| blob | f06e26f59f6fda35903685d6a0fa6921ff59a82f |
1 .file "erfcl.s"
4 // Copyright (c) 2001 - 2003, 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 // 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 //
48 // API
49 //==============================================================
50 // long double erfcl(long double)
51 //
52 // Implementation and Algorithm Notes:
53 //==============================================================
54 // 1. 0 <= x <= 107.0
55 //
56 // erfcl(x) ~=~ P15(z) * expl( -x^2 )/(dx + x), z = x - xc(i).
57 //
58 // Comment:
59 //
60 // Let x(i) = -1.0 + 2^(i/4),i=0,...27. So we have 28 unequal
61 // argument intervals [x(i),x(i+1)] with length ratio q = 2^(1/4).
62 // Values xc(i) we have in the table erfc_xc_table,xc(i)=x(i)for i = 0
63 // and xc(i)= 0.5*( x(i)+x(i+1) ) for i>0.
64 //
65 // Let x(i)<= x < x(i+1).
66 // We can find i as exponent of number (x + 1)^4.
67 //
68 // Let P15(z)= a0+ a1*z +..+a15*z^15 - polynomial approximation of degree 15
69 // for function erfcl(z+xc(i)) * expl( (z+xc(i))^2)* (dx+z+xc(i)) and
70 // -0.5*[x(i+1)-x(i)] <= z <= 0.5*[x(i+1)-x(i)].
71 //
72 // Let Q(z)= (P(z)- S)/S, S = a0, rounded to 16 bits.
73 // Polynomial coeffitients for Q(z) we have in the table erfc_Q_table as
74 // long double values
75 //
76 // We use multi precision to calculate input argument -x^2 for expl and
77 // for u = 1/(dx + x).
78 //
79 // Algorithm description for expl function see below. In accordance with
80 // denotation of this algorithm we have for expl:
81 //
82 // expl(X) ~=~ 2^K*T_1*(1+W_1)*T_2*(1+W_2)*(1+ poly(r)), X = -x^2.
83 //
84 // Final calculations for erfcl:
85 //
86 // erfcl(x) ~=~
87 //
88 // 2^K*T_1*(1+W_1)*T_2*(1+W_2)*(1+ poly(r))*(1-dy)*S*(1+Q(z))*u*(1+du),
89 //
90 // where dy - low bits of x^2 and u, u*du - hi and low bits of 1/(dx + x).
91 //
92 // The order of calculations is the next:
93 //
94 // 1) M = 2^K*T_1*T_2*S without rounding error,
95 // 2) W = W_1 + (W_2 + W_1*W_2), where 1+W ~=~ (1+W_1)(1+W_2),
96 // 3) H = W - dy, where 1+H ~=~ (1+W )(1-dy),
97 // 4) R = poly(r)*H + poly(r),
98 // 5) R = H + R , where 1+R ~=~ (1+H )(1+poly(r)),
99 // 6) G = Q(z)*R + Q(z),
100 // 7) R1 = R + du, where 1+R1 ~=~ (1+R)(1+du),
101 // 8) G1 = R1 + G, where 1+G1 ~=~ (1+R1)(1+Q(z)),
102 // 9) V = G1*M*u,
103 // 10) erfcl(x) ~=~ M*u + V
104 //
105 // 2. -6.5 <= x < 0
106 //
107 // erfcl(x) = 2.0 - erfl(-x)
108 //
109 // 3. x > 107.0
110 // erfcl(x) ~=~ 0.0
111 //
112 // 4. x < -6.5
113 // erfcl(x) ~=~ 2.0
115 // Special values
116 //==============================================================
117 // erfcl(+0) = 1.0
118 // erfcl(-0) = 1.0
120 // erfcl(+qnan) = +qnan
121 // erfcl(-qnan) = -qnan
122 // erfcl(+snan) = +qnan
123 // erfcl(-snan) = -qnan
125 // erfcl(-inf) = 2.0
126 // erfcl(+inf) = +0
128 //==============================================================
129 // Algorithm description of used expl function.
130 //
131 // Implementation and Algorithm Notes:
132 //
133 // ker_exp_64( in_FR : X,
134 // out_FR : Y_hi,
135 // out_FR : Y_lo,
136 // out_FR : scale,
137 // out_PR : Safe )
138 //
139 // On input, X is in register format
140 //
141 // On output,
142 //
143 // scale*(Y_hi + Y_lo) approximates exp(X)
144 //
145 // The accuracy is sufficient for a highly accurate 64 sig.
146 // bit implementation. Safe is set if there is no danger of
147 // overflow/underflow when the result is composed from scale,
148 // Y_hi and Y_lo. Thus, we can have a fast return if Safe is set.
149 // Otherwise, one must prepare to handle the possible exception
150 // appropriately. Note that SAFE not set (false) does not mean
151 // that overflow/underflow will occur; only the setting of SAFE
152 // guarantees the opposite.
153 //
154 // **** High Level Overview ****
155 //
156 // The method consists of three cases.
157 //
158 // If |X| < Tiny use case exp_tiny;
159 // else if |X| < 2^(-6) use case exp_small;
160 // else use case exp_regular;
161 //
162 // Case exp_tiny:
163 //
164 // 1 + X can be used to approximate exp(X)
165 // X + X^2/2 can be used to approximate exp(X) - 1
166 //
167 // Case exp_small:
168 //
169 // Here, exp(X) and exp(X) - 1 can all be
170 // appproximated by a relatively simple polynomial.
171 //
172 // This polynomial resembles the truncated Taylor series
173 //
174 // exp(w) = 1 + w + w^2/2! + w^3/3! + ... + w^n/n!
175 //
176 // Case exp_regular:
177 //
178 // Here we use a table lookup method. The basic idea is that in
179 // order to compute exp(X), we accurately decompose X into
180 //
181 // X = N * log(2)/(2^12) + r, |r| <= log(2)/2^13.
182 //
183 // Hence
184 //
185 // exp(X) = 2^( N / 2^12 ) * exp(r).
186 //
187 // The value 2^( N / 2^12 ) is obtained by simple combinations
188 // of values calculated beforehand and stored in table; exp(r)
189 // is approximated by a short polynomial because |r| is small.
190 //
191 // We elaborate this method in 4 steps.
192 //
193 // Step 1: Reduction
194 //
195 // The value 2^12/log(2) is stored as a double-extended number
196 // L_Inv.
197 //
198 // N := round_to_nearest_integer( X * L_Inv )
199 //
200 // The value log(2)/2^12 is stored as two numbers L_hi and L_lo so
201 // that r can be computed accurately via
202 //
203 // r := (X - N*L_hi) - N*L_lo
204 //
205 // We pick L_hi such that N*L_hi is representable in 64 sig. bits
206 // and thus the FMA X - N*L_hi is error free. So r is the
207 // 1 rounding error from an exact reduction with respect to
208 //
209 // L_hi + L_lo.
210 //
211 // In particular, L_hi has 30 significant bit and can be stored
212 // as a double-precision number; L_lo has 64 significant bits and
213 // stored as a double-extended number.
214 //
215 // Step 2: Approximation
216 //
217 // exp(r) - 1 is approximated by a short polynomial of the form
218 //
219 // r + A_1 r^2 + A_2 r^3 + A_3 r^4 .
220 //
221 // Step 3: Composition from Table Values
222 //
223 // The value 2^( N / 2^12 ) can be composed from a couple of tables
224 // of precalculated values. First, express N as three integers
225 // K, M_1, and M_2 as
226 //
227 // N = K * 2^12 + M_1 * 2^6 + M_2
228 //
229 // Where 0 <= M_1, M_2 < 2^6; and K can be positive or negative.
230 // When N is represented in 2's complement, M_2 is simply the 6
231 // lsb's, M_1 is the next 6, and K is simply N shifted right
232 // arithmetically (sign extended) by 12 bits.
233 //
234 // Now, 2^( N / 2^12 ) is simply
235 //
236 // 2^K * 2^( M_1 / 2^6 ) * 2^( M_2 / 2^12 )
237 //
238 // Clearly, 2^K needs no tabulation. The other two values are less
239 // trivial because if we store each accurately to more than working
240 // precision, than its product is too expensive to calculate. We
241 // use the following method.
242 //
243 // Define two mathematical values, delta_1 and delta_2, implicitly
244 // such that
245 //
246 // T_1 = exp( [M_1 log(2)/2^6] - delta_1 )
247 // T_2 = exp( [M_2 log(2)/2^12] - delta_2 )
248 //
249 // are representable as 24 significant bits. To illustrate the idea,
250 // we show how we define delta_1:
251 //
252 // T_1 := round_to_24_bits( exp( M_1 log(2)/2^6 ) )
253 // delta_1 = (M_1 log(2)/2^6) - log( T_1 )
254 //
255 // The last equality means mathematical equality. We then tabulate
256 //
257 // W_1 := exp(delta_1) - 1
258 // W_2 := exp(delta_2) - 1
259 //
260 // Both in double precision.
261 //
262 // From the tabulated values T_1, T_2, W_1, W_2, we compose the values
263 // T and W via
264 //
265 // T := T_1 * T_2 ...exactly
266 // W := W_1 + (1 + W_1)*W_2
267 //
268 // W approximates exp( delta ) - 1 where delta = delta_1 + delta_2.
269 // The mathematical product of T and (W+1) is an accurate representation
270 // of 2^(M_1/2^6) * 2^(M_2/2^12).
271 //
272 // Step 4. Reconstruction
273 //
274 // Finally, we can reconstruct exp(X), exp(X) - 1.
275 // Because
276 //
277 // X = K * log(2) + (M_1*log(2)/2^6 - delta_1)
278 // + (M_2*log(2)/2^12 - delta_2)
279 // + delta_1 + delta_2 + r ...accurately
280 // We have
281 //
282 // exp(X) ~=~ 2^K * ( T + T*[exp(delta_1+delta_2+r) - 1] )
283 // ~=~ 2^K * ( T + T*[exp(delta + r) - 1] )
284 // ~=~ 2^K * ( T + T*[(exp(delta)-1)
285 // + exp(delta)*(exp(r)-1)] )
286 // ~=~ 2^K * ( T + T*( W + (1+W)*poly(r) ) )
287 // ~=~ 2^K * ( Y_hi + Y_lo )
288 //
289 // where Y_hi = T and Y_lo = T*(W + (1+W)*poly(r))
290 //
291 // For exp(X)-1, we have
292 //
293 // exp(X)-1 ~=~ 2^K * ( Y_hi + Y_lo ) - 1
294 // ~=~ 2^K * ( Y_hi + Y_lo - 2^(-K) )
295 //
296 // and we combine Y_hi + Y_lo - 2^(-N) into the form of two
297 // numbers Y_hi + Y_lo carefully.
298 //
299 // **** Algorithm Details ****
300 //
301 // A careful algorithm must be used to realize the mathematical ideas
302 // accurately. We describe each of the three cases. We assume SAFE
303 // is preset to be TRUE.
304 //
305 // Case exp_tiny:
306 //
307 // The important points are to ensure an accurate result under
308 // different rounding directions and a correct setting of the SAFE
309 // flag.
310 //
311 // If expm1 is 1, then
312 // SAFE := False ...possibility of underflow
313 // Scale := 1.0
314 // Y_hi := X
315 // Y_lo := 2^(-17000)
316 // Else
317 // Scale := 1.0
318 // Y_hi := 1.0
319 // Y_lo := X ...for different rounding modes
320 // Endif
321 //
322 // Case exp_small:
323 //
324 // Here we compute a simple polynomial. To exploit parallelism, we split
325 // the polynomial into several portions.
326 //
327 // Let r = X
328 //
329 // If exp ...i.e. exp( argument )
330 //
331 // rsq := r * r;
332 // r4 := rsq*rsq
333 // poly_lo := P_3 + r*(P_4 + r*(P_5 + r*P_6))
334 // poly_hi := r + rsq*(P_1 + r*P_2)
335 // Y_lo := poly_hi + r4 * poly_lo
336 // Y_hi := 1.0
337 // Scale := 1.0
338 //
339 // Else ...i.e. exp( argument ) - 1
340 //
341 // rsq := r * r
342 // r4 := rsq * rsq
343 // r6 := rsq * r4
344 // poly_lo := r6*(Q_5 + r*(Q_6 + r*Q_7))
345 // poly_hi := Q_1 + r*(Q_2 + r*(Q_3 + r*Q_4))
346 // Y_lo := rsq*poly_hi + poly_lo
347 // Y_hi := X
348 // Scale := 1.0
349 //
350 // Endif
351 //
352 // Case exp_regular:
353 //
354 // The previous description contain enough information except the
355 // computation of poly and the final Y_hi and Y_lo in the case for
356 // exp(X)-1.
357 //
358 // The computation of poly for Step 2:
359 //
360 // rsq := r*r
361 // poly := r + rsq*(A_1 + r*(A_2 + r*A_3))
362 //
363 // For the case exp(X) - 1, we need to incorporate 2^(-K) into
364 // Y_hi and Y_lo at the end of Step 4.
