| blob | 7174a197fbb5bf4ce989a6af99bda249ed0abae6 |
1 .file "erf.s"
4 // Copyright (c) 2001 - 2005, Intel Corporation
5 // All rights reserved.
6 //
7 // Contributed 2001 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
26 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
27 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
28 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
29 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
30 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
31 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
32 // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
33 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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 // 08/15/01 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 // double erf(double)
50 //
51 // Overview of operation
52 //==============================================================
53 // Background
54 //
55 //
56 // There are 9 paths:
57 // 1. x = +/-0.0
58 // Return erf(x) = +/-0.0
59 //
60 // 2. 0.0 < |x| < 0.5
61 // Return erf(x) = x *Pol9(x^2)
62 //
63 // 3. For several subranges of 0.5 <= |x| < 5.90625
64 // Return erf(x) = sign(x)*Pol19(y),
65 // where y = (|x|-b)/a, Pol19(y) = A0 + A1*y^1 + A2*y^2 + ... + A19*y^19
66 //
67 // For each subrange there is particular set of coefficients.
68 // Below is the list of subranges:
69 // 3.1 0.5 <= |x| < 1.0 b = a = 0.5
70 // 3.2 1.0 <= |x| < 2.0, b = a = 1.0
71 // 3.3 2.0 <= |x| < 3.25 b = a = 2.0
72 // 3.4 4.0 <= |x| < 5.90625 b = 4.0, a = 2.0
73 //
74 // 4. 3.25 <= |x| < 4.0
75 // Return erf(x) = sign(x)*Pol14(|x| - 3.25)
76 //
77 // 5. 5.90625 <= |x| < +INF
78 // Return erf(x) = sign(x)*(1.0d - 2^(-63))
79 //
80 // 6. |x| = INF
81 // Return erf(x) = sign(x) * 1.0
82 //
83 // 7. x = [S,Q]NaN
84 // Return erf(x) = QNaN
85 //
86 // 8. x is positive denormal
87 // Return erf(x) = A0*x - x^2,
88 // where A0 = 2.0/sqrt(Pi)
89 //
90 // 9. x is negative denormal
91 // Return erf(x) = A0*x + x^2,
92 // where A0 = 2.0/sqrt(Pi)
93 //
94 // Registers used
95 //==============================================================
96 // Floating Point registers used:
97 // f8, input, output
98 // f32 -> f63
100 // General registers used:
101 // r32 -> r48, r2, r3
103 // Predicate registers used:
104 // p0, p6 -> p15
106 // p6 to filter out case when x = denormal
107 // p7 to filter out case when x = [Q,S]NaN or +/-0,
108 // used also to process denormals
109 // p8 to filter out case when 3.25 <= |x| < 4.0,
110 // used also to process denormals
111 // p9 to filter out case when |x| = inf
112 // p10 to filter out case when |x| < 0.5
113 // p11 set when |x| < 3.25 or |x| > 4.0
