| blob | 266e1e1c911a9670b26648bc30391dffcc4f3e9c |
1 .file "erfcl.s"
4 // Copyright (c) 2001 - 2005, Intel Corporation
5 // All rights reserved.
6 //
7 // Contributed 2001 by the Intel Numerics Group, Intel Corporation
8 //
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38 // http://www.intel.com/software/products/opensource/libraries/num.htm.
39 //
40 // History
41 //==============================================================
42 // 11/12/01 Initial version
43 // 02/08/02 Added missing }
44 // 05/20/02 Cleaned up namespace and sf0 syntax
45 // 02/10/03 Reordered header: .section, .global, .proc, .align;
46 // used data8 for long double table values
47 // 03/31/05 Reformatted delimiters between data tables
48 //
49 // API
50 //==============================================================
51 // long double erfcl(long double)
52 //
53 // Implementation and Algorithm Notes:
54 //==============================================================
55 // 1. 0 <= x <= 107.0
56 //
57 // erfcl(x) ~=~ P15(z) * expl( -x^2 )/(dx + x), z = x - xc(i).
58 //
59 // Comment:
60 //
61 // Let x(i) = -1.0 + 2^(i/4),i=0,...27. So we have 28 unequal
62 // argument intervals [x(i),x(i+1)] with length ratio q = 2^(1/4).
63 // Values xc(i) we have in the table erfc_xc_table,xc(i)=x(i)for i = 0
64 // and xc(i)= 0.5*( x(i)+x(i+1) ) for i>0.
65 //
66 // Let x(i)<= x < x(i+1).
67 // We can find i as exponent of number (x + 1)^4.
68 //
69 // Let P15(z)= a0+ a1*z +..+a15*z^15 - polynomial approximation of degree 15
70 // for function erfcl(z+xc(i)) * expl( (z+xc(i))^2)* (dx+z+xc(i)) and
71 // -0.5*[x(i+1)-x(i)] <= z <= 0.5*[x(i+1)-x(i)].
72 //
73 // Let Q(z)= (P(z)- S)/S, S = a0, rounded to 16 bits.
74 // Polynomial coeffitients for Q(z) we have in the table erfc_Q_table as
75 // long double values
76 //
77 // We use multi precision to calculate input argument -x^2 for expl and
78 // for u = 1/(dx + x).
79 //
80 // Algorithm description for expl function see below. In accordance with
81 // denotation of this algorithm we have for expl:
82 //
83 // expl(X) ~=~ 2^K*T_1*(1+W_1)*T_2*(1+W_2)*(1+ poly(r)), X = -x^2.
84 //
85 // Final calculations for erfcl:
86 //
87 // erfcl(x) ~=~
88 //
89 // 2^K*T_1*(1+W_1)*T_2*(1+W_2)*(1+ poly(r))*(1-dy)*S*(1+Q(z))*u*(1+du),
90 //
91 // where dy - low bits of x^2 and u, u*du - hi and low bits of 1/(dx + x).
92 //
93 // The order of calculations is the next:
94 //
95 // 1) M = 2^K*T_1*T_2*S without rounding error,
96 // 2) W = W_1 + (W_2 + W_1*W_2), where 1+W ~=~ (1+W_1)(1+W_2),
97 // 3) H = W - dy, where 1+H ~=~ (1+W )(1-dy),
98 // 4) R = poly(r)*H + poly(r),
99 // 5) R = H + R , where 1+R ~=~ (1+H )(1+poly(r)),
100 // 6) G = Q(z)*R + Q(z),
101 // 7) R1 = R + du, where 1+R1 ~=~ (1+R)(1+du),
102 // 8) G1 = R1 + G, where 1+G1 ~=~ (1+R1)(1+Q(z)),
103 // 9) V = G1*M*u,
104 // 10) erfcl(x) ~=~ M*u + V
105 //
106 // 2. -6.5 <= x < 0
107 //
108 // erfcl(x) = 2.0 - erfl(-x)
109 //
110 // 3. x > 107.0
111 // erfcl(x) ~=~ 0.0
112 //
113 // 4. x < -6.5
114 // erfcl(x) ~=~ 2.0
116 // Special values
117 //==============================================================
118 // erfcl(+0) = 1.0
119 // erfcl(-0) = 1.0
121 // erfcl(+qnan) = +qnan
122 // erfcl(-qnan) = -qnan
123 // erfcl(+snan) = +qnan
124 // erfcl(-snan) = -qnan
126 // erfcl(-inf) = 2.0
127 // erfcl(+inf) = +0
129 //==============================================================
130 // Algorithm description of used expl function.
131 //
132 // Implementation and Algorithm Notes:
133 //
134 // ker_exp_64( in_FR : X,
135 // out_FR : Y_hi,
136 // out_FR : Y_lo,
137 // out_FR : scale,
138 // out_PR : Safe )
139 //
140 // On input, X is in register format
141 //
142 // On output,
143 //
144 // scale*(Y_hi + Y_lo) approximates exp(X)
145 //
146 // The accuracy is sufficient for a highly accurate 64 sig.
147 // bit implementation. Safe is set if there is no danger of
148 // overflow/underflow when the result is composed from scale,
149 // Y_hi and Y_lo. Thus, we can have a fast return if Safe is set.
150 // Otherwise, one must prepare to handle the possible exception
151 // appropriately. Note that SAFE not set (false) does not mean
152 // that overflow/underflow will occur; only the setting of SAFE
153 // guarantees the opposite.
154 //
155 // **** High Level Overview ****
156 //
157 // The method consists of three cases.
158 //
159 // If |X| < Tiny use case exp_tiny;
160 // else if |X| < 2^(-6) use case exp_small;
161 // else use case exp_regular;
162 //
163 // Case exp_tiny:
164 //
165 // 1 + X can be used to approximate exp(X)
166 // X + X^2/2 can be used to approximate exp(X) - 1
167 //
168 // Case exp_small:
169 //
170 // Here, exp(X) and exp(X) - 1 can all be
171 // appproximated by a relatively simple polynomial.
172 //
173 // This polynomial resembles the truncated Taylor series
174 //
175 // exp(w) = 1 + w + w^2/2! + w^3/3! + ... + w^n/n!
176 //
177 // Case exp_regular:
178 //
179 // Here we use a table lookup method. The basic idea is that in
180 // order to compute exp(X), we accurately decompose X into
181 //
182 // X = N * log(2)/(2^12) + r, |r| <= log(2)/2^13.
183 //
184 // Hence
185 //
186 // exp(X) = 2^( N / 2^12 ) * exp(r).
187 //
188 // The value 2^( N / 2^12 ) is obtained by simple combinations
189 // of values calculated beforehand and stored in table; exp(r)
190 // is approximated by a short polynomial because |r| is small.
191 //
192 // We elaborate this method in 4 steps.
193 //
194 // Step 1: Reduction
195 //
196 // The value 2^12/log(2) is stored as a double-extended number
197 // L_Inv.
198 //
199 // N := round_to_nearest_integer( X * L_Inv )
200 //
201 // The value log(2)/2^12 is stored as two numbers L_hi and L_lo so
202 // that r can be computed accurately via
203 //
204 // r := (X - N*L_hi) - N*L_lo
205 //
206 // We pick L_hi such that N*L_hi is representable in 64 sig. bits
207 // and thus the FMA X - N*L_hi is error free. So r is the
208 // 1 rounding error from an exact reduction with respect to
209 //
210 // L_hi + L_lo.
211 //
212 // In particular, L_hi has 30 significant bit and can be stored
213 // as a double-precision number; L_lo has 64 significant bits and
214 // stored as a double-extended number.
215 //
216 // Step 2: Approximation
217 //
218 // exp(r) - 1 is approximated by a short polynomial of the form
219 //
220 // r + A_1 r^2 + A_2 r^3 + A_3 r^4 .
221 //
222 // Step 3: Composition from Table Values
223 //
224 // The value 2^( N / 2^12 ) can be composed from a couple of tables
225 // of precalculated values. First, express N as three integers
226 // K, M_1, and M_2 as
227 //
228 // N = K * 2^12 + M_1 * 2^6 + M_2
229 //
230 // Where 0 <= M_1, M_2 < 2^6; and K can be positive or negative.
231 // When N is represented in 2's complement, M_2 is simply the 6
232 // lsb's, M_1 is the next 6, and K is simply N shifted right
233 // arithmetically (sign extended) by 12 bits.
234 //
235 // Now, 2^( N / 2^12 ) is simply
236 //
237 // 2^K * 2^( M_1 / 2^6 ) * 2^( M_2 / 2^12 )
238 //
239 // Clearly, 2^K needs no tabulation. The other two values are less
240 // trivial because if we store each accurately to more than working
241 // precision, than its product is too expensive to calculate. We
242 // use the following method.
243 //
244 // Define two mathematical values, delta_1 and delta_2, implicitly
245 // such that
246 //
247 // T_1 = exp( [M_1 log(2)/2^6] - delta_1 )
248 // T_2 = exp( [M_2 log(2)/2^12] - delta_2 )
249 //
250 // are representable as 24 significant bits. To illustrate the idea,
251 // we show how we define delta_1:
252 //
253 // T_1 := round_to_24_bits( exp( M_1 log(2)/2^6 ) )
254 // delta_1 = (M_1 log(2)/2^6) - log( T_1 )
255 //
256 // The last equality means mathematical equality. We then tabulate
257 //
258 // W_1 := exp(delta_1) - 1
259 // W_2 := exp(delta_2) - 1
260 //
261 // Both in double precision.
262 //
263 // From the tabulated values T_1, T_2, W_1, W_2, we compose the values
264 // T and W via
265 //
266 // T := T_1 * T_2 ...exactly
267 // W := W_1 + (1 + W_1)*W_2
268 //
269 // W approximates exp( delta ) - 1 where delta = delta_1 + delta_2.
270 // The mathematical product of T and (W+1) is an accurate representation
271 // of 2^(M_1/2^6) * 2^(M_2/2^12).
272 //
273 // Step 4. Reconstruction
274 //
275 // Finally, we can reconstruct exp(X), exp(X) - 1.
276 // Because
277 //
278 // X = K * log(2) + (M_1*log(2)/2^6 - delta_1)
279 // + (M_2*log(2)/2^12 - delta_2)
280 // + delta_1 + delta_2 + r ...accurately
281 // We have
282 //
283 // exp(X) ~=~ 2^K * ( T + T*[exp(delta_1+delta_2+r) - 1] )
284 // ~=~ 2^K * ( T + T*[exp(delta + r) - 1] )
285 // ~=~ 2^K * ( T + T*[(exp(delta)-1)
286 // + exp(delta)*(exp(r)-1)] )
287 // ~=~ 2^K * ( T + T*( W + (1+W)*poly(r) ) )
288 // ~=~ 2^K * ( Y_hi + Y_lo )
289 //
290 // where Y_hi = T and Y_lo = T*(W + (1+W)*poly(r))
291 //
292 // For exp(X)-1, we have
293 //
294 // exp(X)-1 ~=~ 2^K * ( Y_hi + Y_lo ) - 1
295 // ~=~ 2^K * ( Y_hi + Y_lo - 2^(-K) )
296 //
297 // and we combine Y_hi + Y_lo - 2^(-N) into the form of two
298 // numbers Y_hi + Y_lo carefully.
299 //
300 // **** Algorithm Details ****
301 //
302 // A careful algorithm must be used to realize the mathematical ideas
303 // accurately. We describe each of the three cases. We assume SAFE
304 // is preset to be TRUE.
305 //
306 // Case exp_tiny:
307 //
308 // The important points are to ensure an accurate result under
309 // different rounding directions and a correct setting of the SAFE
310 // flag.
311 //
312 // If expm1 is 1, then
313 // SAFE := False ...possibility of underflow
314 // Scale := 1.0
315 // Y_hi := X
316 // Y_lo := 2^(-17000)
317 // Else
318 // Scale := 1.0
319 // Y_hi := 1.0
320 // Y_lo := X ...for different rounding modes
321 // Endif
322 //
323 // Case exp_small:
324 //
325 // Here we compute a simple polynomial. To exploit parallelism, we split
326 // the polynomial into several portions.
327 //
328 // Let r = X
329 //
330 // If exp ...i.e. exp( argument )
331 //
332 // rsq := r * r;
333 // r4 := rsq*rsq
334 // poly_lo := P_3 + r*(P_4 + r*(P_5 + r*P_6))
335 // poly_hi := r + rsq*(P_1 + r*P_2)
336 // Y_lo := poly_hi + r4 * poly_lo
337 // Y_hi := 1.0
338 // Scale := 1.0
339 //
340 // Else ...i.e. exp( argument ) - 1
341 //
342 // rsq := r * r
343 // r4 := rsq * rsq
344 // r6 := rsq * r4
345 // poly_lo := r6*(Q_5 + r*(Q_6 + r*Q_7))
346 // poly_hi := Q_1 + r*(Q_2 + r*(Q_3 + r*Q_4))
347 // Y_lo := rsq*poly_hi + poly_lo
348 // Y_hi := X
349 // Scale := 1.0
350 //
351 // Endif
352 //
353 // Case exp_regular:
354 //
355 // The previous description contain enough information except the
356 // computation of poly and the final Y_hi and Y_lo in the case for
357 // exp(X)-1.
358 //
359 // The computation of poly for Step 2:
360 //
361 // rsq := r*r
362 // poly := r + rsq*(A_1 + r*(A_2 + r*A_3))
363 //
364 // For the case exp(X) - 1, we need to incorporate 2^(-K) into
365 // Y_hi and Y_lo at the end of Step 4.