365 //
366 // If K > 10 then
367 // Y_lo := Y_lo - 2^(-K)
368 // Else
369 // If K < -10 then
370 // Y_lo := Y_hi + Y_lo
371 // Y_hi := -2^(-K)
372 // Else
373 // Y_hi := Y_hi - 2^(-K)
374 // End If
375 // End If
376 //
378 // Overview of operation
379 //==============================================================
381 // Registers used
382 //==============================================================
383 // Floating Point registers used:
384 // f8, input
385 // f9 -> f14, f36 -> f126
387 // General registers used:
388 // r32 -> r71
390 // Predicate registers used:
391 // p6 -> p15
393 // Assembly macros
394 //==============================================================
395 // GR for exp(X)
396 GR_ad_Arg = r33
397 GR_ad_C = r34
398 GR_ERFC_S_TB = r35
399 GR_signexp_x = r36
400 GR_exp_x = r36
401 GR_exp_mask = r37
402 GR_ad_W1 = r38
403 GR_ad_W2 = r39
404 GR_M2 = r40
405 GR_M1 = r41
406 GR_K = r42
407 GR_exp_2_k = r43
408 GR_ad_T1 = r44
409 GR_ad_T2 = r45
410 GR_N_fix = r46
411 GR_ad_P = r47
412 GR_exp_bias = r48
413 GR_BIAS = r48
414 GR_exp_half = r49
415 GR_sig_inv_ln2 = r50
416 GR_rshf_2to51 = r51
417 GR_exp_2tom51 = r52
418 GR_rshf = r53
420 // GR for erfcl(x)
421 //==============================================================
423 GR_ERFC_XC_TB = r54
424 GR_ERFC_P_TB = r55
425 GR_IndxPlusBias = r56
426 GR_P_POINT_1 = r57
427 GR_P_POINT_2 = r58
428 GR_AbsArg = r59
429 GR_ShftXBi = r60
430 GR_ShftPi = r61
431 GR_mBIAS = r62
432 GR_ShftPi_bias = r63
433 GR_ShftXBi_bias = r64
434 GR_ShftA14 = r65
435 GR_ShftA15 = r66
436 GR_EpsNorm = r67
437 GR_0x1 = r68
438 GR_ShftPi_8 = r69
439 GR_26PlusBias = r70
440 GR_27PlusBias = r71
442 // GR for __libm_support call
443 //==============================================================
444 GR_SAVE_B0 = r64
445 GR_SAVE_PFS = r65
446 GR_SAVE_GP = r66
447 GR_SAVE_SP = r67
449 GR_Parameter_X = r68
450 GR_Parameter_Y = r69
451 GR_Parameter_RESULT = r70
452 GR_Parameter_TAG = r71
454 //==============================================================
455 // Floating Point Registers
456 //
457 FR_RSHF_2TO51 = f10
458 FR_INV_LN2_2TO63 = f11
459 FR_W_2TO51_RSH = f12
460 FR_2TOM51 = f13
461 FR_RSHF = f14
463 FR_scale = f36
464 FR_float_N = f37
465 FR_N_signif = f38
466 FR_L_hi = f39
467 FR_L_lo = f40
468 FR_r = f41
469 FR_W1 = f42
470 FR_T1 = f43
471 FR_W2 = f44
472 FR_T2 = f45
473 FR_rsq = f46
474 FR_C2 = f47
475 FR_C3 = f48
476 FR_poly = f49
477 FR_P6 = f49
478 FR_T = f50
479 FR_P5 = f50
480 FR_P4 = f51
481 FR_W = f51
482 FR_P3 = f52
483 FR_Wp1 = f52
484 FR_P2 = f53
485 FR_P1 = f54
486 FR_Q7 = f56
487 FR_Q6 = f57
488 FR_Q5 = f58
489 FR_Q4 = f59
490 FR_Q3 = f60
491 FR_Q2 = f61
492 FR_Q1 = f62
493 FR_C1 = f63
494 FR_A15 = f64
495 FR_ch_dx = f65
496 FR_T_scale = f66
497 FR_norm_x = f67
498 FR_AbsArg = f68
499 FR_POS_ARG_ASYMP = f69
500 FR_NEG_ARG_ASYMP = f70
501 FR_Tmp = f71
502 FR_Xc = f72
503 FR_A0 = f73
504 FR_A1 = f74
505 FR_A2 = f75
506 FR_A3 = f76
507 FR_A4 = f77
508 FR_A5 = f78
509 FR_A6 = f79
510 FR_A7 = f80
511 FR_A8 = f81
512 FR_A9 = f82
513 FR_A10 = f83
514 FR_A11 = f84
515 FR_A12 = f85
516 FR_A13 = f86
517 FR_A14 = f87
518 FR_P15_0_1 = f88
519 FR_P15_8_1 = f88
520 FR_P15_1_1 = f89
521 FR_P15_8_2 = f89
522 FR_P15_1_2 = f90
523 FR_P15_2_1 = f91
524 FR_P15_2_2 = f92
525 FR_P15_3_1 = f93
526 FR_P15_3_2 = f94
527 FR_P15_4_2 = f95
528 FR_P15_7_1 = f96
529 FR_P15_7_2 = f97
530 FR_P15_9_1 = f98
531 FR_P15_9_2 = f99
532 FR_P15_13_1 = f100
533 FR_P15_14_1 = f101
534 FR_P15_14_2 = f102
535 FR_Tmp2 = f103
536 FR_Xpdx_lo = f104
537 FR_2 = f105
538 FR_xsq_lo = f106
539 FR_LocArg = f107
540 FR_Tmpf = f108
541 FR_Tmp1 = f109
542 FR_EpsNorm = f110
543 FR_UnfBound = f111
544 FR_NormX = f112
545 FR_Xpdx_hi = f113
546 FR_dU = f114
547 FR_H = f115
548 FR_G = f116
549 FR_V = f117
550 FR_M = f118
551 FR_U = f119
552 FR_Q = f120
553 FR_S = f121
554 FR_R = f122
555 FR_res_pos_x_hi = f123
556 FR_res_pos_x_lo = f124
557 FR_dx = f125
558 FR_dx1 = f126
560 // for error handler routine
561 FR_X = f9
562 FR_Y = f0
563 FR_RESULT = f8
565 // Data tables
566 //==============================================================
567 RODATA
568 .align 16
570 // ************* DO NOT CHANGE ORDER OF THESE TABLES ********************
571 LOCAL_OBJECT_START(exp_table_1)
573 data8 0xae89f995ad3ad5ea , 0x00003ffe // x = 0.681..,bound for dx = 0.875
574 data8 0x405AC00000000000 , 0x401A000000000000 //ARG_ASYMP,NEG_ARG_ASYMP
575 data8 0x3FE4000000000000 , 0x3FEC000000000000 //0.625,0.875
576 data8 0xD5126065B720A4e9 , 0x00004005 // underflow boundary
577 data8 0x8000000000000000 , 0x00000001 //FR_EpsNorm
578 LOCAL_OBJECT_END(exp_table_1)
580 LOCAL_OBJECT_START(Constants_exp_64_Arg)
581 data8 0xB17217F400000000,0x00003FF2 //L_hi = hi part log(2)/2^12
582 data8 0xF473DE6AF278ECE6,0x00003FD4 //L_lo = lo part log(2)/2^12
583 LOCAL_OBJECT_END(Constants_exp_64_Arg)
585 LOCAL_OBJECT_START(Constants_exp_64_C)
586 data8 0xAAAAAAABB1B736A0,0x00003FFA // C3
587 data8 0xAAAAAAAB90CD6327,0x00003FFC // C2
588 data8 0xFFFFFFFFFFFFFFFF,0x00003FFD // C1
589 LOCAL_OBJECT_END(Constants_exp_64_C)
591 LOCAL_OBJECT_START(Constants_exp_64_T1)
592 data4 0x3F800000,0x3F8164D2,0x3F82CD87,0x3F843A29
593 data4 0x3F85AAC3,0x3F871F62,0x3F88980F,0x3F8A14D5
594 data4 0x3F8B95C2,0x3F8D1ADF,0x3F8EA43A,0x3F9031DC
595 data4 0x3F91C3D3,0x3F935A2B,0x3F94F4F0,0x3F96942D
596 data4 0x3F9837F0,0x3F99E046,0x3F9B8D3A,0x3F9D3EDA
597 data4 0x3F9EF532,0x3FA0B051,0x3FA27043,0x3FA43516
598 data4 0x3FA5FED7,0x3FA7CD94,0x3FA9A15B,0x3FAB7A3A
599 data4 0x3FAD583F,0x3FAF3B79,0x3FB123F6,0x3FB311C4
600 data4 0x3FB504F3,0x3FB6FD92,0x3FB8FBAF,0x3FBAFF5B
601 data4 0x3FBD08A4,0x3FBF179A,0x3FC12C4D,0x3FC346CD
602 data4 0x3FC5672A,0x3FC78D75,0x3FC9B9BE,0x3FCBEC15
603 data4 0x3FCE248C,0x3FD06334,0x3FD2A81E,0x3FD4F35B
604 data4 0x3FD744FD,0x3FD99D16,0x3FDBFBB8,0x3FDE60F5
605 data4 0x3FE0CCDF,0x3FE33F89,0x3FE5B907,0x3FE8396A
606 data4 0x3FEAC0C7,0x3FED4F30,0x3FEFE4BA,0x3FF28177
607 data4 0x3FF5257D,0x3FF7D0DF,0x3FFA83B3,0x3FFD3E0C
608 LOCAL_OBJECT_END(Constants_exp_64_T1)
610 LOCAL_OBJECT_START(Constants_exp_64_T2)
611 data4 0x3F800000,0x3F80058C,0x3F800B18,0x3F8010A4
612 data4 0x3F801630,0x3F801BBD,0x3F80214A,0x3F8026D7
613 data4 0x3F802C64,0x3F8031F2,0x3F803780,0x3F803D0E
614 data4 0x3F80429C,0x3F80482B,0x3F804DB9,0x3F805349
615 data4 0x3F8058D8,0x3F805E67,0x3F8063F7,0x3F806987
616 data4 0x3F806F17,0x3F8074A8,0x3F807A39,0x3F807FCA
617 data4 0x3F80855B,0x3F808AEC,0x3F80907E,0x3F809610
618 data4 0x3F809BA2,0x3F80A135,0x3F80A6C7,0x3F80AC5A
619 data4 0x3F80B1ED,0x3F80B781,0x3F80BD14,0x3F80C2A8
620 data4 0x3F80C83C,0x3F80CDD1,0x3F80D365,0x3F80D8FA
621 data4 0x3F80DE8F,0x3F80E425,0x3F80E9BA,0x3F80EF50
622 data4 0x3F80F4E6,0x3F80FA7C,0x3F810013,0x3F8105AA
623 data4 0x3F810B41,0x3F8110D8,0x3F81166F,0x3F811C07
624 data4 0x3F81219F,0x3F812737,0x3F812CD0,0x3F813269
625 data4 0x3F813802,0x3F813D9B,0x3F814334,0x3F8148CE
626 data4 0x3F814E68,0x3F815402,0x3F81599C,0x3F815F37
627 LOCAL_OBJECT_END(Constants_exp_64_T2)
629 LOCAL_OBJECT_START(Constants_exp_64_W1)
630 data8 0x0000000000000000, 0xBE384454171EC4B4
631 data8 0xBE6947414AA72766, 0xBE5D32B6D42518F8
632 data8 0x3E68D96D3A319149, 0xBE68F4DA62415F36
633 data8 0xBE6DDA2FC9C86A3B, 0x3E6B2E50F49228FE
634 data8 0xBE49C0C21188B886, 0x3E64BFC21A4C2F1F
635 data8 0xBE6A2FBB2CB98B54, 0x3E5DC5DE9A55D329
636 data8 0x3E69649039A7AACE, 0x3E54728B5C66DBA5
637 data8 0xBE62B0DBBA1C7D7D, 0x3E576E0409F1AF5F
638 data8 0x3E6125001A0DD6A1, 0xBE66A419795FBDEF
639 data8 0xBE5CDE8CE1BD41FC, 0xBE621376EA54964F
640 data8 0x3E6370BE476E76EE, 0x3E390D1A3427EB92
641 data8 0x3E1336DE2BF82BF8, 0xBE5FF1CBD0F7BD9E
642 data8 0xBE60A3550CEB09DD, 0xBE5CA37E0980F30D
643 data8 0xBE5C541B4C082D25, 0xBE5BBECA3B467D29
644 data8 0xBE400D8AB9D946C5, 0xBE5E2A0807ED374A
645 data8 0xBE66CB28365C8B0A, 0x3E3AAD5BD3403BCA
646 data8 0x3E526055C7EA21E0, 0xBE442C75E72880D6
647 data8 0x3E58B2BB85222A43, 0xBE5AAB79522C42BF
648 data8 0xBE605CB4469DC2BC, 0xBE589FA7A48C40DC
649 data8 0xBE51C2141AA42614, 0xBE48D087C37293F4
650 data8 0x3E367A1CA2D673E0, 0xBE51BEBB114F7A38
651 data8 0xBE6348E5661A4B48, 0xBDF526431D3B9962
652 data8 0x3E3A3B5E35A78A53, 0xBE46C46C1CECD788
653 data8 0xBE60B7EC7857D689, 0xBE594D3DD14F1AD7
654 data8 0xBE4F9C304C9A8F60, 0xBE52187302DFF9D2
655 data8 0xBE5E4C8855E6D68F, 0xBE62140F667F3DC4
656 data8 0xBE36961B3BF88747, 0x3E602861C96EC6AA
657 data8 0xBE3B5151D57FD718, 0x3E561CD0FC4A627B
658 data8 0xBE3A5217CA913FEA, 0x3E40A3CC9A5D193A
659 data8 0xBE5AB71310A9C312, 0x3E4FDADBC5F57719
660 data8 0x3E361428DBDF59D5, 0x3E5DB5DB61B4180D
661 data8 0xBE42AD5F7408D856, 0x3E2A314831B2B707
662 LOCAL_OBJECT_END(Constants_exp_64_W1)
664 LOCAL_OBJECT_START(Constants_exp_64_W2)
665 data8 0x0000000000000000, 0xBE641F2537A3D7A2
666 data8 0xBE68DD57AD028C40, 0xBE5C77D8F212B1B6
667 data8 0x3E57878F1BA5B070, 0xBE55A36A2ECAE6FE
668 data8 0xBE620608569DFA3B, 0xBE53B50EA6D300A3
669 data8 0x3E5B5EF2223F8F2C, 0xBE56A0D9D6DE0DF4
670 data8 0xBE64EEF3EAE28F51, 0xBE5E5AE2367EA80B
671 data8 0x3E47CB1A5FCBC02D, 0xBE656BA09BDAFEB7
672 data8 0x3E6E70C6805AFEE7, 0xBE6E0509A3415EBA
673 data8 0xBE56856B49BFF529, 0x3E66DD3300508651
674 data8 0x3E51165FC114BC13, 0x3E53333DC453290F
675 data8 0x3E6A072B05539FDA, 0xBE47CD877C0A7696
676 data8 0xBE668BF4EB05C6D9, 0xBE67C3E36AE86C93
677 data8 0xBE533904D0B3E84B, 0x3E63E8D9556B53CE
678 data8 0x3E212C8963A98DC8, 0xBE33138F032A7A22
679 data8 0x3E530FA9BC584008, 0xBE6ADF82CCB93C97
680 data8 0x3E5F91138370EA39, 0x3E5443A4FB6A05D8
681 data8 0x3E63DACD181FEE7A, 0xBE62B29DF0F67DEC
682 data8 0x3E65C4833DDE6307, 0x3E5BF030D40A24C1
683 data8 0x3E658B8F14E437BE, 0xBE631C29ED98B6C7
684 data8 0x3E6335D204CF7C71, 0x3E529EEDE954A79D
