1.file "erfcl.s" 2 3 4// Copyright (c) 2001 - 2005, Intel Corporation 5// All rights reserved. 6// 7// 8// Redistribution and use in source and binary forms, with or without 9// modification, are permitted provided that the following conditions are 10// met: 11// 12// * Redistributions of source code must retain the above copyright 13// notice, this list of conditions and the following disclaimer. 14// 15// * Redistributions in binary form must reproduce the above copyright 16// notice, this list of conditions and the following disclaimer in the 17// documentation and/or other materials provided with the distribution. 18// 19// * The name of Intel Corporation may not be used to endorse or promote 20// products derived from this software without specific prior written 21// permission. 22 23// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 24// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 25// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 26// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS 27// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, 28// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 29// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 30// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY 31// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING 32// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 33// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 34// 35// Intel Corporation is the author of this code, and requests that all 36// problem reports or change requests be submitted to it directly at 37// http://www.intel.com/software/products/opensource/libraries/num.htm. 38// 39// History 40//============================================================== 41// 11/12/01 Initial version 42// 02/08/02 Added missing } 43// 05/20/02 Cleaned up namespace and sf0 syntax 44// 02/10/03 Reordered header: .section, .global, .proc, .align; 45// used data8 for long double table values 46// 03/31/05 Reformatted delimiters between data tables 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 coefficients 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) ~=~ 2.0 114 115// Special values 116//============================================================== 117// erfcl(+0) = 1.0 118// erfcl(-0) = 1.0 119 120// erfcl(+qnan) = +qnan 121// erfcl(-qnan) = -qnan 122// erfcl(+snan) = +qnan 123// erfcl(-snan) = -qnan 124 125// erfcl(-inf) = 2.0 126// erfcl(+inf) = +0 127 128//============================================================== 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// approximated 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// 377 378// Overview of operation 379//============================================================== 380 381// Registers used 382//============================================================== 383// Floating Point registers used: 384// f8, input 385// f9 -> f14, f36 -> f126 386 387// General registers used: 388// r32 -> r71 389 390// Predicate registers used: 391// p6 -> p15 392 393// Assembly macros 394//============================================================== 395// GR for exp(X) 396GR_ad_Arg = r33 397GR_ad_C = r34 398GR_ERFC_S_TB = r35 399GR_signexp_x = r36 400GR_exp_x = r36 401GR_exp_mask = r37 402GR_ad_W1 = r38 403GR_ad_W2 = r39 404GR_M2 = r40 405GR_M1 = r41 406GR_K = r42 407GR_exp_2_k = r43 408GR_ad_T1 = r44 409GR_ad_T2 = r45 410GR_N_fix = r46 411GR_ad_P = r47 412GR_exp_bias = r48 413GR_BIAS = r48 414GR_exp_half = r49 415GR_sig_inv_ln2 = r50 416GR_rshf_2to51 = r51 417GR_exp_2tom51 = r52 418GR_rshf = r53 419 420// GR for erfcl(x) 421//============================================================== 422 423GR_ERFC_XC_TB = r54 424GR_ERFC_P_TB = r55 425GR_IndxPlusBias = r56 426GR_P_POINT_1 = r57 427GR_P_POINT_2 = r58 428GR_AbsArg = r59 429GR_ShftXBi = r60 430GR_ShftPi = r61 431GR_mBIAS = r62 432GR_ShftPi_bias = r63 433GR_ShftXBi_bias = r64 434GR_ShftA14 = r65 435GR_ShftA15 = r66 436GR_EpsNorm = r67 437GR_0x1 = r68 438GR_ShftPi_8 = r69 439GR_26PlusBias = r70 440GR_27PlusBias = r71 441 442// GR for __libm_support call 443//============================================================== 444GR_SAVE_B0 = r64 445GR_SAVE_PFS = r65 446GR_SAVE_GP = r66 447GR_SAVE_SP = r67 448 449GR_Parameter_X = r68 450GR_Parameter_Y = r69 451GR_Parameter_RESULT = r70 452GR_Parameter_TAG = r71 453 454//============================================================== 455// Floating Point Registers 456// 457FR_RSHF_2TO51 = f10 458FR_INV_LN2_2TO63 = f11 459FR_W_2TO51_RSH = f12 460FR_2TOM51 = f13 461FR_RSHF = f14 462 463FR_scale = f36 464FR_float_N = f37 465FR_N_signif = f38 466FR_L_hi = f39 467FR_L_lo = f40 468FR_r = f41 469FR_W1 = f42 470FR_T1 = f43 471FR_W2 = f44 472FR_T2 = f45 473FR_rsq = f46 474FR_C2 = f47 475FR_C3 = f48 476FR_poly = f49 477FR_P6 = f49 478FR_T = f50 479FR_P5 = f50 480FR_P4 = f51 481FR_W = f51 482FR_P3 = f52 483FR_Wp1 = f52 484FR_P2 = f53 485FR_P1 = f54 486FR_Q7 = f56 487FR_Q6 = f57 488FR_Q5 = f58 489FR_Q4 = f59 490FR_Q3 = f60 491FR_Q2 = f61 492FR_Q1 = f62 493FR_C1 = f63 494FR_A15 = f64 495FR_ch_dx = f65 496FR_T_scale = f66 497FR_norm_x = f67 498FR_AbsArg = f68 499FR_POS_ARG_ASYMP = f69 500FR_NEG_ARG_ASYMP = f70 501FR_Tmp = f71 502FR_Xc = f72 503FR_A0 = f73 504FR_A1 = f74 505FR_A2 = f75 506FR_A3 = f76 507FR_A4 = f77 508FR_A5 = f78 509FR_A6 = f79 510FR_A7 = f80 511FR_A8 = f81 512FR_A9 = f82 513FR_A10 = f83 514FR_A11 = f84 515FR_A12 = f85 516FR_A13 = f86 517FR_A14 = f87 518FR_P15_0_1 = f88 519FR_P15_8_1 = f88 520FR_P15_1_1 = f89 521FR_P15_8_2 = f89 522FR_P15_1_2 = f90 523FR_P15_2_1 = f91 524FR_P15_2_2 = f92 525FR_P15_3_1 = f93 526FR_P15_3_2 = f94 527FR_P15_4_2 = f95 528FR_P15_7_1 = f96 529FR_P15_7_2 = f97 530FR_P15_9_1 = f98 531FR_P15_9_2 = f99 532FR_P15_13_1 = f100 533FR_P15_14_1 = f101 534FR_P15_14_2 = f102 535FR_Tmp2 = f103 536FR_Xpdx_lo = f104 537FR_2 = f105 538FR_xsq_lo = f106 539FR_LocArg = f107 540FR_Tmpf = f108 541FR_Tmp1 = f109 542FR_EpsNorm = f110 543FR_UnfBound = f111 544FR_NormX = f112 545FR_Xpdx_hi = f113 546FR_dU = f114 547FR_H = f115 548FR_G = f116 549FR_V = f117 550FR_M = f118 551FR_U = f119 552FR_Q = f120 553FR_S = f121 554FR_R = f122 555FR_res_pos_x_hi = f123 556FR_res_pos_x_lo = f124 557FR_dx = f125 558FR_dx1 = f126 559 560// for error handler routine 561FR_X = f9 562FR_Y = f0 563FR_RESULT = f8 564 565// Data tables 566//============================================================== 567RODATA 568.align 16 569 570// ************* DO NOT CHANGE ORDER OF THESE TABLES ******************** 571LOCAL_OBJECT_START(exp_table_1) 572 573data8 0xae89f995ad3ad5ea , 0x00003ffe // x = 0.681..,bound for dx = 0.875 574data8 0x405AC00000000000 , 0x401A000000000000 //ARG_ASYMP,NEG_ARG_ASYMP 575data8 0x3FE4000000000000 , 0x3FEC000000000000 //0.625,0.875 576data8 0xD5126065B720A4e9 , 0x00004005 // underflow boundary 577data8 0x8000000000000000 , 0x00000001 //FR_EpsNorm 578LOCAL_OBJECT_END(exp_table_1) 579 580LOCAL_OBJECT_START(Constants_exp_64_Arg) 581data8 0xB17217F400000000,0x00003FF2 //L_hi = hi part log(2)/2^12 582data8 0xF473DE6AF278ECE6,0x00003FD4 //L_lo = lo part log(2)/2^12 583LOCAL_OBJECT_END(Constants_exp_64_Arg) 584 585LOCAL_OBJECT_START(Constants_exp_64_C) 586data8 