366 //
367 // If K > 10 then
368 // Y_lo := Y_lo - 2^(-K)
369 // Else
370 // If K < -10 then
371 // Y_lo := Y_hi + Y_lo
372 // Y_hi := -2^(-K)
373 // Else
374 // Y_hi := Y_hi - 2^(-K)
375 // End If
376 // End If
377 //
379 // Overview of operation
380 //==============================================================
382 // Registers used
383 //==============================================================
384 // Floating Point registers used:
385 // f8, input
386 // f9 -> f14, f36 -> f126
388 // General registers used:
389 // r32 -> r71
391 // Predicate registers used:
392 // p6 -> p15
394 // Assembly macros
395 //==============================================================
396 // GR for exp(X)
397 GR_ad_Arg = r33
398 GR_ad_C = r34
399 GR_ERFC_S_TB = r35
400 GR_signexp_x = r36
401 GR_exp_x = r36
402 GR_exp_mask = r37
403 GR_ad_W1 = r38
404 GR_ad_W2 = r39
405 GR_M2 = r40
406 GR_M1 = r41
407 GR_K = r42
408 GR_exp_2_k = r43
409 GR_ad_T1 = r44
410 GR_ad_T2 = r45
411 GR_N_fix = r46
412 GR_ad_P = r47
413 GR_exp_bias = r48
414 GR_BIAS = r48
415 GR_exp_half = r49
416 GR_sig_inv_ln2 = r50
417 GR_rshf_2to51 = r51
418 GR_exp_2tom51 = r52
419 GR_rshf = r53
421 // GR for erfcl(x)
422 //==============================================================
424 GR_ERFC_XC_TB = r54
425 GR_ERFC_P_TB = r55
426 GR_IndxPlusBias = r56
427 GR_P_POINT_1 = r57
428 GR_P_POINT_2 = r58
429 GR_AbsArg = r59
430 GR_ShftXBi = r60
431 GR_ShftPi = r61
432 GR_mBIAS = r62
433 GR_ShftPi_bias = r63
434 GR_ShftXBi_bias = r64
435 GR_ShftA14 = r65
436 GR_ShftA15 = r66
437 GR_EpsNorm = r67
438 GR_0x1 = r68
439 GR_ShftPi_8 = r69
440 GR_26PlusBias = r70
441 GR_27PlusBias = r71
443 // GR for __libm_support call
444 //==============================================================
445 GR_SAVE_B0 = r64
446 GR_SAVE_PFS = r65
447 GR_SAVE_GP = r66
448 GR_SAVE_SP = r67
450 GR_Parameter_X = r68
451 GR_Parameter_Y = r69
452 GR_Parameter_RESULT = r70
453 GR_Parameter_TAG = r71
455 //==============================================================
456 // Floating Point Registers
457 //
458 FR_RSHF_2TO51 = f10
459 FR_INV_LN2_2TO63 = f11
460 FR_W_2TO51_RSH = f12
461 FR_2TOM51 = f13
462 FR_RSHF = f14
464 FR_scale = f36
465 FR_float_N = f37
466 FR_N_signif = f38
467 FR_L_hi = f39
468 FR_L_lo = f40
469 FR_r = f41
470 FR_W1 = f42
471 FR_T1 = f43
472 FR_W2 = f44
473 FR_T2 = f45
474 FR_rsq = f46
475 FR_C2 = f47
476 FR_C3 = f48
477 FR_poly = f49
478 FR_P6 = f49
479 FR_T = f50
480 FR_P5 = f50
481 FR_P4 = f51
482 FR_W = f51
483 FR_P3 = f52
484 FR_Wp1 = f52
485 FR_P2 = f53
486 FR_P1 = f54
487 FR_Q7 = f56
488 FR_Q6 = f57
489 FR_Q5 = f58
490 FR_Q4 = f59
491 FR_Q3 = f60
492 FR_Q2 = f61
493 FR_Q1 = f62
494 FR_C1 = f63
495 FR_A15 = f64
496 FR_ch_dx = f65
497 FR_T_scale = f66
498 FR_norm_x = f67
499 FR_AbsArg = f68
500 FR_POS_ARG_ASYMP = f69
501 FR_NEG_ARG_ASYMP = f70
502 FR_Tmp = f71
503 FR_Xc = f72
504 FR_A0 = f73
505 FR_A1 = f74
506 FR_A2 = f75
507 FR_A3 = f76
508 FR_A4 = f77
509 FR_A5 = f78
510 FR_A6 = f79
511 FR_A7 = f80
512 FR_A8 = f81
513 FR_A9 = f82
514 FR_A10 = f83
515 FR_A11 = f84
516 FR_A12 = f85
517 FR_A13 = f86
518 FR_A14 = f87
519 FR_P15_0_1 = f88
520 FR_P15_8_1 = f88
521 FR_P15_1_1 = f89
522 FR_P15_8_2 = f89
523 FR_P15_1_2 = f90
524 FR_P15_2_1 = f91
525 FR_P15_2_2 = f92
526 FR_P15_3_1 = f93
527 FR_P15_3_2 = f94
528 FR_P15_4_2 = f95
529 FR_P15_7_1 = f96
530 FR_P15_7_2 = f97
531 FR_P15_9_1 = f98
532 FR_P15_9_2 = f99
533 FR_P15_13_1 = f100
534 FR_P15_14_1 = f101
535 FR_P15_14_2 = f102
536 FR_Tmp2 = f103
537 FR_Xpdx_lo = f104
538 FR_2 = f105
539 FR_xsq_lo = f106
540 FR_LocArg = f107
541 FR_Tmpf = f108
542 FR_Tmp1 = f109
543 FR_EpsNorm = f110
544 FR_UnfBound = f111
545 FR_NormX = f112
546 FR_Xpdx_hi = f113
547 FR_dU = f114
548 FR_H = f115
549 FR_G = f116
550 FR_V = f117
551 FR_M = f118
552 FR_U = f119
553 FR_Q = f120
554 FR_S = f121
555 FR_R = f122
556 FR_res_pos_x_hi = f123
557 FR_res_pos_x_lo = f124
558 FR_dx = f125
559 FR_dx1 = f126
561 // for error handler routine
562 FR_X = f9
563 FR_Y = f0
564 FR_RESULT = f8
566 // Data tables
567 //==============================================================
568 RODATA
569 .align 16
571 // ************* DO NOT CHANGE ORDER OF THESE TABLES ********************
572 LOCAL_OBJECT_START(exp_table_1)
574 data8 0xae89f995ad3ad5ea , 0x00003ffe // x = 0.681..,bound for dx = 0.875
575 data8 0x405AC00000000000 , 0x401A000000000000 //ARG_ASYMP,NEG_ARG_ASYMP
576 data8 0x3FE4000000000000 , 0x3FEC000000000000 //0.625,0.875
577 data8 0xD5126065B720A4e9 , 0x00004005 // underflow boundary
578 data8 0x8000000000000000 , 0x00000001 //FR_EpsNorm
579 LOCAL_OBJECT_END(exp_table_1)
581 LOCAL_OBJECT_START(Constants_exp_64_Arg)
582 data8 0xB17217F400000000,0x00003FF2 //L_hi = hi part log(2)/2^12
583 data8 0xF473DE6AF278ECE6,0x00003FD4 //L_lo = lo part log(2)/2^12
584 LOCAL_OBJECT_END(Constants_exp_64_Arg)
586 LOCAL_OBJECT_START(Constants_exp_64_C)
587 data8 0xAAAAAAABB1B736A0,0x00003FFA // C3
588 data8 0xAAAAAAAB90CD6327,0x00003FFC // C2
589 data8 0xFFFFFFFFFFFFFFFF,0x00003FFD // C1
590 LOCAL_OBJECT_END(Constants_exp_64_C)
592 LOCAL_OBJECT_START(Constants_exp_64_T1)
593 data4 0x3F800000,0x3F8164D2,0x3F82CD87,0x3F843A29
594 data4 0x3F85AAC3,0x3F871F62,0x3F88980F,0x3F8A14D5
595 data4 0x3F8B95C2,0x3F8D1ADF,0x3F8EA43A,0x3F9031DC
596 data4 0x3F91C3D3,0x3F935A2B,0x3F94F4F0,0x3F96942D
597 data4 0x3F9837F0,0x3F99E046,0x3F9B8D3A,0x3F9D3EDA
598 data4 0x3F9EF532,0x3FA0B051,0x3FA27043,0x3FA43516
599 data4 0x3FA5FED7,0x3FA7CD94,0x3FA9A15B,0x3FAB7A3A
600 data4 0x3FAD583F,0x3FAF3B79,0x3FB123F6,0x3FB311C4
601 data4 0x3FB504F3,0x3FB6FD92,0x3FB8FBAF,0x3FBAFF5B
602 data4 0x3FBD08A4,0x3FBF179A,0x3FC12C4D,0x3FC346CD
603 data4 0x3FC5672A,0x3FC78D75,0x3FC9B9BE,0x3FCBEC15
604 data4 0x3FCE248C,0x3FD06334,0x3FD2A81E,0x3FD4F35B
605 data4 0x3FD744FD,0x3FD99D16,0x3FDBFBB8,0x3FDE60F5
606 data4 0x3FE0CCDF,0x3FE33F89,0x3FE5B907,0x3FE8396A
607 data4 0x3FEAC0C7,0x3FED4F30,0x3FEFE4BA,0x3FF28177
608 data4 0x3FF5257D,0x3FF7D0DF,0x3FFA83B3,0x3FFD3E0C
609 LOCAL_OBJECT_END(Constants_exp_64_T1)
611 LOCAL_OBJECT_START(Constants_exp_64_T2)
612 data4 0x3F800000,0x3F80058C,0x3F800B18,0x3F8010A4
613 data4 0x3F801630,0x3F801BBD,0x3F80214A,0x3F8026D7
614 data4 0x3F802C64,0x3F8031F2,0x3F803780,0x3F803D0E
615 data4 0x3F80429C,0x3F80482B,0x3F804DB9,0x3F805349
616 data4 0x3F8058D8,0x3F805E67,0x3F8063F7,0x3F806987
617 data4 0x3F806F17,0x3F8074A8,0x3F807A39,0x3F807FCA
618 data4 0x3F80855B,0x3F808AEC,0x3F80907E,0x3F809610
619 data4 0x3F809BA2,0x3F80A135,0x3F80A6C7,0x3F80AC5A
620 data4 0x3F80B1ED,0x3F80B781,0x3F80BD14,0x3F80C2A8
621 data4 0x3F80C83C,0x3F80CDD1,0x3F80D365,0x3F80D8FA
622 data4 0x3F80DE8F,0x3F80E425,0x3F80E9BA,0x3F80EF50
623 data4 0x3F80F4E6,0x3F80FA7C,0x3F810013,0x3F8105AA
624 data4 0x3F810B41,0x3F8110D8,0x3F81166F,0x3F811C07
625 data4 0x3F81219F,0x3F812737,0x3F812CD0,0x3F813269
626 data4 0x3F813802,0x3F813D9B,0x3F814334,0x3F8148CE
627 data4 0x3F814E68,0x3F815402,0x3F81599C,0x3F815F37
628 LOCAL_OBJECT_END(Constants_exp_64_T2)
630 LOCAL_OBJECT_START(Constants_exp_64_W1)
631 data8 0x0000000000000000, 0xBE384454171EC4B4
632 data8 0xBE6947414AA72766, 0xBE5D32B6D42518F8
633 data8 0x3E68D96D3A319149, 0xBE68F4DA62415F36
634 data8 0xBE6DDA2FC9C86A3B, 0x3E6B2E50F49228FE
635 data8 0xBE49C0C21188B886, 0x3E64BFC21A4C2F1F
636 data8 0xBE6A2FBB2CB98B54, 0x3E5DC5DE9A55D329
637 data8 0x3E69649039A7AACE, 0x3E54728B5C66DBA5
638 data8 0xBE62B0DBBA1C7D7D, 0x3E576E0409F1AF5F
639 data8 0x3E6125001A0DD6A1, 0xBE66A419795FBDEF
640 data8 0xBE5CDE8CE1BD41FC, 0xBE621376EA54964F
641 data8 0x3E6370BE476E76EE, 0x3E390D1A3427EB92
642 data8 0x3E1336DE2BF82BF8, 0xBE5FF1CBD0F7BD9E
643 data8 0xBE60A3550CEB09DD, 0xBE5CA37E0980F30D
644 data8 0xBE5C541B4C082D25, 0xBE5BBECA3B467D29
645 data8 0xBE400D8AB9D946C5, 0xBE5E2A0807ED374A
646 data8 0xBE66CB28365C8B0A, 0x3E3AAD5BD3403BCA
647 data8 0x3E526055C7EA21E0, 0xBE442C75E72880D6
648 data8 0x3E58B2BB85222A43, 0xBE5AAB79522C42BF
649 data8 0xBE605CB4469DC2BC, 0xBE589FA7A48C40DC
650 data8 0xBE51C2141AA42614, 0xBE48D087C37293F4
651 data8 0x3E367A1CA2D673E0, 0xBE51BEBB114F7A38
652 data8 0xBE6348E5661A4B48, 0xBDF526431D3B9962
653 data8 0x3E3A3B5E35A78A53, 0xBE46C46C1CECD788
654 data8 0xBE60B7EC7857D689, 0xBE594D3DD14F1AD7
655 data8 0xBE4F9C304C9A8F60, 0xBE52187302DFF9D2
656 data8 0xBE5E4C8855E6D68F, 0xBE62140F667F3DC4
657 data8 0xBE36961B3BF88747, 0x3E602861C96EC6AA
658 data8 0xBE3B5151D57FD718, 0x3E561CD0FC4A627B
659 data8 0xBE3A5217CA913FEA, 0x3E40A3CC9A5D193A
660 data8 0xBE5AB71310A9C312, 0x3E4FDADBC5F57719
661 data8 0x3E361428DBDF59D5, 0x3E5DB5DB61B4180D
662 data8 0xBE42AD5F7408D856, 0x3E2A314831B2B707
663 LOCAL_OBJECT_END(Constants_exp_64_W1)
665 LOCAL_OBJECT_START(Constants_exp_64_W2)
666 data8 0x0000000000000000, 0xBE641F2537A3D7A2
667 data8 0xBE68DD57AD028C40, 0xBE5C77D8F212B1B6
668 data8 0x3E57878F1BA5B070, 0xBE55A36A2ECAE6FE
669 data8 0xBE620608569DFA3B, 0xBE53B50EA6D300A3
670 data8 0x3E5B5EF2223F8F2C, 0xBE56A0D9D6DE0DF4
671 data8 0xBE64EEF3EAE28F51, 0xBE5E5AE2367EA80B
672 data8 0x3E47CB1A5FCBC02D, 0xBE656BA09BDAFEB7
673 data8 0x3E6E70C6805AFEE7, 0xBE6E0509A3415EBA
674 data8 0xBE56856B49BFF529, 0x3E66DD3300508651
675 data8 0x3E51165FC114BC13, 0x3E53333DC453290F
676 data8 0x3E6A072B05539FDA, 0xBE47CD877C0A7696
677 data8 0xBE668BF4EB05C6D9, 0xBE67C3E36AE86C93
678 data8 0xBE533904D0B3E84B, 0x3E63E8D9556B53CE
679 data8 0x3E212C8963A98DC8, 0xBE33138F032A7A22
680 data8 0x3E530FA9BC584008, 0xBE6ADF82CCB93C97
681 data8 0x3E5F91138370EA39, 0x3E5443A4FB6A05D8
682 data8 0x3E63DACD181FEE7A, 0xBE62B29DF0F67DEC
683 data8 0x3E65C4833DDE6307, 0x3E5BF030D40A24C1
684 data8 0x3E658B8F14E437BE, 0xBE631C29ED98B6C7
685 data8 0x3E6335D204CF7C71, 0x3E529EEDE954A79D