685 data8 0x3E5D9257F64A2FB8, 0xBE6BED1B854ED06C
686 data8 0x3E5096F6D71405CB, 0xBE3D4893ACB9FDF5
687 data8 0xBDFEB15801B68349, 0x3E628D35C6A463B9
688 data8 0xBE559725ADE45917, 0xBE68C29C042FC476
689 data8 0xBE67593B01E511FA, 0xBE4A4313398801ED
690 data8 0x3E699571DA7C3300, 0x3E5349BE08062A9E
691 data8 0x3E5229C4755BB28E, 0x3E67E42677A1F80D
692 data8 0xBE52B33F6B69C352, 0xBE6B3550084DA57F
693 data8 0xBE6DB03FD1D09A20, 0xBE60CBC42161B2C1
694 data8 0x3E56ED9C78A2B771, 0xBE508E319D0FA795
695 data8 0xBE59482AFD1A54E9, 0xBE2A17CEB07FD23E
696 data8 0x3E68BF5C17365712, 0x3E3956F9B3785569
697 LOCAL_OBJECT_END(Constants_exp_64_W2)
700 LOCAL_OBJECT_START(erfc_xc_table)
702 data8 0x0000000000000000, 0x00000000 //XC[0] = +0.00000000000000000000e-01L
703 data8 0x9A79C70000000000, 0x00003FFD //XC[1] = +3.01710337400436401367e-01L
704 data8 0x8C49EF0000000000, 0x00003FFE //XC[2] = +5.48003137111663818359e-01L
705 data8 0xD744FC0000000000, 0x00003FFE //XC[3] = +8.40896368026733398438e-01L
706 data8 0x9837F00000000000, 0x00003FFF //XC[4] = +1.18920707702636718750e+00L
707 data8 0xCD3CE30000000000, 0x00003FFF //XC[5] = +1.60342061519622802734e+00L
708 data8 0x8624F70000000000, 0x00004000 //XC[6] = +2.09600615501403808594e+00L
709 data8 0xABA27E0000000000, 0x00004000 //XC[7] = +2.68179273605346679688e+00L
710 data8 0xD837F00000000000, 0x00004000 //XC[8] = +3.37841415405273437500e+00L
711 data8 0x869E710000000000, 0x00004001 //XC[9] = +4.20684099197387695313e+00L
712 data8 0xA624F70000000000, 0x00004001 //XC[10] = +5.19201231002807617188e+00L
713 data8 0xCBA27E0000000000, 0x00004001 //XC[11] = +6.36358547210693359375e+00L
714 data8 0xF837F00000000000, 0x00004001 //XC[12] = +7.75682830810546875000e+00L
715 data8 0x969E710000000000, 0x00004002 //XC[13] = +9.41368198394775390625e+00L
716 data8 0xB624F70000000000, 0x00004002 //XC[14] = +1.13840246200561523438e+01L
717 data8 0xDBA27E0000000000, 0x00004002 //XC[15] = +1.37271709442138671875e+01L
718 data8 0x841BF80000000000, 0x00004003 //XC[16] = +1.65136566162109375000e+01L
719 data8 0x9E9E710000000000, 0x00004003 //XC[17] = +1.98273639678955078125e+01L
720 data8 0xBE24F70000000000, 0x00004003 //XC[18] = +2.37680492401123046875e+01L
721 data8 0xE3A27E0000000000, 0x00004003 //XC[19] = +2.84543418884277343750e+01L
722 data8 0x881BF80000000000, 0x00004004 //XC[20] = +3.40273132324218750000e+01L
723 data8 0xA29E710000000000, 0x00004004 //XC[21] = +4.06547279357910156250e+01L
724 data8 0xC224F70000000000, 0x00004004 //XC[22] = +4.85360984802246093750e+01L
725 data8 0xE7A27E0000000000, 0x00004004 //XC[23] = +5.79086837768554687500e+01L
726 data8 0x8A1BF80000000000, 0x00004005 //XC[24] = +6.90546264648437500000e+01L
727 data8 0xA49E710000000000, 0x00004005 //XC[25] = +8.23094558715820312500e+01L
728 data8 0xC424F70000000000, 0x00004005 //XC[26] = +9.80721969604492187500e+01L
729 data8 0xD5A27E0000000000, 0x00004005 //XC[27] = +1.06817367553710937500e+02L
730 LOCAL_OBJECT_END(erfc_xc_table)
732 LOCAL_OBJECT_START(erfc_s_table)
734 data8 0xE000000000000000, 0x00003FFE //s[0] = +8.75000000000000000000e-01L
735 data8 0xDCEF000000000000, 0x00003FFE //s[1] = +8.63021850585937500000e-01L
736 data8 0xD79D000000000000, 0x00003FFE //s[2] = +8.42239379882812500000e-01L
737 data8 0xB25E000000000000, 0x00003FFE //s[3] = +6.96746826171875000000e-01L
738 data8 0xB0EA000000000000, 0x00003FFE //s[4] = +6.91070556640625000000e-01L
739 data8 0xAE3F000000000000, 0x00003FFE //s[5] = +6.80648803710937500000e-01L
740 data8 0xAB05000000000000, 0x00003FFE //s[6] = +6.68045043945312500000e-01L
741 data8 0xA7AC000000000000, 0x00003FFE //s[7] = +6.54968261718750000000e-01L
742 data8 0xA478000000000000, 0x00003FFE //s[8] = +6.42456054687500000000e-01L
743 data8 0xA18D000000000000, 0x00003FFE //s[9] = +6.31057739257812500000e-01L
744 data8 0x9EF8000000000000, 0x00003FFE //s[10] = +6.20971679687500000000e-01L
745 data8 0x9CBA000000000000, 0x00003FFE //s[11] = +6.12213134765625000000e-01L
746 data8 0x9ACD000000000000, 0x00003FFE //s[12] = +6.04690551757812500000e-01L
747 data8 0x992A000000000000, 0x00003FFE //s[13] = +5.98297119140625000000e-01L
748 data8 0x97C7000000000000, 0x00003FFE //s[14] = +5.92880249023437500000e-01L
749 data8 0x969C000000000000, 0x00003FFE //s[15] = +5.88317871093750000000e-01L
750 data8 0x95A0000000000000, 0x00003FFE //s[16] = +5.84472656250000000000e-01L
751 data8 0x94CB000000000000, 0x00003FFE //s[17] = +5.81222534179687500000e-01L
752 data8 0x9419000000000000, 0x00003FFE //s[18] = +5.78506469726562500000e-01L
753 data8 0x9383000000000000, 0x00003FFE //s[19] = +5.76217651367187500000e-01L
754 data8 0x9305000000000000, 0x00003FFE //s[20] = +5.74295043945312500000e-01L
755 data8 0x929B000000000000, 0x00003FFE //s[21] = +5.72677612304687500000e-01L
756 data8 0x9242000000000000, 0x00003FFE //s[22] = +5.71319580078125000000e-01L
757 data8 0x91F8000000000000, 0x00003FFE //s[23] = +5.70190429687500000000e-01L
758 data8 0x91B9000000000000, 0x00003FFE //s[24] = +5.69229125976562500000e-01L
759 data8 0x9184000000000000, 0x00003FFE //s[25] = +5.68420410156250000000e-01L
760 data8 0x9158000000000000, 0x00003FFE //s[26] = +5.67749023437500000000e-01L
761 data8 0x9145000000000000, 0x00003FFE //s[27] = +5.67459106445312500000e-01L
762 LOCAL_OBJECT_END(erfc_s_table)
764 LOCAL_OBJECT_START(erfc_Q_table)
765 // Q(z)= (P(z)- S)/S
767 // Pol0
768 data8 0x98325D50F9DC3499, 0x0000BFAA //A0 = +3.07358861423101280650e-26L
769 data8 0xED35081A2494DDD9, 0x00003FF8 //A1 = +1.44779757616302832466e-02L
770 data8 0x9443549BCD0F94CE, 0x0000BFFD //A2 = -2.89576190966300084405e-01L
771 data8 0xC7FD4B98ECF3DBBF, 0x00003FFD //A3 = +3.90604364793467799170e-01L
772 data8 0xB82CE31288B49759, 0x0000BFFD //A4 = -3.59717460644199233866e-01L
773 data8 0x8A8293447BEF69B5, 0x00003FFD //A5 = +2.70527460203054582368e-01L
774 data8 0xB5793E30EE36766C, 0x0000BFFC //A6 = -1.77220317589265674647e-01L
775 data8 0xD6066D16BBDECE17, 0x00003FFB //A7 = +1.04504444366724593714e-01L
776 data8 0xE7C783CE3C997BD8, 0x0000BFFA //A8 = -5.65867565781331646771e-02L
777 data8 0xE9969EBC2F5B2828, 0x00003FF9 //A9 = +2.85142040533900194955e-02L
778 data8 0xDD31D619F29AD7BF, 0x0000BFF8 //A10 = -1.35006514390540367929e-02L
779 data8 0xC63A20EB59768F3A, 0x00003FF7 //A11 = +6.04940993680332271481e-03L
780 data8 0xA8DEC641AACEB600, 0x0000BFF6 //A12 = -2.57675495383156581601e-03L
781 data8 0x87F0E77BA914FBEB, 0x00003FF5 //A13 = +1.03714776726541296794e-03L
782 data8 0xC306C2894C5CEF2D, 0x0000BFF3 //A14 = -3.71983348634136412407e-04L
783 data8 0xBDAB416A989D0697, 0x00003FF1 //A15 = +9.04412111877987292294e-05L
784 // Pol1
785 data8 0x82808893DA2DD83F, 0x00003FEE //A0 = +7.77853035974467145290e-06L
786 data8 0xAE9CD9DCADC86113, 0x0000BFFB //A1 = -8.52601070853077921197e-02L
787 data8 0x9D429743E312AD9F, 0x0000BFFB //A2 = -7.67871682732076080494e-02L
788 data8 0x8637FC533AE805DC, 0x00003FFC //A3 = +1.31072943286859831330e-01L
789 data8 0xF68DBE3639ABCB6E, 0x0000BFFB //A4 = -1.20387540845703264588e-01L
790 data8 0xB168FFC3CFA71256, 0x00003FFB //A5 = +8.66260511047190247534e-02L
791 data8 0xDBC5078A7EA89236, 0x0000BFFA //A6 = -5.36546988077281230848e-02L
792 data8 0xF4331FEDB2CB838F, 0x00003FF9 //A7 = +2.98095344165515989564e-02L
793 data8 0xF909173C0E61C25D, 0x0000BFF8 //A8 = -1.51999213123642373375e-02L
794 data8 0xEC83560A2ACB23E9, 0x00003FF7 //A9 = +7.21780491979582106904e-03L
795 data8 0xD350D62C4FEAD8F5, 0x0000BFF6 //A10 = -3.22442272982896360044e-03L
796 data8 0xB2F44F4B3FD9B826, 0x00003FF5 //A11 = +1.36531322425499451283e-03L
797 data8 0x9078BC61927671C6, 0x0000BFF4 //A12 = -5.51115510818844954547e-04L
798 data8 0xDF67AC6287A63B03, 0x00003FF2 //A13 = +2.13055585989529858265e-04L
799 data8 0xA719CFEE67FCE1CE, 0x0000BFF1 //A14 = -7.96798844477905965933e-05L
800 data8 0xEF926367BABBB029, 0x00003FEF //A15 = +2.85591875675765038065e-05L
801 // Pol2
802 data8 0x82B5E5A93B059C50, 0x00003FEF //A0 = +1.55819100856330860049e-05L
803 data8 0xDC856BC2542B1938, 0x0000BFFB //A1 = -1.07676355235999875911e-01L
804 data8 0xDF225EF5694F14AE, 0x0000BFF8 //A2 = -1.36190345125628043277e-02L
805 data8 0xDAF66A954ED22428, 0x00003FFA //A3 = +5.34576571853233908886e-02L
806 data8 0xD28AE4F21A392EC6, 0x0000BFFA //A4 = -5.14019911949062230820e-02L
807 data8 0x9441A95713F0DB5B, 0x00003FFA //A5 = +3.61954321717769771045e-02L
808 data8 0xB0957B5C483C7A04, 0x0000BFF9 //A6 = -2.15556535133667988704e-02L
809 data8 0xBB9260E812814F71, 0x00003FF8 //A7 = +1.14484735825400480057e-02L
810 data8 0xB68AB17287ABAB04, 0x0000BFF7 //A8 = -5.57073273108465072470e-03L
811 data8 0xA56A95E0BC0EF01B, 0x00003FF6 //A9 = +2.52405318381952650677e-03L
812 data8 0x8D19C7D286839C00, 0x0000BFF5 //A10 = -1.07651294935087466892e-03L
813 data8 0xE45DB3766711A0D3, 0x00003FF3 //A11 = +4.35573615323234291196e-04L
814 data8 0xB05949F947FA7AEF, 0x0000BFF2 //A12 = -1.68179306983868501372e-04L
815 data8 0x82901D055A0D5CB6, 0x00003FF1 //A13 = +6.22572626227726684168e-05L
816 data8 0xBB957698542D6FD0, 0x0000BFEF //A14 = -2.23617364009159182821e-05L
817 data8 0x810740E1DF572394, 0x00003FEE //A15 = +7.69068800065192940487e-06L
818 // Pol3
819 data8 0x9526D1C87655AFA8, 0x00003FEC //A0 = +2.22253260814242012255e-06L
820 data8 0xA47E21EBFE73F72F, 0x0000BFF8 //A1 = -1.00398379581527733314e-02L
821 data8 0xDE65685FCDF7A913, 0x0000BFFA //A2 = -5.42959286802879105148e-02L
822 data8 0xED289CB8F97D4860, 0x00003FFA //A3 = +5.79000589346770417248e-02L
823 data8 0xAA3100D5A7D870F1, 0x0000BFFA //A4 = -4.15506394006027604387e-02L
824 data8 0xCA0567032C5308C0, 0x00003FF9 //A5 = +2.46607791863290331169e-02L
825 data8 0xD3E1794A50F31BEB, 0x0000BFF8 //A6 = -1.29321751094401754013e-02L