0xAAAAAAABB1B736A0,0x00003FFA // C3 587data8 0xAAAAAAAB90CD6327,0x00003FFC // C2 588data8 0xFFFFFFFFFFFFFFFF,0x00003FFD // C1 589LOCAL_OBJECT_END(Constants_exp_64_C) 590 591LOCAL_OBJECT_START(Constants_exp_64_T1) 592data4 0x3F800000,0x3F8164D2,0x3F82CD87,0x3F843A29 593data4 0x3F85AAC3,0x3F871F62,0x3F88980F,0x3F8A14D5 594data4 0x3F8B95C2,0x3F8D1ADF,0x3F8EA43A,0x3F9031DC 595data4 0x3F91C3D3,0x3F935A2B,0x3F94F4F0,0x3F96942D 596data4 0x3F9837F0,0x3F99E046,0x3F9B8D3A,0x3F9D3EDA 597data4 0x3F9EF532,0x3FA0B051,0x3FA27043,0x3FA43516 598data4 0x3FA5FED7,0x3FA7CD94,0x3FA9A15B,0x3FAB7A3A 599data4 0x3FAD583F,0x3FAF3B79,0x3FB123F6,0x3FB311C4 600data4 0x3FB504F3,0x3FB6FD92,0x3FB8FBAF,0x3FBAFF5B 601data4 0x3FBD08A4,0x3FBF179A,0x3FC12C4D,0x3FC346CD 602data4 0x3FC5672A,0x3FC78D75,0x3FC9B9BE,0x3FCBEC15 603data4 0x3FCE248C,0x3FD06334,0x3FD2A81E,0x3FD4F35B 604data4 0x3FD744FD,0x3FD99D16,0x3FDBFBB8,0x3FDE60F5 605data4 0x3FE0CCDF,0x3FE33F89,0x3FE5B907,0x3FE8396A 606data4 0x3FEAC0C7,0x3FED4F30,0x3FEFE4BA,0x3FF28177 607data4 0x3FF5257D,0x3FF7D0DF,0x3FFA83B3,0x3FFD3E0C 608LOCAL_OBJECT_END(Constants_exp_64_T1) 609 610LOCAL_OBJECT_START(Constants_exp_64_T2) 611data4 0x3F800000,0x3F80058C,0x3F800B18,0x3F8010A4 612data4 0x3F801630,0x3F801BBD,0x3F80214A,0x3F8026D7 613data4 0x3F802C64,0x3F8031F2,0x3F803780,0x3F803D0E 614data4 0x3F80429C,0x3F80482B,0x3F804DB9,0x3F805349 615data4 0x3F8058D8,0x3F805E67,0x3F8063F7,0x3F806987 616data4 0x3F806F17,0x3F8074A8,0x3F807A39,0x3F807FCA 617data4 0x3F80855B,0x3F808AEC,0x3F80907E,0x3F809610 618data4 0x3F809BA2,0x3F80A135,0x3F80A6C7,0x3F80AC5A 619data4 0x3F80B1ED,0x3F80B781,0x3F80BD14,0x3F80C2A8 620data4 0x3F80C83C,0x3F80CDD1,0x3F80D365,0x3F80D8FA 621data4 0x3F80DE8F,0x3F80E425,0x3F80E9BA,0x3F80EF50 622data4 0x3F80F4E6,0x3F80FA7C,0x3F810013,0x3F8105AA 623data4 0x3F810B41,0x3F8110D8,0x3F81166F,0x3F811C07 624data4 0x3F81219F,0x3F812737,0x3F812CD0,0x3F813269 625data4 0x3F813802,0x3F813D9B,0x3F814334,0x3F8148CE 626data4 0x3F814E68,0x3F815402,0x3F81599C,0x3F815F37 627LOCAL_OBJECT_END(Constants_exp_64_T2) 628 629LOCAL_OBJECT_START(Constants_exp_64_W1) 630data8 0x0000000000000000, 0xBE384454171EC4B4 631data8 0xBE6947414AA72766, 0xBE5D32B6D42518F8 632data8 0x3E68D96D3A319149, 0xBE68F4DA62415F36 633data8 0xBE6DDA2FC9C86A3B, 0x3E6B2E50F49228FE 634data8 0xBE49C0C21188B886, 0x3E64BFC21A4C2F1F 635data8 0xBE6A2FBB2CB98B54, 0x3E5DC5DE9A55D329 636data8 0x3E69649039A7AACE, 0x3E54728B5C66DBA5 637data8 0xBE62B0DBBA1C7D7D, 0x3E576E0409F1AF5F 638data8 0x3E6125001A0DD6A1, 0xBE66A419795FBDEF 639data8 0xBE5CDE8CE1BD41FC, 0xBE621376EA54964F 640data8 0x3E6370BE476E76EE, 0x3E390D1A3427EB92 641data8 0x3E1336DE2BF82BF8, 0xBE5FF1CBD0F7BD9E 642data8 0xBE60A3550CEB09DD, 0xBE5CA37E0980F30D 643data8 0xBE5C541B4C082D25, 0xBE5BBECA3B467D29 644data8 0xBE400D8AB9D946C5, 0xBE5E2A0807ED374A 645data8 0xBE66CB28365C8B0A, 0x3E3AAD5BD3403BCA 646data8 0x3E526055C7EA21E0, 0xBE442C75E72880D6 647data8 0x3E58B2BB85222A43, 0xBE5AAB79522C42BF 648data8 0xBE605CB4469DC2BC, 0xBE589FA7A48C40DC 649data8 0xBE51C2141AA42614, 0xBE48D087C37293F4 650data8 0x3E367A1CA2D673E0, 0xBE51BEBB114F7A38 651data8 0xBE6348E5661A4B48, 0xBDF526431D3B9962 652data8 0x3E3A3B5E35A78A53, 0xBE46C46C1CECD788 653data8 0xBE60B7EC7857D689, 0xBE594D3DD14F1AD7 654data8 0xBE4F9C304C9A8F60, 0xBE52187302DFF9D2 655data8 0xBE5E4C8855E6D68F, 0xBE62140F667F3DC4 656data8 0xBE36961B3BF88747, 0x3E602861C96EC6AA 657data8 0xBE3B5151D57FD718, 0x3E561CD0FC4A627B 658data8 0xBE3A5217CA913FEA, 0x3E40A3CC9A5D193A 659data8 0xBE5AB71310A9C312, 0x3E4FDADBC5F57719 660data8 0x3E361428DBDF59D5, 0x3E5DB5DB61B4180D 661data8 0xBE42AD5F7408D856, 0x3E2A314831B2B707 662LOCAL_OBJECT_END(Constants_exp_64_W1) 663 664LOCAL_OBJECT_START(Constants_exp_64_W2) 665data8 0x0000000000000000, 0xBE641F2537A3D7A2 666data8 0xBE68DD57AD028C40, 0xBE5C77D8F212B1B6 667data8 0x3E57878F1BA5B070, 0xBE55A36A2ECAE6FE 668data8 0xBE620608569DFA3B, 0xBE53B50EA6D300A3 669data8 0x3E5B5EF2223F8F2C, 0xBE56A0D9D6DE0DF4 670data8 0xBE64EEF3EAE28F51, 0xBE5E5AE2367EA80B 671data8 0x3E47CB1A5FCBC02D, 0xBE656BA09BDAFEB7 672data8 0x3E6E70C6805AFEE7, 0xBE6E0509A3415EBA 673data8 0xBE56856B49BFF529, 0x3E66DD3300508651 674data8 0x3E51165FC114BC13, 0x3E53333DC453290F 675data8 0x3E6A072B05539FDA, 0xBE47CD877C0A7696 676data8 0xBE668BF4EB05C6D9, 0xBE67C3E36AE86C93 677data8 0xBE533904D0B3E84B, 0x3E63E8D9556B53CE 678data8 0x3E212C8963A98DC8, 0xBE33138F032A7A22 679data8 0x3E530FA9BC584008, 0xBE6ADF82CCB93C97 680data8 0x3E5F91138370EA39, 0x3E5443A4FB6A05D8 681data8 0x3E63DACD181FEE7A, 0xBE62B29DF0F67DEC 682data8 0x3E65C4833DDE6307, 0x3E5BF030D40A24C1 683data8 0x3E658B8F14E437BE, 0xBE631C29ED98B6C7 684data8 0x3E6335D204CF7C71, 0x3E529EEDE954A79D 685data8 0x3E5D9257F64A2FB8, 0xBE6BED1B854ED06C 686data8 0x3E5096F6D71405CB, 0xBE3D4893ACB9FDF5 687data8 0xBDFEB15801B68349, 0x3E628D35C6A463B9 688data8 0xBE559725ADE45917, 0xBE68C29C042FC476 689data8 0xBE67593B01E511FA, 0xBE4A4313398801ED 690data8 0x3E699571DA7C3300, 0x3E5349BE08062A9E 691data8 0x3E5229C4755BB28E, 0x3E67E42677A1F80D 692data8 0xBE52B33F6B69C352, 0xBE6B3550084DA57F 693data8 0xBE6DB03FD1D09A20, 0xBE60CBC42161B2C1 694data8 0x3E56ED9C78A2B771, 0xBE508E319D0FA795 695data8 0xBE59482AFD1A54E9, 0xBE2A17CEB07FD23E 696data8 0x3E68BF5C17365712, 0x3E3956F9B3785569 697LOCAL_OBJECT_END(Constants_exp_64_W2) 698 699 700LOCAL_OBJECT_START(erfc_xc_table) 701 702data8 0x0000000000000000, 0x00000000 //XC[0] = +0.00000000000000000000e-01L 703data8 0x9A79C70000000000, 0x00003FFD //XC[1] = +3.01710337400436401367e-01L 704data8 0x8C49EF0000000000, 0x00003FFE //XC[2] = +5.48003137111663818359e-01L 705data8 0xD744FC0000000000, 0x00003FFE //XC[3] = +8.40896368026733398438e-01L 706data8 0x9837F00000000000, 0x00003FFF //XC[4] = +1.18920707702636718750e+00L 707data8 0xCD3CE30000000000, 0x00003FFF //XC[5] = +1.60342061519622802734e+00L 708data8 0x8624F70000000000, 0x00004000 //XC[6] = +2.09600615501403808594e+00L 709data8 0xABA27E0000000000, 0x00004000 //XC[7] = +2.68179273605346679688e+00L 710data8 0xD837F00000000000, 0x00004000 //XC[8] = +3.37841415405273437500e+00L 711data8 0x869E710000000000, 0x00004001 //XC[9] = +4.20684099197387695313e+00L 712data8 0xA624F70000000000, 0x00004001 //XC[10] = +5.19201231002807617188e+00L 713data8 0xCBA27E0000000000, 0x00004001 //XC[11] = +6.36358547210693359375e+00L 714data8 0xF837F00000000000, 0x00004001 //XC[12] = +7.75682830810546875000e+00L 715data8 0x969E710000000000, 0x00004002 //XC[13] = +9.41368198394775390625e+00L 716data8 0xB624F70000000000, 0x00004002 //XC[14] = +1.13840246200561523438e+01L 717data8 0xDBA27E0000000000, 0x00004002 //XC[15] = +1.37271709442138671875e+01L 718data8 0x841BF80000000000, 0x00004003 //XC[16] = +1.65136566162109375000e+01L 719data8 0x9E9E710000000000, 0x00004003 //XC[17] = +1.98273639678955078125e+01L 720data8 0xBE24F70000000000, 0x00004003 //XC[18] = +2.37680492401123046875e+01L 721data8 0xE3A27E0000000000, 0x00004003 //XC[19] = +2.84543418884277343750e+01L 722data8 0x881BF80000000000, 0x00004004 //XC[20] = +3.40273132324218750000e+01L 723data8 0xA29E710000000000, 0x00004004 //XC[21] = +4.06547279357910156250e+01L 724data8 0xC224F70000000000, 0x00004004 //XC[22] = +4.85360984802246093750e+01L 725data8 0xE7A27E0000000000, 0x00004004 //XC[23] = +5.79086837768554687500e+01L 726data8 0x8A1BF80000000000, 0x00004005 //XC[24] = +6.90546264648437500000e+01L 727data8 0xA49E710000000000, 0x00004005 //XC[25] = +8.23094558715820312500e+01L 728data8 0xC424F70000000000, 0x00004005 //XC[26] = +9.80721969604492187500e+01L 729data8 0xD5A27E0000000000, 0x00004005 //XC[27] = +1.06817367553710937500e+02L 730LOCAL_OBJECT_END(erfc_xc_table) 731 732LOCAL_OBJECT_START(erfc_s_table) 733 734data8 0xE000000000000000, 0x00003FFE //s[0] = +8.75000000000000000000e-01L 735data8 0xDCEF000000000000, 0x00003FFE //s[1] = +8.63021850585937500000e-01L 736data8 0xD79D000000000000, 0x00003FFE //s[2] = +8.42239379882812500000e-01L 737data8 0xB25E000000000000, 0x00003FFE //s[3] = +6.96746826171875000000e-01L 738data8 0xB0EA000000000000, 0x00003FFE //s[4] = +6.91070556640625000000e-01L 739data8 0xAE3F000000000000, 0x00003FFE //s[5] = +6.80648803710937500000e-01L 740data8 0xAB05000000000000, 0x00003FFE //s[6] = +6.68045043945312500000e-01L 741data8 0xA7AC000000000000, 0x00003FFE //s[7] = +6.54968261718750000000e-01L 742data8 0xA478000000000000, 0x00003FFE //s[8] = +6.42456054687500000000e-01L 743data8 0xA18D000000000000, 0x00003FFE //s[9] = +6.31057739257812500000e-01L 744data8 0x9EF8000000000000, 0x00003FFE //s[10] = +6.20971679687500000000e-01L 745data8 0x9CBA000000000000, 0x00003FFE //s[11] = +6.12213134765625000000e-01L 746data8 0x9ACD000000000000, 0x00003FFE //s[12] = +6.04690551757812500000e-01L 747data8 0x992A000000000000, 0x00003FFE //s[13] = +5.98297119140625000000e-01L 748data8 0x97C7000000000000, 0x00003FFE //s[14] = +5.92880249023437500000e-01L 749data8 0x969C000000000000, 0x00003FFE //s[15] = +5.88317871093750000000e-01L 750data8 0x95A0000000000000, 0x00003FFE //s[16] = +5.84472656250000000000e-01L 751data8 0x94CB000000000000, 0x00003FFE //s[17] = +5.81222534179687500000e-01L 752data8 0x9419000000000000, 0x00003FFE //s[18] = +5.78506469726562500000e-01L 753data8 0x9383000000000000, 0x00003FFE //s[19] = +5.76217651367187500000e-01L 754data8 0x9305000000000000, 0x00003FFE //s[20] = +5.74295043945312500000e-01L 755data8 0x929B000000000000, 0x00003FFE //s[21] = +5.72677612304687500000e-01L 756data8 0x9242000000000000, 0x00003FFE //s[22] = +5.71319580078125000000e-01L 757data8 0x91F8000000000000, 0x00003FFE //s[23] = +5.70190429687500000000e-01L 758data8 0x91B9000000000000, 0x00003FFE //s[24] = +5.69229125976562500000e-01L 759data8 0x9184000000000000, 0x00003FFE //s[25] = +5.68420410156250000000e-01L 760data8 0x9158000000000000, 0x00003FFE //s[26] = +5.67749023437500000000e-01L 761data8 0x9145000000000000, 0x00003FFE //s[27] = +5.67459106445312500000e-01L 762LOCAL_OBJECT_END(erfc_s_table) 763 764LOCAL_OBJECT_START(erfc_Q_table) 765// Q(z)= (P(z)- S)/S 766// 767// Pol0 768data8 0x98325D50F9DC3499, 0x0000BFAA //A0 = +3.07358861423101280650e-26L 769data8 0xED35081A2494DDD9, 0x00003FF8 //A1 = +1.44779757616302832466e-02L 770data8 0x9443549BCD0F94CE, 0x0000BFFD //A2 = -2.89576190966300084405e-01L 771data8 0xC7FD4B98ECF3DBBF, 0x00003FFD //A3 = +3.90604364793467799170e-01L 772data8 0xB82CE31288B49759, 0x0000BFFD //A4 = -3.59717460644199233866e-01L 773data8 0x8A8293447BEF69B5, 0x00003FFD //A5 = +2.70527460203054582368e-01L 774data8 0xB5793E30EE36766C, 0x0000BFFC //A6 = -1.77220317589265674647e-01L 775data8 0xD6066D16BBDECE17, 0x00003FFB //A7 = +1.04504444366724593714e-01L 776data8 0xE7C783CE3C997BD8, 0x0000BFFA //A8 = -5.65867565781331646771e-02L 777data8 0xE9969EBC2F5B2828, 0x00003FF9 //A9 = +2.85142040533900194955e-02L 778data8 0xDD31D619F29AD7BF, 0x0000BFF8 //A10 = -1.35006514390540367929e-02L 779data8 0xC63A20EB59768F3A, 0x00003FF7 //A11 = +6.04940993680332271481e-03L 780data8 0xA8DEC641AACEB600, 0x0000BFF6 //A12 = -2.57675495383156581601e-03L 781data8 0x87F0E77BA914FBEB, 0x00003FF5 //A13 = +1.03714776726541296794e-03L 782data8 0xC306C2894C5CEF2D, 0x0000BFF3 //A14 = -3.71983348634136412407e-04L 783data8 0xBDAB416A989D0697, 0x00003FF1 //A15 = +9.04412111877987292294e-05L 784// Pol1 785data8 0x82808893DA2DD83F, 0x00003FEE //A0 = +7.77853035974467145290e-06L 786data8 0xAE9CD9DCADC86113, 0x0000BFFB //A1 = -8.52601070853077921197e-02L 787data8 0x9D429743E312AD9F, 0x0000BFFB //A2 = -7.67871682732076080494e-02L 788data8 0x8637FC533AE805DC, 0x00003FFC //A3 = +1.31072943286859831330e-01L 789data8 0xF68DBE3639ABCB6E, 0x0000BFFB //A4 = -1.20387540845703264588e-01L 790data8 0xB168FFC3CFA71256, 0x00003FFB //A5 = +8.66260511047190247534e-02L 791data8 0xDBC5078A7EA89236, 0x0000BFFA //A6 = -5.36546988077281230848e-02L 792data8 0xF4331FEDB2CB838F, 0x00003FF9 //A7 = +2.98095344165515989564e-02L 793data8 0xF909173C0E61C25D, 0x0000BFF8 //A8 = -1.51999213123642373375e-02L 794data8 0xEC83560A2ACB23E9, 0x00003FF7 //A9 = +7.21780491979582106904e-03L 795data8 0xD350D62C4FEAD8F5, 0x0000BFF6 //A10 = -3.22442272982896360044e-03L 796data8 0xB2F44F4B3FD9B826, 0x00003FF5 //A11 = +1.36531322425499451283e-03L 797data8 0x9078BC61927671C6, 0x0000BFF4 //A12 = -5.51115510818844954547e-04L 798data8 0xDF67AC6287A63B03, 0x00003FF2 //A13 = +2.13055585989529858265e-04L 799data8 0xA719CFEE67FCE1CE, 0x0000BFF1 //A14 = -7.96798844477905965933e-05L 800data8 0xEF926367BABBB029, 0x00003FEF //A15 = +2.85591875675765038065e-05L 801// Pol2 802data8 0x82B5E5A93B059C50, 0x00003FEF //A0 = +1.55819100856330860049e-05L 803data8 0xDC856BC2542B1938, 0x0000BFFB //A1 = -1.07676355235999875911e-01L 804data8 0xDF225EF5694F14AE, 0x0000BFF8 //A2 = -1.36190345125628043277e-02L 805data8 0xDAF66A954ED22428, 0x00003FFA //A3 = +5.34576571853233908886e-02L 806data8 0xD28AE4F21A392EC6, 0x0000BFFA //A4 = -5.14019911949062230820e-02L 807data8 0x9441A95713F0DB5B, 0x00003FFA //A5 = +3.61954321717769771045e-02L 808data8 0xB0957B5C483C7A04, 0x0000BFF9 //A6 = -2.15556535133667988704e-02L 809data8 0xBB9260E812814F71, 0x00003FF8 //A7 = +1.14484735825400480057e-02L 810data8 0xB68AB17287ABAB04, 0x0000BFF7 //A8 = -5.57073273108465072470e-03L 811data8 0xA56A95E0BC0EF01B, 0x00003FF6 //A9 = +2.52405318381952650677e-03L 812data8 0x8D19C7D286839C00, 0x0000BFF5 //A10 = -1.07651294935087466892e-03L 813data8 0xE45DB3766711A0D3, 0x00003FF3 //A11 = +4.35573615323234291196e-04L 814data8 0xB05949F947FA7AEF, 0x0000BFF2 //A12 = -1.68179306983868501372e-04L 815data8 0x82901D055A0D5CB6, 0x00003FF1 //A13 = +6.22572626227726684168e-05L 816data8 0xBB957698542D6FD0, 0x0000BFEF //A14 = -2.23617364009159182821e-05L 817data8 0x810740E1DF572394, 0x00003FEE //A15 = +7.69068800065192940487e-06L 818// Pol3 819data8 0x9526D1C87655AFA8, 0x00003FEC //A0 = +2.22253260814242012255e-06L 820data8 0xA47E21EBFE73F72F, 0x0000BFF8 //A1 = -1.00398379581527733314e-02L 821data8 0xDE65685FCDF7A913, 0x0000BFFA //A2 = -5.42959286802879105148e-02L 822data8 0xED289CB8F97D4860, 0x00003FFA //A3 = +5.79000589346770417248e-02L 823data8 0xAA3100D5A7D870F1, 0x0000BFFA //A4 = -4.15506394006027604387e-02L 824data8 0xCA0567032C5308C0, 0x00003FF9 //A5 = +2.46607791863290331169e-02L 825data8 0xD3E1794A50F31BEB, 0x0000BFF8 //A6 = -1.29321751094401754013e-02L 826data8 0xCAA02CB4C87CC1F0, 0x00003FF7 //A7 = +6.18364508551740736863e-03L 827data8 0xB3F126AF16B121F2, 0x0000BFF6 //A8 = -2.74569696838501870748e-03L 828data8 0x962B2D64D3900510, 0x00003FF5 //A9 = +1.14569596409019883022e-03L 