686 data8 0x3E5D9257F64A2FB8, 0xBE6BED1B854ED06C
687 data8 0x3E5096F6D71405CB, 0xBE3D4893ACB9FDF5
688 data8 0xBDFEB15801B68349, 0x3E628D35C6A463B9
689 data8 0xBE559725ADE45917, 0xBE68C29C042FC476
690 data8 0xBE67593B01E511FA, 0xBE4A4313398801ED
691 data8 0x3E699571DA7C3300, 0x3E5349BE08062A9E
692 data8 0x3E5229C4755BB28E, 0x3E67E42677A1F80D
693 data8 0xBE52B33F6B69C352, 0xBE6B3550084DA57F
694 data8 0xBE6DB03FD1D09A20, 0xBE60CBC42161B2C1
695 data8 0x3E56ED9C78A2B771, 0xBE508E319D0FA795
696 data8 0xBE59482AFD1A54E9, 0xBE2A17CEB07FD23E
697 data8 0x3E68BF5C17365712, 0x3E3956F9B3785569
698 LOCAL_OBJECT_END(Constants_exp_64_W2)
701 LOCAL_OBJECT_START(erfc_xc_table)
703 data8 0x0000000000000000, 0x00000000 //XC[0] = +0.00000000000000000000e-01L
704 data8 0x9A79C70000000000, 0x00003FFD //XC[1] = +3.01710337400436401367e-01L
705 data8 0x8C49EF0000000000, 0x00003FFE //XC[2] = +5.48003137111663818359e-01L
706 data8 0xD744FC0000000000, 0x00003FFE //XC[3] = +8.40896368026733398438e-01L
707 data8 0x9837F00000000000, 0x00003FFF //XC[4] = +1.18920707702636718750e+00L
708 data8 0xCD3CE30000000000, 0x00003FFF //XC[5] = +1.60342061519622802734e+00L
709 data8 0x8624F70000000000, 0x00004000 //XC[6] = +2.09600615501403808594e+00L
710 data8 0xABA27E0000000000, 0x00004000 //XC[7] = +2.68179273605346679688e+00L
711 data8 0xD837F00000000000, 0x00004000 //XC[8] = +3.37841415405273437500e+00L
712 data8 0x869E710000000000, 0x00004001 //XC[9] = +4.20684099197387695313e+00L
713 data8 0xA624F70000000000, 0x00004001 //XC[10] = +5.19201231002807617188e+00L
714 data8 0xCBA27E0000000000, 0x00004001 //XC[11] = +6.36358547210693359375e+00L
715 data8 0xF837F00000000000, 0x00004001 //XC[12] = +7.75682830810546875000e+00L
716 data8 0x969E710000000000, 0x00004002 //XC[13] = +9.41368198394775390625e+00L
717 data8 0xB624F70000000000, 0x00004002 //XC[14] = +1.13840246200561523438e+01L
718 data8 0xDBA27E0000000000, 0x00004002 //XC[15] = +1.37271709442138671875e+01L
719 data8 0x841BF80000000000, 0x00004003 //XC[16] = +1.65136566162109375000e+01L
720 data8 0x9E9E710000000000, 0x00004003 //XC[17] = +1.98273639678955078125e+01L
721 data8 0xBE24F70000000000, 0x00004003 //XC[18] = +2.37680492401123046875e+01L
722 data8 0xE3A27E0000000000, 0x00004003 //XC[19] = +2.84543418884277343750e+01L
723 data8 0x881BF80000000000, 0x00004004 //XC[20] = +3.40273132324218750000e+01L
724 data8 0xA29E710000000000, 0x00004004 //XC[21] = +4.06547279357910156250e+01L
725 data8 0xC224F70000000000, 0x00004004 //XC[22] = +4.85360984802246093750e+01L
726 data8 0xE7A27E0000000000, 0x00004004 //XC[23] = +5.79086837768554687500e+01L
727 data8 0x8A1BF80000000000, 0x00004005 //XC[24] = +6.90546264648437500000e+01L
728 data8 0xA49E710000000000, 0x00004005 //XC[25] = +8.23094558715820312500e+01L
729 data8 0xC424F70000000000, 0x00004005 //XC[26] = +9.80721969604492187500e+01L
730 data8 0xD5A27E0000000000, 0x00004005 //XC[27] = +1.06817367553710937500e+02L
731 LOCAL_OBJECT_END(erfc_xc_table)
733 LOCAL_OBJECT_START(erfc_s_table)
735 data8 0xE000000000000000, 0x00003FFE //s[0] = +8.75000000000000000000e-01L
736 data8 0xDCEF000000000000, 0x00003FFE //s[1] = +8.63021850585937500000e-01L
737 data8 0xD79D000000000000, 0x00003FFE //s[2] = +8.42239379882812500000e-01L
738 data8 0xB25E000000000000, 0x00003FFE //s[3] = +6.96746826171875000000e-01L
739 data8 0xB0EA000000000000, 0x00003FFE //s[4] = +6.91070556640625000000e-01L
740 data8 0xAE3F000000000000, 0x00003FFE //s[5] = +6.80648803710937500000e-01L
741 data8 0xAB05000000000000, 0x00003FFE //s[6] = +6.68045043945312500000e-01L
742 data8 0xA7AC000000000000, 0x00003FFE //s[7] = +6.54968261718750000000e-01L
743 data8 0xA478000000000000, 0x00003FFE //s[8] = +6.42456054687500000000e-01L
744 data8 0xA18D000000000000, 0x00003FFE //s[9] = +6.31057739257812500000e-01L
745 data8 0x9EF8000000000000, 0x00003FFE //s[10] = +6.20971679687500000000e-01L
746 data8 0x9CBA000000000000, 0x00003FFE //s[11] = +6.12213134765625000000e-01L
747 data8 0x9ACD000000000000, 0x00003FFE //s[12] = +6.04690551757812500000e-01L
748 data8 0x992A000000000000, 0x00003FFE //s[13] = +5.98297119140625000000e-01L
749 data8 0x97C7000000000000, 0x00003FFE //s[14] = +5.92880249023437500000e-01L
750 data8 0x969C000000000000, 0x00003FFE //s[15] = +5.88317871093750000000e-01L
751 data8 0x95A0000000000000, 0x00003FFE //s[16] = +5.84472656250000000000e-01L
752 data8 0x94CB000000000000, 0x00003FFE //s[17] = +5.81222534179687500000e-01L
753 data8 0x9419000000000000, 0x00003FFE //s[18] = +5.78506469726562500000e-01L
754 data8 0x9383000000000000, 0x00003FFE //s[19] = +5.76217651367187500000e-01L
755 data8 0x9305000000000000, 0x00003FFE //s[20] = +5.74295043945312500000e-01L
756 data8 0x929B000000000000, 0x00003FFE //s[21] = +5.72677612304687500000e-01L
757 data8 0x9242000000000000, 0x00003FFE //s[22] = +5.71319580078125000000e-01L
758 data8 0x91F8000000000000, 0x00003FFE //s[23] = +5.70190429687500000000e-01L
759 data8 0x91B9000000000000, 0x00003FFE //s[24] = +5.69229125976562500000e-01L
760 data8 0x9184000000000000, 0x00003FFE //s[25] = +5.68420410156250000000e-01L
761 data8 0x9158000000000000, 0x00003FFE //s[26] = +5.67749023437500000000e-01L
762 data8 0x9145000000000000, 0x00003FFE //s[27] = +5.67459106445312500000e-01L
763 LOCAL_OBJECT_END(erfc_s_table)
765 LOCAL_OBJECT_START(erfc_Q_table)
766 // Q(z)= (P(z)- S)/S
767 //
768 // Pol0
769 data8 0x98325D50F9DC3499, 0x0000BFAA //A0 = +3.07358861423101280650e-26L
770 data8 0xED35081A2494DDD9, 0x00003FF8 //A1 = +1.44779757616302832466e-02L
771 data8 0x9443549BCD0F94CE, 0x0000BFFD //A2 = -2.89576190966300084405e-01L
772 data8 0xC7FD4B98ECF3DBBF, 0x00003FFD //A3 = +3.90604364793467799170e-01L
773 data8 0xB82CE31288B49759, 0x0000BFFD //A4 = -3.59717460644199233866e-01L
774 data8 0x8A8293447BEF69B5, 0x00003FFD //A5 = +2.70527460203054582368e-01L
775 data8 0xB5793E30EE36766C, 0x0000BFFC //A6 = -1.77220317589265674647e-01L
776 data8 0xD6066D16BBDECE17, 0x00003FFB //A7 = +1.04504444366724593714e-01L
777 data8 0xE7C783CE3C997BD8, 0x0000BFFA //A8 = -5.65867565781331646771e-02L
778 data8 0xE9969EBC2F5B2828, 0x00003FF9 //A9 = +2.85142040533900194955e-02L
779 data8 0xDD31D619F29AD7BF, 0x0000BFF8 //A10 = -1.35006514390540367929e-02L
780 data8 0xC63A20EB59768F3A, 0x00003FF7 //A11 = +6.04940993680332271481e-03L
781 data8 0xA8DEC641AACEB600, 0x0000BFF6 //A12 = -2.57675495383156581601e-03L
782 data8 0x87F0E77BA914FBEB, 0x00003FF5 //A13 = +1.03714776726541296794e-03L
783 data8 0xC306C2894C5CEF2D, 0x0000BFF3 //A14 = -3.71983348634136412407e-04L
784 data8 0xBDAB416A989D0697, 0x00003FF1 //A15 = +9.04412111877987292294e-05L
785 // Pol1
786 data8 0x82808893DA2DD83F, 0x00003FEE //A0 = +7.77853035974467145290e-06L
787 data8 0xAE9CD9DCADC86113, 0x0000BFFB //A1 = -8.52601070853077921197e-02L
788 data8 0x9D429743E312AD9F, 0x0000BFFB //A2 = -7.67871682732076080494e-02L
789 data8 0x8637FC533AE805DC, 0x00003FFC //A3 = +1.31072943286859831330e-01L
790 data8 0xF68DBE3639ABCB6E, 0x0000BFFB //A4 = -1.20387540845703264588e-01L
791 data8 0xB168FFC3CFA71256, 0x00003FFB //A5 = +8.66260511047190247534e-02L
792 data8 0xDBC5078A7EA89236, 0x0000BFFA //A6 = -5.36546988077281230848e-02L
793 data8 0xF4331FEDB2CB838F, 0x00003FF9 //A7 = +2.98095344165515989564e-02L
794 data8 0xF909173C0E61C25D, 0x0000BFF8 //A8 = -1.51999213123642373375e-02L
795 data8 0xEC83560A2ACB23E9, 0x00003FF7 //A9 = +7.21780491979582106904e-03L
796 data8 0xD350D62C4FEAD8F5, 0x0000BFF6 //A10 = -3.22442272982896360044e-03L
797 data8 0xB2F44F4B3FD9B826, 0x00003FF5 //A11 = +1.36531322425499451283e-03L
798 data8 0x9078BC61927671C6, 0x0000BFF4 //A12 = -5.51115510818844954547e-04L
799 data8 0xDF67AC6287A63B03, 0x00003FF2 //A13 = +2.13055585989529858265e-04L
800 data8 0xA719CFEE67FCE1CE, 0x0000BFF1 //A14 = -7.96798844477905965933e-05L
801 data8 0xEF926367BABBB029, 0x00003FEF //A15 = +2.85591875675765038065e-05L
802 // Pol2
803 data8 0x82B5E5A93B059C50, 0x00003FEF //A0 = +1.55819100856330860049e-05L
804 data8 0xDC856BC2542B1938, 0x0000BFFB //A1 = -1.07676355235999875911e-01L
805 data8 0xDF225EF5694F14AE, 0x0000BFF8 //A2 = -1.36190345125628043277e-02L
806 data8 0xDAF66A954ED22428, 0x00003FFA //A3 = +5.34576571853233908886e-02L
807 data8 0xD28AE4F21A392EC6, 0x0000BFFA //A4 = -5.14019911949062230820e-02L
808 data8 0x9441A95713F0DB5B, 0x00003FFA //A5 = +3.61954321717769771045e-02L
809 data8 0xB0957B5C483C7A04, 0x0000BFF9 //A6 = -2.15556535133667988704e-02L
810 data8 0xBB9260E812814F71, 0x00003FF8 //A7 = +1.14484735825400480057e-02L
811 data8 0xB68AB17287ABAB04, 0x0000BFF7 //A8 = -5.57073273108465072470e-03L
812 data8 0xA56A95E0BC0EF01B, 0x00003FF6 //A9 = +2.52405318381952650677e-03L
813 data8 0x8D19C7D286839C00, 0x0000BFF5 //A10 = -1.07651294935087466892e-03L
814 data8 0xE45DB3766711A0D3, 0x00003FF3 //A11 = +4.35573615323234291196e-04L
815 data8 0xB05949F947FA7AEF, 0x0000BFF2 //A12 = -1.68179306983868501372e-04L
816 data8 0x82901D055A0D5CB6, 0x00003FF1 //A13 = +6.22572626227726684168e-05L
817 data8 0xBB957698542D6FD0, 0x0000BFEF //A14 = -2.23617364009159182821e-05L
818 data8 0x810740E1DF572394, 0x00003FEE //A15 = +7.69068800065192940487e-06L
819 // Pol3
820 data8 0x9526D1C87655AFA8, 0x00003FEC //A0 = +2.22253260814242012255e-06L
821 data8 0xA47E21EBFE73F72F, 0x0000BFF8 //A1 = -1.00398379581527733314e-02L
822 data8 0xDE65685FCDF7A913, 0x0000BFFA //A2 = -5.42959286802879105148e-02L
823 data8 0xED289CB8F97D4860, 0x00003FFA //A3 = +5.79000589346770417248e-02L
824 data8 0xAA3100D5A7D870F1, 0x0000BFFA //A4 = -4.15506394006027604387e-02L
825 data8 0xCA0567032C5308C0, 0x00003FF9 //A5 = +2.46607791863290331169e-02L
826 data8 0xD3E1794A50F31BEB, 0x0000BFF8 //A6 = -1.29321751094401754013e-02L