114 // p12 to filter out case when |x| >= 5.90625
115 // p13 set if 4.0 <=|x| < 5.90625
116 // p14 set to 1 for positive x
117 // p15 set to 1 for negative x
119 // Assembly macros
120 //==============================================================
121 rDataPtr = r2
122 rDataPtr1 = r3
124 rBias = r33
125 rCoeffAddr3 = r34
126 rThreeAndQ = r35
127 rCoeffAddr2 = r36
128 rMask = r37
129 rArg = r38
130 rSignBit = r39
131 rAbsArg = r40
132 rSaturation = r41
133 rIndex = r42
134 rCoeffAddr1 = r43
135 rCoeffAddr4 = r44
136 rShiftedArg = r45
137 rShiftedArgMasked = r46
138 rBiasedExpOf4 = r47
139 rShiftedAbsArg = r48
141 //==============================================================
142 fA0 = f32
143 fA1 = f33
144 fA2 = f34
145 fA3 = f35
146 fA4 = f36
147 fA5 = f37
148 fA6 = f38
149 fA7 = f39
150 fA8 = f40
151 fA9 = f41
152 fA10 = f42
153 fA11 = f43
154 fA12 = f44
155 fA13 = f45
156 fA14 = f46
157 fA15 = f47
158 fA16 = f48
159 fA17 = f49
160 fA18 = f50
161 fA19 = f51
162 fArgSqr = f52
163 fArgAbsNorm = f53
164 fSignumX = f54
165 fRes = f55
166 fThreeAndQ = f56
167 fArgAbs = f57
168 fTSqr = f58
169 fTQuadr = f59
170 fTDeg3 = f60
171 fTDeg7 = f61
172 fArgAbsNormSgn = f62
173 fTQuadrSgn = f63
175 // Data tables
176 //==============================================================
177 RODATA
179 .align 64
181 LOCAL_OBJECT_START(erf_data)
182 // Coefficients ##0..15
183 // Polynomial coefficients for the erf(x), 0.5 <= |x| < 1.0
184 data8 0xB69AC40646D1F6C1, 0x00003FD2 //A19
185 data8 0x90AD48C0118FA10C, 0x00003FD7 //A18
186 data8 0x826FBAD055EA4AB8, 0x0000BFDB //A17
187 data8 0x8DAB171246CC2B89, 0x00003FDC //A16
188 data8 0xC0B1D6662F8A7564, 0x00003FDF //A15
189 data8 0xA46374AC35099BAF, 0x0000BFE1 //A14
190 data8 0xB2F230996346EF27, 0x0000BFE4 //A13
191 data8 0xCDEC50950FACE04A, 0x00003FE6 //A12
192 data8 0x826014649396E9D2, 0x00003FE9 //A11
193 data8 0xCDB787DC718B13F9, 0x0000BFEB //A10
194 data8 0x8E0B23C24EE0C8EE, 0x0000BFED //A9
195 data8 0xA49EA40A4E5A3F76, 0x00003FF0 //A8
196 data8 0xB11E30BE912617D3, 0x00003FF0 //A7
197 data8 0xCCF89D9351CE26E3, 0x0000BFF4 //A6
198 data8 0xEFF75AD1F0F22809, 0x00003FF2 //A5
199 data8 0xBB793EF404C09A22, 0x00003FF8 //A4
200 // Polynomial coefficients for the erf(x), 1.0 <= |x| < 2.0
201 data8 0xBAE93FF4174EA59B, 0x00003FE6 //A19
202 data8 0x8A0FD46092F95D44, 0x0000BFEA //A18
203 data8 0xA37B3242B7809E12, 0x00003FEC //A17
204 data8 0xA0330A5CD2E91689, 0x0000BFED //A16
205 data8 0x8E34A678F3497D17, 0x0000BFEC //A15
206 data8 0xAC185D45A2772384, 0x00003FEF //A14
207 data8 0xB0C11347CE7EEDE8, 0x00003FEF //A13
208 data8 0xD3330DC14EA0E4EB, 0x0000BFF2 //A12
209 data8 0xB4A6DFDE578A428F, 0x00003FF1 //A11