829data8 0xED8785714A9A00FB, 0x0000BFF3 //A10 = -4.53051338046340380512e-04L 830data8 0xB325DA4515D8B54C, 0x00003FF2 //A11 = +1.70848714622328427290e-04L 831data8 0x8179C36354571747, 0x0000BFF1 //A12 = -6.17387951061077132522e-05L 832data8 0xB40F241C01C907E9, 0x00003FEF //A13 = +2.14647227210702861416e-05L 833data8 0xF436D84AD7D4D316, 0x0000BFED //A14 = -7.27815144835213913238e-06L 834data8 0x9EB432503FB0B7BC, 0x00003FEC //A15 = +2.36487228755136968792e-06L 835// Pol4 836data8 0xE0BA539E4AFC4741, 0x00003FED //A0 = +6.69741148991838024429e-06L 837data8 0x8583BF71139452CF, 0x0000BFFA //A1 = -3.25963476363756051657e-02L 838data8 0x8384FEF6D08AD6CE, 0x0000BFF9 //A2 = -1.60546283500634200479e-02L 839data8 0xB1E67DFB84C97036, 0x00003FF9 //A3 = +2.17163525195697635702e-02L 840data8 0xFB6ACEE6899E360D, 0x0000BFF8 //A4 = -1.53452892792759316229e-02L 841data8 0x8D2B869EB9149905, 0x00003FF8 //A5 = +8.61633440480716870830e-03L 842data8 0x8A90BFE0FD869A41, 0x0000BFF7 //A6 = -4.22868126950622376530e-03L 843data8 0xF7536A76E59F54D2, 0x00003FF5 //A7 = +1.88694643606912107006e-03L 844data8 0xCCF6FE58C16E1CC7, 0x0000BFF4 //A8 = -7.81878732767742447339e-04L 845data8 0x9FCC6ED9914FAA24, 0x00003FF3 //A9 = +3.04791577214885118730e-04L 846data8 0xEC7F5AAACAE593E8, 0x0000BFF1 //A10 = -1.12770784960291779798e-04L 847data8 0xA72CE628A114C940, 0x00003FF0 //A11 = +3.98577182157456408782e-05L 848data8 0xE2DCC5750FD769BA, 0x0000BFEE //A12 = -1.35220520471857266339e-05L 849data8 0x9459160B1E6F1F8D, 0x00003FED //A13 = +4.42111470121432700283e-06L 850data8 0xBE0A05701BD0DD42, 0x0000BFEB //A14 = -1.41590196994052764542e-06L 851data8 0xE905D729105081BF, 0x00003FE9 //A15 = +4.34038814785401120999e-07L 852// Pol5 853data8 0xA33649C3AB459832, 0x00003FEE //A0 = +9.72819704141525206634e-06L 854data8 0x9E4EA2F44C9A24BD, 0x0000BFFA //A1 = -3.86492123987296806210e-02L 855data8 0xE80C0B1280F357BF, 0x0000BFF2 //A2 = -2.21297306012713370124e-04L 856data8 0xDAECCE90A4D45D9A, 0x00003FF7 //A3 = +6.68106161291482829670e-03L 857data8 0xA4006572071BDD4B, 0x0000BFF7 //A4 = -5.00493005170532147076e-03L 858data8 0xB07FD7EB1F4D8E8E, 0x00003FF6 //A5 = +2.69316693731732554959e-03L 859data8 0xA1F471D42ADD73A1, 0x0000BFF5 //A6 = -1.23561753760779610478e-03L 860data8 0x8611D0ED1B4C8176, 0x00003FF4 //A7 = +5.11434914439322741260e-04L 861data8 0xCDADB789B487A541, 0x0000BFF2 //A8 = -1.96150380913036018825e-04L 862data8 0x9470252731687FEE, 0x00003FF1 //A9 = +7.07807859951401721129e-05L 863data8 0xCB9399AD1C376D85, 0x0000BFEF //A10 = -2.42682175234436724152e-05L 864data8 0x858D815F9CA0A9F7, 0x00003FEE //A11 = +7.96036454038012144300e-06L 865data8 0xA878D338E6E6A079, 0x0000BFEC //A12 = -2.51042802626063073967e-06L 866data8 0xCD2C2F079D2FCB36, 0x00003FEA //A13 = +7.64327468786076941271e-07L 867data8 0xF5EF4A4B2EA426F2, 0x0000BFE8 //A14 = -2.29044563492386125272e-07L 868data8 0x8CE52181393820FC, 0x00003FE7 //A15 = +6.56093668622712763489e-08L 869// Pol6 870data8 0xB2015D7F1864B7CF, 0x00003FEC //A0 = +2.65248615880090351276e-06L 871data8 0x954EA7A861B4462A, 0x0000BFFA //A1 = -3.64519642954351295215e-02L 872data8 0x9E46F2A4D9157E69, 0x00003FF7 //A2 = +4.83023498390681965101e-03L 873data8 0xA0D12B422FFD5BAD, 0x00003FF5 //A3 = +1.22693684633643883352e-03L 874data8 0xB291D16A560A740E, 0x0000BFF5 //A4 = -1.36237794246703606647e-03L 875data8 0xC138941BC8AF4A9D, 0x00003FF4 //A5 = +7.37079658343628747256e-04L 876data8 0xA761669D61B405CF, 0x0000BFF3 //A6 = -3.19252914480518163396e-04L 877data8 0x8053680F1C84607E, 0x00003FF2 //A7 = +1.22381025852939439541e-04L 878data8 0xB518F4B6F25015F9, 0x0000BFF0 //A8 = -4.31770048258291369742e-05L 879data8 0xEFF526AC70B9411E, 0x00003FEE //A9 = +1.43025887824433324525e-05L 880data8 0x970B2A848DF5B5C2, 0x0000BFED //A10 = -4.50145058393497252604e-06L 881data8 0xB614D2E61DB86963, 0x00003FEB //A11 = +1.35661172167726780059e-06L 882data8 0xD34EA4D283EC33FA, 0x0000BFE9 //A12 = -3.93590335713880681528e-07L 883data8 0xED209EBD68E1145F, 0x00003FE7 //A13 = +1.10421060667544991323e-07L 884data8 0x83A126E22A17568D, 0x0000BFE6 //A14 = -3.06473811074239684132e-08L 885data8 0x8B778496EDE9F415, 0x00003FE4 //A15 = +8.11804009754249175736e-09L 886// Pol7 887data8 0x8E152F522501B7B9, 0x00003FEE //A0 = +8.46879203970927626532e-06L 888data8 0xFD22F92EE21F491E, 0x0000BFF9 //A1 = -3.09004656656418947425e-02L 889data8 0xAF0C41847D89EC14, 0x00003FF7 //A2 = +5.34203719233189217519e-03L 890data8 0xB7C539C400445956, 0x0000BFF3 //A3 = -3.50514245383356287965e-04L 891data8 0x8428C78B2B1E3622, 0x0000BFF3 //A4 = -2.52073850239006530978e-04L 892data8 0xAFC0CCC7D1A05F5B, 0x00003FF2 //A5 = +1.67611241057491801028e-04L 893data8 0x95DC7272C5695A5A, 0x0000BFF1 //A6 = -7.14593512262564106636e-05L 894data8 0xD6FCA68A61F0E835, 0x00003FEF //A7 = +2.56284375437771117850e-05L 895data8 0x8B71C74DEA936C66, 0x0000BFEE //A8 = -8.31153675277218441096e-06L 896data8 0xA8AC71E2A56AA2C9, 0x00003FEC //A9 = +2.51343269277107451413e-06L 897data8 0xC15DED6C44B46046, 0x0000BFEA //A10 = -7.20347851650066610771e-07L 898data8 0xD42BA1DFBD1277AC, 0x00003FE8 //A11 = +1.97599119274780745741e-07L 899data8 0xE03A81F2C976D11A, 0x0000BFE6 //A12 = -5.22072765405802337371e-08L 900data8 0xE56A19A67DD66100, 0x00003FE4 //A13 = +1.33536787408751203998e-08L 901data8 0xE964D255CB31DFFA, 0x0000BFE2 //A14 = -3.39632729387679010008e-09L 902data8 0xE22E62E932B704D4, 0x00003FE0 //A15 = +8.22842400379225526299e-10L 903// Pol8 904data8 0xB8B835882D46A6C8, 0x00003FEF //A0 = +2.20202883282415435401e-05L 905data8 0xC9D1F63F89B74E90, 0x0000BFF9 //A1 = -2.46362504515706189782e-02L 906data8 0x8E376748B1274F30, 0x00003FF7 //A2 = +4.34010070001387441657e-03L 907data8 0x98174C7EA49B5B37, 0x0000BFF4 //A3 = -5.80181163659971286762e-04L 908data8 0x8D2C40506AE9FF97, 0x00003FEF //A4 = +1.68291159100251734927e-05L 909data8 0xD9A580C115B9D150, 0x00003FEF //A5 = +2.59454841475194555896e-05L 910data8 0xDB35B21F1C3F99CE, 0x0000BFEE //A6 = -1.30659192305072674545e-05L 911data8 0x99FAADAE17A3050E, 0x00003FED //A7 = +4.58893813631592314881e-06L 912data8 0xBA1D259BCD6987A9, 0x0000BFEB //A8 = -1.38665627771423394637e-06L 913data8 0xCDD7FF5BEA0145C2, 0x00003FE9 //A9 = +3.83413844219813384124e-07L 914data8 0xD60857176CE6AB9D, 0x0000BFE7 //A10 = -9.96666862214499946343e-08L 915data8 0xD446A2402112DF4C, 0x00003FE5 //A11 = +2.47121687566658908126e-08L 916data8 0xCA87133235F1F495, 0x0000BFE3 //A12 = -5.89433000014933371980e-09L 917data8 0xBB15B0021581C8B6, 0x00003FE1 //A13 = +1.36122047057936849125e-09L 918data8 0xAC9D6585D4AF505E, 0x0000BFDF //A14 = -3.13984547328132268695e-10L 919data8 0x975A1439C3795183, 0x00003FDD //A15 = +6.88268624429648826457e-11L 920// Pol9 921data8 0x99A7676284CDC9FE, 0x00003FEF //A0 = +1.83169747921764176475e-05L 922data8 0x9AD0AE249A02896C, 0x0000BFF9 //A1 = -1.88983346204739151909e-02L 923data8 0xCB89B4AEC19898BE, 0x00003FF6 //A2 = +3.10574208447745576452e-03L 924data8 0xEBBC47E30E1AC2C2, 0x0000BFF3 //A3 = -4.49629730048297442064e-04L 925data8 0xD1E35B7FCE1CF859, 0x00003FF0 //A4 = +5.00412261289558493438e-05L 926data8 0xB40743664EF24552, 0x0000BFEB //A5 = -1.34131589671166307319e-06L 927data8 0xCAD2F5C596FFE1B4, 0x0000BFEB //A6 = -1.51115702599728593837e-06L 928data8 0xAE42B6D069DFDDF2, 