0x0000BFEE //A2
270 data8 0x8858A447456DE61D, 0x00003FEA //A1
271 data8 0xFFFFFFBDC88BB107, 0x00003FFE //A0
272 // Polynomial coefficients for the erf(x), 0.0 <= |x| < 0.5
273 data8 0xBE839EDBB36C7FCE //A9
274 data8 0x3EBB7745A18DD242 //A8
275 data8 0xBF4C02DB238F2AFC //A5
276 data8 0x3F7565BCD0A9A3EA //A4
277 data8 0xC093A3581BCF3333, 0x0000BFFD //A1
278 data8 0xBEEF4BB82AD8AE22 //A7
279 data8 0x3F1F9A2A57A218CD //A6
280 data8 0xBF9B82CE3127F4E4 //A3
281 data8 0x3FBCE2F21A042B25 //A2
282 data8 0x906EBA8214DB688D, 0x00003FFF //A0
283 // 1.0 - 2^(-63)
284 data8 0xFFFFFFFFFFFFFFFF, 0x00003FFE
285 // Polynomial coefficients for the erf(x), 3.25 <= |x| < 4.0
286 data8 0x95E91576C7A12250, 0x00003FE7 //A14
287 data8 0x8E5E0D0E1F5D3CB5, 0x0000BFEA //A13
288 data8 0xED761DAFAF814DE9, 0x00003FEB //A12
289 data8 0xB3A77D921D0ACFC7, 0x0000BFEC //A11
290 data8 0xA662D27096B08D7C, 0x0000BFEC //A10
291 data8 0xDA0F410AE6233EA5, 0x00003FEF //A9
292 data8 0xAB4A8B16B3124327, 0x0000BFF1 //A8
293 data8 0xB241E236A5EDCED3, 0x00003FF2 //A7
294 data8 0x8A2A65BA1F551F77, 0x0000BFF3 //A6
295 data8 0xA4852D0B1D87000A, 0x00003FF3 //A5
296 data8 0x963EB00039489476, 0x0000BFF3 //A4
297 data8 0xCD5244FF4F7313A5, 0x00003FF2 //A3
298 data8 0xC6F1E695363BCB26, 0x0000BFF1 //A2
299 data8 0xF4DAF4680DA54C02, 0x00003FEF //A1
300 data8 0xFFFFB7CFB3F2ABBE, 0x00003FFE //A0
301 // A = 2.0/sqrt(Pi)
302 data8 0x906EBA8214DB688D, 0x00003FFF
303 LOCAL_OBJECT_END(erf_data)
306 .section .text
307 GLOBAL_LIBM_ENTRY(erf)
309 { .mfi
310 alloc r32 = ar.pfs, 0, 17, 0, 0
311 fmerge.se fArgAbsNorm = f1, f8 // normalized x
312 adds rSignBit = 0x1, r0
313 }
314 { .mfi
315 addl rDataPtr = @ltoff(erf_data), gp
316 fma.s1 fArgSqr = f8, f8, f0 // x^2
317 addl rThreeAndQ = 0x400A0, r0 // shifted bits of 3.25
318 }
319 ;;
320 { .mfi
321 getf.d rArg = f8 // x in GR
322 fclass.m p6,p0 = f8, 0x0b // is x denormal ?
323 shl rThreeAndQ = rThreeAndQ, 44 // bits of 3.25
324 }
325 { .mfi
326 ld8 rDataPtr = [rDataPtr]
327 nop.f 0
328 addl rBiasedExpOf4 = 0x40100, r0 // shifted bits of 4.0
329 }
330 ;;
331 { .mfi
332 addl rSaturation = 0x4017A, r0 // shifted bits of 5.90625
333 fclass.m p7,p0 = f8, 0xc7 // is x [S,Q]NaN or +/-0 ?
334 shl rSignBit = rSignBit, 63 // mask for sign bit
335 }
336 { .mfi
337 addl rMask = 0x7FF00, r0 // Mask for index bits
338 nop.f 0
339 addl rBias = 0x3FE00, r0 // bias of 0.5 << 8
340 }
341 ;;
342 { .mfi
343 setf.d fThreeAndQ = rThreeAndQ // 3.25 if FP register
344 fclass.m p9,p0 = f8, 0x23 // is x +/- inf?