210 data8 0xA0B4034310D2D9CB, 0x00003FF5 //A10
211 data8 0xF71662D3132B7759, 0x0000BFF5 //A9
212 data8 0x9C88BF157695E9EC, 0x0000BFF7 //A8
213 data8 0xF84B80EFCA43895D, 0x00003FF8 //A7
214 data8 0x9722D22DA628A17B, 0x00003FF7 //A6
215 data8 0x8DB0A586F8F3381F, 0x0000BFFB //A5
216 data8 0x8DB0A5879F87E5BE, 0x00003FFB //A4
217 // Polynomial coefficients for the erf(x), 2.0 <= |x| < 3.25
218 data8 0x9C4AF1F3A4B21AFC, 0x00003FF6 //A19
219 data8 0x8D40D5D5DB741AB8, 0x0000BFF9 //A18
220 data8 0xDEBE7099E0A75BA4, 0x00003FFA //A17
221 data8 0xB99A33294D32429D, 0x0000BFFB //A16
222 data8 0x8109D9C7197BC7C9, 0x00003FFB //A15
223 data8 0xC30DE8E2EFC2D760, 0x00003FFA //A14
224 data8 0x80DDA28C5B35DC73, 0x0000BFFC //A13
225 data8 0x9BE4DE5095BACE0D, 0x00003FF9 //A12
226 data8 0xDA4092509EE7D111, 0x00003FFC //A11
227 data8 0x89D98C561B0C9040, 0x0000BFFD //A10
228 data8 0xD20B26EB2F0881D4, 0x0000BFF9 //A9
229 data8 0xD089C56948731561, 0x00003FFD //A8
230 data8 0xDD704DEFFB21B7E7, 0x0000BFFD //A7
231 data8 0xF0C9A6BBDE469115, 0x00003FF9 //A6
232 data8 0xD673A02CB5766633, 0x00003FFD //A5
233 data8 0x8D162CBAD8A12649, 0x0000BFFE //A4
234 // Polynomial coefficients for the erf(x), 4.0 <= |x| < 6.0
235 data8 0xD4428B75C6FE8FD1, 0x0000BFFC //A19
236 data8 0xF76BE1935675D5C8, 0x00003FFE //A18
237 data8 0xFD6BB3B14AA7A8E6, 0x0000BFFF //A17
238 data8 0x8BE8F573D348DDA4, 0x00004000 //A16
239 data8 0x81E91923A1030502, 0x0000BFFF //A15
240 data8 0xCE7FE87B26CFD286, 0x0000BFFE //A14
241 data8 0x84EF6B4E17404384, 0x00004000 //A13
242 data8 0x91FEF33015404991, 0x0000C000 //A12
243 data8 0xDEDF6A9370747E56, 0x00003FFF //A11
244 data8 0x8397E6FF56CDFD9D, 0x0000BFFF //A10
245 data8 0xFAD1CE912473937B, 0x00003FFD //A9
246 data8 0xC48C1EA8AAA624EA, 0x0000BFFC //A8
247 data8 0xFECAF0097ACF981B, 0x00003FFA //A7
248 data8 0x8829A394065E4B95, 0x0000BFF9 //A6
249 data8 0xED3003E477A53EE7, 0x00003FF6 //A5
250 data8 0xA4C07E9BB3FCB0F3, 0x0000BFF4 //A4
251 //
252 // Coefficients ##16..19
253 // Polynomial coefficients for the erf(x), 0.5 <= |x| < 1.0
254 data8 0x95FA98C337005D13, 0x0000BFF9 //A3
255 data8 0xE0F7E524D2808A97, 0x0000BFFB //A2
256 data8 0xE0F7E524D2808A98, 0x00003FFD //A1
257 data8 0x853F7AE0C76E915F, 0x00003FFE //A0
258 // Polynomial coefficients for the erf(x), 1.0 <= |x| < 2.0
259 data8 0x8DB0A587A96ABCF0, 0x00003FFC //A3
260 data8 0xD488F84B7DE18DA8, 0x0000BFFD //A2
261 data8 0xD488F84B7DE12E9C, 0x00003FFD //A1
262 data8 0xD7BB3D3A08445636, 0x00003FFE //A0
263 // Polynomial coefficients for the erf(x), 2.0 <= |x| < 3.25
264 data8 0xC58571D23D5C4B3A, 0x00003FFD //A3
265 data8 0xA94DCF467CD6AFF3, 0x0000BFFC //A2
266 data8 0xA94DCF467CD10A16, 0x00003FFA //A1