826 data8 0xCAA02CB4C87CC1F0, 0x00003FF7 //A7 = +6.18364508551740736863e-03L
827 data8 0xB3F126AF16B121F2, 0x0000BFF6 //A8 = -2.74569696838501870748e-03L
828 data8 0x962B2D64D3900510, 0x00003FF5 //A9 = +1.14569596409019883022e-03L
829 data8 0xED8785714A9A00FB, 0x0000BFF3 //A10 = -4.53051338046340380512e-04L
830 data8 0xB325DA4515D8B54C, 0x00003FF2 //A11 = +1.70848714622328427290e-04L
831 data8 0x8179C36354571747, 0x0000BFF1 //A12 = -6.17387951061077132522e-05L
832 data8 0xB40F241C01C907E9, 0x00003FEF //A13 = +2.14647227210702861416e-05L
833 data8 0xF436D84AD7D4D316, 0x0000BFED //A14 = -7.27815144835213913238e-06L
834 data8 0x9EB432503FB0B7BC, 0x00003FEC //A15 = +2.36487228755136968792e-06L
835 // Pol4
836 data8 0xE0BA539E4AFC4741, 0x00003FED //A0 = +6.69741148991838024429e-06L
837 data8 0x8583BF71139452CF, 0x0000BFFA //A1 = -3.25963476363756051657e-02L
838 data8 0x8384FEF6D08AD6CE, 0x0000BFF9 //A2 = -1.60546283500634200479e-02L
839 data8 0xB1E67DFB84C97036, 0x00003FF9 //A3 = +2.17163525195697635702e-02L
840 data8 0xFB6ACEE6899E360D, 0x0000BFF8 //A4 = -1.53452892792759316229e-02L
841 data8 0x8D2B869EB9149905, 0x00003FF8 //A5 = +8.61633440480716870830e-03L
842 data8 0x8A90BFE0FD869A41, 0x0000BFF7 //A6 = -4.22868126950622376530e-03L
843 data8 0xF7536A76E59F54D2, 0x00003FF5 //A7 = +1.88694643606912107006e-03L
844 data8 0xCCF6FE58C16E1CC7, 0x0000BFF4 //A8 = -7.81878732767742447339e-04L
845 data8 0x9FCC6ED9914FAA24, 0x00003FF3 //A9 = +3.04791577214885118730e-04L
846 data8 0xEC7F5AAACAE593E8, 0x0000BFF1 //A10 = -1.12770784960291779798e-04L
847 data8 0xA72CE628A114C940, 0x00003FF0 //A11 = +3.98577182157456408782e-05L
848 data8 0xE2DCC5750FD769BA, 0x0000BFEE //A12 = -1.35220520471857266339e-05L
849 data8 0x9459160B1E6F1F8D, 0x00003FED //A13 = +4.42111470121432700283e-06L
850 data8 0xBE0A05701BD0DD42, 0x0000BFEB //A14 = -1.41590196994052764542e-06L
851 data8 0xE905D729105081BF, 0x00003FE9 //A15 = +4.34038814785401120999e-07L
852 // Pol5
853 data8 0xA33649C3AB459832, 0x00003FEE //A0 = +9.72819704141525206634e-06L
854 data8 0x9E4EA2F44C9A24BD, 0x0000BFFA //A1 = -3.86492123987296806210e-02L
855 data8 0xE80C0B1280F357BF, 0x0000BFF2 //A2 = -2.21297306012713370124e-04L
856 data8 0xDAECCE90A4D45D9A, 0x00003FF7 //A3 = +6.68106161291482829670e-03L
857 data8 0xA4006572071BDD4B, 0x0000BFF7 //A4 = -5.00493005170532147076e-03L
858 data8 0xB07FD7EB1F4D8E8E, 0x00003FF6 //A5 = +2.69316693731732554959e-03L
859 data8 0xA1F471D42ADD73A1, 0x0000BFF5 //A6 = -1.23561753760779610478e-03L
860 data8 0x8611D0ED1B4C8176, 0x00003FF4 //A7 = +5.11434914439322741260e-04L
861 data8 0xCDADB789B487A541, 0x0000BFF2 //A8 = -1.96150380913036018825e-04L
862 data8 0x9470252731687FEE, 0x00003FF1 //A9 = +7.07807859951401721129e-05L
863 data8 0xCB9399AD1C376D85, 0x0000BFEF //A10 = -2.42682175234436724152e-05L
864 data8 0x858D815F9CA0A9F7, 0x00003FEE //A11 = +7.96036454038012144300e-06L
865 data8 0xA878D338E6E6A079, 0x0000BFEC //A12 = -2.51042802626063073967e-06L
866 data8 0xCD2C2F079D2FCB36, 0x00003FEA //A13 = +7.64327468786076941271e-07L
867 data8 0xF5EF4A4B2EA426F2, 0x0000BFE8 //A14 = -2.29044563492386125272e-07L
868 data8 0x8CE52181393820FC, 0x00003FE7 //A15 = +6.56093668622712763489e-08L
869 // Pol6
870 data8 0xB2015D7F1864B7CF, 0x00003FEC //A0 = +2.65248615880090351276e-06L
871 data8 0x954EA7A861B4462A, 0x0000BFFA //A1 = -3.64519642954351295215e-02L
872 data8 0x9E46F2A4D9157E69, 0x00003FF7 //A2 = +4.83023498390681965101e-03L
873 data8 0xA0D12B422FFD5BAD, 0x00003FF5 //A3 = +1.22693684633643883352e-03L
874 data8 0xB291D16A560A740E, 0x0000BFF5 //A4 = -1.36237794246703606647e-03L
875 data8 0xC138941BC8AF4A9D, 0x00003FF4 //A5 = +7.37079658343628747256e-04L
876 data8 0xA761669D61B405CF, 0x0000BFF3 //A6 = -3.19252914480518163396e-04L
877 data8 0x8053680F1C84607E, 0x00003FF2 //A7 = +1.22381025852939439541e-04L
878 data8 0xB518F4B6F25015F9, 0x0000BFF0 //A8 = -4.31770048258291369742e-05L
879 data8 0xEFF526AC70B9411E, 0x00003FEE //A9 = +1.43025887824433324525e-05L
880 data8 0x970B2A848DF5B5C2, 0x0000BFED //A10 = -4.50145058393497252604e-06L
881 data8 0xB614D2E61DB86963, 0x00003FEB //A11 = +1.35661172167726780059e-06L
882 data8 0xD34EA4D283EC33FA, 0x0000BFE9 //A12 = -3.93590335713880681528e-07L
883 data8 0xED209EBD68E1145F, 0x00003FE7 //A13 = +1.10421060667544991323e-07L
884 data8 0x83A126E22A17568D, 0x0000BFE6 //A14 = -3.06473811074239684132e-08L
885 data8 0x8B778496EDE9F415, 0x00003FE4 //A15 = +8.11804009754249175736e-09L
886 // Pol7
887 data8 0x8E152F522501B7B9, 0x00003FEE //A0 = +8.46879203970927626532e-06L
888 data8 0xFD22F92EE21F491E, 0x0000BFF9 //A1 = -3.09004656656418947425e-02L
889 data8 0xAF0C41847D89EC14, 0x00003FF7 //A2 = +5.34203719233189217519e-03L
890 data8 0xB7C539C400445956, 0x0000BFF3 //A3 = -3.50514245383356287965e-04L
891 data8 0x8428C78B2B1E3622, 0x0000BFF3 //A4 = -2.52073850239006530978e-04L
892 data8 0xAFC0CCC7D1A05F5B, 0x00003FF2 //A5 = +1.67611241057491801028e-04L
893 data8 0x95DC7272C5695A5A, 0x0000BFF1 //A6 = -7.14593512262564106636e-05L
894 data8 0xD6FCA68A61F0E835, 0x00003FEF //A7 = +2.56284375437771117850e-05L
895 data8 0x8B71C74DEA936C66, 0x0000BFEE //A8 = -8.31153675277218441096e-06L
896 data8 0xA8AC71E2A56AA2C9, 0x00003FEC //A9 = +2.51343269277107451413e-06L
897 data8 0xC15DED6C44B46046, 0x0000BFEA //A10 = -7.20347851650066610771e-07L
898 data8 0xD42BA1DFBD1277AC, 0x00003FE8 //A11 = +1.97599119274780745741e-07L
899 data8 0xE03A81F2C976D11A, 0x0000BFE6 //A12 = -5.22072765405802337371e-08L
900 data8 0xE56A19A67DD66100, 0x00003FE4 //A13 = +1.33536787408751203998e-08L
901 data8 0xE964D255CB31DFFA, 0x0000BFE2 //A14 = -3.39632729387679010008e-09L
902 data8 0xE22E62E932B704D4, 0x00003FE0 //A15 = +8.22842400379225526299e-10L
903 // Pol8
904 data8 0xB8B835882D46A6C8, 0x00003FEF //A0 = +2.20202883282415435401e-05L
905 data8 0xC9D1F63F89B74E90, 0x0000BFF9 //A1 = -2.46362504515706189782e-02L
906 data8 0x8E376748B1274F30, 0x00003FF7 //A2 = +4.34010070001387441657e-03L
907 data8 0x98174C7EA49B5B37, 0x0000BFF4 //A3 = -5.80181163659971286762e-04L
908 data8 0x8D2C40506AE9FF97, 0x00003FEF //A4 = +1.68291159100251734927e-05L
909 data8 0xD9A580C115B9D150, 0x00003FEF //A5 = +2.59454841475194555896e-05L
910 data8 0xDB35B21F1C3F99CE, 0x0000BFEE //A6 = -1.30659192305072674545e-05L
911 data8 0x99FAADAE17A3050E, 0x00003FED //A7 = +4.58893813631592314881e-06L
912 data8 0xBA1D259BCD6987A9, 0x0000BFEB //A8 = -1.38665627771423394637e-06L
913 data8 0xCDD7FF5BEA0145C2, 0x00003FE9 //A9 = +3.83413844219813384124e-07L
914 data8 0xD60857176CE6AB9D, 0x0000BFE7 //A10 = -9.96666862214499946343e-08L
915 data8 0xD446A2402112DF4C, 0x00003FE5 //A11 = +2.47121687566658908126e-08L
916 data8 0xCA87133235F1F495, 0x0000BFE3 //A12 = -5.89433000014933371980e-09L
917 data8 0xBB15B0021581C8B6, 0x00003FE1 //A13 = +1.36122047057936849125e-09L
918 data8 0xAC9D6585D4AF505E, 0x0000BFDF //A14 = -3.13984547328132268695e-10L
919 data8 0x975A1439C3795183, 0x00003FDD //A15 = +6.88268624429648826457e-11L
920 // Pol9
921 data8 0x99A7676284CDC9FE, 0x00003FEF //A0 = +1.83169747921764176475e-05L
922 data8 0x9AD0AE249A02896C, 0x0000BFF9 //A1 = -1.88983346204739151909e-02L
923 data8 0xCB89B4AEC19898BE, 0x00003FF6 //A2 = +3.10574208447745576452e-03L
924 data8 0xEBBC47E30E1AC2C2, 0x0000BFF3 //A3 = -4.49629730048297442064e-04L
925 data8 0xD1E35B7FCE1CF859, 0x00003FF0 //A4 = +5.00412261289558493438e-05L
926 data8 0xB40743664EF24552, 0x0000BFEB //A5 = -1.34131589671166307319e-06L
927 data8 0xCAD2F5C596FFE1B4, 0x0000BFEB //A6 = -1.51115702599728593837e-06L
928 data8 0xAE42B6D069DFDDF2, 0x00003FEA //A7 = +6.49171330116787223873e-07L
929 data8 0xD0739A05BB43A714, 0x0000BFE8 //A8 = -1.94135651872623440782e-07L
930 data8 0xD745B854AB601BD7, 0x00003FE6 //A9 = +5.01219983943456578062e-08L
931 data8 0xCC4066E13E338B13, 0x0000BFE4 //A10 = -1.18890061172430768892e-08L
932 data8 0xB6EAADB55A6C3CB4, 0x00003FE2 //A11 = +2.66178850259168707794e-09L
933 data8 0x9CC6C178AD3F96AD, 0x0000BFE0 //A12 = -5.70349182959704086428e-10L
934 data8 0x81D0E2AA27DEB74A, 0x00003FDE //A13 = +1.18066926578104076645e-10L
935 data8 0xD75FB9049190BEFD, 0x0000BFDB //A14 = -2.44851795398843967972e-11L
936 data8 0xA9384A51D48C8703, 0x00003FD9 //A15 = +4.80951837368635202609e-12L
937 // Pol10
938 data8 0xD2B3482EE449C535, 0x00003FEE //A0 = +1.25587177382575655080e-05L
939 data8 0xE7939B2D0607DFCF, 0x0000BFF8 //A1 = -1.41343131436717436429e-02L
940 data8 0x8810EB4AC5F0F1CE, 0x00003FF6 //A2 = +2.07620377002350121270e-03L
941 data8 0x9546589602AEB955, 0x0000BFF3 //A3 = -2.84719065122144294949e-04L
942 data8 0x9333434342229798, 0x00003FF0 //A4 = +3.50952732796136549298e-05L
943 data8 0xEB36A98FD81D3DEB, 0x0000BFEC //A5 = -3.50495464815398722482e-06L
944 data8 0xAC370EFA025D0477, 0x00003FE8 //A6 = +1.60387784498518639254e-07L
945 data8 0xC8DF7F8ACA099426, 0x00003FE6 //A7 = +4.67693991699936842330e-08L
946 data8 0xAC694AD4921C02CF, 0x0000BFE5 //A8 = -2.00713167514877937714e-08L
947 data8 0xB6E29F2FDE2D8C1A, 0x00003FE3 //A9 = +5.32266106167252495164e-09L
948 data8 0xA41F8EEA75474358, 0x0000BFE1 //A10 = -1.19415398856537468324e-09L
949 data8 0x869D778A1C56D3D6, 0x00003FDF //A11 = +2.44863450057778470469e-10L
950 data8 0xD02658BF31411F4C, 0x0000BFDC //A12 = -4.73277831746128372261e-11L
951 data8 0x9A4A95EE59127779, 0x00003FDA //A13 = +8.77044784978207256260e-12L
952 data8 0xE518330AF013C2F6, 0x0000BFD7 //A14 = -1.62781453276882333209e-12L
953 data8 0xA036A9DF71BD108A, 0x00003FD5 //A15 = +2.84596398987114375607e-13L
954 // Pol11
955 data8 0x9191CFBF001F3BB3, 0x00003FEE //A0 = +8.67662287973472452343e-06L
956 data8 0xAA47E0CF01AE9730, 0x0000BFF8 //A1 = -1.03931136509584404513e-02L