345 shr.u rShiftedArg = rArg, 44
346 }
347 { .mfb
348 andcm rAbsArg = rArg, rSignBit // |x| in GR
349 nop.f 0
350 (p6) br.cond.spnt erf_denormal // branch out if x is denormal
351 }
352 ;;
353 { .mfi
354 and rShiftedArgMasked = rShiftedArg, rMask // bias of x << 8
355 fmerge.s fArgAbs = f1, f8 // |x|
356 shr rShiftedAbsArg = rAbsArg, 44
357 }
358 { .mfb
359 cmp.lt p8, p11 = rThreeAndQ, rAbsArg // p8 = 1 if |x| >= 3.25
360 (p7) fma.d.s0 f8 = f8,f1,f8 // NaN or +/-0
361 (p7) br.ret.spnt b0 // exit for x = NaN or +/-0
362 }
363 ;;
364 { .mfi
365 sub rIndex = rShiftedArgMasked, rBias // index << 8
366 nop.f 0
367 cmp.lt p10, p0 = rShiftedArgMasked, rBias // p10 = 1 if |x| < 0.5
368 }
369 { .mfb
370 // p8 = 1 if 3.25 <= |x| < 4.0
371 (p8) cmp.lt p8, p11 = rShiftedAbsArg, rBiasedExpOf4
372 fms.s1 fArgAbsNorm = fArgAbsNorm, f1, f1
373 (p10) br.cond.spnt erf_near_zero // branch out if |x| < 0.5
374 }
375 ;;
376 .pred.rel "mutex", p8, p11
377 { .mfi
378 (p8) adds rCoeffAddr1 = 1392, rDataPtr // coeff. for 3.25 <=|x|<4.0
379 (p9) fmerge.s f8 = f8,f1 // +/- inf
380 nop.i 0
381 }
382 { .mfb
383 (p11) add rCoeffAddr1 = rDataPtr, rIndex// coeff. ##0,2,..14
384 nop.f 0
385 (p9) br.ret.spnt b0 // exit for x = +/- inf
386 }
387 ;;
388 { .mfi
389 adds rCoeffAddr2 = 16, rCoeffAddr1
390 fmerge.s fSignumX = f8, f1 // signum(x)
391 nop.i 0
392 }
393 { .mfb
394 cmp.lt p12, p0 = rSaturation, rShiftedAbsArg // |x| > 5.90625?
395 nop.f 0
396 (p12) br.cond.spnt erf_saturation // branch out if x |x| >= 6.0
397 }
398 ;;
399 // Here if paths #3,4
400 // if path #4 we'll branch out after loading of 14 necessary coefficients
401 {.mfi
402 ldfe fA19 = [rCoeffAddr1], 32
403 nop.f 0
404 nop.i 0
405 }
406 {.mfi
407 ldfe fA18 = [rCoeffAddr2], 32
408 nop.f 0
409 adds rCoeffAddr3 = 1024, rDataPtr
410 }
411 ;;
412 {.mfi
413 ldfe fA17 = [rCoeffAddr1], 32
414 nop.f 0
415 nop.i 0
416 }
417 {.mfi
418 ldfe fA16 = [rCoeffAddr2], 32
419 nop.f 0
420 nop.i 0
421 }
422 ;;
423 {.mfi
424 ldfe fA15 = [rCoeffAddr1], 32
425 fma.s1 fTSqr = fArgAbsNorm, fArgAbsNorm, f0
426 shr.u rIndex = rIndex, 2
427 }
428 {.mfi
429 ldfe fA14 = [rCoeffAddr2], 32
430 nop.f 0
431 adds rCoeffAddr4 = 16, r0
432 }
433 ;;
434 {.mfi
435 ldfe fA13 = [rCoeffAddr1], 32
436 nop.f 0
437 // address of coefficients ##16..23
438 add rCoeffAddr3 = rCoeffAddr3, rIndex
439 }
440 {.mfi
441 ldfe fA12 = [rCoeffAddr2], 32
442 nop.f 0
443 cmp.lt p15, p14 = rArg, r0
444 }
445 ;;
446 {.mfi
447 ldfe fA11 = [rCoeffAddr1], 32
448 nop.f 0
449 add rCoeffAddr4 = rCoeffAddr3, rCoeffAddr4
450 }
451 {.mfi