267 data8 0xFECD70A13CAF1997, 0x00003FFE //A0
268 // Polynomial coefficients for the erf(x), 4.0 <= |x| < 6.0
269 data8 0xB01D2B4F0D5AB8B0, 0x00003FF1 //A3
270 data8 0x8858A465CE594BD1, 0x0000BFEE //A2
271 data8 0x8858A447456DE61D, 0x00003FEA //A1
272 data8 0xFFFFFFBDC88BB107, 0x00003FFE //A0
273 // Polynomial coefficients for the erf(x), 0.0 <= |x| < 0.5
274 data8 0xBE839EDBB36C7FCE //A9
275 data8 0x3EBB7745A18DD242 //A8
276 data8 0xBF4C02DB238F2AFC //A5
277 data8 0x3F7565BCD0A9A3EA //A4
278 data8 0xC093A3581BCF3333, 0x0000BFFD //A1
279 data8 0xBEEF4BB82AD8AE22 //A7
280 data8 0x3F1F9A2A57A218CD //A6
281 data8 0xBF9B82CE3127F4E4 //A3
282 data8 0x3FBCE2F21A042B25 //A2
283 data8 0x906EBA8214DB688D, 0x00003FFF //A0
284 // 1.0 - 2^(-63)
285 data8 0xFFFFFFFFFFFFFFFF, 0x00003FFE
286 // Polynomial coefficients for the erf(x), 3.25 <= |x| < 4.0
287 data8 0x95E91576C7A12250, 0x00003FE7 //A14
288 data8 0x8E5E0D0E1F5D3CB5, 0x0000BFEA //A13
289 data8 0xED761DAFAF814DE9, 0x00003FEB //A12
290 data8 0xB3A77D921D0ACFC7, 0x0000BFEC //A11
291 data8 0xA662D27096B08D7C, 0x0000BFEC //A10
292 data8 0xDA0F410AE6233EA5, 0x00003FEF //A9
293 data8 0xAB4A8B16B3124327, 0x0000BFF1 //A8
294 data8 0xB241E236A5EDCED3, 0x00003FF2 //A7
295 data8 0x8A2A65BA1F551F77, 0x0000BFF3 //A6
296 data8 0xA4852D0B1D87000A, 0x00003FF3 //A5
297 data8 0x963EB00039489476, 0x0000BFF3 //A4
298 data8 0xCD5244FF4F7313A5, 0x00003FF2 //A3
299 data8 0xC6F1E695363BCB26, 0x0000BFF1 //A2
300 data8 0xF4DAF4680DA54C02, 0x00003FEF //A1
301 data8 0xFFFFB7CFB3F2ABBE, 0x00003FFE //A0
302 // A = 2.0/sqrt(Pi)
303 data8 0x906EBA8214DB688D, 0x00003FFF
304 LOCAL_OBJECT_END(erf_data)
307 .section .text
308 GLOBAL_LIBM_ENTRY(erf)
310 { .mfi
311 alloc r32 = ar.pfs, 0, 17, 0, 0
312 fmerge.se fArgAbsNorm = f1, f8 // normalized x
313 adds rSignBit = 0x1, r0
314 }
315 { .mfi
316 addl rDataPtr = @ltoff(erf_data), gp
317 fma.s1 fArgSqr = f8, f8, f0 // x^2
318 addl rThreeAndQ = 0x400A0, r0 // shifted bits of 3.25
319 }
320 ;;
321 { .mfi
322 getf.d rArg = f8 // x in GR
323 fclass.m p6,p0 = f8, 0x0b // is x denormal ?
324 shl rThreeAndQ = rThreeAndQ, 44 // bits of 3.25
325 }
326 { .mfi
327 ld8 rDataPtr = [rDataPtr]
328 nop.f 0
329 addl rBiasedExpOf4 = 0x40100, r0 // shifted bits of 4.0
330 }
331 ;;
332 { .mfi
333 addl rSaturation = 0x4017A, r0 // shifted bits of 5.90625
334 fclass.m p7,p0 = f8, 0xc7 // is x [S,Q]NaN or +/-0 ?
335 shl rSignBit = rSignBit, 63 // mask for sign bit
336 }
337 { .mfi
338 addl rMask = 0x7FF00, r0 // Mask for index bits
339 nop.f 0
340 addl rBias = 0x3FE00, r0 // bias of 0.5 << 8
341 }
342 ;;
343 { .mfi
344 setf.d fThreeAndQ = rThreeAndQ // 3.25 if FP register
345 fclass.m p9,p0 = f8, 0x23 // is x +/- inf?