957 data8 0xAEABE7F17B01D18F, 0x00003FF5 //A2 = +1.33263784731775399430e-03L
958 data8 0xAC0D6A309D04E5DB, 0x0000BFF2 //A3 = -1.64081956462118568288e-04L
959 data8 0xA08357DF458054D0, 0x00003FEF //A4 = +1.91346477952797715021e-05L
960 data8 0x8A1596B557440FE0, 0x0000BFEC //A5 = -2.05761687274453412571e-06L
961 data8 0xCDA0EAE0A5615E9A, 0x00003FE8 //A6 = +1.91506542215670149741e-07L
962 data8 0xD36A08FB4E104F9A, 0x0000BFE4 //A7 = -1.23059260396551086769e-08L
963 data8 0xD7433F91E78A7A11, 0x0000BFDF //A8 = -3.91560549815575091188e-10L
964 data8 0xC2F5308FD4F5CE62, 0x00003FDF //A9 = +3.54626121852421163117e-10L
965 data8 0xC83876915F49D630, 0x0000BFDD //A10 = -9.10497688901018285126e-11L
966 data8 0xA11C605DEAE1FE9C, 0x00003FDB //A11 = +1.83161825409194847892e-11L
967 data8 0xE7977BC1342D19BF, 0x0000BFD8 //A12 = -3.29111645807102123274e-12L
968 data8 0x9BC3A7D6396C6756, 0x00003FD6 //A13 = +5.53385887288503961220e-13L
969 data8 0xD0110D5683740B8C, 0x0000BFD3 //A14 = -9.24001363293241428519e-14L
970 data8 0x81786D7856A5CC92, 0x00003FD1 //A15 = +1.43741041714595023996e-14L
971 // Pol12
972 data8 0xB85654F6033B3372, 0x00003FEF //A0 = +2.19747106911869287049e-05L
973 data8 0xF78B40078736B406, 0x0000BFF7 //A1 = -7.55444170413862312647e-03L
974 data8 0xDA8FDE84D88E5D5D, 0x00003FF4 //A2 = +8.33747822263358628569e-04L
975 data8 0xBC2D3F3891721AA9, 0x0000BFF1 //A3 = -8.97296647669960333635e-05L
976 data8 0x9D15ACFD3BF50064, 0x00003FEE //A4 = +9.36297600601039610762e-06L
977 data8 0xFBED3D03F3C1B671, 0x0000BFEA //A5 = -9.38500137149172923985e-07L
978 data8 0xBEE615E3B2FA16C8, 0x00003FE7 //A6 = +8.88941676851808958175e-08L
979 data8 0x843D32692CF5662A, 0x0000BFE4 //A7 = -7.69732580860195238520e-09L
980 data8 0x99E74472FD94E22B, 0x00003FE0 //A8 = +5.59897264617128952416e-10L
981 data8 0xCEF63DABF4C32E15, 0x0000BFDB //A9 = -2.35288414996279313219e-11L
982 data8 0xA2D86C25C0991123, 0x0000BFD8 //A10 = -2.31417232327307408235e-12L
983 data8 0xF50C1B31D2E922BD, 0x00003FD6 //A11 = +8.70582858983364191159e-13L
984 data8 0xC0F093DEC2B019A1, 0x0000BFD4 //A12 = -1.71364927865227509533e-13L
985 data8 0xFC1441C4CD105981, 0x00003FD1 //A13 = +2.79864052545369490865e-14L
986 data8 0x9CC959853267F026, 0x0000BFCF //A14 = -4.35170017302700609509e-15L
987 data8 0xB06BA14016154F1E, 0x00003FCC //A15 = +6.12081320471295704631e-16L
988 // Pol13
989 data8 0xA59E74BF544F2422, 0x00003FEF //A0 = +1.97433196215210145261e-05L
990 data8 0xB2814F4EDAE15330, 0x0000BFF7 //A1 = -5.44754383528015875700e-03L
991 data8 0x867C249D378F0A23, 0x00003FF4 //A2 = +5.13019308804593120161e-04L
992 data8 0xC76644393388AB68, 0x0000BFF0 //A3 = -4.75405403392600215101e-05L
993 data8 0x91143AD5CCA229FE, 0x00003FED //A4 = +4.32369180778264703719e-06L
994 data8 0xCE6A11FB6840A974, 0x0000BFE9 //A5 = -3.84476663329551178495e-07L
995 data8 0x8EC29F66C59DE243, 0x00003FE6 //A6 = +3.32389596787155456596e-08L
996 data8 0xBE3FCDDCA94CA24E, 0x0000BFE2 //A7 = -2.76849073931513325199e-09L
997 data8 0xF06A84BDC70A0B0D, 0x00003FDE //A8 = +2.18657158231304988330e-10L
998 data8 0x8B8E6969D056D124, 0x0000BFDB //A9 = -1.58657139740906811035e-11L
999 data8 0x8984985AA29A0567, 0x00003FD7 //A10 = +9.77123802231106533829e-13L
1000 data8 0xA53ABA084300137C, 0x0000BFD2 //A11 = -3.66882970952892030306e-14L
1001 data8 0xA90EC851E91C3319, 0x0000BFCE //A12 = -2.34614750044359490986e-15L
1002 data8 0xEC9CAF64237B5060, 0x00003FCC //A13 = +8.20912960028437475035e-16L
1003 data8 0xA9156668FCF01479, 0x0000BFCA //A14 = -1.46656639874123613261e-16L
1004 data8 0xBAEF58D8118DD5D4, 0x00003FC7 //A15 = +2.02675278255254907493e-17L
1005 // Pol14
1006 data8 0xC698952E9CEAA800, 0x00003FEF //A0 = +2.36744912073515619263e-05L
1007 data8 0x800395F8C7B4FA00, 0x0000BFF7 //A1 = -3.90667746392883642897e-03L
1008 data8 0xA3B2467B6B391831, 0x00003FF3 //A2 = +3.12226081793919541155e-04L
1009 data8 0xCF2061122A69D72B, 0x0000BFEF //A3 = -2.46914006692526122176e-05L
1010 data8 0x817FAB6B5DEB9924, 0x00003FEC //A4 = +1.92968114320180123521e-06L
1011 data8 0x9FC190F5827740E7, 0x0000BFE8 //A5 = -1.48784479265231093475e-07L
1012 data8 0xC1FE5C1835C8AFCD, 0x00003FE4 //A6 = +1.12919132662720380018e-08L
1013 data8 0xE7216A9FBB204DA3, 0x0000BFE0 //A7 = -8.40847981461949000003e-10L
1014 data8 0x867566ED95C5C64F, 0x00003FDD //A8 = +6.11446929759298780795e-11L
1015 data8 0x97A8BFA723F0F014, 0x0000BFD9 //A9 = -4.31041298699752869577e-12L
1016 data8 0xA3D24B7034984522, 0x00003FD5 //A10 = +2.91005377301348717042e-13L
1017 data8 0xA5AAA371C22F3741, 0x0000BFD1 //A11 = -1.83926825395757259128e-14L
1018 data8 0x95352E5597EACC23, 0x00003FCD //A12 = +1.03533666540077850452e-15L
1019 data8 0xCCEBE3043B689428, 0x0000BFC8 //A13 = -4.44352525147076912166e-17L
1020 data8 0xA779DAB4BE1F80BB, 0x0000BFBC //A14 = -8.86610526981738255206e-21L
1021 data8 0xB171271F3517282C, 0x00003FC1 //A15 = +3.00598445879282370850e-19L
1022 // Pol15
1023 data8 0xB7AC727D1C3FEB05, 0x00003FEE //A0 = +1.09478009914822049780e-05L
1024 data8 0xB6E6274485C10B0A, 0x0000BFF6 //A1 = -2.79081782038927199588e-03L
1025 data8 0xC5CAE2122D009506, 0x00003FF2 //A2 = +1.88629638738336219173e-04L
1026 data8 0xD466E7957D0A3362, 0x0000BFEE //A3 = -1.26601440424012313479e-05L
1027 data8 0xE2593D798DA20E2E, 0x00003FEA //A4 = +8.43214222346512003230e-07L
1028 data8 0xEF2D2BBA7D2882CC, 0x0000BFE6 //A5 = -5.56876064495961858535e-08L
1029 data8 0xFA5819BB4AE974C2, 0x00003FE2 //A6 = +3.64298674151704370449e-09L
1030 data8 0x819BB0CE825FBB28, 0x0000BFDF //A7 = -2.35755881668932259913e-10L
1031 data8 0x84871099BF728B8F, 0x00003FDB //A8 = +1.50666434199945890414e-11L
1032 data8 0x858188962DFEBC9F, 0x0000BFD7 //A9 = -9.48617116568458677088e-13L
1033 data8 0x840F38FF2FBAE753, 0x00003FD3 //A10 = +5.86461827778372616657e-14L
1034 data8 0xFF47EAF69577B213, 0x0000BFCE //A11 = -3.54273456410181081472e-15L
1035 data8 0xEF402CCB4D29FAF8, 0x00003FCA //A12 = +2.07516888659313950588e-16L
1036 data8 0xD6B789E01141231B, 0x0000BFC6 //A13 = -1.16398290506765191078e-17L
1037 data8 0xB5EEE343E9CFE3EC, 0x00003FC2 //A14 = +6.16413506924643419723e-19L
1038 data8 0x859B41A39D600346, 0x0000BFBE //A15 = -2.82922705825870414438e-20L
1039 // Pol16
1040 data8 0x85708B69FD184E11, 0x00003FED //A0 = +3.97681079176353356199e-06L
1041 data8 0x824D92BC60A1F70A, 0x0000BFF6 //A1 = -1.98826630037499070532e-03L
1042 data8 0xEDCF7D3576BB5258, 0x00003FF1 //A2 = +1.13396885054265675352e-04L
1043 data8 0xD7FC59226A947CDF, 0x0000BFED //A3 = -6.43687650810478871875e-06L
1044 data8 0xC32C51B574E2651E, 0x00003FE9 //A4 = +3.63538268539251809118e-07L
1045 data8 0xAF67910F5681401F, 0x0000BFE5 //A5 = -2.04197779750247395258e-08L
1046 data8 0x9CB3E8D7DCD1EA9D, 0x00003FE1 //A6 = +1.14016272459029850306e-09L
1047 data8 0x8B14ECFBF7D4F114, 0x0000BFDD //A7 = -6.32470533185766848692e-11L
1048 data8 0xF518253AE4A3AE72, 0x00003FD8 //A8 = +3.48299974583453268369e-12L
1049 data8 0xD631A5699AA2F334, 0x0000BFD4 //A9 = -1.90242426474085078079e-13L
1050 data8 0xB971AD4C30C56E5D, 0x00003FD0 //A10 = +1.02942127356740047925e-14L
1051 data8 0x9ED0065A601F3160, 0x0000BFCC //A11 = -5.50991880383698965959e-16L
1052 data8 0x863A04008E12867C, 0x00003FC8 //A12 = +2.91057593756148904838e-17L
1053 data8 0xDF62F9F44F5C7170, 0x0000BFC3 //A13 = -1.51372666097522872780e-18L
1054 data8 0xBA4E118E88CFDD31, 0x00003FBF //A14 = +7.89032177282079635722e-20L
1055 data8 0x942AD897FC4D2F2A, 0x0000BFBB //A15 = -3.92195756076319409245e-21L
1056 // Pol17
1057 data8 0xCB8514540566C717, 0x00003FEF //A0 = +2.42614557068144130848e-05L
1058 data8 0xB94F08D6816E0CD4, 0x0000BFF5 //A1 = -1.41379340061829929314e-03L
1059 data8 0x8E7C342C2DABB51B, 0x00003FF1 //A2 = +6.79422240687700109911e-05L
1060 data8 0xDA69DAFF71E30D5B, 0x0000BFEC //A3 = -3.25461473899657142468e-06L
1061 data8 0xA6D5B2DB69B4B3F6, 0x00003FE8 //A4 = +1.55376978584082701045e-07L
1062 data8 0xFDF4F76BC1D1BD47, 0x0000BFE3 //A5 = -7.39111857092131684572e-09L
1063 data8 0xC08BC52C95B12C2D, 0x00003FDF //A6 = +3.50239092565793882444e-10L
1064 data8 0x91624BF6D3A3F6C9, 0x0000BFDB //A7 = -1.65282439890232458821e-11L
1065 data8 0xDA91F7A450DE4270, 0x00003FD6 //A8 = +7.76517285902715940501e-13L
1066 data8 0xA380ADF55416E624, 0x0000BFD2 //A9 = -3.63048822989374426852e-14L
1067 data8 0xF350FC0CEDEE0FD6, 0x00003FCD //A10 = +1.68834630987974622269e-15L
1068 data8 0xB3FA19FBDC8F023C, 0x0000BFC9 //A11 = -7.80525639701804380489e-17L
1069 data8 0x8435328C80940126, 0x00003FC5 //A12 = +3.58349966898667910204e-18L
1070 data8 0xC0D22F655BA5EF39, 0x0000BFC0 //A13 = -1.63325770165403860181e-19L
1071 data8 0x8F14B9EBD5A9AB25, 0x00003FBC //A14 = +7.57464305512080733773e-21L
1072 data8 0xCD4804BBF6DC1B6F, 0x0000BFB7 //A15 = -3.39609459750208886298e-22L
1073 // Pol18
1074 data8 0xE251DFE45AB0C22E, 0x00003FEE //A0 = +1.34897126299700418200e-05L
1075 data8 0x83943CC7D59D4215, 0x0000BFF5 //A1 = -1.00386850310061655307e-03L
1076 data8 0xAA57896951134BCA, 0x00003FF0 //A2 = +4.06126834109940757047e-05L
1077 data8 0xDC0A67051E1C4A2C, 0x0000BFEB //A3 = -1.63943048164477430317e-06L
1078 data8 0x8DCB3C0A8CD07BBE, 0x00003FE7 //A4 = +6.60279229777753829876e-08L
1079 data8 0xB64DE81C24F7F265, 0x0000BFE2 //A5 = -2.65287705357477481067e-09L
1080 data8 0xE9CBB7A990DBA8B5, 0x00003FDD //A6 = +1.06318007608620426224e-10L
1081 data8 0x9583D4B85C2ADC6F, 0x0000BFD9 //A7 = -4.24947087941505088222e-12L
1082 data8 0xBEB0EE8114EEDF77, 0x00003FD4 //A8 = +1.69367754741562774916e-13L
1083 data8 0xF2791BB8F06BDA93, 0x0000BFCF //A9 = -6.72997988617021128704e-15L
1084 data8 0x99A907F6A92195B4, 0x00003FCB //A10 = +2.66558091161711891239e-16L
1085 data8 0xC213E5E6F833BB93, 0x0000BFC6 //A11 = -1.05209746502719578617e-17L