827 data8 0xCAA02CB4C87CC1F0, 0x00003FF7 //A7 = +6.18364508551740736863e-03L
828 data8 0xB3F126AF16B121F2, 0x0000BFF6 //A8 = -2.74569696838501870748e-03L
829 data8 0x962B2D64D3900510, 0x00003FF5 //A9 = +1.14569596409019883022e-03L
830 data8 0xED8785714A9A00FB, 0x0000BFF3 //A10 = -4.53051338046340380512e-04L
831 data8 0xB325DA4515D8B54C, 0x00003FF2 //A11 = +1.70848714622328427290e-04L
832 data8 0x8179C36354571747, 0x0000BFF1 //A12 = -6.17387951061077132522e-05L
833 data8 0xB40F241C01C907E9, 0x00003FEF //A13 = +2.14647227210702861416e-05L
834 data8 0xF436D84AD7D4D316, 0x0000BFED //A14 = -7.27815144835213913238e-06L
835 data8 0x9EB432503FB0B7BC, 0x00003FEC //A15 = +2.36487228755136968792e-06L
836 // Pol4
837 data8 0xE0BA539E4AFC4741, 0x00003FED //A0 = +6.69741148991838024429e-06L
838 data8 0x8583BF71139452CF, 0x0000BFFA //A1 = -3.25963476363756051657e-02L
839 data8 0x8384FEF6D08AD6CE, 0x0000BFF9 //A2 = -1.60546283500634200479e-02L
840 data8 0xB1E67DFB84C97036, 0x00003FF9 //A3 = +2.17163525195697635702e-02L
841 data8 0xFB6ACEE6899E360D, 0x0000BFF8 //A4 = -1.53452892792759316229e-02L
842 data8 0x8D2B869EB9149905, 0x00003FF8 //A5 = +8.61633440480716870830e-03L
843 data8 0x8A90BFE0FD869A41, 0x0000BFF7 //A6 = -4.22868126950622376530e-03L
844 data8 0xF7536A76E59F54D2, 0x00003FF5 //A7 = +1.88694643606912107006e-03L
845 data8 0xCCF6FE58C16E1CC7, 0x0000BFF4 //A8 = -7.81878732767742447339e-04L
846 data8 0x9FCC6ED9914FAA24, 0x00003FF3 //A9 = +3.04791577214885118730e-04L
847 data8 0xEC7F5AAACAE593E8, 0x0000BFF1 //A10 = -1.12770784960291779798e-04L
848 data8 0xA72CE628A114C940, 0x00003FF0 //A11 = +3.98577182157456408782e-05L
849 data8 0xE2DCC5750FD769BA, 0x0000BFEE //A12 = -1.35220520471857266339e-05L
850 data8 0x9459160B1E6F1F8D, 0x00003FED //A13 = +4.42111470121432700283e-06L
851 data8 0xBE0A05701BD0DD42, 0x0000BFEB //A14 = -1.41590196994052764542e-06L
852 data8 0xE905D729105081BF, 0x00003FE9 //A15 = +4.34038814785401120999e-07L
853 // Pol5
854 data8 0xA33649C3AB459832, 0x00003FEE //A0 = +9.72819704141525206634e-06L
855 data8 0x9E4EA2F44C9A24BD, 0x0000BFFA //A1 = -3.86492123987296806210e-02L
856 data8 0xE80C0B1280F357BF, 0x0000BFF2 //A2 = -2.21297306012713370124e-04L
857 data8 0xDAECCE90A4D45D9A, 0x00003FF7 //A3 = +6.68106161291482829670e-03L
858 data8 0xA4006572071BDD4B, 0x0000BFF7 //A4 = -5.00493005170532147076e-03L
859 data8 0xB07FD7EB1F4D8E8E, 0x00003FF6 //A5 = +2.69316693731732554959e-03L
860 data8 0xA1F471D42ADD73A1, 0x0000BFF5 //A6 = -1.23561753760779610478e-03L
861 data8 0x8611D0ED1B4C8176, 0x00003FF4 //A7 = +5.11434914439322741260e-04L
862 data8 0xCDADB789B487A541, 0x0000BFF2 //A8 = -1.96150380913036018825e-04L
863 data8 0x9470252731687FEE, 0x00003FF1 //A9 = +7.07807859951401721129e-05L
864 data8 0xCB9399AD1C376D85, 0x0000BFEF //A10 = -2.42682175234436724152e-05L
865 data8 0x858D815F9CA0A9F7, 0x00003FEE //A11 = +7.96036454038012144300e-06L
866 data8 0xA878D338E6E6A079, 0x0000BFEC //A12 = -2.51042802626063073967e-06L
867 data8 0xCD2C2F079D2FCB36, 0x00003FEA //A13 = +7.64327468786076941271e-07L
868 data8 0xF5EF4A4B2EA426F2, 0x0000BFE8 //A14 = -2.29044563492386125272e-07L
869 data8 0x8CE52181393820FC, 0x00003FE7 //A15 = +6.56093668622712763489e-08L
870 // Pol6
871 data8 0xB2015D7F1864B7CF, 0x00003FEC //A0 = +2.65248615880090351276e-06L
872 data8 0x954EA7A861B4462A, 0x0000BFFA //A1 = -3.64519642954351295215e-02L
873 data8 0x9E46F2A4D9157E69, 0x00003FF7 //A2 = +4.83023498390681965101e-03L
874 data8 0xA0D12B422FFD5BAD, 0x00003FF5 //A3 = +1.22693684633643883352e-03L
875 data8 0xB291D16A560A740E, 0x0000BFF5 //A4 = -1.36237794246703606647e-03L
876 data8 0xC138941BC8AF4A9D, 0x00003FF4 //A5 = +7.37079658343628747256e-04L
877 data8 0xA761669D61B405CF, 0x0000BFF3 //A6 = -3.19252914480518163396e-04L
878 data8 0x8053680F1C84607E, 0x00003FF2 //A7 = +1.22381025852939439541e-04L
879 data8 0xB518F4B6F25015F9, 0x0000BFF0 //A8 = -4.31770048258291369742e-05L
880 data8 0xEFF526AC70B9411E, 0x00003FEE //A9 = +1.43025887824433324525e-05L
881 data8 0x970B2A848DF5B5C2, 0x0000BFED //A10 = -4.50145058393497252604e-06L
882 data8 0xB614D2E61DB86963, 0x00003FEB //A11 = +1.35661172167726780059e-06L
883 data8 0xD34EA4D283EC33FA, 0x0000BFE9 //A12 = -3.93590335713880681528e-07L
884 data8 0xED209EBD68E1145F, 0x00003FE7 //A13 = +1.10421060667544991323e-07L
885 data8 0x83A126E22A17568D, 0x0000BFE6 //A14 = -3.06473811074239684132e-08L
886 data8 0x8B778496EDE9F415, 0x00003FE4 //A15 = +8.11804009754249175736e-09L
887 // Pol7
888 data8 0x8E152F522501B7B9, 0x00003FEE //A0 = +8.46879203970927626532e-06L
889 data8 0xFD22F92EE21F491E, 0x0000BFF9 //A1 = -3.09004656656418947425e-02L
890 data8 0xAF0C41847D89EC14, 0x00003FF7 //A2 = +5.34203719233189217519e-03L
891 data8 0xB7C539C400445956, 0x0000BFF3 //A3 = -3.50514245383356287965e-04L
892 data8 0x8428C78B2B1E3622, 0x0000BFF3 //A4 = -2.52073850239006530978e-04L
893 data8 0xAFC0CCC7D1A05F5B, 0x00003FF2 //A5 = +1.67611241057491801028e-04L
894 data8 0x95DC7272C5695A5A, 0x0000BFF1 //A6 = -7.14593512262564106636e-05L
895 data8 0xD6FCA68A61F0E835, 0x00003FEF //A7 = +2.56284375437771117850e-05L
896 data8 0x8B71C74DEA936C66, 0x0000BFEE //A8 = -8.31153675277218441096e-06L
897 data8 0xA8AC71E2A56AA2C9, 0x00003FEC //A9 = +2.51343269277107451413e-06L
898 data8 0xC15DED6C44B46046, 0x0000BFEA //A10 = -7.20347851650066610771e-07L
899 data8 0xD42BA1DFBD1277AC, 0x00003FE8 //A11 = +1.97599119274780745741e-07L
900 data8 0xE03A81F2C976D11A, 0x0000BFE6 //A12 = -5.22072765405802337371e-08L
901 data8 0xE56A19A67DD66100, 0x00003FE4 //A13 = +1.33536787408751203998e-08L
902 data8 0xE964D255CB31DFFA, 0x0000BFE2 //A14 = -3.39632729387679010008e-09L
903 data8 0xE22E62E932B704D4, 0x00003FE0 //A15 = +8.22842400379225526299e-10L
904 // Pol8
905 data8 0xB8B835882D46A6C8, 0x00003FEF //A0 = +2.20202883282415435401e-05L
906 data8 0xC9D1F63F89B74E90, 0x0000BFF9 //A1 = -2.46362504515706189782e-02L
907 data8 0x8E376748B1274F30, 0x00003FF7 //A2 = +4.34010070001387441657e-03L
908 data8 0x98174C7EA49B5B37, 0x0000BFF4 //A3 = -5.80181163659971286762e-04L
909 data8 0x8D2C40506AE9FF97, 0x00003FEF //A4 = +1.68291159100251734927e-05L
910 data8 0xD9A580C115B9D150, 0x00003FEF //A5 = +2.59454841475194555896e-05L
911 data8 0xDB35B21F1C3F99CE, 0x0000BFEE //A6 = -1.30659192305072674545e-05L
912 data8 0x99FAADAE17A3050E, 0x00003FED //A7 = +4.58893813631592314881e-06L
913 data8 0xBA1D259BCD6987A9, 0x0000BFEB //A8 = -1.38665627771423394637e-06L
914 data8 0xCDD7FF5BEA0145C2, 0x00003FE9 //A9 = +3.83413844219813384124e-07L
915 data8 0xD60857176CE6AB9D, 0x0000BFE7 //A10 = -9.96666862214499946343e-08L
916 data8 0xD446A2402112DF4C, 0x00003FE5 //A11 = +2.47121687566658908126e-08L
917 data8 0xCA87133235F1F495, 0x0000BFE3 //A12 = -5.89433000014933371980e-09L
918 data8 0xBB15B0021581C8B6, 0x00003FE1 //A13 = +1.36122047057936849125e-09L
919 data8 0xAC9D6585D4AF505E, 0x0000BFDF //A14 = -3.13984547328132268695e-10L
920 data8 0x975A1439C3795183, 0x00003FDD //A15 = +6.88268624429648826457e-11L
921 // Pol9
922 data8 0x99A7676284CDC9FE, 0x00003FEF //A0 = +1.83169747921764176475e-05L
923 data8 0x9AD0AE249A02896C, 0x0000BFF9 //A1 = -1.88983346204739151909e-02L
924 data8 0xCB89B4AEC19898BE, 0x00003FF6 //A2 = +3.10574208447745576452e-03L
925 data8 0xEBBC47E30E1AC2C2, 0x0000BFF3 //A3 = -4.49629730048297442064e-04L
926 data8 0xD1E35B7FCE1CF859, 0x00003FF0 //A4 = +5.00412261289558493438e-05L
927 data8 0xB40743664EF24552, 0x0000BFEB //A5 = -1.34131589671166307319e-06L
928 data8 0xCAD2F5C596FFE1B4, 0x0000BFEB //A6 = -1.51115702599728593837e-06L
929 data8 0xAE42B6D069DFDDF2, 0x00003FEA //A7 = +6.49171330116787223873e-07L
930 data8 0xD0739A05BB43A714, 0x0000BFE8 //A8 = -1.94135651872623440782e-07L
931 data8 0xD745B854AB601BD7, 0x00003FE6 //A9 = +5.01219983943456578062e-08L
932 data8 0xCC4066E13E338B13, 0x0000BFE4 //A10 = -1.18890061172430768892e-08L
933 data8 0xB6EAADB55A6C3CB4, 0x00003FE2 //A11 = +2.66178850259168707794e-09L
934 data8 0x9CC6C178AD3F96AD, 0x0000BFE0 //A12 = -5.70349182959704086428e-10L
935 data8 0x81D0E2AA27DEB74A, 0x00003FDE //A13 = +1.18066926578104076645e-10L
936 data8 0xD75FB9049190BEFD, 0x0000BFDB //A14 = -2.44851795398843967972e-11L
937 data8 0xA9384A51D48C8703, 0x00003FD9 //A15 = +4.80951837368635202609e-12L
938 // Pol10
939 data8 0xD2B3482EE449C535, 0x00003FEE //A0 = +1.25587177382575655080e-05L
940 data8 0xE7939B2D0607DFCF, 0x0000BFF8 //A1 = -1.41343131436717436429e-02L
941 data8 0x8810EB4AC5F0F1CE, 0x00003FF6 //A2 = +2.07620377002350121270e-03L
942 data8 0x9546589602AEB955, 0x0000BFF3 //A3 = -2.84719065122144294949e-04L
943 data8 0x9333434342229798, 0x00003FF0 //A4 = +3.50952732796136549298e-05L
944 data8 0xEB36A98FD81D3DEB, 0x0000BFEC //A5 = -3.50495464815398722482e-06L
945 data8 0xAC370EFA025D0477, 0x00003FE8 //A6 = +1.60387784498518639254e-07L
946 data8 0xC8DF7F8ACA099426, 0x00003FE6 //A7 = +4.67693991699936842330e-08L
947 data8 0xAC694AD4921C02CF, 0x0000BFE5 //A8 = -2.00713167514877937714e-08L
948 data8 0xB6E29F2FDE2D8C1A, 0x00003FE3 //A9 = +5.32266106167252495164e-09L
949 data8 0xA41F8EEA75474358, 0x0000BFE1 //A10 = -1.19415398856537468324e-09L
950 data8 0x869D778A1C56D3D6, 0x00003FDF //A11 = +2.44863450057778470469e-10L
951 data8 0xD02658BF31411F4C, 0x0000BFDC //A12 = -4.73277831746128372261e-11L
952 data8 0x9A4A95EE59127779, 0x00003FDA //A13 = +8.77044784978207256260e-12L
953 data8 0xE518330AF013C2F6, 0x0000BFD7 //A14 = -1.62781453276882333209e-12L
954 data8 0xA036A9DF71BD108A, 0x00003FD5 //A15 = +2.84596398987114375607e-13L
955 // Pol11
956 data8 0x9191CFBF001F3BB3, 0x00003FEE //A0 = +8.67662287973472452343e-06L
957 data8 0xAA47E0CF01AE9730, 0x0000BFF8 //A1 = -1.03931136509584404513e-02L