0x00003FEA //A7 = +6.49171330116787223873e-07L 929data8 0xD0739A05BB43A714, 0x0000BFE8 //A8 = -1.94135651872623440782e-07L 930data8 0xD745B854AB601BD7, 0x00003FE6 //A9 = +5.01219983943456578062e-08L 931data8 0xCC4066E13E338B13, 0x0000BFE4 //A10 = -1.18890061172430768892e-08L 932data8 0xB6EAADB55A6C3CB4, 0x00003FE2 //A11 = +2.66178850259168707794e-09L 933data8 0x9CC6C178AD3F96AD, 0x0000BFE0 //A12 = -5.70349182959704086428e-10L 934data8 0x81D0E2AA27DEB74A, 0x00003FDE //A13 = +1.18066926578104076645e-10L 935data8 0xD75FB9049190BEFD, 0x0000BFDB //A14 = -2.44851795398843967972e-11L 936data8 0xA9384A51D48C8703, 0x00003FD9 //A15 = +4.80951837368635202609e-12L 937// Pol10 938data8 0xD2B3482EE449C535, 0x00003FEE //A0 = +1.25587177382575655080e-05L 939data8 0xE7939B2D0607DFCF, 0x0000BFF8 //A1 = -1.41343131436717436429e-02L 940data8 0x8810EB4AC5F0F1CE, 0x00003FF6 //A2 = +2.07620377002350121270e-03L 941data8 0x9546589602AEB955, 0x0000BFF3 //A3 = -2.84719065122144294949e-04L 942data8 0x9333434342229798, 0x00003FF0 //A4 = +3.50952732796136549298e-05L 943data8 0xEB36A98FD81D3DEB, 0x0000BFEC //A5 = -3.50495464815398722482e-06L 944data8 0xAC370EFA025D0477, 0x00003FE8 //A6 = +1.60387784498518639254e-07L 945data8 0xC8DF7F8ACA099426, 0x00003FE6 //A7 = +4.67693991699936842330e-08L 946data8 0xAC694AD4921C02CF, 0x0000BFE5 //A8 = -2.00713167514877937714e-08L 947data8 0xB6E29F2FDE2D8C1A, 0x00003FE3 //A9 = +5.32266106167252495164e-09L 948data8 0xA41F8EEA75474358, 0x0000BFE1 //A10 = -1.19415398856537468324e-09L 949data8 0x869D778A1C56D3D6, 0x00003FDF //A11 = +2.44863450057778470469e-10L 950data8 0xD02658BF31411F4C, 0x0000BFDC //A12 = -4.73277831746128372261e-11L 951data8 0x9A4A95EE59127779, 0x00003FDA //A13 = +8.77044784978207256260e-12L 952data8 0xE518330AF013C2F6, 0x0000BFD7 //A14 = -1.62781453276882333209e-12L 953data8 0xA036A9DF71BD108A, 0x00003FD5 //A15 = +2.84596398987114375607e-13L 954// Pol11 955data8 0x9191CFBF001F3BB3, 0x00003FEE //A0 = +8.67662287973472452343e-06L 956data8 0xAA47E0CF01AE9730, 0x0000BFF8 //A1 = -1.03931136509584404513e-02L 957data8 0xAEABE7F17B01D18F, 0x00003FF5 //A2 = +1.33263784731775399430e-03L 958data8 0xAC0D6A309D04E5DB, 0x0000BFF2 //A3 = -1.64081956462118568288e-04L 959data8 0xA08357DF458054D0, 0x00003FEF //A4 = +1.91346477952797715021e-05L 960data8 0x8A1596B557440FE0, 0x0000BFEC //A5 = -2.05761687274453412571e-06L 961data8 0xCDA0EAE0A5615E9A, 0x00003FE8 //A6 = +1.91506542215670149741e-07L 962data8 0xD36A08FB4E104F9A, 0x0000BFE4 //A7 = -1.23059260396551086769e-08L 963data8 0xD7433F91E78A7A11, 0x0000BFDF //A8 = -3.91560549815575091188e-10L 964data8 0xC2F5308FD4F5CE62, 0x00003FDF //A9 = +3.54626121852421163117e-10L 965data8 0xC83876915F49D630, 0x0000BFDD //A10 = -9.10497688901018285126e-11L 966data8 0xA11C605DEAE1FE9C, 0x00003FDB //A11 = +1.83161825409194847892e-11L 967data8 0xE7977BC1342D19BF, 0x0000BFD8 //A12 = -3.29111645807102123274e-12L 968data8 0x9BC3A7D6396C6756, 0x00003FD6 //A13 = +5.53385887288503961220e-13L 969data8 0xD0110D5683740B8C, 0x0000BFD3 //A14 = -9.24001363293241428519e-14L 970data8 0x81786D7856A5CC92, 0x00003FD1 //A15 = +1.43741041714595023996e-14L 971// Pol12 972data8 0xB85654F6033B3372, 0x00003FEF //A0 = +2.19747106911869287049e-05L 973data8 0xF78B40078736B406, 0x0000BFF7 //A1 = -7.55444170413862312647e-03L 974data8 0xDA8FDE84D88E5D5D, 0x00003FF4 //A2 = +8.33747822263358628569e-04L 975data8 0xBC2D3F3891721AA9, 0x0000BFF1 //A3 = -8.97296647669960333635e-05L 976data8 0x9D15ACFD3BF50064, 0x00003FEE //A4 = +9.36297600601039610762e-06L 977data8 0xFBED3D03F3C1B671, 0x0000BFEA //A5 = -9.38500137149172923985e-07L 978data8 0xBEE615E3B2FA16C8, 0x00003FE7 //A6 = +8.88941676851808958175e-08L 979data8 0x843D32692CF5662A, 0x0000BFE4 //A7 = -7.69732580860195238520e-09L 980data8 0x99E74472FD94E22B, 0x00003FE0 //A8 = +5.59897264617128952416e-10L 981data8 0xCEF63DABF4C32E15, 0x0000BFDB //A9 = -2.35288414996279313219e-11L 982data8 0xA2D86C25C0991123, 0x0000BFD8 //A10 = -2.31417232327307408235e-12L 983data8 0xF50C1B31D2E922BD, 0x00003FD6 //A11 = +8.70582858983364191159e-13L 984data8 0xC0F093DEC2B019A1, 0x0000BFD4 //A12 = -1.71364927865227509533e-13L 985data8 0xFC1441C4CD105981, 0x00003FD1 //A13 = +2.79864052545369490865e-14L 986data8 0x9CC959853267F026, 0x0000BFCF //A14 = -4.35170017302700609509e-15L 987data8 0xB06BA14016154F1E, 0x00003FCC //A15 = +6.12081320471295704631e-16L 988// Pol13 989data8 0xA59E74BF544F2422, 0x00003FEF //A0 = +1.97433196215210145261e-05L 990data8 0xB2814F4EDAE15330, 0x0000BFF7 //A1 = -5.44754383528015875700e-03L 991data8 0x867C249D378F0A23, 0x00003FF4 //A2 = +5.13019308804593120161e-04L 992data8 0xC76644393388AB68, 0x0000BFF0 //A3 = -4.75405403392600215101e-05L 993data8 0x91143AD5CCA229FE, 0x00003FED //A4 = +4.32369180778264703719e-06L 994data8 0xCE6A11FB6840A974, 0x0000BFE9 //A5 = -3.84476663329551178495e-07L 995data8 0x8EC29F66C59DE243, 0x00003FE6 //A6 = +3.32389596787155456596e-08L 996data8 0xBE3FCDDCA94CA24E, 0x0000BFE2 //A7 = -2.76849073931513325199e-09L 997data8 0xF06A84BDC70A0B0D, 0x00003FDE //A8 = +2.18657158231304988330e-10L 998data8 0x8B8E6969D056D124, 0x0000BFDB //A9 = -1.58657139740906811035e-11L 999data8 0x8984985AA29A0567, 0x00003FD7 //A10 = +9.77123802231106533829e-13L 1000data8 0xA53ABA084300137C, 0x0000BFD2 //A11 = -3.66882970952892030306e-14L 1001data8 0xA90EC851E91C3319, 0x0000BFCE //A12 = -2.34614750044359490986e-15L 1002data8 0xEC9CAF64237B5060, 0x00003FCC //A13 = +8.20912960028437475035e-16L 1003data8 0xA9156668FCF01479, 0x0000BFCA //A14 = -1.46656639874123613261e-16L 1004data8 0xBAEF58D8118DD5D4, 0x00003FC7 //A15 = +2.02675278255254907493e-17L 1005// Pol14 1006data8 0xC698952E9CEAA800, 0x00003FEF //A0 = +2.36744912073515619263e-05L 1007data8 0x800395F8C7B4FA00, 0x0000BFF7 //A1 = -3.90667746392883642897e-03L 1008data8 0xA3B2467B6B391831, 0x00003FF3 //A2 = +3.12226081793919541155e-04L 1009data8 0xCF2061122A69D72B, 0x0000BFEF //A3 = -2.46914006692526122176e-05L 1010data8 0x817FAB6B5DEB9924, 0x00003FEC //A4 = +1.92968114320180123521e-06L 1011data8 0x9FC190F5827740E7, 0x0000BFE8 //A5 = -1.48784479265231093475e-07L 1012data8 0xC1FE5C1835C8AFCD, 0x00003FE4 //A6 = +1.12919132662720380018e-08L 1013data8 0xE7216A9FBB204DA3, 0x0000BFE0 //A7 = -8.40847981461949000003e-10L 1014data8 0x867566ED95C5C64F, 0x00003FDD //A8 = +6.11446929759298780795e-11L 1015data8 0x97A8BFA723F0F014, 0x0000BFD9 //A9 = -4.31041298699752869577e-12L 1016data8 0xA3D24B7034984522, 0x00003FD5 //A10 = +2.91005377301348717042e-13L 1017data8 0xA5AAA371C22F3741, 0x0000BFD1 //A11 = -1.83926825395757259128e-14L 1018data8 0x95352E5597EACC23, 0x00003FCD //A12 = +1.03533666540077850452e-15L 1019data8 0xCCEBE3043B689428, 0x0000BFC8 //A13 = -4.44352525147076912166e-17L 1020data8 0xA779DAB4BE1F80BB, 0x0000BFBC //A14 = -8.86610526981738255206e-21L 1021data8 0xB171271F3517282C, 0x00003FC1 //A15 = +3.00598445879282370850e-19L 1022// Pol15 1023data8 0xB7AC727D1C3FEB05, 0x00003FEE //A0 = +1.09478009914822049780e-05L 1024data8 0xB6E6274485C10B0A, 0x0000BFF6 //A1 = -2.79081782038927199588e-03L 1025data8 0xC5CAE2122D009506, 0x00003FF2 //A2 = +1.88629638738336219173e-04L 1026data8 0xD466E7957D0A3362, 0x0000BFEE //A3 = -1.26601440424012313479e-05L 1027data8 0xE2593D798DA20E2E, 