1086 data8 0xF41FBBA6B343960F, 0x00003FC1 //A12 = +4.13562069721140021224e-19L
1087 data8 0x98F194AEE31D188D, 0x0000BFBD //A13 = -1.61935414722333263347e-20L
1088 data8 0xC42F5029BB622157, 0x00003FB8 //A14 = +6.49121108201931196678e-22L
1089 data8 0xF43BD08079E50E0F, 0x0000BFB3 //A15 = -2.52531675510242468317e-23L
1090 // Pol19
1091 data8 0x82557B149A04D08E, 0x00003FEF //A0 = +1.55370127331027842820e-05L
1092 data8 0xBAAB433307CE614B, 0x0000BFF4 //A1 = -7.12085701486669872724e-04L
1093 data8 0xCB52D9DBAC16FE82, 0x00003FEF //A2 = +2.42380662859334411743e-05L
1094 data8 0xDD214359DBBCE7D1, 0x0000BFEA //A3 = -8.23773197624244883859e-07L
1095 data8 0xF01E8E968139524C, 0x00003FE5 //A4 = +2.79535729459988509676e-08L
1096 data8 0x82286A057E0916CE, 0x0000BFE1 //A5 = -9.47023128967039348510e-10L
1097 data8 0x8CDDDC4E8D013365, 0x00003FDC //A6 = +3.20293663356974901319e-11L
1098 data8 0x982FEEE90D4E8751, 0x0000BFD7 //A7 = -1.08135537312234452657e-12L
1099 data8 0xA41D1E84083B8FD6, 0x00003FD2 //A8 = +3.64405720894915411836e-14L
1100 data8 0xB0A1B6111B72E159, 0x0000BFCD //A9 = -1.22562851790685744085e-15L
1101 data8 0xBDB77DE6B650FFA2, 0x00003FC8 //A10 = +4.11382657214908334175e-17L
1102 data8 0xCB54E95CDB66978A, 0x0000BFC3 //A11 = -1.37782909696752432371e-18L
1103 data8 0xD959E428A62B1B6C, 0x00003FBE //A12 = +4.60258936838597812582e-20L
1104 data8 0xE7D49EC23F1A16A0, 0x0000BFB9 //A13 = -1.53412587409583783059e-21L
1105 data8 0xFDE429BC9947B2BE, 0x00003FB4 //A14 = +5.25034823750902928092e-23L
1106 data8 0x872137A062C042EF, 0x0000BFB0 //A15 = -1.74651114923000080365e-24L
1107 // Pol20
1108 data8 0x8B9B185C6A2659AC, 0x00003FEF //A0 = +1.66423130594825442963e-05L
1109 data8 0x84503AD52588A1E8, 0x0000BFF4 //A1 = -5.04735556466270303549e-04L
1110 data8 0xF26C7C2B566388E1, 0x00003FEE //A2 = +1.44495826764677427386e-05L
1111 data8 0xDDDA15FEE262BB47, 0x0000BFE9 //A3 = -4.13231361893675488873e-07L
1112 data8 0xCACEBC73C90C2FE0, 0x00003FE4 //A4 = +1.18049538609157282958e-08L
1113 data8 0xB9314D00022B41DD, 0x0000BFDF //A5 = -3.36863342776746896664e-10L
1114 data8 0xA8E9FBDC714638B9, 0x00003FDA //A6 = +9.60164921624768038366e-12L
1115 data8 0x99E246C0CC8CA6F6, 0x0000BFD5 //A7 = -2.73352704217713596798e-13L
1116 data8 0x8C04E7B5DF372EA1, 0x00003FD0 //A8 = +7.77262480048865685174e-15L
1117 data8 0xFE7B90CAA0B6D5F7, 0x0000BFCA //A9 = -2.20728537958846147109e-16L
1118 data8 0xE6F40BAD4EC6CB4F, 0x00003FC5 //A10 = +6.26000182616999972048e-18L
1119 data8 0xD14F4E0538F0F992, 0x0000BFC0 //A11 = -1.77292283439752259258e-19L
1120 data8 0xBD5A7FAA548CC749, 0x00003FBB //A12 = +5.01214569023722089225e-21L
1121 data8 0xAB15D69425373A67, 0x0000BFB6 //A13 = -1.41518447770061562822e-22L
1122 data8 0x9EF95456F75B4DF4, 0x00003FB1 //A14 = +4.10938011540250142351e-24L
1123 data8 0x8FADCC45E81433E7, 0x0000BFAC //A15 = -1.16062889679749879834e-25L
1124 // Pol21
1125 data8 0xB47A917B0F7B50AE, 0x00003FEF //A0 = +2.15147474240529518138e-05L
1126 data8 0xBB77DC3BA0C937B3, 0x0000BFF3 //A1 = -3.57567223048598672970e-04L
1127 data8 0x90694DFF4EBF7370, 0x00003FEE //A2 = +8.60758700336677694536e-06L
1128 data8 0xDE5379AA90A98F3F, 0x0000BFE8 //A3 = -2.07057292787309736495e-07L
1129 data8 0xAB0322293F1F9CA0, 0x00003FE3 //A4 = +4.97711123919916694625e-09L
1130 data8 0x837119E59D3B7AC2, 0x0000BFDE //A5 = -1.19545621970063369582e-10L
1131 data8 0xC9E5B74A38ECF3FC, 0x00003FD8 //A6 = +2.86913359605586285967e-12L
1132 data8 0x9AEF5110C6885352, 0x0000BFD3 //A7 = -6.88048865490621757799e-14L
1133 data8 0xED988D52189CE6A3, 0x00003FCD //A8 = +1.64865278639132278935e-15L
1134 data8 0xB6063CECD8012B6D, 0x0000BFC8 //A9 = -3.94702428606368525374e-17L
1135 data8 0x8B541EB15E79CEEC, 0x00003FC3 //A10 = +9.44127272399408815784e-19L
1136 data8 0xD51A136D8C75BC25, 0x0000BFBD //A11 = -2.25630369561137931232e-20L
1137 data8 0xA2C1C5E19CC79E6F, 0x00003FB8 //A12 = +5.38517493921589837361e-22L
1138 data8 0xF86F9772306F56C1, 0x0000BFB2 //A13 = -1.28438352359240135735e-23L
1139 data8 0xC32F6FEEDE86528E, 0x00003FAD //A14 = +3.15338862172962186458e-25L
1140 data8 0x9534ED189744D7D4, 0x0000BFA8 //A15 = -7.53301543611470014315e-27L
1141 // Pol22
1142 data8 0xCBA0A2DB94A2C494, 0x00003FEF //A0 = +2.42742878212752702946e-05L
1143 data8 0x84C089154A49E0E8, 0x0000BFF3 //A1 = -2.53204520651046300034e-04L
1144 data8 0xABF5665BD0D8B0CD, 0x00003FED //A2 = +5.12476542947092361490e-06L
1145 data8 0xDEA1C518E3EEE872, 0x0000BFE7 //A3 = -1.03671063536324831083e-07L
1146 data8 0x900B77F271559AE8, 0x00003FE2 //A4 = +2.09612770408581408652e-09L
1147 data8 0xBA4C74A262BE3E4E, 0x0000BFDC //A5 = -4.23594098489216166935e-11L
1148 data8 0xF0D1680FCC1EAF97, 0x00003FD6 //A6 = +8.55557381760467917779e-13L
1149 data8 0x9B8F8E033BB83A24, 0x0000BFD1 //A7 = -1.72707138247091685914e-14L
1150 data8 0xC8DCA6A691DB8335, 0x00003FCB //A8 = +3.48439884388851942939e-16L
1151 data8 0x819A6CB9CEA5E9BD, 0x0000BFC6 //A9 = -7.02580471688245511753e-18L
1152 data8 0xA726B4F622585BEA, 0x00003FC0 //A10 = +1.41582572516648501043e-19L
1153 data8 0xD7727648A4095986, 0x0000BFBA //A11 = -2.85141885626054217632e-21L
1154 data8 0x8AB627E09CF45997, 0x00003FB5 //A12 = +5.73697507862703019314e-23L
1155 data8 0xB28C15C117CC604F, 0x0000BFAF //A13 = -1.15383428132352407085e-24L
1156 data8 0xECB8428626DA072C, 0x00003FA9 //A14 = +2.39025879246942839796e-26L
1157 data8 0x98B731BCFA2CE2B2, 0x0000BFA4 //A15 = -4.81885474332093262902e-28L
1158 // Pol23
1159 data8 0xC6D013811314D31B, 0x00003FED //A0 = +5.92508308918577687876e-06L
1160 data8 0xBBF3057B8DBACBCF, 0x0000BFF2 //A1 = -1.79242422493281965934e-04L
1161 data8 0xCCADECA501162313, 0x00003FEC //A2 = +3.04996061562356504918e-06L
1162 data8 0xDED1FDBE8CCAF3DB, 0x0000BFE6 //A3 = -5.18793887648024117154e-08L
1163 data8 0xF27B74EDDCA65859, 0x00003FE0 //A4 = +8.82145297317787820675e-10L
1164 data8 0x83E4415687F01A0C, 0x0000BFDB //A5 = -1.49943414247603665601e-11L
1165 data8 0x8F6CB350861CE446, 0x00003FD5 //A6 = +2.54773288906376920377e-13L
1166 data8 0x9BE8456A30CBFC02, 0x0000BFCF //A7 = -4.32729710913845745148e-15L
1167 data8 0xA9694F7E1033977D, 0x00003FC9 //A8 = +7.34704698157502347441e-17L
1168 data8 0xB8035A3D5AF82D85, 0x0000BFC3 //A9 = -1.24692123826025468001e-18L
1169 data8 0xC7CB4B3ACB905FDA, 0x00003FBD //A10 = +2.11540249352095943317e-20L
1170 data8 0xD8D70AEB2E58D729, 0x0000BFB7 //A11 = -3.58731705184186608576e-22L
1171 data8 0xEB27A61B1D5C7697, 0x00003FB1 //A12 = +6.07861113430709162243e-24L
1172 data8 0xFEF9ED74D4F4C9B0, 0x0000BFAB //A13 = -1.02984099170876754831e-25L
1173 data8 0x8E6F410068C12043, 0x00003FA6 //A14 = +1.79777721804459361762e-27L
1174 data8 0x9AE2F6705481630E, 0x0000BFA0 //A15 = -3.05459905177379058768e-29L
1175 // Pol24
1176 data8 0xD2D858D5B01C9434, 0x00003FEE //A0 = +1.25673476165670766128e-05L
1177 data8 0x8505330F8B4FDE49, 0x0000BFF2 //A1 = -1.26858053564784963985e-04L
1178 data8 0xF39171C8B1D418C2, 0x00003FEB //A2 = +1.81472407620770441249e-06L
1179 data8 0xDEF065C3D7BFD26E, 0x0000BFE5 //A3 = -2.59535215807652675043e-08L
1180 data8 0xCC0199EA6ACA630C, 0x00003FDF //A4 = +3.71085215769339916703e-10L
1181 data8 0xBAA25319F01ED248, 0x0000BFD9 //A5 = -5.30445960650683029105e-12L
1182 data8 0xAAB28A84F8CFE4D1, 0x00003FD3 //A6 = +7.58048850973457592162e-14L
1183 data8 0x9C14B931AEB311A8, 0x0000BFCD //A7 = -1.08302915828084288776e-15L
1184 data8 0x8EADA745715A0714, 0x00003FC7 //A8 = +1.54692159263197000533e-17L
1185 data8 0x82643F3F722CE6B5, 0x0000BFC1 //A9 = -2.20891945694400066611e-19L
1186 data8 0xEE42ECDE465A99E4, 0x00003FBA //A10 = +3.15336372779307614198e-21L
1187 data8 0xD99FC74326ACBFC0, 0x0000BFB4 //A11 = -4.50036161691276556269e-23L
1188 data8 0xC6A4DCACC554911E, 0x00003FAE //A12 = +6.41853356148678957077e-25L
1189 data8 0xB550CEA09DA96F44, 0x0000BFA8 //A13 = -9.15410112414783078242e-27L
1190 data8 0xAA9149317996F32F, 0x00003FA2 //A14 = +1.34554050666508391264e-28L
1191 data8 0x9C3008EFE3F52F19, 0x0000BF9C //A15 = -1.92516125328592532359e-30L
1192 // Pol25
1193 data8 0xA68E78218806283F, 0x00003FEF //A0 = +1.98550844852103406280e-05L
1194 data8 0xBC41423996DC8A37, 0x0000BFF1 //A1 = -8.97669395268764751516e-05L
1195 data8 0x90E55AE31A2F8271, 0x00003FEB //A2 = +1.07955871580069359702e-06L
1196 data8 0xDF022272DA4A3BEF, 0x0000BFE4 //A3 = -1.29807937275957214439e-08L
1197 data8 0xAB95DCBFFB0BAAB8, 0x00003FDE //A4 = +1.56056011861921437794e-10L
1198 data8 0x83FF2547BA9011FF, 0x0000BFD8 //A5 = -1.87578539510813332135e-12L
1199 data8 0xCB0C353560EEDC45, 0x00003FD1 //A6 = +2.25428217090412574481e-14L
1200 data8 0x9C24CEB86E76D2C5, 0x0000BFCB //A7 = -2.70866279585559299821e-16L
1201 data8 0xF01AFA23DDFDAE0E, 0x00003FC4 //A8 = +3.25403467375734083376e-18L
1202 data8 0xB892BDFBCF1D9740, 0x0000BFBE //A9 = -3.90848978133441513662e-20L
1203 data8 0x8DDBBF34415AAECA, 0x00003FB8 //A10 = +4.69370027479731756829e-22L
1204 data8 0xDA04170D07458C3B, 0x0000BFB1 //A11 = -5.63558091177482043435e-24L
1205 data8 0xA76F391095A9563A, 0x00003FAB //A12 = +6.76262416498584003290e-26L
1206 data8 0x8098FA125C18D8DB, 0x0000BFA5 //A13 = -8.11564737276592661642e-28L
1207 data8 0xCB9E4D5C08923227, 0x00003F9E //A14 = +1.00391606269366059664e-29L
1208 data8 0x9CEC3BF7A0BE2CAF, 0x0000BF98 //A15 = -1.20888920108938909316e-31L
1209 // Pol26
1210 data8 0xC17AB25E269272F7, 0x00003FEE //A0 = +1.15322640047234590651e-05L
1211 data8 0x85310509E633FEF2, 0x0000BFF1 //A1 = -6.35106483144690768696e-05L
1212 data8 0xAC5E4C4DCB2D940C, 0x00003FEA //A2 = +6.42122148740412561597e-07L
1213 data8 0xDF0AAD0571FFDD48, 0x0000BFE3 //A3 = -6.49136789710824396482e-09L
1214 data8 0x9049D8440AFD180F, 0x00003FDD //A4 = +6.56147932223174570008e-11L
1215 data8 0xBAA936477C5FA9D7, 0x0000BFD6 //A5 = -6.63153032879993841863e-13L