346 shr.u rShiftedArg = rArg, 44
347 }
348 { .mfb
349 andcm rAbsArg = rArg, rSignBit // |x| in GR
350 nop.f 0
351 (p6) br.cond.spnt erf_denormal // branch out if x is denormal
352 }
353 ;;
354 { .mfi
355 and rShiftedArgMasked = rShiftedArg, rMask // bias of x << 8
356 fmerge.s fArgAbs = f1, f8 // |x|
357 shr rShiftedAbsArg = rAbsArg, 44
358 }
359 { .mfb
360 cmp.lt p8, p11 = rThreeAndQ, rAbsArg // p8 = 1 if |x| >= 3.25
361 (p7) fma.d.s0 f8 = f8,f1,f8 // NaN or +/-0
362 (p7) br.ret.spnt b0 // exit for x = NaN or +/-0
363 }
364 ;;
365 { .mfi
366 sub rIndex = rShiftedArgMasked, rBias // index << 8
367 nop.f 0
368 cmp.lt p10, p0 = rShiftedArgMasked, rBias // p10 = 1 if |x| < 0.5
369 }
370 { .mfb
371 // p8 = 1 if 3.25 <= |x| < 4.0
372 (p8) cmp.lt p8, p11 = rShiftedAbsArg, rBiasedExpOf4
373 fms.s1 fArgAbsNorm = fArgAbsNorm, f1, f1
374 (p10) br.cond.spnt erf_near_zero // branch out if |x| < 0.5
375 }
376 ;;
377 .pred.rel "mutex", p8, p11
378 { .mfi
379 (p8) adds rCoeffAddr1 = 1392, rDataPtr // coeff. for 3.25 <=|x|<4.0
380 (p9) fmerge.s f8 = f8,f1 // +/- inf
381 nop.i 0
382 }
383 { .mfb
384 (p11) add rCoeffAddr1 = rDataPtr, rIndex// coeff. ##0,2,..14
385 nop.f 0
386 (p9) br.ret.spnt b0 // exit for x = +/- inf
387 }
388 ;;
389 { .mfi
390 adds rCoeffAddr2 = 16, rCoeffAddr1
391 fmerge.s fSignumX = f8, f1 // signum(x)
392 nop.i 0
393 }
394 { .mfb
395 cmp.lt p12, p0 = rSaturation, rShiftedAbsArg // |x| > 5.90625?
396 nop.f 0
397 (p12) br.cond.spnt erf_saturation // branch out if x |x| >= 6.0
398 }
399 ;;
400 // Here if paths #3,4
401 // if path #4 we'll branch out after loading of 14 necessary coefficients
402 {.mfi
403 ldfe fA19 = [rCoeffAddr1], 32
404 nop.f 0
405 nop.i 0
406 }
407 {.mfi
408 ldfe fA18 = [rCoeffAddr2], 32
409 nop.f 0
410 adds rCoeffAddr3 = 1024, rDataPtr
411 }
412 ;;
413 {.mfi
414 ldfe fA17 = [rCoeffAddr1], 32
415 nop.f 0
416 nop.i 0
417 }
418 {.mfi
419 ldfe fA16 = [rCoeffAddr2], 32
420 nop.f 0
421 nop.i 0
422 }
423 ;;
424 {.mfi
425 ldfe fA15 = [rCoeffAddr1], 32
426 fma.s1 fTSqr = fArgAbsNorm, fArgAbsNorm, f0
427 shr.u rIndex = rIndex, 2
428 }
429 {.mfi
430 ldfe fA14 = [rCoeffAddr2], 32
431 nop.f 0
432 adds rCoeffAddr4 = 16, r0
433 }
434 ;;
435 {.mfi
436 ldfe fA13 = [rCoeffAddr1], 32
437 nop.f 0
438 // address of coefficients ##16..23
439 add rCoeffAddr3 = rCoeffAddr3, rIndex
440 }
441 {.mfi
442 ldfe fA12 = [rCoeffAddr2], 32
443 nop.f 0
444 cmp.lt p15, p14 = rArg, r0
445 }
446 ;;
447 {.mfi
448 ldfe fA11 = [rCoeffAddr1], 32
449 nop.f 0
450 add rCoeffAddr4 = rCoeffAddr3, rCoeffAddr4
451 }
452 {.mfi