0x00003FEA //A4 = +8.43214222346512003230e-07L 1028data8 0xEF2D2BBA7D2882CC, 0x0000BFE6 //A5 = -5.56876064495961858535e-08L 1029data8 0xFA5819BB4AE974C2, 0x00003FE2 //A6 = +3.64298674151704370449e-09L 1030data8 0x819BB0CE825FBB28, 0x0000BFDF //A7 = -2.35755881668932259913e-10L 1031data8 0x84871099BF728B8F, 0x00003FDB //A8 = +1.50666434199945890414e-11L 1032data8 0x858188962DFEBC9F, 0x0000BFD7 //A9 = -9.48617116568458677088e-13L 1033data8 0x840F38FF2FBAE753, 0x00003FD3 //A10 = +5.86461827778372616657e-14L 1034data8 0xFF47EAF69577B213, 0x0000BFCE //A11 = -3.54273456410181081472e-15L 1035data8 0xEF402CCB4D29FAF8, 0x00003FCA //A12 = +2.07516888659313950588e-16L 1036data8 0xD6B789E01141231B, 0x0000BFC6 //A13 = -1.16398290506765191078e-17L 1037data8 0xB5EEE343E9CFE3EC, 0x00003FC2 //A14 = +6.16413506924643419723e-19L 1038data8 0x859B41A39D600346, 0x0000BFBE //A15 = -2.82922705825870414438e-20L 1039// Pol16 1040data8 0x85708B69FD184E11, 0x00003FED //A0 = +3.97681079176353356199e-06L 1041data8 0x824D92BC60A1F70A, 0x0000BFF6 //A1 = -1.98826630037499070532e-03L 1042data8 0xEDCF7D3576BB5258, 0x00003FF1 //A2 = +1.13396885054265675352e-04L 1043data8 0xD7FC59226A947CDF, 0x0000BFED //A3 = -6.43687650810478871875e-06L 1044data8 0xC32C51B574E2651E, 0x00003FE9 //A4 = +3.63538268539251809118e-07L 1045data8 0xAF67910F5681401F, 0x0000BFE5 //A5 = -2.04197779750247395258e-08L 1046data8 0x9CB3E8D7DCD1EA9D, 0x00003FE1 //A6 = +1.14016272459029850306e-09L 1047data8 0x8B14ECFBF7D4F114, 0x0000BFDD //A7 = -6.32470533185766848692e-11L 1048data8 0xF518253AE4A3AE72, 0x00003FD8 //A8 = +3.48299974583453268369e-12L 1049data8 0xD631A5699AA2F334, 0x0000BFD4 //A9 = -1.90242426474085078079e-13L 1050data8 0xB971AD4C30C56E5D, 0x00003FD0 //A10 = +1.02942127356740047925e-14L 1051data8 0x9ED0065A601F3160, 0x0000BFCC //A11 = -5.50991880383698965959e-16L 1052data8 0x863A04008E12867C, 0x00003FC8 //A12 = +2.91057593756148904838e-17L 1053data8 0xDF62F9F44F5C7170, 0x0000BFC3 //A13 = -1.51372666097522872780e-18L 1054data8 0xBA4E118E88CFDD31, 0x00003FBF //A14 = +7.89032177282079635722e-20L 1055data8 0x942AD897FC4D2F2A, 0x0000BFBB //A15 = -3.92195756076319409245e-21L 1056// Pol17 1057data8 0xCB8514540566C717, 0x00003FEF //A0 = +2.42614557068144130848e-05L 1058data8 0xB94F08D6816E0CD4, 0x0000BFF5 //A1 = -1.41379340061829929314e-03L 1059data8 0x8E7C342C2DABB51B, 0x00003FF1 //A2 = +6.79422240687700109911e-05L 1060data8 0xDA69DAFF71E30D5B, 0x0000BFEC //A3 = -3.25461473899657142468e-06L 1061data8 0xA6D5B2DB69B4B3F6, 0x00003FE8 //A4 = +1.55376978584082701045e-07L 1062data8 0xFDF4F76BC1D1BD47, 0x0000BFE3 //A5 = -7.39111857092131684572e-09L 1063data8 0xC08BC52C95B12C2D, 0x00003FDF //A6 = +3.50239092565793882444e-10L 1064data8 0x91624BF6D3A3F6C9, 0x0000BFDB //A7 = -1.65282439890232458821e-11L 1065data8 0xDA91F7A450DE4270, 0x00003FD6 //A8 = +7.76517285902715940501e-13L 1066data8 0xA380ADF55416E624, 0x0000BFD2 //A9 = -3.63048822989374426852e-14L 1067data8 0xF350FC0CEDEE0FD6, 0x00003FCD //A10 = +1.68834630987974622269e-15L 1068data8 0xB3FA19FBDC8F023C, 0x0000BFC9 //A11 = -7.80525639701804380489e-17L 1069data8 0x8435328C80940126, 0x00003FC5 //A12 = +3.58349966898667910204e-18L 1070data8 0xC0D22F655BA5EF39, 0x0000BFC0 //A13 = -1.63325770165403860181e-19L 1071data8 0x8F14B9EBD5A9AB25, 0x00003FBC //A14 = +7.57464305512080733773e-21L 1072data8 0xCD4804BBF6DC1B6F, 0x0000BFB7 //A15 = -3.39609459750208886298e-22L 1073// Pol18 1074data8 0xE251DFE45AB0C22E, 0x00003FEE //A0 = +1.34897126299700418200e-05L 1075data8 0x83943CC7D59D4215, 0x0000BFF5 //A1 = -1.00386850310061655307e-03L 1076data8 0xAA57896951134BCA, 0x00003FF0 //A2 = +4.06126834109940757047e-05L 1077data8 0xDC0A67051E1C4A2C, 0x0000BFEB //A3 = -1.63943048164477430317e-06L 1078data8 0x8DCB3C0A8CD07BBE, 0x00003FE7 //A4 = +6.60279229777753829876e-08L 1079data8 0xB64DE81C24F7F265, 0x0000BFE2 //A5 = -2.65287705357477481067e-09L 1080data8 0xE9CBB7A990DBA8B5, 0x00003FDD //A6 = +1.06318007608620426224e-10L 1081data8 0x9583D4B85C2ADC6F, 0x0000BFD9 //A7 = -4.24947087941505088222e-12L 1082data8 0xBEB0EE8114EEDF77, 0x00003FD4 //A8 = +1.69367754741562774916e-13L 1083data8 0xF2791BB8F06BDA93, 0x0000BFCF //A9 = -6.72997988617021128704e-15L 1084data8 0x99A907F6A92195B4, 0x00003FCB //A10 = +2.66558091161711891239e-16L 1085data8 0xC213E5E6F833BB93, 0x0000BFC6 //A11 = -1.05209746502719578617e-17L 1086data8 0xF41FBBA6B343960F, 0x00003FC1 //A12 = +4.13562069721140021224e-19L 1087data8 0x98F194AEE31D188D, 0x0000BFBD //A13 = -1.61935414722333263347e-20L 1088data8 0xC42F5029BB622157, 0x00003FB8 //A14 = +6.49121108201931196678e-22L 1089data8 0xF43BD08079E50E0F, 0x0000BFB3 //A15 = -2.52531675510242468317e-23L 1090// Pol19 1091data8 0x82557B149A04D08E, 0x00003FEF //A0 = +1.55370127331027842820e-05L 1092data8 0xBAAB433307CE614B, 0x0000BFF4 //A1 = -7.12085701486669872724e-04L 1093data8 0xCB52D9DBAC16FE82, 0x00003FEF //A2 = +2.42380662859334411743e-05L 1094data8 0xDD214359DBBCE7D1, 0x0000BFEA //A3 = -8.23773197624244883859e-07L 1095data8 0xF01E8E968139524C, 0x00003FE5 //A4 = +2.79535729459988509676e-08L 1096data8 0x82286A057E0916CE, 0x0000BFE1 //A5 = -9.47023128967039348510e-10L 1097data8 0x8CDDDC4E8D013365, 0x00003FDC //A6 = +3.20293663356974901319e-11L 1098data8 0x982FEEE90D4E8751, 0x0000BFD7 //A7 = -1.08135537312234452657e-12L 1099data8 0xA41D1E84083B8FD6, 0x00003FD2 //A8 = +3.64405720894915411836e-14L 1100data8 0xB0A1B6111B72E159, 0x0000BFCD //A9 = -1.22562851790685744085e-15L 1101data8 0xBDB77DE6B650FFA2, 0x00003FC8 //A10 = +4.11382657214908334175e-17L 1102data8 0xCB54E95CDB66978A, 0x0000BFC3 //A11 = -1.37782909696752432371e-18L 1103data8 0xD959E428A62B1B6C, 0x00003FBE //A12 = +4.60258936838597812582e-20L 1104data8 0xE7D49EC23F1A16A0, 0x0000BFB9 //A13 = -1.53412587409583783059e-21L 1105data8 0xFDE429BC9947B2BE, 0x00003FB4 //A14 = +5.25034823750902928092e-23L 1106data8 0x872137A062C042EF, 0x0000BFB0 //A15 = -1.74651114923000080365e-24L 1107// Pol20 1108data8 0x8B9B185C6A2659AC, 0x00003FEF //A0 = +1.66423130594825442963e-05L 1109data8 0x84503AD52588A1E8, 0x0000BFF4 //A1 = -5.04735556466270303549e-04L 1110data8 0xF26C7C2B566388E1, 0x00003FEE //A2 = +1.44495826764677427386e-05L 1111data8 0xDDDA15FEE262BB47, 0x0000BFE9 //A3 = -4.13231361893675488873e-07L 1112data8 0xCACEBC73C90C2FE0, 0x00003FE4 //A4 = +1.18049538609157282958e-08L 1113data8 0xB9314D00022B41DD, 0x0000BFDF //A5 = -3.36863342776746896664e-10L 1114data8 0xA8E9FBDC714638B9, 0x00003FDA //A6 = +9.60164921624768038366e-12L 1115data8 0x99E246C0CC8CA6F6, 0x0000BFD5 //A7 = -2.73352704217713596798e-13L 1116data8 0x8C04E7B5DF372EA1, 0x00003FD0 //A8 = +7.77262480048865685174e-15L 1117data8 0xFE7B90CAA0B6D5F7, 0x0000BFCA //A9 = -2.20728537958846147109e-16L 1118data8 0xE6F40BAD4EC6CB4F, 0x00003FC5 //A10 = +6.26000182616999972048e-18L 1119data8 0xD14F4E0538F0F992, 0x0000BFC0 //A11 = -1.77292283439752259258e-19L 1120data8 0xBD5A7FAA548CC749, 0x00003FBB //A12 = +5.01214569023722089225e-21L 1121data8 0xAB15D69425373A67, 0x0000BFB6 //A13 = -1.41518447770061562822e-22L 1122data8 0x9EF95456F75B4DF4, 0x00003FB1 //A14 = +4.10938011540250142351e-24L 1123data8 0x8FADCC45E81433E7, 0x0000BFAC //A15 = -1.16062889679749879834e-25L 1124// Pol21 1125data8 0xB47A917B0F7B50AE, 