958 data8 0xAEABE7F17B01D18F, 0x00003FF5 //A2 = +1.33263784731775399430e-03L
959 data8 0xAC0D6A309D04E5DB, 0x0000BFF2 //A3 = -1.64081956462118568288e-04L
960 data8 0xA08357DF458054D0, 0x00003FEF //A4 = +1.91346477952797715021e-05L
961 data8 0x8A1596B557440FE0, 0x0000BFEC //A5 = -2.05761687274453412571e-06L
962 data8 0xCDA0EAE0A5615E9A, 0x00003FE8 //A6 = +1.91506542215670149741e-07L
963 data8 0xD36A08FB4E104F9A, 0x0000BFE4 //A7 = -1.23059260396551086769e-08L
964 data8 0xD7433F91E78A7A11, 0x0000BFDF //A8 = -3.91560549815575091188e-10L
965 data8 0xC2F5308FD4F5CE62, 0x00003FDF //A9 = +3.54626121852421163117e-10L
966 data8 0xC83876915F49D630, 0x0000BFDD //A10 = -9.10497688901018285126e-11L
967 data8 0xA11C605DEAE1FE9C, 0x00003FDB //A11 = +1.83161825409194847892e-11L
968 data8 0xE7977BC1342D19BF, 0x0000BFD8 //A12 = -3.29111645807102123274e-12L
969 data8 0x9BC3A7D6396C6756, 0x00003FD6 //A13 = +5.53385887288503961220e-13L
970 data8 0xD0110D5683740B8C, 0x0000BFD3 //A14 = -9.24001363293241428519e-14L
971 data8 0x81786D7856A5CC92, 0x00003FD1 //A15 = +1.43741041714595023996e-14L
972 // Pol12
973 data8 0xB85654F6033B3372, 0x00003FEF //A0 = +2.19747106911869287049e-05L
974 data8 0xF78B40078736B406, 0x0000BFF7 //A1 = -7.55444170413862312647e-03L
975 data8 0xDA8FDE84D88E5D5D, 0x00003FF4 //A2 = +8.33747822263358628569e-04L
976 data8 0xBC2D3F3891721AA9, 0x0000BFF1 //A3 = -8.97296647669960333635e-05L
977 data8 0x9D15ACFD3BF50064, 0x00003FEE //A4 = +9.36297600601039610762e-06L
978 data8 0xFBED3D03F3C1B671, 0x0000BFEA //A5 = -9.38500137149172923985e-07L
979 data8 0xBEE615E3B2FA16C8, 0x00003FE7 //A6 = +8.88941676851808958175e-08L
980 data8 0x843D32692CF5662A, 0x0000BFE4 //A7 = -7.69732580860195238520e-09L
981 data8 0x99E74472FD94E22B, 0x00003FE0 //A8 = +5.59897264617128952416e-10L
982 data8 0xCEF63DABF4C32E15, 0x0000BFDB //A9 = -2.35288414996279313219e-11L
983 data8 0xA2D86C25C0991123, 0x0000BFD8 //A10 = -2.31417232327307408235e-12L
984 data8 0xF50C1B31D2E922BD, 0x00003FD6 //A11 = +8.70582858983364191159e-13L
985 data8 0xC0F093DEC2B019A1, 0x0000BFD4 //A12 = -1.71364927865227509533e-13L
986 data8 0xFC1441C4CD105981, 0x00003FD1 //A13 = +2.79864052545369490865e-14L
987 data8 0x9CC959853267F026, 0x0000BFCF //A14 = -4.35170017302700609509e-15L
988 data8 0xB06BA14016154F1E, 0x00003FCC //A15 = +6.12081320471295704631e-16L
989 // Pol13
990 data8 0xA59E74BF544F2422, 0x00003FEF //A0 = +1.97433196215210145261e-05L
991 data8 0xB2814F4EDAE15330, 0x0000BFF7 //A1 = -5.44754383528015875700e-03L
992 data8 0x867C249D378F0A23, 0x00003FF4 //A2 = +5.13019308804593120161e-04L
993 data8 0xC76644393388AB68, 0x0000BFF0 //A3 = -4.75405403392600215101e-05L
994 data8 0x91143AD5CCA229FE, 0x00003FED //A4 = +4.32369180778264703719e-06L
995 data8 0xCE6A11FB6840A974, 0x0000BFE9 //A5 = -3.84476663329551178495e-07L
996 data8 0x8EC29F66C59DE243, 0x00003FE6 //A6 = +3.32389596787155456596e-08L
997 data8 0xBE3FCDDCA94CA24E, 0x0000BFE2 //A7 = -2.76849073931513325199e-09L
998 data8 0xF06A84BDC70A0B0D, 0x00003FDE //A8 = +2.18657158231304988330e-10L
999 data8 0x8B8E6969D056D124, 0x0000BFDB //A9 = -1.58657139740906811035e-11L
1000 data8 0x8984985AA29A0567, 0x00003FD7 //A10 = +9.77123802231106533829e-13L
1001 data8 0xA53ABA084300137C, 0x0000BFD2 //A11 = -3.66882970952892030306e-14L
1002 data8 0xA90EC851E91C3319, 0x0000BFCE //A12 = -2.34614750044359490986e-15L
1003 data8 0xEC9CAF64237B5060, 0x00003FCC //A13 = +8.20912960028437475035e-16L
1004 data8 0xA9156668FCF01479, 0x0000BFCA //A14 = -1.46656639874123613261e-16L
1005 data8 0xBAEF58D8118DD5D4, 0x00003FC7 //A15 = +2.02675278255254907493e-17L
1006 // Pol14
1007 data8 0xC698952E9CEAA800, 0x00003FEF //A0 = +2.36744912073515619263e-05L
1008 data8 0x800395F8C7B4FA00, 0x0000BFF7 //A1 = -3.90667746392883642897e-03L
1009 data8 0xA3B2467B6B391831, 0x00003FF3 //A2 = +3.12226081793919541155e-04L
1010 data8 0xCF2061122A69D72B, 0x0000BFEF //A3 = -2.46914006692526122176e-05L
1011 data8 0x817FAB6B5DEB9924, 0x00003FEC //A4 = +1.92968114320180123521e-06L
1012 data8 0x9FC190F5827740E7, 0x0000BFE8 //A5 = -1.48784479265231093475e-07L
1013 data8 0xC1FE5C1835C8AFCD, 0x00003FE4 //A6 = +1.12919132662720380018e-08L
1014 data8 0xE7216A9FBB204DA3, 0x0000BFE0 //A7 = -8.40847981461949000003e-10L
1015 data8 0x867566ED95C5C64F, 0x00003FDD //A8 = +6.11446929759298780795e-11L
1016 data8 0x97A8BFA723F0F014, 0x0000BFD9 //A9 = -4.31041298699752869577e-12L
1017 data8 0xA3D24B7034984522, 0x00003FD5 //A10 = +2.91005377301348717042e-13L
1018 data8 0xA5AAA371C22F3741, 0x0000BFD1 //A11 = -1.83926825395757259128e-14L
1019 data8 0x95352E5597EACC23, 0x00003FCD //A12 = +1.03533666540077850452e-15L
1020 data8 0xCCEBE3043B689428, 0x0000BFC8 //A13 = -4.44352525147076912166e-17L
1021 data8 0xA779DAB4BE1F80BB, 0x0000BFBC //A14 = -8.86610526981738255206e-21L
1022 data8 0xB171271F3517282C, 0x00003FC1 //A15 = +3.00598445879282370850e-19L
1023 // Pol15
1024 data8 0xB7AC727D1C3FEB05, 0x00003FEE //A0 = +1.09478009914822049780e-05L
1025 data8 0xB6E6274485C10B0A, 0x0000BFF6 //A1 = -2.79081782038927199588e-03L
1026 data8 0xC5CAE2122D009506, 0x00003FF2 //A2 = +1.88629638738336219173e-04L
1027 data8 0xD466E7957D0A3362, 0x0000BFEE //A3 = -1.26601440424012313479e-05L
1028 data8 0xE2593D798DA20E2E, 0x00003FEA //A4 = +8.43214222346512003230e-07L
1029 data8 0xEF2D2BBA7D2882CC, 0x0000BFE6 //A5 = -5.56876064495961858535e-08L
1030 data8 0xFA5819BB4AE974C2, 0x00003FE2 //A6 = +3.64298674151704370449e-09L
1031 data8 0x819BB0CE825FBB28, 0x0000BFDF //A7 = -2.35755881668932259913e-10L
1032 data8 0x84871099BF728B8F, 0x00003FDB //A8 = +1.50666434199945890414e-11L
1033 data8 0x858188962DFEBC9F, 0x0000BFD7 //A9 = -9.48617116568458677088e-13L
1034 data8 0x840F38FF2FBAE753, 0x00003FD3 //A10 = +5.86461827778372616657e-14L
1035 data8 0xFF47EAF69577B213, 0x0000BFCE //A11 = -3.54273456410181081472e-15L
1036 data8 0xEF402CCB4D29FAF8, 0x00003FCA //A12 = +2.07516888659313950588e-16L
1037 data8 0xD6B789E01141231B, 0x0000BFC6 //A13 = -1.16398290506765191078e-17L
1038 data8 0xB5EEE343E9CFE3EC, 0x00003FC2 //A14 = +6.16413506924643419723e-19L
1039 data8 0x859B41A39D600346, 0x0000BFBE //A15 = -2.82922705825870414438e-20L
1040 // Pol16
1041 data8 0x85708B69FD184E11, 0x00003FED //A0 = +3.97681079176353356199e-06L
1042 data8 0x824D92BC60A1F70A, 0x0000BFF6 //A1 = -1.98826630037499070532e-03L
1043 data8 0xEDCF7D3576BB5258, 0x00003FF1 //A2 = +1.13396885054265675352e-04L
1044 data8 0xD7FC59226A947CDF, 0x0000BFED //A3 = -6.43687650810478871875e-06L
1045 data8 0xC32C51B574E2651E, 0x00003FE9 //A4 = +3.63538268539251809118e-07L
1046 data8 0xAF67910F5681401F, 0x0000BFE5 //A5 = -2.04197779750247395258e-08L
1047 data8 0x9CB3E8D7DCD1EA9D, 0x00003FE1 //A6 = +1.14016272459029850306e-09L
1048 data8 0x8B14ECFBF7D4F114, 0x0000BFDD //A7 = -6.32470533185766848692e-11L
1049 data8 0xF518253AE4A3AE72, 0x00003FD8 //A8 = +3.48299974583453268369e-12L
1050 data8 0xD631A5699AA2F334, 0x0000BFD4 //A9 = -1.90242426474085078079e-13L
1051 data8 0xB971AD4C30C56E5D, 0x00003FD0 //A10 = +1.02942127356740047925e-14L
1052 data8 0x9ED0065A601F3160, 0x0000BFCC //A11 = -5.50991880383698965959e-16L
1053 data8 0x863A04008E12867C, 0x00003FC8 //A12 = +2.91057593756148904838e-17L
1054 data8 0xDF62F9F44F5C7170, 0x0000BFC3 //A13 = -1.51372666097522872780e-18L
1055 data8 0xBA4E118E88CFDD31, 0x00003FBF //A14 = +7.89032177282079635722e-20L
1056 data8 0x942AD897FC4D2F2A, 0x0000BFBB //A15 = -3.92195756076319409245e-21L
1057 // Pol17
1058 data8 0xCB8514540566C717, 0x00003FEF //A0 = +2.42614557068144130848e-05L
1059 data8 0xB94F08D6816E0CD4, 0x0000BFF5 //A1 = -1.41379340061829929314e-03L
1060 data8 0x8E7C342C2DABB51B, 0x00003FF1 //A2 = +6.79422240687700109911e-05L
1061 data8 0xDA69DAFF71E30D5B, 0x0000BFEC //A3 = -3.25461473899657142468e-06L
1062 data8 0xA6D5B2DB69B4B3F6, 0x00003FE8 //A4 = +1.55376978584082701045e-07L
1063 data8 0xFDF4F76BC1D1BD47, 0x0000BFE3 //A5 = -7.39111857092131684572e-09L
1064 data8 0xC08BC52C95B12C2D, 0x00003FDF //A6 = +3.50239092565793882444e-10L
1065 data8 0x91624BF6D3A3F6C9, 0x0000BFDB //A7 = -1.65282439890232458821e-11L
1066 data8 0xDA91F7A450DE4270, 0x00003FD6 //A8 = +7.76517285902715940501e-13L
1067 data8 0xA380ADF55416E624, 0x0000BFD2 //A9 = -3.63048822989374426852e-14L
1068 data8 0xF350FC0CEDEE0FD6, 0x00003FCD //A10 = +1.68834630987974622269e-15L
1069 data8 0xB3FA19FBDC8F023C, 0x0000BFC9 //A11 = -7.80525639701804380489e-17L
1070 data8 0x8435328C80940126, 0x00003FC5 //A12 = +3.58349966898667910204e-18L
1071 data8 0xC0D22F655BA5EF39, 0x0000BFC0 //A13 = -1.63325770165403860181e-19L
1072 data8 0x8F14B9EBD5A9AB25, 0x00003FBC //A14 = +7.57464305512080733773e-21L
1073 data8 0xCD4804BBF6DC1B6F, 0x0000BFB7 //A15 = -3.39609459750208886298e-22L
1074 // Pol18
1075 data8 0xE251DFE45AB0C22E, 0x00003FEE //A0 = +1.34897126299700418200e-05L
1076 data8 0x83943CC7D59D4215, 0x0000BFF5 //A1 = -1.00386850310061655307e-03L
1077 data8 0xAA57896951134BCA, 0x00003FF0 //A2 = +4.06126834109940757047e-05L
1078 data8 0xDC0A67051E1C4A2C, 0x0000BFEB //A3 = -1.63943048164477430317e-06L
1079 data8 0x8DCB3C0A8CD07BBE, 0x00003FE7 //A4 = +6.60279229777753829876e-08L
1080 data8 0xB64DE81C24F7F265, 0x0000BFE2 //A5 = -2.65287705357477481067e-09L
1081 data8 0xE9CBB7A990DBA8B5, 0x00003FDD //A6 = +1.06318007608620426224e-10L
1082 data8 0x9583D4B85C2ADC6F, 0x0000BFD9 //A7 = -4.24947087941505088222e-12L
1083 data8 0xBEB0EE8114EEDF77, 0x00003FD4 //A8 = +1.69367754741562774916e-13L
1084 data8 0xF2791BB8F06BDA93, 0x0000BFCF //A9 = -6.72997988617021128704e-15L
1085 data8 0x99A907F6A92195B4, 0x00003FCB //A10 = +2.66558091161711891239e-16L
1086 data8 0xC213E5E6F833BB93, 0x0000BFC6 //A11 = -1.05209746502719578617e-17L