452 ldfe fA10 = [rCoeffAddr2], 32
453 nop.f 0
454 nop.i 0
455 }
456 ;;
457 {.mfi
458 ldfe fA9 = [rCoeffAddr1], 32
459 nop.f 0
460 nop.i 0
461 }
462 {.mfi
463 ldfe fA8 = [rCoeffAddr2], 32
464 nop.f 0
465 nop.i 0
466 }
467 ;;
468 {.mfi
469 ldfe fA7 = [rCoeffAddr1], 32
470 fms.s1 fArgAbs = fArgAbs, f1, fThreeAndQ
471 nop.i 0
472 }
473 {.mfb
474 ldfe fA6 = [rCoeffAddr2], 32
475 nop.f 0
476 (p8) br.cond.spnt erf_3q_4 // branch out if 3.25 < |x| < 4.0
477 }
478 ;;
479 {.mfi
480 ldfe fA5 = [rCoeffAddr1], 32
481 fma.s1 fTDeg3 = fArgAbsNorm, fTSqr, f0
482 nop.i 0
483 }
484 {.mfi
485 ldfe fA4 = [rCoeffAddr2], 32
486 fma.s1 fTQuadr = fTSqr, fTSqr, f0
487 nop.i 0
488 }
489 ;;
490 // Path #3 Polynomial Pol19(y) computation; y = fArgAbsNorm
491 {.mfi
492 ldfe fA3 = [rCoeffAddr3], 32
493 fma.s1 fArgAbsNormSgn = fArgAbsNorm, fSignumX, f0
494 nop.i 0
495 }
496 {.mfi
497 ldfe fA2 = [rCoeffAddr4], 32
498 nop.f 0
499 nop.i 0
500 }
501 ;;
502 {.mfi
503 ldfe fA1 = [rCoeffAddr3], 32
504 fma.s1 fRes = fA19, fArgAbsNorm, fA18
505 nop.i 0
506 }
507 {.mfi
508 ldfe fA0 = [rCoeffAddr4], 32
509 nop.f 0
510 nop.i 0
511 }
512 ;;
513 { .mfi
514 nop.m 0
515 fma.s1 fA17 = fA17, fArgAbsNorm, fA16
516 nop.i 0
517 }
518 ;;
519 { .mfi
520 nop.m 0
521 fma.s1 fA15 = fA15, fArgAbsNorm, fA14
522 nop.i 0
523 }
524 ;;
525 { .mfi
526 nop.m 0
527 fma.s1 fTDeg7 = fTDeg3, fTQuadr, f0
528 nop.i 0
529 }
530 { .mfi
531 nop.m 0
532 fma.s1 fA13 = fA13, fArgAbsNorm, fA12
533 nop.i 0
534 }
535 ;;
536 { .mfi
537 nop.m 0
538 fma.s1 fA11 = fA11, fArgAbsNorm, fA10
539 nop.i 0
540 }
541 ;;
542 { .mfi
543 nop.m 0
544 fma.s1 fA9 = fA9, fArgAbsNorm, fA8
545 nop.i 0
546 }
547 ;;
548 { .mfi
549 nop.m 0
550 fma.s1 fRes = fRes, fTSqr, fA17
551 nop.i 0
552 }
553 { .mfi
554 nop.m 0
555 fma.s1 fA7 = fA7, fArgAbsNorm, fA6
556 nop.i 0
557 }
558 ;;
559 { .mfi
560 nop.m 0
561 fma.s1 fA5 = fA5, fArgAbsNorm, f0
562 nop.i 0
563 }
564 ;;
565 { .mfi
566 nop.m 0
567 fma.s1 fA15 = fA15, fTSqr, fA13
568 nop.i 0
569 }
570 { .mfi
571 nop.m 0
572 fma.s1 fA4 = fA4, fArgAbsNorm, fA3
573 nop.i 0
574 }
575 ;;
576 { .mfi
577 nop.m 0
578 fma.s1 fA2 = fA2, fArgAbsNorm, fA1
579 nop.i 0
580 }
581 ;;
582 { .mfi
583 nop.m 0
584 fma.s1 fA11 = fA11, fTSqr, fA9
585 nop.i 0
586 }
587 ;;
588 { .mfi
589 nop.m 0
590 fma.s1 fA7 = fA7, fTSqr, fA5
591 nop.i 0
592 }
593 ;;
594 { .mfi
595 nop.m 0
596 fma.s1 fRes = fRes, fTQuadr, fA15
597 nop.i 0
598 }
599 ;;
600 { .mfi
601 nop.m 0
602 fma.s1 fA4 = fA4, fTSqr, fA2
603 nop.i 0
604 }
605 ;;
606 { .mfi
607 nop.m 0
608 fma.s1 fRes = fRes, fTQuadr, fA11
609 nop.i 0
610 }
611 ;;