0x00003FEF //A0 = +2.15147474240529518138e-05L 1126data8 0xBB77DC3BA0C937B3, 0x0000BFF3 //A1 = -3.57567223048598672970e-04L 1127data8 0x90694DFF4EBF7370, 0x00003FEE //A2 = +8.60758700336677694536e-06L 1128data8 0xDE5379AA90A98F3F, 0x0000BFE8 //A3 = -2.07057292787309736495e-07L 1129data8 0xAB0322293F1F9CA0, 0x00003FE3 //A4 = +4.97711123919916694625e-09L 1130data8 0x837119E59D3B7AC2, 0x0000BFDE //A5 = -1.19545621970063369582e-10L 1131data8 0xC9E5B74A38ECF3FC, 0x00003FD8 //A6 = +2.86913359605586285967e-12L 1132data8 0x9AEF5110C6885352, 0x0000BFD3 //A7 = -6.88048865490621757799e-14L 1133data8 0xED988D52189CE6A3, 0x00003FCD //A8 = +1.64865278639132278935e-15L 1134data8 0xB6063CECD8012B6D, 0x0000BFC8 //A9 = -3.94702428606368525374e-17L 1135data8 0x8B541EB15E79CEEC, 0x00003FC3 //A10 = +9.44127272399408815784e-19L 1136data8 0xD51A136D8C75BC25, 0x0000BFBD //A11 = -2.25630369561137931232e-20L 1137data8 0xA2C1C5E19CC79E6F, 0x00003FB8 //A12 = +5.38517493921589837361e-22L 1138data8 0xF86F9772306F56C1, 0x0000BFB2 //A13 = -1.28438352359240135735e-23L 1139data8 0xC32F6FEEDE86528E, 0x00003FAD //A14 = +3.15338862172962186458e-25L 1140data8 0x9534ED189744D7D4, 0x0000BFA8 //A15 = -7.53301543611470014315e-27L 1141// Pol22 1142data8 0xCBA0A2DB94A2C494, 0x00003FEF //A0 = +2.42742878212752702946e-05L 1143data8 0x84C089154A49E0E8, 0x0000BFF3 //A1 = -2.53204520651046300034e-04L 1144data8 0xABF5665BD0D8B0CD, 0x00003FED //A2 = +5.12476542947092361490e-06L 1145data8 0xDEA1C518E3EEE872, 0x0000BFE7 //A3 = -1.03671063536324831083e-07L 1146data8 0x900B77F271559AE8, 0x00003FE2 //A4 = +2.09612770408581408652e-09L 1147data8 0xBA4C74A262BE3E4E, 0x0000BFDC //A5 = -4.23594098489216166935e-11L 1148data8 0xF0D1680FCC1EAF97, 0x00003FD6 //A6 = +8.55557381760467917779e-13L 1149data8 0x9B8F8E033BB83A24, 0x0000BFD1 //A7 = -1.72707138247091685914e-14L 1150data8 0xC8DCA6A691DB8335, 0x00003FCB //A8 = +3.48439884388851942939e-16L 1151data8 0x819A6CB9CEA5E9BD, 0x0000BFC6 //A9 = -7.02580471688245511753e-18L 1152data8 0xA726B4F622585BEA, 0x00003FC0 //A10 = +1.41582572516648501043e-19L 1153data8 0xD7727648A4095986, 0x0000BFBA //A11 = -2.85141885626054217632e-21L 1154data8 0x8AB627E09CF45997, 0x00003FB5 //A12 = +5.73697507862703019314e-23L 1155data8 0xB28C15C117CC604F, 0x0000BFAF //A13 = -1.15383428132352407085e-24L 1156data8 0xECB8428626DA072C, 0x00003FA9 //A14 = +2.39025879246942839796e-26L 1157data8 0x98B731BCFA2CE2B2, 0x0000BFA4 //A15 = -4.81885474332093262902e-28L 1158// Pol23 1159data8 0xC6D013811314D31B, 0x00003FED //A0 = +5.92508308918577687876e-06L 1160data8 0xBBF3057B8DBACBCF, 0x0000BFF2 //A1 = -1.79242422493281965934e-04L 1161data8 0xCCADECA501162313, 0x00003FEC //A2 = +3.04996061562356504918e-06L 1162data8 0xDED1FDBE8CCAF3DB, 0x0000BFE6 //A3 = -5.18793887648024117154e-08L 1163data8 0xF27B74EDDCA65859, 0x00003FE0 //A4 = +8.82145297317787820675e-10L 1164data8 0x83E4415687F01A0C, 0x0000BFDB //A5 = -1.49943414247603665601e-11L 1165data8 0x8F6CB350861CE446, 0x00003FD5 //A6 = +2.54773288906376920377e-13L 1166data8 0x9BE8456A30CBFC02, 0x0000BFCF //A7 = -4.32729710913845745148e-15L 1167data8 0xA9694F7E1033977D, 0x00003FC9 //A8 = +7.34704698157502347441e-17L 1168data8 0xB8035A3D5AF82D85, 0x0000BFC3 //A9 = -1.24692123826025468001e-18L 1169data8 0xC7CB4B3ACB905FDA, 0x00003FBD //A10 = +2.11540249352095943317e-20L 1170data8 0xD8D70AEB2E58D729, 0x0000BFB7 //A11 = -3.58731705184186608576e-22L 1171data8 0xEB27A61B1D5C7697, 0x00003FB1 //A12 = +6.07861113430709162243e-24L 1172data8 0xFEF9ED74D4F4C9B0, 0x0000BFAB //A13 = -1.02984099170876754831e-25L 1173data8 0x8E6F410068C12043, 0x00003FA6 //A14 = +1.79777721804459361762e-27L 1174data8 0x9AE2F6705481630E, 0x0000BFA0 //A15 = -3.05459905177379058768e-29L 1175// Pol24 1176data8 0xD2D858D5B01C9434, 0x00003FEE //A0 = +1.25673476165670766128e-05L 1177data8 0x8505330F8B4FDE49, 0x0000BFF2 //A1 = -1.26858053564784963985e-04L 1178data8 0xF39171C8B1D418C2, 0x00003FEB //A2 = +1.81472407620770441249e-06L 1179data8 0xDEF065C3D7BFD26E, 0x0000BFE5 //A3 = -2.59535215807652675043e-08L 1180data8 0xCC0199EA6ACA630C, 0x00003FDF //A4 = +3.71085215769339916703e-10L 1181data8 0xBAA25319F01ED248, 0x0000BFD9 //A5 = -5.30445960650683029105e-12L 1182data8 0xAAB28A84F8CFE4D1, 0x00003FD3 //A6 = +7.58048850973457592162e-14L 1183data8 0x9C14B931AEB311A8, 0x0000BFCD //A7 = -1.08302915828084288776e-15L 1184data8 0x8EADA745715A0714, 0x00003FC7 //A8 = +1.54692159263197000533e-17L 1185data8 0x82643F3F722CE6B5, 0x0000BFC1 //A9 = -2.20891945694400066611e-19L 1186data8 0xEE42ECDE465A99E4, 0x00003FBA //A10 = +3.15336372779307614198e-21L 1187data8 0xD99FC74326ACBFC0, 0x0000BFB4 //A11 = -4.50036161691276556269e-23L 1188data8 0xC6A4DCACC554911E, 0x00003FAE //A12 = +6.41853356148678957077e-25L 1189data8 0xB550CEA09DA96F44, 0x0000BFA8 //A13 = -9.15410112414783078242e-27L 1190data8 0xAA9149317996F32F, 0x00003FA2 //A14 = +1.34554050666508391264e-28L 1191data8 0x9C3008EFE3F52F19, 0x0000BF9C //A15 = -1.92516125328592532359e-30L 1192// Pol25 1193data8 0xA68E78218806283F, 0x00003FEF //A0 = +1.98550844852103406280e-05L 1194data8 0xBC41423996DC8A37, 0x0000BFF1 //A1 = -8.97669395268764751516e-05L 1195data8 0x90E55AE31A2F8271, 0x00003FEB //A2 = +1.07955871580069359702e-06L 1196data8 0xDF022272DA4A3BEF, 0x0000BFE4 //A3 = -1.29807937275957214439e-08L 1197data8 0xAB95DCBFFB0BAAB8, 0x00003FDE //A4 = +1.56056011861921437794e-10L 1198data8 0x83FF2547BA9011FF, 0x0000BFD8 //A5 = -1.87578539510813332135e-12L 1199data8 0xCB0C353560EEDC45, 0x00003FD1 //A6 = +2.25428217090412574481e-14L 1200data8 0x9C24CEB86E76D2C5, 0x0000BFCB //A7 = -2.70866279585559299821e-16L 1201data8 0xF01AFA23DDFDAE0E, 0x00003FC4 //A8 = +3.25403467375734083376e-18L 1202data8 0xB892BDFBCF1D9740, 0x0000BFBE //A9 = -3.90848978133441513662e-20L 1203data8 0x8DDBBF34415AAECA, 0x00003FB8 //A10 = +4.69370027479731756829e-22L 1204data8 0xDA04170D07458C3B, 0x0000BFB1 //A11 = -5.63558091177482043435e-24L 1205data8 0xA76F391095A9563A, 0x00003FAB //A12 = +6.76262416498584003290e-26L 1206data8 0x8098FA125C18D8DB, 0x0000BFA5 //A13 = -8.11564737276592661642e-28L 1207data8 0xCB9E4D5C08923227, 0x00003F9E //A14 = +1.00391606269366059664e-29L 1208data8 0x9CEC3BF7A0BE2CAF, 0x0000BF98 //A15 = -1.20888920108938909316e-31L 1209// Pol26 1210data8 0xC17AB25E269272F7, 0x00003FEE //A0 = +1.15322640047234590651e-05L 1211data8 0x85310509E633FEF2, 0x0000BFF1 //A1 = -6.35106483144690768696e-05L 1212data8 0xAC5E4C4DCB2D940C, 0x00003FEA //A2 = +6.42122148740412561597e-07L 1213data8 0xDF0AAD0571FFDD48, 0x0000BFE3 //A3 = -6.49136789710824396482e-09L 1214data8 0x9049D8440AFD180F, 0x00003FDD //A4 = +6.56147932223174570008e-11L 1215data8 0xBAA936477C5FA9D7, 0x0000BFD6 //A5 = -6.63153032879993841863e-13L 1216data8 0xF17261294EAB1443, 0x00003FCF //A6 = +6.70149477756803680009e-15L 1217data8 0x9C22F87C31DB007A, 0x0000BFC9 //A7 = -6.77134581402030645534e-17L 1218data8 0xC9E98E633942AC12, 0x00003FC2 //A8 = +6.84105580182052870823e-19L 1219data8 0x828998181309642C, 0x0000BFBC //A9 = -6.91059649300859944955e-21L 1220data8 0xA8C3D4DCE1ECBAB6, 0x00003FB5 //A10 = +6.97995542988331257517e-23L 1221data8 0xDA288D52CC4C351A, 0x0000BFAE //A11 = -7.04907829139578377009e-25L 1222data8 0x8CEEACB790B5F374, 0x00003FA8 //A12 = +7.11526399101774993883e-27L 1223data8 0xB61C8A29D98F24C0, 0x0000BFA1 //A13 = -7.18303147470398859453e-29L 1224data8 0xF296F69FE45BDA7D, 0x00003F9A //A14 = +7.47537230021540031251e-31L 1225data8 0x9D4B25BF6FB7234B, 0x0000BF94 //A15 = -7.57340869663212138051e-33L 1226// Pol27 1227data8 0xC7772CC326D6FBB8, 0x00003FEE //A0 = +1.18890718679826004395e-05L 1228data8 0xE0F9D5410565D55D, 0x0000BFF0 //A1 = -5.36384368533203585378e-05L 1229data8 0x85C0BE825680E148, 0x00003FEA //A2 = +4.98268406609692971520e-07L 1230data8 0x9F058A389D7BA177, 0x0000BFE3 //A3 = -4.62813885933188677790e-09L 1231data8 0xBD0B751F0A6BAC7A, 0x00003FDC //A4 = +4.29838009673609430305e-11L 1232data8 0xE0B6823570502E9D, 0x0000BFD5 //A5 = -3.99170340031272728535e-13L 1233data8 0x858A9C52FC426D86, 0x00003FCF //A6 = +3.70651975271664045723e-15L 1234data8 0x9EB4438BFDF1928D, 0x0000BFC8 //A7 = -3.44134780748056488222e-17L 1235data8 0xBC968DCD8C06D74E, 0x00003FC1 //A8 = +3.19480670422195579127e-19L 1236data8 0xE0133A405F782125, 0x0000BFBA //A9 = -2.96560935615546392028e-21L 1237data8 0x851AFEBB70D07E79, 0x00003FB4 //A10 = +2.75255617931932536111e-23L 1238data8 0x9E1E21A841BF8738, 0x0000BFAD //A11 = -2.55452923487640676799e-25L 1239data8 0xBBCF2EF1C6E72327, 0x00003FA6 //A12 = +2.37048675755308004410e-27L 1240data8 0xDF0D320CF12B8BCB, 0x0000BF9F //A13 = -2.19945804585962185550e-29L 1241data8 0x8470A76DE5FCADD8, 0x00003F99 //A14 = +2.04056213851532266258e-31L 1242data8 0x9D41C15F6A6FBB04, 0x0000BF92 //A15 = -1.89291056020108587823e-33L 1243LOCAL_OBJECT_END(erfc_Q_table) 1244 1245 1246.section .text 1247GLOBAL_LIBM_ENTRY(erfcl) 1248 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;; 1260 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;; 1271 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;; 1283 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;; 1296 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;; 1307 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;; 1320 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 1326 1327} 1328{ .mfb 1329 nop.m 0 1330(p8) fma.s0 f8 = f1, f1, f0 1331(p8) br.ret.spnt b0 1332} 1333;; 1334 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;; 1346 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;; 1358 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;; 1370 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;; 1382 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;; 1395 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;; 1408 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 1420 1421} 1422;; 1423 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;; 1430 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;; 1443 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;; 1451 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;; 1463 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 1475 1476} 1477;; 1478 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;; 1487 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 1492 1493} 1494{ .mfi 1495 shladd GR_ShftXBi = GR_IndxPlusBias, 4, GR_ShftXBi_bias 1496 nop.f 0 1497 nop.i 0 1498} 1499;; 1500 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;; 1507 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 1512 1513 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;; 1521 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 1531 1532} 1533;; 1534 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;; 1546 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;; 1558 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;; 1570 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;; 1582 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;; 1594 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;; 1606 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;; 1618 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;; 1630 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;; 1642 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;; 1654 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;; 1666 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;; 1678 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;; 1690 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;; 1702 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;; 1709 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;; 1721 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;; 1733 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;; 1745 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;; 1757 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} 1763 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;; 1770 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;; 1782 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;; 1789 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;; 1796 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;; 1803 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;; 1810 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;; 1822 1823{ .mfi 1824 nop.m 0 1825 fma.s1 FR_M = FR_T_scale, FR_S, f0 1826 nop.i 0 1827} 1828;; 1829 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;; 1836 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;; 1843 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;; 1850 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;; 1857 1858{ .mfi 1859 nop.m 0 1860 fma.s1 FR_Q = FR_A1, FR_LocArg, FR_Q 1861 nop.i 0 1862} 1863;; 1864 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;; 1876 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 1881 1882} 1883;; 1884 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;; 1891 1892{ .mfi 1893 nop.m 0 1894 fma.s0 FR_Tmpf = f8, f1, f0 // flag d 1895 nop.i 0 1896} 1897;; 1898 1899{ .mfi 1900 nop.m 0 1901 fnma.s1 FR_dU = FR_Xpdx_lo, FR_U, FR_Tmp 1902 nop.i 0 1903} 1904;; 1905 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 1912 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 1918 1919} 1920;; 1921 1922{ .mfi 1923 nop.m 0 1924 fma.s1 FR_G = FR_R, FR_Q, FR_Q 1925 nop.i 0 1926 1927} 1928;; 1929 1930{ .mfi 1931 nop.m 0 1932 fma.s1 FR_Tmp = FR_R, f1, FR_dU // R + du 1933 nop.i 0 1934 1935} 1936;; 1937 1938{ .mfi 1939 nop.m 0 1940(p7) fnma.s1 FR_Tmp2 = FR_Tmp1, f1, FR_2 //p7: x < 0 1941 nop.i 0 1942 1943} 1944;; 1945 1946{ .mfi 1947 nop.m 0 1948 fma.s1 FR_G = FR_G, f1, FR_Tmp 1949 nop.i 0 1950 1951} 1952;; 1953 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 1958 1959} 1960;; 1961 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 1966 1967} 1968;; 1969 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 1974 1975} 1976;; 1977 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 1982 1983} 1984;; 1985 1986 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 1990 1991ERFC_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};; 2003 2004GLOBAL_LIBM_END(erfcl) 2005libm_alias_ldouble_other (erfc, erfc) 2006 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 2012 2013LOCAL_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};; 2060 2061LOCAL_LIBM_END(__libm_error_region) 2062.type __libm_error_support#,@function 2063.global __libm_error_support# 2064