1087 data8 0xF41FBBA6B343960F, 0x00003FC1 //A12 = +4.13562069721140021224e-19L
1088 data8 0x98F194AEE31D188D, 0x0000BFBD //A13 = -1.61935414722333263347e-20L
1089 data8 0xC42F5029BB622157, 0x00003FB8 //A14 = +6.49121108201931196678e-22L
1090 data8 0xF43BD08079E50E0F, 0x0000BFB3 //A15 = -2.52531675510242468317e-23L
1091 // Pol19
1092 data8 0x82557B149A04D08E, 0x00003FEF //A0 = +1.55370127331027842820e-05L
1093 data8 0xBAAB433307CE614B, 0x0000BFF4 //A1 = -7.12085701486669872724e-04L
1094 data8 0xCB52D9DBAC16FE82, 0x00003FEF //A2 = +2.42380662859334411743e-05L
1095 data8 0xDD214359DBBCE7D1, 0x0000BFEA //A3 = -8.23773197624244883859e-07L
1096 data8 0xF01E8E968139524C, 0x00003FE5 //A4 = +2.79535729459988509676e-08L
1097 data8 0x82286A057E0916CE, 0x0000BFE1 //A5 = -9.47023128967039348510e-10L
1098 data8 0x8CDDDC4E8D013365, 0x00003FDC //A6 = +3.20293663356974901319e-11L
1099 data8 0x982FEEE90D4E8751, 0x0000BFD7 //A7 = -1.08135537312234452657e-12L
1100 data8 0xA41D1E84083B8FD6, 0x00003FD2 //A8 = +3.64405720894915411836e-14L
1101 data8 0xB0A1B6111B72E159, 0x0000BFCD //A9 = -1.22562851790685744085e-15L
1102 data8 0xBDB77DE6B650FFA2, 0x00003FC8 //A10 = +4.11382657214908334175e-17L
1103 data8 0xCB54E95CDB66978A, 0x0000BFC3 //A11 = -1.37782909696752432371e-18L
1104 data8 0xD959E428A62B1B6C, 0x00003FBE //A12 = +4.60258936838597812582e-20L
1105 data8 0xE7D49EC23F1A16A0, 0x0000BFB9 //A13 = -1.53412587409583783059e-21L
1106 data8 0xFDE429BC9947B2BE, 0x00003FB4 //A14 = +5.25034823750902928092e-23L
1107 data8 0x872137A062C042EF, 0x0000BFB0 //A15 = -1.74651114923000080365e-24L
1108 // Pol20
1109 data8 0x8B9B185C6A2659AC, 0x00003FEF //A0 = +1.66423130594825442963e-05L
1110 data8 0x84503AD52588A1E8, 0x0000BFF4 //A1 = -5.04735556466270303549e-04L
1111 data8 0xF26C7C2B566388E1, 0x00003FEE //A2 = +1.44495826764677427386e-05L
1112 data8 0xDDDA15FEE262BB47, 0x0000BFE9 //A3 = -4.13231361893675488873e-07L
1113 data8 0xCACEBC73C90C2FE0, 0x00003FE4 //A4 = +1.18049538609157282958e-08L
1114 data8 0xB9314D00022B41DD, 0x0000BFDF //A5 = -3.36863342776746896664e-10L
1115 data8 0xA8E9FBDC714638B9, 0x00003FDA //A6 = +9.60164921624768038366e-12L
1116 data8 0x99E246C0CC8CA6F6, 0x0000BFD5 //A7 = -2.73352704217713596798e-13L
1117 data8 0x8C04E7B5DF372EA1, 0x00003FD0 //A8 = +7.77262480048865685174e-15L
1118 data8 0xFE7B90CAA0B6D5F7, 0x0000BFCA //A9 = -2.20728537958846147109e-16L
1119 data8 0xE6F40BAD4EC6CB4F, 0x00003FC5 //A10 = +6.26000182616999972048e-18L
1120 data8 0xD14F4E0538F0F992, 0x0000BFC0 //A11 = -1.77292283439752259258e-19L
1121 data8 0xBD5A7FAA548CC749, 0x00003FBB //A12 = +5.01214569023722089225e-21L
1122 data8 0xAB15D69425373A67, 0x0000BFB6 //A13 = -1.41518447770061562822e-22L
1123 data8 0x9EF95456F75B4DF4, 0x00003FB1 //A14 = +4.10938011540250142351e-24L
1124 data8 0x8FADCC45E81433E7, 0x0000BFAC //A15 = -1.16062889679749879834e-25L
1125 // Pol21
1126 data8 0xB47A917B0F7B50AE, 0x00003FEF //A0 = +2.15147474240529518138e-05L
1127 data8 0xBB77DC3BA0C937B3, 0x0000BFF3 //A1 = -3.57567223048598672970e-04L
1128 data8 0x90694DFF4EBF7370, 0x00003FEE //A2 = +8.60758700336677694536e-06L
1129 data8 0xDE5379AA90A98F3F, 0x0000BFE8 //A3 = -2.07057292787309736495e-07L
1130 data8 0xAB0322293F1F9CA0, 0x00003FE3 //A4 = +4.97711123919916694625e-09L
1131 data8 0x837119E59D3B7AC2, 0x0000BFDE //A5 = -1.19545621970063369582e-10L
1132 data8 0xC9E5B74A38ECF3FC, 0x00003FD8 //A6 = +2.86913359605586285967e-12L
1133 data8 0x9AEF5110C6885352, 0x0000BFD3 //A7 = -6.88048865490621757799e-14L
1134 data8 0xED988D52189CE6A3, 0x00003FCD //A8 = +1.64865278639132278935e-15L
1135 data8 0xB6063CECD8012B6D, 0x0000BFC8 //A9 = -3.94702428606368525374e-17L
1136 data8 0x8B541EB15E79CEEC, 0x00003FC3 //A10 = +9.44127272399408815784e-19L
1137 data8 0xD51A136D8C75BC25, 0x0000BFBD //A11 = -2.25630369561137931232e-20L
1138 data8 0xA2C1C5E19CC79E6F, 0x00003FB8 //A12 = +5.38517493921589837361e-22L
1139 data8 0xF86F9772306F56C1, 0x0000BFB2 //A13 = -1.28438352359240135735e-23L
1140 data8 0xC32F6FEEDE86528E, 0x00003FAD //A14 = +3.15338862172962186458e-25L
1141 data8 0x9534ED189744D7D4, 0x0000BFA8 //A15 = -7.53301543611470014315e-27L
1142 // Pol22
1143 data8 0xCBA0A2DB94A2C494, 0x00003FEF //A0 = +2.42742878212752702946e-05L
1144 data8 0x84C089154A49E0E8, 0x0000BFF3 //A1 = -2.53204520651046300034e-04L
1145 data8 0xABF5665BD0D8B0CD, 0x00003FED //A2 = +5.12476542947092361490e-06L
1146 data8 0xDEA1C518E3EEE872, 0x0000BFE7 //A3 = -1.03671063536324831083e-07L
1147 data8 0x900B77F271559AE8, 0x00003FE2 //A4 = +2.09612770408581408652e-09L
1148 data8 0xBA4C74A262BE3E4E, 0x0000BFDC //A5 = -4.23594098489216166935e-11L
1149 data8 0xF0D1680FCC1EAF97, 0x00003FD6 //A6 = +8.55557381760467917779e-13L
1150 data8 0x9B8F8E033BB83A24, 0x0000BFD1 //A7 = -1.72707138247091685914e-14L
1151 data8 0xC8DCA6A691DB8335, 0x00003FCB //A8 = +3.48439884388851942939e-16L
1152 data8 0x819A6CB9CEA5E9BD, 0x0000BFC6 //A9 = -7.02580471688245511753e-18L
1153 data8 0xA726B4F622585BEA, 0x00003FC0 //A10 = +1.41582572516648501043e-19L
1154 data8 0xD7727648A4095986, 0x0000BFBA //A11 = -2.85141885626054217632e-21L
1155 data8 0x8AB627E09CF45997, 0x00003FB5 //A12 = +5.73697507862703019314e-23L
1156 data8 0xB28C15C117CC604F, 0x0000BFAF //A13 = -1.15383428132352407085e-24L
1157 data8 0xECB8428626DA072C, 0x00003FA9 //A14 = +2.39025879246942839796e-26L
1158 data8 0x98B731BCFA2CE2B2, 0x0000BFA4 //A15 = -4.81885474332093262902e-28L
1159 // Pol23
1160 data8 0xC6D013811314D31B, 0x00003FED //A0 = +5.92508308918577687876e-06L
1161 data8 0xBBF3057B8DBACBCF, 0x0000BFF2 //A1 = -1.79242422493281965934e-04L
1162 data8 0xCCADECA501162313, 0x00003FEC //A2 = +3.04996061562356504918e-06L
1163 data8 0xDED1FDBE8CCAF3DB, 0x0000BFE6 //A3 = -5.18793887648024117154e-08L
1164 data8 0xF27B74EDDCA65859, 0x00003FE0 //A4 = +8.82145297317787820675e-10L
1165 data8 0x83E4415687F01A0C, 0x0000BFDB //A5 = -1.49943414247603665601e-11L
1166 data8 0x8F6CB350861CE446, 0x00003FD5 //A6 = +2.54773288906376920377e-13L
1167 data8 0x9BE8456A30CBFC02, 0x0000BFCF //A7 = -4.32729710913845745148e-15L
1168 data8 0xA9694F7E1033977D, 0x00003FC9 //A8 = +7.34704698157502347441e-17L
1169 data8 0xB8035A3D5AF82D85, 0x0000BFC3 //A9 = -1.24692123826025468001e-18L
1170 data8 0xC7CB4B3ACB905FDA, 0x00003FBD //A10 = +2.11540249352095943317e-20L
1171 data8 0xD8D70AEB2E58D729, 0x0000BFB7 //A11 = -3.58731705184186608576e-22L
1172 data8 0xEB27A61B1D5C7697, 0x00003FB1 //A12 = +6.07861113430709162243e-24L
1173 data8 0xFEF9ED74D4F4C9B0, 0x0000BFAB //A13 = -1.02984099170876754831e-25L
1174 data8 0x8E6F410068C12043, 0x00003FA6 //A14 = +1.79777721804459361762e-27L
1175 data8 0x9AE2F6705481630E, 0x0000BFA0 //A15 = -3.05459905177379058768e-29L
1176 // Pol24
1177 data8 0xD2D858D5B01C9434, 0x00003FEE //A0 = +1.25673476165670766128e-05L
1178 data8 0x8505330F8B4FDE49, 0x0000BFF2 //A1 = -1.26858053564784963985e-04L
1179 data8 0xF39171C8B1D418C2, 0x00003FEB //A2 = +1.81472407620770441249e-06L
1180 data8 0xDEF065C3D7BFD26E, 0x0000BFE5 //A3 = -2.59535215807652675043e-08L
1181 data8 0xCC0199EA6ACA630C, 0x00003FDF //A4 = +3.71085215769339916703e-10L
1182 data8 0xBAA25319F01ED248, 0x0000BFD9 //A5 = -5.30445960650683029105e-12L
1183 data8 0xAAB28A84F8CFE4D1, 0x00003FD3 //A6 = +7.58048850973457592162e-14L
1184 data8 0x9C14B931AEB311A8, 0x0000BFCD //A7 = -1.08302915828084288776e-15L
1185 data8 0x8EADA745715A0714, 0x00003FC7 //A8 = +1.54692159263197000533e-17L
1186 data8 0x82643F3F722CE6B5, 0x0000BFC1 //A9 = -2.20891945694400066611e-19L
1187 data8 0xEE42ECDE465A99E4, 0x00003FBA //A10 = +3.15336372779307614198e-21L
1188 data8 0xD99FC74326ACBFC0, 0x0000BFB4 //A11 = -4.50036161691276556269e-23L
1189 data8 0xC6A4DCACC554911E, 0x00003FAE //A12 = +6.41853356148678957077e-25L
1190 data8 0xB550CEA09DA96F44, 0x0000BFA8 //A13 = -9.15410112414783078242e-27L
1191 data8 0xAA9149317996F32F, 0x00003FA2 //A14 = +1.34554050666508391264e-28L
1192 data8 0x9C3008EFE3F52F19, 0x0000BF9C //A15 = -1.92516125328592532359e-30L
1193 // Pol25
1194 data8 0xA68E78218806283F, 0x00003FEF //A0 = +1.98550844852103406280e-05L
1195 data8 0xBC41423996DC8A37, 0x0000BFF1 //A1 = -8.97669395268764751516e-05L
1196 data8 0x90E55AE31A2F8271, 0x00003FEB //A2 = +1.07955871580069359702e-06L
1197 data8 0xDF022272DA4A3BEF, 0x0000BFE4 //A3 = -1.29807937275957214439e-08L
1198 data8 0xAB95DCBFFB0BAAB8, 0x00003FDE //A4 = +1.56056011861921437794e-10L
1199 data8 0x83FF2547BA9011FF, 0x0000BFD8 //A5 = -1.87578539510813332135e-12L
1200 data8 0xCB0C353560EEDC45, 0x00003FD1 //A6 = +2.25428217090412574481e-14L
1201 data8 0x9C24CEB86E76D2C5, 0x0000BFCB //A7 = -2.70866279585559299821e-16L
1202 data8 0xF01AFA23DDFDAE0E, 0x00003FC4 //A8 = +3.25403467375734083376e-18L
1203 data8 0xB892BDFBCF1D9740, 0x0000BFBE //A9 = -3.90848978133441513662e-20L
1204 data8 0x8DDBBF34415AAECA, 0x00003FB8 //A10 = +4.69370027479731756829e-22L
1205 data8 0xDA04170D07458C3B, 0x0000BFB1 //A11 = -5.63558091177482043435e-24L
1206 data8 0xA76F391095A9563A, 0x00003FAB //A12 = +6.76262416498584003290e-26L
1207 data8 0x8098FA125C18D8DB, 0x0000BFA5 //A13 = -8.11564737276592661642e-28L
1208 data8 0xCB9E4D5C08923227, 0x00003F9E //A14 = +1.00391606269366059664e-29L
1209 data8 0x9CEC3BF7A0BE2CAF, 0x0000BF98 //A15 = -1.20888920108938909316e-31L
1210 // Pol26
1211 data8 0xC17AB25E269272F7, 0x00003FEE //A0 = +1.15322640047234590651e-05L
1212 data8 0x85310509E633FEF2, 0x0000BFF1 //A1 = -6.35106483144690768696e-05L
1213 data8 0xAC5E4C4DCB2D940C, 0x00003FEA //A2 = +6.42122148740412561597e-07L
1214 data8 0xDF0AAD0571FFDD48, 0x0000BFE3 //A3 = -6.49136789710824396482e-09L
1215 data8 0x9049D8440AFD180F, 0x00003FDD //A4 = +6.56147932223174570008e-11L
1216 data8 0xBAA936477C5FA9D7, 0x0000BFD6 //A5 = -6.63153032879993841863e-13L