453 ldfe fA10 = [rCoeffAddr2], 32
454 nop.f 0
455 nop.i 0
456 }
457 ;;
458 {.mfi
459 ldfe fA9 = [rCoeffAddr1], 32
460 nop.f 0
461 nop.i 0
462 }
463 {.mfi
464 ldfe fA8 = [rCoeffAddr2], 32
465 nop.f 0
466 nop.i 0
467 }
468 ;;
469 {.mfi
470 ldfe fA7 = [rCoeffAddr1], 32
471 fms.s1 fArgAbs = fArgAbs, f1, fThreeAndQ
472 nop.i 0
473 }
474 {.mfb
475 ldfe fA6 = [rCoeffAddr2], 32
476 nop.f 0
477 (p8) br.cond.spnt erf_3q_4 // branch out if 3.25 < |x| < 4.0
478 }
479 ;;
480 {.mfi
481 ldfe fA5 = [rCoeffAddr1], 32
482 fma.s1 fTDeg3 = fArgAbsNorm, fTSqr, f0
483 nop.i 0
484 }
485 {.mfi
486 ldfe fA4 = [rCoeffAddr2], 32
487 fma.s1 fTQuadr = fTSqr, fTSqr, f0
488 nop.i 0
489 }
490 ;;
491 // Path #3 Polynomial Pol19(y) computation; y = fArgAbsNorm
492 {.mfi
493 ldfe fA3 = [rCoeffAddr3], 32
494 fma.s1 fArgAbsNormSgn = fArgAbsNorm, fSignumX, f0
495 nop.i 0
496 }
497 {.mfi
498 ldfe fA2 = [rCoeffAddr4], 32
499 nop.f 0
500 nop.i 0
501 }
502 ;;
503 {.mfi
504 ldfe fA1 = [rCoeffAddr3], 32
505 fma.s1 fRes = fA19, fArgAbsNorm, fA18
506 nop.i 0
507 }
508 {.mfi
509 ldfe fA0 = [rCoeffAddr4], 32
510 nop.f 0
511 nop.i 0
512 }
513 ;;
514 { .mfi
515 nop.m 0
516 fma.s1 fA17 = fA17, fArgAbsNorm, fA16
517 nop.i 0
518 }
519 ;;
520 { .mfi
521 nop.m 0
522 fma.s1 fA15 = fA15, fArgAbsNorm, fA14
523 nop.i 0
524 }
525 ;;
526 { .mfi
527 nop.m 0
528 fma.s1 fTDeg7 = fTDeg3, fTQuadr, f0
529 nop.i 0
530 }
531 { .mfi
532 nop.m 0
533 fma.s1 fA13 = fA13, fArgAbsNorm, fA12
534 nop.i 0
535 }
536 ;;
537 { .mfi
538 nop.m 0
539 fma.s1 fA11 = fA11, fArgAbsNorm, fA10
540 nop.i 0
541 }
542 ;;
543 { .mfi
544 nop.m 0
545 fma.s1 fA9 = fA9, fArgAbsNorm, fA8
546 nop.i 0
547 }
548 ;;
549 { .mfi
550 nop.m 0
551 fma.s1 fRes = fRes, fTSqr, fA17
552 nop.i 0
553 }
554 { .mfi
555 nop.m 0
556 fma.s1 fA7 = fA7, fArgAbsNorm, fA6
557 nop.i 0
558 }
559 ;;
560 { .mfi
561 nop.m 0
562 fma.s1 fA5 = fA5, fArgAbsNorm, f0
563 nop.i 0
564 }
565 ;;
566 { .mfi
567 nop.m 0
568 fma.s1 fA15 = fA15, fTSqr, fA13
569 nop.i 0
570 }
571 { .mfi
572 nop.m 0
573 fma.s1 fA4 = fA4, fArgAbsNorm, fA3
574 nop.i 0
575 }
576 ;;
577 { .mfi
578 nop.m 0
579 fma.s1 fA2 = fA2, fArgAbsNorm, fA1
580 nop.i 0
581 }
582 ;;
583 { .mfi
584 nop.m 0
585 fma.s1 fA11 = fA11, fTSqr, fA9
586 nop.i 0
587 }
588 ;;
589 { .mfi
590 nop.m 0
591 fma.s1 fA7 = fA7, fTSqr, fA5
592 nop.i 0
593 }
594 ;;
595 { .mfi
596 nop.m 0
597 fma.s1 fRes = fRes, fTQuadr, fA15
598 nop.i 0
599 }
600 ;;
601 { .mfi
602 nop.m 0
603 fma.s1 fA4 = fA4, fTSqr, fA2
604 nop.i 0
605 }
606 ;;
607 { .mfi
608 nop.m 0
609 fma.s1 fRes = fRes, fTQuadr, fA11