1216 data8 0xF17261294EAB1443, 0x00003FCF //A6 = +6.70149477756803680009e-15L
1217 data8 0x9C22F87C31DB007A, 0x0000BFC9 //A7 = -6.77134581402030645534e-17L
1218 data8 0xC9E98E633942AC12, 0x00003FC2 //A8 = +6.84105580182052870823e-19L
1219 data8 0x828998181309642C, 0x0000BFBC //A9 = -6.91059649300859944955e-21L
1220 data8 0xA8C3D4DCE1ECBAB6, 0x00003FB5 //A10 = +6.97995542988331257517e-23L
1221 data8 0xDA288D52CC4C351A, 0x0000BFAE //A11 = -7.04907829139578377009e-25L
1222 data8 0x8CEEACB790B5F374, 0x00003FA8 //A12 = +7.11526399101774993883e-27L
1223 data8 0xB61C8A29D98F24C0, 0x0000BFA1 //A13 = -7.18303147470398859453e-29L
1224 data8 0xF296F69FE45BDA7D, 0x00003F9A //A14 = +7.47537230021540031251e-31L
1225 data8 0x9D4B25BF6FB7234B, 0x0000BF94 //A15 = -7.57340869663212138051e-33L
1226 // Pol27
1227 data8 0xC7772CC326D6FBB8, 0x00003FEE //A0 = +1.18890718679826004395e-05L
1228 data8 0xE0F9D5410565D55D, 0x0000BFF0 //A1 = -5.36384368533203585378e-05L
1229 data8 0x85C0BE825680E148, 0x00003FEA //A2 = +4.98268406609692971520e-07L
1230 data8 0x9F058A389D7BA177, 0x0000BFE3 //A3 = -4.62813885933188677790e-09L
1231 data8 0xBD0B751F0A6BAC7A, 0x00003FDC //A4 = +4.29838009673609430305e-11L
1232 data8 0xE0B6823570502E9D, 0x0000BFD5 //A5 = -3.99170340031272728535e-13L
1233 data8 0x858A9C52FC426D86, 0x00003FCF //A6 = +3.70651975271664045723e-15L
1234 data8 0x9EB4438BFDF1928D, 0x0000BFC8 //A7 = -3.44134780748056488222e-17L
1235 data8 0xBC968DCD8C06D74E, 0x00003FC1 //A8 = +3.19480670422195579127e-19L
1236 data8 0xE0133A405F782125, 0x0000BFBA //A9 = -2.96560935615546392028e-21L
1237 data8 0x851AFEBB70D07E79, 0x00003FB4 //A10 = +2.75255617931932536111e-23L
1238 data8 0x9E1E21A841BF8738, 0x0000BFAD //A11 = -2.55452923487640676799e-25L
1239 data8 0xBBCF2EF1C6E72327, 0x00003FA6 //A12 = +2.37048675755308004410e-27L
1240 data8 0xDF0D320CF12B8BCB, 0x0000BF9F //A13 = -2.19945804585962185550e-29L
1241 data8 0x8470A76DE5FCADD8, 0x00003F99 //A14 = +2.04056213851532266258e-31L
1242 data8 0x9D41C15F6A6FBB04, 0x0000BF92 //A15 = -1.89291056020108587823e-33L
1243 LOCAL_OBJECT_END(erfc_Q_table)
1246 .section .text
1247 GLOBAL_LIBM_ENTRY(erfcl)
1249 { .mfi
1250 alloc r32 = ar.pfs, 0, 36, 4, 0
1251 fma.s1 FR_Tmp = f1, f1, f8 // |x|+1, if x >= 0
1252 nop.i 0
1253 }
1254 { .mfi
1255 addl GR_ad_Arg = @ltoff(exp_table_1), gp
1256 fms.s1 FR_Tmp1 = f1, f1, f8 // |x|+1, if x < 0
1257 mov GR_rshf_2to51 = 0x4718 // begin 1.10000 2^(63+51)
1258 }
1259 ;;
1261 { .mfi
1262 ld8 GR_ad_Arg = [GR_ad_Arg] // Point to Arg table
1263 fcmp.ge.s1 p6,p7 = f8, f0 // p6: x >= 0 ,p7: x<0
1264 shl GR_rshf_2to51 = GR_rshf_2to51,48 // end 1.10000 2^(63+51)
1265 }
1266 { .mlx
1267 mov GR_rshf = 0x43e8 // begin 1.1000 2^63 for right shift
1268 movl GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc // signif. of 1/ln2
1269 }
1270 ;;
1272 { .mfi
1273 mov GR_exp_2tom51 = 0xffff-51
1274 fclass.m p8,p0 = f8,0x07 // p8: x = 0
1275 shl GR_rshf = GR_rshf,48 // end 1.1000 2^63 for right shift
1276 }
1277 { .mfi
1278 nop.m 0
1279 fnma.s1 FR_norm_x = f8, f8, f0 //high bits for -x^2
1280 nop.i 0
1281 }
1282 ;;
1284 .pred.rel "mutex",p6,p7
1285 { .mfi
1286 setf.sig FR_INV_LN2_2TO63 = GR_sig_inv_ln2 // form 1/ln2 * 2^63
1287 (p6) fma.s1 FR_AbsArg = f1, f0, f8 // |x|, if x >= 0
1288 nop.i 0
1289 }
1290 { .mfi
1291 setf.d FR_RSHF_2TO51 = GR_rshf_2to51 //const 1.10 * 2^(63+51)
1292 (p7) fms.s1 FR_AbsArg = f1, f0, f8 // |x|, if x < 0
1293 mov GR_exp_mask = 0x1FFFF // Form exponent mask
1294 }
1295 ;;
1297 { .mfi
1298 ldfe FR_ch_dx = [GR_ad_Arg], 16
1299 fclass.m p10,p0 = f8, 0x21 // p10: x = +inf
1300 mov GR_exp_bias = 0x0FFFF // Set exponent bias
1301 }
1302 { .mlx
1303 setf.d FR_RSHF = GR_rshf // Right shift const 1.1000 * 2^63
1304 movl GR_ERFC_XC_TB = 0x650
1305 }
1306 ;;
1308 .pred.rel "mutex",p6,p7
1309 { .mfi
1310 setf.exp FR_2TOM51 = GR_exp_2tom51 // 2^-51 for scaling float_N
1311 (p6) fma.s1 FR_Tmp = FR_Tmp, FR_Tmp, f0 // (|x|+1)^2,x >=0
1312 nop.i 0
1313 }
1314 { .mfi
1315 ldfpd FR_POS_ARG_ASYMP,FR_NEG_ARG_ASYMP = [GR_ad_Arg], 16
1316 (p7) fma.s1 FR_Tmp = FR_Tmp1, FR_Tmp1, f0 // (|x|+1)^2, x<0
1317 mov GR_0x1 = 0x1
1318 }
1319 ;;
1321 //p8: y = 1.0, x = 0.0,quick exit
1322 { .mfi
1323 ldfpd FR_dx,FR_dx1 = [GR_ad_Arg], 16
1324 fclass.m p9,p0 = f8, 0x22 // p9: x = -inf
1325 nop.i 0
1327 }
1328 { .mfb
1329 nop.m 0
1330 (p8) fma.s0 f8 = f1, f1, f0
1331 (p8) br.ret.spnt b0
1332 }
1333 ;;
1335 { .mfi
1336 ldfe FR_UnfBound = [GR_ad_Arg], 16
1337 fclass.m p11,p0 = f8, 0xc3 // p11: x = nan
1338 mov GR_BIAS = 0x0FFFF
1339 }
1340 { .mfi
1341 nop.m 0
1342 fma.s1 FR_NormX = f8,f1,f0
1343 nop.i 0
1344 }
1345 ;;
1347 { .mfi
1348 ldfe FR_EpsNorm = [GR_ad_Arg], 16
1349 fmerge.s FR_X = f8,f8
1350 nop.i 0
1351 }
1352 { .mfi
1353 nop.m 0
1354 fma.s1 FR_xsq_lo = f8, f8, FR_norm_x // low bits for -x^2
1355 nop.i 0
1356 }
1357 ;;
1359 { .mfi
1360 add GR_ad_C = 0x20, GR_ad_Arg // Point to C table
1361 nop.f 0
1362 add GR_ad_T1 = 0x50, GR_ad_Arg // Point to T1 table
1363 }
1364 { .mfi
1365 add GR_ad_T2 = 0x150, GR_ad_Arg // Point to T2 table
1366 nop.f 0
1367 add GR_ERFC_XC_TB = GR_ERFC_XC_TB, GR_ad_Arg //poin.to XB_TBL
1368 }
1369 ;;
1371 { .mfi
1372 getf.exp GR_signexp_x = FR_norm_x // Extr. sign and exponent of x
1373 fma.s1 FR_Tmp = FR_Tmp, FR_Tmp, f0 // (|x|+1)^4
1374 add GR_ad_W1 = 0x100, GR_ad_T2 // Point to W1 table
1375 }
1376 { .mfi
1377 ldfe FR_L_hi = [GR_ad_Arg],16 // Get L_hi
1378 nop.f 0
1379 add GR_ad_W2 = 0x300, GR_ad_T2 // Point to W2 table
1380 }
1381 ;;
1383 // p9: y = 2.0, x = -inf, quick exit
1384 { .mfi
1385 sub GR_mBIAS = r0, GR_BIAS
1386 fma.s1 FR_2 = f1, f1, f1
1387 nop.i 0
1388 }
1389 { .mfb
1390 ldfe FR_L_lo = [GR_ad_Arg],16 // Get L_lo
1391 (p9) fma.s0 f8 = f1, f1, f1
1392 (p9) br.ret.spnt b0
1393 }
1394 ;;
1396 // p10: y = 0.0, x = +inf, quick exit
1397 { .mfi
1398 adds GR_ERFC_P_TB = 0x380, GR_ERFC_XC_TB // pointer to P_TBL
1399 fma.s1 FR_N_signif = FR_norm_x, FR_INV_LN2_2TO63, FR_RSHF_2TO51
1400 and GR_exp_x = GR_signexp_x, GR_exp_mask
1401 }
1402 { .mfb
1403 adds GR_ERFC_S_TB = 0x1C0, GR_ERFC_XC_TB // pointer to S_TBL
1404 (p10) fma.s0 f8 = f0, f1, f0
1405 (p10) br.ret.spnt b0
1406 }
1407 ;;
1409 // p12: |x| < 0.681... -> dx = 0.875 (else dx = 0.625 )
1410 // p11: y = x, x = nan, quick exit
1411 { .mfi
1412 ldfe FR_C3 = [GR_ad_C],16 // Get C3 for normal path
1413 fcmp.lt.s1 p12,p0 = FR_AbsArg, FR_ch_dx
1414 shl GR_ShftPi_bias = GR_BIAS, 8 // BIAS * 256
1415 }
1416 { .mfb
1417 sub GR_exp_x = GR_exp_x, GR_exp_bias // Get exponent
1418 (p11) fma.s0 f8 = f8, f1, f0
1419 (p11) br.ret.spnt b0
1421 }
1422 ;;
1424 { .mfi
1425 ldfe FR_C2 = [GR_ad_C],16 // Get A2 for main path
1426 nop.f 0
1427 nop.i 0
1428 }
1429 ;;
1431 //p15: x > POS_ARG_ASYMP = 107.0 -> erfcl(x) ~=~ 0.0
1432 { .mfi
1433 ldfe FR_C1 = [GR_ad_C],16 // Get C1 for main path
1434 (p6) fcmp.gt.unc.s1 p15,p0 = FR_AbsArg, FR_POS_ARG_ASYMP // p6: x >= 0
1435 nop.i 0
1436 }
1437 { .mfb
1438 nop.m 0
1439 (p12) fma.s1 FR_dx = FR_dx1, f1, f0 //p12: dx = 0.875 for x < 0.681
1440 nop.b 0
1441 }
1442 ;;
1444 //p14: x < - NEG_ARG_ASYMP = -6.5 -> erfcl(x) ~=~ 2.0
1445 { .mfi
1446 nop.m 0
1447 (p7) fcmp.gt.unc.s1 p14,p0 = FR_AbsArg,FR_NEG_ARG_ASYMP // p7: x < 0
1448 shladd GR_ShftXBi_bias = GR_mBIAS, 4, r0
1449 }
1450 ;;
1452 { .mfi
1453 nop.m 0
1454 fma.s0 FR_Tmpf = f1, f1, FR_EpsNorm // flag i
1455 nop.i 0
1456 }
1457 { .mfi
1458 nop.m 0
1459 fms.s1 FR_float_N = FR_N_signif, FR_2TOM51, FR_RSHF
1460 nop.i 0
1461 }
1462 ;;
1464 // p8: x < UnfBound ~=~ 106.53... -> result without underflow error
1465 // p14: y ~=~ 2, x < -6.5,quick exit
1466 { .mfi
1467 getf.exp GR_IndxPlusBias = FR_Tmp // exp + bias for (|x|+1)^4
1468 fcmp.lt.s1 p8,p0 = FR_NormX,FR_UnfBound
1469 nop.i 0
1470 }
1471 { .mfb
1472 nop.m 0
1473 (p14) fnma.s0 FR_RESULT = FR_EpsNorm,FR_EpsNorm,FR_2
1474 (p14) br.ret.spnt b0
1476 }
1477 ;;
1479 // p15: y ~=~ 0.0 (result with underflow error), x > POS_ARG_ASYMP = 107.0,
1480 // call __libm_error_region
1481 { .mfb
1482 (p15) mov GR_Parameter_TAG = 207
1483 (p15) fma.s0 FR_RESULT = FR_EpsNorm,FR_EpsNorm,f0
1484 (p15) br.cond.spnt __libm_error_region
1485 }
1486 ;;
1488 { .mfi
1489 getf.sig GR_N_fix = FR_N_signif // Get N from significand
1490 nop.f 0
1491 shl GR_ShftPi = GR_IndxPlusBias, 8
1493 }
1494 { .mfi
1495 shladd GR_ShftXBi = GR_IndxPlusBias, 4, GR_ShftXBi_bias
1496 nop.f 0
1497 nop.i 0
1498 }
1499 ;;
1501 { .mmi
1502 add GR_ERFC_S_TB = GR_ERFC_S_TB, GR_ShftXBi //poin.to S[i]
1503 add GR_ERFC_XC_TB = GR_ERFC_XC_TB, GR_ShftXBi //poin.to XC[i]
1504 sub GR_ShftPi = GR_ShftPi, GR_ShftPi_bias // 256*i
1505 }
1506 ;;
1508 { .mfi
1509 ldfe FR_Xc = [GR_ERFC_XC_TB]
1510 fma.s1 FR_Xpdx_hi = FR_AbsArg, f1, FR_dx // x + dx
1511 add GR_ShftA14 = 0xE0, GR_ShftPi // pointer shift for A14
1514 }
1515 { .mfi
1516 ldfe FR_S = [GR_ERFC_S_TB]
1517 fnma.s1 FR_r = FR_L_hi, FR_float_N, FR_norm_x//r= -L_hi*float_N+x
1518 add GR_ShftA15 = 0xF0, GR_ShftPi // pointer shift for A15
1519 }
1520 ;;
1522 { .mfi
1523 add GR_P_POINT_1 = GR_ERFC_P_TB, GR_ShftA14 // pointer to A14
1524 fcmp.gt.s1 p9,p10 = FR_AbsArg, FR_dx //p9: x > dx, p10: x <= dx
1525 extr.u GR_M1 = GR_N_fix, 6, 6 // Extract index M_1
1526 }
1527 { .mfi
1528 add GR_P_POINT_2 = GR_ERFC_P_TB, GR_ShftA15 // pointer to A15
1529 nop.f 0
1530 nop.i 0
1532 }
1533 ;;
1535 { .mfi
1536 ldfe FR_A14 = [GR_P_POINT_1], -32
1537 nop.f 0
1538 extr.u GR_M2 = GR_N_fix, 0, 6 // Extract index M_2
1539 }
1540 { .mfi
1541 ldfe FR_A15 = [GR_P_POINT_2], -32
1542 nop.f 0
1543 shladd GR_ad_W1 = GR_M1,3,GR_ad_W1 // Point to W1
1544 }
1545 ;;
1547 { .mfi
1548 ldfe FR_A12 = [GR_P_POINT_1], -64
1549 nop.f 0