1217 data8 0xF17261294EAB1443, 0x00003FCF //A6 = +6.70149477756803680009e-15L
1218 data8 0x9C22F87C31DB007A, 0x0000BFC9 //A7 = -6.77134581402030645534e-17L
1219 data8 0xC9E98E633942AC12, 0x00003FC2 //A8 = +6.84105580182052870823e-19L
1220 data8 0x828998181309642C, 0x0000BFBC //A9 = -6.91059649300859944955e-21L
1221 data8 0xA8C3D4DCE1ECBAB6, 0x00003FB5 //A10 = +6.97995542988331257517e-23L
1222 data8 0xDA288D52CC4C351A, 0x0000BFAE //A11 = -7.04907829139578377009e-25L
1223 data8 0x8CEEACB790B5F374, 0x00003FA8 //A12 = +7.11526399101774993883e-27L
1224 data8 0xB61C8A29D98F24C0, 0x0000BFA1 //A13 = -7.18303147470398859453e-29L
1225 data8 0xF296F69FE45BDA7D, 0x00003F9A //A14 = +7.47537230021540031251e-31L
1226 data8 0x9D4B25BF6FB7234B, 0x0000BF94 //A15 = -7.57340869663212138051e-33L
1227 // Pol27
1228 data8 0xC7772CC326D6FBB8, 0x00003FEE //A0 = +1.18890718679826004395e-05L
1229 data8 0xE0F9D5410565D55D, 0x0000BFF0 //A1 = -5.36384368533203585378e-05L
1230 data8 0x85C0BE825680E148, 0x00003FEA //A2 = +4.98268406609692971520e-07L
1231 data8 0x9F058A389D7BA177, 0x0000BFE3 //A3 = -4.62813885933188677790e-09L
1232 data8 0xBD0B751F0A6BAC7A, 0x00003FDC //A4 = +4.29838009673609430305e-11L
1233 data8 0xE0B6823570502E9D, 0x0000BFD5 //A5 = -3.99170340031272728535e-13L
1234 data8 0x858A9C52FC426D86, 0x00003FCF //A6 = +3.70651975271664045723e-15L
1235 data8 0x9EB4438BFDF1928D, 0x0000BFC8 //A7 = -3.44134780748056488222e-17L
1236 data8 0xBC968DCD8C06D74E, 0x00003FC1 //A8 = +3.19480670422195579127e-19L
1237 data8 0xE0133A405F782125, 0x0000BFBA //A9 = -2.96560935615546392028e-21L
1238 data8 0x851AFEBB70D07E79, 0x00003FB4 //A10 = +2.75255617931932536111e-23L
1239 data8 0x9E1E21A841BF8738, 0x0000BFAD //A11 = -2.55452923487640676799e-25L
1240 data8 0xBBCF2EF1C6E72327, 0x00003FA6 //A12 = +2.37048675755308004410e-27L
1241 data8 0xDF0D320CF12B8BCB, 0x0000BF9F //A13 = -2.19945804585962185550e-29L
1242 data8 0x8470A76DE5FCADD8, 0x00003F99 //A14 = +2.04056213851532266258e-31L
1243 data8 0x9D41C15F6A6FBB04, 0x0000BF92 //A15 = -1.89291056020108587823e-33L
1244 LOCAL_OBJECT_END(erfc_Q_table)
1247 .section .text
1248 GLOBAL_LIBM_ENTRY(erfcl)
1250 { .mfi
1251 alloc r32 = ar.pfs, 0, 36, 4, 0
1252 fma.s1 FR_Tmp = f1, f1, f8 // |x|+1, if x >= 0
1253 nop.i 0
1254 }
1255 { .mfi
1256 addl GR_ad_Arg = @ltoff(exp_table_1), gp
1257 fms.s1 FR_Tmp1 = f1, f1, f8 // |x|+1, if x < 0
1258 mov GR_rshf_2to51 = 0x4718 // begin 1.10000 2^(63+51)
1259 }
1260 ;;
1262 { .mfi
1263 ld8 GR_ad_Arg = [GR_ad_Arg] // Point to Arg table
1264 fcmp.ge.s1 p6,p7 = f8, f0 // p6: x >= 0 ,p7: x<0
1265 shl GR_rshf_2to51 = GR_rshf_2to51,48 // end 1.10000 2^(63+51)
1266 }
1267 { .mlx
1268 mov GR_rshf = 0x43e8 // begin 1.1000 2^63 for right shift
1269 movl GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc // signif. of 1/ln2
1270 }
1271 ;;
1273 { .mfi
1274 mov GR_exp_2tom51 = 0xffff-51
1275 fclass.m p8,p0 = f8,0x07 // p8: x = 0
1276 shl GR_rshf = GR_rshf,48 // end 1.1000 2^63 for right shift
1277 }
1278 { .mfi
1279 nop.m 0
1280 fnma.s1 FR_norm_x = f8, f8, f0 //high bits for -x^2
1281 nop.i 0
1282 }
1283 ;;
1285 .pred.rel "mutex",p6,p7
1286 { .mfi
1287 setf.sig FR_INV_LN2_2TO63 = GR_sig_inv_ln2 // form 1/ln2 * 2^63
1288 (p6) fma.s1 FR_AbsArg = f1, f0, f8 // |x|, if x >= 0
1289 nop.i 0
1290 }
1291 { .mfi
1292 setf.d FR_RSHF_2TO51 = GR_rshf_2to51 //const 1.10 * 2^(63+51)
1293 (p7) fms.s1 FR_AbsArg = f1, f0, f8 // |x|, if x < 0
1294 mov GR_exp_mask = 0x1FFFF // Form exponent mask
1295 }
1296 ;;
1298 { .mfi
1299 ldfe FR_ch_dx = [GR_ad_Arg], 16
1300 fclass.m p10,p0 = f8, 0x21 // p10: x = +inf
1301 mov GR_exp_bias = 0x0FFFF // Set exponent bias
1302 }
1303 { .mlx
1304 setf.d FR_RSHF = GR_rshf // Right shift const 1.1000 * 2^63
1305 movl GR_ERFC_XC_TB = 0x650
1306 }
1307 ;;
1309 .pred.rel "mutex",p6,p7
1310 { .mfi
1311 setf.exp FR_2TOM51 = GR_exp_2tom51 // 2^-51 for scaling float_N
1312 (p6) fma.s1 FR_Tmp = FR_Tmp, FR_Tmp, f0 // (|x|+1)^2,x >=0
1313 nop.i 0
1314 }
1315 { .mfi
1316 ldfpd FR_POS_ARG_ASYMP,FR_NEG_ARG_ASYMP = [GR_ad_Arg], 16
1317 (p7) fma.s1 FR_Tmp = FR_Tmp1, FR_Tmp1, f0 // (|x|+1)^2, x<0
1318 mov GR_0x1 = 0x1
1319 }
1320 ;;
1322 //p8: y = 1.0, x = 0.0,quick exit
1323 { .mfi
1324 ldfpd FR_dx,FR_dx1 = [GR_ad_Arg], 16
1325 fclass.m p9,p0 = f8, 0x22 // p9: x = -inf
1326 nop.i 0
1328 }
1329 { .mfb
1330 nop.m 0
1331 (p8) fma.s0 f8 = f1, f1, f0
1332 (p8) br.ret.spnt b0
1333 }
1334 ;;
1336 { .mfi
1337 ldfe FR_UnfBound = [GR_ad_Arg], 16
1338 fclass.m p11,p0 = f8, 0xc3 // p11: x = nan
1339 mov GR_BIAS = 0x0FFFF
1340 }
1341 { .mfi
1342 nop.m 0
1343 fma.s1 FR_NormX = f8,f1,f0
1344 nop.i 0
1345 }
1346 ;;
1348 { .mfi
1349 ldfe FR_EpsNorm = [GR_ad_Arg], 16
1350 fmerge.s FR_X = f8,f8
1351 nop.i 0
1352 }
1353 { .mfi
1354 nop.m 0
1355 fma.s1 FR_xsq_lo = f8, f8, FR_norm_x // low bits for -x^2
1356 nop.i 0
1357 }
1358 ;;
1360 { .mfi
1361 add GR_ad_C = 0x20, GR_ad_Arg // Point to C table
1362 nop.f 0
1363 add GR_ad_T1 = 0x50, GR_ad_Arg // Point to T1 table
1364 }
1365 { .mfi
1366 add GR_ad_T2 = 0x150, GR_ad_Arg // Point to T2 table
1367 nop.f 0
1368 add GR_ERFC_XC_TB = GR_ERFC_XC_TB, GR_ad_Arg //poin.to XB_TBL
1369 }
1370 ;;
1372 { .mfi
1373 getf.exp GR_signexp_x = FR_norm_x // Extr. sign and exponent of x
1374 fma.s1 FR_Tmp = FR_Tmp, FR_Tmp, f0 // (|x|+1)^4
1375 add GR_ad_W1 = 0x100, GR_ad_T2 // Point to W1 table
1376 }
1377 { .mfi
1378 ldfe FR_L_hi = [GR_ad_Arg],16 // Get L_hi
1379 nop.f 0
1380 add GR_ad_W2 = 0x300, GR_ad_T2 // Point to W2 table
1381 }
1382 ;;
1384 // p9: y = 2.0, x = -inf, quick exit
1385 { .mfi
1386 sub GR_mBIAS = r0, GR_BIAS
1387 fma.s1 FR_2 = f1, f1, f1
1388 nop.i 0
1389 }
1390 { .mfb
1391 ldfe FR_L_lo = [GR_ad_Arg],16 // Get L_lo
1392 (p9) fma.s0 f8 = f1, f1, f1
1393 (p9) br.ret.spnt b0
1394 }
1395 ;;
1397 // p10: y = 0.0, x = +inf, quick exit
1398 { .mfi
1399 adds GR_ERFC_P_TB = 0x380, GR_ERFC_XC_TB // pointer to P_TBL
1400 fma.s1 FR_N_signif = FR_norm_x, FR_INV_LN2_2TO63, FR_RSHF_2TO51
1401 and GR_exp_x = GR_signexp_x, GR_exp_mask
1402 }
1403 { .mfb
1404 adds GR_ERFC_S_TB = 0x1C0, GR_ERFC_XC_TB // pointer to S_TBL
1405 (p10) fma.s0 f8 = f0, f1, f0
1406 (p10) br.ret.spnt b0
1407 }
1408 ;;
1410 // p12: |x| < 0.681... -> dx = 0.875 (else dx = 0.625 )
1411 // p11: y = x, x = nan, quick exit
1412 { .mfi
1413 ldfe FR_C3 = [GR_ad_C],16 // Get C3 for normal path
1414 fcmp.lt.s1 p12,p0 = FR_AbsArg, FR_ch_dx
1415 shl GR_ShftPi_bias = GR_BIAS, 8 // BIAS * 256
1416 }
1417 { .mfb
1418 sub GR_exp_x = GR_exp_x, GR_exp_bias // Get exponent
1419 (p11) fma.s0 f8 = f8, f1, f0
1420 (p11) br.ret.spnt b0
1422 }
1423 ;;
1425 { .mfi
1426 ldfe FR_C2 = [GR_ad_C],16 // Get A2 for main path
1427 nop.f 0
1428 nop.i 0
1429 }
1430 ;;
1432 //p15: x > POS_ARG_ASYMP = 107.0 -> erfcl(x) ~=~ 0.0
1433 { .mfi
1434 ldfe FR_C1 = [GR_ad_C],16 // Get C1 for main path
1435 (p6) fcmp.gt.unc.s1 p15,p0 = FR_AbsArg, FR_POS_ARG_ASYMP // p6: x >= 0
1436 nop.i 0
1437 }
1438 { .mfb
1439 nop.m 0
1440 (p12) fma.s1 FR_dx = FR_dx1, f1, f0 //p12: dx = 0.875 for x < 0.681
1441 nop.b 0
1442 }
1443 ;;
1445 //p14: x < - NEG_ARG_ASYMP = -6.5 -> erfcl(x) ~=~ 2.0
1446 { .mfi
1447 nop.m 0
1448 (p7) fcmp.gt.unc.s1 p14,p0 = FR_AbsArg,FR_NEG_ARG_ASYMP // p7: x < 0
1449 shladd GR_ShftXBi_bias = GR_mBIAS, 4, r0
1450 }
1451 ;;
1453 { .mfi
1454 nop.m 0
1455 fma.s0 FR_Tmpf = f1, f1, FR_EpsNorm // flag i
1456 nop.i 0
1457 }
1458 { .mfi
1459 nop.m 0
1460 fms.s1 FR_float_N = FR_N_signif, FR_2TOM51, FR_RSHF
1461 nop.i 0
1462 }
1463 ;;
1465 // p8: x < UnfBound ~=~ 106.53... -> result without underflow error
1466 // p14: y ~=~ 2, x < -6.5,quick exit
1467 { .mfi
1468 getf.exp GR_IndxPlusBias = FR_Tmp // exp + bias for (|x|+1)^4
1469 fcmp.lt.s1 p8,p0 = FR_NormX,FR_UnfBound
1470 nop.i 0
1471 }
1472 { .mfb
1473 nop.m 0
1474 (p14) fnma.s0 FR_RESULT = FR_EpsNorm,FR_EpsNorm,FR_2
1475 (p14) br.ret.spnt b0
1477 }
1478 ;;
1480 // p15: y ~=~ 0.0 (result with underflow error), x > POS_ARG_ASYMP = 107.0,
1481 // call __libm_error_region
1482 { .mfb
1483 (p15) mov GR_Parameter_TAG = 207
1484 (p15) fma.s0 FR_RESULT = FR_EpsNorm,FR_EpsNorm,f0
1485 (p15) br.cond.spnt __libm_error_region
1486 }
1487 ;;
1489 { .mfi
1490 getf.sig GR_N_fix = FR_N_signif // Get N from significand
1491 nop.f 0
1492 shl GR_ShftPi = GR_IndxPlusBias, 8
1494 }
1495 { .mfi
1496 shladd GR_ShftXBi = GR_IndxPlusBias, 4, GR_ShftXBi_bias
1497 nop.f 0
1498 nop.i 0
1499 }
1500 ;;
1502 { .mmi
1503 add GR_ERFC_S_TB = GR_ERFC_S_TB, GR_ShftXBi //poin.to S[i]
1504 add GR_ERFC_XC_TB = GR_ERFC_XC_TB, GR_ShftXBi //poin.to XC[i]
1505 sub GR_ShftPi = GR_ShftPi, GR_ShftPi_bias // 256*i
1506 }
1507 ;;
1509 { .mfi
1510 ldfe FR_Xc = [GR_ERFC_XC_TB]
1511 fma.s1 FR_Xpdx_hi = FR_AbsArg, f1, FR_dx // x + dx
1512 add GR_ShftA14 = 0xE0, GR_ShftPi // pointer shift for A14
1515 }
1516 { .mfi
1517 ldfe FR_S = [GR_ERFC_S_TB]
1518 fnma.s1 FR_r = FR_L_hi, FR_float_N, FR_norm_x//r= -L_hi*float_N+x
1519 add GR_ShftA15 = 0xF0, GR_ShftPi // pointer shift for A15
1520 }
1521 ;;
1523 { .mfi
1524 add GR_P_POINT_1 = GR_ERFC_P_TB, GR_ShftA14 // pointer to A14
1525 fcmp.gt.s1 p9,p10 = FR_AbsArg, FR_dx //p9: x > dx, p10: x <= dx
1526 extr.u GR_M1 = GR_N_fix, 6, 6 // Extract index M_1
1527 }
1528 { .mfi
1529 add GR_P_POINT_2 = GR_ERFC_P_TB, GR_ShftA15 // pointer to A15
1530 nop.f 0
1531 nop.i 0
1533 }
1534 ;;
1536 { .mfi
1537 ldfe FR_A14 = [GR_P_POINT_1], -32
1538 nop.f 0
1539 extr.u GR_M2 = GR_N_fix, 0, 6 // Extract index M_2
1540 }
1541 { .mfi
1542 ldfe FR_A15 = [GR_P_POINT_2], -32
1543 nop.f 0
1544 shladd GR_ad_W1 = GR_M1,3,GR_ad_W1 // Point to W1
1545 }
1546 ;;
1548 { .mfi
1549 ldfe FR_A12 = [GR_P_POINT_1], -64
1550 nop.f 0