610 nop.i 0
611 }
612 ;;
613 { .mfi
614 nop.m 0
615 fma.s1 fA4 = fA7, fTDeg3, fA4
616 nop.i 0
617 }
618 ;;
619 { .mfi
620 nop.m 0
621 fma.s1 fRes = fRes, fTDeg7, fA4
622 nop.i 0
623 }
624 ;;
625 { .mfi
626 nop.m 0
627 // result for negative argument
628 (p15) fms.d.s0 f8 = fRes, fArgAbsNormSgn, fA0
629 nop.i 0
630 }
631 { .mfb
632 nop.m 0
633 // result for positive argument
634 (p14) fma.d.s0 f8 = fRes, fArgAbsNormSgn, fA0
635 br.ret.sptk b0
636 }
638 // Here if 3.25 < |x| < 4.0
639 .align 32
640 erf_3q_4:
641 .pred.rel "mutex", p14, p15
642 { .mfi
643 ldfe fA5 = [rCoeffAddr1], 32
644 fma.s1 fTSqr = fArgAbs, fArgAbs, f0
645 nop.i 0
646 }
647 { .mfi
648 nop.m 0
649 fma.s1 fRes = fA19, fArgAbs, fA18
650 nop.i 0
651 }
652 ;;
653 { .mfi
654 nop.m 0
655 fma.s1 fA17 = fA17, fArgAbs, fA16
656 nop.i 0
657 }
658 { .mfi
659 nop.m 0
660 fma.s1 fA15 = fA15, fArgAbs, fA14
661 nop.i 0
662 }
663 ;;
664 { .mfi
665 nop.m 0
666 fma.s1 fA13 = fA13, fArgAbs, fA12
667 nop.i 0
668 }
669 { .mfi
670 nop.m 0
671 fma.s1 fA11 = fA11, fArgAbs, fA10
672 nop.i 0
673 }
674 ;;
675 { .mfi
676 nop.m 0
677 fma.s1 fA9 = fA9, fArgAbs, fA8
678 nop.i 0
679 }
680 { .mfi
681 nop.m 0
682 fma.s1 fArgAbsNormSgn = fArgAbs, fSignumX, f0
683 nop.i 0
684 }
685 ;;
686 { .mfi
687 nop.m 0
688 fma.s1 fTQuadr = fTSqr, fTSqr, f0
689 nop.i 0
690 }
691 ;;
692 { .mfi
693 nop.m 0
694 fma.s1 fRes = fRes, fTSqr, fA17
695 nop.i 0
696 }
697 ;;
698 { .mfi
699 nop.m 0
700 fma.s1 fA15 = fA15, fTSqr, fA13
701 nop.i 0
702 }
703 ;;
704 { .mfi
705 nop.m 0
706 fma.s1 fA11 = fA11, fTSqr, fA9
707 nop.i 0
708 }
709 { .mfi
710 nop.m 0
711 fma.s1 fA7 = fA7, fArgAbs, fA6
712 nop.i 0
713 }
714 ;;
715 { .mfi
716 nop.m 0
717 fma.s1 fTDeg7 = fTQuadr, fTSqr, f0
718 nop.i 0
719 }
720 { .mfi
721 nop.m 0
722 fma.s1 fRes = fRes, fTQuadr, fA15
723 nop.i 0
724 }
725 ;;
726 { .mfi
727 nop.m 0
728 fma.s1 fA11 = fA11, fTSqr, fA7
729 nop.i 0
730 }
731 ;;
732 { .mfi
733 nop.m 0
734 fma.s1 fRes = fRes, fTDeg7, fA11
735 nop.i 0
736 }
737 ;;
738 { .mfi
739 nop.m 0
740 // result for negative argument
741 (p15) fms.d.s0 f8 = fRes, fArgAbsNormSgn, fA5
742 nop.i 0
743 }
744 { .mfb
745 nop.m 0
746 // result for positive argument
747 (p14) fma.d.s0 f8 = fRes, fArgAbsNormSgn, fA5
748 br.ret.sptk b0
749 }
750 ;;
752 // Here if |x| < 0.5
753 .align 32
754 erf_near_zero:
755 { .mfi
756 adds rCoeffAddr1 = 1280, rDataPtr // address of A9
757 fma.s1 fTSqr = fArgSqr, fArgSqr, f0 // x^4
758 nop.i 0
759 }
760 { .mfi
761 adds rCoeffAddr2 = 1328, rDataPtr // address of A7
762 nop.f 0
763 nop.i 0
764 }
765 ;;