612 { .mfi
613 nop.m 0
614 fma.s1 fA4 = fA7, fTDeg3, fA4
615 nop.i 0
616 }
617 ;;
618 { .mfi
619 nop.m 0
620 fma.s1 fRes = fRes, fTDeg7, fA4
621 nop.i 0
622 }
623 ;;
624 { .mfi
625 nop.m 0
626 // result for negative argument
627 (p15) fms.d.s0 f8 = fRes, fArgAbsNormSgn, fA0
628 nop.i 0
629 }
630 { .mfb
631 nop.m 0
632 // result for positive argument
633 (p14) fma.d.s0 f8 = fRes, fArgAbsNormSgn, fA0
634 br.ret.sptk b0
635 }
637 // Here if 3.25 < |x| < 4.0
638 .align 32
639 erf_3q_4:
640 .pred.rel "mutex", p14, p15
641 { .mfi
642 ldfe fA5 = [rCoeffAddr1], 32
643 fma.s1 fTSqr = fArgAbs, fArgAbs, f0
644 nop.i 0
645 }
646 { .mfi
647 nop.m 0
648 fma.s1 fRes = fA19, fArgAbs, fA18
649 nop.i 0
650 }
651 ;;
652 { .mfi
653 nop.m 0
654 fma.s1 fA17 = fA17, fArgAbs, fA16
655 nop.i 0
656 }
657 { .mfi
658 nop.m 0
659 fma.s1 fA15 = fA15, fArgAbs, fA14
660 nop.i 0
661 }
662 ;;
663 { .mfi
664 nop.m 0
665 fma.s1 fA13 = fA13, fArgAbs, fA12
666 nop.i 0
667 }
668 { .mfi
669 nop.m 0
670 fma.s1 fA11 = fA11, fArgAbs, fA10
671 nop.i 0
672 }
673 ;;
674 { .mfi
675 nop.m 0
676 fma.s1 fA9 = fA9, fArgAbs, fA8
677 nop.i 0
678 }
679 { .mfi
680 nop.m 0
681 fma.s1 fArgAbsNormSgn = fArgAbs, fSignumX, f0
682 nop.i 0
683 }
684 ;;
685 { .mfi
686 nop.m 0
687 fma.s1 fTQuadr = fTSqr, fTSqr, f0
688 nop.i 0
689 }
690 ;;
691 { .mfi
692 nop.m 0
693 fma.s1 fRes = fRes, fTSqr, fA17
694 nop.i 0
695 }
696 ;;
697 { .mfi
698 nop.m 0
699 fma.s1 fA15 = fA15, fTSqr, fA13
700 nop.i 0
701 }
702 ;;
703 { .mfi
704 nop.m 0
705 fma.s1 fA11 = fA11, fTSqr, fA9
706 nop.i 0
707 }
708 { .mfi
709 nop.m 0
710 fma.s1 fA7 = fA7, fArgAbs, fA6
711 nop.i 0
712 }
713 ;;
714 { .mfi
715 nop.m 0
716 fma.s1 fTDeg7 = fTQuadr, fTSqr, f0
717 nop.i 0
718 }
719 { .mfi
720 nop.m 0
721 fma.s1 fRes = fRes, fTQuadr, fA15
722 nop.i 0
723 }
724 ;;
725 { .mfi
726 nop.m 0
727 fma.s1 fA11 = fA11, fTSqr, fA7
728 nop.i 0
729 }
730 ;;
731 { .mfi
732 nop.m 0
733 fma.s1 fRes = fRes, fTDeg7, fA11
734 nop.i 0
735 }
736 ;;
737 { .mfi
738 nop.m 0
739 // result for negative argument
740 (p15) fms.d.s0 f8 = fRes, fArgAbsNormSgn, fA5
741 nop.i 0
742 }
743 { .mfb
744 nop.m 0
745 // result for positive argument
746 (p14) fma.d.s0 f8 = fRes, fArgAbsNormSgn, fA5
747 br.ret.sptk b0
748 }
749 ;;
751 // Here if |x| < 0.5
752 .align 32
753 erf_near_zero:
754 { .mfi
755 adds rCoeffAddr1 = 1280, rDataPtr // address of A9
756 fma.s1 fTSqr = fArgSqr, fArgSqr, f0 // x^4
757 nop.i 0
758 }
759 { .mfi
760 adds rCoeffAddr2 = 1328, rDataPtr // address of A7
761 nop.f 0
762 nop.i 0
763 }
764 ;;
765 { .mfi
766 ldfpd fA9, fA8 = [rCoeffAddr1], 16