1551 extr GR_K = GR_N_fix, 12, 32 // Extract limite range K
1552 }
1553 { .mfi
1554 ldfe FR_A13 = [GR_P_POINT_2], -64
1555 nop.f 0
1556 shladd GR_ad_T1 = GR_M1,2,GR_ad_T1 // Point to T1
1557 }
1558 ;;
1560 { .mfi
1561 ldfe FR_A8 = [GR_P_POINT_1], 32
1562 nop.f 0
1563 add GR_exp_2_k = GR_exp_bias, GR_K // Form exponent of 2^k
1564 }
1565 { .mfi
1566 ldfe FR_A9 = [GR_P_POINT_2], 32
1567 nop.f 0
1568 shladd GR_ad_W2 = GR_M2,3,GR_ad_W2 // Point to W2
1569 }
1570 ;;
1572 { .mfi
1573 ldfe FR_A10 = [GR_P_POINT_1], -96
1574 nop.f 0
1575 shladd GR_ad_T2 = GR_M2,2,GR_ad_T2 // Point to T2
1576 }
1577 { .mfi
1578 ldfe FR_A11 = [GR_P_POINT_2], -96
1579 fnma.s1 FR_r = FR_L_lo, FR_float_N, FR_r //r = -L_lo*float_N + r
1580 nop.i 0
1581 }
1582 ;;
1584 { .mfi
1585 ldfe FR_A4 = [GR_P_POINT_1], 32
1586 (p10) fms.s1 FR_Tmp = FR_dx,f1, FR_Xpdx_hi //for lo of x+dx, x<=dx
1587 nop.i 0
1588 }
1589 { .mfi
1590 ldfe FR_A5 = [GR_P_POINT_2], 32
1591 (p9) fms.s1 FR_Tmp = FR_AbsArg, f1, FR_Xpdx_hi //for lo of x+dx, x>dx
1592 nop.i 0
1593 }
1594 ;;
1596 { .mfi
1597 ldfe FR_A6 = [GR_P_POINT_1], -64
1598 frcpa.s1 FR_U,p11 = f1, FR_Xpdx_hi // hi of 1 /(x + dx)
1599 nop.i 0
1600 }
1601 { .mfi
1602 ldfe FR_A7 = [GR_P_POINT_2], -64
1603 nop.f 0
1604 nop.i 0
1605 }
1606 ;;
1608 { .mfi
1609 ldfe FR_A2 = [GR_P_POINT_1], -32
1610 nop.f 0
1611 nop.i 0
1612 }
1613 { .mfi
1614 ldfe FR_A3 = [GR_P_POINT_2], -32
1615 nop.f 0
1616 nop.i 0
1617 }
1618 ;;
1620 { .mfi
1621 ldfe FR_A0 = [GR_P_POINT_1], 224
1622 nop.f 0
1623 nop.i 0
1624 }
1625 { .mfi
1626 ldfe FR_A1 = [GR_P_POINT_2]
1627 fms.s1 FR_LocArg = FR_AbsArg, f1, FR_Xc // xloc = x - x[i]
1628 nop.i 0
1629 }
1630 ;;
1632 { .mfi
1633 ldfd FR_W1 = [GR_ad_W1],0 // Get W1
1634 nop.f 0
1635 nop.i 0
1636 }
1637 { .mfi
1638 ldfd FR_W2 = [GR_ad_W2],0 // Get W2
1639 fma.s1 FR_poly = FR_r, FR_C3, FR_C2 // poly = r * A3 + A2
1640 nop.i 0
1641 }
1642 ;;
1644 { .mfi
1645 ldfs FR_T1 = [GR_ad_T1],0 // Get T1
1646 (p10) fma.s1 FR_Xpdx_lo = FR_AbsArg,f1, FR_Tmp//lo of x + dx , x <= dx
1647 nop.i 0
1648 }
1649 { .mfi
1650 ldfs FR_T2 = [GR_ad_T2],0 // Get T2
1651 (p9) fma.s1 FR_Xpdx_lo = FR_dx,f1, FR_Tmp // lo of x + dx, x > dx
1652 nop.i 0
1653 }
1654 ;;
1656 { .mfi
1657 nop.m 0
1658 fnma.s1 FR_Tmp1 = FR_Xpdx_hi, FR_U, FR_2 // N-R, iter. N1
1659 nop.i 0
1660 }
1661 { .mfi
1662 nop.m 0
1663 fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r
1664 nop.i 0
1665 }
1666 ;;
1668 { .mfi
1669 setf.exp FR_scale = GR_exp_2_k // Set scale = 2^k
1670 fma.s1 FR_P15_1_1 = FR_LocArg, FR_LocArg, f0 // xloc ^2
1671 nop.i 0
1672 }
1673 { .mfi
1674 nop.m 0
1675 fma.s1 FR_P15_0_1 = FR_A15, FR_LocArg, FR_A14
1676 nop.i 0
1677 }
1678 ;;
1680 { .mfi
1681 nop.m 0
1682 fma.s1 FR_P15_1_2 = FR_A13, FR_LocArg, FR_A12
1683 nop.i 0
1684 }
1685 { .mfi
1686 nop.m 0
1687 fma.s1 FR_poly = FR_r, FR_poly, FR_C1 // poly = r * poly + A1
1688 nop.i 0
1689 }
1690 ;;
1692 { .mfi
1693 nop.m 0
1694 fma.s1 FR_P15_2_1 = FR_A9, FR_LocArg, FR_A8
1695 nop.i 0
1696 }
1697 { .mfi
1698 nop.m 0
1699 fma.s1 FR_P15_2_2 = FR_A11, FR_LocArg, FR_A10
1700 nop.i 0
1701 }
1702 ;;
1704 { .mfi
1705 nop.m 0
1706 fma.s1 FR_U = FR_U, FR_Tmp1, f0 // N-R, iter. N1
1707 nop.i 0
1708 }
1709 ;;
1711 { .mfi
1712 nop.m 0
1713 fma.s1 FR_P15_3_1 = FR_A5, FR_LocArg, FR_A4
1714 nop.i 0
1715 }
1716 { .mfi
1717 nop.m 0
1718 fma.s1 FR_P15_3_2 = FR_A7, FR_LocArg, FR_A6
1719 nop.i 0
1720 }
1721 ;;
1723 { .mfi
1724 nop.m 0
1725 fma.s1 FR_P15_4_2 = FR_A3, FR_LocArg, FR_A2
1726 nop.i 0
1727 }
1728 { .mfi
1729 nop.m 0
1730 fma.s1 FR_W = FR_W1, FR_W2, FR_W2 // W = W1 * W2 + W2
1731 nop.i 0
1732 }
1733 ;;
1735 { .mfi
1736 nop.m 0
1737 fmpy.s1 FR_T = FR_T1, FR_T2 // T = T1 * T2
1738 nop.i 0
1739 }
1740 { .mfi
1741 nop.m 0
1742 fma.s1 FR_P15_7_1 = FR_P15_0_1, FR_P15_1_1, FR_P15_1_2
1743 nop.i 0
1744 }
1745 ;;
1747 { .mfi
1748 nop.m 0
1749 fma.s1 FR_P15_7_2 = FR_P15_1_1, FR_P15_1_1, f0 // xloc^4
1750 nop.i 0
1751 }
1752 { .mfi
1753 nop.m 0
1754 fma.s1 FR_P15_8_1 = FR_P15_1_1, FR_P15_2_2, FR_P15_2_1
1755 nop.i 0
1756 }
1757 ;;
1759 { .mfi
1760 nop.m 0
1761 fnma.s1 FR_Tmp = FR_Xpdx_hi, FR_U, FR_2 // N-R, iter. N2
1762 nop.i 0
1763 }
1765 { .mfi
1766 nop.m 0
1767 fma.s1 FR_poly = FR_rsq, FR_poly, FR_r // poly = rsq * poly + r
1768 nop.i 0
1769 }
1770 ;;
1772 { .mfi
1773 nop.m 0
1774 fma.s1 FR_P15_9_1 = FR_P15_1_1, FR_P15_4_2, FR_A0
1775 nop.i 0
1776 }
1777 { .mfi
1778 nop.m 0
1779 fma.s1 FR_P15_9_2 = FR_P15_1_1, FR_P15_3_2, FR_P15_3_1
1780 nop.i 0
1781 }
1782 ;;
1784 { .mfi
1785 nop.m 0
1786 fma.s1 FR_W = FR_W, f1, FR_W1 // W = W + W1
1787 nop.i 0
1788 }
1789 ;;
1791 { .mfi
1792 nop.m 0
1793 fma.s1 FR_T_scale = FR_T, FR_scale, f0 // T_scale = T * scale
1794 nop.i 0
1795 }
1796 ;;
1798 { .mfi
1799 nop.m 0
1800 fma.s1 FR_P15_13_1 = FR_P15_7_2, FR_P15_7_1, FR_P15_8_1
1801 nop.i 0
1802 }
1803 ;;
1805 { .mfi
1806 nop.m 0
1807 fma.s1 FR_U = FR_U, FR_Tmp, f0 // N-R, iter. N2
1808 nop.i 0
1809 }
1810 ;;
1812 { .mfi
1813 nop.m 0
1814 fma.s1 FR_P15_14_1 = FR_P15_7_2, FR_P15_9_2, FR_P15_9_1
1815 nop.i 0
1816 }
1817 { .mfi
1818 nop.m 0
1819 fma.s1 FR_P15_14_2 = FR_P15_7_2, FR_P15_7_2, f0 // xloc^8
1820 nop.i 0
1821 }
1822 ;;
1824 { .mfi
1825 nop.m 0
1826 fma.s1 FR_M = FR_T_scale, FR_S, f0
1827 nop.i 0
1828 }
1829 ;;
1831 { .mfi
1832 nop.m 0
1833 fnma.s1 FR_Tmp = FR_Xpdx_hi, FR_U, FR_2 // N-R, iter. N3
1834 nop.i 0
1835 }
1836 ;;
1838 { .mfi
1839 nop.m 0
1840 fma.s1 FR_Q = FR_P15_14_2, FR_P15_13_1, FR_P15_14_1
1841 nop.i 0
1842 }
1843 ;;
1845 { .mfi
1846 nop.m 0
1847 fms.s1 FR_H = FR_W, f1, FR_xsq_lo // H = W - xsq_lo
1848 nop.i 0
1849 }
1850 ;;
1852 { .mfi
1853 nop.m 0
1854 fma.s1 FR_U = FR_U, FR_Tmp, f0 // N-R, iter. N3
1855 nop.i 0
1856 }
1857 ;;
1859 { .mfi
1860 nop.m 0
1861 fma.s1 FR_Q = FR_A1, FR_LocArg, FR_Q
1862 nop.i 0
1863 }
1864 ;;
1866 { .mfi
1867 nop.m 0
1868 fnma.s1 FR_Tmp = FR_Xpdx_hi, FR_U, f1 // for du
1869 nop.i 0
1870 }
1871 { .mfi
1872 nop.m 0
1873 fma.s1 FR_R = FR_H, FR_poly, FR_poly
1874 nop.i 0
1875 }
1876 ;;
1878 { .mfi
1879 nop.m 0
1880 fma.s1 FR_res_pos_x_hi = FR_M, FR_U, f0 // M *U
1881 nop.i 0
1883 }
1884 ;;
1886 { .mfi
1887 nop.m 0
1888 fma.s1 FR_R = FR_R, f1, FR_H // R = H + P(r) + H*P(r)
1889 nop.i 0
1890 }
1891 ;;
1893 { .mfi
1894 nop.m 0
1895 fma.s0 FR_Tmpf = f8, f1, f0 // flag d
1896 nop.i 0
1897 }
1898 ;;
1900 { .mfi
1901 nop.m 0
1902 fnma.s1 FR_dU = FR_Xpdx_lo, FR_U, FR_Tmp
1903 nop.i 0
1904 }
1905 ;;
1907 // p7: we begin to calculate y(x) = 2 - erfcl(-x) in multi precision
1908 // for -6.5 <= x < 0
1909 { .mfi
1910 nop.m 0
1911 fms.s1 FR_res_pos_x_lo = FR_M, FR_U, FR_res_pos_x_hi
1912 nop.i 0
1914 }
1915 { .mfi
1916 nop.m 0
1917 (p7) fnma.s1 FR_Tmp1 = FR_res_pos_x_hi, f1, FR_2 //p7: x < 0
1918 nop.i 0
1920 }
1921 ;;
1923 { .mfi
1924 nop.m 0
1925 fma.s1 FR_G = FR_R, FR_Q, FR_Q
1926 nop.i 0
1928 }
1929 ;;
1931 { .mfi
1932 nop.m 0
1933 fma.s1 FR_Tmp = FR_R, f1, FR_dU // R + du
1934 nop.i 0
1936 }
1937 ;;
1939 { .mfi
1940 nop.m 0
1941 (p7) fnma.s1 FR_Tmp2 = FR_Tmp1, f1, FR_2 //p7: x < 0
1942 nop.i 0
1944 }
1945 ;;
1947 { .mfi
1948 nop.m 0
1949 fma.s1 FR_G = FR_G, f1, FR_Tmp
1950 nop.i 0
1952 }
1953 ;;
1955 { .mfi
1956 nop.m 0
1957 (p7) fnma.s1 FR_Tmp2 = FR_res_pos_x_hi, f1, FR_Tmp2 //p7: x < 0
1958 nop.i 0
1960 }
1961 ;;
1963 { .mfi
1964 nop.m 0
1965 fma.s1 FR_V = FR_G, FR_res_pos_x_hi, f0 // V = G * M *U
1966 nop.i 0
1968 }
1969 ;;
1971 { .mfi
1972 nop.m 0
1973 (p7) fma.s1 FR_res_pos_x_lo = FR_res_pos_x_lo, f1, FR_V //p7: x < 0
1974 nop.i 0
1976 }
1977 ;;
1979 { .mfi
1980 nop.m 0
1981 (p7) fnma.s1 FR_Tmp2 = FR_res_pos_x_lo, f1, FR_Tmp2 //p7: x < 0
1982 nop.i 0
1984 }
1985 ;;
1988 //p6: result for 0 < x < = POS_ARG_ASYMP
1989 //p7: result for - NEG_ARG_ASYMP <= x < 0
1990 //p8: exit for - NEG_ARG_ASYMP <= x < UnfBound
1992 ERFC_RESULT:
1993 .pred.rel "mutex",p6,p7
1994 { .mfi
1995 nop.m 0
1996 (p6) fma.s0 f8 = FR_M, FR_U, FR_V // p6: x >= 0
1997 nop.i 0
1998 }
1999 { .mfb
2000 mov GR_Parameter_TAG = 207
2001 (p7) fma.s0 f8 = FR_Tmp2, f1, FR_Tmp1 // p7: x < 0
2002 (p8) br.ret.sptk b0
2003 };;
2005 GLOBAL_LIBM_END(erfcl)
2007 // call via (p15) br.cond.spnt __libm_error_region
2008 // for x > POS_ARG_ASYMP
2009 // or
2010 //
2011 // after .endp erfcl for UnfBound < = x < = POS_ARG_ASYMP
2013 LOCAL_LIBM_ENTRY(__libm_error_region)
2014 .prologue
2015 { .mfi
2016 add GR_Parameter_Y=-32,sp // Parameter 2 value
2017 nop.f 0
2018 .save ar.pfs,GR_SAVE_PFS
2019 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
2020 }
2021 { .mfi
2022 .fframe 64
2023 add sp=-64,sp // Create new stack
2024 nop.f 0
2025 mov GR_SAVE_GP=gp // Save gp
2026 };;
2027 { .mmi
2028 stfe [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack
2029 add GR_Parameter_X = 16,sp // Parameter 1 address
2030 .save b0, GR_SAVE_B0
2031 mov GR_SAVE_B0=b0 // Save b0
2032 };;
2033 .body
2034 { .mib
2035 stfe [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack
2036 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
2037 nop.b 0
2038 }
2039 { .mib
2040 stfe [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack
2041 add GR_Parameter_Y = -16,GR_Parameter_Y
2042 br.call.sptk b0=__libm_error_support# // Call error handling function
2043 };;
2044 { .mmi
2045 nop.m 0
2046 nop.m 0
2047 add GR_Parameter_RESULT = 48,sp
2048 };;
2049 { .mmi
2050 ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
2051 .restore sp
2052 add sp = 64,sp // Restore stack pointer
2053 mov b0 = GR_SAVE_B0 // Restore return address
2054 };;
2055 { .mib
2056 mov gp = GR_SAVE_GP // Restore gp
2057 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
2058 br.ret.sptk b0 // Return
2059 };;
2061 LOCAL_LIBM_END(__libm_error_region)
2062 .type __libm_error_support#,@function
2063 .global __libm_error_support#