766 { .mfi
767 ldfpd fA9, fA8 = [rCoeffAddr1], 16
768 nop.f 0
769 nop.i 0
770 }
771 { .mfi
772 ldfpd fA7, fA6 = [rCoeffAddr2], 16
773 nop.f 0
774 nop.i 0
775 }
776 ;;
777 { .mfi
778 ldfpd fA5, fA4 = [rCoeffAddr1], 16
779 nop.f 0
780 nop.i 0
781 }
782 { .mfi
783 ldfpd fA3, fA2 = [rCoeffAddr2], 16
784 nop.f 0
785 nop.i 0
786 }
787 ;;
788 { .mfi
789 ldfe fA1 = [rCoeffAddr1]
790 nop.f 0
791 nop.i 0
792 }
793 { .mfi
794 ldfe fA0 = [rCoeffAddr2]
795 nop.f 0
796 nop.i 0
797 }
798 ;;
799 { .mfi
800 nop.m 0
801 fma.s1 fTQuadr = fTSqr, fTSqr, f0
802 nop.i 0
803 }
804 ;;
805 { .mfi
806 nop.m 0
807 fma.s1 fRes = fA9, fArgSqr, fA8
808 nop.i 0
809 }
810 { .mfi
811 nop.m 0
812 fma.s1 fA7 = fA7, fArgSqr, fA6
813 nop.i 0
814 }
815 ;;
816 { .mfi
817 nop.m 0
818 fma.s1 fA3 = fA3, fArgSqr, fA2
819 nop.i 0
820 }
821 { .mfi
822 nop.m 0
823 fma.s1 fA5 = fA5, fArgSqr, fA4
824 nop.i 0
825 }
826 ;;
827 { .mfi
828 nop.m 0
829 fma.s1 fA1 = fA1, fArgSqr, fA0
830 nop.i 0
831 }
832 { .mfi
833 nop.m 0
834 fma.s1 fTQuadrSgn = fTQuadr, f8, f0
835 nop.i 0
836 }
837 ;;
838 { .mfi
839 nop.m 0
840 fma.s1 fRes = fRes, fTSqr, fA7
841 nop.i 0
842 }
843 ;;
844 { .mfi
845 nop.m 0
846 fma.s1 fA1 = fA3, fTSqr, fA1
847 nop.i 0
848 }
849 ;;
850 { .mfi
851 nop.m 0
852 fma.s1 fRes = fRes, fTSqr, fA5
853 nop.i 0
854 }
855 ;;
856 { .mfi
857 nop.m 0
858 fma.s1 fA1 = fA1, f8, f0
859 nop.i 0
860 }
861 ;;
862 { .mfb
863 nop.m 0
864 fma.d.s0 f8 = fRes, fTQuadrSgn, fA1 // x*Pol9(x^2)
865 br.ret.sptk b0 // Exit for |x| < 0.5
866 };;
868 // Here if 5.90625 <= |x| < +inf
869 .align 32
870 erf_saturation:
871 { .mfi
872 adds rDataPtr = 1376, rDataPtr // address of A0
873 nop.f 0
874 nop.i 0
875 }
876 ;;
877 { .mfi
878 ldfe fA0 = [rDataPtr]
879 nop.f 0
880 nop.i 0
881 }
882 ;;
883 { .mfb
884 nop.m 0
885 fma.d.s0 f8 = fA0, fSignumX, f0 // sign(x)*(1.0 - 2^(-63))
886 // Exit for 5.90625 <= |x| < +inf
887 br.ret.sptk b0 // Exit for 5.90625 <=|x|< +inf
888 }
889 ;;
891 // Here if x is double precision denormal
892 .align 32
893 erf_denormal:
894 { .mfi
895 adds rDataPtr = 1632, rDataPtr // address of A0
896 fclass.m p7,p8 = f8, 0x0a // is x -denormal ?
897 nop.i 0
898 }
899 ;;
900 { .mfi
901 ldfe fA0 = [rDataPtr] // A0
902 nop.f 0
903 nop.i 0
904 }
905 ;;
906 { .mfi
907 nop.m 0
908 fma.s1 fA0 = fA0,f8,f0 // A0*x
909 nop.i 0
910 }
911 ;;
912 { .mfi
913 nop.m 0
914 (p7) fma.d.s0 f8 = f8,f8,fA0 // -denormal
915 nop.i 0
916 }
917 { .mfb
918 nop.m 0
919 (p8) fnma.d.s0 f8 = f8,f8,fA0 // +denormal
920 br.ret.sptk b0 // Exit for denormal
921 }
922 ;;
924 GLOBAL_LIBM_END(erf)