767 nop.f 0
768 nop.i 0
769 }
770 { .mfi
771 ldfpd fA7, fA6 = [rCoeffAddr2], 16
772 nop.f 0
773 nop.i 0
774 }
775 ;;
776 { .mfi
777 ldfpd fA5, fA4 = [rCoeffAddr1], 16
778 nop.f 0
779 nop.i 0
780 }
781 { .mfi
782 ldfpd fA3, fA2 = [rCoeffAddr2], 16
783 nop.f 0
784 nop.i 0
785 }
786 ;;
787 { .mfi
788 ldfe fA1 = [rCoeffAddr1]
789 nop.f 0
790 nop.i 0
791 }
792 { .mfi
793 ldfe fA0 = [rCoeffAddr2]
794 nop.f 0
795 nop.i 0
796 }
797 ;;
798 { .mfi
799 nop.m 0
800 fma.s1 fTQuadr = fTSqr, fTSqr, f0
801 nop.i 0
802 }
803 ;;
804 { .mfi
805 nop.m 0
806 fma.s1 fRes = fA9, fArgSqr, fA8
807 nop.i 0
808 }
809 { .mfi
810 nop.m 0
811 fma.s1 fA7 = fA7, fArgSqr, fA6
812 nop.i 0
813 }
814 ;;
815 { .mfi
816 nop.m 0
817 fma.s1 fA3 = fA3, fArgSqr, fA2
818 nop.i 0
819 }
820 { .mfi
821 nop.m 0
822 fma.s1 fA5 = fA5, fArgSqr, fA4
823 nop.i 0
824 }
825 ;;
826 { .mfi
827 nop.m 0
828 fma.s1 fA1 = fA1, fArgSqr, fA0
829 nop.i 0
830 }
831 { .mfi
832 nop.m 0
833 fma.s1 fTQuadrSgn = fTQuadr, f8, f0
834 nop.i 0
835 }
836 ;;
837 { .mfi
838 nop.m 0
839 fma.s1 fRes = fRes, fTSqr, fA7
840 nop.i 0
841 }
842 ;;
843 { .mfi
844 nop.m 0
845 fma.s1 fA1 = fA3, fTSqr, fA1
846 nop.i 0
847 }
848 ;;
849 { .mfi
850 nop.m 0
851 fma.s1 fRes = fRes, fTSqr, fA5
852 nop.i 0
853 }
854 ;;
855 { .mfi
856 nop.m 0
857 fma.s1 fA1 = fA1, f8, f0
858 nop.i 0
859 }
860 ;;
861 { .mfb
862 nop.m 0
863 fma.d.s0 f8 = fRes, fTQuadrSgn, fA1 // x*Pol9(x^2)
864 br.ret.sptk b0 // Exit for |x| < 0.5
865 };;
867 // Here if 5.90625 <= |x| < +inf
868 .align 32
869 erf_saturation:
870 { .mfi
871 adds rDataPtr = 1376, rDataPtr // address of A0
872 nop.f 0
873 nop.i 0
874 }
875 ;;
876 { .mfi
877 ldfe fA0 = [rDataPtr]
878 nop.f 0
879 nop.i 0
880 }
881 ;;
882 { .mfb
883 nop.m 0
884 fma.d.s0 f8 = fA0, fSignumX, f0 // sign(x)*(1.0 - 2^(-63))
885 // Exit for 5.90625 <= |x| < +inf
886 br.ret.sptk b0 // Exit for 5.90625 <=|x|< +inf
887 }
888 ;;
890 // Here if x is double precision denormal
891 .align 32
892 erf_denormal:
893 { .mfi
894 adds rDataPtr = 1632, rDataPtr // address of A0
895 fclass.m p7,p8 = f8, 0x0a // is x -denormal ?
896 nop.i 0
897 }
898 ;;
899 { .mfi
900 ldfe fA0 = [rDataPtr] // A0
901 nop.f 0
902 nop.i 0
903 }
904 ;;
905 { .mfi
906 nop.m 0
907 fma.s1 fA0 = fA0,f8,f0 // A0*x
908 nop.i 0
909 }
910 ;;
911 { .mfi
912 nop.m 0
913 (p7) fma.d.s0 f8 = f8,f8,fA0 // -denormal
914 nop.i 0
915 }
916 { .mfb
917 nop.m 0
918 (p8) fnma.d.s0 f8 = f8,f8,fA0 // +denormal
919 br.ret.sptk b0 // Exit for denormal
920 }
921 ;;
923 GLOBAL_LIBM_END(erf)
924 libm_alias_double_other (erf, erf)