1550 extr GR_K = GR_N_fix, 12, 32 // Extract limite range K
1551 }
1552 { .mfi
1553 ldfe FR_A13 = [GR_P_POINT_2], -64
1554 nop.f 0
1555 shladd GR_ad_T1 = GR_M1,2,GR_ad_T1 // Point to T1
1556 }
1557 ;;
1559 { .mfi
1560 ldfe FR_A8 = [GR_P_POINT_1], 32
1561 nop.f 0
1562 add GR_exp_2_k = GR_exp_bias, GR_K // Form exponent of 2^k
1563 }
1564 { .mfi
1565 ldfe FR_A9 = [GR_P_POINT_2], 32
1566 nop.f 0
1567 shladd GR_ad_W2 = GR_M2,3,GR_ad_W2 // Point to W2
1568 }
1569 ;;
1571 { .mfi
1572 ldfe FR_A10 = [GR_P_POINT_1], -96
1573 nop.f 0
1574 shladd GR_ad_T2 = GR_M2,2,GR_ad_T2 // Point to T2
1575 }
1576 { .mfi
1577 ldfe FR_A11 = [GR_P_POINT_2], -96
1578 fnma.s1 FR_r = FR_L_lo, FR_float_N, FR_r //r = -L_lo*float_N + r
1579 nop.i 0
1580 }
1581 ;;
1583 { .mfi
1584 ldfe FR_A4 = [GR_P_POINT_1], 32
1585 (p10) fms.s1 FR_Tmp = FR_dx,f1, FR_Xpdx_hi //for lo of x+dx, x<=dx
1586 nop.i 0
1587 }
1588 { .mfi
1589 ldfe FR_A5 = [GR_P_POINT_2], 32
1590 (p9) fms.s1 FR_Tmp = FR_AbsArg, f1, FR_Xpdx_hi //for lo of x+dx, x>dx
1591 nop.i 0
1592 }
1593 ;;
1595 { .mfi
1596 ldfe FR_A6 = [GR_P_POINT_1], -64
1597 frcpa.s1 FR_U,p11 = f1, FR_Xpdx_hi // hi of 1 /(x + dx)
1598 nop.i 0
1599 }
1600 { .mfi
1601 ldfe FR_A7 = [GR_P_POINT_2], -64
1602 nop.f 0
1603 nop.i 0
1604 }
1605 ;;
1607 { .mfi
1608 ldfe FR_A2 = [GR_P_POINT_1], -32
1609 nop.f 0
1610 nop.i 0
1611 }
1612 { .mfi
1613 ldfe FR_A3 = [GR_P_POINT_2], -32
1614 nop.f 0
1615 nop.i 0
1616 }
1617 ;;
1619 { .mfi
1620 ldfe FR_A0 = [GR_P_POINT_1], 224
1621 nop.f 0
1622 nop.i 0
1623 }
1624 { .mfi
1625 ldfe FR_A1 = [GR_P_POINT_2]
1626 fms.s1 FR_LocArg = FR_AbsArg, f1, FR_Xc // xloc = x - x[i]
1627 nop.i 0
1628 }
1629 ;;
1631 { .mfi
1632 ldfd FR_W1 = [GR_ad_W1],0 // Get W1
1633 nop.f 0
1634 nop.i 0
1635 }
1636 { .mfi
1637 ldfd FR_W2 = [GR_ad_W2],0 // Get W2
1638 fma.s1 FR_poly = FR_r, FR_C3, FR_C2 // poly = r * A3 + A2
1639 nop.i 0
1640 }
1641 ;;
1643 { .mfi
1644 ldfs FR_T1 = [GR_ad_T1],0 // Get T1
1645 (p10) fma.s1 FR_Xpdx_lo = FR_AbsArg,f1, FR_Tmp//lo of x + dx , x <= dx
1646 nop.i 0
1647 }
1648 { .mfi
1649 ldfs FR_T2 = [GR_ad_T2],0 // Get T2
1650 (p9) fma.s1 FR_Xpdx_lo = FR_dx,f1, FR_Tmp // lo of x + dx, x > dx
1651 nop.i 0
1652 }
1653 ;;
1655 { .mfi
1656 nop.m 0
1657 fnma.s1 FR_Tmp1 = FR_Xpdx_hi, FR_U, FR_2 // N-R, iter. N1
1658 nop.i 0
1659 }
1660 { .mfi
1661 nop.m 0
1662 fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r
1663 nop.i 0
1664 }
1665 ;;
1667 { .mfi
1668 setf.exp FR_scale = GR_exp_2_k // Set scale = 2^k
1669 fma.s1 FR_P15_1_1 = FR_LocArg, FR_LocArg, f0 // xloc ^2
1670 nop.i 0
1671 }
1672 { .mfi
1673 nop.m 0
1674 fma.s1 FR_P15_0_1 = FR_A15, FR_LocArg, FR_A14
1675 nop.i 0
1676 }
1677 ;;
1679 { .mfi
1680 nop.m 0
1681 fma.s1 FR_P15_1_2 = FR_A13, FR_LocArg, FR_A12
1682 nop.i 0
1683 }
1684 { .mfi
1685 nop.m 0
1686 fma.s1 FR_poly = FR_r, FR_poly, FR_C1 // poly = r * poly + A1
1687 nop.i 0
1688 }
1689 ;;
1691 { .mfi
1692 nop.m 0
1693 fma.s1 FR_P15_2_1 = FR_A9, FR_LocArg, FR_A8
1694 nop.i 0
1695 }
1696 { .mfi
1697 nop.m 0
1698 fma.s1 FR_P15_2_2 = FR_A11, FR_LocArg, FR_A10
1699 nop.i 0
1700 }
1701 ;;
1703 { .mfi
1704 nop.m 0
1705 fma.s1 FR_U = FR_U, FR_Tmp1, f0 // N-R, iter. N1
1706 nop.i 0
1707 }
1708 ;;
1710 { .mfi
1711 nop.m 0
1712 fma.s1 FR_P15_3_1 = FR_A5, FR_LocArg, FR_A4
1713 nop.i 0
1714 }
1715 { .mfi
1716 nop.m 0
1717 fma.s1 FR_P15_3_2 = FR_A7, FR_LocArg, FR_A6
1718 nop.i 0
1719 }
1720 ;;
1722 { .mfi
1723 nop.m 0
1724 fma.s1 FR_P15_4_2 = FR_A3, FR_LocArg, FR_A2
1725 nop.i 0
1726 }
1727 { .mfi
1728 nop.m 0
1729 fma.s1 FR_W = FR_W1, FR_W2, FR_W2 // W = W1 * W2 + W2
1730 nop.i 0
1731 }
1732 ;;
1734 { .mfi
1735 nop.m 0
1736 fmpy.s1 FR_T = FR_T1, FR_T2 // T = T1 * T2
1737 nop.i 0
1738 }
1739 { .mfi
1740 nop.m 0
1741 fma.s1 FR_P15_7_1 = FR_P15_0_1, FR_P15_1_1, FR_P15_1_2
1742 nop.i 0
1743 }
1744 ;;
1746 { .mfi
1747 nop.m 0
1748 fma.s1 FR_P15_7_2 = FR_P15_1_1, FR_P15_1_1, f0 // xloc^4
1749 nop.i 0
1750 }
1751 { .mfi
1752 nop.m 0
1753 fma.s1 FR_P15_8_1 = FR_P15_1_1, FR_P15_2_2, FR_P15_2_1
1754 nop.i 0
1755 }
1756 ;;
1758 { .mfi
1759 nop.m 0
1760 fnma.s1 FR_Tmp = FR_Xpdx_hi, FR_U, FR_2 // N-R, iter. N2
1761 nop.i 0
1762 }
1764 { .mfi
1765 nop.m 0
1766 fma.s1 FR_poly = FR_rsq, FR_poly, FR_r // poly = rsq * poly + r
1767 nop.i 0
1768 }
1769 ;;
1771 { .mfi
1772 nop.m 0
1773 fma.s1 FR_P15_9_1 = FR_P15_1_1, FR_P15_4_2, FR_A0
1774 nop.i 0
1775 }
1776 { .mfi
1777 nop.m 0
1778 fma.s1 FR_P15_9_2 = FR_P15_1_1, FR_P15_3_2, FR_P15_3_1
1779 nop.i 0
1780 }
1781 ;;
1783 { .mfi
1784 nop.m 0
1785 fma.s1 FR_W = FR_W, f1, FR_W1 // W = W + W1
1786 nop.i 0
1787 }
1788 ;;
1790 { .mfi
1791 nop.m 0
1792 fma.s1 FR_T_scale = FR_T, FR_scale, f0 // T_scale = T * scale
1793 nop.i 0
1794 }
1795 ;;
1797 { .mfi
1798 nop.m 0
1799 fma.s1 FR_P15_13_1 = FR_P15_7_2, FR_P15_7_1, FR_P15_8_1
1800 nop.i 0
1801 }
1802 ;;
1804 { .mfi
1805 nop.m 0
1806 fma.s1 FR_U = FR_U, FR_Tmp, f0 // N-R, iter. N2
1807 nop.i 0
1808 }
1809 ;;
1811 { .mfi
1812 nop.m 0
1813 fma.s1 FR_P15_14_1 = FR_P15_7_2, FR_P15_9_2, FR_P15_9_1
1814 nop.i 0
1815 }
1816 { .mfi
1817 nop.m 0
1818 fma.s1 FR_P15_14_2 = FR_P15_7_2, FR_P15_7_2, f0 // xloc^8
1819 nop.i 0
1820 }
1821 ;;
1823 { .mfi
1824 nop.m 0
1825 fma.s1 FR_M = FR_T_scale, FR_S, f0
1826 nop.i 0
1827 }
1828 ;;
1830 { .mfi
1831 nop.m 0
1832 fnma.s1 FR_Tmp = FR_Xpdx_hi, FR_U, FR_2 // N-R, iter. N3
1833 nop.i 0
1834 }
1835 ;;
1837 { .mfi
1838 nop.m 0
1839 fma.s1 FR_Q = FR_P15_14_2, FR_P15_13_1, FR_P15_14_1
1840 nop.i 0
1841 }
1842 ;;
1844 { .mfi
1845 nop.m 0
1846 fms.s1 FR_H = FR_W, f1, FR_xsq_lo // H = W - xsq_lo
1847 nop.i 0
1848 }
1849 ;;
1851 { .mfi
1852 nop.m 0
1853 fma.s1 FR_U = FR_U, FR_Tmp, f0 // N-R, iter. N3
1854 nop.i 0
1855 }
1856 ;;
1858 { .mfi
1859 nop.m 0
1860 fma.s1 FR_Q = FR_A1, FR_LocArg, FR_Q
1861 nop.i 0
1862 }
1863 ;;
1865 { .mfi
1866 nop.m 0
1867 fnma.s1 FR_Tmp = FR_Xpdx_hi, FR_U, f1 // for du
1868 nop.i 0
1869 }
1870 { .mfi
1871 nop.m 0
1872 fma.s1 FR_R = FR_H, FR_poly, FR_poly
1873 nop.i 0
1874 }
1875 ;;
1877 { .mfi
1878 nop.m 0
1879 fma.s1 FR_res_pos_x_hi = FR_M, FR_U, f0 // M *U
1880 nop.i 0
1882 }
1883 ;;
1885 { .mfi
1886 nop.m 0
1887 fma.s1 FR_R = FR_R, f1, FR_H // R = H + P(r) + H*P(r)
1888 nop.i 0
1889 }
1890 ;;
1892 { .mfi
1893 nop.m 0
1894 fma.s0 FR_Tmpf = f8, f1, f0 // flag d
1895 nop.i 0
1896 }
1897 ;;
1899 { .mfi
1900 nop.m 0
1901 fnma.s1 FR_dU = FR_Xpdx_lo, FR_U, FR_Tmp
1902 nop.i 0
1903 }
1904 ;;
1906 // p7: we begin to calculate y(x) = 2 - erfcl(-x) in multi precision
1907 // for -6.5 <= x < 0
1908 { .mfi
1909 nop.m 0
1910 fms.s1 FR_res_pos_x_lo = FR_M, FR_U, FR_res_pos_x_hi
1911 nop.i 0
1913 }
1914 { .mfi
1915 nop.m 0
1916 (p7) fnma.s1 FR_Tmp1 = FR_res_pos_x_hi, f1, FR_2 //p7: x < 0
1917 nop.i 0
1919 }
1920 ;;
1922 { .mfi
1923 nop.m 0
1924 fma.s1 FR_G = FR_R, FR_Q, FR_Q
1925 nop.i 0
1927 }
1928 ;;
1930 { .mfi
1931 nop.m 0
1932 fma.s1 FR_Tmp = FR_R, f1, FR_dU // R + du
1933 nop.i 0
1935 }
1936 ;;
1938 { .mfi
1939 nop.m 0
1940 (p7) fnma.s1 FR_Tmp2 = FR_Tmp1, f1, FR_2 //p7: x < 0
1941 nop.i 0
1943 }
1944 ;;
1946 { .mfi
1947 nop.m 0
1948 fma.s1 FR_G = FR_G, f1, FR_Tmp
1949 nop.i 0
1951 }
1952 ;;
1954 { .mfi
1955 nop.m 0
1956 (p7) fnma.s1 FR_Tmp2 = FR_res_pos_x_hi, f1, FR_Tmp2 //p7: x < 0
1957 nop.i 0
1959 }
1960 ;;
1962 { .mfi
1963 nop.m 0
1964 fma.s1 FR_V = FR_G, FR_res_pos_x_hi, f0 // V = G * M *U
1965 nop.i 0
1967 }
1968 ;;
1970 { .mfi
1971 nop.m 0
1972 (p7) fma.s1 FR_res_pos_x_lo = FR_res_pos_x_lo, f1, FR_V //p7: x < 0
1973 nop.i 0
1975 }
1976 ;;
1978 { .mfi
1979 nop.m 0
1980 (p7) fnma.s1 FR_Tmp2 = FR_res_pos_x_lo, f1, FR_Tmp2 //p7: x < 0
1981 nop.i 0
1983 }
1984 ;;
1987 //p6: result for 0 < x < = POS_ARG_ASYMP
1988 //p7: result for - NEG_ARG_ASYMP <= x < 0
1989 //p8: exit for - NEG_ARG_ASYMP <= x < UnfBound
1991 ERFC_RESULT:
1992 .pred.rel "mutex",p6,p7
1993 { .mfi
1994 nop.m 0
1995 (p6) fma.s0 f8 = FR_M, FR_U, FR_V // p6: x >= 0
1996 nop.i 0
1997 }
1998 { .mfb
1999 mov GR_Parameter_TAG = 207
2000 (p7) fma.s0 f8 = FR_Tmp2, f1, FR_Tmp1 // p7: x < 0
2001 (p8) br.ret.sptk b0
2002 };;
2004 GLOBAL_LIBM_END(erfcl)
2005 // call via (p15) br.cond.spnt __libm_error_region
2006 // for x > POS_ARG_ASYMP
2007 // or
2008 //
2009 // after .endp erfcl for UnfBound < = x < = POS_ARG_ASYMP
2011 LOCAL_LIBM_ENTRY(__libm_error_region)
2012 .prologue
2013 { .mfi
2014 add GR_Parameter_Y=-32,sp // Parameter 2 value
2015 nop.f 0
2016 .save ar.pfs,GR_SAVE_PFS
2017 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
2018 }
2019 { .mfi
2020 .fframe 64
2021 add sp=-64,sp // Create new stack
2022 nop.f 0
2023 mov GR_SAVE_GP=gp // Save gp
2024 };;
2025 { .mmi
2026 stfe [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack
2027 add GR_Parameter_X = 16,sp // Parameter 1 address
2028 .save b0, GR_SAVE_B0
2029 mov GR_SAVE_B0=b0 // Save b0
2030 };;
2031 .body
2032 { .mib
2033 stfe [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack
2034 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
2035 nop.b 0
2036 }
2037 { .mib
2038 stfe [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack
2039 add GR_Parameter_Y = -16,GR_Parameter_Y
2040 br.call.sptk b0=__libm_error_support# // Call error handling function
2041 };;
2042 { .mmi
2043 nop.m 0
2044 nop.m 0
2045 add GR_Parameter_RESULT = 48,sp
2046 };;
2047 { .mmi
2048 ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
2049 .restore sp
2050 add sp = 64,sp // Restore stack pointer
2051 mov b0 = GR_SAVE_B0 // Restore return address
2052 };;
2053 { .mib
2054 mov gp = GR_SAVE_GP // Restore gp
2055 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
2056 br.ret.sptk b0 // Return
2057 };;
2059 LOCAL_LIBM_END(__libm_error_region)
2060 .type __libm_error_support#,@function
2061 .global __libm_error_support#